United States
Environmental Protection
Agency
Environmental Research
Laboratory
At hens G A 30613
EPA 600 6-85 '002t>
September 1985
Revised
Research and Develooment
Water Quality
Assessment:

A Screening
Procedure for Toxic and
Conventional Pollutants in
Surface and Ground
Water—Part II
(Revised 1985)
                         Printed on Recycled Paper

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                                                      EPA/600/6-85/002b
                                                      September  1985
                    HATER QUALITY ASSESSMENT:
                 A  Screening  Procedure  for Toxic
                    and Conventional Pollutants
                         (Revised 1985)

                            Part II
                              by

W.B. Mills, D.B. Porcella,  M.J.  Ungs, S.A.  Gherini,  K.V.  Summers,
            Lingfung Mok, G.L.  Rupp, and G.L.  Bowie
                   Tetra Tech,  Incorporated
                 Lafayette, California  94549

                             and

                          O.A.  Haith
                      Cornell  University
                    Ithaca, New York 14853

                         Produced by:

                        JACA Corporation
              Fort  Washington,  Pennsylvania 19034

                    Contract No. 68-03-3131
            Prepared  in  Cooperation  with  U.S.  EPA's

               Center for  Water  Quality Modeling
               Environmental  Research  Laboratory
                      Athens, Georgia

              Monitoring and  Data  Support Division
            Office  of Water Regulations and Standards
                        Office of  Water
                        Washington,  D.C.
                      Technology  Transfer
        Center  for  Environmental  Research  Information
                      Cincinnati,  Ohio
              ENVIROWENTAL  RESEARCH LABORATORY
              OFFICE OF RESEARCH AND DEVELOPMENT
             U.S. ENVIRONMENTAL PROTECTION AGENCY
                     ATHENS, GEORGIA    30613

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                                DISCLAIMER
     tention of trade nones or commercial  products does  not  constitute  endorse-
ment or recommendation for use by the U.S. Environmental  Protection  Agency.
                                 -11-

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                                  ABSTRACT
      New technical  developments  1n  the  field of water quality  assessment  and
 a  reordering  of water quality  priorities prompted a  revision of the first  two
 editions of this Manual.  The  utility of the revised manual 1s enhanced by
 the  Inclusion of Methods to predict the transport and fate of toxic chemicals
 1n ground water, and by methods  to  predict the fate of metals In rivers.   In
 addition, major revisions were completed on Chapter 2 (organic toxicants),
 Chapter  3 (waste loadings), and  Chapter 5 (Impoundments) that reflect recent
 advancements  in these fields.

      Applying the manual *s simple techniques, the user 1s now capable of
 assessing the loading and fate of conventional pollutants (temperature,
 biochemical oxygen  demand-dissolved oxygen, nutrients, and sediments) and
 toxic pollutants (from the U.S.  EPA 11st of priority pollutants) 1n streams,
 impoundments, estuaries, and ground waters.  The techniques are readily
 programmed on hand-held calculators or microcomputers.  Most of the data
 required for using  these procedures are contained in the manual.

     Because of Us size,  the manual has been divided into two parts.  Part
 I contains the Introduction and chapters on the aquatic  fate of toxic organic
 substances, waste loading calculations, and the assessment of water quality
 parameters in rivers and streams.  Part II  continues with chapters on the
 assessment of Impoundments, estuaries, and  ground water  and appendices E,  H,
 I, and J.  Appendices D, F, and G are provided on microfiche in the EPA-printed
manual.  Appendices A,  B.  and C,  which appeared in the first two editions,
 are now out of date and  have been deleted.

     This report 1s submitted in  fulfillment  of Contract  No.  68-03-3131 by
JACA Corp. and Tetra Tech,  Inc. under the  sponsorship of  the U.S.  Environ-
mental Protection  Agency.   Work was completed  as  of  May  1985.
                                 -iii-

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                             TABLE OF CONTENTS
                                   PART II


     DISCLAIMER	    11

     ABSTRACT	   111

     LIST OF FIGURES (Part II)	   ' 1x

     LIST OF TABLES (Part II)	      xv

5    IMPOUNDMENTS 	     1

     5.1      INTRODUCTION	     1

     5.2      IMPOUNDMENT STRATIFICATION	     2
     5.2.1    Discussion	     2
     5.2.2    Prediction of Thermal  Stratification	     6

     5.3      SEDIMENT ACCUMULATION	    19
     5.3.1    Introduction	    19
     5.3.2    Annual  Sediment Accumulation. 	    20
     5.3.3    Short-Term Sedimentation Rates	    23
     5.3.4    Impoundment Hydraulic Residence Time	    29
     5.3.5    Estimation of Sediment Accumulation 	    43

     5.4      EUTROPHICATION AND CONTROL	    49
     5.4.1    Introduction	    49
     5.4.2    tatHents, Eutrophy,  and Algal  Growth	    50
     5.4.3    Predicting Algal  Concentrations 	    51
     5.4.4    Mass Balance of Phosphorus	    52
     5.4.5    Predicting Algal  Productivity, Secchl  Depth,
              and  Blomass	    60
     5.4.6    Restoration Measures	    64
     5.4.7    Water Column Phosphorus Concentrations	    64

     5.5      IMPOUNDMENT DISSOLVED OXYGEN	    71
     5.5.1    Simulating Impoundment Dissolved Oxygen  	    73
     5.5.2    A Simplified Impoundment Dissolved Oxygen Model  	    74
     5.5.3    Temperature Corrections 	    85

     5.6      TOXIC CHEMICAL SUBSTANCES 	    97
     5.6.1    Overall  Processes  	    99
     5.6.2    Guidelines for Toxics  Screening 	   104

     5.7      APPLICATION OF METHODS AND EXAMPLE PROBLEM	   109
     5.7.1    The  Occoquan Reservoir	   110
     5.7.2    Stratification	   Ill
     5.7.3    Sedimentation	   115
     5.7.4    Eutrophl cation	   123
     5.7.5    HypoHmnetic 00 Depletion	   128
     5.7.6    Toxicants	   133
                                     -v-

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Chapter                                                                      p.a.9g


       REFERENCES	    136

       GLOSSARY OF TERMS	    139

  6    ESTUARIES	    142

       6.1      INTRODUCTION	    142
       6.1.1    General	    142
       6.1.2    EstuaMne Definition	    143
       6.1.3    Types of Estuaries	    143
       6.1.4    Pollutant Flow 1n an Estuary	    145
       6.1.5    EstuaMne Complexity and Major Forces	    149
       6.1.6    Methodology Summary	    151
       6.1.7    Present Water-Quality Assessment	    153

       6.2      ESTUARINE CLASSIFICATION*	    155
       6.2.1    General	    155
       6.2.2    Classification Methodology	    155
       6.2.3    Calculation Procedure 	    155
       6.2.4    Stratification-Circulation Diagram Interpretation ....    157
       6.2.5    Flow Ratio Calculation	    163

       6.3      FLUSHING TIME CALCULATIONS	    165
       6.3.1    General	    165
       6.3.2    Procedure	    165
       6.3.3    Fraction of Fresh Water Method	    170
       6.3.4    Calculation of Flushing Time by Fraction of Freshwater
                Method	    171
       6.3.5    Branched Estuaries and the Fraction of Freshwater
                Method	    176
       6.3.6    Modified Tidal Prism Method 	    176

       6.4      FAR FIELD APPROACH TO POLLUTANT DISTRIBUTION IN
                ESTUARIES	    184
       6.4.1    Introduction	    184
       6.4.2    Continuous Flow of Conservative Pollutants	    185
       6.4.3    Continuous Flow Non-Conservative Pollutants 	    197
       6.4.4    Multiple Waste Load Parameter Analysis	    204
       6.4.5    D1spers1on-Advect1on Equations for Predicting
                Pollutant Distributions 	    207
       6.4.6    PMtchard's Two-Dimens1onal Box Model for Stratified
                Estuaries	    216

       6.5      POLLUTANT DISTRIBUTION FOLLOWING DISCHARGE FROM A
                MARINE OUTFALL	   226
       6.5.1    Introduction	   226
       6.5.2    Prediction of Initial  Dilution	   227
       6,5.3    Pollutant Concentration Following Initial  Dilution.  ...   248
       6.5.4    pH Following Initial  Dilution 	   250
       6.5.5    Dissolved Oxygen Concentration Following Initial
                Dilution	   255
       6.5.6    Far Field Dilution and Pollutant Distribution 	   257
       6.5.7    Farfield Dissolved Oxygen  Depletion 	   263

       6.6      THERMAL POLLUTION 	   266
       6.6.1    General	   266

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Chapter                                                                      Page


       6.6.2    Approach	    267
       6.6.3    Application	    269

       6.7      TURBIDITY	    274
       6.7.1    Introduction	    274
       6.7.2    Procedure  to Assess  Impacts of Wastewater Discharges
                on Turbidity or Related  Parameters	    276

       6.8      SEDIMENTATION	    282
       6.8.1    Introduction	    282
       6.8.2    Qualitative Description  of Sedimentation	    282
       6.8.3    Estuarlne  Sediment Forces and Movement	    283
       6.8.4    Settling Velocities  	    287
       6.8.5    Null Zone  Calculations	    291

       REFERENCES	    295

  7    GROUND WATER	    300

       7.1      OVERVIEW	    300
       7.1.1    Purpose of Screening Methods	    300
       7.1.2    Ground Water vs. Surface Water	    301
       7.1.3    Types of Ground' Water Systems Suitable for Screening
                Method	    302
       7.1.4    Pathways for Contamination	    303
       7.1.5    Approach to Ground Water Contamination Problems  	    305
       7.1.6    Organization of This Chapter	    309

       7.2      AQUIFER CHARACTERIZATION	    310
       7.2.1    Physical  Properties of Water	    310
       7.2.2    Physical  Properties of Porous Media  	    310
       7.2.3    Flow Properties of Saturated Porous Media 	    319
       7.2.4    Flow Properties of Unsaturated Porous Media  	    323
       7.2.5    Data Acquisition or Estimation	    329

       7.3      GROUND WATER FLOW REGIME	    345
       7.3.1    Approach to Analysis of  Ground Water Contamination
                Sites	    345
       7.3.2    Water Levels and Flow Directions	    346
       7.3.3    Flow Velocities and Travel Times	    353

       7.4      POLLUTANT  TRANSPORT PROCESSES 	    363
       7.4.1    Dispersion and Diffusion	    363
       7.4.2    Chemical  and Biological  Processes Affecting  Pollutant
                Transport	    374

       7.5      METHODS FOR PREDICTING THE FATE AND TRANSPORT OF
                CONVENTIONAL AND TOXIC POLLUTANTS 	    382
       7.5.1    Introduction to Analytical  Methods	    382
       7.5.2    Contaminant Transport to Deep Wells	    390
       7.5.3    Solute Injection Wells:  Radial  Flow	    396
       7.5.4    Contaminant Release on the Surface with 1-D  Vertical
                Downward  Transport	    403
       7.5.5    Two-Dimensional Horizontal  Flow with a Slug Source. . .  .    410
       7.5.6    Two-Dimensional Horizontal  Flow with Continuous
                Solute Line Sources	    417

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Chapter
Page
      7.6      INTERPRETATION  OF  RESULTS 	    423
      7.6.1    Appropriate Reference Criteria	    423
      7.6.2    Quantifying Uncertainty  	    424
      7.6.3    Guidelines  for  Proceeding to  More Detailed Analysis  ...    429

      REFERENCES	    435
      References  Sited  	    435
      Additional  References  on  Ground Water  Sampling  	    444

 APPENDIX A	    A-l

 APPENDIX B	    B-l

 APPENDIX C	    C-l

 APPENDIX D    IMPOUNDMENT THERMAL  PROFILES	    D-l

 APPENDIX E    MODELING THERMAL STRATIFICATION  IN  IMPOUNDMENTS  	    E-l

 APPENDIX F    RESERVOIR SEDIMENT DEPOSITION SURVEYS  	    F-l

 APPENDIX G    INITIAL DILUTION TABLES  	    G-l

 APPENDIX H    EQUIVALENTS BY COMMONLY  USED  UNITS  OF MEASUREMENTS.  ...    H-l

 APPENDIX I    ADDITIONAL  AQUIFER PARAMETERS 	    1-1

 APPENDIX J    MATHEMATICAL  FUNCTIONS	   J-l

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                                  LIST  OF  FIGURES
                                     PART  II
V-l      Mater Density as a Function of Temperature and Dissolved
         Solids Concentration  ......................      3
V-2      Water Flowing Into an Impoundment Tends to Migrate toward
         a Region of Similar Density.  ....  ..............      3
V-3      Annual Cycle of Thermal Stratification and Overturn in
         an Impoundment  .........................      5
V-4      Thermal Profile Plots Used 1n Example V-l ............     15
V-5      Thermal Profile Plots Appropriate for Use In Example V-2  ....     18
V-6      Sediment Rating Curve Showing Suspended Sediment Discharge
         as a Function of Flow ......................     21
V-7      Relationship between the Percentage of Inflow-Transported
         Sediment Retained within an Impoundment and Ratio of
         Capacity to Inflow .......................     22
V-8      Plot of C/R and CR2 Versus R ..................     25
V-9      Drag Coefficient (C) as Function of Reynold's Number (R)
         and Particle Shape .......................     26
V-10     Schematic Representation of Hindered Settling of Particles
         in Fluid Column .........................     27
V-ll     Velocity Correction Factor for Hindered Settling ........     27
V-12     Upper and Lower Lakes and Environs, Long Island, New York. ...     32
V-13     Impoundment Configurations Affecting Sedimentation .......     34
V-14     Kellis Pond and Surrounding Region, Long Island, New York. ...     37
V-l 5     Hypothetical Depth Profiles for Kellis Pond ...........     38
V-16     Hypothetical Flow Pattern in Kellis Pond ...........       38
V-17     Hypothetical Depth Profiles for Kellis Pond Not Showing
         Significant Shoaling ......................     39
V-18     Lake Owyhee and Environs ....................    41
V-19     New Millpond and Environs ....................    42
V-20     Significance of Depth Measures  D,  D' and D" and the Assumed
         Sedimentation Pattern ......................    44
V-21     Settling Velocity for Spherical  Particles ............    45
V-22     Nomograph for Estimating Sediment  Trap Efficiency ........    46

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Figure                                                                      Page





V-23     Formulations for Evaluating Management  Options  for Pollutants
V-24

V-25
V-26

V-27
V-28
V-29
V-30
V-31

V-32
V-33
V-34
V-35
V-36
V-37
V-38

V-39

VI-1

VI-2

VI-3

VI-4
VI-5
VI-6
VI-7
US OECD Date Applied to Vollenwelder (1976) Phosphorus Loading
and Mean Depth/ Hydraulic Residence Time Relationship 	
Relationship between Summer Chlorophyll and Spring Phosphorus. .
Maximal Primary Productivity as a Function of Phosphate

Conceptualization of Phosphorus Budget Modeling 	
Typical Patterns of Dissolved Oxygen (DO) 1n Hyrum Reservoir . .
Geometric Representation of a Stratified Impoundment 	
Quality and Ecologic Relationships 	
Rate of BOD Exertion at Different Temperatures Showing the
First and Second Deoxygenatlon Stages 	
Quiet Lake and Environs 	


Generalized Schematic of Lake Computations 	
The Occoquan River Basin 	 . 	
Thermal Profile Plots for Occoquan Reservoir 	
Summary of Reservoir Sedimentation Surveys Made in the
United States through 1970 	
Dissolved Oxygen Depletion Versus Time in the Occoquan
Reservoir 	
Typical Main Channel Salinity and Velocity for Stratified
Estuaries 	
Typical Main Channel Salinity and Velocity Profiles for Well
Mixed Estuaries 	
Typical Main Channel Salinity and Velocity Profiles for
Partially Mixed Estuaries 	
Estuarine Dimensional Definition 	
Suggested Procedure to Predict Estuarine Hater Quality 	
Estuarine Circulation-Stratification Diagram 	
Examples of Estuarine Classification Plots 	

55
61

63
66
72
74
75

78
86
93
106
110
111
114

116

132

146

147

148
150
154
156
156

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 Figure


 VI-8      Circulation and Stratification  Parameter Diagram  	    158

 VI-9      The Stuart Estuary	    160

 VI-10     Stuart Estuary Data for Classification Calculations	    161

 VI-11     EstuaMne Circulation-Stratification Diagram	    162

 VI-12     Alsea Estuary Seasonal Salinity Variations  	    163

 VI-13     Estuary Cross-Section for Tidal Prism Calculations  	    165

 VI-14     Patuxent Estuary Salinity Profile and Segmentation Scheme
          Used in Flushing Time Calculations	    175

 VI-15     Hypothetical Two-Branched Estuary	    178

 VI-16     Cumulative Upstream Water Volume, Fox Mill  Run Estuary  	    182

 VI-17     River Borne Pollutant Concentration for One Tidal Cycle	    190

 VI-18     Alsea Estuary Rlverborne Conservative Pollutant Concentration.  .    192

 VI-19     Pollutant Concentration from an Estuarine Outfall	    193

 VI-20     Hypothetical Concentration of Total  Nitrogen  1n Patuxent
          Estuary	    196

 VI-21    Relative Depletions of Three Pollutants Entering the
          Fox Mill  Run Estuary, Virginia	    203

 VI-22    Additive Effect of Multiple Waste Load Additions  	    204

 VI-23    Dissolved Oxygen Saturation as a Function of Temperature
         and Salinity	    213

 VI-24    Predicted Dissolved Oxygen Profile In James River	    215

 VI-25    Definition Sketch for PMtchard's  Two-Dimensional  Box Model. . .    218

 VI-26    Patuxent  Estuary Model Segmentation	    225

 VI-27    Waste Field Generated by Marine Outfall	    228

 VI-28    Example Output  of MERGE - Case 1	   240

 VI-29    Example Output  of MERGE - Case 2	   241

 VI-30    Schematic of Plume Behavior Predicted by  MERGE 1n  the Present
         Usage	   244

VI-31    Cross Diffuser  Merging 	   247

VI-32    Plan  View of Spreading Sewage Field	   259

VI-33    Outfall  Location,  Shellfish Harvesting  Area, and Environs.  ...   262

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VI-34    Dissolved Oxygen Depletions Versus Travel Time  	    265

VI-35    Centerllne Dilution of Round Buoyant Jet In Stagnant
         Uniform Environment	    274

VI-36    Mean Suspended Solids in San Francisco Bay	    276

VI-37    Water Quality Profile of Selected Parameters Near a Municipal
         Outfall in Puget Sound, Washington 	    279

VI-38    Sediment Movement in San Francisco Bay System	    287

VI-39    Idealized Estuarine Sedimentation	    288

VI-40    Particle Diameter vs Settling Fall per Tidal Cycle Under
         Quiescent Conditions 	    291

VI-41    Estuarine Null Zone Identification	    293

VII-1    Major Aquifers of the United States	    304

VI1-2    Geologic Section in Western Suffolk County, Long Island,
         Showing Both Confined and Unconfined Aquifers	    305

VII-3    Detailed Quaternary Geologic Map of Morris County	    306

VI1-4    Generalized Cross-sections Showing Features Common in Arid
         Western Regions of the United States 	    307

VI1-5    Number of Waste Impoundments by State	    308

VII-6    Schematic Showing the Solid, Liquid and Gaseous Phases in a
         Unit Volume of Soil	    312

VI1-7    Soil Texture Trllinear Diagram Showing Basic Soil Textural
         Classes	    315

VI1-8    Typical Particle-Size Distribution Curves for Various Soil
         Classifications	    315

VI1-9    Schematic Cross-section Showing Both a Confined and an
         Unconfined Aquifer 	    320

VII-10   Schematic of Matric and Osmotic Soil-Water Potential  ......    326

VII-11   Characteristic Curves of Moisture Content as a Function of
         Matric Potential  for Three Different Soils 	    328

VI1-12   Characteristic Curves of Moisture Content and Hydraulic
         Conductivity as a Hysteretlc Function of Matric Potential
         for a Naturally Occurring Sandy Soil	    330

VI1-13   Hydraulic Conductivity as a Function of Moisture Content
         for Three Different Soils	    331

VI1-14   Cross-Sectional  Diagram Showing the Water Level  as  Measured
         by Piezometers Located at Various Depths  	    348

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                                                                             Page
VI1-15   An Example of a Contour  Plot  of  Water  Level  Data  With
         Inferred Flow Directions	   351

VI1-16   Schematic Showing the Construction of  Flow  Direction Lines
         from Equipotential Lines  for  Isotropic Aquifers and
         Anisotropic Aquifers  	   352

VI1-17   Schematic Diagrams Showing  Permeameters  to  Demonstrate
         Darcy's Law	   354

VI1-18   Schematic Showing How Travel  Time Can  Be Calculated for
         Solute Transport When the Flow Velocity  Varies:   a) Original
         Problem, t>) Discretized Representation of the Flow Line	   360

VI1-19   Example Problem:  Calculation of Travel  Time for  Sulfate
         from Holding Basin to River	   362

VI1-20   Schematic Showing the Effect  of  Scale  on Hydrodynamic
         Dispersion Processes  	   365

VI1-21   Field Measured Values of Longitudinal  Dispersivity as a
         Function of Scale Length for  Saturated Porous Media	   367

VII-22   A Plot of Longitudinal Dispersivity vs.  Scale Length for
         Saturated Porous Media 	    368

VII-23   A Plot of Longitudinal Oispersivity vs.  Scale Length for
         Unsaturated Porous Media  	    369

VI1-24   Schematic Showing the Solution of Equation VII-50 and the
         Effect of Dispersion  	    371

VI1-25   Schematic Showing Hypothetical Vertical Variation in the
         Ground Water Flow Velocity  	    375

VI1-26   Major Equilibrium and Rate Processes in Natural  Waters	    376

VI1-27   Hypothetical  Adsorption Curves for Cations and Anions
         Showing Effect of pH and Organic Matter	    379

VI1-28   Dehydrochlorination Rate of Tetrachloroethylene and the
         Production Rate  of its Dechlorination  Products 	    383

VI1-29   Summary of Model  Describing Contaminant Transfer to Deep
         Wells	    385

VI1-30   Summary of Model  Describing Radial  Flow from an Injection
         Well	    386

VI1-31   Summary of Model  Describing One-Dimensional, Vertically
         Downward Transport of a Contaminant  Released on the Surface. .  .    387

VI1-32   Summary of Model  Describing Two-Dimensional  Horizontal  Flow
         With  a Slug Source	    388

VI1-33   Summary of Model  Describing Two-Dimensional  Horizontal  Flow
         With  Continuous  Solute Line Sources	    389
                                      -xiii-

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Figure                                                                       Page

VII-34   Schematic of ROM to a Well Beneath a Contaminated  Zone	    392
VI1-35   Normalized Solute Concentration vs. Dlmenslonless Time  	    393
VI1-36   Schematic of Example Problem for Row to Well from  a Shallow
         Contaminated Zone	    395
VI1-37   Schematic View of a Well Injection Solute Into a Confined
         Aquifer	    397
VI1-38   Schematic of the Example Problem Showing Radial Flow of
         Plating Waste from an Injection Well	    401
VI1-39   Schematic Showing Equation for 1-0 Vertical Transport from
         a Surface Waste Source 	    404
VI1-40   Schematic of Example 1-0 Problem 	    407
VII-41   Schematic Showing a Slug Discharge of Waste Into a  Reflonal
         Flow Field	    412
VI1-42   Schematic Showing a Continuous Discharge of Waste Into a
         Regional  Flow Field	    419
VI1-43   General Sequence to Determine If a Modeling Effort  1s Needed .  .    433
VI1-44   Steps Involved 1n Model  Application	    434
                                      -x1v-

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                                 LIST OF TABLES



                                     PART II
Table
V-l
V-2


V-3
V-4
V-5

V-6

V-7

V-8

V-9

V-10
v-n
V-12
V-13
V-14
V-15
V-16
V-17

V-18

V-19

V-20
V-21

Parameter Values Used 1n Generation of Thermal Gradient Plots. .
Temperature, Cloud Cover, and Dew Point Data for the Ten
Geographic Locales Used to Develop Thermal Stratification
Plots 	
Limpid Lake Characteristics 	
Physical Characteristics of Lake Smith 	
Comparison of Monthly Cl imatologic Data for Shreveport,
Louisiana and Atlanta, Georgia . 	
Hypothetical Physical Characteristics and Computations
for Upper Lake, Brookhaven, Suffolk County, New York 	
Hypothetical Physical Characteristics and Computations
for Lower Lake, Brookhaven, Suffolk County, New York 	
Hypothetical Physical Characteristics and Computations

Preliminary Classification of Trophic State Based on

Classification of Lake Restoration Techniques 	
Oxygen Demand of Bottom Deposits 	
Solubility of Oxygen in Water 	
Characteristics of Quiet Lake 	
Water Quality and Flow Data for Tributaries to Quiet Lake. . . .
Precipitation and Runoff Data for Quiet Lake Watershed 	
DO Sag Curve for Quiet Lake Hypolimnion 	
Significant Processes Affecting Toxic Substances in Aquatic
Ecosystems 	
Comparison of Modeled Thermal Profiles to Observed Temperatures
1n Occoquan Reservoir 	
Annual Sediment and Pollutant Loads in Occoquan Watershed in
Metric Tons per Year 	
Sediment Loaded into Lake Jackson 	
Calculation Format for Determining Sediment Accumulation in
Reservoirs 	
8


9
14
16

17

31

33

36

56
65
79
81
87
87
90
97

98

115

118
118

119
                                      -XV-

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Table
V-22     Particle Sizes in Penn Silt Loan ................    120

V-23     Calculation Format for Determining Sediment Accumulation in
         Reservoirs ...........................    121

V-24     Sewage Treatment Plant Pollutant Loads in Bull Run Sub-Basin
         in Metric Tons per Year .....................    125

V-25     Calculated Annual Pollutant Loads to Occoquan Reservoir .....    125

V-26     Observed Annual Pollutant Loads to Occoquan Reservoir ......    126

V-27     Calculated and Observed Mean Annual Pollutant Concentrations
         in Occoquan Reservoir ......................    127

VI -1     Summary of Methodology for Estuarine Mater Quality Assessment.  .    152

VI -2     Tidal Prisms  for Some U.S. Estuaries ..............    166

VI-3     Sample Calculation Table for Calculation of Flushing Time by
         Segmented Fraction of Freshwater Method .............    173

VI -4     Patuxent Estuary Segment Characteristics for Flushing Time
         Calculations  ..........................    175

VI-5     Flushing Time for Patuxent Estuary ...............    177

VI-6     Sample Calculation Table for Estuarine Flushing Time by the
         Modified Tidal  Prism Method ...................    180

VI-7     Data and Flushing Time Calculations for Fox Mill  Run Estuary .  .    184

VI-8     Pollutant Distribution in the Patuxent River ..........    188

VI-9     Incremental  Total Nitrogen in Patuxent River, Expressed as
         Kilograms ............................    188

VI-10    Sample Calculation Table for Distribution of a Locally
         Discharged Conservative Pollutant by the Fraction of
         Freshwater Method ........................    194

VI-11    Nitrogen Concentration in Patuxent Estuary Based  on Local
         Discharge ............................   195

VI-12    Typical  Values  for Decay Reaction Rates 'k1 ...........   198

VI-13    Sample Calculation Table for Distribution of a Locally
         Discharged Non-conservative Pollutant by the Modified
         Tidal Prism Method .......................   20C

VI-14    Salinity and  CBOD Calculations for Fox Mill  Run Estuary .....   202

Vl-15    Distribution  of Total  Nitrogen in the Patuxent Estuary Due
         to Two Sources  of Nitrogen ...................   207

VI-16    Tidally Averaged Dispersion Coefficients for Selected Estuaries.   209
                                      -xvi-

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Table


 VI-17    Tidally Averaged Dispersion Coefficients 	   210

 VI-18    Salinity and  Pollutant  Distribution in Patuxent Estuary Under
          Low How Conditions	   224

 VI-19a   Water Densities  (Expressed  as Sigma-T) Calculated Using the
          Density Subroutine Found  1n Merge	   231

 VI-19b   Water Densities  (Expressed  as S1gma-T) Calculated Using the
          Density Subroutine Found  in Merge	   233

 VI-19c   Water Densities  (Expressed  as Sigma-T) Calculated Using the
          Density Subroutine Found  in Merge	   235

 VI-20    Plume Variables, Units, and Similarity Conditions	   238

 VI-21    Values of Equilibrium Constants and Ion Product of Water as
          a Function of Temperature for Freshwater and Salt Water	   251

 VI-22    Estimated pH  Values After Initial  Dilution  	   253

 VI-23    Dissolved Oxygen Profile  in Commencement Bay,  Washington ....   256

 VI-24    Subsequent Dilutions for  Various Initial Field Widths  and
          Travel Times  	   260

 VI-25    Data  Needed for  Estuary Thermal  Screening	   268

 VI-26    Allowable Channel  Velocity  to Avoid Bed Scour	   284

 VI-27    Sediment  Particle  Size  Ranges	   289

 VI-28    Rate  of Fall  1n  Water of  Spheres of Varying Radii and
          Constant  Density of 2 as  Calculated by Stokes1 Law	   290

 VII-1    Aquifer Parameters and  Their Relative Importance as Screening
          Parameters	   311

 VI1-2    Range and Mean Values of  Dry Bulk  Density	   314

 VI1-3    Effective Grain  Size and  the Range of Soil  Particle Sizes for
          Various Materials	   316

 VI1-4    Range and Mean Values of  Porosity	   318

 VI1-5    Typical  Values of  Saturated Hydraulic Conductivity and Intrinsic
          Permeability  	   321

 VI1-6    Summary of Methods for  Measuring Soil  Moisture 	   333

 VI1-7    Techniques for Measuring  Saturated Hydraulic Conductivity.  ...   336

 VII-8    Sample Size for  Various Confidence Levels Using the Student's
          t-Distribution 	   342

 VI1-9    Standard  Normal  Distribution Function	   343

-------
Table                                                                        Page

 VII-10   Percentage Points  of  the Student's  t-Distribution	   343
 VII-11   Methods  for Measuring Ground  Water  How Velocity	   358
 VI1-12   Summary  of Solution Methods	   384
 VI1-13   Primary  Drinking Water Standards  	   425
 VII-14   Interim  Secondary  Drinking Water  Standards	   426
 VI1-15   Data  Needs for  Numerical  Models	   432
                                     -XV111-

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                                        CHAPTER 5
                                       IMPOUKOMENTS

 5.1  INTRODUCTION
      This  chapter contains  several  methods  for assessing water quality  and physical
 conditions  1n  Impoundments.   The  general  topics  covered  are  sediment  accumulation.
 thermal  stratification,  DO-BOD, eutroph1cat1on,  and  toxicant  concentrations.   These
 topics  cover the  major water  problems  likely  to  occur  1n impoundments.   The methods
 developed  are  easy to use and require  readily obtainable data.   Because the methods
 depend  upon a  number of  simplifying assumptions,  estimates should  be  taken only  as a
 guide pending  further analysis.   Also,  since  pollutant inputs are  dependent on
 previous calculations, familiarity  with the methods  in previous  chapters will  be very
 helpful  and expand understanding  of the various  processes.
      Some  of the  techniques are more mechanistic  and reliable than  others.  For
 example, the thermal stratification technique is  based upon output  of a calibrated
 and validated  hydrothermal model.   The  model  has  been shown to be  a good one,  and to
 the extent  that physical conditions  in  the  studied impoundments  resemble those of the
 model,  results should be very reliable.   On the other hand, the  methods  for predict-
 ing eutrophication are empirical  and based  upon correlations  between  historical  water
 quality  conditions  and algal  productivity In  a number of lakes and  reservoirs.
 Because  algal  blooms are sensitive  to environmental  factors and  the presence of
 toxicants and  factors other than  those  involved in the estimation methods,  the
 methods  for predicting eutrophication will  occasionally  be inapplicable.   Additional
 approaches  have been developed to broaden the applicability of these empirical
 models.
      In  using  the  techniques  to be  presented, it  1s  important to apply  good "engi-
 neering  judgment"  particularly where sequential application of methods  is  likely to
 result in cumulative errors.  Such  would  be the case, for example, in evaluating
 Impoundment  hypolimnlon DO problems  resulting from algal  blooms.  If methods presented
 below are used to  evaluate hypolimnlon  DO, the planner should determine when strati-
 fication occurs, the magnitude of point and nonpoint source BOD loads, and  algal
 productivity and settling rates.  From  all of this,  he may then predict  BOD and DO
 levels in the  hypolimnlon.  Since each of these techniques has an error associated
 with  It, the-end result of the computation will have a significant error envelope and
 results must be interpreted accordingly.  The best way to use any of the techniques
 1s  to assume a range of values for  important  coefficients 1n order to obtain a range
 of  results  within which the studied  impoundment is likely to fall.
     Although scientists  and engineers  are familiar with  the  metric system of  units,
planners, local interest  groups,  and the general  public  are more  accustomed to  the
English  system.  Most  morphometric data on lakes  and  impoundments are  in English
                                          -1-

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units.  The conversion tables in Appendix H should be thoroughly familiar  before
using these techniques and users should be able to perform calculations  in either
system even though metric units are simpler to use.  Also, dimensional analysis
techniques using unit conversions are very helpful in performing the calculations.
     The methods presented below are arranged in an order such that the  planner
should be able to use each if he has read preceding materials.  The order  of presen-
tation is:
        •    Impoundment stratification (5.2)
        •    Sediment accumulation (5.3)
        •    Eutrophication (5.4)
        •    Impoundment dissolved oxygen (5.5)
        •    Fate of Priority Pollutants (Toxics) (5.6).
     It is strongly recommended that all materials presented be read and examples
worked prior to applying any of the methods.  In this way a better perspective can be
obtained on the kinds of problems covered and what can be done using hand calculations.
A glossary of terms has been placed after the reference section so that equation
terms can easily be checked.
     The final  section (5.7) is an example application to a selected site.   This
example allows the user to have an integrated view of an actual problem and applica-
tion.  Also "the goodness of fit" to measured results can be evaluated.

5.2  IMPOUNDMENT STRATIFICATION

5.2.1  Discussion
     The density of water 1s strongly influenced by  temperature and by the  concentra-
tion of dissolved and suspended matter.   Figure V-l  shows densities for water as a
function of temperature and dissolved solids concentration (from Chen and Orlob,
1973).
     Regardless of the reason for density differences,  water of lowest density
tends to move upward and reside on the surface of an  impoundment while water  of
greatest density tends to sink.   Inflowing water seeks  an impoundment level contain-
ing water of the same density.   Figure V-2 shows this effect  schematically.
     Where density gradients are very steep, mixing  1s  Inhibited.   Thus,  where  the
bottom water of an Impoundment  is significantly more  dense than surface water,
vertical  mixing is likely to be unimportant.  The fact  that low density water tends
to reside atop higher density water and that mixing 1s inhibited by steep gradients
often results in impoundment stratification.  Stratification, which is the  establish-
ment of distinct layers of different densities, tends to be enhanced by quiescent
conditions.  Conversely, any phenomenon encouraging mixing, such as wind stress,
turbulence due to large inflows, or destabilizing changes in water temperature will
tend to reduce or eliminate strata.

                                          -2-

-------
     .0090
     1.0070
     1.0050
     1.0030
  *•«
  0
     1.00(0
    0.9990
    0.9970
                                               Dissolved  solids, ppm
               35   40    45    50    55    60    65
                                      Temperature, °F
                                       70
75
80
85
FIGURE V-l
WATER DENSITY AS A FUNCTION OF  TEMPERATURE AND  DISSOLVED SOLIDS
CONCENTRATION (FROM CHEN AND ORLOB,  1973)
                       STRATIFIED
                      IMPOUNDMENT
                                                 PROFILE
                                                                   Dentity *f
                                                                   W«rm I* fluent
     FIGURE V-2  WATER PLOWING INTO AN IMPOUNDMENT TENDS TO MIGRATE TOWARD
                  A REGION OP SIMILAR DENSITY
                                       -3-

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5.2.1.1  Annual Cycle 1n a Thermally Stratified Impoundment
     Figure V-3 shows schematically the processes of thermal stratification and
overturn which occur in many Impoundments.  Beginning at "a" 1n the figure (winter),
cold water (at about 4°C) flows Into the Impoundment which may at this point be
considered as fully mixed.  There Is no thermal gradient over depth and the Impound-
ment temperature 1s about 6°C.  During spring ("b*), Inflowing water 1s slightly
warmer than that of the Impoundment because of the exposure of the tributary stream
to warmer air and increasingly intense sunlight.  This trend continues during the
summer ("c"), with tributary water being much warmer and less dense than the deep
waters of the impoundment.  At the same time, the surface water of the Impoundment 1s
directly heated by insolation.  Since the warm water tends to stay on top of the
Impoundment, thermal strata form.
     As fall approaches ("d"), day length decreases, air temperatures drop, and solar
intensity decreases.  The result is cooler inflows and a cooling trend in the surface
of the impoundment.  The bottom waters lag behind the surface in the rate of tempera-
ture change, and ultimately the surface may cool to the temperature of the bottom.
Since continued increases in surface water density result In Instability, the Impound-
ment water mixes (overturns).

5.2.1.2  Konomictlc and Dimictic Impoundments
     The stratification and overturn processes described in Figure V-3 represent what
occurs in $ monocnictic or single-overturn water body.  Some Impoundments, especially
those north of 40°N latitude and those at high elevation, may undergo two periods of
stratification and two overturns.  Such impoundments are termed "d1m1ct1c."  In
addition to the summer stratification and resulting fall overturn, such impoundments
stratify in late winter.  This occurs because water is most dense near 4*C, and
bottom waters may be close to this temperature, while inflowing water is colder and
less dense.  As the surface goes below 4°C, strata are established.  With spring
wanning of the surface to 4°C, wind induced mixing occurs.

5.2.1.3  Importance of Stratification
     Stratification is likely to be the single most important phenomenon affecting
water quality in many impoundments.  Where stratification is absent, water mixes
vertically, and net horizontal  flow is significant to considerable depths.  Since the
water is mixed vertically, DO replenishment usually occurs  even to the bottom and
anoxic (literally "no oxygen") conditions are unlikely.  Generally speaking, fully
mixed impoundments do not have DO deficiency problems.
     When stratification occurs, the situation is vastly different.  Flow within the
impoundment is especially limited to the epllimnlon (surface layer).  Thus surface
velocities are somewhat higher in an impoundment when stratified than when unstrati-

                                          -4-

-------
 L»TI FALL-WMTEK
                                                                    FALL
                                 I* tO M
                                 TI'CI
     $e«INC
                  OuMlO*-;
                                                                   • UMMCft
                           D i  c rt to n
                                ITI-CI
FIGURE  V-3   ANNUAL CYCLE  OF  THERMAL  STRATIFICATION AND  OVERTURN  IN AN  IMPOUNDMENT

                                            -5-

-------
fied.  Since vertical mixing is inhibited by stratification, reaeration of the
hypo limn ion (bottom layer) is virtually nonexistent.  The thenwcline (layer of steep
thermal gradient between epilimnion and hypolimnion) is often at considerable depth.
Accordingly, the euphotic (literally "good light") zone Is likely to be limited to
the ep111 inn ion.  Thus photosynthetlc activity does not serve to reoxygenate the
hypolimnion.  The water that becomes the hypolimnion has some oxygen demand prior to
the establishment of strata.  Because bottom (benthic) matter exerts a further
demand, and because some settling of paniculate matter into the hypolimnion may
occur, the 00 level in the hypolimnion will  gradually decrease over the period of
stratification.
     Anoxic conditions in the hypolimnion result in serious chemical and biological
changes.  Hicrobial activity leads to hydrogen sulflde (HgS) evolution as well  as
to formation of other highly toxic substances, and these may be harmful  to Indigenous
biota.
     It should be noted that the winter and spring strata and overturn are relatively
unimportant here since the major concern 1s  anoxlc conditions in the hypolimnion In
summer.  Thus all Impoundments will be considered as monomlctic.
     Strong stratification is also important in prediction of sedimentation rates and
trap efficiency estimates.  These topics are to be covered later.

5.2.2  Prediction of Thermal  Stratification
     Computation of impoundment heat influx  is relatively straightforward,  but
prediction «f thermal  gradients is complicated by prevailing physical  conditions,
physical  mixing phenomena, and impoundment geometry.  Such factors  as  depth and
shape of impoundment bottom,  magnitude and configuration of inflows, and degree of
shielding from the wind are  much more difficult to quantify than insolation,  back
radiation, and still air evaporation rates.   Since the parameters which  are difficult
to quantify are critical to predicting stratification characteristics, no attempt has
been made to develop a simple calculation procedure.  Instead,  a tested model  (Chen
and Orlob, 1973; Lorenzen and Fast, 1976) has been subjected to a sensitivity analysis
and the results plotted to show thermal  profiles over depth and over time for some
representative geometries and climatolovjical  conditions.  The plots are  presented 1n
Appendix D.
     The plots show the variation in temperature (*C) with depth (meters).   Temper-
ature is used as an index of density.  Engineering judgment about defining  layers
Is based on the pattern of temperature with  depth.  If stratification  takes place,
the plot will  show an upper  layer of uniform or slightly declining  temperature
(epllimnion),  an intermediate layer of sharply declining temperature (thermocHne),
and a bottom layer (hypolimnion).   A rule of  thumb requires  a temperature change  of
at least 1'C/meter to define  the thermocline.   However,  this can be tempered  by the
observation of a well  defined mixed layer.

                                          -6-

-------
      To  assess  thermal  stratification  1n  an  Impoundment,  1t  is necessary  only to
 determine  which of  the  sets  of plots most closely approximates climatic and hydro-
 logic conditions  in the impoundment studied.  Parameters  which were varied to gener-
 ate  the  plots and values used are shown In Table V-l.
      Table V-2  shows  the cUmatological conditions used to represent the  geographic
 locales  listed  1n Table V-l.  For details of the simulation technique, see Appendix E,

 5.2.2.1  Using  the  Thermal Plots
      Application  of the plots to assess stratification characteristics begins with
 determining  reasonable  values for the  various parameters  listed in Table  V-l.  For
 geographic locale,  the  user should determine whether the  impoundment of interest is
 near one of  the ten areas for which thermal plots have been generated.  If so, then
 the  set of plots  for  that area should  be used.  If the Impoundment 1s not near one of
 the  ten areas,  then the user may obtain data for the parameters listed in Table V-2
 (climatologlc data) and  then select the modeled locale which best matches the region
 of interest.
      Next, the  user must obtain geometric data for the impoundment.  Again, if
 the  Impoundment of  Interest 1s like one for which plots have been generated,  then
 that  set should be  used.  If not, the  user should bracket the studied Impoundment.
 As an example,  1f the studied Impoundment Is 55 feet deep (maximum),  with a surface
 area  of about 4xl07 feet2, then the 40 and 75 foot deep impoundment plots should
 be used.
     Mearr  hydraulic  residence time  (TW, years)  may be estimated using  the mean
total inflow rate (Q,  m3/year) and  the impoundment volume (V, m3):
                                T
                                 W
                                       V/Q                                   (V-l)
Again, the sets of plots bracketing the value of  TW ,should be examined,   khere
residence times are greater than 200 days,  the residence  time has  little  influence  on
stratification (as may be verified  in Appendix 0) and  either  the 200  day  or  infinite
time plots may be used.
     Finally, the wind mixing coefficient was used to  generate plots  for  windy  areas
(high wind) and for very well protected areas (low wind).   The user must  judge  where
his studied impoundment falls and interpolate in  the plots accordingly  (See  Appendix
D).
                                          -7-

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                              TABLE Y-l
                PARAMETER VALUES USED IN GENERATION OF
                 THERMAL GRADIENT PLOTS (APPENDIX D)
    Parameter
         Value
 Geographic Locale
Geometry
Atlanta, Georgia
6111 ings, Montana
Burlington, Vermont
Flagstaff, Arizona
Fresno, California
M1nneapol1s, M1nnesota
Salt Lake City, Utah
San Antonio, Texas
Washington, D.C.
Wichita, Kansas
Depth
(maximum,
feet)
20
40
75
100
200
Surface 9
Area (feet*)
8.28 x 106
3.31 x 107
1.16 x 108
2.07 x 108
8.28 x 108
Volume (feet3)
7.66 x 107
6.13 x 108
4.04 x 109
9.58 x 109
7.66 x 1010
Mean Hydraulic Residence Time
Wind Mixing'
•See Appendix E.
          Days
                                               10
                                               30
                                               75
                                               250
          High
          Low
                               -8-

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                           TABLE V-2

         TEMPERATURE, CLOUD COVER, AND DEW POINT DATA
    FOR THE TEN GEOGRAPHIC LOCALES USED TO DEVELOP THERMAL
STRATIFICATION PLOTS (APPENDIX 0).  SEE FOOT OF TABLE FOR NOTES.
Temoerature ( F)
Max. Mean

January
February
March
April
May
June
July
August
September
October
November
December

January
February
March
April
May
June
July
August
September
October
November
December
Atlanta
54
57
63
72
81
87
88
88
83
74
62
53
killings
27
32
38
51
60
68
79
7S
67
55
38
32
(Lat:
45
47
52
61
70
77
79
78
73
63
51
44
(Lat:
18
22
27
38
47
54
63
61
52
42
29
22
Mln,
33.8°N,
36
37
41
50
57
66
69
68
63
52
40
35
45.8°N,
9
12
16
26
34
40
46
45
37
30
20
14
Dew C
. Point (°F) F
Long:84.4°W)
34
34
39
48
57
65
68
67
62
51
40
34
Long:108.5°W)
11
16
20
28
38
46
48
46
38
31
22
15
loud Cover Wind
faction (MPH)

.63
.62
.61
.55
.55
.58
.63
.57
.53
.45
.51
.62

.68
.63
.71
.70
.64
.60
.40
.42
.54
.56
.66
.66

11
12
12
11
9
8
8
8
8
9
10
10

13
12
12
12
11
11
10
10
10
11
13
13
                             -9-

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TABLE y-2 • COHT,
Temoerature I F)

Max.
Mean
Burlington (Lit:
January
February
March
April
May
June
July
August
September
October
November
December
27
29
38
53
67
54
82
80
71
59
44
31
18
19
29
43
56
66
71
68
60
49
38
23
Flagstaff (Lat:
January
February
March
April
May
June
July
August
September
October
November
December
40
43
50
59
68
77
81
79
75
63
51
44
27
30
36
43
51
60
66
64
59
47
36
30
Mill.
44.5°K.
9
1Q
20
33
44
77
59
57
49
39
29
15
35.2°H,
14
17
22
28
34
*2
50
49
42
31
21
17
Dew Cloud Cover Wind
Point (°F) Fraction (HPH)
Lat:73.2°W)
12
12
20
32
43
54
59
58
51
40
30
17
Long:111.3°H)
14
16
17
20
22
25
43
43
35
25
20
15

.72
.69
.66
.67
.67
.61
.58
.57
.60
.65
.79
.78

.59
.49
.50
.49
.41
.24
.54
.53
.29
.31
.34
.44

10
10
10
10
9
9
8
8
8
9
10
10

8
9
11
12
11
11
9
9
8
8
8
7
     -10-

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TABLE V-2 CONT.
Temperature (°F)

Max.
Mean
Min.
Dew .
Point (°F)
Cloud Cover Wind
Fraction (MPH)
Fresno (L*t:36.7°N, Long:119.8°W)
January
February
March
April
May
June
July
August
September
October
November
December

January
February
March
April
May
June
July
August
September
October
November
December
55
61
68
76
85
92
100
98
92
81
68
57
Mlnneapol
22
26
37
56
70
79
85
82
72
60
40
27
46
51
55
61
68
75
81
79
74
65
54
47
1s (Lat:
12
16
28
45
58
67
76
71
61
48
31
18
37
40
42
46
52
57
63
61
56
49
40
38
45.0°N,
3
5
18
33
46
56
61
59
49
37
21
9
38
41
41
44
45
48
51
52
51
46
42
40
Long : 93. 3° W)
6
10
20
32
43
55
60
59
50
40
25
13
.67
.61
.53
.44
.34
.19
.11
.11
.15
.28
.44
.70

.65
.62
.67
.65
.64
.60
.49
.51
.51
.54
.69
.69
6
6
7
7
8
8
7
6
6
5
5
5

11
11
12
13
12
11
9
9
10
11
12
11
      -11-

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TABLE V-2 CONT.
Temoerature (°F)

January
February
March
April
May
June
July
August
September
October
November
December

January
February
March
April
May
June
July
August
September
October
November
December
Max
Salt
37
42
51
62
72
82
92
90
80
66
49
40
San
62
66
72
79
85
92
94
94
89
82
70
65
Mean
Lake City (Lat:
27
33
40
50
58
67
76
75
65
53
38
23
Min.
40.8°K
18
23
30
37
45
52
61
59
50
39
28
32
Antonio (Lat:29.4°N.
52
55
61
68
75
82
84
84
79
71
59
42
42
45
50
58
65
72
74
73
69
60
49
54
Dew Cloud Cover
Point (°F) Fraction .
. Long: 111
20
23
26
31
36
40
44
45
38
34
28
24
Long: 98. 5°
39
42
45
55
64
68
68
67
65
56
46
41
.9°W)
.69
.70
.65
.61
.54
.42
'.35
.34
.34
.43
.56
.69
w)
.64
.65
.63
.64
.62
.54
.50
.46
.49
.46
.54
.57
Wind
(MPH)

7
8
9
9
10
9
9
10
9
9
8
7

9
10
10
11
10
10
10
8
8
8
9
9
       -12-

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TABLE V-2 COKT.
Temperature 1
Max. Mean

January
February
March
April
May
June
July
August
September
October
November
December
Washington
44
46
54
60
76
83
87
85
79
68
57
46
. D.C.
37
38
45
56
66
74
78
77
70
59
48
43
Wichita (Lat:37.
January
February
March
April
May
June
July
August
September
October
November
December
42
47
56
68
77
88
92
93
84
72
34
45
32
36
45
57
66
77
81
81
71
60
55
36
(°F) 1
Wn. Po
(Lat:38.9°N.
30
29
36
46
56
65
69
68
61
50
39
31
7°N, Long:97.
22
26
33
45
55
65
69
69
59
48
44
27
Dew „
Int (°
Long:
25
25
29
40
52
61
65
64
59
48
36
26
3°W)
21
25
30
41
53
62
65
53
55
43
33
25
Cloud Cover Wind
F) Fraction (MPH)
77.0°W)
.61
.56
.56
.54
.54
.51
.51
.51
.48
.47
.54
.58

.50
.51
.52
.53
.53
.46
.39
.38
.39
.40
.44
.50

11
11
12
11
10
10
9
8
9
9
10
10

12
13
15
15
13
13
12
11
12
12
13
12
    -13-

-------
                                 TABLE V-2  CONT.
      Notes:  Mean:       Normal dally  average temperature, °F.
              Max.:       Normal dally  maximum temperature, °F.
              Min.:       Normal dally  minimum temperature, °F.
              Wind:       Mean wind speed,  MPH
              Dew Point:  Mean dew point  temperature,  °F.

             *Complete  data were not  available for Billings.  Tabulated
              data are  actually a synthesis of available data for
              Billings, Montana and Yellowstone, Wyoming.

              All data  taken from Climatic  Atlas of the U.S., 1974.
	   EXAMPLE V-l    	

                            Thermal  Stratification

     Suppose one wants to know the likelihood  that hypothetical Limpid Lake 1s
 stratified during June.  The first step  1s  to  compile the physical conditions for
 the  lake in terms of the variables listed in Table V-l.  Table V-3 shows how this   j
 might lie done.  Next, refer to the indexes  provided  in Appendix D to locate the
 plot set for conditions most similar to  those  of  the studied impoundment.  In this
 case, the Wichita plots for a 200-foot deep impoundment with no inflow and high     J
 mixing  rate would be chosen (see Table V-3).   Figure V-4 is a reproduction of the   I
 appropriate page from Appendix D.                                                   |
                                                                                   i
                                                                                   I
                                                                                   i
                                     TABLE V-3                                    I
                             LIMPID LAKE CHARACTERISTICS                         •
1 tern
location
Depth, ft (maximum)
Volume, ft3
Mean residence time (T )
Mi x i no
Limpid Lake
Manhattan, Kansas
180
6 x 1010
500 days
high (windy)
Available Plot
Wichita, Kansas
200
7.66 x 1010
oo (no inflow)
high coefficient
                                      -14-

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-15-

-------
I           According to the plots, Limpid Lake 1s likely to be strongly  strati-
i
|   fled  in  June.  Distinct strata fora 1n Hay and overturn probably  occurs  1n
j   December.  During June, the epillnnlon should extend down to a  depth  of  about
j   eight or ten feet, and the thenwcllne should extend down to about  30 feet.  The
;   gradient in the thennocHne should be about 1° C per meter.
                              END OF EXAMPLE V-l	'
	  EXAMPLE  V-2    	
I                                                                                      I
I                             Thermal  Stratification                                    I
i                             • '—••- ™ ••    ™^^^—^^.^^.^^^                                    ,
I                                                                                      I
|   What are the stratification characteristics of Lake Smith?                          |
j        The hypothetical  lake 1s located east of Carthage, Texas, and Table V-4 shows  j
j   its characteristics along with  appropriate values for the thermal plots.            j
i                                                                                      i
I                                                                                      I
1                                      TABLE V-4                                       j

                      PHYSICAL CHARACTERISTICS  OF LAKE  SMITH
                  - - — - —        	— — —		— —      _  .   _ -    i
         Mem	Lake  Smith	Plot Values	    I
                             "        '^^«^^-^^—^H_^—^MM    (
      Location                   15 miles  east of                                    \
                                 Carthage  Texas                                       |
      Depth,  ft (maximum)               23                          20                j
      Volume,  ft3                    3 x  108                    1.66 x  10®            j
      Mean residence  time            250  days                        co                J
      Mixing                       low (low wind)          low mixing coefficient
        From the available data for Lake Smith,  it  appears that plots for a 20-foot
   deep  impoundment with no inflow and low mixing coefficient should give a good
   indication of the degree of summertime stratification.  The one remaining problem
   is  climate.  Data for nearby Shreveport, Louisiana  compare well with those of
   Atlanta  (Table V-5), for which plots are provided in Appendix D, and latitudes are
   similar.  Shreveport 1s somewhat warmer and Insolation 1s higher, but this Is a
   relatively uniform difference over the year.  The net effect should be to shift
   the thermal plots to a slightly higher temperature  but to Influence the shape of
   the plots and the timing of stratification little.  As a result, the plots for
                                         -16-

-------
                                   TABLE V-5

                    COMPARISON OF MONTHLY CLIMATOLOGIC DATA
                 FOR SHREVEPORT, LOUISIANA AND  ATLANTA, GEORGIA
                    DATA ARE PRESENTED AS SHREVEPORT/ATLANTA
                       (CLIMATIC ATLAS OF THE U.S.,  1974)
Temperature. °F

January
February
March
April
May
June
July
August
September
October
November
December
Shreveport
Atlanta Lat
Max.
57/54
60/57
67/63
75/72
83/81
91/87
92/88
94/88
88/83
79/74
66/62
59/53
Lat: 32. 5°
:33.8°N,
Mean
48/45
50/47
57/52
65/61
73/70
81/77
82/79
83/78
78/73
67/63
55/51
50/44
N, Long:94°W
Long:84.4°W,
Mln.
38/36
41/37
47/41
55/50
63/57
71/66
72/69
73/68
67/63
55/52
45/40
40/35

Dew
Point, °F
38/34
40/34
44/39
54/48
62/57
69/65
71/68
70/67
65/62
55/51
45/40
39/34

Cloud
Cover,
Fraction
.60/.63
.S8/.62
.54/.61
.50/.55
.48/.S5
.44/.5S
.46/.63
.40/.57
.40/.53
.38/.4S
.46/.51
.S8/.62

Wind,
MPH
9/11
9/12
10/12
9/11
9/9
8/8
7/8
7/8
7/8
7/9
8/10
9/10

Atlanta may be used, bearing 1n mind that  the temperatures are likely to be biased
uniformly low.  Figure V-5 (reproduced  from Appendix D) shows thermal plots for a
20-foot deep Atlanta area  impoundment having no significant inflow and low wind
stress.  From the figure,  1t 1s clear that the lake is likely to stratify from
April or May through September, the  epilimnion will be very shallow, and the
thermocHne will  extend down to a  depth of about 7 feet.  The thermal gradient is
in the range of about 7°C  per meter,  as an upper limit, during June.  Bottom water
warms slowly during the summer until  the Impoundment becomes fully mixed 1n
October.
                                      -17-

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-18-

-------
 5.3  SEDIMENT ACCUMULATION

 5.3.1  Introduction
      Reservoirs,  lakes, and other  Impoundments are usually more quiescent than
 tributary  streams, and thus act as  large settling basins for suspended participate
 matter.  Sediment deposition 1n Impoundments gradually diminishes water storage
 capacity to the point where lakes  fill 1n and reservoirs become useless.  In some
 cases,  sediment accumulation may reduce the useful life of a reservoir to as little
 as  ten  to  twenty years (Marsh, et^ al_., 1975).
      Just  how much suspended matter settles out as water passes through an impound-
 ment, as well as the grain size distribution of matter which remains suspended, is of
 interest to the planner for several reasons.  Suspended sediment within an impound-
 ment  may significantly reduce light penetration thus limiting algal and bottom-rooted
 plant (macrophyte) growth.  This, 1n turn, can adversely affect food availability for
 indigenous fauna, or may slow plant succession, as part of the natural aging process
 of  lakes.
      Settling of suspended matter may eliminate harborage on impoundment bottoms
 thus  reducing populations of desirable animal species.  More directly, suspended
 particulates impinging on the gills of fish may cause disease or death.
      Some minerals, particularly clays, are excellent adsorbents.   As a result,
 farm  chemicals and pesticides applied to the land find their way to an impoundment
 bottom and into its food chain.  The sediment which settles is likely to have a
 substantial component of organic matter which can exert an oxygen demand, and under
 conditions of thermal stratification, anoxic conditions on the impoundment bottom (in
 the hypolimnion) can result in generation of toxic gases.   Indigenous biota may be
 harmed or even killed as a result.
      Knowing the rate of sediment transport and the deposition within an impoundment
 allows for effective planning to be Initiated.   If sedimentation rates are unaccept-
 able, then the planner can begin to determine where sediments originate,  and how to
 alleviate the problem.  For example, densely planted belts may be  established between
highly credible fields and transporting waterways, farming and crop management  prac-
tices may be changed, or zoning may be modified to prevent a worsening of conditions.
     These considerations, along with others relating to sediment  carriage and
deposition in downstream waterways, make estimates of sedimentation rates of interest
here.  Impoundment -sediment computation methods  discussed  in this  section will  permit
the planner to estimate annual  impoundment  sediment  accumulation as well  as  short
term accumulation (assuming constant hydraulic  conditions).   Application  of the
methods  will  permit the planner to  estimate the amount of  sediment removed from
transport in a river system due to  water passage  through any number of impoundments.
                                         -19-

-------
5.3.2  Annual Sediment Accumulation
     Three different techniques are used to estimate annual sediment accumulation:
available data, sediment rating curves, and a three step procedure to determine
short-term sedimentation rates.  As discussed under each technique, caution should be
used 1n selecting one method or another.  If data are not available, 1t may not be
feasible to use one or more techniques.  When drawing conclusions, the uncertainty 1n
the results should be considered 1n drawing conclusions based on whichever analysis
that 1s selected.  In addition, each technique has Its own degree of uncertainty,
which should be considered when drawing conclusions.

5.3.2.1  Use of Available Data
     Data provided In Appendix F permit estimation of annual  sediment accumulation 1n
acre-feet for a large number of Impoundments 1n the U.S.  The data and other materials
presented provide some basic Impoundment statistics useful  to the planner In addition
to annual sediment accumulation rates.
     To use Appendix F, first determine which Impoundments within the study area are
of Interest 1n terms of annual sediment accumulation.  Refer to the U.S. map Included
1n the appendix and find the Index numbers of the region within which the Impoundment
1s located.  The data tabulation in the appendix, total  annual  sediment accumulation
1n acre feet, 1s given by multiplying average annual sediment accumulation 1n acre
feet per square mile of net drainage area ("Annual Sediment Accum.") by the net
drainage area ("Area") 1n square miles:

              Total Accumulation  •  Annual  Sediment Accum. x Area           (V-2)

To convert to average annual loss of capacity expressed as a percent, divide total
annual accumulation by storage capacity (from Appendix F), and  multiply by 100.  Mote
that this approach and those presented later do not account for packing of the
sediment under its own weight.  This results in an overestimate In loss of capacity.
Note also that other data 1n Appendix F may be of interest in terms of drainage area
estimates for determining river sediment loading and assessment of storm water
sediment transport on an annual basis.

5.3.2.2  Trap Efficiency and the Ratio of Capacity to Inflow
     Where data are not available 1n Appendix F for a specific  Impoundment, the
following method will permit estimation of annual or short-term sediment accumulation
rates.  The method 1s only useful, however,  for normal  ponded reservoirs.
     To use this approach, a suspended sediment rating curve should be obtained
for tributaries to the impoundment.  An example of a sediment rating curve 1s
provided 1n Figure V-6.

                                          -20-

-------
       IQOOO
                                                  1,000
             SUSPENDED SEDIMENT DISCHARGE, S; (tons/day)
                                        100,000
            FIGURE  V-6    SEDIMENT RATING CURVE SHOWING  SUSPENDED
                           SEDIMENT DISCHARGE  AS A  FUNCTION  OF FLOW
                           (AFTER  LINSLEY, KOHLER,  AND PAULHUS,  1958)

      On the  basis of such a curve,  one can estimate the mean  sediment mass transport
 rate (S^  In mass per unit time  for tributaries.  If neither  rating curve nor data
 are available, one may estimate  sediment transport rates on a basis of data from
 nearby  channels, compensating for differences by using  mean velocities.  To a first
 approximation, 1t would be expected that:
S, « 3A7T-
 where
                                                                           (V-3)
        Si  -  sediment  transport rate to be determined in tributary "1"  in mass
               per unit  time
        Sj  «  known  transport rate for comparable tributary (j) in same  units
               as Si
        Vi  •  mean velocity for tributary 1  over the time period
        Vj  •  mean velocity In tributary j  over the same time period as  V}.
     Once average transport rates over the time period of interest  have been deter-
mined, the proportion, and accordingly the weight of sediment settling out in the
impoundment may be estimated.  Figure V-7 is  a graph showing the relationship between
percent of sediment trapped in an Impoundment versus the ratio of capacity to inflow
rate.  The implicit relationship  Is:
where
                                                                          (V-4)
              percent of Inflowing  sediment trapped
              capacity of the Impoundment 1n acre-feet
                                       -21-

-------
      0001
0003   OOO7
  003     0.07      O.I  0.3  O.S
Ratio  of  Capacity to  Inflow
                                                                                 5  T  10
FIGURE V-7   PELATIONSHIP  BETWEEN THE  PERCENTAGE OF INFLOW-TRANSPORTED SEDIMENT
              RETAINED WITHIN AN  IMPOUNDMENT  AND PATIO OF  CAPACITY TO  INFLOW
              (LlNSLEY, KOHLER, AND PAULHUS,  195R)
         Q-j  •  water inflow  rate  in acre-feet per year.
       Data used for development  of the curves in Figure V-7  Included 41 Impound-
  ments of various sizes throughout.the U.S.  (Linsley,  Kohler, and Paulhus, 1958).
       To estimate the amount  of  suspended sediment trapped within an Impoundment
  using this method, the capacity of the impoundment in  acre-feet must first be
  determined.  Next, average annual inflow, or better, average flow for the time
  period of interest is estimated.
  Then:

                              H  -  sip                                    (V-5)
  where
         St  «  weight of sediment trapped per time period t
         P   «  trap efficiency  (expressed as a decimal)  from Figure V-7.
       A word of caution is in order here.  The above described techniques for evalua-
  ting  sediment deposition in  impoundments are capable of  providing reasonable esti-
  mates, but only where substantial periods of time are  involved - perhaps six months
  or  longer.  The methods may  be  used for shorter study  periods, but results must then
  be  taken only as very rough  estimates, perhaps order-of-magnitude.
                                          -22-

-------
 5.3.3  Short-Term Sedimentation Rates
      The three-step procedure presented  below provides  a  means  to make short-term
 sediment accumulation rate estimates  for storm-event  analysis  and to estimate amounts
 of different  grain-size fractions  passing through  an  Impoundment.   The steps  are:
         •    Determine terminal  fall  velocities  for the grain  size distribution
         •    Estimate hydraulic residence time
         •    Compute trap  (sedimentation) rate.

 5.3.3.1   Pall  Velocity Computation
      When a particle  1s released 1n standing  water, It  will remain roughly  stationary
 if its density equals  that  of the water.   If  the two  densities  differ,  however, the
 particle  will  begin  to rise or  fall relative  to the water.  It  will  then tend  to
 accelerate until  the  drag  force  Imposed  by the water  exactly counterbalances the
 force accelerating  the particle.  Beyond  this  point,  velocity 1s essentially constant,
 and the  particle  has  reached terminal velocity.  For  spheres of specific gravity
 greater  than  1, Stokes'  law expresses the relationship  between  fall  velocity  (terminal
 velocity)  and  several  other physical parameters of water and the particles:
                          Vmax " Ttf VVd  * TK
-------
criterion 1s met.  For large particles, how far conditions deviate from this may be
observed using the following approach (Camp, 1968).  According to Newton's law for
drag, drag force on a particle 1s given by:
                                   tt • ttojfll                             (V-8)

where
        F
                               max " v/Tf	p	
                                             w
     All variables 1n the expression for V    (Equation V-9)  may be easily
estimated except C, since C Is dependent upon Reynold's number.   According  to Equa-
tion V-7, Reynolds number is a function of v.  Thus a "trial  and error"  or  iterative
procedure *ould ordinarily be necessary to estimate C.  However, a somewhat simple"*
approach is available to evaluate the drag coefficient and Reynolds number.  First,
estimate CR2 using the expression (Camp. 1968):

                             CR2 • AD..  (o_  -  pj  gd3/3u2                (V-10)
                                     W   j)     W

Then, using the plot in Figure V-8, estimate R and then C.  For  R>0.1  use of Equation
V-9 will give better estimates of V    than will Equation V-6.
     generally, one of the two approaches for spherical particles will give good
estimates of particle fall velocity in  an effectively laminar flow field (1n Im-
poundments).  Occasionally, however, it may prove desirable to compensate for
nonsphericity of particles.  Figure V-9, which shows the effect  of particle shape on
the  drag coefficient C, may be used to do this.  Note that for R < 1,  shape of
particle does not materially affect C, and no correction is necessary.
     A  second problem in application of the Newton/Stokes approach described above is
that it does not account for what is called hindrance.  Hindrance occurs when the
region  of fluid surrounding a falling particle Is disrupted (by  the particle motion)
and  the velocity of other nearby particles is thereby decreased.  Figure V-10 shows
this effect schematically.
     A  very limited amount of research has been done to determine the  effect of
particle concentration on fall velocity (Camp, 1968).  Some data have  been  collected
                                         -24-

-------
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 FIGURE V-8  PLOT  OF C./R AND  rP2 vERSus " (CAMP,  1968)
                            -25-

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                                                       LEGEND'
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                           0 - Discs
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  Reynolds  Numbtr,  R
      FIGURE V-9  ORAG  INEFFICIENT  (C)  AS FUNCTION  OF REYNOLD'S NUMBER  (R)
                   AND PARTICLE  SHAPE  (CAMP,  1968)
however, and Figure V-ll 1s a plot  of a velocity correction factor, v  /v, as a
function of volumetric concentration.  Volumetric concentration 1s given by:
where
           ,
                                  'vol
                volumetric concentration
                                                                          (v-n)
              »  weight concentration.
As an approximation, the curve for  sand may be used  to correct v as a  function
of Cvol•
                                        -26-

-------
 Particles which
 velocity is offtcttd
 by vertical velocity
 fitld
                                   Region of disruption,
                                   upward fluid motion

                                   Settling sphere
                                                            Water column
                                                            containing settling
                                                            particles
    FIGURE V-10  SCHEMATIC REPRESENTATION OF HINDERED  SETTLING
                   OF  PARTICLES  IN  FLUID  TOLUMN
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FIGURE V-ll  VELOCITY CORRECTION FACTOR FOR HINDERED SETTLINS (FROM CAMP, 1968)
                                     -27-

-------
j	EXAMPLE V-3   	1
i                                                                                        i
j                                Settling Velocity                                       j

i                                                                                        i
        Assume that a swiftly moving tributary to a large reservoir receives a heavy    •
!   loading of sediment which 1s mostly clay particles.  The particles tend to clump
{   somewhat, and average diameters are on the order of 2 microns.  The clumps have a   \
I   specific gravity of 2.2.  Applying Stokes1 law for 20"C water:                      I
             n  .        %  • &.
     V
     'max   T8u  x"p   *V

          •  	—	c-x  [(2.2  x  62.4/32.2)  -  (62.4/32.2)]  x  (6.56  x  10'6)2
            (18  x 2.1 x  10-b)
          •  8.53 x 10-6  ft  sec-l  .  .03 ft  hr-1

   Thus the  particles of clay  might  be expected  to  fall  about  nine Inches  per
   day  in the reservoir.  It should  be noted  that for such  a low  settling  rate,
   turbulence in the water  can cause very  significant errors.   In  fact,  the  estimate
   1s  useful  only in still  waters having a very  uniform  flow lacking substantial
   vertical  components.
'.	END  OF  EXAMPLE  V-3	

	   EXAMPLE  V-4 	
I                                                                                        !
I                      Settling  Velocity  for a  Sand  and  Clay                              '
i                                                                                        j
j        Suppose a  river  1s  transporting  a substantial  sediment  load which  1s mainly      |
j   sand  and clay.   The clay tends to clump  to  form  particles  of 10 micron  diameter       j
•   while the sand  is  of  0.2 mm  diameter.  The  sand  particles  are very  Irregular  1n       j
•   shape tending toward  a somewhat  flattened plate  form.   The specific  gravity of the    j
'   clay  is  about 1.8  while  that  of  the sand is near 2.8.   Given that the water
j   temperature  is  about  5eC, the terminal velocity  of  the  clay  may be estimated  as 1n    !
I   Example  V-3:                                                                          I
i                              2                                                         i
I     Vmax  ' TaV   (pp ' Pw} d                                                          I

           ' (16 x  fll  x 10-5)  * '°-8 * «•*  / ".2)  x  (3.28 x 10-5,2                   j
                                                                                        i
           • 9.4 x  lO'5  ft  sec"1                                                        !
           • 8  ft  day-1                                                                  I
                                          -28-

-------
 I   For  the  sand,  apply Equation V-10:

 j        CR2  -  4ow (Cp - 0J gd3/3u2
 j                  ,   62.4    1.8 x 62.4   32.2 x  (6.56 x IP"4)3
                   *  x -jj-j      j^3 x (3.17 x 10-5)2
 |         CR2  . 82
 I   Referring  to Figure V-8, a  value of CR2 equal  to 82 represents RS2.8 and
 |   CaiO.3.   From Figure  V-9,  the corrected drag  coefficient for discs Is close
 j   to 10.3  (no correction really necessary).  Then, using Equation V-9 as an approxi-
    nation:
                     /49 (p  - p J d
             v     «  '      °
             max  \
                      I  4
                    J  3
          V    .   /  " « 32.2 x  (1.8 x 62.4 / 32.2) x 6.56 x IP"4
           max    J  3 x 10.3 x  62.4 / 32.2
          .„„   0.07 ft  sec'1 • 252 ft hr'1
           max
Thus the clay will settle about  8 feet  per day while the sand will  settle  about
6,048 feet per day (252 feet per hour).
                               END OF EXAMPLE V-4
 5.3.4   Impoundment Hydraulic Residence Time
     Once settling velocities have been estimated for selected grain sizes, the final
 preparatory step 1n estimating sediment deposition rates 1s to compute hydraulic
 residence time.
     Hydraulic residence time represents the mean time a particle of water resides
 within  an impoundment.  It is not, as is sometimes thought, the time required to
 displace all water 1n the impoundment with new.  In some impoundments,  inflowing
 water may be conceptualized as moving In a vertical  plane from Inflow to discharge.
 This is called plug flow.  In long, narrow, shallow impoundments with high inflow
 velocities, this 1s often a good assumption.  As discussed later, however, adoption
 of this model  leads to another problem, namely, is water within the plug uniform or
 does sediment concentration vary over depth within the plug?
     A second model assumes that water flowing into an Impoundment Instantaneously
mixes laterally with the entire receiving layer.  The layer may or may  not represent
the entire impoundment depth.  This simplification is often a  good one  in large
surfaced, exposed impoundments having many small Inflows.
     Regardless of the model  assumed  for the process  by  which  water traverses
an impoundment from Inflow to discharge, hydraulic residence time 1s computed
                                         -29-

-------
 as  1n  Equation  V-l.   That  is:
       %  •  V/Q
 The only important qualification  is that to be meaningful, V must be computed
 taking account  of stagnant areas, whether these are regions of the impoundment
 isolated from the main flow by a  sand spit of promontory, or whether they are
 isolated by  a density gradient, as in the themocline and hypolimnion.  Ignoring
 stagnant areas  may result  in a very substantial overestimate of TM, and in sediment
 trap computations, an overestimate in trap efficiency.  Actually TH computed in
 this way is  an  adjusted hydraulic residence time.  All references to hydraulic
 residence  time  in the remainder of Section 5.3 refer to adjusted TM.
     Hydraulic  residence time is  directly influenced by such physical variables as
 impoundment  depth, shape,  side slope, and shoaling, as well as hydraulic character-
 istics such  as  degree of mixing,  stratification, and flow velocity distributions.
 The concepts Involved in evaluating many of these factors are elementary.  The
 evaluation itself is complicated, however, by irregularities in Impoundment shape and
 data inadequacies.  Commonly, an  impoundment cannot be represented well by a simple
 3-dimensional figure, and shoaling and other factors may restrict flow to a laterally
 narrow swath through the water body.
     In most  cases,  hydraulic  residence  time  may  be  estimated,  although it  is  clear
that certain  circumstances  tend  to make  the  computation error-prone.   The  first step
in the estimation process  is  to  obtain  impoundment  inflow,  discharge,  and  thermal
regime data as  well  as topographic/bathymetric  maps  of  the  system.   Since  a  number of
configuration types  are  possible,  the methods  are perhaps best  explained using
examples.
 	EXAMPLE V-5	

              Hydraulic Residence Time in Unstratificd Impoundments

        The first step in estimating hydraulic residence  time for  purposes  of
   sedimentation analysis is to determine whether there are significant  stagnant
   areas.  These would include not only regions cut  off from the main  flow  through
   the body, but also layers isolated by dense strata.  Consequently,  it must  be
   determined whether or not the impoundment stratifies.   Consider Upper Lake  located
   on the Carmans River, Long Island, New York.  The lake and surrounding region  are
   shown in Figure V-12, and hypothetical geometry data are presented  in Table V-6.
   Based upon Upper Lake's shallowness, its long, narrow  geometry, and high tributary
   inflows, it is safe to assume that Upper Lake is  normally unstratified.   Also,
   because of turbulence likely at the high flows, one can assume  that the  small  sac
   northeast of the discharge is not stagnant  and that Upper Lake  represents a slow
                                         -30-

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                                   TABLE V-6
                   HYPOTHETICAL PHYSICAL CHARACTERISTICS AND
       COMPUTATIONS FOR UPPER LAKE, BROOKHAVEN, SUFFOLK COUNTY,  NEW YORK
Distance Downstream
from Inflow
Miles (feet)
0.05 (264)
0.10 (528)
0.15 (792)
0.20 (1,056)
0.25 (1,320)
0.30 (1,534)
0.35 (1,848)
0.40 (2,112)
0.45 (2,376)
0.50 (2,640)

D
Average
Depth
ft.
3
4
6
7
7
8
7
8
7
10

W
Average
Width
ft.
63
no
236
315
340
315
550
550
354
350

CSA
Cross-sectional
Area.,D x W
ft2
189
440
1,416
2.205
2,380
2,520
3,850
4,400
2.478
3,500
mean 2,338











   Total length • 0.5 mi.  (2,640  ft.)
   Inflow from upstream »  380 cfs  )
   Outflow to downstream » 380 cfs I
steady-state}
   Computation
   Volume (Vol) * Total length x mean cross-sectional  area
                « 2,640 ft. x 2,338  ft2 « 6.17  x  106  ft3
  Residence  time  (T  )  «  Vol/flow
                       -  6.17  x  106 ft3/(380 ft3/sec)  •  1.62 x 104  sec  (4.5  hr)
  Velocity  (Vel)  «
                 » 2,640  ft/1.62  x  10  sec  = .163 ft/sec
moving river reach.   With these assumptions,  the  computation of hydraulic residence
time is as shown in  Table V-6.
     Also shown in Figure V-12  is  Lower  Lake.   According to the hypothetical data
presented in Table V-7,  Lower Lake is much  deeper  than Upper Lake.   Its volume is
significantly greater also,  but the  inflow  rate is similar.  In this case, par-
ticularly during the summer,  it should be determined if the lake stratifies.  For
this example, however, we will  assume that  the  time of the year makes stratifica-
                                      -31-

-------
            FIGURE  V-12   UPPER AND LOWER  LAKES  AND ENVIRONS,,
                           LONG ISLAND, NEW YORK
tion very unlikely, and that  Lower Lake 1s a slow moving river reach.  We then

compute hydraulic residence time as shown 1n Table V-7.  Figure V-13,  1n particular
diagram 1,  shows what these assumptions mean 1n terms of a flow pattern for both
lakes.
                                     -32-

-------
                               TABLE V-7

                HYPOTHETICAL  PHYSICAL CHARACTERISTICS AND
    COMPUTATIONS FOR  LOWER LAKE, BROOKHAVEN, SUFFOLK COUNTY, NEW YORK
Distance Downstream
from Inflow
Miles (feet)
0.075 { 396)
0.150 { 792)
0.225 (1.188)
0.300 (1,584)
0.375 (1.980)
0.450 (2,376)
0.525 (2,772)
0.600 (3.168)
0.675 (3.564)
0.750 (3.960)
0.825 (4,356)
0.900 (4,752)
0.975 (5,148)
1.050 (5.544)
1.125 (5.940)

Total length « 1.125 mi (5
0
Average
Depth
ft.
15
20
20
25
35
30
35
35
40
42
41
51
42
40
37

,940 ft.)
Inflow from upstre«m 400 cfs |
> (surface
Outflow to downstream 390 cfs )
Average flow « 395 cfs
Comoutation


W
Average
Width
ft.
157
165
173
197
197
228
232
197
220
315
433
591
551
433
323


rising)


CSA
Cross-sectional
Area,,D x W
ft2
2.355
3,300
3,460
4,925
6.895
6,840
8,120
6,895
8,800
13,230
17,753
30,141
23,142
17,320
11,951
mean 11 ,008




 Volume (Vol)  * Total  lenath x mean cross-sectional  area
              - 5,940  ft.  x  11,008 ft2 • 6.54 x 107  ft3

Residence Time (t ) «  Vol/flow

                    « 6.54 x  107/(395  ft3/sec)  »  1.65  x 105 sec (46 hr)
Velocity (Vel) • length/fw

               • 5,940 ft/1.65 x 105 sec •  .036 ft/sec
                                  -33-

-------
                                                I
                           MMMACtO. HOMMniT (MALLOW J
                           OMIKT, VfKT LO* VfLOClTlK  I
                    //
                   •UUft*. WOC Hl«(0 (TU«*UCC«T)
            (41
                      %xx'x*x*> *•*••••' L«?*» •.-;:"-:-:-:-::;^-x
                     Ktr.
                                  1iM*uiC*T
                                                                 T —
    FIGURE  V-13   IMPOUNDMENT  CONFIGURATIONS AFFECTING SEDIMENTATION
	  END OF  EXAMPLE V-5
                                          -J4-

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r	EXAMPLE V-6	'
i                                                                                       i
j        Assume for this example that Lower Lake 1s stratified during the period of     |
j   interest.   This significantly changes the computation of residence time.   To a      j
•   first approximation, one can merely revise the effective depth of the impoundment   j
!   to be from the surface to the upper limit of the thermocline rather than  to the
j   bottom.  Figure V-13 shows schematically what this simple model  suggests  for Lower  .
   Lake as a  stratified impoundment (diagram 2 or possibly 3).   The figure also shows  '
   wind-driven shallow, and deep impoundments.  To the right of each diagram is a      I
   plot of the temperature profile  over depth.  Actually,  the profile could  represent  |
   a salinity gradient as well  as a thermal gradient.                                  j
        Table V-8 shows the procedure to estimate travel time for stratified Lower
   Lake.  The upper boundary of the thermocline 1s assumed to be at a depth  of
   10 feet.  For all  later computations of sediment accumulation, this same  10
   foot depth would be adopted.  Such an assumption is valid presuming that  the        {
   thermocline and hypolimn ion  are  relatively quiescent.  Thus  once a particle enters  I
   the thermocline it  can only  settle,  and cannot leave the impoundment.
  	END  OF  EXAMPLE  V-6	'

  	  EXAMPLE  V-7  	
                                                                                       I
                                                                                       i
                       Large,  Irregular  Surface  Impoundment                             I
                                                                                       j
        Figure  V-14  shows  Kellis  Pond  and surrounding topography.   This  small           (
   pond  is  located near Bridgehampton, New  York  and has a  surface area of  about         j
   36  acres.    From  the surface shape  of the pond, 1t is clear  that  it cannot           j
   be  considered  as  a  stream reach.
        Figure  V-15  shows  a set of  hypothetical  depth profiles  for  the pond.
   From  the profiles,  1t is evident that considerable shoaling  has  resulted in          j
   the formation  of  a  relatively  well  defined  flow channel thorugh  the pond.            I
   Peripheral stagnant  areas have also formed.   Hypothetical velocity vectors           |
   for the  pond are  presented  in  Figure  V-16.  Based upon  them, it  is reasonable        j
   to  consider  the pond as being  essentially the hatched area in Figure  V-15.           j
   To  estimate-travel  times, the  hatched area may be handled in the  same way as
   for the  Upper  Lake  exampl«  presented  above.   It should  be noted,  however, that       !
   this  approach  will  almost certainly result  1n underestimation of  sediment depo-      J
   sition in  later computations.  This is true for two reasons.  First,  estimated       I
   travel time  will  be  smaller than the  true value since impoundment volume is
   underestimated.   Second, since the  approach Ignores the low  flow  velocities to
                                         -35-

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                                      TABLE V-8

                     HYPOTHETICAL PHYSICAL CHARACTERISTICS AND
           COMPUTATIONS FOR LOWER LAKE, BROOKHAVEN, SUFFOLK COUNTY,  NEW  YORK
                      (ASSUMING AN EPILIMNION DEPTH OF 10 FEET)
Distance Downstream
from Inflow
Miles (feet)
0.075
0.150
0.225
0.300
0.375
0.450
0.525
0.600
0.675
0.750
0.825
0.900
0.975
1.050
1.125
D
Average
Depth
ft.
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
w
Average
Width
ft.
160
170
175
200
198
230
233
200
222
316
435
590
552
435
325
CSA
Cross-sectional
Area,JJ x W
ftr
1,600
1.700
1.750
2,000
1.980
2,300
2,330
2.000
2.220
3,160
4,350
5.900
5,520
4,350
3,250
        Total  length • 1.125 mi  (5,940 ft.)               mean CSA « 2,961 ft*

        Inflow from upstream 397 cfs   )     (steady-state  surface,  difference
        Outflow to downstream 393 cfs )
        Average flow » 395 cfs
due to loss to water table)
        Computation

        Volume  (Vol)  »  Total  length  x mean cross-sectional  area
                     -  5,940 ft.  x 2,961  ft2 • 1.76 x 107

      Residence Time (~w) • Vol/flow
                          - 1.76 x 107/(395 ft3/sec) • 4.46 x 104 sec  (12.3  hr)       j
I      Velocity (Vel) - length/T
                       5,940 ft/4.46 x 10  sec - 0.133 ft/sec
                                         -36-

-------
  SOUTHAMPTON
                                             BRIDGE HAMPTON
                                       1/2
                                      MILES
FIGURE V-14   KELLIS POND AND SURROUNDING REGION,  LONG  ISLAND,
             NEW YORK
                            -37-

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                        INFLOW.
                                          PLAN VIEW
      FIGURE V-15   HYPOTHETICAL  DEPTH PROFILES
                    FOR  KELLIS  POND
     STAGNANT
STAGNANT-
FIGURE V-16   HYPOTHETICAL FLOW PATTERN IN KELLIS POND
                        -38-

-------
                                   V
                                                        TRANSECTS
                                                         ^^•H
                                                         A

     -FIGURE V-17
HYPOTHETICAL DEPTH PROFILES  FOR  KELLIS  POND
NOT  SHOWING SIGNIFICANT SHOALING
either side  of  the central channel and nonunlform  velocities within it, heavier
sedimentation than computed is likely.
     Still  more difficult to evaluate 1s the situation where shoaling and scour
have not resulted 1n  formation of a distinct central  channel.  Figure V-17 shows
hypothetical  depth profiles for Kellis Pond for such  a case.
     Here,  velocity distribution data should be obtained,  particularly if the
impoundment  1s  of much  Importance.  If such data are  not available but it is
deemed worthwhile to  do field studies, methods  available for evaluating 'low
patterns -include dye-tracing and drogue floats.  A simple  but adequate method (at
least to evaluate the surface velocity distribution)  is to pour a large number of
citrus fruits (oranges, grapefruit) which float just  below the surface, into the
impoundment,  and to monitor both their paths and velocities.  Although it is true
that surface velocities may be greater than the velocity averaged over depth, this
                                      -39-

-------
I   will permit estimation of hydraulic residence time directly or generation of data    |
j   to use in the prescribed method.  In the latter case, the data might be used to      j
'   define the major flow path through an Impoundment of a form like Kellls Pond.        j
*                                                                                        '
!	END OF EXAMPLE V-7  	
.	EXAMPLE V-8	1
t     .                                                                                  i
                               Complex Geometries
I                                                                                       I
I        The final hydraulic residence time example shows the degree of complex-
I   1ty that sediment deposition problems may entail.  Although U 1s possible
|   to make rough estimates of sediment accumulation, 1t 1s recommended that for
j   such impoundments more rigorous methods be used - mathematical  modeling and/or      j
j   detailed field investigations.                                                       j
        Figure V-18 shows Lake Owyhee in eastern Oregon.  This impoundment is well
   outside the range of complexity of water bodies which can be evaluated using these  !
|   calculation methods.  Because of geometry, the number of tributaries, and size,  1t  j
I   is not feasible to conceptually reduce the Impoundment 1n such a way as to estimate I
|   travel  times.   Flow patterns are likely to be very  complex,  and  sediment  deposition |
j   is difficult  to predict both in terms  of  quantity  and location.                      j
        In contrast,  Figure V-19 shows New Mlllpond near Islip,  New York  and surround- j
   ing features.   Although this water  body does  not have a  simple surface geometry,
!   it can  be  reduced  to three relatively  simple  components  as  shown in  the figure.
I   Bearing in  mind the limitations  imposed by wind mixing,  stratification,  and  the      j
I   presence of  stagnant regions described  In  earlier  examples,  deposition might        I
|   nevertheless  be estimated in arms  A,  B, and C.   Because  of  the difficulty of        |
i   predicting  velocities and turbulence  in section D,  estimates  of  sedimentation        |
:   cannot  be  reliably made there.   However,  it is  likely that  much  of  inflowing        j
   sediments  will  have settled out by  the  time water  flows  through  the  arms  and Into
   section D.
I                                                                                       I
                                         -40-

-------
FIGURE V-18  LAKE OWYHEE  AND ENVIRONS
                -41-

-------
                                                  SMITHTOWN
                                         0
                                         I
 1/2
_J	
                                                   MILES
        FIGURE V-19  NEW  MILLPOND AND ENVIRONS,   NEW MILLPOND is
                     SUBDIVIDED FOR PURPOSES OF  FSTIMATING SFPI-
                     MENTATION IN REGIONS A, B,  AND (*.,
	  END OF  EXAMPLE  V-8  	
                                                                   	I
                                   -42-

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 5.3.5  Estimation of Sediment Accumulation
     Estimation of quantities of sediment retained in an impoundment follows directly
 from the computations of settling velocity and travel time, although the computation
 depends upon whether the adopted model is plug flow, or a fully mixed layer or
 impoundment.
     In the case of plug flow, one of two subordinate assumptions is made:   that the
 plug 1s fully mixed as 1n turbulent flow, or that 1t moves in a "laminar" flow
 through the impoundment.  In terms of sediment accumulation estimates,  the fully
 mixed plug assumption is handled in the same way as the fully mixed Impoundment
 model.  Thus we have two kinds of computations:
        Case A    •    Plug flow with the plug not mixed vertically.
                  •    Plug flow assuming a vertically mixed plug
        Case B
                  •    A fully mixed impoundment or stratum.
     Equation V-12 is pertinent to both cases A and B.  It defines the mass of
sediment trapped as a function of trap efficiency and inflowing sediment mass.
Equation V-13 should be used for case A, and Equation V-14 for case B:

                                      St - S,P                               (V
                                p  .  ((T^V)  * 0" -0 J/D"
                                        D'
where
        P    «  mean proportion of S\  trapped (1  _>_ P _>. 0)
        S^   «  mass of sediment trapped per unit time
        S-j   «  mass of sediment in inflows  per unit time
         v   -  particle settling velocity
         D   •  discharge channel depth
         D'   »  flowing layer depth
         D"   «  inflow channel  depth.
      Figure V-20 shows the  significance of  the various  depth measures D,  D', D'',
 and the assumed sedimentation  pattern.   In  case  B,  in the  absence  of substantial
 erratic turbulence and unpredicted vertical  velocity  components, and within the
 constraints of «vailable data,  it is  clear  that  this  approach  can  give  reasonable
 estimates of trap  efficiencies.   In case A,  however,  small  changes  in D or D*' can
 strongly affect trap efficiencies.  It  is  important  to  remember  in  applying case A
 that Pisa mean,  preferably used over a period  of  time.   It is  also important to
 recognize that conditions within an impoundment  leading to  selection of case A or B
 are subject to change, thus  affecting estimates.
      For convenience.  Figure V-21 1s  included  to  provide estimates  of v
                                                                        max

                                         -43-

-------
    -5L
             PLUG FLOW, PLUG NOT MIXED VERTICALLY


T
^N



>
/






















|

1
j























£•
/[:•:


"*-
•"«*•"•**




;.;-;•;
"•"•X
::::"•'•(
.:••:,-':• 0
• • . • 4
•"•*•*•***.*•*.*.*.***

                       Hypolimmon
                       5«aiment Loytr ;.;.;.v.v.;.;.v.y

                       •IMPOUNDMENT 	
                                                        CASE A
  Flow
  no-
               PLUG FLOW, VERTICALLY  MIXED PLUG










1 '




I
t












                       IMPOUNDMENT
             FULLY  MIXED IMPOUNDMENT OR STRATUM
                              Lay«f vX'.'-vX1'--

                       IMPOUNDMENT 	
                                                        CASE B
FIGURE  V-20  SIGNIFICANCE OF DEPTH MEASURES  D,  D', AND
              D". AND THE ASSUMED  SEDIMENTATION PATTERN
                            -44-

-------
                                                             35
V-21
                   -45-

-------
       10
       10
       10
                                         S«tt11ng velocity In feet/
                                         second
                                         Hydraulic residence  tine
   in seconds
D': Flowing layer depth
   Mass of sediment trapped
   Mass of sediment entering
   impoundment
       10°
     FIGURE V-22   NOMOGRAPH  FOR  ESTIMATING SEDIMENT  TRAP  EFFICIENCY
for spherical particles of 2.7 specific gravity.  The data  are  presented  as  a
function of particle diameter and temperature.  Figure V-22 1s  a  nomograph relating
trap efficiency, P (in percent) to depth D', V    • and  TW.  The  nomograph is
useful only for case B assumptions.
                                          -46-

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 	   EXAMPLE V-9   	

                     Sedimentation in Upper and Lower Lakes
I

   of Example V-4, for case A:
!        Using the data from Table V-6 and settling velocities for the clay an-J sand
                              4
                   T  • 1.6x10  sec
             fop day « 8 ft day"1
                                    l
        Vmax  for sand * 252 ft hour                                                    I
                                                                                       *
        Although it is not specified  in Table V-6,  the Inflow  channel  depth  at          j
   the entrance to Upper Lake  is  3 feet.   The discharge channel  depth  is  10  feet.       I
   Assuming "laminar" flow with minimal vertical components (Case A), for clay:          |
                                                                                       '
               [{T  x v) t D"  -  D]                                                    !
          p .  - 2 -                                                    i
                     D"                                                                !
          p . [(1.6 x 104 x 9.3 x 10-5) + 3 - IQ]                                       '
                          3                                                            I
            - -5.5                                                                     j
  The negative value implies that the proportion settling out  is virtually  zero.        |
  Thus the clay will to a large extent pass through Upper Lake.   However, TW for        j
  this example is very small (4.5 hours).  Many  impoundments will  have substantially
  larger values.
  For the  sand:
           p  m  [(1.6  x  10* x 7 x  10-2)  +3-10]
                          3
             -  371
  All of the sand will  clearly be retained.  Note that a clay  or very fine silt of
  V     » 5xlO~4  ft  sec'l would be only partially trapped:
           p «  [(1.6  x  104 x S x  10-*)  *  3 - 10]
                          3
            •  0.33
  Thus  about one-third of this sediment  loading would be retained.  Note that
  if D  is  large, trap  efficiency  drops using this algorithm.   For the silt,  a
  discharge channel  depth (at the outflow from Upper Lake) of  11 feet rather
  than  10 would  give:
           p .  [(1.6  x  104 x 5 x  10-*)  ^  3 - 11]
                                         -47-

-------
1   Thus with 0 • 11, all silt exits the Impoundment.  If D 1s only 9 feet, then:        I
1           p   [(1.6 x 10* x 5 x 10-*) * 3 - 9]                                         j
i             '             3                                                            i
             • .66                                                                      j
!   Two-thirds of the silt 1s retained.  Remember that P represents a mean value.
{   Clearly during some periods none of the silt will be retained (due to turbulence,    ;
I   higher velocities) while during other periods, all of the silt will  be trapped.      j
|   The key here 1s the word "mean.'                                                     I
|        If the Impoundment 1s assumed to be vertically nixed (case B),  compute          j
j   the mean depth 0:                                                                    j
                 n
I           D -   I  D./n                                                                 I
i                                                                                        i
   where
          n    •  the number  of  cross-sections
I          QI   »  depth  at  the  1th  cross-section.                                         j
I   For Upper Lake:                                                                      I
i                                                                                        i
I           0 - 6.7  - D'                                                                 I
I   Then:                                                                                j
I                 v  T                                                                    1
   For the ciay:
           P . 9.3 x 1(TS x 1.6 x 104
                        6.7
             - 0.22
   About one-fourth of the clay 1s retained:
   For the sand:
           P . 7  x 10-2 x 1.6 x 10*
                        6.7
             • 167
   All of the sand will be trapped within about 1/167 times the length of the
   lake.  If the  dally Influent loading of sand Is one ton, while the loading
   of clay Is  fifteen tons, then the dally accumulation will be one ton of sand
   and 0.22 x-15  «.-3.3 tons of clay.
        Finally,  as an example of use of Figures V-21 and V-22, assume that the
   sediment loading consists primarily of silt particles in the sl2e range of
   .002mm diameter, and that the water temperature is 5*C.  Further, assume Tw has
   been estimated as 2.77 days (104 seconds), and that 0* « 50 feet.  From
   Figure V-21, the settling velocity is about 1 x 10"4 feet per second.
                                          -48-

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 I        In  Figure  V-22,  draw  a  line  from  10~4 on  the  V  axis  to  104  on  the
 j   Tw  axis.  The point of  Intersection with  axis  I  1s L*.  Next, compute
 j   1°91050  " 1-699.   Draw  a line  from this point  or the D' axis to  L*.
 •  Where  this  line crosses the  St/Si (I)  axis gives the log  of the  percent
 •   of  the sediment trapped.   This  1s 1QO-3 » 1.99321.
 I
 I	END OF EXAMPLE V-9	
 5.4   EUTROPHICATION  AND  CONTROL

 5.4.1   Introduction
      Eutroph1cat1on  1s the process of Increasing nutrients 1n surface waters.
 The  presence  of  nutrients in an  impoundment generally favors plant growth.  Depending
 upon antecedent  conditions, the  relative abundance of nitrogen, phosphorus, light,
 and  heat, and the status of a number of other physical and chemical variables, the
 predominant forms may be diatoms, other microscopic or macroscopic algae, or bottom-
 rooted  or free-floating macrophytes.  The quantity of plant matter present In an
 Impoundment 1s Important for several reasons.  First, plant cells produce oxygen
 during  photosynthesis, thereby providing an Important source of dissolved oxygen to
 the  water column during daylight hours.  Plant cells also consume oxygen through the
 process of respiration.  Respiration occurs along with photosynthesis during the day,
 but  occurs at night when photosynthesis does not.  Oxygen consumed at night may be
 considerable, not only because it serves to sustain the plant cells, but because the
 cells actively perform various vital metabolic functions in the dark.  Also, cells
 that  fall below the photic zone will consume additional  oxygen irrespective of the
 time of day.
     Plant growth within an impoundment is also important because plant biomass is a
 major source of nutrition for Indigenous fauna,  and the growth of plants constitutes
 what is called "primary production."  The stored energy  and nutrients provide  food
 for  various grazers higher in the food chain, either through  direct consumption of
 living plant tissue by fishes and zooplankton or through consumption of detritus by
 fishes, microorganisms, and zooplankton.  The grazers, 1n turn,  provide food for
 predatory fishes, mammals.  Insects,  and other higher forms.  The kinds and amounts of
 primary producers effect the other members of the food chain  resulting In a  good
 sport fishery or "trash fish,"  depending on nutrient conditions.
     Finally, plant development in Impoundments  1s  important  because  It tends  to
 accelerate Impoundment aging.   As plants grow,  organic matter and sediment accumulate.
 As the Impoundment fills with  rock fragments,  soil,  and  plant detritus,  an excellent
 substrate forms upon which  more suspended matter may be  trapped  and which may  ulti-
mately support the growth of higher  plants and  trees.  The  gradual  filling in  of  an
                                         -49-

-------
 Impoundment  In this way  reduces  Us usefulness, and may finally eliminate the  Impound-
 ment completely.

 5.4.2   Nutrients, Eutrophy, and  Algal Growth
     Eutrophy means literally a  state of good nutrition.  Plants require a number of
 nutrients, but to vastly different degrees.  Some nutrients, such as carbon, nitrogen,
 potassium, and phosphorus, are needed 1n large quantity.  These are termed macronutrl-
 ents.   The micronutMerits, e.g.  Iron, cobalt, manganese, zinc, and copper, are needed
 in very small amounts.   In nature, the nricronutrlents, carbon, and potassium are
 usually in adequate supply (although not always), while nitrogen and phosphorus are
 commonly growth limiting.
     Nitrogen, particularly as nitrate and ammonium Ions, 1s available to water-borne
 plant cells to be used in synthesis of proteins, chlorophyll a_, and plant hormones.
 Each of these substances 1s vital for plant survival.
     Phosphorus, an element found in a number of metabolic cofactors, 1s also neces-
 sary for plant nutrition.  The biosynthesis and functioning of various biochemical
 cofactors rely on the availability of phosphorus, and these cofactors lie at the very
 foundation of plant cell  metabolism. Without adequate phosphorus,  plant cells cannot
 grow.
     Since nitrogen and phosphorus are commonly in limited supply, many impoundments
 tend inherently to be clear and essentially free of clogging algae and vascular
 plants.  Over long periods of time and depending on geological  conditions, natural
 sources of nutrients may lead to eutrophication in lakes.   Because of society's
 ever-increasing size and need for food, chemical  sources of nitrogen and phosphorus
 are synthesized and spread over vast tracts of farmland.  Stormwater washes off these
 nutrients, which then flow through streams  and into natural  and artificial  impound-
ments.  Also, excessive nutrients occur in  wastewaters from municipalities and
 industry.  Due to the fact that many impoundments have very low flow velocities,
 impoundments represent excellent biological cultunng vessels,  and often become
 choked with plant life when nutrients  Increase.
     Since a plant cell has at any point in time a specific need  for nitrogen and  for
 phosphorus, one or the other or both may limit cell  growth or replication.  Where
 nitrogen is the nutrient  that restricts the rate of plant  growth,  that is,  where all
 other nutrients aod /actors -are present in  excess.-we *ay  that  nitrogen 1s  growth
 limiting.  In general, N:P mass ratios in the range of 5 to 10 are usually associ-
 ated with plant growth being both nitrogen  and phosphorus  limited.  Where the ratio
 is greater than 10, phosphorus tends to be  limiting,  and for ratios below 5,  nitrogen
 tends to be limiting (Chiaudani, et_ al^, 1974).  In most lakes, phosphorus 1s the
 limiting nutrient.  In many nitrogen-limited lakes, phosphorus  1s  still  controlling
 because of the process of nitrogen fixation.  Thus, the focus In this manual  is on
 phosphorus.

                                         -50-

-------
      In  addition  to  nitrogen  and  phosphorus,  any  necessary  nutrient  or physical
 condition may limit  plant  growth.  For  example,  1n  high  nutrient  (eutrophic)  waters,
 algal  biomass may increase until  light  cannot  penetrate,  and  light  Is  then  limiting.
 At  such  a point,  a dynamic equilibrium  exists  in  which algal  cells are consumed,
 settle or lyse (break) at  the  same  rate as new cells  are  produced.   In other  cases,
 light  may be limiting due  to  non-algal  partlculate  material.
      To  summarize, the process of eutrophlcation  (or  fertilization)  is enrichment  of
 a  lake with  nutrients, particularly nitrogen and  phosphorus.  However,  the problems of
 eutrophication are caused  by  increased  plant biomass  as a result of  enrichment.
 Therefore, the objective 1s to predict  plant biomass  as related to nutrient concen-
 trations. The method for  predicting plant biomass  is based on the rate of phosphorus
 supply (loading), the concentration of  phosphorus 1n  the  lake, and the amount of
 plant  biomass that is predicted based on the phosphorus concentration.  The plant
 biomass  is exemplified by  the  phytoplankton (algae) concentration but  macrophytes
 (aquatic weeds) are  also of concern.  The plant biomass and related  variables define
 the scalar relationships of eutrophlcation.

 5.4.3  Predicting Algal  Concentrations
     Predicting algal blooms or predominance of macrophytes  using a mechanistic
 approach  can  be a very complex problem,  and most methods  are not  suited to a simple
 hand calculation technique.  However,  relationships  regarding algal  productivity
 have been derived that permit  an evaluation of the eutrophic state of an impoundment.
 Because  the methods permit  algal biomass to be estimated  with relatively little.
 easily obtained data, and because algae  are very important in  assessing impoundment
 water quality, these techniques are  useful  here.  The methods  presented below are
 based upon the fact that  in most cases  (perhaps 60 percent)  phosphorus  is  the biomass
 limiting   nutrient  (EPA,  1975).  One  such approach  has  been developed  by Vollenweider
 (Vollenweider,  1976;   Vollenweider and Kerekes. 1981;  Lorenzen,  1976).   It may be
 used to  predict the degree  of  impoundment eutrophication  as  a  function  of  phosphorus
 loading.

 5.4.3.1   Nutrient  Limitation

     Before considering  application  of any  of  the methods  to assess  eutrophlcation,
 it  is important to examine  the nitrogen  to  phosphorus  ratio.  This  Indicates  whether
 any of the methods presented below is  likely to give realistic results.  Gener-
 ally, an   average algal cell has an elemental composition  for the  macronutrients  of
 ^106 N16   ^1*   H^tn ^ atoms of nitrogen  for each  atom  of  phosphorus,  the average
composition by weight 1s  6.3 percent nitrogen  and  0.87 percent phosphorus  or  an N/P
 ratio of   7.2/1.  Although all  nutrient requirements  must  be  met,  the  relative  rate
of  supply is  significant  and must  be determined to know which  is  limiting.   For N/P
                                         -51-

-------
ratios greater than 7.2, phosphorus would be less available for growth ("limiting")
and when less than 7.2, nitrogen would be limiting.  In paractice, values of less
than 5 are considered nitrogen Uniting, greater than 10 are phosphorus limiting, and
between 5 and 10. both are limiting.
     In many cases of eutrophlc lakes, nitrogen 1s not limiting because of the
process of nitrogen fixation.  Some blue-green algae, a particularly noxious type of
algae, have enzymatic processes for the biochemical conversion of dissolved elemental
nitrogen into reduced nitrogen (amlne groups) suitable for growth and metabolism.
Special cells called heterocysts perform this process and only appear when nitrogen
is limiting. It can be argued that In general nitrogen is not limiting (Schindler,
1977) and a "worst case" analysis can be made for a screening approach using phos-
phorus.  This is the basis for the eutrophlcation screening method.  However, it
should be remembered that the chlorophyll produced Is affected by the N/P ratio as
are the algal species (Smith, 1979).

5.4.3.2  Nutrient Avail ability
     Availability of nutrients is also important.  Partlculate nitrogen and phosphorus
in the inflowing tributaries generally settle and can therefore be considered unavail-
able.  Few estimates of bioavailable nutrients have been made.  The estimates have
been made primarily for phosphorus using algal assay techniques.  Cowen and Lee
(1976) indicated that 30 percent or less of urban runoff phosphorus was available to
algae whil* Dorich et_ aj_. (1980) found a value of 20 to 30 percent for sediment bound
phosphorus (as would occur in rural runoff).  It appears that a fraction of 0.3 would
provide a conservative estimate of bioavailable phosphorus in the absence of actual
measurements.

5.4.4  Mass Balance of Phosphorus
     A material  entering a lake or impoundment will partition between the aqueous and
solid phases.  The solid phase can settle and become bottom sediment or outflow can
remove suspended and aqueous phase material.  A diagrams tic presentation of the
concept of Inflow, partitioning and settling, and outflow is shown in Figure V-23.
The concentration of the material  can be calculated very simply after making several
assumptions:  the lake is completely mixed, the lake is at steady state and inflowing
water equals outflow, and the annual average rates are constant.  Although these
assumptions are not met entirely for phosphorus, they are satisfied well  enough to
meet requirements for a screening analysis of eutrophlcation.  Based on Its histor-
ical development the eutrophication screening method is termed the "Vollenweider
Relationship".
     As shown 1n Figure V-23, any of three different forms of the steady  state
equation can be used to predict phosphorus concentrations 1n lakes. Each  form may be
                                          -52-

-------
                                              A • AREA
     QI  -  INFLOW
     XI « CONCENTRATION
         OF POLLUTANT
                               WATER
                      V
                          / / / / j / / / / v / /
                                    OUTFLOW » Q
                                         SEDIMENTS
                                               V - VOLUME

                              X « CONCENTRATION IN LAKE


  For Example - Phosphorus,  P • X


  LOADING

          Lp  " QI •  PI  / A,  mg/ral year


  MASS BALANCE

      Assumptions: completely mixed, steady state. Q a QI, annual average
                   rates are  constant

      Definitions: Mean depth, Z   • V/A;  hydraulic flushing or dilution
                   rate, D • Q/Y; hydraulic loading, q  » Q/A;   M  •
                   QI • PI; K « net rate  of solid phase removal  and
                   release (proportional  to P),  typically negative when
                   averaged over the annual  cycle.
            - KP •  0




                (Mass Balance Form)   U)


                (Mass Inflow Form)     (2)


                (Loading Form)        (3)
      Solving  for P,

           „ _  D • PI
             •HhlTT
          P •
               zi
D * K)
FIGURE V-23    FORMULATIONS FOR  EVALUATING MANAGEMENT OPTIONS
                FOR  POLLUTANTS IN  LAKES  AND RESERVOIRS
                                 -53-

-------
more or  less suitable for a specific data set.  The Important variables are the
hydraulic flushing or dilution rate (Q/V, Inverse of residence time), lake volume to
area ratio  (V/A, equals mean depth), phosphorus 1n the Influent (PI), and the net
rate of  removal (K).
     The variables Q, V, A must be determined from other data.  The influent phosphorus
can be based on measurements or estimated from calculations performed as in Chapter 3
and including any municipal  and industrial effluents.  Generally, effluents are
considered totally available for growth.  Nonpoint sources should be assessed as 100
percent available and as 30 percent available to provide limits for screening purposes.
     Estimation of the net rate of removal (K) 1s not as clear.  Vollenweider (1976)
and Larsen and Hercier (1976) Independently estimated the net rate of removal  as
a function of dilution rate:

        K «  Vb~~~
This is the most accepted approach for screening.  Jones & Bachmann (1976) estimated
that K - 0.65 by least squares fitting of data for 143 lakes.
     Equivalently, Vollenweider and Kerekes (1981) provide a derivation of the mass
balance equation (Equation 1, Figure V-23) in terms of phosphorus residence time and
based on regression analysis:
        P - 	l-	 (PI) -     P1
                            1 + "/D
Regression of predicted phosphorus and actual phosphorus for 87 lakes showed a
reasonable correlation (r • 0.93) but indicated that there was a predicted slight
underestimate at low concentrations (<8 ^g/1 ) and a slight overestimate at higher
concentrations (<20ng/l) (Vollenweider and Kerekes, 1981).
     Also the value of K can be estimated from the ratio (R) of the measured mass
phosphorus retained (in minus out) and the mass inflow:
        R m QI-PI - Q-P ..  PI-P
              QI • PI   *   PI
            P-7
     To assess the placement of a specific lake relative to  a set  of  lakes,  phosphorus
loading (Lp) is graphed as a function of hydraulic loading (q )  (Figure V-24).
The data for 49 measurements of U.S. lakes are shown.   (Some lakes occur more than
once because of multi-year studies.)
     Hore recently, Vollenweider and Kerekes (1981)  have presented the OECD  Eutrophl-
cation Program results showing that lakes can be  classified  Into discrete groups
according to their eutrophication characteristics (Table V-9).  However, as  they
note, there is overlap between the different categories  showing  that  these charac-
teristics are not complete descriptors of trophic state  but  are  relative Indicators.
                                         -54-

-------
10
"^
>*
^
E
X
Q.
Z 1
O
z
o
PHOSPHORUS L0>
o
OOl
o
; 	 1 i i -i i i ii| i i 1 i i i ii| 	 1 	 1 — r— r-r-TTTj r i i i i i i
1 "• *» l« 121 X
; EUTROPHIC • * /EXCESSIVE
." 1 .« / '
* • »50 / 'PERMISSIBLE
•« **« ' /
-«T 22 •* 30 «» ' X
n • •* • • / x
r • .j **• «, « / /
: „- "»$•»•'','
: • , v ••$''&/
•^— -<^ ^.X INVESTIC»TO*-l*OlCATrD
	 — '" ^-^ TROPHIC STATC •
j3.493 2J-i -*•-" •-EOTRO^MIC
o ?SA^O.^ A -*«t SOT^O^HIC
	 O~*"" O?4-l O -OLICOTWOPMIC
2*-*
: o«z
0«
'*C02I
g 4i OLIGOTROPHIC
1 1 1 1 1 1 III 1 1 t 1 1 1 1 ll 1 t 1 1 1 1 1 it 1 1 1 1 1 1 1
I 1 10 100 10


-
-

oc
         MEAN DEPTH 2/HYDRAULIC RESIDENCE TIME. Tw
                          ( m/yr )


FIGURE V-24   US OECD DATA APPLIED TO  VOLLENWEIDER (1976)
              PHOSPHORUS  LOADING AND MEAN  DEPTH/HYDRAULIC
              RESIDENCE TIME RELATIONSHIP  (TAKEN  FROM RAST
              AND LEE, 1973)
                          -55-

-------
                                      TABLE V-9

      PRELIMINARY CLASSIFICATION OF TROPHIC STATE BASED OH INVESTIGATOR OPINION
                     (ADAPTED FROM VOLLENUEIDER AND KEREKES. 1981)


        Variable*	OHqotropMc	Hesotrophlc     EutrooMc

     Total Phosphorus
          wan                    8                  27              84
          range (n)              3-18(21)          11-96(19)       16-390(71)

     Total Nitrogen
          •can                    660                750             1900
          range (n)            310-1600(11)       360-1400(8)     390-6100(37)

     Chlorophyll a
          •can   ~               1.7                4.7              14
          range (n)            0.3-4.5(22)           3-11(16)      2.7-78(70)

     Peak Chlorophyll a
          •can       ~          4.2                 16             43
          range (n)            1.3-11(16)           5-50(12)       10-280(46)

     Secchl  Depth, •
          •can                   9.9                4.2             2.4
          range (n)            5.4-28(13)         1.5-8.1(20)     0.8-7.0(70)
       *g/l(or ng/m )  except  Secchl  depth;  Means  are  geometric  annual  »eans
       {Iog10),  except peak chlorophyll  i.
                            ••  EXAMPLE  V-10
                             Big Reservoir  and

                       The Vollenweider  Relationship


     To use the Vollenweider relationship  for phosphorus  loading, data on long-

term phosphorus loading rates  must  be  available.   It  is also  important that the

rates represent average loading  conditions  over time  because  transient phosphorus

loading pulses will  give  misleading  results.  Big  Reservoir is a squarish reservoir

and has the following  characteristics:


                              Big  Reservoir

                  Available  Data (all  values are means):

        Length                                         2.0 mi  • 3.22 k«

        Width                                            5. ml  « .805 km

        Depth (Z)                                       200 ft  - 20 m

        Inflow (Q)                                       50 cfs - 1.42 cms


                                      -56-

-------
         Total  phosphorus concentration 1n water column            0.482 ppm
         Total  nitrogen concentration in water column                2.2 ppm
         Total  phosphorus concentration In the inflow                1.0 ppm
      In order to apply the plot In Figure V-24, the first  step  is  to make  as
 certain as possible that algal  growth is phosphorus limited.   In  this  case,
 the weight to weight N:P ratio  is 2.2/.4S « 4.6.  Presumably, algal  growth
 in Big Reservoir is not phosphorus limited, and the Vollenweider  relationship  for
 phosphorus is not a good one to use.  In this case a  rigorous model  should be
 used.  If nitrogen fixation is  observed to occur (heterocystous blue-green algae),
 an estimate of the potential problem can be obtained  by  assuming  phosphorus to  be
 limiting:
      V   - length • depth • width
          »  322Chi • 805m • 20m  • 51.8 million m3
             1.42 m3       86400 sec    365 day   0.865
                         '            '
 Plotting Lp and q   on  Figure  V-24 shows  that  the  reservoir could  be extremely
            Q/A - 7rw » 20/1.16 - 17.2 m/yr
           >
eutrophic.

	 END OF EXAMPLE V-10
	   EXAMPLE  V-ll  	
                            Bigger Reservoir  and
                        The  Vollenweider Relationship
      The  physical  characteristics of Bigger  Reservoir are:

                              Bigger Reservoir
                   Available  Data  (all values are means):
      Length                                            20 mi « 32.2 km
     Width                                             10 mi  « 16.1 km
      Depth  (D                                        200 ft  • 61 m
      Inflow  (Q)                                       500 cfs
      Total phosphorus concentration in  inflow                   0.8 ppm
      Total nitrogen concentration In inflow                    10.6 ppm
      As in the preceding example, first determine whether phosphorus is likely to
 be  growth limiting.  Since data are available only for influent water, and since
                                       -57-
             sec 51. 8         da>           *'      yr                                 I
      T   »  1.16 years                                                               |
      K   • VB . 0.93/yr                                                            j
      p   ' Trrr " °-482 m*/]                                                      \
      Lp  •  Q • PI/A «  17.3 g/m2 yr                                                  j

-------
I    no  additional data are available on  Impoundment water quality, N:P for Influent
j    water will be used.
j           N:P « 10.6/0.8 » 13.25
j        Thus algal growth 1n Bigger Reservoir 1s probably phosphorus United.
•   Compute the approximate surface area, volume  and the hydraulic residence  time.
j           Volume (V) * 20 n1  x 10 ml  x 200 ft x 52&02-
j                        1.12 x 1012ft3 • 3.16 x 1010«3
j           Hydraulic residence time (TW) • V/Q «
;              1.12 x 1012ft3/500 ft^ec"1 » 2.24 x 109sec • 71 yr
           Surface area (A) • 20 mi x 10 ml x 52802 •
j              5.57 x 109ft2 • 5.18 x 108m2
j           Next, compute q$

i              <' • T/T-
              q  • 61 m/71 yr « 0.86 m yr
!           Compute annual Inflow, Q
              Q• Q x 3.15 x 107 sec yr"1
'              Qy - 1.58 x 1010ft3yr"1
!   Phosphorus concentration In the Inflow 1s 0.8 ppm or 0.8 mg/1.   Loading  (Lp)
I   in grams per square meter per year 1s computed from the phosphorus  concentration,
1   1n mg/1:

j                 ft3     lOOOmg      *      5.18xl08m2    '          yr
                       -2  -1
I           Lp • 0.70 gm  yr
|   Now,  referring  to  the  plot  In Figure V-24,  we  would  expect  that  Bigger Reservoir
j   is eutrophlc, possibly with severe summer algal  blooms.
                             -  END  Of  EXAMPLE  V-ll
                                •-EXAMPLE V-12
                          The  Vollenweldcr  Relationship
                        Using  Monthly Inflow Quality  Data

        Is Frog Lake  eutrophlc?   Frog Lake's physical  characteristics are as shown
   below:
                                         -58-

-------
1
i
i
•
i
i
i
i
i
•
i
i


i
i
i
i
i
i

,
i
!
i







q

Month
October
November
December
January
February
March
April
May
June
July
August
September


Frog Lake
Available Data:
Mean length 2 mi
Mean width 1/2 mi
Mean depth 25 ft
Available Inflow Hater Quality Data:

(monthly mean, cfs) Total P (mg/1) Inorganic N (mg/1)

1972 1974 1972 1974 1972 1974
50 65 0.1 0.08 7.2 6.0
80 90 0.02 0.02 6.3 2.4
40 40 0.03 0.04 3.1 1.5
_ _ - — _ -
- -
60 58 0.01 0.02 2.0 1.9
80 BO 0.01 0.01 2.3 0.50
75 76 0.04 0.05 0.55 0.52
40 70 0.03 0.08 1.20 1.35
25 - 0.11 - 2.01
38 20 0.09 0.04 3.50 1.29
38 25 0.06 0.05 2.80 1.00


j First, estimate the mean annual flow and the hydraulic residence time. To compute
i
i
i
i
i
i
i
j
i

i
i

.
i
mean annual flow,
y
Q • ( L
1-1
where
Qi.j "
y
n.
Q
Now estimate the
V » 2
1.
A * 2


n.
1 y
r QJ i\/ z n.
j»l i*l

the individual flow measurements
the number of years of data
the number of observations per year
1050/19 - 55.3 cfs • 1.75 x 109ft3/yr
volume, surface area, hydraulic residence time, and q$
ml n 1/2 mi x 25 ft x (^280 ft) - 5 07 x in^ft3 -
mi
98 x 107m3 2
mi it 1/2 mi x (5280 ft) , £ 79 x io7ft2 - 2 59 x lO^m2

1
i
i
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i
i
*
i
i
*
i
i
•
i
i
i
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i
i
*
i
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i
i
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4
1
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*
'

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-59-

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I           T   .  V/Q « 6.97 x 108ft3/55.3 cfs « 1.26 x 107 sec - 0.4 yr               ,
j           «s  '  I/Tw                                                                 I
j           q   .  25 ft. °'3048 "V0.4 yr « 19.05 m/yr                                  j
!            s              ft
J   Next, calculate the weighted mean Inflow phosphorus and nitrogen concentrations     [
I  7 and TT as follows:                                                                  I
I                                                                                       j
i                        y    ni                 y    ni                                  i
!           7 (or if) - ( z    z  tL , x c, J/(r    r  Q<  J
|                       i-l  j-l  1§J     >J   1-1  J-l   'J                            |
j           7 » 43.86/1050 • 0.042 mg/1                                                  j
j           TJ - 2671.902/1050 • 2.54 mg/1                                                j
   The N:P ratio in the inflows is 60.  Therefore if one of the two is growth limiting,-
   it is probably phosphorus.  Compute the phosphorus loading, Lp.
                           1 g  x 0.042 mg K      1     x  1.75xl09ft3                  j
                         lOOOmg      /       2.59xl06mZ        yr                      I
(           Lp » 0.80 g/m2 yr                                                           !
|   Now, referring to the plot in Figure V-24 with Lp « 0.80 g/m  yr and q$ • 19 m/yr,  |
I   the impoundment is well into the mesotrophic region.                                I
i                                                                                       i
!	END OF EXAMPLE V-12	:
5.4.5  Predicting Algal  Productivity, Secchi Depth, and Biomass
     The prediction of eutrophication effects is based primarily on prediction of
chlorophyll a_ concentrations from phosphorus concentrations rather than on general
impoundment trophic status.  The method r>as been advanced by several  researchers
including Sakamoto (1966), Lund (1971), Dillon (1974), and Dillon and Rigler (1975).
Originally, the method related mean summer chlorophyll a_ concentrations to spring
mean total phosphorus.  As shown in Figure V-25, the relationship is highly correlated,
and a regression of the log of summer mean chlorophyll a_ on the log of spring mean
phosphorus is linear (units are i^g/1).  Using a least squares method gives the equation
of the line as (Lorenzen, 1978):
        log (chl £) - 1.5 log (P)-l.l
or
        chl a_ • O.O^P)1'5 for P<250 mg/m3 - 0.25 ppm
     More recently (Vollenweider and Kerekes, 1981), additional data have been
compiled and equations have been derived for predicting annual average chlorophyll j»
from annual average total phosphorus (r « 0.88, n»78):

                               chl a - 0.27(P)°'99                           (V-15)

                                         -60-

-------
                        1000
                       m
                       2
                       x
                       (9
                         100-
                       a.
                       g "OH
                       o
                       
-------
                    • •*  *SD
 where
         I     »   Initial  light  Intensity,  light units
         o
         I_D  •   Intensity  at Secchl  depth,  light  units
         SD    *   Secchl depth,  m
         k     •   extinction coefficient, 1/m.

     Algal  blooms reduce transparency.  Algal  blooms are measured using the average
 summertime  (July-August) chlorophyll ^ concentration (CA. ng/1) 1n the mixed layer
 epilimnion) since non-plant materials do not contain chlorophyll.  Lorenzen (1973,
 1980) showed that the extinction coefficient (k) could be considered 1n two parts;
 that is, light attenuation would be the result of absorption and scattering by algal
 cells and by the water and non-algal materials in the water column:
        k « a + b • CA
 Hutchinson  (1957) and others have shown that the Secchl depth occurs over a relatively
 narrow range of light intensity ratios (I/I ).  If 1t 1s assumed that this ratio
 is a constant (ln(I/I ) » R), we can substitute (A - a/R; B • b/R). and solve for
 Secchi depth as a function of chlorophyll aj
        1/SD - A + B * CA
     In the equation, A represents non-algal attenuation while B*CA represents
 attenuation by chlorophyll  a_.  Larsen and Kalueg (1981) used data from several lakes
 to compute  this relationship.  Similarly, data from 226 lakes were used to obtain the
 foil owing- equation:
        1/SD « 0.02 CA * 0.6
 However, B  is considered a constant (B • 0.02, Megard et_ i]_., 1980), while A will vary
 with the background light attenuation in the water due to dissolved and particulate
 matter (Lorenzen, 1980).   It should be noted that as the particulate matter increases,
 the relationship will be less likely to hold.
     Figure V-26 shows a plot of maximal  primary production In terms of milligrams
 carbon incorporated in algae per square meter per day as a function of phosphate
phosphorus levels.   As was  the  case with  predicting chlorophyll  ^ concentrations, the
relationship appears to be  reasonably robust and therefore useful.
     Because dried  algae contain  very roughly 3 percent chlorophyll £ (J.A.  Elder,
pers.   comm., 1977), dry algal  biomass may be estimated from chlorophyll ^ concentra-
tion by multiplying by thirty-three.  Similarly, carbon productivity, as  In  the plot
in Figure V-26,  may be converted  to total  algal biomass.   Since  approximate  analysis
of dried algae has  been determined as (Stumm and Morgan,  1970):

        C106H263°110N16P1
                                          -62-

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     2500-
   o
  •o
  tvi
  0 2000-
  c
  o
     1500-
o
h_
0.
>>
^
§
V_
CL
     1000-
     500-
                             0.05                  0.10
                                   P04S (os P, mg/l)
                                                                     0.15
   FIGURE  V-26   MAXIMAL PRIMARY PRODUCTIVITY AS  A FUNCTION  OF PHOSPHATE
                  CONCENTRATION (AFTER CHIAUDANI,  EI AL,, 1974)
the gravimetric  factor 1s -ywyr^.S.   Thus, maximal carbon productivity  may
be multiplied  by 2.8 to give a rough  estimate of maximal algal  biomass  productivity.
     The user  should bear in mind that  applying this technique  can  only  lead to rough
estimates.   If it is desired to predict biomass or productivity with  accuracy, more
sophisticated  approaches may be necessary.
  	  EXAMPLE V-13
j                      Phosphorus and Summer Chlorophyll  a
i
j   Lake  Sara mean annual  total  phosphorus concentration,  P  -  .03 mg/l - 30 mg/m"
                                     0.99
                       chl  a. -  0.27(PT
                       chl  £ »  7.8 mg/m'
          algal dry biomass  »  7.8 x 33 - 258 mg/m
                                               3
   Peak chlorophyll  a^ would  be  22 mg/rrr.  If calculated  from  loading rates, the
                                        -63-

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   numbers would differ.  Secchi depth would be approximately  1.3 meters  assuming
   that the average background light extinction was 0.6.
                               END OF EXAMPLE V-13
     In the absence of measured data, the in-lake concentration (P) can be computed
based on the various point and nonpoint loadings (n):
Then chlorophyll j> can be estimated as shown in the previous paragraphs.

5.4.6  Restoration Measures
     Control of eutrophication in lakes can be evaluated by a variety of approaches
(Table V-10).  Some methods are directed at external sources (PI) and others at
recycling from in-lake sources (K).  Changes in volume (V) and inflow (Q) obviously
will affect predicted results.  For example, on a long term basis dredging will
decrease the return of phosphorus for the sediments (i.e. increase K) and increase
the volume land therefore decrease the dilution rate, 0).  If the input concentration
(PI) is the critical  variable, then source controls should be investigated.  If
internal sources are involved, then in-lake controls should be evaluated.  In many
lakes, both source and in-lake controls will be needed.
     Problem treatment is directed at the productivity directly.  These controls are
often the only alternative for many lake situations.  These methods are evaluated
only in a qualitative way.  Indexes for evaluating lake restoration have been devel-
oped (Carlson, 1977; Poreel la et^al_., 1980).  These are useful  for prioritizing lake
restoration projects and for evaluating progress.

5.4.7  Mater Column Phosphorus Concentrations
     The relationships described in 5.4.5 for predicting algal  biomass are predicated
on phosphorus levels within the impoundment.  A more precise mechanism for estimating
phosphorus lake concentrations based on Interactions between bottom sediments and
overlying water has been developed.
     lorenzen, et^ al_. (1976) developed a phosphorus budget model (Figure V-27)  which
may be used to estimate water column and sediment bound phosphorus in a fully mixed
system.  A mass balance on both sediment and water column phosphorus concentrations
                                         -64-

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                                  TABLE V-10

               CLASSIFICATION OF  LAKE RESTORATION TECHNIQUES
 I.   Source Controls
     A.   Treatment of  inflows
     B.   Diversion of  inflows
     C.   Watershed management (land uses, practices, nonpoint source
          control, regulations and/or treatments).
     0.   Lake riparian regulation or modification
     E.   Product modification or regulation

II.  In-Lake Controls
     A.   Dredging
     B.   Volume changes other than by dredging or compaction of
          sediments
     C.   Nutrient inactivation
     D.   Dilution/Flushing
     E.   Flow adjustment
     F.   Sediment exposure and dessication
     G.   Lake bottom sealing
     H.   In-lake sediment leaching
     I.   Shoreline modification
     J.   Riparian treatment of lake water
     K.   Selective discharge

III.  Problem Treatment (directed at  biological  consequences of lake
          condition)
     A.   Physical  techniques (harvesting,  water level  fluctutations,
          habitat manipulations)
     B.   Chemical  (algicides,  herbicides,  pesticides)
     C.   Biological  (predator-prey  manipulations,  pathological
          reactions).
     D.   Mixing  (aeration,  mechanical  pumps,  lake  bottom modification)
     E.   Aeration  (add  DO;   e.g.  hypolimnetic  aeration)
                                  -65-

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      Water Column
               Sediment
                                                                          :(*)Q(o)
          FIGURE V-27  CONCEPTUALIZATION OF  PHOSPHORUS BUDGET
                         MODELING  (LORENZEN ET AL,,  1976)
yields the coupled  differential equations:
                       dt
                                                                        (V-17)
                                                                        (V-18)
                      ~ar
        M
        V

        vs
        A
        Q
•  average  annual total phosphorus concentration 1n water column (g/m )
*  total  exchangeable phosphorus concentration  1n the sediments (g/m )
•  total  annual phosphorus loading (g/yr)
•  lake  volume  (m )
•  sediment  volume  (m )
•  lake  surface area (m ) - sediment area  (•  )
•  annual outflow (m /yr)
•  specific  rate of phosphorus transfer to the  sediments (n/yr)
•  specific  rate of phosphorus transfer from  the sediments (m/yr)
*  fraction  of total phosphorus Input to sediment that 1s unavailable
   for the exchange process
                                        -66-

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     When the differential equations relating water column phosphorus to the
various controlling phenomena are solved analytically, the following
equation results for steady-state water column phosphorus concentration:
or
                                                                           (V-20)
where
        C    •  steady-state water column phosphorus  concentration  1n  ppm
        C.   •  steady-state Influent phosphorus concentration  In ppm
     The steady-state sediment phosphorus concentration 1s  then given  by:
                               S   K2(l

     It 1s Important to observe that these relationships  are  valid  only  for  steady-
state conditions.  Where phosphorus loading 1s changing with  time,  where sediment
deposition or physical  characteristics are changing,  or where there are  long-term
changes 1n physical conditions, the steady-state  solutions  are not  applicable.
     Lorenzen applied the model to Lake Washington  data and obtained very good
results.  With their data set,  the most satisfactory  coefficients had the following
values:
        K:  -  43 m/yr
        K2  •  0.0014 »/yr
        *3  "  °-5
It should be recognized, however,  that this model  1s  relatively  untested and that
coefficient values for other impoundments will vary from  those cited here.

| -------------------  EXAMPLE V-14 ------------------------ 1
I
                             A Comprehensive  Example
                       Impoundment Water Column  Phosphorus

        What will  be the steady-state concentration  of  phosphorus  1n the water
   column of Lake  Jones following  diversion of flow? How will  this affect  algal
   abundance?

                                          -67-


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        Lake Jones:                                                                 i
               Area, A.                 20 miles2 • 5.6 x 10Bft2 -5.2 x 107m2       |
               Volume, V.            3.08 x 10Uft3 • 8.73 x 10V                  j
                     Available Data (prior to diversion):                           |
        Inflows:                                                                    j
                                         Mean Annual                                 j
                                          Flow, cfs          Mean  P,  mg/1
             1.   Janes River                75                  .15                 !
             2.   Jennies River              22                  .07                 |
             3.   Johns Creek                 5                  .21                 I
             4.   Direct stormwater Influx (nominal,  may be disregarded)             |
     The diversion, which is for Irrigation purposes, has decreased the mean        j
annual  inflow from Jennies River to 1 cfs with an average annual phosphorus         j
concentration of 0.01 mg/1.  Additionally, there 1s a reduction of flow in Janes
River to 55 cfs. but the mean P concentration stays the same.
     To apply the Vollenwelder relationship, first to the prediversion status of    ;
Lake Jones, compute q :                                                             I
       2  .  6.73xlQ9m3 n
            S.2xloV
     Based upon the conceptualization (see Figure V-27),  it 1s reasonable that the
coefficients interact.  For example, Kj, the rate of phosphorus uptake by the
sediment must be related to the rate of phosphorus release by the sediment.  The
model requires however, that the product K^K-j be constant.  The value used by
Lorenzen, et_ al_.  was 21.6.  As they point out,  the coefficients must satisfy
certain conditions, specifically those established by the derived equations.   The
equations are:

                                 C   '   	                            (V-22)
                                  w
and
                                 7- "                                     (V-23)
                                  s    K-K
From (V-22)
                                          M-QCW
                                                                          (V-24)
                                                                                    I
                                      -68-

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   Computation of K., therefore, requires a value for K-.   This  coefficient,
   (K3) unfortunately, 1s usually unavailable.   It  represents the  fraction of
   phosphorus entering the sediment which 1s  not  returned to the water column.
   Processes contributing to this phenomenon  are  burial caused by  steady-state
   sediment accumulation, and steady-state chemical  precipitation  of phosphorus,
   such as with iron to form Fe3(P04)« 8H20 (vivianlte).  Lorenzen's value for
   Lake Washington was SO percent.  Because the fraction is likely to vary signifi-
   cantly from system to system and because the coefficient is difficult to evaluate.
   the planner is advised to use 30 percent as the  lower limit,  50 percent as a
   probable value, and 70 percent as an  upper limit  for estimating sediment
   phosphorus content.  The water column  concentration is independent of changes in
   K» because the product of K,  and IU is a constant.
        Using Equation (V-24),  K7 uniquely defines  K, .  Then, from Equation
   (V-23):
      is therefore also  defined by fixing K,, providing C  and C  are known
                             , 2B.3U       11  g    , 3.16xl07sec                     j
                                ft        1000 mg  *     y7I

          M • 1.24x10^ gP/yr                                                         J

j          Q .  (75+22-5)ft3    3.16xlQ7sec . 3.22x10^   9.13xlQ7m3                 1
j                   sec            yr              yr             yr                  j

I          TW • B^SxloV/g.lSxloVyr-1 - 95.6 yr                                  I
j                                                                                      j
i          qs "  168/95.6 » 1.76 m yr'1                                               j
j                                                                                      i
|   Compute phosphorus  loading:                                                         I
I                                                                                      I
!          Lp" "5"                                                                    j
;          . , . 1.24xl07 q yr"1   ...   -2  -1
          Lp « 	—*-i	 0.24 gm V                                          I
                5.2xl07m2
                                         .69-

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 I   Referring to  Figure V-24 with  q$  •  1.76 and  Lp • 0.24.  one can  see  that  this
 |   lake  may  have eutrophlcatlon problems  under  pre-dlverslon  conditions.
 j   After the diversion,
                8.73 x  lo
           T  . - --. - «  125 yr
 I           *   6.98 x  lOV/yr
    Assuming  the  lake  depth  Is  not materially  changed over the short term,               j
           q$  -  168/125  -  1.34 5L-                                                       !
                                                                                        t
    For  the new conditions,
           H • 8.33 x 106 gP yr"1                                                       j
           Lp  . 8.33  « 106 g yr-1 .       ^2                                           -
                C 7 „ inlL                                                             '
                3.i X 10 m                                                              i
   Now, according to the Vollenwelder plot (Figure V-24), this is in the region         \
   between "dangerous" and "permissible" - the mesotrophic region.  Under the           j
   new circumstances, algal  blooms are less likely than before the flow diversions      I
   were established,  but blooms are by no means to be ruled out.                        |
   Turning now to an estimate of algal biomass under pre-diversion,conditions, we       j
   must calculate the inlake concentration (P).                                         j
           First,     D - I/TW - 1/125 « 0.008;  K - VT - 0.09                        j
   Since our  data are already In the loading form:                                      j
           P.   ft    1
                 0.24        1            ,.    . 3
             »   -    -     -15 mg/m
                 168     0.008*0.09
   Based on annual  average chlorophyll a^,
                          °'79
           chl  a - 0.37(P)
           chl  a_ « 3.1 mg/m
   Under post -divers ion conditions,
                   168     0.008*0.09
                                           10
                   chl a_ « 2.3 mg/m"
   Note that these low levels of chlorophyll ^ almost certainly mean that the
j   lake 1s oligotrophic to mesotrophic, and that the Vollenwelder method suggests
•   worse conditions than may actually exist in this case (Table V-9).
        Consequently, one might choose to use the Lorenzen model  to evaluate K.
I   and K3 and determine whether the impoundment is at steady state with respect
I   to phosphorus levels in the water column and sediment.  Generally, this Is
|   the case where K^ lies in the range of 20 to 40.  If K.K, 1s outside of
                                         -70-

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I   this range, field data should be obtained for current water column phosphorus.

I           Sediment volume, V                 Irrelevant for steady-state solution
I           Phosphorus (water column)          .15 mg/1
i
I
  0.5
  M-Q(
  *JJ
               M-QCW
               0.15 «g/l •  .015 g/»3
.  /1.24xlD7gP _ g.nxicfm3 x ^^3\ /
   \    yr           yr          m  //
                     yr            yr
                            x  5.2  x lo       - 28.3
                        m
              •  44 x 0.5 - 14

j        This result, therefore,  gives reason to suspect  non  steady-state  conditions
I   for water column phosphorus.   If more definitive  answers  are  needed, additional
|   field data should be collected.
i
   	  END OF EXAMPLE  V-14 	

5.5  IMPOUNDMENT DISSOLVED OXYGEN
     Organic substances Introduced into an  impoundment  with  inflowing water,  falling
onto its surface, or generated  in the water column Itself  through photosynthesis, may
be oxidized by indigenous biota.    The process  consumes oxygen which may,  in  turn, be
replenished through surface reaeration, photosynthetic  activity, or dissolved oxygen
in inflowing water.  The dynamic  balance between  DO consumption and replenishment
determines the net DO concentration at any  point  in time and at any location  within
the water column.
     These processes result in  characteristic dissolved oxygen (DO) concentrations in
the water columns of stratified lakes and reservoirs  (Figure V-28).  During strati-
fication, typically during summer months, the DO  is highest on the surface due to
photosynthesis and reaeration.  It decreases through  the thermocHne and then, in the
hypolimnion, the DO decreases to  zero in those  lakes  that  have high organic matter
concentrations.
     During spring, after turnover, when lakes  are not  stratified, the DO  is  essen-
tially uniform.  However, in highly organic lakes  benthic  processes can already begin
to deplete oxygen from lower depths,  as shown 1n  Figure V-28.
                                         -71-

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                                                                April 17. 1973
                           Dissolved  Oxygen, mg/1

          FIGURE V-28  TYPICAL  PATTERNS OF  DISSOLVED OXYGEN  (DO)  IN
                         HYRUM RESERVOIR (DRURY, EI AL,,  1975)
     Essentially,  the  patterns result from processes that  are  restricted due to
incomplete mixing.   The  overall effects of such patterns as  shown  1n Figure V-28, are
to restrict fishery  habitat and create water quality problems  for  downstream users,
especially for deep  water discharge.
     BOD exertion  1s not the only sink for DO.  Some important sources and sinks of
impoundment dissolved  oxygen are listed below:
                    Sources
             Photosynthesis
             Atmospheric  reaeration
             Inflowing water
             Rainwater
           Sinks
Water Column BOD
Benthic BOD
Chemical oxidation
Deoxygenatlon at  surface
Plant and animal  respiration
     Many  of  the  processes listed above have a complex  nature.  For example, the
atmospheric reaeration rate Is dependent In part  upon the near-surface velocity
gradient over depth.  The gradient, 1n turn, 1s Influenced by the magnitude, dlrec-
                                        -72-

-------
tlon, and duration of wind, as well as the depth and geometry of the impoundment.
     Photosynthetic  rates are affected by climatological conditions, types of cells
photosynthesizing, temperature, and a number of biochemical and biological factors.
Exertion of BOD is dependent upon the kind of substrate, temperature, dissolved
oxygen concentration, presence of toxicants, and dosing rate.
     Despite this degree of complexity, a number of excellent models of varying
degrees of sophistication have been developed which include simulation of impoundment
dissolved oxygen.

5.5.1  Simulating Impoundment Dissolved Oxygen
     Because an unstratified impoundment generally may be considered as a slow-moving
stream reach, only stratified impoundments are of interest here.  For estimating DO
in unstratified impoundments, one should refer to the methods described in Chapter 4.
     To understand the phenomena affecting dissolved oxygen in a stratified impound-
ment and to gain an appreciation of both the utility and limitations of the approach
presented later, 1t is useful to briefly examine a typical  dissolved oxygen model.
Figure V-29 shows a geometric representation of a stratified impoundment.  As indi-
cated in the diagram, the model  segments the impoundment into horizontal  layers.
Each horizontal layer is considered fully mixed at any point in time, and the model
advects and diffuses mass vertically into and out of each layer.  The constituents
and interrelationships modeled are shown schematically in Figure V-30.
     The phenomena usually taken into account in an impoundment DO model  include:
       ~i    Vertical advection
        •    Vertical diffusion
        •    Correction for element volume change
        •    Surface replenishment (reaeration)
        •    BOD exertion utilizing oxygen
        •    Oxidation of ammonia
        •    Oxidation of nitrite
        •    Oxidation of detritus
        •    Zoopl ante ton respiration
        •    Algal  growth (photosynthesis) and respiration
        •    DO contribution from inflowing water
        •    DO removal  due to withdrawals.
     Hany of the processes are complex and calculations in  detailed models  involve
simultaneous solution of many cumbersome equations.   Among  the processes  simulated
are zooplankton-phytoplankton interactions,  the  nitrogen cycle,  and advection-
diffuslon.   Thus 1t  is clear that a model  which  is  comprehensive and potentially
capable of  simulating DO in impoundments with good  accuracy is not  appropriate  for
hand calculations.   A large amount of  data (coefficients, concentrations) are  needed
                                         -73-

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                                                          tributary
                                                              inflow,
                             evaporation
                  tributary
                  inflow
                                 Vertical
                                edvection
                        outflow
         FIGURE V-29   GEOMETRIC REPRESENTATION OF A  STRATIFIED
                        IMPOUNDMENT  (FROM HEC,  1974)
to apply  such a model, and  solution is most easily done by computer.  Furthermore,
some of the terms in the model equation of state do not improve prediction under some
circumstances.  This is true,  for example, where there are no withdrawals or in an
oligotrophic impoundment where chlorophyll a_ concentrations are very low.
     Hand calculations must be based upon a greatly simplified model to be practical.
Since some DC-determining phenomena are more important than others, it 1s feasible  to
develop such a model 1f some assumptions are made about the impoundment Itself.

5.5.2  A  Simplified Impoundment Dissolved Oxygen Model
     For  purposes of developing a model for hand calculations, the  following assump-
                                       -74-

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                                 <
 6ENTHIC
 ANIMALS
                                       ORGAUIC
                                       SEOIMEHT
                                      SUSFEMtfD  V.
                                      DETPITLIS  >P-
                                                                            TOTAL
                                                                           INORGANIC
                                                                            CARBON
1
1 M^
|
< 	 '
t f7\ '
'•Ml


M^>
| HARVEST

B .
                  A Aeration
                  B Bocttnal De:ov
                  C Chemical Eerier
                  E Eicrero
                  G Growrn
M f.'ortality
P Pnotosynthetis
R Respiration
S Settling
H Harvest
                  FIGURE V-30   QUALITY AND ECOLOGIC RELATIONSHIPS
                                  (FROM NEC,  1974)

tions are made:
        •    The only condition  where  DO levels may become dangerously  low  is
             in an impoundment hypolimnion and during wanm weather.
        •    Prior to stratification,  the impoundment is mixed.  After  strata
             form, the epllimnion and  hypolimnion are each fully mixed.
        •    Dissolved oxygen  in  the hypolimnion is depleted essentially through  BOD
             exertion.   Significant BOD sources and sinks to the water  column  prior
             to stratification are algal  mortality, BOD settling, and outflows.   A
                                          -75-

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             minor source 1s Influent BOD.  Following formation of strata, sources
             and sinks of BOD are BOD settling out onto the bottom, water column BOD
             at the time of stratification, and benthlc BOD.
        •    Photosynthesis 1s unimportant 1n the hypolimnlon as a source of DO.
        •    Once stratification occurs (a theraocline gradient of 1°C or greater per
             meter of depth) no mixing of thermocllne and hypolimnlon  waters occurs.
        •    BOD loading to the unstratlfled Impoundment and to the hypolimnlon
             are 1n steady-state for the computation period.

5.5.2.1  Estimating a Steady-State BOD Load to the Impoundment
     Equation V-25 1s an expression to describe the rate of change of  BOD concentra-
tion as a function of time:

                          $  •   ".  -  V  •  k>c   '  ^                  (v-25)
where
        C   «  the concentration of BOD in the water column in mgl-1
        ka  «  the mean rate of BOO loading from all sources in mgl-l  day!
        ks  «  the mean rate of BOD settling out onto the impoundment  bottom in
               day"1
        k^  «  the mean rate of decay of water colunm BOD in day1
        0   •  mean export flow rate in liters day -1
        V   •  impoundment volume in liters.
Integrating Equation V-25 gives:

                                 
-------
 5.5.2.2   Rates  of  Carbonaceous  and  Nitrogenous  Demands
      The rate of exertion  of  BOD and  therefore  the  value  of  kj  1s  dependent
 upon  a number of physical,  chemical,  and  biological  factors.  Among these are
 temperature,  numbers  and kinds  of microorganisms, dissolved  oxygen concentration,
 and the  kind  of organic substance Involved.   Nearly  all of the  biochemical oxygen
 demand 1n impoundments 1s  related to  decaying plant  and animal  matter.  All such
 material  consists  essentially of carbohydrates,  fats, and proteins along with a vast
 number of minor constituents.   Some of these  are  rapidly  utilized by bacteria, for
 example,  the  simple sugars, while some, such  as  the  celluloses, are metabolized
 slowly.
      Much of  the decaying matter in impoundments  is  carbonaceous.  Carbohydrates
 (celluloses,  sugars,  starches)  and fats are essentially devoid  of nitrogen.  Proteins,
 on the other  hand, are high in  nitrogen (weight of carbon/ weight of nitrogen  ?• 6)
 and proteins  therefore represent both carbonaceous and nitrogenous demands.
      The  rate of exertion of carbonaceous and nitrogenous demands differ.  Figure
 V-31, which shows  the difference graphically and as  a function  of time and tempera-
 ture, may be  considered to  represent the  system  response to  a slug dose of mixed
 carbonaceous  and nitrogenous demands.  In each two-section curve, especially where
 concentrated  carbonaceous wastes are present, the carbonaceous  demand is exerted
 first, and this represents the  first stage of deoxygenation.  Then nitMfiers increase
 in numbers and  ammonia is oxidized through nitrite and ultimately to nitrate.  This
 later phase is  called the second phase of deoxygenation.
      BOD  decay  (either nitrogenous or carbonaceous alone)  may be represented by first
 order kinetics.  That is,  the rate of oxidation is directly proportional  to the
 amount of material  remaining at time t:

                                      g|  • -kC                                (V-28)

     The  rate constant,  k,  is a function of temperature, bacterial  types  and numbers,
composition and structure  of the substrate,  presence of  nutrients and  toxicants,  and
a number of other factors.   The value of the  first stage constant  kj was  first
determined by Phelps in  1909 for sewage  filter samples.   The value was  0.1  (Camp,
 1968).  More recent data  show that at 20°C,  the value can  range  from 0.01  for slowly
metabolized industrial waste organics to 0.3  for relatively  fresh  sewage  (Camp,
 1968).
     The typical effect  of  temperature on  organic reactions  is to  double  reaction
rates  for each temperature  rise  of 15°C.   The  relationship for correcting  kj  for
temperature is:
                                         -77-

-------
     "0     4    8    12    16   20
      Period of Incubation, Days
      FIGURE  V-31   RATE  OF BOD EXERTION  AT DIFFERENT TEMPERATURES
                     SHOWING THE FIRST AND SECOND DEOXYGENATION
                     STAGES
                                      ki.(20'0 e(T'2n)
(V-29)
where
        I  «  the temperature of  reaction
        6  «  correction  constant • 1.047.
However, Thereault has  used  a value foreof 1.02, while Moore calculated  values
of 1.045 and 1.065 for  two sewages and 1.025 for river water (Camp,  1968).
     Streeter has determined the  rate of the nitrification or second deoxygenation
stage in polluted streams.   At 20°C, kj for nitrification is about 0.03 (Camp,
1968).  Mobre found the value to  be .06 at 20°C and .035 at 10°C  (Camp, 1968).  For
purposes of this analysis, BOO exertion will be characterized as  simple first order
decay using a single rate constant.
     Bentnic demand, which is important in later computations, may vary over a
wide range because in addition to the variability due to the chemical nature of
the benthic matter,  rates of oxidation are limited by upward diffusion rates of
oxidizable substances through pores in the benthos.  Since the nature of  the sediment
is highly variable,  benthic  oxygen demand rates vary more than values for kj 1n the
water column.  In a  study using sludges through which oxygenated  water was passed,
initial  rates of demand ranged from 1.02 g/m2 day (see Table V-I1) for a sludge
depth of 1.42 cm up  to  4.6g  g/m2 day for a sludge depth of 10.2 cm (Camp, 1968).
                                        -78-

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                                         TABLE V-ll
                              OXYGEN DEMAND OF BOTTOM DEPOSITS
                                     (AFTER CAMP, 1968}
Initial Area Osr.snd
Benthic
Depth
(mean) cm
10.2
4.75
2.55
1.42
1.42
Initial
Vol ume of _2
Sol Ids, koirf
3.77
1.38
0.513
0.188
0.188
L (gnf2)
739
426
227
142
134
initial
Demand
om" dav"
4.65
3.09
1.70
1.08
1.02
day"1
k4(20°C)
.0027
.0031
.0032
.0033
.0033
 In  that  study, the values found were for Initial demand since the sludge was not
 replenished.  The rate per centimeter of sludge depth, then, can vary from a low of
 0.46 g/m2 day for 10.2 centimeter depth sludge up to 0.76 g/m2 day for 1.42
 centimeter depth sludge.
     The constant loading rate (ka) used 1n Equation V-25 1s best estimated
 from historical data.  Alternatively, Inflow loading (see Chapter IV) and algal
 productivity estimates (this chapter) may be used.   In the latter case,  a value
 must be adopted for the proportion of algal biomass ultimately exerted as BOD.
 To a first approximation, ka may be estimated using this value and adopting
 some percentage of maximal primary productivity {see Figure V-25).  Thus:
where
                           ka(algae) - SMP x 10-3/D
algal contribution to BOD loading rate
stoichlometric conversion from algal  biomass as carbon  to
BOD « 2.67
proportion of algal  biomass  expressed as an oxygen demand
(unltless)
Primary production 1n m
                                                          (V-30)
        ka(algae)
        S

        M

        P
     The difference between algal  biomass and the parameter  M representing  the
proportion of algal biomass exerted  as  BOD may be conceptualized  as  accounting  for
such phenomena as incorporation of algal  biomass  Into fish tissue which  either  leaves
the Impoundment or Is harvested, loss of  carbon to the atmosphere as  CH4, and loss
                                         -79-

-------
due to outflows.
     The settling rate coefficient, k$ 1n Equation V-25 must be estimated for
the Individual case.  It represents the rate at which dead plant and animal matter
(detritus) settles out of the Mater column prior to oxidation.  Clearly, this co-
efficient Is sensitive to the composition and physical characteristics of suspended
matter and the turbulence of the system.  Quiescence and large particle sizes in the
organic fraction will tend to give high values for ks while turbulence and small
organic fraction particle sizes will give small values for ks.

5.5.2.3  Estimating a Pre-Strat1f1cation Steady-State Dissolved Oxygen Level
     Prior to stratification, the impoundment Is assumed to be fully mixed.  One of
the important factors leading to this condition Is wind stress, which also serves to
reaerate the water.  As a rule, unless an Impoundment acts as a receiving body for
large amounts of nutrients and/or organic loading, dissolved oxygen levels are likely
to be near saturation during this period (O.J. Smith, pers. comm.,  November,  1976).
Table V-12 shows saturation dissolved oxygen levels for fresh and  saline waters  as a
function of temperature and chloride concentrations, and 00 levels  may be estimated
accordingly.
     The hypolimnetic saturation dissolved oxygen concentration Is  determined
by using the average (or median) temperature for the hypo11ranion as determined
during the period of interest throughout the depth of the hypol1mn1on.  Informa-
tion on the hypolimnion is obtained using the procedures described  1n Section
S.2.  For example, hypolimnetic water at the onset of stratification might be
4-5°C and during the critical summer months be 10°C.  The value 10°C should be
used having a saturation DO of 11.3 mg/1.
     Most lakes are near sea level (<2000 ft elevation) and are relatively fresh
(<2000 mg TDS/1).  For lakes that do not meet these criteria, corrections for atmos-
pheric pressure differences and salting out due to salinity might  be needed.   Pressure
effects can be approximated by using a ratio of barometric pressure (B) for the
elevation of interest and sea level  (BSTP) as follows:
e.g.  B at 4600 ft elevation,

        _JL . 6*2 , in m Hg,
        BSTP   760          *
             - 0.84

        DOsat at 10°C « 0.84 x 11.3
                      « 9.5 mg/1.
Chloride is an estimator of dilutions of sea water 1n fresh water where 20000
mg Chloride/1 is equivalent to 35000 mg salt (TOS/1), that 1s, typical  ocean  water.
                                         -80-

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                     TABLE V-12





SOLUBILITY OF OXYGEN IN WATER (STANDARD METHODS,  1971)
Chloride Concentration in Water - mg/1
Temp.
in
°C
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
IB
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
0

14.6
14.2
13.8
13.5
13.1
12.8
12.5
12.2
11.9
11.6
11.3
11.1
10.8
10.6
10.4
10.2
10.0
9.7
9.5
9.4
9.2
9.0
8.8
8.7
8.5
8.4
8.2
8.i
7.9
7.8
7.6
7.5
7.4
7.3
7.2
7.1
5,000

13.8
13.4
13.1
12.7
12.4
12.1
11.8
11.5
11.2
11.0
10.7
10.5
10.3
10.1
9.9
9.7
9.5
9.3
9.1
8.9
B.7
8.6
8.4
8.3
8.1
8.0
7.8
7.7
7.5
7.4
7.3





10,000
Dissolved
13.0
12.6
12.3
12.0
11.7
11.4
11.1
10.9
10.6
10.4
10.1
9.9
9.7
9.5
9.3
9.1
9.0
8.8
8.6
8.5
8.3
8.1
8.0
7.9
7.7
7.6
7.4
7.3
7.1
7.0
6.9





15,000
Oxygen - mg/1
12.1
11.8
11.5
11.2
11.0
10.7
10.5
10.2
10.0
9.8
9.6
9.4
9.2
9.0
8.8
8.6
8.5
8.3
8.2
8.0
7.9
7.7
7.6
7.4
7.3
7.2
7.0
6.9
6.8
6.6
6.5





Sea
Water

11.3
11.0
10.8
10.5
10.3
10.0
9.8
9.6
9.4
9.2
9.0
8.8
8.6
8.5
8.3
8.1
8.0
7.8
7.7
7.6
7.4
7.3
7.1
7.0
6.9
6.7
6.6
6.5
6.4
6.3
6.1





Difference
- per 100 mg
Chloride
0.017
0.016
0.015
0.015
0.014
O.OH
0.014
0.013
0.013
0.012
0.012
0.011
0.011
0.011
0.010
0.010
0.010
0.010
0.009
0.009
0.009
0.009
0.008
0.008
0.008
0.008
0.008
0.008
0.008
0.008
0.008





                       -81-

-------
 5.5.2.4   Estimating  Hypo11mn1on  DO  Levels
      The  final  step  in use of this  model 1s preparation of a DO-versus-time plot  for
 the hypo 11 ran ion  (or  at least estimation of 00 at  Incipient overturn) and estimation
 of BOO and phosphorus loadings which result in acceptable hypo limn ion DO levels.  An
 equation  to compute  00 at any point in time during the period of stratification
 is:

                               — •
                               dt

where
        0   »  dissolved oxygen 1n ppm
        *4  «  benthic decay rate In day'1
        L   «  a real BOO load in gnr2
        0   «  depth in m.
     The  second  term in the equation requires that an estimate be made of the magni-
tude of BOD loading  in benthic deposits.  To do this within the present framework, it
is assumed that  BOO settles out throughout the period of stratification.  Although
many different assumptions have been made concerning benthic BOO decay. 1t was
assumed that benthic demand was a function of BOD settling and the rate of benthic
BOD decay.  This BOD includes that generated In the system by algal  growth and that
which enters in  tributaries and waste discharges.  Based upon the rate of settling
used earlfer in estimating a steady-state BOD concentration (Equation V-25) and rate
of decay  for conditions  prior to stratification,  the rate of benthic matter accumula-
tion is:


                               •T » kSCSsl>-k4l.                              
                               dt

where
        Css  •  concentration of BOD in the water column  in gm-3 at  steady-state.
The assumption of steady-state BOD concentration  reduces  Equation V-32 to the
same form as Equation V-25 and integration gives:

                                               ksDCss                       (Y-33)
    For steady-state deposition  (dL/dt  »  0,  OksCss  »  constant):

                                                                             (V-34)
                                         -82-

-------
 where
         Lss  •  steady-state benthic BOD load in  gnr2.
      Application of Equation V-34 with ks  and k4  appropriately  chosen  for  the
 month or two preceding stratification will  give an  estimate  of  the  benthic  BOD  load
 upon stratification.   Application of Equation V-33  gives the  response  of L  to different
 water column BOD (steady-state)  loading  rates and changes  in  rate coefficients.
      After strata form,  benthic  matter decays while hypolimnion water  column BOD
 decays  and settles.   The change  in L over  the period of stratification  Is:

                                   — - -k4L + DksC                            (V-35)
                                   dt

 Since
                               •- -ksC -kiC • -(k!+ks)C                       (V-36)
 and
                                      - C0 e-(*l * k$)t                       (v-37)
                             — » -k4L + DksC0e-(kl * ks)t                    (V-38)
                             dt
then
     Water column BOD in the hypolimnion is  given by  Equation  V-36 and  the  integrated
form is Equation V-37.
     Note that ks, the settling coefficient  is  equal  to vs/D where vs is  the
settling velocity of the BOD,  and  D is  the depth  of  the hypolimnion (or when the
impoundment is unstratified, D is  the depth  of  the entire  impoundment).  Also  note
that we usually assume that  the DO 1s at saturation  at  the onset  of stratification.
Thus we can ignore the assumptions and  calculations  (Equation  V-32 to V-34) done  for
periods prior to onset.
     The equation presented  earlier (Equation V-31)  for hypolimnion DO  was:
        dt
                                         -83-

-------
Equation V-31 1s not Integrable 1n Its present form, but since L and C are defined as
functions of t (Equations V-39 and V-37 respectively), 1t 1s possible to determine
dissolved oxygen 1n the water column.  The equation for oxygen at time t 1s:

                                 Ot  " 0Q  - AOL  -  AOC                            (V-40)

where
         O^   •  dissolved oxygen at  time  t
         00   •  dissolved oxygen at  time  t • 0
         &OL  •  dissolved oxygen decrease due to  benthlc demand
         ADC  •  dissolved oxygen decrease due to  hypol1mn1on  BOO.
From Equation V-39, and using 155 as  L0  and Css  as Co:
and from Equation V-37:

                                                                                (V-42)
                              c -  £4»  f l-e-<
                              c    kj+fcj  y
Solution of Equation V-40 gives an estimated  00 concentration  1n the hypol1mn1on
as a function of time.
     To compute equation V-40,  a simpler  form of equation  V-41 can be derived by
substituting as follows:
        since Lss »  s* ss  ,
                      "4
To simplify computations,  the  following  stepwlse  solutions can be made:
        A -
                                         -84-

-------
 then
               A
(•-I)
        £0C • E •  F

 5.5.3  Temperature Corrections
      All  reactions are computed  on  the basis  of  the  optimum  temperature,  but  the
 environment 1s often at different temperatures.   Some  rate coefficients  for chemical
 and  biological  reactions  vary with  temperature.   A simple correction  for  such  rate
 coefficients to 20°C 1s as  follows:
         „     „    x ,  047 (T - 20'C)
         l\   * JvT^n     *
 For  example. 1f a  rate at 20°C - 0.01  and  the  lake is  at 10°C, then:
         KT  - 0.01  x 1.047 (1° "  20)
         Hy  - 0.00632.
 Generally the  following optima are  used:
        k.  - first  order  decay rate for water  column BOD,
             use 20eC
        k.  - benthie BOD  decay,  use 20°C
        P   - productivity rate,  use 30QC.
 In the  screening methods  we do not have to correct for temperature except in the
 oxygen  calculation  for  the  rate  coefficients,  K., K4, P and 1n the toxics
 section (5.6)  for the  biodegradatlon rate coefficients.

	 EXAMPLE V-15	
                                   Quiet Lake
                             (Comprehensive Example)

        Quiet Lake is located a few miles south of CoIton, New York.  The lake
   is roughly circular In plan view (Figure V-32) and receives inflows from three
   tributaries.   There 1s one natural  outlet from the lake and one withdrawal  used
   for quarrying purposes.
        The first step in evaluation of lake hypolimnion DO levels is physical
   and water quality data collection.   Table V-13 shows characteristics of Quiet
   Lake,  Table V-14 shows tributary discharge data along with  withdrawal  and outflow
   levels,  and Table V-15 provides  precipitation and runoff information.
        In  order to evaluate hypolimnion DO as a function of time, the very first
   question to be answered is,  does the impoundment stratify?   If  so, what are  the
   beginning and ending dates of the stratified period, how deep  Is the upper  surface
                                         -85-

-------
                                 D
PUMP HOUSE
STftEAM QUALITY
AND FLOW STATION
RUNOFF QUALITY
SAMPLING STATION
SAMPLES TAKEN MOM SMALL
EROSION CHANNELS  NEAft LAKf
FIGURE V-32  OUIET  LAKE  AND  ENVIRONS
                       -86-

-------
                         TABLE V-13
                 CHARACTERISTICS OF QUIET LAKE
  Length (in direction of  flow)
  Width
  Mean Depth
  Maximum Depth
  Water Column P
3.5 miles • 18,480  ft.
4.0 miles « 21,120  ft.
22 ft.
27 ft.
0.014
-------
TABLE V-14  (Continued)
First Creek (Station 5)
Month

October
November
December
January
February
March
April
May
June
July
August
September

Month

October
November
December
January
February
March
April
May
June
July
August
September
Mean Flow, cfs

5
3
2
2
3
4
6
8
10
8
6
4
Second Creek
Mean Flow, cfs

14.0
i:.o
12.5
5.0
1.2
2.0
2.5
4.0
8.0
12.0
8.0
5.5
Total K

1.0
2.0
0.5
1.2
1.3
2.3
2.0
1.8
1.6
1.4
1.5
0.8
{Sution 4)
Total N

15
16
10
9
12
13
8
6
5
7
6
8
Total P
ppn
.01
.01
.02
.01
.02
.01
.01
.02
.01
.01
.00
.00

Total P
ppm
.15
.08
.20
.15
.12
.10
.11
.07
.08
.20
.22
.25
BOO

0.5
1.0
1.5
1.0
0.8
0.6
0.5
0.6
0.8
0.8
1.0
1.2

BOO

7
8
10
7
7
6
7
9
12
3
4
8
          -88-

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                                TABLE V-14  (Continued)
Swift
Month
October
November
December
January
February
March
April
May
June
July
August
September
River (Stations 2 and 3}
Pumped
Withdrawal, cfs
22.6
22.0
3.5
1.2
0.8
0.4
12.0
24.0
30.7
89.5
29.8
43.9
and Pumoed Withdrawal
Mean Monthly
Station ?
69.5
50.0
20.0
7.5
1.2
9.1
44.5
63.2
100.0
168.5
80.6
91.3
Flow, cfs
Station 3
?7.0
55.0
22.0
9.0
1.4
10.1
48.75
69.5
110.0
184.8
88.5
100.25
       Notes:  All three tributaries have  their  headwaters  within the shed.
       Trie net inflow-outflow to the groundwater is  known to be close to
       zero in the two creeks.  Swift River  is usually  about 105  effluent over
       its entire length (105 of flow comes  into  the river  from the
       groundwater table).
|   of the hypolimnion, and what 1s its volume, and what is the distribution of
I   hypolimnion mean temperatures during the period?  To answer these questions.
|   either use field observation data, or apply some computation technique such as
j   that presented earlier in this section.  Assuming that methods presented earlier
j   are used, the selection of appropriate thermal  profile curves hinges around three
   factors.  These are:
           •    Climate and location
j           •    Hydraulic residence time
j           •    Impoundment geometry.
I
                                         -89-

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                                    TABLE V-15
              PRECIPITATION AND RUNOFF DATA FOR QUIET  LAKE  WATERSHED.
              VALUES ARE MEANS OF DATA COLLECTED FROM  BOTH  STATIONS
              (SEE FIGURE V-31).  THE WATERSHED HAS AN AREA OF 55
              SQUARE MILES INCLUDING THAT OF THE LAKE
Mean Total
Monthly Prccipi
tation. inches

October
November
December
January
February
March
April
May
June
July
August
September
Total

3.0
2.4
1.0
0.5
0.3
0.6
2.0
2.8
4.2
7.6
3.5
4.2
32.1
Runoff Quality
Total N

6.0
6.5
4.0
3.0
1.0
1.5
2.5
3.2
3.6
7.0
7.8
9.2
Total P
ppm
0.1
0.2
0.1
0.008
0.07
0.1
0.15
0.25
0.20
0.40
0.60
0.80
BOO

27
37
46
34
33
30
40
50
40
37
45
50
Note:   Infiltration to the water table on a monthly basis accounts for roughly 301   |
       of precipitation volume.                                                      I
     In terms of climate and location, the Quiet Lake area is similar to Burlington,
Vermont.  Examination of the Burlington plots from Appendix D reveals that  a
20-foot maximum depth impoundment can stratify in an area shielded from the wind.
The area surrounding Quiet Lake does provide good shielding,  so the next task  1s
to estimate the hydraulic residence time to select a specific set  of plots.
     Inspection of all  Burlington plots indicates that  stratification is likely to
occur at most from May  to August.  Accordingly,  for purposes  of plot selection, we
are most Interested 1n  a twan hydraulic residence time  based  on flows in the
period from about March to August.  Since hydraulic residence time (T ) 1s
given by-r^ - v/Q, we compute mean Q (Q~).   "§ represents  the
                                       -90-

-------
average of tributary Inflows during this period, computed as follows:
     w   6 + 40 * 55 + 85 + 150 + 70 .  4+6+8+10+8+6  .
     U	5	*	5	
                (Swift River)                (First Creek)
         2+2.5+4+8+12+8
                    6
              (Second Creek)
        • 68 + 7 + 6.08 • 81.1 cfs
However,  1n order to fully account for  mass transport as well  as properly estimate
hydraulic residence time, one more factor should be considered.  This 1s non-point
inflow.  At this point,  we have enough  Information to estimate  the stormwater
contribution directly to Quiet Lake.   In view of the available  data,  the computa-
tion is as follows:
                   -L)-(  :
          Q » APK(1-
            S             \i«l
 where                                                                               I
                                                                                     i
         QS   «   stormwater  or  non-point  inflow  in  cfs  (excluding  rivers  and           I
                creeks)                                                               j
         A   »   area  of  shed In  square miles                                          j
         n   -   number of tributaries
         Q.J   »   monthly  mean pickup  (in  cfs) in the 1th tributary
         P   «   monthly  total  precipitation, in inches per month                      !
         1^  «   percent  (expressed as a  decimal) of flow contributed                  j
                by exfiltration  (from the water table into the channel)               I
         L  •   the proportion of precipitation lost by infiltration into the         |
                soil  (expressed as a decimal)                                         j
         K  «   unit correction « 0.895  ft3mo mi"2in"1sec"1.                          j
                                                                                     i
As an example,  the computation for October 1s:
                  ?       in           ft3                                           I
        Q  • 55 mi  x 3.0 — x 0.896   I1 mo   x  (1-0.3)  -                           .'
                          00         miSn sec                                        J
          (54(1-0.1) + 5(1-0.0) + 14(1-0.0) + (77-69.5)(1-0.1))     - 29.1 cfs         J
Now, since we know the pumped  withdrawal rates  as  well  as  the difference between     I
flows at  stations 2 and  the sum of 1, 4, and 5, and that  the Impoundment surface     j
is at steady-state over  the mouth,  we also can  estimate the net  infiltration rate    j
from the  lake Into the groundwater.   The infiltration  rate Is (again,  for October):   J
        Net  efflux -  Q($t-  j + 4 + 5) -  Q^-Q,                                      j
                   -  73.0 - 69.5 + 29.1  - 22.6  -  10.0  cfs
     Note that  the pickup in each channel  above Quiet  Lake is equal  to the  flow
at the pertinent sampling station.   This is the case because the  three channels      '
                                      -91-

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have their headwaters within the watershed.  If one were concerned about a subshed
with tributary headwaters above the subshed boundary, the difference in Q between
each of stations 1, 4, and 5 and the respective flows at the upstream subshed
boundary would be used.
     To estimate hydraulic residence time add the mean stormwater contribution
over the months of interest to that of the tributaries, as computed earlier.
The individual stormwater computations are not shown.  The method is as just
described.
                         6.6 t- 20.7 + 29.4 * 41.4 + 92.5 + 36.6
               . 81.1 *  	~,	 - 119 cfs
Then the hydraulic residence time Is given by:
                  V/Q . irr*0/Q
                        x  5280
    where
            L   •  length of the lake 1n ml
            H   •  width of the lake In ml
            D   »  mean depth 1n ft
            r   •  radius in ft.
                 3.14  x
x 5280    x 22/119
               « 5.69 x 10  sec - 658 days

Accordingly, the infinite hydraulic residence time plots for a 20-foot deep,
wind-protected, Burlington, Vermont, impoundment should suffice.  Note that
the entire impoundment volume was used in the above computation.  Strictly,
one should use the epilimnion volume during stratification.  In this case,
such a change would not alter selection of the plots because T^ would still  be
greater than 200 days.  A reproduction of the appropriate plot from Appendix D is
presented in Figure V-33.  As indicated. Quiet Lake is likely to be weakly strati-
fied from May to August inclusive, with a thermocline temperature gradient of
about l°ft~ .  The hypolimnion should extend downward to the bottom from a
depth of about 3-1/2 meters, giving a mean hypolimnion depth of:
                 22 ft
             3.29 ft m
                      7J~" - 3.5 m • 3.2 meters
                                       -92-

-------
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BURLINGTON. VERMONT j
20' IN1TIHL MPXtMUH DEPTH j
IMF1NHE MXOR. RES. TIME
niNinun nixiNC !
|
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THERMAL PROFILE PLOTS FOR USE IN QUIET LAKE EXAMPLE I















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-93-

-------
   The approximate hypo11*n1on volune, then, 1s:
I           V  • |4£x 1.9X1011!- 9.2xl010l
'            H   o./ffi
.   Over the period of Interest, the hypol1mn1on mean  temperature  distribution
                                             Mean
                                        Temperature,  *C
j                       narcn                   2.0
j                       April                   5.5
                                               9.5
                                              12.5                                      :
                                              14.0                                      !
                                              15.5                                      I
        The next step in use of  the DO  model  Is  to determine a steady-state or          I
                                                                                       i
   mean water column BOD loading (k^) and  DO  level prior to stratification.             |
   This is a multi-step  process  because of the several 600 sources.  The sources are    i
   tributaries,  runoff,  and  primary productivity.  First, we estimate algal produc-     j
   tivity using  methods  of this  chapter (or better,  field data),
        Using the curve  in Figure  V-26  and phosphorus data from Table V-14, the
                                                                 -2   -1               I
   maxima"!  primary productivity  should  be  1n  the range 1,400 mg CM  day                 ;
   to 1,900 mgCm  day  .  To convert to loading  in mgl  day" . divide by                I
   (1000 1m"3 x  6.7m).   This gives  the  loading as 0.21 to 0.28 mgl~lday~ .              j
        Now assuming that maximal  productivity occurs at  about  30°C and  that  produc-    I
   tivity rates obey the same temperature rule as  BOO decay, temperature-adjusted       |
   estimates of productivity rates can be made.   Using the maximal  rate  range of 0.21   j
   to O.ZSmgl'^ay"1, the adjusted rates are:                                          j
           Productivity  - (0.21, 0.28)  x 1.047{3'75"30>                                 j
                        • (.06,.08) mgl"1 day"1
   Then, according to Equation V-30 and assuming M  • 1,  k  due  to algae  is
   estimated by:

           ka(algae) " 2'67  x ('06' '08) " ('16' '21) "tf'W"1                        j
        The next contributor to water column  BOD is  BOD  loading of  Inflowing  waters.
   The value to be computed  1s the loading in milligrams  per liter  of  impoundment       j
   water per day:                                                                      I
                                         -94-

-------
          Da fly BOO loading  rate
                                      (n   L4            \   / .
                                      «  A«u'tJ   /«•
                                     i«l  j«l            ' '  k»l
I   where
|           n   •  the number of time periods of measurement
|           V   •  volume of Impoundment  1n liters
j           d   •  the number of days per time period
j           L   •  the number of Inflows.
.   For all  Inflows, the value is therefore approximately:
I
j   *        '  (2185 + 48.3 + 643.9 + 14240) x 2.45 x 106 x
    a(Tr1b)             .       .              .           - — -
              (Swift  (First (Second  (Storm   (Units      (Impound-
              River)  Creek)  Creek)  water   Conversion)  ment
                                    Runoff)               Volume)
              0.22
I   Now,  summing the two contributions:

!           ka ' ka (algae)  * ka(Tr1b)            .     .
I           ka - (.16, .21) + .22 •  (.38,  .43) ragTNlay'1
|        The  value of k^  will  be  assumed as 0.1 at 20°C with  6 1n Equation
j   (V-29) equal to 1.047.  Then  at  3.75°C:

l'           kl(3.75'C) -kl(20-C)x  1.047<3-75-ZO>
                     • .1 x 1.047("16'25) - 0.047
   Now ^(discharge) ^mean for ^^^ arxl April) and V are  known, with:
           Qf,Hcrh,«,^  • 26-8 (Swift River, Station 2)
            (discharge)                             ?R S? »           i
                       + 6.2 (pumped withdrawal) x  **•*'* . 9351 sec 1
                                                   ft                                i
I                      11                                                            I
!           V  «  1.9 x 1011!
!   then                                                                             !
I                              38   43                                                !
j           °ss  '  {0.3*. 047 M935/1.9 x  1011))  ' 4>94> 5'58                        |
|   For further  computations, C   • 5.25 will be assumed.                              J
|        Since k   has been defined as .03,  a steady-state areal  concentration           I
j   of benthlc BOO prior to stratification  can be estimated.   If ^4(20*0 *             I
j   .003 and C$s - 5.25, using Equation (V-34):                                        j
           k4(3.75«C) ' -003x1.
                     • .0014
                                        -95-

-------
        ,      .03 x 5.25 x 6.7
         ss "       .0014
            • 754 gm'2
     The next step 1n evaluating hypol1inn1on DO depression Is to estimate pre-
stratification DO levels.  If we assume saturation at the mean temperature
1n April (S.5°C), the dissolved oxygen concentration at onset of strata should be
about 12.7 (from Table V-12).
     Now we have all values needed to plot hypol1mn1on DO versus time using
Equations V-40 through V-42.
Using
        Lo ' Lss
        co - css
        k,  - O.lxl.047(9'5~20) • .062, (T - 9.50C for May)

        ks • 0.03
        k4 - .003x1.047(9'5'20) • .002
        t  • 5 days
and applying Equation V-42:
              0-062x5.25    ,   -(0.062+0.03)5
then, according to Equation  V-41:

              A..     k.C    \ /
       AO,  -
           .  /7S4       0.03x5.25    \ /,  .-0.002x5 \ /     0.03x5.25   \
         L    ^3.2   0.03-K).062-0.002 I I '"*         I" I 0.03*0.062-0.002 )

              /   0.002   \ /. .-(0.062*0.03)5\«  2.35
              I 0.062+0.03 ) I'"e               /
then from Equation V-40:
       ot - oo  -
       0,  •  12.7  -  1.30 -  2.35  -  9.05
                                      -96-

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 I   Solving the same equations  with Increasing  t  gives  the  data  in  Table  V-16.           |
 |   If 1t has been necessary  to develop  more  data for the remainder of  the  stratified    I
 j   period, appropriately  updated  coefficients  might be used  starting at  the beginning   j
 !   of each month.                                                                      i
                                    TABLE V-16
                      DO SAG CURVE FOR QUIET LAKE HYPOLIMNION
 j                   Date	^j.	_c	t
 j                   t « 0          0            0            12.70
 j                   5/5           2.35         1.30          9.05
 j                   5/10          4.68         2.13          5.89
 j                   5/15          6.99         2.65          3.06
                    5/20          9.22         2.98          0.50
 !                   5/25         11.54         3.18          0.00                      !
 |                 	                    I

 ;       Finally, if It is desired to evaluate the  Impact  of altered  BOO  or  phosphorus   ;
 j  loadings, the user must go back to the appropriate step  in the evaluation  process    j
 I  and properly modify the loadings.                                                   !
 i                                                                                      •
 i                                                                                      !
 :	—-	END OF EXAMPLE V-15	'•

 5.6   TOXIC CHEMICAL SUBSTANCES
      Although reasonably accurate and precise methods have  been prepared for  screening
 only  a few of the many priority pollutants (Hudson and Porcella,  1981),  a reasonable
 approach for assessing priority pollutants 1n lakes based on the  methods presented  1n
 Chapter 2 can be made 1f certain assumptions  are made:
        t    The major processes affecting the fate and transport of toxicants
             in aquatic ecosystems are known
        •    That reasonable safety factors are incorporated by making reasonable
             most case analyses
        •    Because 1t is a screening approach, prioritlzatlon can  be done to
             identify significant constituents, lakes where human health or ecological
             problems can realistically be expected,  and  processes which might
             require detailed study.
     The major processes affecting toxicants  are listed 1n  Table  V-17.   The primary
measure of the impact of a toxic chemical  1n  a  lake depends  on  Its concentration in
the water column.  Thus, these screening methods are  primarily  directed  at  fate and
                                         -97-

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                                     TABLE V-17
                           SIGNIFICANT PROCESSES AFFECTING
                        TOXIC SUBSTANCES IN AQUATIC ECOSYSTEMS
                   Processes
Rate Coefficient Symbol, time
                                                                            -1
         Physical-Chemical  Processes
           Sorption  and  sedimentation
           Volatilization
           Hydrolysis
           Photolysis
           Oxidation
           Precipitation
         SED
         k.
         not assessed
         not assessed
         Biological Processes
           Biodegradation
           Bioconcentration
         B
         BCF (unltless)
transport of toxic chemicals.  A secondary target 1s the concentration in aquatic
biota, principally fish.  Because of the complexity of various routes of exposure  and
bioaccumulation processes, the approach of bioconcentration 1s used to Identify
compounds likely to accumulate 1n fish.  These can be applied to lakes using  the
following method:
        •    A fate model  is used that incorporates sediment transport,  sorption,
             partitioning, and sedimentation
        •    Significant processes include the kinetic effects of sedimentation,
             volatilization and biodegradation
        •    Significant biochemical  processes can affect the fate of a  toxic chemical
             as well  as affect biota, such, as, bioaccumulation, biodegradation, and
             toxicity
        •    In keeping with the conservative approach of the toxics screening
             methodology,  some important processes are neglected for simplicity;
             for example,  lake stratification, photolysis,  oxidation, hydrolysis,
             coagulation-flocculation, and precipitation are neglected.   Also,
             it 1s assumed that the organic matter 1s associated with Inorganic
             particles and therefore organic matter settles with the Inorganic
             particles.
     Generally the toxic chemical  concentrations are calculated  conservatively,
that is, higher concentrations are calculated than would occur 1n nature because of
the assumptions that  are made.  The water column concentrations  are calculated  as  the
                                         -98-

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primary focus of the screening method. Then bloconcentration 1s estimated, based on
water concentration.  To determine concentration and bioaccumulation, point and
nonpoint source loadings of the chemicals being studied are needed.  Other data
(hydrology, sediments, morphology) are obtained from the problems previously done in
earlier chapters or sections of this chapter.  The person doing the screening would
have to compile or calculate such data.
     Occasionally, such Information must be estimated based on production, use. and
discharge data.  Information on chemical  and physical properties 1s important to
determine the significance of these estimates.

5.6.1  Overall  Processes
     Several processes affecting distribution of toxic chemicals are more  significant
than others.  Equilibrium aquatic processes Include suspended  sediment  sorption of
chemicals.   Organics in sediments can have a significant effect on  chemical  sorption.
Hydrolysis  and  acid-base equilibria can alter sorption equilibria.   Volatilization  is
an equilibrium  process that tends to remove toxic chemicals from aquatic ecosystems.
Removal  processes include settling of toxics sorted on sediments, volatilization, and
biodegradation.   Chemical  reactions for hydrolysis and photolysis are included  and
precipitation and redox reactions could be included 1f refinement of the method were
desired.  Generally, bioaccumulation will  be neglected as a removal  process.
     These  removal  processes are treated  as first-order  reactions that  are simply
combined for a  toxicant  (C, mg/1 ) to give:

                                    dC/dt  « - K x  C                          (V-44)
where
        K    •  SEO + B + k  + k  + k.
                           v    p    h
        SED  «  sedimentation rate, toxicant at equilibrium with sediments
        ky   »  volatilization rate
        B    •  biodegradation rate
        k    •  photolysis rate
        *h   -  hydrolysis rate.
     This equation is analogous to the BOD decay rate equation used in  the hypolimnetic
00 screening method.
     The input  of toxic chemical substances is computed simply (refer to Figure
V-23):
                                 d£ . Q
                                 dt   7
x C1n -                               (V-45)
where
        C-n-  the concentration in the Inflow  (tributary  or  discharge);
        flow (Q), volume of reservoir  (V)  and  time  (t) are as  defined  previously.
                                         -99-

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     At steady state, accounting for Inflow (Q*C1n) and outflow (Q-C), and
using Q/V « I/T^:

                           dC , I  (c.n - c)  -  K  x C - 0                     (V-46)
                                 w

and solving:
                                C • Cin/(l +  TW x K)                         (V-47)


To determine the concentration at any time during a non-steady state condition
(assuming c.  1s a constant):

                            C • -p  (1 - e"  t/Tw) + co e~ft/T*               (V-48)

where
        f   •  1 + T^ x K
        C   -  reservoir concentration  at  t  «  0.

5.6.1.1  Sorption and Sedimentation
     Suspended sediment sorption 1s treated  as an equilibrium reaction which Includes
partitioning between water (C¥) and the sediment organic phases (Cs).   The
concentration sorbed on sediment can be computed as follows:
                                   Ce
                                   •^ •  a x Kp x S                         (V-49)
where
        C   •  the total concentration (c  + C ), mg/1
        S   •  input suspended organic sediment • OC x  So, mg/1
        OC  •  fraction of organic carbon.
        So  •  input of suspended sediment, mg/1
        K   •  distribution coefficient between organic sediment and water
        a   •  fraction of pollutant in solution
If K  1s large, essentially all of the compound will be sorbed onto the sediments.
Note that S and C must be estimated or otherwise obtained.
     The organic matter content of suspended sediment and the lipld solubility
of the compound are important factors for certain organic chemicals.  Other sorption
can be ignored for screening.  A simple linear expression can be used to calculate
the sediment partition coefficient (K ) based on the organic sediment carbon
concentration  (OC) and the octanol-water coefficient (kow) for the chemical:
                                         -100-

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        kp - 0.63  (kow)  (OC)
     The sedimentation rate (SED) of a toxic chemical 1s computed as follows:

                                 SED - a x D x K                             (V-50)
where
        D    «  P x S x Q/V, sedimentation rate constant
        P    •  sediment trapping efficiency
        Q/V  «  I/TW

5.6.1.2  B1odegradat1on
     The blodegradatlon rate (B) 1s obtained from the literature or 1s computed as
follows:
     Modification to the rate can be made for nutrient limitation using phosphorus
(C ) as the limiting nutrient:

                                      B (0.0277)0,,
                          a n«it.H .          ' P^                          (v-52)
                                      1 * 0.177 x C

     Temperature correction can be performed using the following equation:

                            B(T) - 8(20'C) x 1.072(T'20)                      (V-53)

     Previous exposure to the pollutant 1s important for  most toxic organic compounds.
Higher rates of degradation occur in environments with frequent or longterm loading
(discharges, nonpoint sources, frequent spills) than infrequent loadings  (one-time
spills).  In pristine areas, rates of one to two orders of magnitude less should  be
used.
     It is assumed that the suspended sediment  decay rate 1s the same as  aqueous
phase decay.  Also benthic decay is disregarded because bottom sediment release may
be negligible.

5.6.1.3  Volatilization
     Many organics are not volatile so this  process is applied only to  those which
are.   It is assumed that the mass flux of volatile organics  Is directly proportional
to the concentration difference between the  actual  concentration and  the  concentra-
tion at equilibrium with the atmosphere.   The latter can  be neglected 1n  lakes.
                                         -101-

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 Also,  only  the  most  volatile are assessed.
 Thus:

                                     IT •

 where
         ky   »   volatilization  rate constant, hr
 The  rate coefficient  1s derived  from the 2 resistance Model for the 11 quid-gas
 Interface,  but  It  can be estimated using correlation with the oxygen reaeratlon
 coefficient (based on Z1son  et_al_., 1978):

                                    k • Ka (Dw/Do)                           (V-5S)

         and  estimate  (Dw/Do)   •   (32/mw)1/2
         and  the  surface film thickness, SFT »  (200-60 •  Ww ) x 10"6
         and Kal  «  Oo/SFT
         Ka  • Kal/ZB
 where
         Ka   *   reaeration rate, hr"
         Dw   •  pollutant d1ffus1v1ty 1n water
         Do   •   dlffuslvHy of oxygen In water  (2.1 x 10"9 m2/sec, 20*C)
         mw   -  pollutant molecular weight
        U~   «  wind speed, in/sec
        7    •  mean depth, m.
The volatilization rate  coefficient (ky, hr"1)  1s determined  by  ky • Ka  x k where k
Is obtained  from literature values or computed  as above  (VDw/Oo).  The rate should be
correct*
effect:
corrected for temperature (kyt) even though temperature has only a relatively small
                                         x 1.024(T"20)                       (V-56)
5.6.1.4  Hydrolysis
     Not all compounds hydrolyze and those that do can be divided Into three groups:
acid catalyzed, neutral, and base catalyzed reactants.  A pseudo first-order hydrolysis
constant (*h) Is estimated for the hydrolysis of the compound:

                                    IT • -kh ' c                             

The rate constant Uh) 1s pH dependent and varies as discussed 1n Chapter 2.
The typical pH of the lake for the appropriate season should be obtained  for  the

                                        -102-

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 necessary calculations.   Generally,  the  pH  1s  a  common Measurement  and  1s  available
 for most lakes.   If not,  pH values  for most open lakes He  between  6-9  and  can  be
 estimated based  on the following  empirical  values based on  HutcMnson,  (1957):

                                               Hardness
                                            (or Alkalinity)      £H
           add  lakes                            <25         6   -   6.5
           neutral  lakes                        25 -  75     6.5 -   7.5
           hard water lakes                     75 - 200     7.5 -   8.5
           eutrophic  and alkaline  lakes           0-300     8.0 - 10.0
 Median  values on a  range  of  values can be used to evaluate  the significance of
 hydrolysis as a  factor affecting  the fate of compounds.
 5.6.1.5  Photolysis
     Generally, photolysis 1s a reaction between ultraviolet light  (UV,  260 to 380 nm
 is  most  Important) and photosensitive chemicals.  Not all  compounds are subject to
 photolysis  nor does  UV light penetrate significantly 1n turbid lakes.  In the absence
 of  turbidity data, light transmission can be estimated by  seasonally averaged SeccM
 disk readings according to the following equation:
         In  (ISD/Io)  « -ke(SD)  -  In 0.1  • -2.3
                 ke  »  2.3/SD
 where
         ke              »  the extinction coefficient
         SD              •  the Secchi depth in meters
         (ISD/Io « 0.1)  •  relative  intensity based  on  Hutchinson  (1957).
     Photolysis for appropriate chemicals (discussed  in detail  in  Chapter 2) depends
 on  a first  order rate constant (k  )  incorporating environmental  variables  (solar
 irradiance, Io)  and chemical variables  (quantum yield, *,  and  absorbance,  E).
 Turbidity effects are included as  estimated as above  since turbidity data  are  generally
 not available.   These values are Incorporated into the  rate  constant and the concen-
 tration reduced  as  described in Chapter  2:

                                    £  '  V                                (V-58)

where
       kr   •  f  (Io. *,  E. ke, Z)

 and
        k   .   i.
         P     ke-I
                                         -103-

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where
        k   «  photolysis rate constant unconnected for depth and turbidity
               of the lake.
     Depth (Z) 1s generally applied only to the photic zone; mean depth (Z)
1s an appropriate measure since It approximates the mixed depth and the photic
zone.

5.6.1.6  Bloconcentratlon
     B1 concentration 1s a complex subject that depends  on many variables.  The
simplest approach has been developed for organic compounds using the octanol-water
coefficient (kow) to calculate tissue concentrations (Y):

                    Y • BCF x  C,  g/kg fresh weight  of  fish flesh             (V-59)
where
        BCF      «  Bloconcentratlon factor
        log BCF  •  0.75 log kow  - 0.23
(The coefficients for the equation (0.75. - 0.23) are median estimates obtained
from correlation equations and are default values for occasions where no other data
are available.)

5.6.2  Guidelines for Toxics Screening
     Generally metals do not biodegrade nor volatilize.   However, pK, hardness,
aUalinity and other ions are very important and can cause their removal  by precipi-
tation.  The conservative approach is taken here and metals are calculated  without
removal (K • 0).
     Organics may have variable sorption, volatilization,  and biodegradatlon rates.
If data are available in the literature, these should be used. Otherwise, a conserva-
tive approach should be used and calculations made without removal  (K • 0).  For
chlorinated (and other halogens)  compounds or refractory compounds, biodegradation
should be assumed to be zero.
                                  EXAMPLE V-16
I                     Estimating Trichloroethylene and  Pyrenc
|                        Concentrations in an Impoundment
I
•        An impoundment with a single tributary is located in  a windy valley.
   The following conditions are known for E.G. Lake:
           Mean tributary flow rate « 3.6 x 104m3/hour
I           Total volume - 1.1 x 108m3
                                         -104-

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I         Mean depth  •  11 m
j         Tributary average sediment load » 200 mg/1
j         Sediment average organic carbon content •  .05
j         Inlet average pyrene concentration • 50 wg/1
          Inlet average trlchloroethylene concentration « lOOng/1
;         Lake average phosphorus concentration • 50 ug/1
          Mean water temperature • 15"C
          Mean wind speed • 6 m/sec (35 mph)
          Seech1 depth • 1  m

   Determine the steady state concentration  of pyrene and trlchloroethylene in the
   lake, assuming V max for  the sediment (mostly  clay) 1s 3.2 x 10   feet/second.
   The trapping  efficiency  1s  obtained  from  Figure V-34..
           Other data                   Pyrene              Trlchloroethylene
              kow                      148000                       190
              B                       IxlO"4
              ky                        -                          0.45xKa
   The processes  of photolysis  and  hydrolysis  can  be  neglected  because turbidity
   prevents  photolysis (SO «  1  meter) and these compounds  have  negligible hydrolysis
   (see Chapter  2).
        We use the  summary equation V-47 for the analysis:
|        The  hydraulic  residence time of E.G. Lake 1s:
j          T^  -   1.1  x  108m3/(3.6 x loV/hr)
I              -   3048 hours
j              «   127  days
j              «   .349 year
j              «   1.1  x  106 seconds

,  Sedimentation
        First, the suspended sediment concentration in E.G. Lake must be estimated.
,  The trapping efficiency of the impoundment is estimated from Figure V-34.
j  Da*a;
        V max  •  5 x  10   fps
!        TW     «  1.1  x 10  sec
        D1     •  11 m  •  36.1 ft                             1.56
)  A value of 101*95 is obtained which  yields:
          P » 90 • 0.9
                                         -105-

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 1C
     V
   .,1
 10
   -ex
 1C
   -51
: ic
-24.
Toxics
Example
                                        Settling  velocity in feet/
                                        second
                                        Hydraulic  residence time
                                        \n seconds
                                        Flowing  layer depth
                                        Mass  of  sedim-nt tracped
                                             of  setf-.T.ert eru-nng
            FIGURE V-34 NOMOGRAPH FOR ESTIMATING SEDIMENT TRAP EFFICIENCY
                                         -106-

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         In the Inflowing stream, the toxicants are assumed to be at equilibrium
   with  the organic matter.  Thus:
           S - OC x So • .05 x 200 x 10"6  • 1 x 10"5 kg/1
   Therefore, for pyrene:
           K   - 0.63 x 148000 x 0.05 - 4660
           aP  - 1/(1 * 4660 x 1 x 10'5) • 0.955
           £|  - 0.955 x 4660 x 1 x 10"5 • 0.044
   and                                                                                 !
           SED -  a  x D x  K                                                              \
           D   -  P  x S x  Q/V                                                           I
           D   -  0.9 x 200  x 10'6  x ^jjj hours                                          j
           D   •  5.91  x  10'8 hour                                                       I
           SED *  .955  x  5.91 x  10'8 x 4660                                              \
           SED •  2.63  x  10'4 hr'1                                                       j
   For trlchloroethylene:                                                               j
           Kp  •  .63  x  190 x  1 x  .05 - 6                                                 j
           a   - 1/{1 * 6 x  1 x  10"5) • 1                                                j
           ^  • 1 x  6  x 1 x  10'5 • 6 x 10"5 * 0                                         j

I   and                                                                                 I
           SED -  1 x 5.91 x  10'8 x 6                                                    j
!           SED -  3.54  x 10'7 hr"1
j   Biodegradation                                                                       '
       Assume that the presence of trichloroethylene does not affect the
|   biodegradation of pyrene.  Trlchloroethylene does not biodegrade.  The
I   temperature corrected and  nutrient limited rate constant for microblal decay         J
|   of  pyrene are:                                                                       I
I           Bo     » 1. x 10'4 hr'1                                                       !
           B      - .0277 x 50/  (1 * .0277 x 50)
                 • .58
           B(15)  - .58 x 1.  x 10"4 x 1.072(15"20)
                - 4.1 x 10'5 hr'1
   Volatilization
   	
       The reaeration coefficient for E.G. Lake will be estimated for trichloro-
   ethylene only, because pyrene does not volatilize:
           Kal  • 2.1 x 10"9  / (200 - 60 x 61/2 ) 10'6
              - 3.96 x 10"5 m/sec
              «  .143 m/hr

                                         -107-

-------
I            Ka   •  (.143 m/nr)  /  11 • •  .013 hr'1                                         j
j    For  trlchloroethylene  (TCE):                                                         |
1            k  - [HW(TCE)/NW(OO] • Ka  •  .45 x  .013 »  .0058 hr'1                         '
1                                                                                        i
|    When adjusted  for  temperature:                                                       J
I            ky • .0058 x 1.024<15-20)                                                    !
j              - .0052 hr"1                                                              |
|   Volatilization  for pyrene may be  neglected.                                           I
j   Pollutant Mass  Balance                                                                |
|        The overall  decay  rate constants  are:   K  • SED + B  *  ky                          I
j        Pyrene:              K - 2.63 x  10~4 + 4.1 x  10'5                                j
j                              • .000304 hr'1                                             j
        TMchloroethylene:  K • 3.54 x  10"7 + 0 * 0.0051
!                              • .0052 hr"1                                               '
I        Using the  steady state equation:                                                 !

•           C ' C1n'                                                             j
I   For Pyrene:                                                                           !
1                                                  -1                                     I
'           C • 50^9/l /  (1  * 3048 hr x .000304 hr *)                                    j
!           C • 27  Kg/T                                                                  !
I        Note: WQC for human health  Is  0.0028 ng/1  at  10"6 Risk  (FR:                     \
I   11/28/80 p.  79339).                                                                  j
j   For Trrehloroethylene:                                                                I
j           C • 100 K9/1  /  (1 * 3048  hr  x  .0052  hr"1)                                     j
j             • 5.9 HQ/1                                                                  I
j        Note: WQC for human health  Is  2.7 ng/1 at  10"6  Risk  (FR:   11/28/80              j
j   P.  79341)                                                                            j
        Tissue burdens (Y) can be calculated:                                            !
I                                                                                        I
j           Y « BCF x C                                                                  j

i   where                                                                                i
•           log BCF • .75 log kow - 0.23                                                 j
•   For Pyrene:                                                                           ;
|       J	                                                                           I
j           Y • 4330  x  27 • 120000 ^g/kg fish flesh                                      j
•   For Tr1chloroethylene:
j           Y • 30  x  6 • 180  »*g/kg fish  flesh                                             j
•   Comments
        Several  conclusions  are apparent  from this  analysis:
!           •    Certain processes dominate the  overall  fate for  a  specific toxic         ,
                                         -108-

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I              chemical  so that, practically speaking, errors In estimating coeffic-     I
j              1ents are negligible except for the Important processes.  After           |
j              Identifying the Important processes, the coefficients can be varied       j
              to determine the range of concentrations.   For example,  sedimentation     •
!              of trlchloroethylene can be Ignored;  however, volatilization  should
!              be studied.
I         •     The more  stringent Water  Quality Criteria are  for toxicants that have     I
i                                                                                       *
I              significant  bloconcentratlon;  e.g.  compare pyrene to trlchloroethylene. I
{         •     Volatilization of trlchloroethylene  would be Investigated in detail        |
j              since this  process might  not be significant In this lake because of       j
j              Its depth.   Also, the physical properties are  Important;  e.g.            •
              trlchloroethylene has a specific gravity of about 1.5.  Thus, It may
!              accumulate  on the bottom  of the reservoir and  remain there unless It      '
!              Is completely dispersed.                                                  j
I         •     Based on  this analysis, sources of pyrene would be assessed first.        I
|              then trlchloroethylene.                                                   I
j         •     What other  observations can you draw from this analysis?                  j
i                                                                                       i
I                                                                                       I
	END OF EXAMPLE V-16	
 5.7  APPLICATION OF METHODS AND EXAMPLE PROBLEM
     This chapter has presented several approaches to evaluation of five impoundment
 problem areas.  These are thermal  stratification, sediment accumulation, eutrophica-
 tion, hypolimnion DO/BOD, and toxic chemicals.  Figure V-35 shows how the different
 approaches are linked together with their data needs.  In studying any or all  of the
 potential problem areas in an impoundment, the user should first define the potential
 problems a* clearly as he can.  Often the nature of a problem will  change entirely
 when its various facets are carefully described and examined  en masse.
     Once the decision is made that an aspect of impoundment  water quality should be
 evaluated and the problem is clearly stated,  the user should  examine available
 solution techniques presented both in this document and  elsewhere.   The examination
 should address the questions of applicability, degree of accuracy,  and need for data.
 The user will generally know what  funds are available for data collection as well  as
 the likelihood of procuring the needed data from previously developed  bases.  Also,
 the decision concerning needed accuracy rests with the user,  and he should make
decisions based upon the way in which his results will be used.
     Once appropriate methods have been selected, the next  task is  to  set down
 the data and to manipulate It according to computational  requirements.  Data are best
displayed first in tabular form and then plotted 1n some meaningful  way.   Careful
tabulation of data and graphing can themselves sometimes provide a  solution to a
                                        -109-

-------
                                                   iiti«cvt
                                                   IOTA l«i» '••
                                                      VOUM. MfA. Ml MVTH
                                                      MO •»>•*•! C»"»ITI«"1
                                                        HIM »«IUtl»t*
                                                       MfMl •!•» »IIOC!TT*
                                                               tirr-
                                                     i(»IH(»T LMM l*tO
           FIGURE  V-35   GENERALIZED  SCHEMATIC OF  LAKE COMPUTATIONS

problem,  negating need for further  analysis.  To Illustrate these Steps, a  conpre-
hensive application to a river basin  system was performed  in this section.

5.7.1  The  Qccoquan Reservoir
     The  Occoquan River basin in  Virginia was used to demonstrate the screening
approach.   A basin map is shown in  Figure V-36.  Because the Occoquan Reservoir
is a public drinking water supply downstream from metropolitan areas, water quality
data were available to compare to the  screening method's outputs.
                                          -110-

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                              LOUOOUN
                                   COUNTY
                                                                  Fairfax
                                                                     OCOOQUOO
                                                                       Dam
                                                      KLOMCTCR*
                                                      I  I  I  I I  I
                                                      01  1  » 4  •
                   FIGURE V-36  THE OCCOQUAN  RIVER  BASIN
5.7.2  Stratification
     Occoquan Reservoir  is  about  32 kin  southwest of Washington, D.C.  and has
the following morphemetrie  characteristics:
                -3  •  3.71 x  107
                                     ,6
        Volume,  m'
                       o
        Surface  area,  m   •   7.01  x  10"
        Maximum  depth, m  «   7.1  (Occoquan  Dam)
        Mean depth,  m   •  5.29
     Based upon  the  above  geometry and the  thermal plots, determine whether the
lake will  stratify,  the thickness  of  the epilimnlon and the hypol1mn1on, the depth to
the thenmocline, and the interval  and starting and ending date of stratification.
Also note  the temperature  of  the  hypolimnion at the onset of stratification.
     Predicting  the  extent of shielding from the wind requires use of topographic
maps.  The reservoir is situated  among hills that rise 25 meters or more above the
lake surface within  200 meters  of  the shore.  The relief provides little access for
wind to the lake surface.  Average annual wind speeds are 15.6 km/hr in Washington,
O.C.  and  12.6 km/hr in Richmond,  VA. Inflow comes essentially from two creeks, the
                                        -111-

-------
Occoquan River and Bull Run River (Figure V-35).
     First, determine needed Information and then do metric/English conversions
as necessary.
     The first step 1n assessing Impoundment water quality is to determine whether
the Impoundment thermally stratifies. This requires knowledge of local  climate.
Impoundment geometry, and Inflow rates.  Using this Information, thermal  plots likely
to reflect conditions 1n the prototype are selected from Appendix D.
     For the thermal plots to realistically describe the thermal behavior of the
prototype, the plots must be selected for a locale climatically similar to that of
the area under study.  Because the Occoquan Reservoir 1s within 32 kilometers of
Washington, D.C., the Washington thermal  plots (Appendix D) should best reflect the
climatic conditions of the Occoquan watershed.
     The second criterion for selecting a set of thermal  plots 1s the degree of
wind stress on the reservoir.  This 1s determined by evaluating the amount of pro-
tection from wind afforded the reservoir and estimating the Intensity of  the local
winds.  Table V-2 shows annual  wind speed frequency distribution for  Washington, D.C.
and Richmond, Virginia. The data suggest that winds 1n the Occoquan area  are of
moderate intensity.
     Predicting the extent of shielding from the wind requires use of topographic
maps.  The reservoir is situated among hills that rise 25 meters or more  above
the lake surface within 200 meters of the shore.  The relief provides little access
for wind to the lake surface.  The combination of shielding and moderate  winds
implies that low wind stress plots are appropriate.
     The geometry of the reservoir 1s the third criterion used 1n the selection
of thermal plots.  Geometric data for the Occoquan Reservoir are summarized in
the problem.  The volume, surface area, and maximum depth are all nearly  midway
between the parameter values used in the 40-foot and 75-foot maximum-depth plots.
However, the mean depth is much closer to the mean depth of the 40-foot plot.
     The mean depth represents the ratio of the volume of the impoundment to its
surface area.  Because the volume and surface area are proportional to  the  thermal
capacity and heat transfer rates respectively, the mean depth should  be useful  in
characterizing the thermal response of the impoundment.  It  follows that  the 40-foot
thermal profiles should match the temperatures in the Occoquan Reservoir  more closely
than the 75-foot profiles.  However, it is desirable to use both plots  in order to
bracket the actual temperature.
     Flow data provide the final information needed to determine which  thermal
plots should be used.  The inflow from the two tributaries adds up to be  20.09
m /sec.
                                         -112-

-------
      The  hydraulic  residence time can be estimated by using the expression:

        TW  .  V . 3.71 x IQf m3
                  20.09 
-------
                          AT*
 IX
                   12
o      **T        o	a*-
                                                        12
   C    10   20   I*     0    10   39   M    0   10   20   It    0   10  20   10
      unr. C           TCnr. c           Ttnr. c           Ttnr.  c
                                             Iff
                                                               »CT
b.
UJ
O
 i:
o   10   ?e   J3
   TEMP. C
                   12
0   10   20   JO
   TErtP.  C
 0   10   20   10
    TE«P.  C
                  12,
                                                         0   10   20   10
                                                            TE«P.  C
X
>—
o.
ta>
O
                   12
   0    10   !•   II    O   10   JC   »•
      Unr.  C            UnP.  C
     WASHINGTON, D.C.

     40'  INITIAL «oxinun
     30  D«T  MYOR- RES. T1«E
     MlNlnun nixiwc
     FIGURE V-37   THERMAL PROFILE PLOTS FOR OCCOQUAN  RESERVOIR
                                -114-

-------
                                       TABLE V-18
                       COMPARISON OF MODELED THERMAL PROFILES TO
                       OBSERVED TEMPERATURES IN OCCOQUAN RESERVOIR
Mean Epi 1 imnion Temp., *C
Month 40-foot Plot*
March
April
May
June
July
August
September
October
November
December
7
13.5
19
24
26
26
22
17
11
7
Observed0
8.4
12.6
20.5
24.8
26.6
26.5
23.8
17.2
12.2
6.2
Mean Hypo limn ion Temp., *C,
40-foot Plot6
6
10
15
18
20
21
20
16
10
7
Observed0 *
6.3
9.2
14.4
17.2
21.2
23.7
20.2
15.8
11.6
5.8
Epi 1 imnion
Depth
(•)
10-foot Plotb
—
--
4.5
5.0
6.5
7
--
—
--
--
Source:  Northern Virginia Planning  District  Commission.   January,  1979.
*Mean temperatures in epilimn ion from thermal plots with T  • 30 days and a maximum
 depth of 40 feet.                                        *
 Mean temperatures 1n thermocline and hypolimnion from  thermal  plots  with ^  «  30
 days and a maximum depth of 40 feet.                                      w
cMeans of observed temperatures in "upper"  and "lower"  layers of Occoquan Reservoir for
 1974-1976. at Sandy Run.	

thermal plots should predict results relatively close to  the two low-flow years.   The
differences expected for 1975 would be less pronounced  when averaged  with the other
two.
      In conclusion, Occoquan Reservoir does apparently  stratify, the  depth to
the thermocline or the epllimnion approximates the mean depth (5.29), the hypolimnion
has a depth of 11.8 m (17.1-5.3), and the Interval  of stratification  approximates May
1 to mid September or 138 days.  The hypolimnetic temperature 1s about 11 degrees C,
typical ly.

5.7.3  Sedimentation
     To evaluate potential  sedimentation  problems.  Appendix F 1s examined to see  1f
any data exist on the upstream reservoir  (Jackson)  or Occoquan  Reservoir  (Figure
V-36).  Some data exist for Jackson but not for Occoquan Reservoir  (Figure V-38 taken

                                         -115-

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FIGURE V-38  SUMMARY OF RESERVOIR SEDIMENTATION SURVEYS MADE  IN THE UNITED STATES THROUGH  1970
                                                -116-

-------
 from Appendix F).   Thus,  we  can detenrlne  the  trapping  of  sediment  1n  Jackson  Reservoir
 but trapping must  be  calculated for the Occoquan.   To refine  the  analysis,  calculations
 on Jackson Reservoir  will  also be  made  and the results  calibrated.
      To apply the  Stokes1  law  approach  to  a reservoir,  we  need to know the  loading
 first.   The necessary sediment loading  estimates for the tributaries were provided by
 the methods 1n Chapter 3  and are listed in Table V-19 (Dean «* al_.t 1980) Before they
 are used  1n further computations,  a delivery factor must be applied to these values.
 This factor {the sediment  delivery  ratio or SDR) accounts  for the fact that not all
 the sediment  removed  from  the  land  surface actually reaches the watershed outlet.
 Nonpoint  loads from urban  sources  are presumed to enter the reservoir through Bull
 Run River since most  of the urbanized portion of the watershed lies In this sub-basin.
      Computing the  annual  sediment load  Into Occoquan Reservoir 1s complicated
 by  the  presence of  Lake Jackson  Immediately upstream from the reservoir.  The
 trap efficiency must  be computed for Lake  Jackson as well  1n order to determine
 the amount  of  sediment entering  the Occoquan Reservoir from Lake Jackson.  The
 steps involved are  to  compute  the  sediment delivered (Table V-20)  , the size range,
 the fraction trapped  for each  size range and the total  amount trapped.  A table has
 been devised to simplify these  steps (Table V-21).
      Soil types provide an Indication of the particle sizes in the basin under
 study.  Soils  in the Occoquan basin are predominately silt  loams.   Particle size data
 on  the  principal  variety, Penn silt loam, are given in Table V-22.  These data and
 all  calculations  are transcribed Into Table V-23.
     Some effort  can be conserved by first  calculating the  smallest  particle size
 that will be completely trapped 1n the Impoundment.  To  do  so, P,  the  trap efficiency,
 must first be computed.  Because both reservoirs are long and  narrow and  have rela-
 tively  small residence times,  the flow will be  assumed to approximate  vertically
mixed plug flow (Case  Bl). In  this  case, P  is found from the expression:
where
         I
        D   •  mean flowing layer depth,  m.
     To calculate the smallest particle that  1s  trapped  in  the  Impoundment,  P
is set equal  to unity and the above  equation  1s  solved for  V    :
                                                           Ma A
        v
           *      Tw
This expression for V(Mx  is  then  substituted  Into the  fall velocity equation
(Stokes1  law),  which in turn is solved  for d:
                                        -117-

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                                TABLE V-19

              ANNUAL  SEDIMENT  AND  POLLUTANT  LOADS  IN  OCCOOUAN

                   WATERSHED  IN METRIC  TONS PER YEAR*
Type of Load
•Sediment
Total Nitrogen
Available Nitrogen
Total Phosphorus
Available
Phosphorus
BOD5
Rainfall Nitrogen
Kettle
Run
46.898
164.46
16.45
39.01
2.18
328.92
0.72
Cedar
Run
396,312
1.457.42
145.74
341.95
14.95
2.925.63
5.50
Broad
Run
142.241
518.91
51.89
114.22
5.57
1.042.45
2.00
Bull
Run
232,103
789.24
78.92
202.71
12.50
1.578.47
3.92
Occoquan
River
139,685
469.46
46.05
119.42
8.43
925.85
2.48
Urban
Runoff
12,699
12.88
5.38
2.59
1.27
77.47
-
* Estimates provided by Midwest Research Institutes Honpoint Source Calculator.
  These values have not yet had a sediment delivery ratio (SOR) applied to
  them.  We will  use 0.1 and 0.2 as lower and upper bounds.   The SDR does not
  apply to rainfall nitrogen.

  Note:  A large  number of significant figures have been retained in these
         values to ensure the  accuracy of later calculations.
                                 TABLE  V-20

                      SEDIMENT  LOADED  INTO LAKE  JACKSON,
                                 1,000 Kg/Year

Tributaries
to
Lake Jackson
Kettle Run
Cedar Run
Broad Run
Total

Total
Available
Sediment
46,898
396,312
142,241

Sediment
Lake
Case I
(SOR-0.1)
4,690
39,fi30
14.220
58,540
Delivered to
Jackson
Case II
($DR«0.2)
9,380
79,260
28.440
117,080
                                   -118-

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                                   TABLE  V-21




CALCULATION FORMAT FOR DETERMINING SEDIMENT  ACCUMULATION IN RESERVOIRS (NOTE  UNITS)
Size
Fi.ict ion

Percent
Coni|K)$ it ion

Density
Absolute

bulk

(lean
Particle
Diameter

Vniax

Fraction
Irappoil (P)
A

0

Test Case

i ncoHi i ng
Sediment

Trapped
Sediment

                                            -119-

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                                      TABLE  V-22
                           PARTICLE SIZES IN PENH SILT LOAM
Particle Size - °f Particles Smaller Than
(ran) (By Height)
4.76
2.00
0.42
0.074
0.05
0.02
0.005
0.002
4.8 x 10* (Dn - D } d* n,
V p w / D
u
The resulting expression is:
' D' u
100
99
93
84
78
50
26
16


              *   4.8 x 106 (0  -  D^)  •  TW

     The trap efficiency  of  Lake  Jackson is  calculated  first.  The  data required
for these calculations  are:
        V   - 1.893 x 106m3
        Q   - 12.47 n»3sec
        U   • 3.34 n
        H-   • l.ll   (Assuming  T  « 16*C  as in  Occoquan  Reservoir)

         T. . V  .  	1.893 x 106 «3       	. , ,(
                                                          >
              w   12.47 m3 •  sec"1 • 86400 sec - day*1
     The »ini*u» particle  size  for  100 percent trapping is computed as:
                1.34 m x 1.11                                  A
                ~"                       ~  5.14 x 10"^ or
                     x 10b (2.66 - 1.0)  •  1.76
                                        -120-

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                                     TABLE  V-23



CALCULATION FORMAT FOR DETERMINING SEDIMENT ACCUMULATION  IN RESERVOIRS  (NOTE UNITS)
Mean
Size Percent Density Particle
Fraction Composition Absolute Bulk Diameter
cin
.000514 0.3 2.66 2.24 N/A
.00050 5 2.66 2.24 N/A
.00035 5 2.66 2.24 N/A
.00020 16 2.66 1.28 N/A
>. 000518 73.7 2.66 2.33 N/A
(average)


Example
Calculation SDR - 0.115
Vo) • 24750 m3/yr
Vol of Jackson Reservoir
(75 yrs lifetime)
Fraction
Trapped (P)
'max A B
m/day
1.90 N/A 1.00
1.79 N/A 0.94
0.88 N/A 0.46
0.29 N/A 0.15
N/A 1.00
Totals
Trapped
last per year «
Test Case

I
11
1
11
1
11
1
II
I
11
I mtons/yr
II mtons/yr
I m3/yr
11 m*/yr
24750m3/yr -
1893000m3
m
Incoming
Sediment

176
352
2927
5854
2927
5854
9366
18732
43144
8628S
48822
97644
21523
43046
1.3X/year
ton/vr
Trapped
Sediment
•^/yr
176 79
352 158
2751 1228
5502 1356
601
2582 1209
1405 1098
2810 2196
43144 19000
86288 37000


                                                  -121-

-------
      The  amount  trapped  of  each  size  fraction 1$ computed separately for Case
6-1  from  the  equation:

        p » V>na* T*
                D'
For example, for size fraction 0.00035 on:
        p .  (0.88)(1.76) . Q.46
                (3.34)      u
A composite trapping efficiency can be obtained by determining the total percent
trapped (48822/58540 • 0.83).
     The sediment accumulated in Lake Jackson for each Size range 1s determined
from the expression:

        St ' '  ' S1
where
        P  »   trap efficiency
        S1  •  sediment load from tributary 1
        S   *  sediment trapped.
For the two cases (I, II):
        St • (0.1,  0.1} x 0.83 [46898 * 132241] metric tons/year
           « (48822. 97644) metric tons/year.

Data obtained from Appendix f of the screening manual show that the estimated
rate of sedimentation in Lake Jackson is 56,153 metric tons/year.  This indicates
tnat an SDR of 0.115 would be appropriate.
     Bulk density (g/cc) includes the water that fills pore spaces in sediment
that has settled to the bottom and this must be accounted for when determining
volume lost due to  sedimentation.   Bulk density varies with particle size and
some approximate values for the size ranges for sand (0.005-0.2 cm), silt (0.0002-
0.005 cm), and clay (<0.0002 cm)  are as follows:  2.56 for sand,  2.24 for silt and
1.28 for clay.   Thus, using an SDR of .115, 24,750m3 (or 1.31) of reservoir
volume would be lost per year.  In comparing to Appendix F data,  we find that this
value is conservative.   The loss of volume was estimated by the SCS to be 47.5 acre
feet/year while these calculations snow only 20 acre feet/year being lost.   The
estimated bulk density  used by the SCS was 0.93 g/cc and we used  a more conservative
value.  If the SCS  figure is used, the volume lost is determined  to be 46.4 acre
feet /year .
     Now we compute the sedimentation in  Occoquan Reservoir.  The  minimum particle
size that is completely trapped is computed using the following values:
        D'  - 5.29
        K   • 1.11  (T - 16"C • mean of Table V-18)
                                         -122-

-------
         D   - 2.66 g on'
         D^  • 1.0 g on"
         T   • 21.4 days.
 Under stratified conditions,  the epllimnlon thickness  should be  used for 0'.
 Since stratification 1s uncertain In this  case and the predicted average hypolimnion
 thickness, 5.75 m, 1s greater than the mean depth, the latter value  trill  be used.  All
 particles with diameter, d.  such that:
              r—
             V   4.
25 « i-*1	  - 1.86 x 1(T4 en
 3 x 10° (2.66 -  1.0)  •  21.4
 will be completely trapped 1n the Occoquan Reservoir.   Because  this  value  1s  smaller
 than the smallest size calculated for  Lake Jackson  (2  x  10*  cm), our computations
 are simple, we assumed that  84  percent  of the  sediment  1s totally trapped and the
 remainder is trapped at an efficiency  calculated  for particle sizes  of 0.0001 cm:
     v
      max
           .  1-3  x  1C6 (2-66  -  1.) (1  x IP"4)'
           » O.C72

         p «  V* T*  „  0.072  '  21.4   „  Q 29
         f   —tf            ^g        U.M

The annual sediment trapped 1s:

        St ' P ' S1
but corrections for sources and  SDR must be made:
        S^  •  SDR x sediment  from each  source.
        S1  -  13390 (Lake Jackson, already corrected  for SDR)  0.115 (232103)
               (Bull Run) + 0.115 (139685) (Occoquan River)  + 12699 (Urban  Runoff
        S.j  •  68845 metric tons/year
Assuming the distribution of particle sizes for  all  sources  are essentially the
same and accounting for  the fractions (f) of  material  that are  In  the  two different
size ranges:
        S,  -  fj Pj S,  * f2 P2  S<
        St  -  (0.84)  (1.0) (68845)  *  (0.16) (0.29)  (68845)
        St  -  57830 ;  3194 • 61024  metric tons

The volume lost is  ^^   - 65620 m3/year or 0.2 percent per year of the reservoir volume.

5.7.4  Eutrophication
     What  would be  the consequences to eutrophlcatlon  in Occoquan Reservoir of
instituting 90  percent phosphorus removal  at the treatment plant?   If, in addition to
                                         -123-

-------
phosphorus removal, nonpolnt source (NPS) phosphorus was reduced by 90 percent by
Instituting urban runoff and erosion control, green belts, and other NPS controls,
would an Improvement 1n lake quality occur?
     Several  assumptions concerning pollutants 1n the Occoquan watershed-reservoir
system are necessary In order to calculate the desired annual  loads:
        •    The unavailable phosphorus 1s adsorbed on sediment particles.   Therefore,
             of the unavailable forms coming Into Lake Jackson, only  the fraction (1
             - PC [Jackson]} 1s delivered to the Occoquan Reservoir;  available P
             gets through Jackson,
        •    All of the phosphorus and nitrogen from the sewage treatment plants
             (STPs) 1s 1n available form.
        9    The output of STPs outside the Bull Run sub-basin Is negligible compared
             to that of the STPs 1n Bull Run.  This 1s justified by the fact that
             during the period:   under study, the plants In Bull Run  had a  combined
             capacity several  tiees larger than tne few plants outside the  sub-basin.
        •    The problems of eutrophlcatlon depend on loading  of phosphorus.
     By applying these assumptions to the nonpolnt source data 1n Tables V-19
and V-24 the total  load of each pollutant type may be calculated (Table V-25).
The computation for the total  annual  phosphorus load 1n Occoquan Reservoir  1s
computed in the following paragraphs.  First the quantity of total  phosphorus
coming Into the Occoquan Reservoir through Lake Jackson 1s calculated by:
        TP,  . enn - (i - p        ) x [Total P - Available P]  * Available P
          Jacicson         cjackson
The total phosphorus from Broad run, Cedar Run, and Kettle Run are summed and
the available phosphorus loads are subtracted to give the unavailable load.  This
load is multiplied by the trap efficiency of the lake, P  • 0.83, which yields
the unavailable load passing through.  This value, plus the available load, 1s an
estimate of the total  phosphorus entering Occoquan Reservoir from Lake Jackson.   This
quantity is 103.24 metric tons yr"1 (Table V-25).  This value  1s added to the
non-urban, nonpolnt source loads from Bull  Run and areas adjacent to  the Occoquan
Reservoir (Table V-18):
        TNPNU  -  202.71 * 119.42 * 103.24
               • 425.37 metric tons yr"1
This quantity is modified by the sediment delivery ratio.  The urban  nonpolnt
loads and STP (Table V-24) loads are added to complete the calculation:
        TP - (0.115) (425) * 2.59 * 11.92
           • 63.3 metric tons yr
Similarly the SDR was applied to nonpolnt sources of nitrogen  and BOD .  The results
of load calculations are summarized in Table V-25.
     The calculated annual total  phosphorus and nitrogen loads (Table V-25)  may
                                         -124-

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                                       TABLE V-24

                         SEWAGE TREATMENT PUNT POLLUTANT LOADS
                     IN BULL RUN SUB-BASIN IN METRIC TONS PER YEAR*


                     Total  Nitrogen     Total Phosphorus      BOD5
                         108.0
            11.92
                 54.80
                     Source:   Northern Virginia Planning District
                              Commission,  March 1979.
                     'Averages for July 1974 - December 1977	
                                     TABLE  V-25

                CALCULATED ANNUAL  POLLUTANT LOACS  TO  OCCOQUAN  RESERVOIR
Load Source
Urban runoff
Sewage treatment
Rainfall
Other fJonpoint Source*
TOTAL

Total N
12.38
103.00
14.62
391.00
525.50
Metric
Avail. N
5.38
108.00
14.62
39.10
167.10
Tons /Ve»"
Total P
2.59
11.92
-
48.83
63.34

Avail.?
1.27
11.92
-
2.65
15.84

BODc
77.47
54.30
-
802.00
934.27
       Nonpoint Source %
80
35
81
25
                                                                             94
       Point Source *
       Used  SDR  of  0.115.
20
65
19
75
be compared with the observed loads listed in Table V-26.   The loads observed

are 1.5 to 6 times higher than highest calculated loads  for nitrogen.   Compari-

son of loadings (kg/ha year) with literature values suggest that  Grizzard  1s  most
accurate (Likens et^ a_l_.,  1977).

     The first method of  predicting algal  growth  is known  as the  Vollenweider
Relationship.  In the graph of total  phosphorus load (g  nf2 vr"1)  versus mean
                                         -125-

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                                      TABLE  V-26

                OBSERVED ANNUAL POLLUTANT LOADS TO OCCOQUAN RESERVOIR
Mean Flow*
Rate
Period (m3 sec"1 )
10/74
7/75
7/76
- 9/75 24.7
- 6/76 24.0
- 6/77 10.4
Total Nitrogen Load Total Phosphorus Load
(metric tons year ) (metric tons year" )
805* 110b
1905° 188C
4763° 454C
 * Source:  USGS Regional Office, Richmond, Virginia.

 * Grizzard et. a1_., 1977

 e Northern Virginia Planning District Commission, Karch, 1979.
   Data gathered by Occoquan Watershed honitoring Laboratory.
 depth (m)  divided  by  hydraulic  retention  time  (yrs)  (see Figure  V-24), areas can *e
 defined that  roughly  correspond  to  tne  nutritional state of the  Impoundment.  For the
 Occoquan Reservoir, the  values  of the parameters  are:

      Lp . (63.34) x  10s g/yr .  g Q4 g  .-2 yr-l
             7.01 x 106 oi2
     .  S.29 a
     0.0585 yr
                             vr
                             yr
                               -l
     According to the Vollenweider Relationship,  Occoquan  Reservoir is  well  Into  tne
eutrophic region for loading of total  phosphorus.   Based on  these  predictions  a more
in-depth study of the algal  productivity  seems  to  be  in order.
     Solving for the phosphorus concentration in  this  reservoir:
                  1
    Lp
p • —
     z
                             9.04 g m
               P  «  0.0305  g/«» 80.5 ug/1.
     Calculated and observed pollutant concentrations  are list»d  in T»ble  v-?-.
The mean summer concentrations of phosphorus and  nitrogen are  closer to  tfe  concen-
trations calculated tnan would be expected  on the basis  of the comparison  of ar-~'*'
loads.
                                         -126-

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                                    TABLE V-27

                   CALCULATED AND OBSERVED MEAN  ANNUAL POLLUTANT
                        CONCENTRATIONS  IN OCCOQUAN RESERVOIR
                                      Total  b       Available          Total
                                    Nitrogen        Nitrogen        Phosphorus
          	(g m-3)         (g ,-3)	(9  m"3)

           Calculated  (SDR  -  0.115)    0.831           0.264            0.08
           Observed  Values8

               Mean                  0.88            0.16             0.08

               Max.                   1.50            0.24             0.12

               M1n.                   0.35            0.10             0.04
          a Assuming no removal processes for nitrogen.
          b Averages for April-October between 1973 and 1977.
            Source:  Northern Virginia Planning District Conuiission,
                     March, 1979.
      The  ratio of nitrogen to phosphorus concentration 1n the reservoir can be used
 to  estimate which nutrient will limit the rate of plant growth.  For the Occoquan

 Reservoir, the N:P ratios are 10 to 1 for total N to total P.  The calculated nutri-

 ent  ratios and the N:P ratio of the observed data (11.0) Indicates that phosphorus Is
 probably growth limiting.

      The available data also permits the estimation of the maximal primary production

 of algae from the Chiaudani and Vighi Curve (Figure V-26).  The theoretical phosphorus

 concentration should be about 0.08 g m   according to calculations.  The maximal

 primary production of algae is found from Figure V-26 to be about 2500 mgC m"2

day   .  This level of algal  production is roughly the maximum production shown on

the curve.  Both this result and the VoMenweider Relationship suggest algal  growth

will contribute significantly to the BOD load  in the impoundment.

     Effects of 90 percent P removal  at  treatment plant on TP loading:
        M   • 52.61 m ton/yr

        i      52.6!  x 10 n/vr      -, cn     -2  -1
        L   •   ,  ;,,    iJi  7"     /.50gm   y
                7.01  x ltf> m*           y     J

        qs  « 90 m yr"1

Although improved, we conclude that  \oad1ng  1s  still  too great according to Figure
V-24.

     Effects  of 90 percent STP removal of TP plus  90 percent  NPS  removal of TP:


                                         -127-

-------
        M   •  6.334 n ton/yr
                       _ -. Q              A   «
        L   .  6;3r * 'Tg  •  0.90 g m   y

This would move Occoquan Reservoir Into the bottom of the mesotrophlc range.
     Lake concentrations of total  P would be:

          p '  (5.25i7:5i21.2-J  ' 66-9  «/]
                 ,       .,,
              (5.19) •  (21. Z)
                                 8 ug/1
                                   P8/
     Although the screening method shows narked Improvement In Occoquan eutro-
phlcatlon, 90 percent control  of phosphorus UPS would be very expensive.  Careful
analysis of assumptions made 1n the screening method and of control  alternatives
would be necessary before proceeding to map such a control  strategy. Moreover,
careful study of reservoir TP sources and sinks and of algal  productivity would be
necessary.  The screening method has served to Illustrate the feasibility and
potential  value of such further analysis.

5.7.5  Hypolimnetlc DO Depletion
     Excessive nutrient loading plus Inputs of BODs suggest that 00 problems 1n
the hypo 11 ran Ion could result,   we will  use the data obtained  1n the first three
problems to determine the hypolimnetlc  DO.  These data are summarized below.
All rate coefficients listed have already been corrected for  temperature.
Physical /Biological
        Area • 7.01 x 106m2
        Volume • 3.71 x 107m3
        Q • 20.09 m3 sec"1 • 1.74 x 106m3 day"1
        Depth to thermocHne • 5.29 m (average depth)
        Interval of stratification (May to mid-September) « 138 days
        BOD loading • 934.27 106g . yr"1
        Algal loading • 1800 mgCm   day!
        BOD concentration - 934.27 x 10  g/yr          „ Q_069    }
                            3.71 x 10 m  x 365 days/yr
        Temperature • 10*C
Rates and Input Values
        M   •  0.8                         k1     •  0.063 day"1
        S   «  2.67                        k      •  0.0378 day"1
        P   -  0.824 gC m"2 day"1          k4     -  0.0019 day"1
        V   •  5.29 m                      00$at  -  11.3 mg/1
            -  21.4 day                    t      -138
                                         -128-

-------
      The simplified  model  used  to  predict hypoHnmlon dissolved oxygtn  levels  assumes
 that the only  substantial  dissolved oxygen  sinks are Mater column and benthic  deposit
 BOD (Section  5.5).   Additionally,  all  sources of oxygen, photosynthesis, etc., are
 neglected  1n the  hypol1mn1on after the onset of stratification.  Thus, the procedure
 requires that  pre-stratification levels of  BOO and dissolved oxygen be estimated in
 order to compute  the post-stratification rates of oxygen disappearance.  The pre-
 stratification concentration of water  column BOD 1s determined first.  A simple mass
 balance  leads  to  the following  relationship, if steady state conditions are assumed:
where
        GSS   •  steady state concentration of BOD in water column, mg/l~
        k     *  mean rate of BOD loading from all sources g •"  day"
        s    -  •*, • ki  -4
where
        kc   '   vc/^ " mean rate of BOD settling out onto
                                      -1
                impoundment bottom, day
        k,   •   mean rate of decay of water column BOD, day"
                                       31
        Q    •   mean export flow rate, tn  day"
        V    *   impoundment volume, m
        Vs   •   settling velocity, m day"
        7    •   impoundment mean depth, m.
     The BOD load to the impoundment originates in two principal  sources:   algal
growth and tributary loads.  The algal BOD loading rate is computed from the expression:

        ka (algae) ' SMP'7
where
        S  •  stoichiometric  conversion from algal  biomass  as  carbon  to BOD •
              2.67
        M  •  proportion of  algal  biomass expressed  as oxygen  demand
        P  «  algal  primary  production,  g m   day.
     Since the Chiaudani and  Vighi  curve (Figure V-26) gives the  maximal algal  pro-
duction, a correction should  be made for the actual  epilimnion temperature.   If the
maximal  rate occurs  at  30"C and the productivity decreases  by  half for  each  15"C
decrease in  temperature, the  algal  production can be corrected for temperature  using
the expression:

        'IT,' ',30,  »  1.0«7
According to the data  in Table  1, the epilimnion temperature during the month
prior to stratification  is approximately  13°C.   Thus:
        P{13., - (1.8) gC m-2 day"1  x i.^13^30^
               • 0.824 gC m"2 day"1

                                         -129-

-------
 If M 1$ assumed to be 0.8, then:
         k         . 2.67 x 0.8 x 0.824 qC m"2 day'1
          a(algae)
                   « 0.333 g »"3 day'1
 The BOD load bome by tributaries 1s found by the expression:
         k        . Mean Dally BOD fro« Tributaries  (Table  V-18)
          a(tr1b)           Impoundment Volt'
                  . 034.27 x 106 q yr"1     1  yr
                      3.7! , IOV      ' *
                  « 0.069 g m"3 day
 The total  BOO load to Occoquan Reservoir 1s then:
         ka  ' kt<»19««)  * *a  (tr1b)
            « 0.33 9 m"3 day"1  * 0.069 g  »~3 day"1
            • 0.402 g m    day"1
      Before the  water column BOO concentration  can be  computed, the  constants
 comprising  kfa must be evaluated.  The first  of  these,  k$, requires knowledge
 of  the  settling  velocities of BOO particles.  Ideally  these would be determined by
 using values of  the physical properties  of the  particles and the water 1n the settling
 velocity  equation,  V-6.   Because  such data are  lacking, a settling velocity of 0.2 m
 day"  reported for detritus will  be substituted.  The  reported values He between
 0 and 2 meters day   , with most  values close to 0.2 m  day"1 (Z1son et^ al_. ,
 1978).  Then:
        k$  -  0.2 m day"l/5.29 m -0 .0378 day"1
      The  second  constant  comprising k& 1s the first-order decay rate constant for
 water column  BOD.   Reported values of  kj vary widely depending on the degree of waste
 treatement.   21 son  et_ al_. (1978)  presents data for rivers, but contains only two
 values  for  kj  In lakes and estuaries.  Both are kj • 0.2 day"1.  Camp (1968) reports
 values  from  0.01 for  slowly metabolized industrial  wastes to 0.3 for raw sewage.
 Because there  is considerable sewage discharge Into the Occoquan Reservoir,  k.
 may be  assumed to be  1n the upper range of these values, between 0.1  and 0.3 or 0.15
 day"  .  Like  the algal production rate, kj must  be corrected for the  water
 temperature.   In April, the mean water temperature Is about ll'C.
 Then:
        k • 0.095 day"1 x 1.047 (n*c-20'C)
          » 0.063 day"1
Finally, kfa  is evaluated as  follows:
        kb » -0.0378 day"1 - 0.063 day"1 -
           « -0.148 day"1
Next, k  and k  may be substituted Into the following  equation  to  obtain C
                                                                          ss
                                         -130-

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         C   -  -a
          ss    1T
                *
               0.402            -3
      Once  the  water  column BOD concentration  1s  known, the benthic BOD 1s
 computed from  the  expression:

        L»  •  ^
 where
        k.   «  mean  rate of benthic BOD decay, day"
     Values  for the  benthie SOD decay rate constant span a greater range than
 those  for water column BOD.  Camp (1968), however, reports values of k^ very
 near 0.003 day"  for a range of benthic depth from 1.42 to 10.2 cm (Table
 V-10).  Assuming this to be a good value, a temperature-corrected value of k.
 may be  computed at an April hypolimnion temperature of 10°C (Table V-18):
        k4 - 0.003 day"1 x 1.047(10"20) « 0.0019 day"1

               0.0378 day"1 x 2.72 g m"3 x 5.29 m
        Lss "            0.0019 day"1
            -  286 g  m"2
     Prior to  stratification the impoundment 1s assumed to be fully mixed and
 saturated with oxygen.  During April, the hypolimnion temperature is 10°C.  Saturated
 water at this  temperature contains 11.3 ppm oxygen (Table V-12).
     Finally,  the dissolved oxygen level in the hypolimnion may be predicted during
 the period of  stratification.  The applicable expressions are:

                 A      B       C       E  8
        AOL • (1.04)  [(53.1)  (0.231) - (1/53.1)]
        M)L • 12.74

                F    E
        AOC «  (1.7)  (1) - 1.7
         Ot •  11.3 - 12.74 - 1.7

Therefore  the hypolimnion Is  depleted  of oxygen  at  the end  of  the  stratification
period (138 days).   By  selecting  different  conditions  for decay  rates  and  for time  of
stratification  a  family  of  curves  was  generated  that  can  be compared with  actual
observations  (Figure  V-39).   As  car  be seen  situations 3  and  4 (BOD decay  of  0.3
later  corrected for temperature  and  a  total  BOD  loading of  0.36  or 0.57 g  • m
day' ) gave a reasonable fit  of  observed data at the  deepest  station  (Occoquan
Dam, 1973}.
                                         -131-

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                                               o i
                                               o i
                                               0}
                                               03
                                            High Oam (ItfOt
                                            Oceoquan Oam (19/3)
                                                    •	• Calculaftd
                                                    •	• Ohservtd Potnl t
               30       40       M       CO       ?0

                  TIME AFTER SinATIFICATION (DAYS)
FIGURE V-39
DISSOLVED  OXYGEN DEPLETION  VERSUS  TIME  IN THE
OCCOQUAN RESERVOIR
        -132-

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      Interpretation of  the dissolved oxygen-time data at High Dan  1n  1970 presented
 1n  Figure  V-39 1s  complicated by the Introduction of fresh oxygen  after the onset of
 stratification.  Although a direct comparison of oxygen depletion  tines 1s not
 possible,  the  rates of  oxygen level follows curve 2 of Figure V-39 very closely,
 while during the second period of oxygen consumption the oxygen concentrations
 closely match  those of  curve 1.  Since the reservoir 1s shallowest at High Dam and
 the substantially  lower than average flow rate 1n 1970 resulted 1n strongly stratified
 conditions, the oxygen depletion rates 1n this case should be among the highest
 likely to  be observed 1n the Impoundment.  Curve 1 represents the  fastest decay rates
 predicted  by the model.  Thus, the observed oxygen consumption times should be
 greater than the lower limit predicted by the model  1n nearly all  cases.
      The above agreement of the observed with the predicted limits for the range of
 oxygen depletion times in Occoquan Reservoir Implies that the typical  or  average time
 must  also  fall  within the predicted range.   Since 1t was for "average" conditions
 that  the impoundment was modeled, it may be concluded that  the model  does accurately
 describe the behavior of the Occoquan Reservoir.

 5.7.6 Toxicants
      It was not possible to obtain data on  toxicants in  Occoquan Reservoir.   In
 order to provide a problem with  some realism,  published  data  on  a  priority  pollutant
 in another reservoir were obtained.   In Coralville Reservoir, Iowa, commercial
 fishing was banned in 1976 because of excessive  accumulation  of  dleldrln  residues in
 flesh of commercially important  bottom feeding fish  (Schnoor, 1981).   The dieldrln
 arose from biodegraded aldrin, an insecticide  in  wide  use along  with dleldrln  before
 cancellation of registration  of  both pesticides by USEPA in  1975.
     After 1976 there was  steady  diminution  of dieldrin  in the waters,  fish, and
bottom sediments of Coralville Reservoir, until the  late  1970's  when dleldrln  levels
 in fish flesh declined to  less than  0.3 mg/kg  (Food  &  Drug Administration guideline).
 In 1979,  the fishing  ban was  rescinded.
     Using  the  screening methods  and data abstracted from Schnoor's paper, the
potential  dieldrin  problem can be evaluated  in Coralville Reservoir.  Available
and  back-calculated data include  the  following values:
                   Reservoir                    Dleldrln
       Tw   - 14 days  •  336 hrs         kow  •  305000
       1   •   8  feet - 2.4 n          koc  -  35600
        C    - 0.05  ng/1  dieldrin        solubility 1n fresh water » 200
        OC   « 0.05  (estimate)
        So   • 200 jig/1  (estimate)
            -  200  x  10'6  kg/kg
        P   • 0.9 (estimate)

                                        -133-

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      Assuming that  conditions  retained constant, the steady state  concentration
of dleldrln can be  computed using the approach described 1n Section  5.6 as  follows:
where
        C • Cin/  (1 * TW  . k,
        K  •  SED + B + k  + k  + kh
                         V    p    n
     Evaluation of K depends on estimation of the separate rate constants.  Informa-
tion 1n Chapter 2 and 1n Callahan, et^ al_. (1977) Indicate that the blodegradatlon
rate (6) in aquatic systems 1s extremely small. Similarly volatilization (ky) and
hydroloysls (kh) are negligible processes affecting the fate of dleldrln. Photoly-
sis (k ) can be significant In some circumstances but the high turbidity 1n
Coralv1lie Reservoir Indicates that minimal  photolysis takes place.  Consequently, K
» SED.  These assumptions are supported by Schnoor (1961).
     Calculation of the sedimentation rate constant (SED) 1s as follows:
        SED - 4 x D x K
        k   • 0.63 x kow x OC
            - 0.63 x 305000 x 0.05
            • 9610
        D   • P x 50 x ^
        0   - 0.9 x 200 x 10'6 x -33^ •  5.36  x 10'V1
        a   - I/ (1 + kpS)
        S   • OC x 50 • .05 x 200 x 10'6 - 1 x 10"5
        a   • 0.912 x 5.36 x 10'5 x 9610
            • 0.0047 m~l
     The steady state concentration of  dieldrin in Coralvilie Reservoir is  estimated
to be:
        C • 0.05 Kg/1  (1 + (0.0047 hr"1 x 336 hr))
        C • 0.019 ng/1
This value is much greater than the present  fresh water quality criteria of 0.0023
dieldrin ng/1  (Federal  Register:   79318-79379.  Nov.  26,  1980)  and  would indicate  a
serious potential  problem in the reservoir that would  require significant action and
study.
     Evaluation of bioconcentration supports this conclusion:
        Y • BCF x  C
If the default estimate is used (Section 5.6.1.6):
        log BCF - 0.75 log KOW - 0.23
                - 3.88
            BCF • 7642
              Y • 7642 x 0.019 • 145 ng/kg fish flesh
                                         -134-

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This value would be less than the FDA guideline. However, two published BCF values
are available:  35600 from Chapter 2;  70000 from Schnoor (1981).  These values
produce much higher tissue burdens, both of which violate the FDA guideline:
        Y - 35600 x 0.019 • 676
        Y • 70000 x 0.019 • 1330
     In 1979, H 1s estimated that C1n « 0.01 (calculated frow Schnoor, 1981).
Therefore, assuming other conditions are constant:
        C • 0.01/ (1 + (.0047 x 336))
          - 0.0039 ng/1
A value about double the water quality criterion.   Flesh  concentration would be
(using BCF • 70000):
        Y - 70000 x 0.0039 • 270 ng/kg
This value (0.27 Mg/kg)  would be less than  the FDA  guidelines  of 0.3 Kg/kg  and
support the conclusion to 11ft the fishing  ban.  Schnoor  (1981)  shows the  following
measured data that can be compared to the screening  results:
                                1970                     1979

Screening
Measured
Water
0.019
0.015
Fish
1300
1100
Water
0.04
0.005
F1sh
270
250
                                        -135-

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Callahan, M.. M. Slimak. N. Gabel, I. May, C. Fowler. R. Freed, P. Jennings,  R.
     Durfee, F. WMtmore, B. Maestri, W. Mabey, B. Holt, C. Gould.  1979.  Water-
     Related Environmental Fate of 129 Priority Pollutants, Volumes 1  and  2.   U.S.
     Environmental Protection Agency Report.   EPA 440/4-79-029a,  b.  NTIS  Reports:
     PB80 204373, PBBO 204381.

Camp, T.R.  1968.  Water and Its Impurities.   Relnhold Book Corporation. New  York.

Carlson, R.E.  1977.  A Trophic State Index for Lakes.  Llmnol.  Oceanogr.  22:361-369.

Chen, C.W., and G.T. Orlob.  1973.  Ecologlc  Study of Lake Koocanusa L1bby  Oam.   U.S.
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Chiaudanl, G.. and M. V1gh1.  1974.   The N:P  Ration and Tests  with Selenastrum
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Cowen. W.F., and G.F. Lee.  1976.  Phosphorus Availability 1n  Paniculate Materials
     Transported by Urban Runoff.  JWPCF 48:580-591.

Dean, J.D., R.J.M. Hudson, and W.B.  Mills.   1979.   Chesapeake-Sandusky: Non-designated
      208 Screening Methodology Demonstration.  Midwest Research  Institute, Kansas
      City, MO.  U.S. Environmental  Protection Agency Rept.  for Env. Res. Lab,
      Athens, GA.  In Press.

Dillon, P.  1974.  A Manual for Calculating the Capacity of  a  Lake for Develop-
     ment.  Ontario Ministry of the  Environment.

Dillon, P., and F. Rlgler.  1975.  Journal  Fisheries  Research  Board of Canada
     32(9).

Dorich, R.A., D.W. Nelson, and L.E.  Sommers.   1980.  Algal  Availability of  Sediment
     Phosphorus in Drainage Water of the Black Creek  Watershed.  J. Environ. Qual.
     9:557-563.

Drury, O.D., D.B. Porcella, and R.A. Gearheart.  1975.  The Effects of Artificial
     Destratlfication on the Water Quality  and Microbial  Populations of Hyrmn
     Reservoir.  PRJEW011-1.  Utah State University,  Logan,  UT.

Grizzard, T.J., J.P. Hartigan, C.W.  Randall,  J.I.  Kim, A.S.  Librach, and M. Derewlanka.
     1977.  Characterizing Runoff Pollution-Land  Use.   Presented  at  MSDGC-AMSA Workshop,
     Chicago.  VPISU, Blacksburg, VA.  66 pp.

Hudson, R.J.M., and D.B. Porcella,  1980.  Selected Organic  Consent  Decree Chemicals:
     Addendum to Water Quality Assessment,  A  Screening Method  for Non-designated 208
     areas.  U.S. Environmental  Protection  Agency  Rept.  for  Env.  Res. Lab,  Athens,
     &A.  In Press.

Hutchinson, G.E.  1957.   A Treatise  on  Limnology,  Volume I.  John Wiley ft Sons,  New
     York.  1015 pp.

Hydrologic Engineering Center (HEC), Corps of Engineers.  1974.  Water Quality
     for River-Reservoir Systems.  U.S. Army  Corp of  Engineers.

Jones, J.R., and R.W. Bachmann.  1976.   Prediction of Phosphorus  and Chlorophyll
     Levels in Lakes.  JWPCF 48:2176-2182.
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 Larsen, D.P., and K.W.  Malueg.  1981.  Whatever Became of Shagawa Lake?   In:   Inter-
     national Symposium on Inland Waters and Lake Restoration.  U.S. Environmental
     Protection Agency.  Washington, D.C.  p. 67-72.  EPA 440/5-81-010.

 Larsen, D.P., and H.T. Herder.  1976.  Phosphorus Retention Capacity of Lakes.  J.
     Fish.  Res. Board Can. 33:1731-1750.

 Likens, 6.E.  et^ al_.  1977.  B1ogeochem1stry of a Forested Ecosystem. Springer-
     Verlog, New York.  146 pp.

 Llnsley. R.K.. M.A. Kohler, and J.H. Paulhus.  1958.  Hydrology for Engineers.
     McGraw-Hill, New York.

 Lorenzen, M.W.  1978.  Dhosphorus Models and Eutrophication.  In press.

 Lorenzen, M.W.  1980.  Use of Chlorophyll-Secchl Disk Relationships.  Llmnol.
     Oceanogr.  25:371-3727.

 Lorenzen, M.W., and A. Fast.  1976.  A guide to Aeration/Circulation Techniques
     for Lake Management.  For U.S. Environmental Protection Agency, CorvalUs,
     OR.

 Lorenzen, M.W. et^ al_.  1976.  Long-term Phosphorus Model  for Lakes:  Application
     to Lake Washington.  In:  Modeling Biochemical  Processes In Aquatic Ecosystems.
     Ann Arbor Science, Ann Arbor, MI.  pp.  75-91.

 Lund, J.  1971.  Water Treatment and Examination 19:332-358.

 Marsh, P.S.  1975.  Slltatlon Rates and Life Expectancies of Small  Headwater Reser-
     voirs  1n Montana.  Report No. 65, Montana University Joint Water Resources
     Research Center.

 Megard, R.O., J.C. Settles,  H.A. Boyer, and W.S. Combs, Jr.   1980.   Light, Secchl
     Disks, and Trophic States.   Limnol.   Oceanogr.   25:373-377.

 Porcella, D.B., S.A. Peterson, and D.P. Larson.   1980.  An Index to  Evaluate Lake
     Restoration.   Journal  Environmental  Engineering Division ASCE  106:1151-1169.

 Rast, W., and G.F. Lee.   1978.  Summary Analysis of  the North American  (US Portion)
     OECO Eutrophication Project.   U.S. Environmental  Protection Agency, Corvallis,
     OR.  454 pp.   EPA-600/3-78-008.

 Sakamoto, M.  1966.   Archives of Hydrobiology  62:1-28.

 Schnoor, J.L.  1981.  Fate  and Transport  of Oieldrin in Coralville Reservoir:
     Residues in Fish and Water  Following  a Pesticide Ban.   Science  211:804-842.

 Smith,  V.H., and J.  Shapiro.   1981.  Chlorophyll-Phosphorus  Relations  in Individual
     Lakes:   Their Importance to Lake Restoration Strategies.   Env.  Sci.  and Tech.
     15:444-451.

 Stumm,  W.,  and J.J.  Morgan.   1970.   Aquatic Chemistry.  Wiley-Interscience.  New
     York.

 Vollenweider, R.A.   1976.  Advances  in  Defining  Critical  Loading Levels  for  Phosphorus
     in Lake Eutrophication.   Mem.  1st.  Hal.  Idrobiol.   33:53-83.

Vollenweider, R.A.,  and  J.J.  Kerekes.   1981.   Background  and  Summary Results of the
     OECD Cooperative  Program on Eutrophication.   In:  International Symposium  on
     Inland  Waters and Lake Restoration.  U.S. Environmental  Protection Agency,
     Washington, D.C.   p. 25-36.   EPA 440/5-81-010.


                                        -137-

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U.S. Department of Commerce.  1974.  Climatic Atlas of the United States.  U.S.
     Department of Commerce, Environmental  Sciences Services Administration, Environ-
     mental  Data Service, Washington, D.C.

U.S. Environmental  Protection Agency.  1975.   National  Water Quality  Inventory,
     Report  to Congress.   EPA-440/9-7S-014.

Zison,  S.W., W.B. Hills.  D.  Deimer,  and C.W.  Chen.   1978.   Rates,  Constants,  and
     Kinetics Formulations  in Surface Water Quality Hodellng. U.S. Environmental
     Protection Agency, Athens,  GA.   316 pp.   EPA-600/3-78-105.
                                        -138-

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                             GLOSSARY OF TERMS

     Significant variables are shown with typical units.  Units must be compati-
ble or use conversion factors (Chapter 1).  Note that son* symbols are used for
more than one tern.
                                 2                   2
A            Lake surface area. m  - sediment area, •
a            Fraction of pollutant In solution • 1/(1+K  x S)), unltless
B            B1odegradat1on rate, hr"
B(T)         B1odegradat1on rate, corrected for temperature T, hr
BCF          61 oconcent ration factor, unltless
Bo           Initial nricroblal biodegradatlon rate, uncorrected for temperature
               or nutrient concentration, hr
C            Reservoir concentration at time, t, mgl
C            Initial concentration, mgl"
                                              -1
C            Concentration of phosphorus, tigPl
 P                                                                            .3
C            Total exchangeable phosphorus concentration 1n the sediments, g m
 5                                                          .1
C,           Toxicant concentration sorted on sediment, mg 1
 »                                               _i
C.           Concentration of BOD at time t, mg 1
 1                                             _i
C            Concentration in water phase, mg 1
 *                                                                   -1    -3
C            Steady-state water column phosphorus  concentration, mg 1   , gm
C^          Steady state influent concentration,  mg/1
                                               -3
C            Steady-state water column BOD.  g m
C            Weight concentration
 wt
C  ,          Volumetric concentration
D            Depth, m
D            Discharge channel depth, ft
D            Sedimentation rate constant • P x S x Q/V, mg 1   day
D            Dilution rate,  day"1
D1           Flowing layer depth, ft
D"           Inflow channel  depth, ft
U            Mean depth,  m
TT            Depth to thermocline, m
D.            Mean hypolimnion depth, m
Dj            Depth at the 1th cross-section, m
Do           Diffusivity  of  oxygen in water (2.1xlO~9 m2 sec"1, 20*C)
D            Weight density  of a particle, Ib ft"3
                                            33
DW           Weight density  of water, Ib ft" , g cm
DW           Pollutant diffusivity in water, m2  sec"1
d            Number of days  per time period, days
d            Particle diameter, cm
                                         -139-

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f            1 * (TW x K), unltless)
g            Acceleration due to gravity, 32.2 ft sec"
I            Intensity of light at Secchl depth,  relative units
I            Initial Intensity of light at surface,  relative units
K            Pollutant removal  rate, • SED + B +  ky  + kp  + k^,  hr"1
K            Net rate of phosphorus removal, hr"
K.           Specific rate of phosphorus transfer to the  sediments, m yr"
 J                                                                        _i
10           Specific rate of phosphorus transfer from the sediments, m yr
K.           Fraction of total  phosphorus Input to sediment that  1s available
               for the exchange process, unltless
K            Reaeratlon rate, hr"
 a                                       .1
Ka,          Reaeratlon coefficient, m hr
K            Distribution coefficient between organic sediment  and water,
               unitless
K.           First order decay  rate for water column  800  at 20*C, day"
 *                                             ,1
K.           Benthlc BOD decay  rate at 20*C, day
                                                           -3   -1
K            Mean rate of BOD loading from all  sources, g m day
 a                                                     -3-1
K < 1  a )     Al9al  contribution to BOD loading rate,  g •   day
             Tributary or point source contribution to BOD loading rate,
                   •*
               g m  day
 a \ i               •*    ,
 S           --Ks -K1 -d/Tw), day"1
 k            Extinction coefficient, IB"
 e                              _i
 *h           Hydrolysis rate, hr
 k            Photolysis rate, hr'1
 *            Photolysis rate constant uncorrected for depth and turbidity
               of the lake, m"1
 k            Hean rate of BOD settling out onto the impoundment bottom,

               """'
 ky           Volatilization rate, hr
 koc          Organic carbon based partition coefficient,  unltless
 kow          Octanol-water coefficient, unitless
 L            Areal BOD load, gm"2
 L            Phosphorus loading, g m" yr"
 LSS          Steady-state benthic BOD load, g m"2
 H            Total annual  phosphorus loading, g yr
 M            Proportion of algal biomass expressed as an  oxygen demand (unltless)
 HW           Molecular weight, g mole"
 OC           Sediment organic carbon fraction, unltless
^°c          Dissolved oxygen decrease due to hypollmnion BOO,  mg 1
A\          Dissolved oxygen decrease due to benthic demand, mg l"1
                                         -140-

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 0            Dissolved  oxygen  at  time t • 0,  mg l"
 0+           Dissolved  oxygen  at  time t, mg l"
 p            Sediment trapping efficiency,  unltless  1 _>  P _>  0
 P            Primary productivity rate,  g Carbon •  day"
 P            Total  phosphorus  1n  the  water  column, mg m"
 PI            Influent phosphorus,  mg  1
 QI            Mean annual  Inflow,  m yr
 Q            Mean annual  outflow,  •   yr"
 q            Hydraulic  loading  (7/Tw),myr~
 R            Reynolds number,  unltless
 r            Radius, ft
 S            Sto1ch1ometr1c conversion  from algal blomass as carbon to BOD,
              2.67,  unltless
 S            Input  suspended organic  sediment •  OC x So, mg 1
 S,            Mass of sediment  In Inflow  per unit time, mg l"
  1                                            _i
 SQ            Input  of suspended sediment, mg 1
 S             Sediment trapped, metric tons yr"
 SO            Secchl depth, m
 SDR           Sediment delivery ratio, unltless
 SED           Sorptlon and sedimentation  rate (toxicant at equilibrium with
              sediments), hr
 T             Temperature, degrees centrlgrade
 V             Lake or impoundment volume, m
 Vu            Hypolimnlon  volume, 1
                               3
 V             Sediment volume, m
  5                                                             1
 Vmmw          Terminal velocity of a spherical  particle, ft sec
 TTiaX                           «
W            Wind speed, m sec"
 Y             Tissue concentration of pollutant,  g kg"1 fish flesh
 y             Number of years
 Z             Depth, m
 7            Mean depth, m
 n             Absolute vlscosdty of water, Ib  sec ft"2,  g sec on"2
 P            Mass density of a  particle, slugs ft
                                            _3
 pw           Mass density of water, slugs ft
T            Mean hydraulic residence time (V/Q), days
                                        -141-

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                                        CHAPTER 6
                                        ESTUARIES

6.1  INTRODUCTION

6.1.1  General
     Estuaries are of primary social, economic, and ecologic importance to America.
Forty-three of 110 of the Department of Commerce's Standard Metropolitan Statistical
Areas are or estuaries (DeFalco, 1967).  Estuaries are the terminal or transfer point
for essentially all waterborne national and international commerce in this country,
and biologically are more productive on a mass per unit area basis than any other
type of water body.  Essentially all conservative wastes and much of the nonconserv-
ative wastes discharged into any inland stream in America eventually pass into an
estuary.  Yet these coastal formations on which there is such a demand for services
are less stable geologically than any other formation found on the continent (Schubel,
1971).   Sedimentation processes, for example, are filling, destroying, or at least
altering all estuaries.  While this process is always rapid in a geological sense,
the actual length of time reouired for complete estuarlne sedimentation is a function
primarily of the stability of the sea level, the rate of sediment influx, and the
intra-estuarine circulation pattern (Schubel, 1971).   The instability, variation, and
complexity of estuaries make water quality assessment and prediction especially
difficult, yet the demands placed on estuaries require a most active water quality
management program.
     This chapter will describe a systematic approach which may be used to provide
estuarine water quality assessment and prediction.  Its purpose is two-fold.  First,
the planner wi11 be provided the capability of making elementary assessments of
current estuarine water quality.  Second, methodologies are presented by which the
planner can evaluate changes in water quality which might result from future changes
in waste loading.
     Chapter 3 provided methodologies for assessing the waste load directly entering
an estuary.  Chapter 4 provided methodologies which can be used to assess the water
quality of a river or stream as it enters an estuary.  The output of these chapters
will provide information about present and projected  estuarine water quality which
can be  used to identify regions having greatest water quality problems, water quality
parameters of special concern, and areas for which subsequent computer study is nec-
essary.  Methods presented below comprise a screening tool which may be used by the
planner to focus attention on critical spatial regions and water Quality parameters.
These can then be fully assessed using computer models or other techniques, as
desired.
                                         -142-

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6.1.2  Estuarine Definition
      It  1$ difficult to provide a concise, comprehensive definition of  an  estuary.
The basic elements included In most current definitions are that an estuary  is:
         o    A semi-enclosed coastal body of water
         o    Freely connected to the open sea
         o    Influenced by tidal action
         o    A water body In which sea water 1s measurably diluted with fresh
             water derived from land drainage (Prltchard, 1967; Pritchard  and
             Schubel, 1971).
     The seaward end of an estuary is established by the requirement that  an estuary
be semi-enclosed.  Because this boundary 1s normally defined by physical land features,
it can be specifically identified.   The landward boundary 1s not as easily defined,
however.  Generally tidal influence in a river system extends further Inland than
does salt intrusion.  Thus the estuary is limited by the requirement that both salt
and fresh water be measurably present.  Accordingly, the landward boundary may be
defined  as the furthest measurable  inland penetration of sea salts.  The location of
this inland boundary will vary susbstantial1y from season to season as a function of
stream flows and stream velocities  and may be many miles upstream from the estuarine
mouth (e.g., approximately 40 miles upstream on the Potomac River, 27 miles on the
James River, and approximately 16 miles upstream for the small Alsea Estuary in
Oregon)  (Pritchard, 1971).   This definition also separates estuaries from coastal
bays (embayments) by the requirement for a fresh water Inflow and measurable sea
water dilution.

6.1.3  Types of Estuaries
     While the above definition provides adequate criteria for segregating estuaries
from other major types of water bodies, it does not provide a means to separate the
various types of estuaries  from one another.   The variations in estuarine circulation
patterns and resulting variations in pollution dispersion from estuary to estuary
make classification a necessary part of any water quality assessment.   Two basic
estuarine classification systems have been used in recent years to accomplish
estuarine subclass separation:   a topographical  system and a physical  processes
system (Dyer, 1973, Chapter 2  or Ippen, 1966, Chapter 10).

6.1.3.1  Topographical Classification
     Under a topographical  system,  estuaries  are divided into four subclasses.
These are briefly described below.
             •    Drowned River Valley  (Coastal Plain Estuary).  These estuaries  are
                 the result of a recent (within  the  last 10,000 years)  sea  level rise
                                         -143-

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             which has kept ahead of sedimentation processes at a river's mouth.
             Such estuaries are, quite literally, rivers whose lower basins have been
             drowned by the rising oceans.  Coastal plain estuaries are characteris-
             tically broad, relatively shallow estuaries (rarely over 30 m deep) with
             extensive layers of recent sediment.
        •    Fjord-Uke Estuaries.  These estuaries are usually glacial ly formed and
             are extremely deep (up to BOO «) with shallow sills at the estuarine
             mouth.   Fjord-like estuaries are restricted to high latitude mountainous
             regions and are not found in the United States outside of Alaska and
             Puget Sound in the state of Washington.
        0    Bar-built Estuaries.  When offshore barrier sand islands build above sea
             level and form a chain between headlands broken by one or more inlets, e
             bar-built estuary is formed.  These estuaries are characteristically
             very shallow, elongated, parallel to the coast, and frequently are fed
             by more than one river system.  As a result bar-built estuaries are
             usually very complex hydrodynamically.  A number of examples of bar-built
             estuaries can be found along the southeast coast of the United States.
        •    Tectonic Process Estuaries.   Tectonic estuaries exist as the result of
             major tectonic events (movement of tectonic plates with associated
             faulting or subsidence and coastal volcanic activity).   San Francisco
             Bay 1s  a good example of an  American estuary of this  type.
Based on this topographic classification system, the vast majority of American
estuaries fall into  the drowned river class.  As a result, this system is not
functional for categorization of American estuaries.  The classification system
described below is based on physical  processes and is more useful.  Further, the
parameters used in physical classification are directly applicable to estuarine
pollution analysis.   Consequently, a  physical parameter classification system will  be
used for the water quality assessment approach to be presented.

6.1.3.2  Physical Process Classification
     Physical process classification  systems are generally based on the velocity
and salinity patterns in an estuary.   Using these two parameters,  estuaries can
be divided into three classes, each of which is of potential importance to planners
concerned with American coastal plain estuaries.  The classes are:  stratified,
partial 1y mixed, and well mixed.
     The general behavior of salinity and velocity regimes  in the three types
of estuaries has been described by a number of researchers  (Glenne, 1967, Ouxbury,
1970, Pritchard, I960, and Dyer, 1973, among others) and is summarized below:
        t    Stratified (Salt Wedge)  Estuary.  In this type of estuary, large
             fresh water inflows ride over a salt water  layer which intrudes landward
                                         -144-

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              along the estuary bottom.   Generally there is a continuous inland flow
              1n the salt water layer as some of this salt  water is entrained into the
              upper seaward-moving  fresh water flow.   Tidal action is not sufficient
              to mix the separate layers.   Salinity (S)  and Velocity (U) profiles and
              a longitudinal  schematic  of  this flow pattern are shown in Figure VI-1.
              The Mississippi  River Estuary is usually a salt  wedge estuary.
         •    Well Mixed.  In  a well  mixed estuary, the  tidal  flow (or the  tidal
              prism*)  is much  greater than the river  outflow.   Tidal  mixing forces
              create a vertically well mixed water column with flow reversing from ebb
              to flood at all  depths.  Typical  salinity  and velocity profiles and a
              longitudinal  flow schematic  for a well  mixed  estuary are shown  in Figure
              VI-2.   As examples, the Delaware and Raritan  River estuaries  are both
              normally wel1 mixed.
         •    Partially Mixed.   Partially  mixed estuaries lie  between stratified
              and well mixed  in terms of flow and  stratification characteristics.
              Tide-related  flows  in such estuaries are substantially greater  than
              river  flows.  Significant  salinity gradients  exist as in fully  strati-
              fied estuaries,  but are much less steep.   While  velocity at all depths
              normally reverses with  ebb and flood  tide  stages,  it  is  possible for net
              inland flow to be maintained in  the  lowest  layers.   Typical salinity and
              velocity profiles and  a longitudinal  schematic flow diagram are shown in
              Figure VI-3.  There are many partially  mixed  coastal  plain estuaries in
              the  United  States; the  lower James River Estuary is  typical.
      Classification primarily  depends on  the  river discharge  at  the  time of  classi-
 fication.   Large  river flows result  in  more stratified  estuaries  while  low flow
 conditions  in  the same  estuaries can lead  to  full  mixing.  Thus  the  classification of
 any  single  estuary  is  likely to vary from season  to  season as river  flows  vary.   As
 examples, many  West Coast  estuaries  are partially  mixed  in winter  when  river  flows
 are  high  and  are  well  mixed in summer when  river  flows  are very  low.

6.1.4  Pollutant Flow  in an Estuary
     The  importance of understanding the basic types of estuarine systems may
be appreciated by briefly reviewing the general advective movements of a pollutant
released  Into each of the three types of estuaries (summarized from Prltchard, 1960).
The associated spatial and temporal variability of pollutant  levels have water system
management as well as  water quality implications.
     If a pollutant  flow of density greater than the  receiving water column is
introduced into a salt wedge  type estuary, the pollutant tends to sink into the
•The tidal prism is that volume of water which enters an estuary during an
 incoming (flood) tide and equals high tide estuarine volume minus low tide volume.
                                         -145-

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               SURFACE
               BOTTOM
                                  VELOCITY
                                  	0	
SALINITY
                          corr«i*o*« to creti ttctiofit
            FIGURE  VI-1   TYPICAL MAIN CHANNEL  SALINITY AND VELOCITY
                            FOR  STRATIFIED  ESTUARIES
bottom salt water  layer  and  a portion can be advectively carried Inland toward
the head of the estuary.   Frictlonally  Induced vertical entrainment of the pollutant
into the surface water flow  is  slow, residence time of the pollutant is high,  and the
time required to flush the pollutant from the estuary is also high.  Some pollutants
which are sufficiently dense and stable remain in or settle to the bottom layer of
water, and are not  transported  out of a salt wedge estuary.  Such constituents bu^d
up in the estuarine sediment layer.
     Conversely, if a pollutant of lower density than the receiving water column is
introduced into a  salt wedge estuary, it remains 1n the surface layer and is  readily
                                        -146-

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                                 vELOcrrr
                                     o	
il
SALINITY
             SURFACE
             BOTTOM
                             C,0
                   •L»tt«ri correspond to crt«nn«l cross-icctions.
          FIGURE  VI-2   TYPICAL MAIN CHANNEL  SALINITY  AND VELOCITY
                         PROFILES  FOR WELL NIXED ESTUARIES
flushed from the  system.  This  is the case because seaward flows strongly  predominate
in this layer.
     At the opposite  end of the estuary classification scale, a pollutant  introduced
into a well mixed  estuary is advectively transported in a manner independent  of  the
pollutant's density.   Tidal forces cause turbulent vertical  and lateral  mixing.   The
pollutant  is carried  back and forth with the oscillatory motion of  the tides  and is
slowly carried  seaward with the net flow.
     Pollutants introduced  into partially mixed estuaries are dispersed  in a  manner
                                        -147-

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                               	JL --:
                                                         SAUNITY
                             ch«nn«l
           FIGURE VI-3   TYPICAL MAIN  CHANNEL SALINITY AND VELOCITY
                          PROFILES FOR  PARTIALLY MIXED ESTUARIES
intermediate between the  transport patterns exhibited in well mixed  and stratified
estuaries.  Pollutant transport is density dependent but nevertheless  Involves
considerable vertical mixing.  Eventual flushing of the pollutant  from an estuary in
this case depends on the  relative magnitudes of the net river outflow  and the tidal
seawater  inflow.
                                       -148-

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6,1,5  Estuarine Complexity and Major Forces
     Before outlining the complexities of estuarine systems, a brief review of
the nomenclature used in this chapter will be helpful.  This information 1s shown in
Figure Vl-4.  This figure shows top, side, and cross sectional  views of an estuary
and indicates the basic estuarine dimensions.  Additionally, the relationship between
tidal elevation (or tidal stage) and surface water velocity 1s  shown 1n the upper
right quadrant of Figure Vl-4.
     The complexities of estuarine hydrodynamics are evident from even the brief
qualitative descriptions presented above.  Many variations in flow pattern and many
of the forces acting on an estuarine water column have beer omitted In order to
permit a verbal description of the normally predominant phenomena, and it should be
understood that the descriptions do not fully account for the complexities of estuarine
motion.  Estuarine circulation may be conceived as a thre^-dimenslcnal flow field
with variations possible in salinity and velocity along the longitudinal, the vertical,
and the lateral axes.  As a result of this complexity, and because an estuary 1s a
transitional zone between fresh water and marine systems, great variations in a
number of  major water quality and physical parameters are possible.  For example:
        •     £H.   Typical  concern pH is 7.8 to 8.4.   Typically, rivers are slightly
             acidic (pH<7).   Thus the pH can change from slightly acidic to basic
             across an estuary with resulting major changes in  chemical characteris-
             tics of dissolved and suspended constituents.  pH  variations from 6.8 to
             9.25 across an  estuary have been recorded (Perkins,  1974, p.  29).
        •     Salinity.  Over the length of an estuary, salinity varies from fresh
             water levels  (typically less than 1 ppt)  to oceanic  salinity levels
             (usually 32 ppt to 34 ppt)*.   Moreover,  salinity at  any given location
             in an estuary may vary substantially over one tidal  cycle and over the
             depth of the  water column at any single  point in time.   Salinity varia-
             tions are especially significant  in estuarine calculations for a variety
             of reasons.   First,  salinity distribution can be used to predict the
             distribution  of pollutants;  second, salinity is  a  prime determinant of
             water density;  and third,  variations  in  salinity affect other major
             water quality parameters.   For  example,  the saturated dissolved  oxygen
             concentration normally diminishes by  2 mg/1  as  salinity increases  from
             0 to 35 ppt.
        •     River Flow.   River flow is  a major determinant of  estuarine  circulation
             and  flushing  characteristics.   Instantaneous flow  rates for  some western
             rivers vary by  orders of  magnitude from  winter high  flow  to  summer low
             flow periods  (Goodwin, Q _a_K,  1970).  These differences  In  river  flow
             result in major variations  in estuarine  water quality characteristics.
*ppt represents parts per thousand by mass.   Sometimes the symbol  °/oo is used.

                                        -149-

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TOP VIEW
                                 Lint
SIDE VIEW

 V	
Meon High Tide (MHT)
M«on Low Tidt (MLT)
                                -Low Tide Volumt
                 ESTUARY LENGTH	__ \

CROSS SECTIONAL VIEW
         -Tidol Prism
 VMHT //-LowTidtVolumi
TIDE
HEIGHT
                                                       11* ••» — jfc.ii •-> '*•'-*> ".•*
                  FIGURE VM  ESTUARINE DIMENSIONAL DEFINITION
                                        -150-

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        •    Time.  Estuarine water quality parameters vary over several separate
             time scales.  First, variations occur with each tidal cycle over a
             period of hours.  Second, tidal cycles vary in mean amplitude from
             spring (maximum amplitude) to neap tides (minimum amplitude) every two
             weeks.  This affects water quality since flushing characteristics are in
             part dependent on the tidal prism which is, in turn, dependent on tide
             stage.  Third, there are seasonal variations in river flow, temperature
             and waste loadings.
     The four factors just listed affecting the range and rate of variation of
estuarine parameters pose part of the difficulty in analyzing estuarine water
quality.  In order to avoid large errors, both small time increments and small
spatial increments must be used.  This, in turn, necessitates a large number of
individual calculations to fully analyze the variation of even a single parameter
over the estuary and sometimes requires the use of a computer model.
     Further complicating the analytical process is the large number of independent
forces acting on the estuarine water column which should be considered.  This group
includes (from Harleman and Lee, 1969):
        •    Ocean tides
        •    Local wind stresses
        •    Bottom roughness and bottom sediment types
        •    Channel geometry
        •    Coriolis forces*
        •    Nearby coastal features and coastal processes.

6.1.6  Methodology Summary
     A variety of techniques are presented in this chapter to assess water quality in
estuaries.  Table Vl-1 summarizes the techniques and indicates if they are applicable
to one-dimensional (well-mixed) or two-dimensional (vertically stratified)  estuaries.
Many of the techniques can be applied to conventional or toxic pollutants.   If decay
rates for toxic pollutants are needed. Chapter 2 can be used.
     It is redundant to describe in detail each method at this point in the chapter,
because the procedures are presented  later.  As a general statement, however, most of
the methods for prediction of water quality apply to continuous, steady-state dis-
charges of pollutants.  The discharges can be located anywhere within the estuary,
*Cor1olis forces reflect the effect of a rotating reference plane (the earth) on
 particle motion.  The net effect is to cause a water flow to drift to one side as 1t
 moves down a channel.  The same effect tends to laterally segregate fresh water
 flows (moving from head to mouth) and salt water inflows '.moving from mouth to head)
 in an estuary and in the northern hemisphere to create a counterclockwise flow
 pattern with fresh water to the right (looking from the head of the estuary toward
 the mouth) flowing toward the sea and salt water on the left flowing toward the head
 of the estuary.
                                         -151-

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                                              TABLE VI-1
                 SUMMARY OF METHODOLOGY  FOR  ESTUARINE  WATER QUALITY  ASSESSMENT
      Calculations
                   Methods
Type of Estuary Applicable*
 Estuarine  Classification
 Flushing  Time
 Pollutant  Distribution
 Thermal Pollution
 Turbidity
 Sedimentation
 • Hansen and Rattray
 • Flow ratio
 • Fraction of freshwater
 • Modified tidal  prisai
 • Fraction of+freshwat«r (conservative
  pollutants)
 • Modified tidal  prisai (conservative  or
  first-order decay pollutants)'
 • Olspersion-advectlon equations
  (conservative.first-order decay pollutants,
  and dissolved oxygen)
 • Pritchard's^Box Model  (conservative
  pollutants)*
 • Initial  dilution
 • Pollutant concentration at completion
  of initial  dilution (conservative
  pollutants/ DH.  dissolved oxygen)
• Farfield distribution  (Conservative and
  first-order pollutants,  tnd dissolved
  oxygen)
• AT of water passing through condenser
• Maximum  discharge temperature
• Thermal  block, criterion
 • Surface  area criterion
• Surface  temperature criterion
• Turbidity at completion of Initial
  dilution
• Suspended solids  at the completion  of
  initial  dilution
• Light attenuation and  turbidity
  relationship
 • Seechi disk and turbidity relationship
• Description of  sediment movement
 • Settling velocity determination
• Null  zone calculations
 one- or two-dimensional
 one- or two-dimensional
 one-dimensional
 one-dimensional

 one-dimensional

 one-dimensional

 one-dimensional

 two-dimensional
 one- or two-dimensional

 one- or two-dimensional

 two-dimensional
 not applicable
 not applicable
 one- or two-dimensional
 one- or two-dimensional
 one- or two-dimensional

 one- or two-dimensional

 one- or two-dimensional

 one- or two-dimensional
 one- or two-dimensional
 one- or two-dimensional
 one- or two-dimensional
 two-dimensional
•One c.mensiona!  means  a  vertically well mixed system.  A two dimensional estuary is vertically stratified.
 These  wethods apply  to either conventional or toxic pollutants.
                                                  -152-

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from head to mouth.  Multiple  sources  of  pollutants  can  be  analyzed  by applying  the
method of superposition, which  is  illustrated  subsequently.
     Although no  single sequence of calculations must be followed  to use  the  method-
ology. Figure VI-5  shows a  suggested procedure.  It  1s often  useful  to  begin  by
classifying the estuary by  season  to find out  when it 1s  well mixed  and when  it  is
stratified.  If the estuary is  never well mixed, then the tools  listed  in Table  VI-1
pertaining to one-dimensional estuaries should not be used.
     Users are cautioned that the methods in this chapter are of a simplified
nature, and consequently there  are errors inherent in the calculations.   Additionally,
inappropriate data can produce  further systematic errors.  Data  used  should be
appropriate for the period  being studied.  For example,  when  salinity profiles are
needed, they should correspond  to  steady  flow  periods close to the critical period
being analyzed.
     Even though  the methods presented in this chapter are amenable  to  hand calcula-
tions, some methods are more difficult to apply than others.  The fraction of fresh-
water and modified tidal prism methods are relatively easy to apply,  while the
advective-dispersion equations  offer greater computational challenge.   Since  the
advective-dispersion equations  require numerous calculations, the user might  find 1t
advantageous to program the methods on a  hand calculator  (e.g. TI-59  or HP-41C).

6.1.7  Present Water-Quality Assessment
     The first step in the  estuarine water quality assessment should  be the evaluation
of existing water quality.   Before an analysis of the impact of future waste  load
changes is made, the planner should know whether or not  current estuarine water
quality is acceptable, marginal, or substandard.
     By far the best way to assess existing water quality is to measure it.  The
planner should attempt to locate other agencies which might have already collected
acceptable samples and/or data.  Candidate organizations include the United States
Geologic Survey, the U.S.  Army Corps of Engineers,  state water quality control and
monitoring agencies, and engineering and oceanographic departments of local colleges
and universities.   If such  data cannot be located,  a data collection program could be
undertaken.   If at all possible, high tide,  and especially low tide in-situ measure-
ments and samples should be collected along  the full  length of the estuary's main
channel  and  in all significant  side embavments.  Analyses should then be made in an
appropriate laboratory facility.  If funds for such data collection efforts are not
available, the use of a mathematical  estimation of  existing  water quality is an
alternative.   The methods  presented in subsequent sections and applied to the exist-
ing discharges can be used.   However,  it  should be  remembered  that  actual data are
preferable to a mathematical estimate of  existing water  quality.
                                         -153-

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                  U.11II'' Cl'V
               £«y*ri«Mt uoMOvtnvt
                 TOIIC 1XX.HtMiTI H
                  • lIMtrt* «I'M«'
                                           -^/£it^,
                                             V Siuii'iu
                                              IJUIXM1I*!
                                              iMi UtIM SlTCMU'l
                                                   [  \f» «• fetfiilM  A
                                                   V   t4tC4*»fiMt   )
\
P
C^lflCAv **|«t *••
^
	 ' ^

•two*

FIGURE  VI-5   SUGGESTED PROCEDURE  TO  PREDICT  ESTUARJNE  WATER  QUALITY
                                       -154-

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6.2   ESTUARINE  CLASSIFICATION

6.2.1   General
      Section 6.1.7 discussed making  a first estimate of current  estuarine  water
quality.   This  section begins  a calculation methodology designed to  look at  the
effect  of  future  changes  in waste  loading patterns.
      The goal of  the classifications process presented below  is  to predict the
applicability of  the hand calculations to be presented.  The  classification
process  is  normally the first  step to be taken  in the calculation procedure
since  it reveals  which techniques can be applied.

6.2.2   Classification Methodology
     The classification system recommended for  purposes of hand calculations  is
based on salinity and velocity profiles within  the estuary.   As both of these
parameters  vary seasonally and spatially for each estuary, their use will  result  in  a
range of values rather than in one single classification number.  The following
section will describe in detail the procedure for use of this system, and  show
examples of the procedure.

6.2.3   Calculation Procedure
     Hansen and Rattray (1966) developed an estuarine classification system  using
both salinity stratification and water circulation patterns (based on water  column
velocities).  This procedure involves the calculation of values for two parameters at
various points along the main estuarine channel and the plotting of these  intersec-
tions on the graph shown in Figure VI-6.  Figure VI-7 shows plots made by Hansen  and
Rattray for various estuaries at a single point in time.   It  should be noted that
each estuary is not represented by a point but by a line connecting the points
calculated  for the mouth and head areas.
     The area designations (e.g. la, Ib, 2b) on Figure VI-6 were related by Hansen
and Rattray to previously used classification titles (e.g. stratified, well mixed).
In general, area  la corresponds to well  mixed estuaries.   Area Ib has the water
circulation pattern of a well  mixed estuary yet shows increased stratification.
Areas 2 and 3 correspond to the "partially  mixed" class  of estuaries  with area 3
showing more significant vertical  circulation within the  estuary.  Designations  2a/b
and 3a/b, as was true of la and Ib, indicate increasing  degrees of  vertical strati-
fication.  Type 3b includes fjord-type estuaries.   Area  4 represents  highly stratified
salt wedge estuaries.
                                         -155-

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      Increasing longitudinal circulation
     to
                                                               A
                                                          10
FIGURE  VI-6   ESTUARINE CIRCULATION-STRATIFICATION DIAGRAM
         {Station  code: M, Mississippi River mouth; C, Columbia
         River estuary; J. James  River estuary;  MM, Narrows of
         the Mersey estuary; OF,  Strait of Juan  de Fuca; S,
         Silver Bay. Subscripts h and 1 refer to high and low
         river discharge; numbers indicate distance (in miles)
         from mouth of the James  River estuary,

FIGURE  VI-7   EXAMPLES OF ESTUARINE  CLASSIFICATION PLOTS

               (FROM  HANSEN AND RATTRAY,  1966)
                              -156-

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   6.2.A  Stratification-Circulation Diagram  Interpretation
        The closer an estuary falls to the lower  left hand corner of a stratification-
   circulation diagram, the more vertically and laterally homogeneous It  1s.  On the
   stratification-circulation diagram (Figure VI-6), two types of zonal demarcation can
   be seen.  First are the diagonally striped divisions between adjacent  estuarine
   classifications used by Kansen and Rattray to  indicate a transitional  zone between
   separate classifications.  The second is a wide solid band arching around the lower
   left corner of the diagram.  Estuaries falling primarily Inside of this band (to the
   lower left of the band) are those for which the one dimensional calculation methods
   may be applied to obtain reasonably accurate results.  If an estuary falls outside of
   this band, the planner should use only the methods presented which pertain to strati-
   fied estuaries, or use computer analyses.   Within the band 1s a borderline of marginal
   zone.  Calculations for one-dimensional  estuaries can be used for estuaries falling
   principally within this zone, however the  accuracy of the calculations  will be
   uncertain.
        The two parameters used with the stratification-circulation diagram are described
   below:
        a.    Stratification Parameter:   The stratification parameter Is  defined as:

                                                          AS
                               Stratification Parameter = »-                     (VI-1)
                                                           o
           where
               &S  •  time averaged difference in salinity  between  surface and  bottom
                       water  I
                S   «  cross-section mean salinity,  ppt.
   The diagrammatic relationship of these values 1s  shown  in Figure VI-8.
   b.   Circulation Parameter:   The circulation parameter  is defined as:
                                                  Us
                           Circulation Parameter - —                      (VI-2)
                                                  uf
   where
        Us  •   net  non-tidal  sectional  surface velocity  (surface  velocity
               through  the  section  averaged  over a tidal cycle) measured  in
               ft/sec.   See Figure  VI-8 for  a  diagrammatic  representation  of
               V
        Uf.  «   mean fresh water  velocity through the  section,  ft/sec.
In equation  form:
                                           -157-

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CIRCULATION PARA
Velocity *
4 ?


MtTtR

• v

ftmT Tfffc*
STRATIFICATION
Salinity *
y AS ^
1 K 7
N
f. . *• \ V
PARAMETER

-4

!
i
                 °f A
 *6oth velocity and salinity  values  for these profiles are averaged over a tidal cycle
  (net velocity and salinity)  rather than being Instantaneous values.  Of the two the
  stratification parameter  is  much less sensitive to variations over a tidal cycle and
  can be approximated  by mean  tide values for salinity.  Surface velocity (Us) must be
  averaged over a tidal  cycle.

  FIGURE  VI-8   CIRCULATION AND STRATIFICATION  PARAMETER  DIAGRAM
        where
             R  »  fresh water  (river)  inflow  rate,  ft /sec
             A  '  cross-sectional  area of  the estuary through the point being
                   used to calculate  the  circulation  pattern and stratification
                   parameters based on  a  mean  tide  surface elevation, ft .
     If good cross-sectiona)  area data  are  not  available, cross-sectional profiles
can be approximated from the U.S. Geological Survey  (USGS) coastal series topographical
maps, or, more recently, from NOAA  National Ocean Survey charts.  The circulation and
stratification parameters should be plotted for  high  and low river flow periods and
for stations near the  mouth and head  of the estuary.  The area enclosed by these four
points should then include the  full range of possible instantaneous estuary hydro-
dynamic characteristics.  In  interpreting the  significance of this plotted atea, by.
far the greater weight should be given  to the  low river flow periods as these periods
are associated with the poorest pollutant flushing characteristics and the lowest
estuarine water quality.  The  interpretation of  the  circulation-stratification
diagrams will be explained more fully after an example of parameter computation.
                                        -158-

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                                  EXAMPLE VI-1
         Calculation of Stratification and Circulation Parameters

     The estuary for this example 1s the Stuart Estuary which is shown in Figure
VI-9.  The estuary is 64,000 feet long, is located on the U.S. west coast, and is
fed by the Scott River.  Two stations were selected for parameter calculation (A
and B) with station A located on the southern edge of the main channel 6,500 feet
from the estuary's mouth and station B in center channel 47,500 feet from the
mouth (16,500 feet from the head of the estuary).
     Necessary salinity data were obtained from the coastal engineering department
of a nearby university.  USGS gage data were available for river flow, and, as a
result of Its own dredging program, the local district office of the U.S.   Corps
of Engineers could provide cross-sectional  profiles 1n the approximate areas of
both stations.  The cross-sections are labeled (1) and (2) on Figure VI-9.  The
mean low tide depth reading on NOAA Coastal charts was used to verify Corps data.
Current meters were tied to buoy channel  markers at A and B to provide velocity
data.  The information obtained from these various sources is shown 1n graphical
form in Figure VI-10.
   The calculations proceed as follows:
   a.  Stratification Parameter:
                                                 STATION
AS
bottom  " surface
33 - 30 _
\\ e w .u«

31.5 - 24.2 _
27.8 ^
14.5 - 10.5 . „
TV K " "*

4 - 2A - 5B
3.25 ^°
SUMMER


WINTER

    Circulation Parameter:
    1.   Calculate A.'s  using cross  sectional  information on Figure VI-10:
                                                                             I
        Afl «  (630 ft)  (20 ft)  (1/2) *  (630 ft)  (20 ft) +  (1590 ft)  (20 ft)  (1/2)     |
          «  34,800 ft                                                               j
        Ab -  (2580 ft)  (16 ft)  (1/2) +  (1720 ft)  (16 ft)  (1/2)
          «  34,400 ft                                                               I
        For most cross-sections  it  is  advisable to use more finely  divided           j
        segments than  in the simple example above In order to reduce the error       I
        associated with this approximation.  The method for this calculation,        i
                                      -159-

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          OCEAN
                           FIGURE VI-9   THE STUART  ESTUARY
!       however,  1s  Identical regardless of the number of regular segments
I       used.
I   2.   Calculate Uf's  (with R and A1 values obtained from Figure VI-10):

!                                       STATION
I
;                           A                              B
R
*1

550 ft3/sec ,_ , SB , iff2ft/-cr

3.48 x 10'ft"
1800 ft3/ sec . , .. j0-2ft,MC

3.48 x lO'ft^
550 ft3/sec . . ,0 10-3ft/

3.44 x l(Tft"
1800 ft3/sec . f „, 10-2f

3.44 x 10 ff
SUMMER
WINTER
   3.  Calculate  i 's:
                 Uf
       U$ values are read  fro*  Figure VI-10.  The precise value for
       U$ 1s the Integral  of  the  velocity curve (area under "ebb"
       velocity curve minus the area under the "flood" velocity curve)
       divided by the elapsed time period (length of one tidal cycle).
       If the elapsed time for  flood flow at a station Is only slightly
       below the elapsed  time for ebb flow U  may be approximated as
       (L)ebb(max) ' uflood(max)
                                        -160-

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           S(%.) AT MEAN TIDE
      Swrfi
       Bottom
                                           2000
                                                J  F  MAMJUlASlO
                               N  0
                                               MONTHS

                                               • Monthly *»»rog< Dtsctwry* ftotw
         Flood
        U«   0
      (FT/SEC)
                                     WINTER  ,
                         SUMMER
          ebb
        CROSS SECTION OF A
CROSS SECTION OF.




S              4300'
                                         F
                               1
I    FIGURE VI-10  STUART ESTUARY DATA  FOR CLASSIFICATION  CALCULATIONS     '
                                         STATION
0.15 ft/sec _ a F
1.58 x 10"2 ft/sec ^^
0.2 ft/sec , 3 9
5.17 x 10"2 ft/sec
0.3 ft/sec _ ,n „
1.60 x 10~* ft/sec
0.4 ft/sec _ , „
	 1 	 " /.OD
5.23 x 10"^ ft/sec
r i IMMTD
bUrflcR
UT UTTD
WINTcR
                                      -161-

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                            10
                                     10
                                             "L
                                             Uf
         FIGURE  VI-11  ESTUARINE CIRCULATION-STRATIFICATION DIAGRAM
           The circulation-stratification plots  for  the  Stuart Estuary are shown
      in Figure Vl-11 with points A$ (station  A,  summer  value), A^  (station A,
      winter Value), B  (station B,  summer value), and B  (station  B, winter
      value).
           As indicated, this estuary shows a  significant  amount of vertical strati-
      fication (especially at station A)  but little  evidence  of major vertical
      variations in net circulation.
	END OF EXAMPLE  VI-1
     Turning to Figure VI-11, the Stratification-Circulation  diagram for the Stuart
Estuary, it is apparent that this estuary lies  principally within the marginal area.
Moreover, the low flow classification (line A -8  )  also  lies  primarily within
the marginal area.  Thus,  the planner for the Stuart Estuary  should calculate an
additional criterion (see  below)  to help  determine  the suitability of using the
calculation procedures for well mixed estuaries.   If the  Stuart Estuary plotted more
predominately below the marginal  zone, the planner  could  proceed with flushing time
calculations since the estuary would then meet  the  well mixed classification criteria.
     It should be noted that the  data for the Stuart Estuary  produced a fairly
tight cluster of data points.  As can be  seen  in  Figure Vl-12, the salinity profiles
for one west coast estuary (the Alsea River and Estuary  along the central Oregon
coast) vary considerably more from season to season than  those of the Stuart Estuary.
                                        -162-

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                                       ALSEA  RIVER
                    a
                    UJ
                    o
                                      S(%.) AT HIGH TIDE
                            2515
                               i"P ?
                            WINTER-Ftb.9,1968
                                      20
                               33   302S|t5lp5
 '.,.'i'.jf l •;.>".:<*••, '- ;  /«"l£«*  '•:.
SPRING -Moy 9,1968
                          0
                         10
                         20
                                    33  30 25  20
                         15
10  5
                           SUMMER-Aug. 9,1968
                           [
                           0  I   2   3  4  5  6  7  B  9  10  II  12  13 14
                                        MILES UPSTREAM

                  FIGURE VI-12  ALSEA ESTUARY SEASONAL SALINITY
                                  VARIATIONS  (FROM  GIGER, 1972)
This increased  variation would produce a far  greater spread in the summer and  winter
AS/S  parameter values.

6.2.5  Flow Ratio Calculation

     If  application of the above classification procedure results in an  ambiguous
outcome  regarding estuary classification,  another criterion should b« applied.
This is  the flow-ratio calculation.   Schultz  and Simmons (1957) first observed
the correlation between the flow ratio and estuary type.  They defined the flow
ratio for an estuary as:
         '•*
                                                                           (VI-4)
                                       -163-

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where
        F  «  the flow ratio,
        R  «  the river flow measured over one tidal cycle (measured  in fir or
              ft3)
        P  •  the estuary tidal prism (in nr or ft ).
     Thus the flow ratio compares the tidally induced flow in an estuary with
the river induced flow.  Schultz and Simmons observed that when this ratio was
on the order of 1.0 or greater, the associated estuary was normally highly strati-
fied. Conversely, ratios of about 0.1 or less were usually associated with very
well-mixed estuaries and ratios in the range of 0.25 were associated with partially
mixed estuaries.  A flow ratio of 0.2 or less warrants inclusion of the estuary in
the hand calculation process for one dimensional estuaries.  Flow ratios in the range
0.2 to 0.3 should be considered marginal.  Estuaries with flow ratios greater than
0.3 should not be included in the one-dimensional category.
                                  EXAMPLE VI-2
                   Calculation of the Flow Ratio for an Estuary                        i
                                                                                       i
                                                                                       I
   The following data appply to the Patuxent Estuary, Maryland:                        •
        R, total river discharge over one tidal cycle » 1.42 x 10 m  (low flow)
                                                        3.58 x 106m3 (high flow)       \
        P, estuary tidal prism volume « 3,51 x 10 m3                                   I
   The flow ratios for the Patuxent Estuary at low and high river flows are thus:      I
                        1.42 x  105m3
                        3.51 x  10V
                        0.004
                        3.56 x  106m3
                        3.51 x  IflV
                      «  0.10
   Values of FjCO.l  are usually  associated  with  well  mixed  estuaries.   The  F  values
   calculated above indicate a  well mixed  estuary.   However,  historical  data indicate
   the Patuxent  River Estuary is  partially stratified  at moderate  and  high river
   flows.
                               END OF  EXAMPLE  VI-2
     When tidal  data are not  available,  NOAA coastal  charts may  be  used  to  estimate
the difference between mean  high  tide  and  mean  low  tide  estuary  surface  areas.   As
                                         -164-

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                                              /-MHT Surface*
                         Mean Tide—y      /
                                     \    /  ^MLT Surface*
                  TIDAL
                  HEIGHT"*
                 P, (section 1) « section Length * tidal  height  K  (™T width » NIT ,1dth j

                 P  estuary    «  £p  for all sections
                                 1
                 • widths obtained from NOAA tide table for the  area
                 "Available from local Coast Guard Stations


      FIGURE  VI-13    ESTUARY CROSS-SECTION  FOR  TIDAL PRISM CALCULATIONS
can be seen 1n the cross-section diagram in Figure VI-13 the estuarlne tidal prism
can be approximated by averaging the MLT and MHT surface areas and multiplying this
averaged area by the local tidal height.  Mean tidal heights (approximately 1 week
before or after spring tides) should be used for this calculation.  As indicated in
Figure VI-13, the estuary can be conveniently subdivided into longitudinal sections
for this averaging process, to reduce the resulting error.   Table VI-2 lists tidal
prisms estimated for many U.S. estuaries.  These values may be used as an alternate
to tidal prism calculations.

6.3  FLUSHING TIME CALCULATIONS

6.3.1  General
     Flushing time is a measure of the time required to transport a conservative
pollutant from some specified location within the estuary (usually, but not always,
the head) to the mouth of the estuary.  Processes such as pollutant decay or sedimen-
tation which can alter the pollutant's distribution within  the estuary are not
considered in the concept of  flushing time.
     It  was mentioned earlier in this chapter that  the net  non-tidal  flow in  an
                                         -16S-

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              TABLE VI-2
 TIDAL PRISMS FOR SOME U.S.  ESTUARIES
(FROM O'BRIEN, 1969 AND JOHNSON,  1973)
Estuary
Plum Island Sound, Mass.
Fire Island Inlet, N.Y.
Jones Inlet, N.Y.
Beach Haven Inlet {Little
Egg Bay), N.J.
Little Egg Inlet (Great
Bay), N.J.
Brigantine Inlet, N.J.
Absecon Inlet (before
jetties), N.J.
Great Egg Harbor Entr, N.J.
Townsend Inlet, N.J.
Hereford Inlet, N.J.
Chincoteague Inlet, Va.
Oregon Inlet, N.C.
Ocracoke Inlet, N.C.
Drum Inlet, N.C.
Beaufort Inlet, N.C.
Carolina Beach Inlet, N.C.
Stono Inlet, S.C.
North Edisto River, S.C.
St. Helena Sound, S.C.
Port Royal Sound, S.C.
Cali bog tie Sound, S.C.
Wassaw Sound, Ga.
Ossabaw Sound, Ga.
Sapelo Sound, Ga.
St. Catherines Sound, Ga.
Doboy Sound, Ga.
Altamaha Sound, Ga.
Hampton River, Ga.
St. Simon Sound, Ga.
St. Andrew Sound, Ga.
Ft. George Inlet, Fla.
Old St. Augustine Inlet,
Fla.
Coast
Atlantic
Atlantic
Atlantic
Atlantic

Atlantic

Atlantic
Atlantic

Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic

Tidal Prism (ft3)
1.32 x 109
2.18 x 109
1.50 x 109
1.51 x 109

1.72 x 109

5.23 x 108
1.65 x 109

2.00 x 109
5.56 x 108
1.19 x 109
1.56 x 109
3.98 x 109
5.22 x 109
5.82 x 108
5.0 x 109
5.25 x 108
2.86 x 109
4.58 x 109
1.53 x 1010
1.46 x 1010
3.61 x 109
8.2 x 109
6.81 x 109
7.36 x 109
6.94 x 109
4.04 x 109
2.91 x 109
1.01 x 109
6.54 x 109
9.86 x 109
3.11 x 108
1.31 x 109

                -166-

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TABLE  VI-2    (Cont.)
Estuary
Ponce de Leon, Fla.
(before jetties)
Delaware Bay Entrance
Fire Island Inlet, N.Y.
East Rockaway Inlet, N.Y.
Rockaway Inlet, N.Y.
Masonboro Inlet, N.C.
St. Lucie Inlet, Fla.
Nantucket Inlet, Mass.
Shinnecock Inlet, N.Y.
Moriches Inlet, N.Y.

Shark River Inlet, N.J.
Manasguan Inlet, N.J.
Barnegat Inlet, N.J.
Absecon Inlet, N.J.
Cold Springs Harbor
(Cape May), N.J.
Indian River Inlet, Del.
Winyah Bay, S.C.
Charleston, S.C.
Savannah River (Tybee
Roads), Ga.
St. Marys (Fernandina
Harbor), Fla.
St. Johns River, Fla.
Fort Pierce Inlet, Fla.
Lake Worth Inlet, Fla.
Port Everglades, Fla.
Bakers Haulover, Fla.
Captiva Pass, Fla.
Boca Grande Pass, Fla.
Gasparilla Pass, Fla.
Stump Pass, Fla.
Midnight Pass, Fla.
Big Sarasota Pass, Fla.
New Pass, Fla.
Longboat Pass, Fla.
Coast
Atlantic

Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Atlantic

Atlantic
Atlantic
Atlantic
Atlantic
Atlantic

Atlantic
Atlantic
Atlantic
Atlantic

Atlantic

Atlantic
Atlantic
Atlantic
Atlantic
Atlantic
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Tidal Prism (ft3)
5.74 x 106

1.25 x 1011
1.86 x 109
7.6 x 108
3.7 x 109
8.55 x 108
5.94 x 108
4.32 x 108
2.19 x 108
1.57 x 10-J
8.46 x 108
1.48 x 108
1.75 x 108
6.25 x 108
1.48 x 109
6.50 x 108

5.25 x 108
3.02 x 109
5.75 x 109
3.1 x 109

4.77 x 109

1.73 x 109
5.81 x 108
9.0 x 108
3.0 x 108
3.6 x 108
1.90 x 109
1.26 x 1010
4.7 x 108
3.61 x 108
2.61 x 108
7.6 x TO8
4.00 x 108
4.90 x 108
        -167-

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TABLE  VI-2 (Cont.)
Estuary
Sarasota Pass, FT a.
Pass-a-Grille
Johns Pass, Fla.
Little (Clear-water)
Pass, Fla.
Big (Ounedin) Pass, Fla.
East (Destin) Pass, Fla.
Pensacola Bay Entr., Fla.
Perdido Pass, Ala.
Mobile Bay Entr., Ala.
Barataria Pass, La.
Caminada Pass, La.
Calcasieu Pass, La.
San Luis Pass, Tex.
Venice Inlet, Fla.
Galveston Entr. , Tex.
Aransas Pass, Tex.
Grays Harbor, Wash.
Willapa, Wash.
Columbia River, Wash. -Ore.
Necanicum River, Ore.
Nehalem Bay, Ore.
Tillamook Bay, Ore.
Netarts Bay, Ore.
Sane Lake, Ore.
Nestucca River, Ore.
Salmon River, Ore.
Devils Lake, Ore.
Siletz Bay, Ore.
Yaquina Bay, Ore.
Alsea Estuary, Ore.
Siuslaw River, Ore.
Umpqua, Ore.
Coos Bay, Ore.
Caquil le River, Ore .
Floras Lake, Ore .
Coast
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico

Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Gulf of Mexico
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Tidal Prism (ft3)
8.10 x 108
1.42 x 109
5.03 x 108
6.8 x 108

3.76 x 108
1.62 x 109
9.45 x 109
5.84 x 108
2.0 x 1010
2.55 x 109
6.34 x 108
2.97 x 109
5.84 x 108
8.5 x 10
1.59x 1010
1.76 x TO9
1.3 x 1010
1.3 x 1010
2.9 x 1010
4.4 x 107
4.3 x 10B
2.5 x 109
5.4 x 10fl
1.1 x 108
2.6 x 108
4.3 x 107
1.1 x 108
3.5 x 108
8.4 x 108
5.1 x 108
2.8 x 108
1.2 x 109
1.9 x 109
1.3 x 108
6.8 x 107
     -168-

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                                   TABLE  VI-2  (Cont.)
Estuary
Rogue River, Ore.
Chetco River, Ore.
Smith River, Ca.
Lake Earl, Ca.
Freshwater Lagoon, Ca.
Stove Lagoon, Ca.
Big Lagoon, Ca .
Mad River, Calif.
Humbolt Bay, Calif.
Eel River, Calif.
Russian River, Calif.
Bodega Bay, Calif.
Tomales Bay, Calif.
Abbotts Lagoon, Calif.
Drakes Bay, Calif.
Bolinas Lagoon, Calif.
San Francisco Bay, Calif.
Santa Cruz Harbor, Calif.
Moss Landing, Calif.
Morro Bay, Calif.
Marina Del Rey, Calif.
Alamitos Bay, Calif.
Newport Bay, Cal if.
Camp Pendleton, Calif.
Aqua Hedionda, Calif.
Mission Bay, Cal if.
San Diego Bay, Calif.
Coast
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Pacific
Tidal Prism (ft3)
1.2
2.9
9.5
5.1
4.7
1.2
3.1
2.4
2.4
3.1
6.3
1.0
1.0
3.5
2.7
1.0
5.2
4.3
9.4
8.7
6.9
6.9
2.1
1.1
4.9
3.3
1.8
xlO8
x 107
xlO7
xlO8
x 107
xlO8
x 108
x 107
x 109
x 108
x 107
x 108
x 109
x 107
x 108
x 108
xlO10
xlO6
xlO7
xlO7
xlO7
xlO7
xlO8
xlO7
x 107
x 108
x 109
estuary is usually seaward* and Is dependent on the river discharge.  The non

tidal flow is one of the driving forces behind estuarine flushing.  In the absence of
this advective displacement,  tidal oscillation and wind stresses still operate to
*While net flow is always seaward for the estuaries being considered here, it
 is possible to have a net upstream flow in individual embayments of an estuary.
 While this occurrence Is rare in the United States, an example of such a situation
 is the South Bay of San Francisco Bay where freshwater Inflows are so small that
 surface evaporation exceeds freshwater inflow.  Thus, net flow is upstream during
 most of the year.
                                        -169-

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disperse  and flush pollutants.   However,  the  advective  component  of  flushing  can be
extremely important.  Consider Tomales Bay, California  as  an  example.   This  small,
elongated  bay has essentially no fresh water  inflow.  As a result  there  is no  advective
seaward motion and Pollutant removal  is dependent upon  dispersion  and diffusion
processes.  The flushing time for the bay  is  approximately 140 days  (Johnson,  et  al. ,
1961).  This can be compared with the Alsea Estuary In  Oregon having a flushing  time
of approximately 8 days, with the much larger St. Croix Estuary in Nova Scotia
having a  flushing time of approximately B  days (Ketchur and Keen,  1951), or with  the
very  large Hudson River Estuary with  a short  flow flushing  time of approximately  10.5
Cays  (Ketchum, 1950).

6.3.2  Procedure
      Flushing times for a given estuary vary over the course of a year as river
discharge  varies.  The critical time  is the low river flow  period since this period
corresponds with the minimum flushing rates.  The planner might also want to calcu-
late  the best flushing characteristics (high river flow) for an estuary.  In addition
to providing a more complete picture of the estuarine system, knowledge of the full
range of annual flushing variations can be useful in evaluating the Impact of  seasonal
discharges (e.g., fall and winter cannery operation in an estuary with a character-
istic summer fresh water low flow).   Further,  storm sewer runoff normally coincides
with  these best flushing conditions (high flow)  and not with the low flow, or poorest
flushing conditions.   Thus analysis of storm runoff is often better suited for high
flow  flushing conditions.   However,  the low flow calculation should be considered for
use in primary planning purposes.
      There are several ways of calculating flushing time.  Two methods are presented
here:  the fraction of freshwater method and the modified tidal prism method.

6.3.3  Fraction of Fresh Water Method
      The flushing time of a pollutant, as determined by the fraction of freshwater
method is:
where
        V^  «  volume of freshwater in the estuary
        T^  -  flushing time of a pollutant which enters the head of the estuary
               with the river flow.
Equation VI-5 is equivalent to the following concept of flushing time which is
                                         -170-

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more intuitively meaningful:
                                      T, - "                                  (VI-6)
                                       f   M
where
        M  •  total mass of conservative pollutant contained in the estuary
        M  -  rate of pollutant entry into the head of the estuary with the river
              water.
     Since the volume of freshwater in the estuary is the product of the fraction of
freshwater (f) and the total volume of water (V), Equation VI-5 becomes:

                                    Tf - ™                                   (VI-7)

If the estuary is divided into segments the flushing time becomes:

                                           fiV1
                                   Tf " l  V~                                (VI-8)
                                             1

Equation VI-8  is more general  and  accurate than  the three previous expressions
because both f^  (the fraction  of freshwater  in the  ith segment) and R^  (the fresh-
water discharge  through  the  ith segment) can vary over distance within  the estuary.
Note  that  the  flushing time  of a pollutant discharged from  some location other  than
the head of the  estuary  can  be computed by summing contributions  over the segments
seaward of the discharge.
      A  limitation  of the fraction  of freshwater method is that it assumes uniform
salinity throughout each segment.  A second  limitation is that it assumes during
each  tidal cycle a volume of water equal to  the  river discharge moves into a given
estuarine  segment  fron the  adjacent upstream segment, and that an equal volume  of the
water originally in the  segment moves on to  the  adjacent one downstream.  Once  this
exchange has taken place, the  water within each  segment  is  assumed to be instantane-
ously and  completely mixed  and to  again become a homogeneous water mass.  Proper
selection  of estuarine segments can reduce these errors.

6.3.4  Calculation of Flushing Time by Fraction of Freshwater Method
      This  is a six step  procedure:
      1.  Graph the estuarine salinity profiles.
      2.  Divide  the estuary  into segments.   There is no minimum or maximum number of
         segments  required, nor must all segments be of the same  length.  The divisions
         should be selected  so that mean segment salinity is relatively constant over
                                         -171-

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          the  full  length  of  the  segment.   Thus,  stretches of steep salinity gradient
          will  have  short  segments  and  stretches  where salinity remains constant may
          have  very  long segments.   Example VI-3  provides  an  illustration.
          Calculate  each segment's  fraction of  fresh water by:
                                      f1
          where
          f^   «   fraction  of  fresh  water  for  seqment  "I"
          S    •   salinity  of  local  sea water*.  °/oo
          S,   •   mean salinity for  segment "1", °/oo.
      4.   Calculate the  quantity of fresh water 1n each segment by:

                                      Wf  - f1 x V1                             (VI-10)
          where
          W1   «   quantity  of  fresh  water  1n segment "1"
          Vj   .   total volume of segment  "1"  at MIL.
      5.   Calculate the  exchange time  (flushing time)  for each segment by:
          where
          T,   »  segment  flushing  time,  1n  tidal  cycles
          R    »  river discharge  over  one tidal  cycle.
      6.   Calculate the entire estuary flushing  time  by sumroinq  the  exchange  times  for
          the individual  segments:
                                            I  T                              (VI-12)
         where
         T^  «  estuary flushing time, in tidal cycles
         n   -  number of segments.
Table VI-3 shows a suggested method for calculating flushing time by the fraction of
freshwater method.
*Sea surface salinity along  U.S.  shores vary spatially.   Neuman and Pierson (1966)
 mapped Pacific mean coastal surface salinities as varying from 32.4 °/oo at Puget
 Sound to 33.9 °/oo at the U.S. -Mexico border;  Atlantic  mean coastal surface
 salinities as varying from  32.5  °/oo in Maine  to 36.2 °/oo at the southern
 extreme of Florida; and  Gulf coast salinities  as varying between 36.2 °/oo and
 36.4 °/oo.  Surface coastal salinities in Long Island Sound (Hardy, 1972)  and off
 Long Island south coast  (Hydroscience, 1974) vary between 26.5 and 28.5 °/oo.

                                         -172-

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                                                      TABLE VI-3


                              SAMPLE CALCULATION TABLE FOR CALCULATION OF FLUSHING TIME
                                      BY SEGMENTED FRACTSON OF FRESHWATER METHOD
Segment
Number














Mean
Segment
Salinity
S^ppt)














Mean
Segment
Length
(«)














Mean Segment
Cross-sectional
Area (m'j














Segment Mean
Tide Volume
V1 (m*)














Fraction of
River Water
. Ss-Sl
ft Ss














River Water
Volume
W « f xV
"l 11
On3)














n
EV
1=1 '
Segment
Flushing Time
T1 - Wj/R
(tidal cycles)















I/I
u>

Q.
                                                            -173-

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   -------------------  EXAMPLE VI-3

            Flushing Time Calculation by Fraction of Fresh Water Method

        This example pertains to the Patuxent Estuary.  This estuary has no major
   side embayments, and the Patuxent River is by far Its largest source of fresh
   water.  This estuary therefore lends itself well to analysis by the segmented
   fraction of fresh water method.
        Salinity profiles for July 19, 1978 are used to find segment salinity
   values.  Chesapeake Bay water at the mouth of the Patuxent Estuary had a salinity
   of 10.7 ppt (Sj).  The Patuxent River discharge over the duration of one tidal
   cycle is:
           R - (12 m3/sec) (12.4 hr/tidal  cycle) (3600 sec/hr)
             « 5.36 x I0*m /tidal cycle
   A segmentation scheme based on the principles laid out above is used to divide the
   estuary into eight segments;  their measured characteristics are shown Table VI-4.
   The segmentation is shown graphically on the estuary salinity profile (Figure
   VI-14).
        The next step is to find the fraction of fresh water for each segment.
   For segment 1:
j   where
j           f,   «  fraction of fresh water,  segment 1
:           S$   «  salinity of local seawater
           S   »  measured mean salinity for segment 1
   The calculation is reported in Table IV-4 for segments 2 through 8.
        The volume of fresh water (river water)  in each segment is next  found
'   using the formula:                                                                  j
           Wi  ' fi  * Vi
              i  x vi                                                                 j
For segment 1:                                                                       ;
     H,  • f,  x  V,   -  0.93 (0.79 x 107m3)
                              A -J                                                   I
                   «  7.35 x  10V                                                   i

The flushing  time for each segment is next  calculated by:
        T.  .  w./R                                                                   ;
                                         -174-

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                                  TABLE VI-4
                   PATUXENT ESTUARY  SEGM£NT CHARACTERISTICS FOR
                           FLUSHING TIME CALCULATIONS
                                                                                I
I
Segment  Mean Segment Salinity  Segment  Length
Number         S4,  ppt             meters
                                   Mean Tide
                 Mean Segment    Segment Volume I
            Cross-Sectional Area       V^   .    ;
                   meter2
                                                                       meters
   8

   7

   6

   5

   4

   3

   2

   1
                10.3

                 9.5

                 8.7

                 7.6

                 5.8

                  3.3

                  1.8

                  0.8
10.400

10.400

 6.100

 6.100

 5,800

 5,000

 4.650

 4.650
16,000

12,500

11,400

 7.500

 4,300

 3,100

 2,200

 1,700
16.6xl07

13.0xl07    j

 6.95xl07   j

 4.58x107   I
           •

 2.49xl07   |

 l.SSxlO7   !

 1.02xl07   !

 0.79xl07   :
                  10            20            30            40            - -    i  i
                    DISTANCE FROM HEAD OF ESTUARY (Km)     CHESAPEAKE BAY  /
                                                                         50  /i
 FIGURE  VI-14  PATUXENT ESTUARY SALINITY PROFILE AND  SEGMENTATION SCHEME:
                USED  IN  FLUSHING TIME CALCULATIONS,
                                      -175-

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I   For  segment 1:
1           Tj • Wj/R • 7.35 x 106m3/(5.36 x I05m3/t1dal cycle)
j              - 13.7 tidal cycles
I   Fraction of freshwater, river water volume  and flushing time values  for  the
j   eight  segments  are compiled  in Table VI-5.
        The final  step is to determine the flushing time for the estuary.   In
!   this case:
1                  8
!           Tf  "  Z  T1  "
I            f    1-1  1
1           11.4 *  27.2 + 24.6 + 24.8 + 21.5 +  20.0 + 15.8 + 13.7
i           « 159 tidal cycles, or 2.74 months
6.3.5  Branched Estuaries and the Fraction of Freshwater Method
     Branched estuaries, where more than one source of freshwater contributes
to the salinity distribution pattern, are common.  The fraction of freshwater
method can  be directly applied to estuaries of this description.  Consider the
estuary  shown in Figure VI-15, having two major sources of freshwater (River 1,
R,;  and River 2, R,).  The flushing time for pollutants entering the estuary
with river  flow R-  is:

         Tf  (R,) " T, + T2 + T, + T, + Ts + T» »

                  fiV,   fjV2   f.,V,   fvVk    f$V5    f.V.
                    R2     R2     R2     R2    Ri+R2   Ri+Rj

For the pollutants entering  with R., the flushing time is:

         T   (RlJ.   V* t fbVb , Vc ,  f»V»  ,  f^
         f          R1     RI     RI    Ri+R2   Rt*R2

The flushing time computations are similar in concept for the case of a single
freshwater  source, modified  to account for a flow rate of R,  + R. in segments 5
and 6.

6.3.6  Modified Tidal Prism  Method
     This method divides an  estuary into segments whose lengths are defined by
the maximum excursion path of a water particle during a tidal cycle.   Within each
segment  the tidal prism is compared to the total  segment volume as a measure of the
                                         -176-

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                                                        TABLE VI-5
                                           FLUSHING  TIME FOR PATUXENT ESTUARY
Segment Nunber
8
;
6
5
4
3
2
V
ffe*n Segment
Salinity
Sj. ppt
10. J
9.5
8.7
7.6
5.8
3.3
1.8
0.8
Segment Length
meterj
10.400
10,400
6.100
6.100
5.800
5.000
4.650
4.650
Mean Segment
Cross-Sectional Area
peter1
16.000
12.500
11.400
7.500
4.300
3.100
2.200
1.700
Segment Mean
Tide Volume
VI
meter'
16.6x10'
13.0x10'
6.95x10'
4.58x10'
2.49x10'
1.55x10'
1.02x10'
0.79x10'
fraction of
River Water
. Ss-Si
ft " ~V^
(5, -S10.7)
0.037
0.112
0.19
0.29
0.46
0.69
0.83
0.93
River Water
Volume
W, • f, x V.
Vtirs')1
6.14x10*
14.6x10'
13.2x10*
13.3x10*
11.5x10*
10.7x10*
8.47x10*
7.35x10*
Segment
flush Time
7« * "i/B
tidal cycles
11. <
27.2
24.6
24.8
21.5
20.0
15.8
13.7
•In this numbering scheme segment  I is the most upstre** segment.
                                                                                                                  Sow • 159 tidal cycles
                                                                                                                       or 2.74 months
                                                              END OF  EXAMPLE VI-3
                                                                     -177-

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              FIGURE  VI-15  HYPOTHETICAL  TWO-BRANCHED ESTUARY
flushing potential of that segment  per  tidal  cycle  (Dyer,  1973).  The method assumes
complete mixing of the incoming  tidal prism waters  with the  low tide vo limes within
each segment.  Best results have been obtained  In estuaries  when the number of seg-
ments 1s large (i.e.  when river  flow is very  low) and when estuarine cross-sectional
area increases fairly quickly downstream (Dyer,  1973).
     The modified tidal  prism method does  not require knowledge of the  salinity
distribution.  It provides some  concept of mean  segment velocities since each
segment length is tied to particle  excursion  length over one tidal cycle.  A dis-
advantage of the method  is that  in  order to predict the flushing time of a pollutant
discharged midway down the estuary, the method  still has to  be applied  to the entire
estuary.
     The modified tidal  prism method is a  four-step methodology.  The steps are:
     1.  Segment the estuary. For  this method  an estuary must be segmented so that
         each segment length reflects the  excursion distance a particle can travel
         during one tidal cycle.  The innermost  section must then have  a tidal prism
         volume completely supplied by  river  flow.  Thus:
where
   P
                   tidal  prism  (intertidal volume) of segment "0"
                   river  discharge  over one tidal cycle.
                                         -178-

-------
               The  low tide  volume  in this  section  (VQ)  1s  that water volume
          occupying  the space  under the  intertidal  volume PQ  (which  has  Just
          been  defined as  being  equal  to  R).   The seaward  limit of the next  seaward
          segment  is placed  such that  its low tide  volume  (Vj)  is defined  by:

                                     Vj • PO+ V0                               (V

               P,  is then  that  intertidal volume which,  at  high tide,  resides
          above V  .   Successive  segments  are  defined  in  an  identical  manner  to
          this  segment so  that:

                                 V1 • Pi-l * Vi-l                             (VI-14)

               Thus  each segment  contains, at high  tide, the  volume of water contained
          in  the next  seaward section  at  low  tide.
      2.   Calculate  the exchange  ratio (r) by:
              Thus the exchange ratio for a segment is a measure of a portion of
         water associated with that segment which is exchanged with adjacent segments
         during each tidal cycle.
     3.  "Calculate segment flushing time by:
                                          r                                  (VI-16)
                                          ri
         where
            T.  «  flushing time for segment "i", measured in tidal cycles.
     4.  Calculate total estuarine flushing time by summing the individual segment
         flushing times:
         where
            Tf  «  total  estuary flushing time
            n   «  number of segments.
Table VI-6 shows a suggested method for calculating flushing time by the modified
tidal prism method.
                                         -179-

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                                                       TABLE VI-6
                               SAMPLE CALCULATION  TABLE  FOR  ESTUARINE  FLUSHING TIME BY
                                            THE MODIFIED  HDAL  PR ISM HETHOO
Seoroent
Number
















Segment Dimensions
Starting
Distance
Above Mouth
f»)
















Ending
Distance
Above Mouth
(m)
















Distance
of Center
Above Mouth
(m)
















Segment
Length
(m)
















Subtidal
Water
Volume, V)
(i-M
















Jntertfdal
Mater Volume
'I',
















Segment
Exchange
Ratio
ri
















n
£ T' '
Segment
Flushing
Time, Tj
(Tidal Cycles)

















>>
8
                                                               -180-

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                                  EXAMPLE VI-4
                    Estuary Mushing Time Calculation by the                            •
                           Modified Tidal Prism Method
I                          -                                  I
i                                                                                       i
J       The Fox Mill  Run  Estuary,  Virginia,  was selected  for this  example.   During       j
I  low  flow conditions, the discharge  of  Fox Mill  Run has been measured  at  0.031  m3/sec.l
J       R  »  river  discharge over one tidal cycle                                         J
I          -  0.031  m3/sec  x  12.4 hrs/tidal cycle x  3600 sec/hr                            I
I          •  1384 m3/tidal cycle                                                          j
j   The  estuary flushing time  is found  in  four  steps:                                     j
j        1.   Segmentation
j                From bathymetric maps and tide gage  data, cumulative upstream
            volume was plotted for  several positions  along the estuary (see Figure       !
!            VI-16).                                                                      I

           Since:                                                                        !
              P0  '
           Reading across the graph from "a"  to the intertidal volume curve,  then down !
           the subtldal  volume curve and across to -b":                                 '
              V0  »  490 m3                                                             !
                                                                                       I
           The known  cumulative  upstream water  volume  also  establishes the  downstream  !
           segment boundary.   Reading  downward  from the  subtidal  volume curve  to  "c", a'
           VQ  of 490  m3  corresponds  to  an upstream distance of 2.700  meters for         I
           the segment 0 lower boundary.                                                j
                The low  tide  water volume tor the  next segment can  be found by the      j
           equation:

              vi  '  "o *  vo                                                              i
           or                                                                           i
              Vj  »  1384  * 490  • 1874 m3                                                 j
           Since  the graphs of Figure VI-16 are cumulative  curves,  it  is necessary,     j
           when entering a V^ value  in order to determine a P. value, to sum
           the upstream  V^'s.  For V, the cumulative upstream  low-tide volume           !
           1s:                                                                           I
             VQ * Vj • 490 + 1874 - 2364 m3                                            )
          Entering the graph where the subtidal volume is equal to 2,364 m3           j
           (across from "d"), we can move upward to read  the corresponding cumulative  I
           Intertidal  volume  "e"  on the vertical scale,  and  downward to read the        i
                                        -181-

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1000-,
                        mt»rtidal volume

                     10      15 '     20   '    25  "    30

                  Distance above mouth (100's of maters)
   FIGURE VI-16  CUMULATIVE UPSTREAM WATER VOLUME,
                  Fox  MILL RUN  ESTUARY
                            -182-

-------
I       downstream boundary of segment 1 at "f" on the horizontal  scale.   The
|       cumulative upstream intertldal volume  Is 5900 m  .
j       Since:
j          5900 m3 - PQ + Pj
                                      .3
I             PL - 5900 - 1384 - 4516 m"
I          For segment 2:
I             V. « P. + V. » 1874 + 4516 • 6390 m3
|          To find P., it is necessary to enter the graph at a cumulative
|          subtidal volume of:
I             Vn + V. + V, • 490 + 1874 + 6390 - 8759 m3 (across from "g")
i              U    1    t                                       -5
I          This yields a cumulative intertidal volume of 14,000 m  (across from
j          "h") and a downstream segment boundary of 1,650m "1".
j          The tidal  prism of Segment  2 is found by:
j             14000 • PO + Pj + P2
I          °r
|             P2 + 14000 - 1384 - 4516 * 8100 m3
I          The procedure is identical  for Segment 3.  For this final  segment:
j             V3 • 14,490 m3
|             P3 • 36,000 m3
j          Dimensions  and  volumes of the four segments  established  by this procedure
          are compiled  in Table  VI-7.
      2.   The exchange  ratio for segment 0 is found by:
!             r  - Pn   .     1384 m3
I              °   P0*V0   1384 m3 + 490 m3
(          Exchange ratios are calculated similarly for  the  other three  segments.
i      3.   Flushing time for each segment "i" is given  by:
          so
          Exchange  ratios  and  flushing times  for  the four  segments are shown
          in Table  IV-7.
      4.   Flushing  time  for  the  whole estuary is  found by:
                                         -183-

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1
i DATA ANJ FLUSHING
4
1
TABLE VI-7
TIME CALCULATIONS FOR FOX MILL RUN ESTUARY
; Segment Dimensions Mater
1
Starts at this Stops at this
1 Segment Distance Above Distance Above
' Number Mouth-meters Mouth -meters
j 0 3.200 2.700
1 2.700 2.240
2 2.240 1.650
3 1.650 180
1
i
I or
' T - 1.35 + 1.41 * 1.79
1 • 5.96 tidal cycles
| • 73.9 hours
j « 3.1 days
i
Volume it Jntertldal Exchange
Center Point Segment Low Tide Volume Ratio for
Distance Above Length Vj Pj Segment 1
Mouth-meters meters meterj3 meters3 r(
2.950 500 490 1.384 0.74
2.470 460 1.874 4.516 0.71
1.945 590 6.390 8.100 0.56
915 1.470 14.490 36.000 0.71

Hushing
Time for
Segment 1
1.35
1.41
1.79
1.41
IT • 5.96 tidal cycles
+ 1.41
6.4  FAR FIELD APPROACH TO POLLUTANT DISTRIBUTION IN ESTUARIES

6.4.1  Introduction
     Analysis of pollutant distribution 1n estuaries can be accomplished  in a
number of ways.  In particular, two approaches, called the far field and  near
field approaches, are presented here (Sections 6.4 and 6.5, respectively).  As
operationally defined in this document, the far Held approach Ignores buoyancy
and momentum effects of the wastewater as it 1s discharged into the estuary.
The pollutant Is assumed to be instantaneously distributed over the entire cross-
section of the estuary (in the case of a well-mixed estuary) or to be distributed
over a lesser portion of the estuary in the case of a two-dimensional analysis.
Whether or not these assumptions are realistic depends on a variety of factors,
including the rapidity of mixing compared to the kinetics of the process being
analyzed (e.g. compared to dissolved oxygen depletion rates).  It should  be noted
that far field analysis (either one- or two-dimensional) can be used even 1f actual
mixing is less than assumed by the method.  However, the predicted pollutant concen-
trations will be lower than the actual concentrations.
                                         -184-

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     Near field analysis considers the buoyancy and momentum of  the wastewater
as  it  is discharged  into the receiving water.  Pollutant distribution  can  be  calcu-
lated  on a smaller spatial scale, and assumptions such as "complete mixing" or
"partial mixing" do  not have to be made.  The actual amount of mixing  which occurs  is
predicted as an integral part of the method itself.  This is a great advantage  in
analyzing compliance with water quality standards which are frequently specified  in
terms  of a maximum allowable pollutant concentration in the receiving  water at  the
completion of  initial dilution.  (Initial dilution will be defined later in Section
6.5.2.)
     The following far field approaches for predicting pollutant distribution
are presented  in this chapter:
        •    Fraction of freshwater method
        •    Modified tidal prism method
        t    Oispersion-advection equations
        •    Pritchard's Box Model.
The near field analysis uses tabulated results from an initial dilution model called
MERGE.  At the completion of initial dilution predictions can be made  for  the following:
        •    Pollutant concentrations
        •    pH levels
        •    Dissolved oxygen concentrations.
The near field pollutant distribution results are then used as input to an analytical
technique for predicting pollutant  decay or dissolved oxygen levels subsequent to
initial dilution.   The remainder of Section 6.4 will discuss those methods applicable
to the far field approach.

6.4.2  Continuous  Flow of Conservative Pollutants
     The concentration of a conservative pollutant entering  an estuary in a continuous
flow varies  as a function of the entry point location.   It  is convenient to separate
pollutants entering  an estuary at the head of  the  estuary (with the river discharge)
from those entering  along the estuary's sides.   The two impacts will  then be addressed
separately.

6.4.2.1  River Discharges of Pollutants
     The length of time required to flush a pollutant from  an estuary after it
is introduced with the river discharge has already been calculated, and is the
estuarine flushing time.  Now consider a conservative pollutant continuously dis-
charged into a river upstream of the estuary.   As  pollutant  flows into the estuary,
it begins to disperse and move toward the mouth of the  estuary with the net flow.
If,  for example,  the estuary flushing time is  10 tidal  cycles,  then 10 tidal cycles
following its initial flow into the estuary, some  of the  pollutant  is  flushed  out to

                                         -185-

-------
the  ocean.  Eventually,  a  steady-state  condition  1s  reached  1n  which a certain amount
of pollutant enters  the  estuary,  and  the  same  mount  1s  flushed out  of the  estuary
during each tidal cycle.   The amount  of this pollutant which  resides in the estuary
at steady-state  1s a function of  the  flushing  time.   From  the definition of flushing
time, the  amount of  fresh  water (river water)  in  the  estuary  may be  calculated by:
                                            Tf R
                                                                              (Vl-18)
where
        We  •  Quantity of freshwater  in the estuary
        Tf  •  estuary flushing time
        R   «  river discharge over one tidal cycle.
Using the same approach, the quantity  of freshwater in  any segment of the estuary  is
given by:
                                            T1R
                                                                              (VI-19)
where
        V
        Ti  -
               quantity of freshwater in the i   segment of the estuary
               flushing time for the i   segment calculated by the fraction
               of freshwater method.
If a conservative pollutant enters an estuary with the river flow, it can be assumed
that its steady-state distribution will be identical  to that of the river water
itself.   Thus:
                                                                             (VI-20)
and
                                                                             (VI-21)
        Cr
        Ci
where
        M^  «  quantity of pollutant in estuary segment "i"
               concentration of pollutant in the river inflow
               concentration of pollutant in estuary segment "1" assuming
               all of pollutant "i" enters the estuary with the river discharge.
               Thus direct discharges into the estuary are excluded.
        V-  «  water volume segment "i".
The same values for C^ and M1 may also be obtained by using the fraction of
                                         -186-

-------
freshwater, f., for each segment by:

                                      Ci • f1 Cr                              (VI-22)

and

                                      M^ - C1 V1                             (VI-23)

     Thus both the quantity of a pollutant 1n each segment and Us concentration
within each segment are readily obtainable by either of the above methods.   The
use of one of these methods will be demonstrated in Example Vl-5 below for calculation
of both C^ and M..

	EXAMPLE VI-5	,
I                                                                                       I
J                  Calculation  of Concentration of  Conservative                          I
I                      River  Borne Pollutant  in an  Estuary                               |
i
j        Th«  Patuxent Estuary is the  subject of this  example.  The  problem  is to
   predict the incremental  concentration  increase  of total  nitrogen  (excluding N?       j
   gas)  in the estuary, given  that the concentration in river water  at the estuary
   head  is 1.88 mgN/1.                                                                  !
        Assume that total nitrogen  is conservative  and that the nitrogen concentration  j
   in  local  seawater is negligible.  The segmentation scheme used  in Example VI-2       I
   (fraction of freshwater  calculation) wi11  be retained here.  For  each segment, the   |
   total  nitrogen  concentration is directly proportional to the fraction of freshwater  I
   in  the  segment:

          C1  ' fi Cr                                                                   I
   The total nitrogen  concentration  for the uppermost segment is therefore given        j

                                                                                       i
          Cj  • 0.93 (1.88 mgN/1)                                                       j
              • 1.75 mgN/1
   For the next segment It  is:
                                                                                       I
          C?  • 0.83 (1.88 mgN/1) «  1.56 mgN/1
   and so  on.  Nitrogen concentrations for all the segments are compiled in Table
   VI-8.   Note that these are not necessarily total concentrations, but only nitrogen   J
   inputs  from the Patuxent River.                                                      I
                                                                                       4
         The incremental mass  of nitrogen  in  each  segment  is found by:                  |

            M   '  W C                                                                   '
                                        -187-

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                    TABLE VI-8

   POLLUTANT DISTRIBUTION IN THE PATUXENT RIVER
Segment Nuaber*
8
7
6
5
4
3
2
I
River
•From Example
"These are the
Fraction of Freshwater*
1n Segaent f<
0.037
0.112
0.19
0.29
0.46
0.69
0.83
0.93
1.00
VI-2
Increment concentrations of total
Resultant Pollutants**
Concentration
•f1 x 1.88 mgN/1
0.07
0.21
0.36
0.55
0.86
1,30
1.56
1.88
1.68
nitrogen 1n the estuary
due to the river-borne input.
                  TABLE VI-9

INCREMENTAL TOTAL NITROGEN IN PATUXENT RIVER,
            EXPRESSED AS KILOGRAMS
              (See Problem VI-5)
Segment Number
8
7
6
5
4
3
2
1
River Water
Volume
vvv
meters
6.14xl06
14.6 xlO6
13.2 xlO6
13.3 xlO6
11.5 xlO6
10.7 xlO6
8.47xl06
7.35xl06
Incremental Total N
M. - W1 (1.88)
kilograms
11,500
27.400
24,800
25,000
21.600
20,100
15,900
13,800
                      -188-

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I   The H. values for the eight segments were determined in Example VI-2. For
|   segment 1, the incremental nitrogen is given by:
            l " Hl Cr
              • (7.35 x 10V)(1.88 mgN/l)(103l/Bi3)
I
j              - 1.38 x 1010 ng or 13,800 kg                                             |
I    Increased total nitrogen (in kilograms) for the entire estuary is shown  in Table     i
j    «-'•                                                                                i
I	END OF EXAMPLE VI-5	'

      In this example, low tide volumes were used to calculate H. since low tide
volumes had been used to calculate f^'s.  The approach assumes that C^'s are
constant over the tidal cycle and that M^'s are constant over the tidal cycle.
This  leads to the assumption that calculation of a low tide C, and M^ will
fully characterize a pollutant in an estuary.  This, however, is not strictly true.
Figure VI-17 depicts one tidal cycle in an estuary and shows the periods of the cycle
during which a pollutant is flushed out of the estuary and during which river discharge
brings pollutants into the estuary.  During periods of high tide, rising tidal
elevation tlodcs river discharge and backs up river flow in the  lower stretches of
the river.  Figure VI-17 also shows the resulting quantity of a pollutant in residence
in  the estuary (W_J over the tidal cycle.  This variation over the tidal cycle
                 ™
as  a  percentage of M- is dependent on the flushing time but is usually small.   The
change in the total volume of water in an estuary over a tidal cycle is equal  to the
tidal prism which is often of the same magnitude as the low tide volume.   As an example,
the Alsea Estuary in Oregon has ?t • 5.1 x 108 ft3 while Vt - 2.1 x 108 (Goodwin,
Emmet, and Glenne, 1970).   Thus the variation in estuarine volume is 2.5  times the
low tide volume.  As a result, estuarine volume variations over a tidal cycle  have a
much greater impact on variations in pollutant concentrations in the estuary than do
changes in the quantity of pollutant present in the estuary over a tidal  cycle.   It
is  important to note, however, that low tidal volume and low Mr nearly coincide,
so  that variations in mean pollutant concentrations are less severe than  are estuarine
water mass changes.
     This qualitative description of pollutant flow into and out of an estuary
is  somewhat simplistic since it assumes that high  tide and low tide at the mouth  of
an  estuary coincide with those at the head of the  estuary.   This is usually not  the
case.  There is normally a lag time between tidal  events at an estuarine  mouth and
those at its head.  Thus river discharge into the  estuary which depends on tidal
conditions at the head,  and tidal  discharge which  depends  on tidal  conditions  at  the
mouth, are not  as directly tied to each other as  indicated  in Figure VI-17.
     While Wr does not  vary substantially over a tidal  cycle under  steady-state
                                        -189-

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                  TIDAL
                  ELEVATION
                  W,
                   PE
              FIGURE  VI-17   RIVER  BORNE  POLLUTANT  CONCENTRATION
                              FOR  ONE TIDAL CYCLE

conditions',  the mean concentration of  a pollutant in an estuary (Cp) does.  Alsea
Estuar> data can be used to show this  C^ variation over a tidal cycle.  Using
data for the estuary as a whole (mean  concentration), the equations  for this compari-
son are:
                                                                         (VI-24)
and
with
or
Then:
and
                                      ME/(Vt * Pt)
        Wr  -   (566.4ng/ft3) (4.64 x 106ft3/tidal cycle)
        Wr  •   2.628 x loVg/tidal cycle.
            «   (2.628 x 10>g/tidal cycle)(20.8 tidal cycle)
            -   5.466 x 101CVg
        CE(low)   *  5'466 x 1010Hg/2.1  x  108ft3
(VI-25)
                                       -190-

-------
or
        CCM  ,   *  260.31 Kg/ft3, or 46 percent of river concentration.
         c.( low;
However:
        CE(high)  *  5'466 x ""Wtt.l x 108ft3 + 5.1 x 108ft3)
        Cf... h»  «  75.92 ng/ft  or 13 percent of river concentration.
     In an actual estuary, the concentration of a pollutant is not a stepwise
function as indicated by segment C, values, but is more realistically a contin-
uous spectrum of values.  By assigning the longitudinal midpoint of each segment a
concentration value equal to that segment's C^, a resulting continuous curve can
be constructed as shown in Figure VI-18.  This type of plot is useful 1n estimating
pollutant concentrations within the estuary.  It can also be used, however, to
estimate maximum allowable C  to maintain a given level of water quality at any
point within the estuary.  This latter use of Figure VI-18 1s based on determining
the desired concentration level (C ) and then using the ratio of C  to C
to calculate an allowable Cr.

6.4.2.2  Other Continuous Conservative Pollutant Inflows
     In the previous section, an analysis was made of the steady-state distri-
bution of a continuous flow pollutant entering at the head of an estuary.   The
result was a graph of the longitudinal pollutant concentration within the  estuary
(Figure VI-18).   This section addresses a continuous, conservative pollutant flow
entering_along the side of an estuary.  Such a pollutant flow (e.g. the conservative
elements of a municipal sewer discharge, industrial  discharge, or minor tributary) is
carried both upstream and downstream by tidal mixing, with the highest concentration
occurring in the vicinity of the outfall.  Once a steady state has been achieved, the
distribution of  this pollutant is directly related to the distribution of  fresh river
water (Dyer, 1973).
     The average cross-sectional concentration at the outfall under steady-state
conditions is:
                                           Qn
                                      C  «-£f                              (VI-26)
                                       o    R  o

where
        CQ  • mean  cross-sectional concentration of a pollutant at the point  of
              discharge,  mass/volume
        Qp  » discharge rate of pollutant,  mass/tidal cycle
        fQ  « segment fraction of freshwater
        R   « river discharge rate, volume/tidal  cycle.
     Downstream  of the outfall, the pollutant must pass through  any cross  section at
                                        -191-

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      10     120     30    40     50     60     TO     ISO
        DISTANCE U) FROM HEAD OF ESTUARY (in 1000FT)

FIGURE  VI-18  ALSEA ESTUARY  RIVERBORNE CONSERVATIVE
                POLLUTANT  CONCENTRATION
a rate equal  to the rate of discharge.   Thus:
                                   vO
                          f
                                                                       90
                x

                0
                                   V$0
                                                                           (VI-27)
where
        Sx,  CK  and fx denote downstream  cross-sectional values
        S ,  C.  and f  denote the cross-sectional values at the discharge
                     point (or segment  into which discharge is made).
     Upstream of  the outfall, the quantity  of  pollutant diffused and advectively
carried upstream  is balanced by that carried downstream by the nontidal flow  so
that the net pollutant transport through any cross section is zero.   Thus,  the
pollutant distribution is directly proportional  to salinity distribution  and  (Dyer,
1973):

                                    CX-C0^                            (VI-28)
                                            5o
     Downstream of  the outfall, the pollutant  concentration resulting from a  point
discharge is directly proportional to river-borne  pollutant concentration.  Upstream
from the discharge  point,  1t is inversely proportional to river-borne pollutant
concentrations.  Figure VI-19  is a graph of fx versus  distance from the  estuary
                                        -192-

-------
                  f, 00
                                                                    -p*
0          '-      10.5
DISTANCE FROM HEAD  »
                                                                 110
                       *L • Totol E»toonn« Ungth

               FIGURE VI-19  POLLUTANT CONCENTRATION  FROM AN
                               ESTUARINE OUTFALL  (AFTER KETCHUM, 1950)
head for a typical  estuary.   The  solid f   line  Is also a measure of pollutant
concentration for all  points  downstream of a pollutant outfall (either discharge
location A or B).   The actual concentration (C  ) for any point is equal to this
fx value multiplied by Q /R which is  a constant over all x.  Upstream concen-
trations decrease from C  in  a  manner proportional to upstream salinity reduction
(see dotted lines).  It is important  to note how even a small downstream shift in
discharge location creates a  very significant reduction in upstream steady-state
pollutant concentration.  Table VI-10 shows a suggested format for tabulating pollutant
concentrations by the  fraction  of freshwater method.
                               -  EXAMPLE VI-6
               Calculation  of Conservative Pollutant Concentration
                             for  a Local Discharge

        This example  will  again utilize the eight-segment scheme devised for the
   Patuxent Estuary in  Example VI-2.  The objective is to predict the concentration
   distribution of  total nitrogen  in the estuary resulting from a discharge of  80,000
   mgN/sec Jnto segment 4.
        The first  step  is to determine the nitrogen concentration in segment 4.
                                        -193-

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                                         TABLE VI-10

            SAMPLE  CALCULATION TABLE FOR DISTRIBUTION OF A  LOCALLY  DISCHARGED
               CONSERVATIVE  POLLUTANT BY THE FRACTION OF FRESHWATER METHOD
From Table VI-3
Segment
Number

Segment
Containing
Discharge

Fraction of
Freshwater
fi



Mean Segment
Salinity
(ppt)



fi
~o

I

S1
S

1

Pollutant
Concentrations*
(mg/1)

     *Po "Mutant concentration  -«
      where Cn«
                                      f .
                                   C0  —  ,  down  estuary of the discharge

                                      o
                                   C0  — ,  up estuary of the discharge
1
•   From Equation  VI-26:

           c  m Op  f0 f  (8xlQ4 mgN/sec x 12.4 hrs/tidal  cycle x 3600 sec/hr)(0.46)

                                     5.36xl05m3/tida)  cycle
                          3.065 mgN/1
I   For segments  1-3,  upstream from the discharge,  nitrogen  concentration is
J   found by Equation  VI-28:

!           ci  •  c.
i
                                        -194-

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1 For segment 1:
1
! S, - 0.8%.
1
1 5 * 5 4 * b.o 7oo
<
i
j CA » 3.065 mgN/1
1 so


I \5.8700/
; Nitrogen concentrations in segments 2
j VI-11 summarizes the information used
i
i


i
i
i
*
|
« 0.42 mgN/1
1
and 3 are found in an identical way. Table
I
in the calculation. [
1 For the segments downstream of the discharge, total nitrogen concentration is 1
| found using Equation VI-27:
i c. - c i-
• 1 0 T
' In segment 5:
1 f, - 0.29

1 f . f . 0.46
1
,
1
i
»
1
i
1
i
1
i
1
•
1 TABLE VI-11 !
1 NITROGEN CONCENTRATION IN PATUXENT ESTUARY !
| BASED ON


1
Fraction of
1 Segment Freshwater
! Number f ^
i
1 8 0.037
<
1
j 7 0.112
j 6 0.19
1 5 0.29
! Discharge _ 4 0.46
! 3 0.69
1
2 0.83
j 1 0.93
LOCAL DISCHARGE |
i
|
Mean Si f< j
Segment »- -r- Concentration \
Salinity o o mgN/1 |
1
10.3 - 0.08 0.25 I
1
1
9.5 - 0.24 0.74 j
8.7 - 0.41 1.26 j
7.6 - 0.63 1.93 1
5.8 1 1 3.06 !
3.3 0.57 - 1.75
1
1.8 0.31 - 0.95 j
0.8 0.14 - 0.43 j
-195-

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and
             3.065  mgN/1
 so
        C5 •  3.065 mgN/1
,.93 mgN/1
                                                                                   I
 The  same procedure yields nitrogen concentrations  in segments 6-8, also downstream   |

 of the  discharge.                                                                  j

     Figure VI-20 below shows the nitrogen  concentration distribution over the

 entire  estuary.  Note that the nearer  a  discharge  is to the estuary's mouth,  the

 greater the protection rendered the upstream reaches of the estuary.                j
     4.0-1
     3.CT-
 z
 Oi


 \   2.0H
 0
 9
 o
      1.0-
                       10
   i

  20
 i

30
 I

40
                                                      discharge

                       Distance above estuary mouth UOOO's of meters)




       FIGURE VI-20  HYPOTHETICAL  CONCENTRATION OF  TOTAL  NITROGEN

                        IN PATUXENT ESTUARY
                              END OF EXAMPLE VI-6
                                      -196-

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6.4.3  Continuous Flow Non-Conservative Pollutants
     Most pollutant discharges into estuaries have some components which behave
non-conservatively.  A number of processes mediate the removal of compounds from
natural waters, among these:
        •    Sorption by benthic sediments on suspended matter
        •    Partitioning
        •    Decay (by photolysis or biologically mediated reactions)
        •    Biological uptake
        •    Precipitation
        •    Coagulation.
The latter two processes are particularly significant in estuaries.   Thus,  in addition
to dispersion and tidal mixing, a time-dependent component is incorporated  when
calculating the removal of non-conservative pollutants from estuarine waters.   The
concentrations of non-conservative pollutants are always lower than those of conserva-
tive pollutants (which have a decay rate of zero) for equal discharge concentrations.
The results of the previous section for conservative constituents serve to set upper
limits for the concentration of non-conservative continuous flow pollutants.  Thus,
if plots similar to Figure VI-17 for river discharges and to Figure Vl-19 for other
direct discharges have been prepared for flow rates equal to that of the non-conserva-
tive pollutant under study, some reasonable approximations can be made for steady-
state non-conservative pollutant concentrations without requiring additional data.
Assuming a first order decay rate for the non-conservative constituent, its concentra-
tion is given by:

                                     Ct « C0e'kt                            (VI-29)

where
        C^  •  pollutant concentration at time "t"
        CD  «  initial pollutant concentration
        k   «  decay rate constant.
     For conservative pollutants k • 0 and C « CD under steady-state conditions.
Decay rates are determined empirically and depend on a large number  of variables.
Typical decay rates for BOD and coliform bacteria are shown in Table VI-12.   If data
are not available for a particular estuary, the use of these average values  will
provide estimates.
     It should be noted that decay rates are dependent upon temperature.  The  values
given assume  a temperature of 20*C.   Variations in k values for differing temperatures
are given by  Equation VI-30:

                                               T-20-                        (VI-30)
                                    kT   *20' 9
                                        -197-

-------
                                      TABLE Vl-12
                      TYPICAL VALUES FOR DECAY REACTION RATES 'k1*

                      	Source	BOD	Collforn
                      Dyer,  1973                            .578
                      fetchem,  1955                         .767
                      Chen and  Orlob,  1975     .1           .5
                      Hydrosdence,  1971     .05-.125       1-2
                      McGaughhey,  1968         .09
                      Harletnan.  1971           .069
                      *k  values  for  all  reactions given  on  a  per
                      tidal  cycle basis,  20*  C.	
where
        ky   «  decay rate at temperature T
        k20  «  decay rate at 20*C (as given 1n Table Vl-12)
        6    «  a constant {normally between 1.03 and 1.05).
Thus an ambient temperature of 10"C would reduce a k value of 0.1 per tidal cycle to
0.074 for a-6 • 1.03.
     Decay Affects can be compared to flushing effects by setting time equal to
the flushing time and comparing the resulting decay to the known pollutant removal
rate as a result of flushing.  If kt in Equation VI-29 1s less than 0.5 for t •
Tf, decay processes reduce concentration by only about one-third over the flushing
time.  Here mixing and advective effects dominate and non-conservative decay plays a
minor role.  When kTf > 12 decay effects reduce a batch pollutant to 5 percent of
Us original concentration in less than one-fourth of the flushing time.   In this
case, decay processes are of paramount importance in determining steady-state concen-
trations.  Between these extremes, both processes are active in removing  a pollutant
from the estuary with 3 < kTf < 4 being the range for approximately equal contri-
butions to removal.  Dyer (1973) analyzed the situation for which decay and tidal
exchange are of equal magnitude for each estuarine segment.   Knowing the  conservative
concentration, the non-conservative steady-state concentration in a segment is
given by:
                                                                            (W-31)
                                        -198-

-------
and
                   S.            /    r        \  for segments upstream      (VI-32)
           V  Co  S^  i-l^-.n  I j (1.r  )c-kJ  of the outfall
where
               non-conservative constituent mean concentration in segment  "1
        L1
        C   -  conservative constituent mean concentration in segment of discharge
         o
        r1  •  the exchange ratio for segment "i-  as defined by the modified
               tidal prism method
        n   «  number of segments away from the outfall  (i.e. n »  1 for segments
               adjacent to the outfall; n « 2 for segments next to these segments,
               etc.)
        Other parameters are as previously defined.
     In the case of a non-conservative pollutant entering  from the river,  n «  1,  and
the only concentration expression necessary is:

                                                 !«                          (VI-33)
where
                                                                            (VI-34)
Table VI-13 shows a suggested format for tabulating pollution concentrations by
the modified tidal prism method.
j.	  EXAMPLE VI-7	1

i                                                                                       i
              Continuous Discharge of a Non-Conservative Pollutant                     j
!                           into the Head of an Estuary
I                                                                                       I
i                                                                                       '
|        The Fox Mill Run Estuary (see Example VI-3)  is downstream of the Gloucester,    j
   Virginia, sewage treatment plant.   Knowing the discharge rate of CBOD in the plant   |
   effluent, the purpose of this example is to determine the concentration of CBOD     |
   throughout the estuary.                                                             j
        It is first necessary to determine the concentration of CBOD in Fox Mill Run    •
   as it enters the estuary (assume no CBOD decay within the river).  The following    •
   information has been collected:                                                     \
           Cr,  Background CBOD in river                    »   3 mg/1
                                         -199-

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                                                    TABLE  VI-13



                        SAMPLE  CALCULATION'TABLE  FOR'DISTRIBUTION  OF  A LOCALLY  DISCHARGED

                          MOW-CONSERVATIVE  POLLUTANT BY  THE  MODIFIED  TIDAL  PRISM METHOD
From Table VI-6

Segment
Number

Distance of
Center Above
Mouth
(m)

Segment
Exchange
Ratio


Mean Salinity
(from salinity
plot)
Si
ppt


Fraction of
River Water
f - *'


B1



Pollutant
Concentration
(mg/1)

i.
1C

a
                                                           -200-

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i           Q ,  River flow below treatment plant discharge  -    0.031  m /sec
j           Qd,  Treatment plant discharge rate              «    0.006  m /sec
j           Cd,  Treatment plant effluent CBOD               «   45 mg/1
   The CBOD concentration 1n the river downstream of  the treatment  plant  is found      j
   using the equation:                                                                j
I               Cr(Qr-Qd) * CdQd
I           C"       %                                                               !
|   or                                                                                 I
j           c „ 3 mg/1(.031-.006 m3/sec)+45 mg/l(0.006 m3/sec)                          j
•                              0.031 m3/sec                                            j
!             - 11.1 mg/1
!   To find the CBOD concentration distribution in the estuary,  the  following  additional.
j   data are used:                                                                     '
!           S    Chesapeake Bay salinity  «  19.0 °/oo (at  the mouth of
j                                                       Fox Mill  Run Estuary)           (
I           k,    CBOD decay constant      «  0.3/day                                   j
j           T,    Tidal cycle              -  12.4 hours                               I
i   so                                                                                 |
|           kt « 0.3/day x 12.4 hr x 1  day/24 hours                                    I
j              • 0.155                                                                 I
I   Also necessary are mean salinity values for each estuary segment.  Values for       J
|   the Fox Mill  Run Estuary  are summarized in Table VI-14.  Fraction of freshwater     I
j   values for each segment are found using the formula:                                |
                Vsi
           f'"ir
|   The variables are as  previously  defined.
        Next,  values of  the  coefficient  B.  must  be calculated for each segment
   "1."  For segment 0:
           r^,  the segment exchange ratio,  « 0.74
   and
           B          rO             °-74
            ° "  l-(l-r0)e-"   "  l-(l-0.74)e-u-1"
              «  0.95
   Coefficient  values  for all  segments  are compiled in Table VI-14.
   Finally, CBOD concentrations  for the  individual* segment are calculated, beginning
   with the uppermost  segment  and working  downstream.  The concentration in segment
   "i" is found  by:
                                        -201-

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                      TABLE  VI-14




SALINITY AND CBOD CALCULATIONS FOR FOX MILL  RUN  ESTUARY
from Problem VI -3

Center Point
Distance Above Exchange Ratio
Est. Mouth, For Segment
Segment Number Meters r^
River (>3200)
0 2950 0.74
1 2470 0.71
2 1945 0.56
3 915 0.71


Fraction of
Mean Segment Fresh (River)
Salinity , s" i
Si, ppt ri S«
(From Sal. Plot) (Sj- 19.0)
-0 I. 00
4.7 0.75
8.6 0.55
11.6 0.39
15.3 0.19


Concentration of
CBODU
f .
n r «r a
Bi C1 ci-l fM 8i
(mg/1 )
11.1
0.95 8.1
0.94 5.5
0.90 3.6
0.94 1.6

                          -202-

-------
I   For segment 0,  the  river  1s taken as segment "1-1", and the  calculation  1s as       j
j   follows:                                                                          !
I

!   For segment 1:

          CQ » 11.13 mg/1  f ~]  0.95  -  8.1 mg/1
                        /•55\
          C, • 8.1 mg/1  (— I  0.94  « 5.6 mg/1
j   and so on.                                                                        1
j        Figure VI-21  depicts this estimate of the distribution of CBOD in the estuary, j
   In addition, hypothetical concentrations of a conservative pollutant (k » 0) and    •
!   conform bacteria  (k  •  1.0) are plotted.  Downstream  concentration diminishes
'   faster for substances having  larger decay constants,  as might be expected.
i                                                                                     !
i                                                                                     I
    |2
    u
    o
    U

conservative
 pollutant
                                                              coWorma
                           10
                           20
                       Distance Above Mouth Of Eatuary (100'* of meters)
                                                                     30 river   36
                                                                        mouth
    FIGURE VI-21   RELATIVE DEPLETIONS  OF THRES POLLUTANTS ENTERING  THE    !
                     Fox MILL RUN  ESTUARY, VIRGINIA                              I
                                 END OF  EXAMPLE VI-7
                                                                                   .J
                                        -203-

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6.4.4  Multiple Waste Load Parameter Analysis
     The preceding analysis allowed calculation of the longitudinal  distribution
of a pollutant, either conservative or non-conservative,  resulting from a single
waste discharge.  However, the planner will  probably want to simultaneously assess
both conservative and non-conservative elements front several  separate  discharges.
This can be accomplished by graphing all  desired single element  distributions  on one
graph showing concentration versus length of the estuary.   Once  graphed,  the resulting
concentration may be linearly added to obtain a total  waste load.
     The pollutant concentration increment from each source is calculated by assuming
the source is the sole contribution of pollution (i.e.  other waste loadings  are
temporarily set equal to zero).   This method, called superposition,  is valid as  the
long as volumetric discharge from any of  the sources does not significantly influence
the salinity distribution within the estuary.  This  assumption is  typically true,
unless the estuary is extremely small and poorly flushed,  and the  volumetric discharge
is targe relative to tidal and advective  flushing components.
     An example of the superposition procedure is shown in Figure  VI-22.   Three  local
              z
              Ul
              a
                                            Water Quality Standard

                                 New Pollutant
                                 Concentration
                                 •Current Pollutant
                                 Concentration

                                 Sum
                   DISTANCE FROM HEAD
       FIGURE  VI-22  ADDITIVE  EFFECT OF  MULTIPLE  HASTE  LOAD  ADDITIONS
                                         -204-

-------
point  sources of pollutants discharge at locations  A,  8,  and C.   A background  source
enters the estuary with the river discharge.   The contribution due to  each  source can
be found from the fraction of freshwater method (assuming  the pollutants act conserva-
tively) as follows:
             WR
        C  • -  f, x > 0, where x 1s aeasured  from  the  head of  the  estuary
WA
-^f
 R  x
                         X>A
              	O £   A         _
              T f B T   '  x < B
        cc'
               Tfx  '
               wc     sx
where
        Cfe          •  concentration due to river discharge
        CA,  Cg,  CQ   •  concentrations due to sources A, B, and C, respectively
        R           •  river flow rate
        f»,  f»,  ff   •  fraction of freshwater at locations A, B, C,  respectively
        SA,  Sg,  S^   •  salinity at locations A, 6,  C, respectively.
                                        -205-

-------
 The pollutant concentration (above background) at any location in the estuary  is:
         Sum • CA + Cg + G£
 and is shown in Figure VI-22.  When this 1s added to the background level, the
 total  pollutant concentration becomes:
         CT • (CA + CB + Cc) «• Cb
 The dotted line in Figure VI-22 depicts Cj.
     The technique of graphing outfall location and characteristics  with resulting
 estuarine pollutant concentration can be done for all anticipated discharges.   This
will provide the planner with  a good perspective on the source of potential water
quality problems.
     Where the same segmentation scheme has been used to define Incremental pollutant
distributions resulting from several sources, the results need not even be plotted to
determine the total resultant concentrations.  In this case, the estuary is evaluated
on a segment-by-segment basis.  The total pollutant concentration in each segment  is
calculated as the arithmetic sum of the concentration increments resulting from the
various sources.
 	 EXAMPLE VI-8
        The previous two example problems  involved calculations of nitrogen concentra-  •
   tion in the Patuxent Estuary resulting from individual nitrogen sources.  The        '
   objective of this example is to find the total nitrogen concentration  In the         j
   estuary resulting from both nitrogen sources.                                         I
        The eight-segment scheme of Examples VI-6 and VI-7 is retained for this         |
   problem.  For each segment, the incremental nitrogen increases are summed to give    j
   the total concentration:                                                             j

           c • cb * CA                                                                  i
   where                                                                                j
           C^  »  concentration resulting from the H source discharging into the
                  estuary at point A.
   For segment 1, the calculation is:                                                   |
           C « 1.75 mg/1 (from river) + 0.43 mg/1 (from local source)
             « 2.18 mg/1 total nitrogen                                                 j
   Necessary data and final concentrations for each segment are shown in Table          I
   Vl-15.                                                                                i
                                          -206-

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                                       TABLE  VI-15
                      DISTRIBUTION  OF  TOTAL NITROGEN IN  THE PATUXENT
                         ESTUARY  DUE TO TWO SOURCES  Of NITROGEN
Segment Number
8
7
6
5
4
3
2
1
River
Results From
Problem VI -4
Total Nitrogen
From River
ngN/1, Cj,
0.07
0.21
0.36
0.55
0.80
1.30
1.56
1.75
1.88
Results From
Problem VI-5
Total Nitrogen
From Point A Source
(Segment 4)
mgN/1, CA
0.25
0.74
1.26
1.93
3.06
1.74
0.95
0.43
0.00
Resultant
Concentration
c"cb * CA
rooN/l
0.32
0.95
1.62
2.48
3.92
3.04
2.51
2.18
1.88
i                                                                                        !
:	END OF EXAMPLE VI-8	'
6.4.5  Dispersion-Advection Equations for Predicting Pollutant Distributions
     Disperslon-advect1on equations offer an attractive method, at least theoretically,
of predicting pollutant and dissolved oxygen concentrations in estuaries.  However,
from the point of view of hand calculation, the advection-dispersion equations are
usually tedious to solve, and therefore mistakes can unknowingly be Incorporated into
the calculations.
     Dispersion-advection equations have been developed in a variety of forms,
including one-, two-, and three-dimensional representations.  The equations in this
section are limited to one-dimensional representations in order to reduce the amount
of data and calculations required.
     One-dimensional  dlspersion-advectlon equations can be expressed In quite diver-
gent forms, depending on boundary conditions, cross-sectional  area variation over
distance, and source-sink terms.   O'Connor (1965),  for example, developed a variety
of one-dimensional advection-dispersion equations for pollutant and dissolved oxygen
analyses in estuaries, some of which are infeaslble for use on the hand-calculation
level.

                                         -207-

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     The advection-dispersion equations to be presented subsequently In this chapter
 can be used to  predict:
        •    Distributions of conservative or non-conservative pollutants
        •    Pol Mutant distributions 1n embayments
        •    Dissolved oxygen concentrations.
 Solutions from  advect1cm-dispersion can be superposed to account for multiple
 discharges.  Example VI-9, to be presented subsequently, will illustrate this
 process.
     As the name of the equations implies, dispersion coefficients are  needed in
 order to solve  advectIon-dispersion equations.  Tidally averaged dispersion coeffic-
 ients are required for the steady-state formulations used here.   The tidally averaged
 dispersion coefficient (EL) can be estimated from the following  expression:

                                   r  .	RS_                             (VI-35)
                                    L   A dS/dx
                                                                            (VI'36)
                                       x+Ax
where
        S    •  tidal ly and cross sectional ly averaged salinity in vicinity of
                discharge
        2Ax  »  distance between the salinity measurements $4   (at a distance
               Ax down estuary) and Sx    (at a distance of AX up estuary)
        R    «  freshwater flow rate in vicinity of discharge.
The distance interval 2Ax should be chosen so that no tributaries are contained
within the interval .
     In the absence of site specific data, the dispersion coefficients shown  in
Tables VI-16 and VI-17 can provide estimates of dispersion coefficients.
     For pollutants which decay according  to first  order  decay kinetics, the steady
state mass balance equation describing their distribution  is:
                                      •        - «  • 0                   (V.-37)

The solution to Equation VI-37 is:
                                         x > 0(down estuary)             (VI-38a)
                        C •
                             £ e J|X     x < 0(up estuary)
                              o
                                        -208-

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                                   TABLE VI-16



               TIDALLY AVERAGED  DISPERSION  COEFFICIENTS  FOR SELECTED

                        ESTUARIES  (FROM HYDROSCIENCE,  1971)
Estuary
Delaware River
Hudson River (N.Y.)
East River (N.Y.)
Cooper River (S.C.)
Savannah R. (Ga. , S.C.)
Lower Raritan R. (N.J.)
South River (N.J.)
Houston Ship Channel (Texas)
Cape Fear River (N.C.)
Potomac River (Va. )
Compton. Creek (N.J.)
Uappinger and
Fishkill Creek (N.Y.)
*1 mi2/day « 322.67 ft2/sec
rtiere
J2 « 	 fl -\/l + -
2AEL \^ V
Freshwater
Inflow
(cfs)
2,500
5,000
0
10,000
7.000
150
23
900
1,000
550
10

2

F A2\
bL\
R1 /
Low Flow
Net Uontidal
Velocity ( fps)
Head - Mouth
0.12-0.009
0.037
0.0
0.2G
0.7-0.17
0.047-0.029
0.01
0.05
0.48-0.03
0.006-0.0003
0.01-0.013

0.004-0.001

f)i spers ion
Coeff ic icnl
? *
5
2U
10
3D
10-20
5
5
?7
2-10
1-10
1

0.5-1

       j,
  R    /     /
      [1 +W
2AE       v
       Co-  -
        0    R ./l+(4kEL/ir)




        U   »  net velocity


        k   «  decay  rate


        W   »  discharge rate of pollutant (at x • 0).


     For Equations VI-38a and VI-38b to accurately estimate the pollutant distribution

in an estuary, the cross-sectional area of the estuary should be fairly constant over
                                        -209-

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                              TABLE VI-17

                TIDALLY AVERAGED DISPERSION COEFFICIENTS
                          (FROM OFFICER.  1976)
   Estuary
Dispersion Coefficient
    Range (ft2/sec)
            Comments
San Francisco Bay
     Southern Arm
     Northern Arm
Hudson River
Narrows of Mercey
Potomac River
Severn Estuary
Tay Estuary



Thames Estuary



Yaquina Estuary
     200-2,000
     500-20,000
   4,800-16,000
   1,430-4,000
      65-650
      75-750
   (by Stomnel}
     580-1,870
     (Bowden)
     530-1,600
    (up  estuary)
   1,600-7,500
   (down estuary)
     600-1,000
    (low flow)
      3,600
    (high flow)
     650-9,200
    (high How)
     140-1,060
    (low flow)
 Measurements  were made  at  slack
 water over  a  period of  one to  a
 few days.   The  fraction of
 freshwater  method was used.
 Measurements  were taken over
 three tidal cycles at 25
 locations.
 The dispersion  coefficient was
 derived by  assuming Ei   to  be
 constant for  the reach  studied,
 and that it varied only with
 flow.  A good relationship
 resulted between EL and flow,
 substantiating  the assumption.
 The  fraction of freshwater
 method was used by taking mean
 values of salinity over a  tidal
 cycle at different cross
 sections.
 The dispersion  coefficient  was
 found  to be a function  of  dis-
 tance below the Chain Bridge.
 Both salinity distribution
 studies (using  the fraction of
 freshwater method) and  dye
 release studies were used  to
 determine E, .
 Bowden recalculated  L  values
 originally determined by
 Stommel, who  had used the
 fraction of freshwater  method.
 Bowden included the fresh-
 water  inflows from tributaries,
 which produced  the larger
 estimates of  E,  .

 The  fraction of freshwater
 method was used.  At a  given
 location, EL was found  to vary
with freshwater inflow  rate.
Calculations were  performed
 using the fraction of fresh-
water method,  between 10 and
 30 miles below London Bridge.
The dispersion coefficients for
high flow conditions  were  sub-
stantially higher  than  for  low
flow conditions, at  the  same
locations.   The  fraction of
freshwater method  was used.
                                   -210-

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 distance,  and  the estuary  should be relatively long.  For screening purposes the
 first  constraint can be met by choosing a cross-sectional area representative of the
 length of  estuary being investigated.  If the estuary 1s very short, however, pollut-
 ants might be  washed out of the estuary fast enough to prevent attainment of a
 steady-state distribution  assumed by Equations VI-38a and VI-38b.  For shorter
 estuaries  the  fraction of  freshwater method, modified tidal prism method, or near
 field  approach  are more appropriate.
     At  times  when the freshwater flow rate in an estuary 1s essentially zero pollutant
 concentrations might increase to substantial levels, if tidal flushing 1s small.
 Under  these conditions the mass-balance expression for a pollutant obeying first
 order  kinetics  is:
                                  E.  d2C  - kc
                                   L    -
                                                       (VI-39)
The solution to this equation is:
                        exp
CQ exp
where
                                            for  x  >  0 {down estuary)
                                            for x <0  (up estuary)
                                                       (Vl-40a)
                                                                            (VI-40b)
                                                                            (VI-41)
When the pollutant is conservative  (i.e.,  k  •  0),  Equation  VI-39  reduces  to:

                                          d2C
The solution is:
                                       E.  	 - 0
                                        L dxj
         CQ  ,  x < 0 (up estuary)
                                                      (VI-42)
                                                                           (VI-43a)
                              	  (L-x)  +  C.   ,  x > 0 (down estuary)      (vi-43b)
                              ELA
where
        Co * CL
                  HI
        CL  «  background concentration of the pollutant at the mouth of the
               estuary
        L   «  distance from the discharge location to the mouth of the estuary.
                                        -211-

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Equation Vl-43 Illustrates the important concept that the concentrations of conserva-
tive pollutants are constant up estuary from the discharge location (when the river
discharge  is negligible) and decrease linearly from the discharge point to the mouth
of the estuary.  Equations VI-40 and VI-43 apply to estuaries of constant,  or approxi-
mately constant, cross-sectional area (e.g. sloughs).  If the cross-sectional  area
increases  rapidly with distance toward the mouth, the methods presented in  Section
6.5 are more appropriate.
     The dissolved oxygen deficit equation (where deficit is  defined  as the difference
between the saturation concentration and the actual dissolved oxygen  concentration)
for one-dimensional estuaries at steady-state conditions is:

                                L'-D
                                —    L  n - kP * kL
                                cx       dx*    *
where
        D   •  dissolved oxygen deficit
        L   •  BOO concentration
        k,  «  reaeration rate
        k   «  BOO decay rate.
Using Equation IV-38 to represent  the  BOD distribution, the  expression  for the
deficit D u:
                  exp  	 * I  -  —=z  exp
    -      (»:&\
* Tr exp\~l—  /
                                                                             (VI-45)
where
        The plus sign (*) is used to predict concentrations  up estuary  (x  <  0)
        The minus sign (-) is used to predict concentrations down estuary  (x >  0)
         a,  -  U^

        a2  »  U2 t
         M  •   mass  flux  of dissolved oxygen deficit contained in the discharge.
         W  «   mass  flux  of ultimate BOD contained in the discharge, (Cs - Ce)^e.
        Cs  »   saturation concentration of dissolved oxygen.
        Cf  «   effluent concentration of dissolved oxygen.
        *e  «   effluent flowrate.
The advantage of expressing  the  dissolved  oxygen  concentration in  terms of the
deficit is that the  principle of superposition  can be  invoked  for  multiple discharges
within a single estuary.   Specifically:

                                      D • L D                                (Vl-46)
                                         -212-

-------
and
                                       cs -  z o,
(VI-47)
where
        0,   «   dissolved oxygen deficit resulting  from  the  i— discharge
        C   •   final dissolved oxygen concentration
        Cs  »   dissolved oxygen saturation level.
Figure VI-23 shows  the relationship between dissolved  oxygen saturation and temperature
and salinity.
           FIGURE VI-23   DISSOLVED OXYGEN SATURATION AS  A FUNCTION
                            OF TEMPERATURE AND  SALINITY
                                EXAMPLE VI-9
       Dissolved Oxygen  Concentration Resulting from Two Sources of BOD               I
                                                                                    i
       Two municipal  wastewater treatment plants discharge  significant quantities of  |
  BOD into the James  River  in Virginia.  One discharges  near Hopewell, and the        j
  second 10 miles further down estuary, near West Point.  Calculate the dissolved
  oxygen concentration in the estuary as a function of distance.  Pertinent data
  are:                                                                              I
                                       -213-

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           BOD, in Hopewell plant effluent • 69,000 Ibs/day                             1
              *                                                                         i
           BOD, 1n West Point plant effluent, located 10 miles downstream from          |
             Hopewell • 175,000 Ibs/day                                                 I
           Freshwater flow rate » 2,900 cfs                                             |
           Dissolved oxygen saturation » 8.2 mg/1                                        j
           Cross sectional area • 20,000 ft2                                            j
           Reaeration rate • 0.2/day
           Deoxygenatlon rate • 0.3/day                                                 J
           Dispersion coefficient • 12.5 m12/day                                         I
                                                                                        i
           Effluent dissolved oxygen - 0.0 mg/1.                                         |
        The dissolved oxygen deficit due to each of the  two  contributions  can  be         j
   determined independently of the  other using  Equation  IV-45.  The  results  are          j
   plotted  in Figure VI-24.   The deficits are added to produce  the total deficit
   (D(x)) due to both discharges (Figure VI-24a).   The distance scale  in Figure
   VI-24a  Is referenced to the Hopewell  plant.  The West Point  plant  1s placed at        !
   mile  10.   When the deficit at this location  due  to the West  Point plant  1s  calcu-     j
   lated, set x • 0 in Equation VI-45.   The dissolved oxygen concentration then          I
   becomes  C(x)  • 8.2-D(x),  and is  shown in Figure  VI-24b.                               |
        One example calculation of  dissolved oxygen deficit  will  be  shown  to Illus-      j
   trate the process.   Consider the deficit produced at  mile 0.0, due  to the Hopewell    j
   plant.   The waste loading front the Hopewell  plant is:
           69,000 x 1.46 « 100,000  Ibs/day, BOD-ultimate                                j
                         • 1.16 Ibs/sec
   When  x   -  0,  Equation VI-45 simplifies  to:                                           !
                                                                                        I
                           /2900\2     4(.3)(12.5)(5280)(5280)          ft2           ;
I          a, • IT «• 4k  E.  (	1   +   	  •  .077  	
j                         L  \20000/           81400 • 86400               sec2          j
j   so                                                                                  j
I                                                                                       j
j                                 \TaT - .278 ft/sec                                    \
I                                    ,                                                  I
j          a2 - U2 * 4k2EL « 0.058 ft2/sec2

!   »                                                                                  j
                                                                                       !
                                     1 -242 ft/sec                                     |

                                         -214-

-------
 0>
 O
O
•o
 •
"5
 n
 7.0-

6.0-

5.0-

4.0-

3.0-

2.0-

1.0-
                                 	Deficit due to Hopewell
                                 	  Deficit due to West Point
                                 — —  Total deficit
      -15  -10
                  0        10
               Hopewell  WestrPomt
20
30
40
50
                             Miles Below Hopewell
                                      (a)
    8.0-
§   7.0-
g
u
6
TJ
0)
"5
at
10
    5.0 H
    4.0-
3.0-
                         _di£8£jved_px^pen ^saturation
      -15   -10
                               10
                                    20
         30
                                                       40
                   50
                             Miles Below Hopewell
                                     (h)
      FIGURE VI-24   PREDICTED DISSOLVED OXYGEN  PROFILE
                       IN  JAMES  RIVER
                                 -215-

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1 The deficit 1s:
I (.3){1.16)
1 n *
r i IT
. o t v m-5 iK/ft
! 20000(.2-.3) L -278 .242 _
• This value 1s then plotted in Figure VI-24 at mile point 0.0.
. at this location due to West Point is evaluated at x • -10 ml
! VI -45, since West Point 1s located 10 miles down estuary of H
1 of 0.6 mg/1 is found, and 1s plotted In Figure VI-24 at mile
I deficit at Hopewell is 1.5 + 0.6 • 2.1 mg/1, as shown 1n the
t
I
'. 	 run nr PYAMPI P VT.Q 	
1
i
3 « 1.5 mg/1 j
i
The deficit :
les in Equation
opewell. A deficit !
point 0.0. The total '
*
figure. |
i
6.4.6  Prltchard's Two-Dimensional Box Model for Stratified Estuaries
     Many estuaries 1n the United States are either stratified or partially mixed.
Because the circulation of stratified systems 1s fairly complex, few hand calculation
methods are available for their analysis.  Instead computerized solutions are gener-
al ly used.
     One method developed by Pritchard (1969) which predicts the distribution
of pollutants In partially mixed or stratified estuaries is suitable for hand
calculations provided the user does not require too much spatial resolution.
This method, called the "two-dimensional box model," divides the estuary horizontally
from head to mouth into a series of longitudinal segments.  Each segment is divided
into a surface layer and a bottom layer.  The analysis results 1n a system of n
simultaneous linear equations with n unknowns, where n equals twice the number of
horizontal segments.  The unknowns are the pollutant concentrations in each  layer.
     Division of the estuary into only two horizontal segments results in four
simultaneous equations, which is probably the most one would like to solve entirely
by hand.  However, many programmable hand calculators contain library routines for
solving systems of 10 or more simultaneous equations, which would allow the estuary
to be divided into 5 or more horizontal segments.   If many more segments are desired,
the solution could be easily implemented on a computer using a numerical  technique
such as Gaussian elimination to solve the resulting system of simultaneous linear
equations.
     The following information is required for the two-dimensional box analysis:
1) the freshwater flow rate due to the river; 2) the pollutant mass loading rates;
and 3) the longitudinal salinity profiles along the length of the estuary in the
upper and lower layers, ana the salinity at the boundary between these two layers.
The upper layer represents the portion of the water column having a net nontidal flow
directed seaward, and the lower layer represents the portion of the water column
having net nontidal flow directed up to the estuary.  If no velocity data are avail-
                                         -216-

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able, these  layers can generally be estimated based on the vertical  salinity  profiles.
     Figure Vl-25 shows the parameters used  in the analysis, which are  defined
as follows:
             n           « segment number, Increasing from head toward mouth
             (S )        » salinity in upper layer of segment n
             ($,)        - salinity in lower layer of segment n
             (Sy)n       « salinity at the boundary between the upper and
                           lower layers of segment n
             (Sy)n ,   n  « salinity In the upper layer at the boundary
                           between segments n-1 and n
             (Sj)n_j   n  « salinity in the lower layer at the boundary
                           between segments n-1 and n
             (Qu)n_^   n  « net nontidal flow rate in the upper layer from
                           segment n-1 to n
             (Qi)n i   n  " net nontidal flow rate in the lower layer from
               A n ™ i t i
                           segment n to n-1
             ^v^n       * nc* uP*ard vertical  flow from the lower to the
                           upper layer of segment n
             E           » vertical exchange coefficient between the lower and
                           upper layers of segment n
             R           » freshwater flow rate due to river
             (qu)n       » pollutant mass loading rate to upper layer of
                           segment n (from external sources)
             (Qj)n       • pollutant mass loading rate to lower layer of
                           segment n (from external sources)
             ^u^n       * Poll0**"* concentration in the upper layer of
                           segment n)
             (C^)n       « pollutant concentration in the lower layer of
                           segment n.
     Pritchard's two-dimensional box analysis as presented  here requires the following
assumptions:
        •    Steady-state  salinity distribution
        •    The pollutant is  conservative
        •    The concentration of the  pollutant is uniform  within  each  layer of
             each segment  and
        •    The pollutant concentration  at  the boundary between  segments or layers
             is equal  to  the  average of the  concentrations  in the  two adjacent
             segments  or  layers.
     Application of the two-dimensional box  model  involves  six  steps.  These are:
             1.   Plot the longitudinal salinity profiles in  the  upper  and  lower
                                         -217-

-------
       n-1
                   «Mn
                                                                                    n-M
                Jn-1,n
                                    t          (Svl  —
           __  —  -•  —  — "" r-  — ~~
  .•.,*• • ..•: ••"•'•i ••••'•
•.••..*•••••«. •.•••.•'•.
                                                 , ,,

                                        ';•••.'••••::'••.•.;
                                        .•»••.••.••••  •••.
'.«•'..* •;•'«;• ".»..•".'• •'.   » •
•;^ ; ••• :•••.• «'.•.•/•.».. •;.:.•••'.••.»'.
:-'-V.i'..-*';..y-:V:.>:-.-.'.:-.''-'i---:v:V
FIGURE VI-25  DEFINITION  SKETCH FOR PRITCHARD'S  TWO-DIMENSIONAL  Box  MODEL
                   layers,  and at the interface between the two  layers.   If informa-
                   tion on  the net nontidal velocity distribution  is  not  available to
                   define the layers, the boundary may be estimated for  a given
                   section  of the estuary as the depth at which  the vertical  salinity
                   gradient is maximum.  The resulting plots  wi11  be  used to determine
                   the  average salinities in each segment and layer,  and  the salini-
                   ties at  the boundaries between each segment  and layer.
                   Segment  the estuary.  The number of segments  will  depend on the
                   degree of spatial resolution desired, and  the limitations  of the
                   hand calculators used to solve the system  of  simultaneous equations.
                   The  accuracy of the results will generally  Increase with the number
                   of segments used, since the assumptions of  the  analysis are better
                   satisfied.  A minimum of three horizontal  segments should probably
                   be used  to obtain even a rough estimate of  the  pollutant distribution
                   in the estuary.  This will require the solution of six equations
                   and  six  unknowns.
                   Compute  the net nontidal  flows in the upper layer  and  lower layer
                   at the boundary between each horizontal segment using  Knudson's
                                          -218-

-------
                 Hydrographlcal  Theorem {Dyer,  1973):
(Q''"-'-"
                                        <*.>„...  .-'Vn-l. n
                                                                            (VI-4S)
                         (Q,)
                           1  "• "-1      n *  
-------
                                           n-1
                                                                              (VI-53)
                                        - E.
             for the lower layer of segment n.

     Since oust pollutant discharges are buoyant, they should be considered as
loadings to the upper layer, even though they My be physically Introduced  at
the bottom.  Pollutants which are denser than the upper waters and which would
sink to the bottom should be considered as loadings to the lower layer.   However,  the
analysis 1s not applicable to pollutants which  tend to remain near the bottom and
accumulate 1n or react with the bottom sediments.
     The above mass balance equations can be simplified and rearranged Into the
following form:
          (Q
            u n-]
         u>n  +  [2En +
            *v  n
.
                                                                              (VI-54)
for the upper layer of segment n and
- (Q..).
                                   n   *^v n
).   +
             u n
                                                             -2E.
                                          Vl
                                                                             (VI-55)
 for the  lower  layer of segment n.  This pair of equations Is written for each
 segment, resulting 1n a system of simultaneous equations where the concentra-
 tions,  (Cu)n and  (Cj)n, *^« the unknowns, the terms enclosed in square brackets
 are the  coefficients, and the terns on the right hand side of the equations are the
 constants.
     However,  since each equation involves both the upstream and downstream segments
                                         -E20-

-------
for a given layer, the boundary conditions at both the upstream and downstream end of
the estuary must be applied so that there will not be more unknowns than equations.
At the upstream end of the estuary, the following boundary conditions apply:
         (0  )  j  n " R * river fl°* rate
            n. Alternatively,
the concentration outside the mouth may be  assumed to equal some fraction  of the
concentration Inside the mouth, or:
                - fc (Cu)n
                                        -221-

-------
 where f  is  the selected  fraction.   The previous assumption (Cu)n+1 • {Cy)n
 1s  one case  of  this second assumption where the fraction equals one (f  * 1).
 Using  the second more general assumption, the equation of the upper layer of the  last
 downstream segment  simplifies to:
.  „]
' fc 
                                                   «n
                                                                              (VI -60)
     Step (6) of the two-dimensional box analysis Involves computing all of the
coefficients and constants in the system of equations defining each segment and
layer (Equations VI-54 and VI-55) and applying the boundary conditions to produce
equations for the first upstream and last downstream segments 1n the estuary (Equations
Vl-56 through VI -60).  The coefficients and constants are functions of the variables
previously computed in steps (3) through (5).  The resulting equations are then
solved using library routines in programmable hand calculators, or by programming an
appropriate numerical technique such as Gaussian elimination on either a programmable
hand calculator or a computer.
     Since the analysis requires application of the boundary conditions at the
freshwater^ head of the estuary  and the coastal mouth of the estuary to obtain
the same number of equations as unknowns, the entire estuary must be Included
In the first cut analysis.  The initial analysis will yield the overall pollutant
distribution throughout the entire estuary.  Once this is determined, the analysis
could be repeated to obtain more detail for smaller portions of the estuary by  using
the first cut results to estimate the pollutant boundary conditions at each end of
the region of concern, and then rearranging equations (7) and (8) so the terms
involving the concentrations outside the specified regions are treated as constants
and moved to the right hand side of the equations.
     The Pritchard Model theoretically allows external pollutant loading to be
introduced directly into any segment along the estuary.  By moving external loadings
from the head to near the mouth of the estuary, the planner can predict how pollutant
levels are affected.  However,  experience with the model has shown that when external
side loadings are considerably  larger than those which enter at the head of the
estuary, model instabilities can arise.  When this occurs, the pollutant profile
oscillates from segment to segment, and negative concentrations can result.  It  is
recommended that the user first run the Pritchard Model by putting all pollutant
loading into the head of the estuary.  This situation appears to be always stable,
and, as the following example shows, reasonable pollutant profiles are predicted.
                                         -2?2-

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I	EXAMPLE  VI-10	'
i                                                                                        !
!                   Pollutant  Distribution 1n a Stratified Estuary                        |
i                                                                                        i
         The Patuxent  River  1n Maryland  1s  a partially stratified estuary, where         j
.    the  degree  of  stratification depends on the freshwater flow rate discharged
!    at the  head  of the estuary.  Table VI-18 shows the salinity distribution within      !
j    the  estuary  under  low  flow conditions for each segment and layer.  The location of   j
I    each layer  Is  shown  In Figure Vl-26.  Also shown 1n the table 1s the pollutant       I
|    distribution by  layer  and segment for a Mass flux of 125 Ibs/day (57 kg/day) of      |
j    conservative pollutant Input at the head of the estuary.                             j
j         The pollutant distribution was predicted by solving on a computer the
    12-segment,  2-1ayer  system (24 simultaneous equations).  The salinity distribution   <
!    shown 1n Table  VI-18 was used as Input data.  As a point of Interest, the same       !
!    network  was  solved using the model WASP (courtesy of Robert Ambrose, ERL, U.S.       {
I    Environmental  Protection Agency, Athens, Georgia), which 1s a dynamic two-d1men-     I
»                                                                                        i
|    slonal estuary model.  Instead of using salinity directly. WASP predicts the         |
j    salinity distribution based on dispersive and advectlve exchange rates.  The         j
j    salinity distribution predicted by WASP 1s the same as shown 1n Table VI-18, which   j
    was  u*ed n  Input to PHtchard's Model.  After running WASP to steady-state          '
,    conditions,, the  pollutant distribution throughout the estuary was virtually the
I    same  as  predicted by PrUchard's Model.
I         The pollutant distribution 1n the Patuxant estuary will be solved In detail
|    using 4  segments Instead of 12.  The resulting system of 8 simultaneous equations
j    can  be solved on a variety of hand-held calculations.  The tabulations below show
j    salinities at each segment boundary, and the horizontal  flow rates 1n the upper
    and  lower layers.
          Boundary   (Vn-l,n    (Vn-l,n   
-------
, TABLE VI -18 j
1 SALINITY AND POLLUTANT DISTRIBUTION IN PATUXENT !
j ESTUARY UNDER LOW FLOW CONDITIONS f
i
! Salinity
| {as Chloride, mg/1)
1 Segment Number Upper Layer
1
j 1 496.
j 2 1831 .
i
1 3 3771.
1 4 6050.
! 5 8040.
6 9310
1
7 10010.
1
j 8 10790.
j 9 11240.
1 '10 11830.
1 El 12100.
! 12 12750.
boundary 13500.
1
i
1
| The salinities within each layer,
Lower Layer
524.
1940.
3970.
6280.
8220.
9910.
10660.
11070.
11760.
12120.
12650.
12850.
13500.

the salinity and
Pollutant Concentration
Upper Layer
0.193
0.173
0.144
0.100
0.081
0.062
0.051
0.040
0.033
0.025.
0.021
0.011
0.0

Lower Layer J
i
0.192 j
0.171 1
0.141 J
0.108 !
0.078
1
0.053
0.042 j
0.036 j
0.025 1
0.020 !
0.013 !
I
0.009 j
0.0 j
1
i
flow rate between the interface j
1 of each layer, and the exchange coefficients are tabulated below. 1
i
1 C A — 	 M + ' ^. t / «fc ^ ^ J _
i oegment u n v n
n mg/l-Cl mg/l-Cl
! 1 1830 1890
j 2 8040 8130
j 3 10790 10930
{ 4 12100 12380

mg/l-Cl m /sec
1940 113.
B220 23.
11070 -45.
12650 63.
' The flow rates were found from Equation VI-50, and
1 from Equation VI-51.
1 Substituting these data into
the pollutant ma;

m /sec
3260.
3140.
930.
280.
the exchange
is balance exp
I
i
i
i
i
i
coefficients
1
resslons (Equations 1
-224-

-------
FIGURE VI-26  PATUXENT ESTUARY MODEL  SEGMENTATION
                      -225-

-------
 t   VI-54 through  VI-59),  the following system of equations result:
   -6528.
    6411.
     117.
       0.
       0.

       0.
       0.
 6638.
-6525.
    0.0
    0.
    0.
    0.
    0.
 -117.
    0.0
-6275.
 6252.
  139.
    0.
    0.
    0.
    0.
  113.
 6297.
.6275.
    0.0
 -136.
    0.
    0.
    0.
    0.
 -139.
    0.0
.1856.
 1901
   94.
    0.
    0.
    0.
    0.
  136
 1811.
.1856.
    0.0
  -91.
o.
0.
°-
0.
-94.
0.0
-561
499.
0."
0.
0.
0.
0.
91.
624.
.561








(cu>;
(c])1
(CU>2
3
4
2
 3
 4
                                OF EXAMPLE VI-10 -•
6.5  POLLUTANT DISTRIBUTION FOLLOWING DISCHARGE FROM A KARINE OUTFALL

6.5.1  Introduction
     Numerous coastal states have enacted water quality standards which limit
the maximum allowable concentration of pollutants, particularly metals and organic
                                         -226-

-------
toxicants, which can be discharged  into estuaMne and coastal waters.   The  standards
normally  permit that an exempt area, called a mixing zone, be defined around  the
outfall where water quality standards are not applicable.  For example,  the Water
Quality Control Plan for Ocean Waters of California (State Hater Resources  Control
Board, 1978) sets forth the following statement directed at toxic substance limitations:
             "Effluent limitations  shall be imposed in a manner prescribed
        by the State Board such that the concentrations set forth ... as
        water quality objectives, shall not b* exceeded in the receiving
        water upon the completion of initial dilution."
     The  mixing zone, or zone of initial dilution (ZID), 1s non-r1gorously defined as
the volume of water where the wastewater and ambient saline water mix during the
first few minutes following discharge, when the plume still has momentum and buoyancy.
As the wastewater 1s discharged, it normally begins to rise because of Its buoyancy
and momentum, as Illustrated 1n Figure VI-27.
     If the ambient water column is stratified and the water depth is great enough,
the rising plume will not reach the surface of the water, but rather will stop at the
level where the densities of the plume and receiving water become equal.  This level
is called the plume's trapping level.  (See Figure Vl-27.)  Due to residual  momentum,
the plume might continue to rise beyond the trapping level, but will tend to fall
back aftar the momentum 1s completely dissipated.   Once the plume stops rising, the
waste field begins to drift away from the ZID with the ambient  currents.  At this
time, initial dilution is considered complete.  Section 6.5.2,  which follows, shows
how initial dilution is calculated, and then Sections  6.5.3 and 6.5.4 Illustrate how
pollutanv concentrations at the completion of initial  dilution  can be predicted.
Sections  6.5.5 and 6.5.6 explain methods of predicting pollutant  and dissolved oxygen
concentrations,  respectively,  as  the waste field migrates away  from  the ZID.
     The  methods  presented  1n  Sections  6.5.2 through 6.5.6 are  applicable to strati-
fied or non-stratified  estuaries,  embayments,  and  coastal  waters.   The methods assume
that reentrainment of previously  discharged effluent back into  the ZID is negligible.
Reentrainment can  occur if  the wastewater  1s discharged  into  a  confined  area where
free circulation  is impaired  or because of tidal  reversals  in narrow estuaries.

6.5.2  Prediction of Initial  Dilution

6.5.2.1   General
     Discharge to bodies of water through submerged diffusers is a common waste
water management technique.  A diffuser 1s typically a pipe with discharge ports
spaced at regular intervals.  Such discharges are often buoyant with high exit
velocity relative to the ambient velocity.  The resulting waste streams act as plumes
or buoyant jets.  The velocity shear between ambient and plume fluids results in the
                                         -227-

-------
                                                               Ptrticutite*
                                                             (which  settle  out
                                                              of  dntt field)
       Effluent leaving
        difruser ports

           FIGURE  VI-27  WASTE FIELD  GENERATED  BY MARINE OUTFALL


Incorporation of ambient  fluid  into  the plume,  a  process  called  entralnment.   Initial

dilution results from the entrainment  of ambient  fluid Into the  plume  as the plume
rises to Its trapping level.

     The magnitude  of Initial dilution depends  on a  number of  factors  including,

but not limited to, the depth of water,  ambient density  stratification, discharge
                                        -228-

-------
 rate, buoyancy,  port  spacing  (I.e.  plume  merging),  and  current  velocity.   These
 factors may  be  referred  to  collectively as  the  dlffuser flow configuration or simply
 the  flow  configuration.   Depending  on  the flow  configuration, the Initial  dilution
 may  be  less  than  10 or greater  than 500.   As  attaining  water quality  criteria may
 often require relatively  high Initial  dilution, the  need to  be  able to  estimate
 Initial dilution  for  various  flow configurations  becomes apparent.
     Other than  actually  sampling the  water after a  facility 1s In operation,
 there are various ways to estimate  pollutant  concentrations  achieved  in the  vicinity
 of a particular dlffuser.   A scale  model  faithful to all similarity criteria  could
yield the necessary dilution Information.   Dimensional  analysis  and empirical  formulae
may  also be  very  useful.  Alternatively,  a  numerical model based  on the laws  of
physics may  be developed.   This method is chosen  to provide  initial dilution  estimates
here because it is more cost-effective than field sampling and  more accurate  than a
scale model.
     Any numerical model  used to provide  dilution estimates  should faithfully
replicate the relevant plume relationships  and should be verified for accuracy.
The plume model MERGE (Frlck, 1981c) accounts for the effects of  current ambient
density stratification and  port spacing on  plume  behavior.   In  addition, it has been
extensively verified  (Frick, 1981a,  1981b; Tesche et_ a]_., 1980;  Pollcastro et^ al_.,
1980; Cawiar! et_ aj_., 1981).
     There are several ways of presenting  the initial dilution estimates.   MERGE may
be run for specific cases or run for many  cases spanning a range of conditions and
presented in nomogram or tabular form.   The latter method Is the most compact.  The
resulting inRial dilution  tables display  values of dilution achieved at the indicated
depths and densimetric Froude numbers.   One hundred tables are presented in Appendix
G for various combinations  of port  spacing, density stratification, and effluent-to-
current velocity  ratio.
     Before describing the  tables in more detail and discussing examples,  it may be
helpful  for some users to read the  following, occasionally technical, discussions of
the plume model  MERGE (Section 6.5.2.2) and of basic principles  of similarity (Section
6.5.2.3).   Others may want  to advance directly to Section 6.5.2.4 describing table
usage.

6.5.2.2  The Plume Model  MERGE
     MERGE 1s the latest in a series of models whose development began in  1973.
Various stages of model  development  have been recorded (Winiarski and Frick,  1976 and
1978; Frick,  1981c).   In the realm of plume modeling, MERGE  belongs  to the  Lagrangian
minority since more models «re Eulerian.   The  model  can  be  demonstrated  to  be basically
equivalent to its Eulerian counterparts (Frick and Winiarksi, 1975;  Frick,  1981c).
Time is the independent  variable which  is  incremented in every program iteration
based on the  rate of entrainaent.

                                        -229-

-------
      To simplify the problem, many assumptions and approximations are made 1n
 plume modeling.   In MERGE,  steady-state 1s assumed and the plume 1s assumed to
 have a round cross section  everywhere.
      The MERGE user may Input arbitrary current and ambient density profiles.
 The model Includes a compressible equation of continuity  so that the predictions
 are also valid for highly buoyant plumes.   It accounts for merging of adjacent
 plumes but only  when the ambient current dilution 1s normal to  the dlffuser pipe.   In
 many cases,  this 1s not a significant  restriction as many dlffusers are oriented to
 be normal to the prevailing current direction.
      The model contains an  option for  using either constant or  variable coefflents
 of bulk expansion 1n the equation of state.  The water densities 1n Table VI-19
 are generated using the model's density subroutine based  on actual  temperatures
 and salinities (I.e. effectively using  variable coefficients).   If temperature
 and salinity data are unavailable then  the model can be run based on density data
 alone.   The  latter method Is satisfactory  for relatively  high temperatures and
 salinities because the equation of state 1s relatively linear with these variables  1n
 that range.   However, for low densities and temperatures  gross  Inaccuracies may
 result.  Unfortunately, the Initial dilution tables are based on the latter method.
 A nore accurate  representation would greatly Increase the number of tables necessary
 to cover all the cases.  Users with applications Involving cold, low salinity water
 are urged ro run the more accurate form of the model.
     The  success of MERGE In predicting plume behavior 1s  primarily attributable
to two  unique model  features.  The first of these relates  to the expression of
forced  entralnment.  Entralnment may be attributed to the  velocity shear present even
1n the  absence of currents.  I.e. aspiration, and to current-Induced entrainment,
sometimes  called forced entrainment.
     The  forced entrainment  algorithm In MERGE 1s based on the assumption that
all  fluid  flowing through the upstream projected area of the plume 1s entrained.
This hypothesis 1s based on  we11-established principles and observations (Rawn
«!«!., I960; Jlrka and Harlman 1973).   Paradoxically, the hypothesis has never
been implemented In numerical models before.  The projected area normally contains
linear and quadratic terms 1n plume diameter, whereas in conventional modeling,
forced entrainment is generally expressed as a linear function of diameter.  It 1s
necessary to Include additional sources of entrainment to  make up the difference when
so expressed.
     The second feature 1s the use of a constant aspiration coefficient.  This
coefficient 1s often considered to be variable (e.g. Fan,  1967).  The need for
a variable coefficient 1s attributable  to the fact that many models predict centerllne
plume values.  For plumes discharged vertically upward Into density stratified
ambient water, such models are expected  to predict the maximum penetration of the
plume.  To achieve agreement requires a  relatively small aspiration coefficient.

                                         -230-

-------
WATER DENSITIES (EXPRESSED AS SIGMA-T)* CALCULATED
   USING THE DENSITY SUBROUTINE FOUND IN NEKGE
Salinity
(°/oo) 0
0
5
10
IS
20
-0.093
.721
1.535
2.348
3.159
3.970
4.781
5.590
6.399
7.207
8.015
8.822
9.628
10.434
11.240
127015-
[?.850
13.654
14.459
15.263
I6.06F
16.870
17.674
18.478
19.281
-0.034
.776
1.586
2.395
3.203
4.010
4.817
5.623
6.428
7.233
8.037
8.840
9.643
10.446
11.248
12.019
12.851
H.652
14.453
15.254
16.051
16.855
17.655
18.455
19.225
2 4
.007 .031 .039 .030
.814 .835 .839 .827
1.620 1.637 1.638 1.623
2.425 2.439 2.437 2.419
3.230 3.240 3.234 3.213
4.033 4.040 4.031 4.007
4.836 4.840 4.818 4.800
5.639 5.639 5.623 5.593
6.441 6.437 6.418 6.385
7.242 7.235 7.213 7.176
8.042 8.032 8.007 7.967
8.842 8.829 8.801 8.758
9.642 9.625 9.594 9.548
10.441 10.421 10.387 10.338
11.240 11.217 11.179 11.127
12.038 12.012 11.971 11.916
12.836 12.807 12.763 12.705
13.634 13.602 13.555 13.494
14.432 14.396 14.346 14.282
15.229 15.190 15.137 15.071
16.027 15.985 15.929 15.859
16.824 16.779 16.720 16.647
17.621 17.573 17.511 17.436
18.418 18.367 18.302 18.224
19.255 19.161 19.093 19.012
TEMPERATURE (°C)
5 8
.006
.800
1.593
2.385
3.177
3.968
4.758
5.548
6.337
7.125
7.913
8.701
9.488
10.275
11.062
11.848
12.634
13.420
14.205
14.991
15.777
16.562
17.347
18.133
18.919
-0.032
.758
1.548
2.338
3.126
3.914
4.701
5.488
6.274
7.060
7.845
8.630
9.415
10.199
10.983
11.766
12.549
13.332
14.115
14.898
15.661
16.464
17.247
18.030
18.813
-0.086
.702
1.489
2.276
3.061
3.847
4.631
5.415
6.199
6.982
7.764
8.546
9.328
10.109
10.890
11.671
12.452
13.232
14.013
14.793
15.573
16.354
17.134
17.914
18.694
-0.154
.632
1.416
2.200
2.983
3.765
4.547
5.329
6.109
6.890
7.670
8.449
9.228
10.007
10.786
11.564
12.342
13.120
13.898
14.676
15.453
16.231
17.009
17.787
18.565
10
-0.235
.548
1.329
2.111
2.691
3.671
4.450
5.229
6.007
6.785
7.563
8.340
9.116
9.893
10.669
11.445
12.220
12.996
13.771
14.547
15.322
16.097
16.873
17.648
18.424

-0.330
.450
1.230
2.006
2.786
3.564
4.341
5.117
5.893
6.668
7.443
8.218
8.992
9.766
10.540
11.313
12.087
12.860
13.633
14.406
lb.179
15.952
16.725
17.498
18.271
12
-0.438
.340
1.117
1.893
2.669
3.444
4.218
4.992
5.766
6.539
7.312
8.084
8.856
9.628
10.399
11.170
11.941
12.712
13.483
14.254
15.025
15.796
16,566
17.337
18.108

-0.558
.217
.992
1.766
2.539
3.312
4.064
4.856
5.627
6.398
7.168
7.939
8.708
9.478
10.247
11.016
11.785
12.554
13.322
14.091
14.860
15.628
16.397
17.166
17.935
14
-0.691
.082
.854
1.626
2.397
3.16tJ
3.938
4.708
5.477
6.245
7.UI4
7.782
8.549
9.317
10.1)84
10.851
11.618
12.384
13.151
13.917
14.684
15.451
16.217
16.984
17.751
                    -231-

-------
TABLE Vl-19a
(Continued)
Salinity
(o/oo) 0
25 20.055
20.838
21.692
22.496
23.300
30 24.104"

20.056
20.856
21.657
22.457
23.258
24.059
2
20.012
20.810
21.607
22.405
23.202
24.001

19.955
20.749
21.544
22.338
23.133
23.929
4
19.884
20.676
21.467
22.259
23.051
23.843

19.801
20.589
21.378
22.167
22.956
23.746
TEMPEHATUKE (°C
5
19.704
20.490
21.276
22.063
22.849
23.636
19.596
20.379
21.162
21.946
22.730
23.514
)
8
19.475
20.256
21.037
21.818
22.599
23.381

19.343
20.121
20.900
21.678
22.458
23.237
10
19.199
19.975
20.751
21.528
22.305
23.082

19.045
19.819
20.592
21.367
22.141
22.916
12
18.880
19.651
20.423
21.195
21.967
22.740

18.704
19.473
20.243
21.103
21.783
22.554
14
16.518
19.285
20.053
20.821
21.5B9
22.358
         25.713  25.662  25.598  25.520  25.429  25.326   25.211   25.084  24.946  24.797  24.637  24.467  24.287  24.097  23.897
         26.518  26.464  26.397  26.316  26.223  26.117   25.999   25.870  25.729  25.578  25.416  25.243  25.061  24.869  24.667
         27.324  27.267  27.196  27.113  27.016  26.908   26.788   26.656  26.513  26.359  26.195  26.020  25.836  25.641  25.437
    35   28.130  25.070  27.996  77^10  27.611  27.700   27.577   27.422  27.297  27.141  26.974  26.798  26.611  26.414  26.208
         25.936  28.873  26.737  Zfl./OB  28.606  28.492   28.366   28.230  28.082  27.923  27.754  27.575  27.357  27.185  26.950
         29.743  29.677  29.598  29.506  29.401  29.285   29.157   19.017  28.867  28.706  28.535  28.354  28.163  27.963  27.753
         30.550  30.482  30.399  30.305  30.197  30.078   29.948   29.806  29.653  29.490  29.317  29.133  28.940  28.738  28.526
         31.358  31.287  31.202  31.104  30.994  30.872   30.739   30.595  30.440  30.275  20.099  29.913  29.718  29.514  29.300
    40   32.167  32.042  32.605  31.904  31.732  31.667   31.53?   31.3B5  31.227  31.060  30.682  30.694  30.497  36.290  30.075
•Stg«a-t (ff»)  is defined as:   (densUy-1)  x  103.   For  example,  for  seawater xlth a density of 1.02500 g/cm3, vt • 25.
                                                                 -232-

-------
                  TABLE VI-19b

MATER UENSITIES {EXPRESSED AS SIGMA-T)* CALCULATED
   USING THE DENSITY SUBROUTINE FOUND IN MERGE
Salinity
(°/oo)
0 -0.836
-0.065
.705
1.475
2.24*
5 3.012
3.780
4.548
5.315
6.082
10 6.848
7.614
8.379
9.145
9.910
15 10.675^
11.439^
12.204
12.969
13.733
20 14.498~
15. 26^
16.027
16.792
17.557
16
-0.993
-0.224
.544
1.312
2.079
2.845
3.611
4.377
5.142
5.907
6.671
7.435
8.198
8.962
9.725
10.488
11.251
12.013
12.776
13.539
14.301
15.064
15.827
16.590
17.353

-1.161
-0.394
.372
1.138
1.903
2.667
3.431
4.195
4.958
5.721
6.483
7.245
8.007
8.768
9.530
10.291
VI . 052
11.813
12.573
13.334
14.095
14.856
15.617
16.378
17.139
18
-1.341
-0.576
.189
.952
1.716
2.478
3.240
4.002
4.763
5.524
6.285
7.045
7.805
8.565
9.324
10.083
10.843
11.602
12.361
13.120
13.879
14.638
15.397
16.156
16.916

-1.532
-0.768
-0.006
.756
1.518
2.279
2.039
3.799
4.558
5.317
6.076
6.835
7.593
8.351
9.108
9.866
10.623
11.381
12.138
12.895
13.653
T4.410
15.168
15.925
16.683
20
-1.733
-0.971
-0.211
.550
1.309
?.06B
2.827
3.585
4.343
5.100
5.857
6.614
7.371
8.127
8.883
9.639
10.395
11.150
11.906
12.662
13.417
14.173
14.929
15.685
16.441
TEMPERATURE (°C
22
-1.945
-1.185
-0.426
.333
1.091
1.848
2.605
3.362
4.118
4.873
5.629
6.3B4
7.139
7.893
8.648
9.402
10.156
10.910
11.664
12.418
13.173
13.927
14.681
15.436
16.190
-2.167
-1.409
-0.651
.106
.862
1.618
2.373
3.128
3.882
4.636
5.390
6.144
6.897
7.650
8.403
9. 156^
9.908
10.661
11.413
12.166
12.919
13.671
14.424
15.177
15.931
)
-2.399
-1.642
-0.887
-0.131
.623
1.377
2.131
2.884
3.637
4.390
5.142
5.894
6.646
7.397
8.149
6.900
9.6M
10.402
11.153
H.904
12.656
13.407
14.158
14.910
15.662
24
-2.641
-1.885
-1.132
-0.378
.375
1.127
1.880
2.631
3.383
4.134
4.885
5.635
6.385
7.135
7.885
8.635
9.385
10.134
10.884
11.634
12.384
13.134
13.884
14.634
15.384

-2.893
-2.139
-1.387
-0.635
.117
.868
1.619
2.369
3.119
3.868
4.618
5.367
6.116
6.864
7.613
6.361
9.109
9.858
10.606
11.354
12.103
22.851
13.600
14.349
15.098
26
-3.154
-2.402
-1.651
-0.901
-0.150
.599
1.348
2.097
2.846
3.594
4.342
5.089
5.837
6.584
7.331
8.078
8.825
9.572
10.319
11.066
11.813
12.560
13.308
14.056
14.803

-3.425
-2.674
-1.925
-1.176
-0.427
.321
1.069
1.816
2.563
3.310
4.057
4.803
5.549
6.295
7.041
7.786
8.532
9.278
10.023
10.769
11.515
12.261
13.007
13.754
14.500
28
-3.704
-2.956
-2.208
-1.460
-0.713
.034
.780
1.526
2.272
3.017
3.763
4.507
5.252
5.997
6.741
7.486
8.230
8.975
9.719
10.464
11.208
11.953
12.698
13.443
14.189

-3.993
-3.246
-2.499
-1.753
-1.007
-0.262
.483
1.228
1.972
2.716
3.460
4.Z03
4.947
5.690
6.433
7.176
7.920
8.663
9.406
10.149
10.893
11.637
12.381
13.125
13.869
                       -233-

-------
TABLE Vl-195
(Continued)
Salinity
25 18.322
19.087
19.853
20.619
21.385
30 22.152
22.919
23.687
24.455
25.224
35 25.993
2 7 '.534
28.305
29.077
40 29.850
16
18.116
18.880
19.643
20.408
21.172
21.937
22.702
23.468
24.235
25.001
75.769
26.537
27.306
28.075
28.846
29.617

17.901
19.424
20.187
20.949
21.713
22.476
23.240
24.005
24.770
25.536
26. 302
27.069
27.837
28.605
29.375
18
17.676
18.436
19.196
19.957
20.718
21.479
22.241
23.003
23. 766
24.530
25.294
26. 058
26.824
27.590
28.357
29.124

17.441
18.200
18.958
19.717
20.477
21.236
21.997
22. 757
23.519
24.281
25.043
25.806^
26.570
27.334
28.100
28.866
20
17.198
17.955
18.712
19.469
20.227
20.985
21.744
22.503
23.263
24.023
?4.?84
25.545
26.308
27.071
27.834
28.599
TEMPERATURE (°C)
22
16.945
17.701
16.456
19.212
19.968
20.725
21.482
22.240
22.998
23.757
24.516
25.277
26.037
26. 799
27.561
28. 324
16.684
17.438
18.192
18.946
19.701
20.456
21.212
21.968
22.725
23.483
24.241
24.999
25. 759
26.519
27.280
28.042
16.414
17.166
17.919
18.672
19.425
20.179
20.934
21.669
22.444
23.200
23.957
24.714
25.472
26.231
26.991
27.751
24
16.135
16.886
17.637
18.389
19.141
19.894
20.647
21.401
22.155
22.910
23.665
24.421
25.178
25.936
26.694
27.453

15.848
16.597
17.347
18.098
18.849
19.600
20.352
21.104
21.857
22.611
23.365
24.120
24.876
25.632
26.390
27.148
26
15.552
16.300
17.049
17.798
18.548
19.298
20.049
20.800
21.552
22.304
23.058
23.811
24.566
25.321
26.078
26.835

15.247
15.995
16.742
17.490
18.239
18.988
19.738
20. 488
21.239
21.990
22.742
23.495
24.248
25.003
25.758
26.514"
28
14.935
15.631
16.428
17.175
17.922
18.670
19.419
20.168
20.917
21.668
22.419
23.171
23.923
24.677
25.431
26.186

14.614
15.359
16.105
16.851
17.597
16.344
19.091
19.840
20.588
21.338
22.088
22.839
23.590
24.343
25.096
25.651
*S1g»a-t (
-------
                  TABU  VI-19C

WATER DENSITIES (EXPRESSED AS S1CMA-T)* CALCULATED
   USING THE DENSITY SUBROUTINE FOUND IN MERGE
SaHnity
(°/oo) 30
0 -4.291
-3.545
-2.800
-2.055
-1.311
5 -0.567
.177
.920
1.663
2.406
10 3.148
3.890
4.633
5.375
6.117
15 6.859
7.601
8.343
9.085
9.827
20 10.569
11.312
12.055
12.798
13.541

-4.597
-3.853
-3. 109
-2.366
-1.623
-0.880
-0.1 38
.604
1.345
2.087
2.828
3.569
4.310
5.051
5.792
6.532
7.2/3
8.014
8.755
9.496
10.237
10.979
11.721
12.463
13.205
32
-4.912
-4.169
-3,427
-2.685
-1.943
-1.202
-0.461
.279
1.019
i.759
2.499
3.239
3.979
4.718
5.458
6.198
6.937
7.677
8.417
9.157
9.847
10.636
11.378
12.119
12.861

-5.235
-4.494
-3.753
-3.013
-2.273
-1.533
-0.793
-0.054
.685
1.424
2.162
2.901
3.639
4.378
5.116
5.855
6.593
7.332
8.070
8.809
9.549
10.268
11.028
11.768
12.508
34
-5.567
-4.827
-4.088
-3.349
-2.610
-1.872
-1.134
-0.396
.342
1.079
1.817
2.554
3.291
4.029
4.766
5.503
6.241
6.978
7.716
8.454
9.192
9.931
10.669
11.408
12.148

-5.906
-5.168
-4.430
-3.693
-2.956
-2.219
-1.482
-0.475
-0.009
.727
1.463
2.199
2.935
3.671
4.408
5.144
5.880
6.617
7.353
8.090
8.827
9.565
10.303
11.041
11.780
TEMPERATURE (°C
36
-6.254
-5.518
-4.781
-4.045
-3.309
-2.574
-1.839
-1.103
-0.368
.367
1.101
1.836
2.571
3.306
4.041
4.776
5.511
6.247
6.982
7.718
6.45$
9.191
9.928
10.666
11.403
-6.610
-5.875
-5.140
-4.405
-3.671
-2.937
-2.203
-1.469
-0.736
-0.002
.731
1.465
2.199
2.932
3.666
4.400
5.134
5.869
6.604
7.338
8.074
6.809
9.546
10.282
11.015
38
-5.973
-6.240
-5.507
-4.774
-4.041
-3.308
-2.576
-1.843
-1.111
-0.379
.354
1.086
1.818
2.551
3,284
4.016
4.750
5.483
6.217
6.951
7.685
8.420
9.155
9.891
10.627

-7.345
-6.613
-5.881
-5.150
-4. 418
-3.687
-2.956
-2.225
-1.494
-0.783
-0.032
.699
1.430
2.161
2.893
3.625
4.357
5.089
5.822
6.555
7.288
8.022
8.757
9.491
10.227
40
-7.723
-6.993
-6.263
-5.534
-4.804
-4.074
-3.345
-2.615
-1.886
-1.156
-0.426
.304
1.034
1.764
2.494
3.225
3.956
4.687
5.419
6.151
6.884
7.617
8.350
9.084
9.819

-8.110
-7.381
-6.653
-5.925
-5.197
-4.469
-3.741
-3.013
-2.285
-1.556
-0.828
-0.099
.629
1.358
2.088
2.817
3.547
4.277
5.008
5.739
6.471
7.203
7.936
8.669
9.403
42
-8. 503
-7.777
-7.050
-6. 324
-5.597
-4.871
-4.145
-3.418
-2.691
-1.965
-1.238
-0.510
.217
.945
1.673
2.401
3.130
3.660
4.589
5.320
6.050
6.782
7.514
8.246
8.980

-8.904
-7.180
-7.455
-6.730
-6.006
-5.281
-4.556
-3.831
-3.106
-2.380
-1.655
-0.929
-0.203
.524
1.251
1.978
2.706
3.434
4.163
4.892
5.622
6.353
7.0B4
7.816
8.548
44
-9.313
-8.590
-7.867
-7.144
-6.421
-b.698
-4.975
-4.252
-3.528
-2.804
-2.080
-1.355
-0.630
.095
.820
1.547
2.273
3.001
3.728
4.457
5.186
5.915
6.646
7.377
8.109
                      -235-

-------
TABLE V1-19C
(Continued)
Salinity
{°/oo) 30
25 14.285 13.948
15.029 14.691
15.773 15.434
16.518 16.178
17.264 16.923
30 18.010 17.668
18.757 18.414
19.504 19.160
20.252 19:907
21.000 20.655
35 21.749 21.403
22.499 22.1b3
23.250 22.903
24.002 23.653
24.754 24.405
40 25.508 25.158
*Stg«a-t (»t)  x 103.

12.519
13.258
13.999
14.739
15.481
16.223
16.965
1 7 . 709
18.453
19.198
19.944
20.690
21.438
22.187
22.936
23.687
For ex
TEMPERATURE (°C)
36 38
12.142
12.881
13.620
14.360
15.101
15.842
16.S84
17.327
18.070
18.615
19.560
20.306
21.054
21.802
22.551
11.757
12.495
13.233
13.973
14.713
15.454
16.195
16.937
17.680
18.424
19.169
19.915
20.662
21.409
22.158
11.364
12.101
12.839
13.578
14.317
15.057
15.798
16.540
17.283
18.026
18.771
19.516
20.263
21.010
21.759
23.301 22.808 2Z.508
ample t for seawater with

10.963
11.700
12.437
13.175
13.914
14.654
15.394
16.135
16.678
17.621
18.365
19.110
19.856
20.603
21.352
22.101
a densl
40
10.554
11.241
12.027
12.765
13.503
14.242
14.982
15.723
16.465
17.208
17.95Z
18.696
19.442
20.190
20.938
Z1.6B7
ty of 1

10.138
10.874
11.610
12.347
13.084
13.823
14.563
15.303
16.045
16.787
17.531
18.276
19.021
19.768
20.517
42
9.714
10.449
11.184
11.921
12.658
13.396
14.136
14.876
15.617
16.359
17.103
17.647
18.593
19.340
20.088
21.Z66 20.838
.02500 g/cm3, v^

9.282
10.016
10.751
11.487
12.224
12.962
13.701
14.441
15.182
15.924
16.667
17.412
18.157
18.904
19.653
20.402
• 25.
44
8.842
9.576
10.310
11.046
11.782
12.520
13.258
13.996
14.739
15.461
16.224
16.969
17.714
18.461
19.210
"19.960
-236-

-------
 However,  when  the  same  models  are used to predict  the trajectories of horizontally
 discharged  buoyant plumes,  a  larger coefficient  1s required.   Consequently the
 aspiration  coefficient  must be variable.
      Although  relatively  advanced,  MERGE  does  have Its limitations.   Sorse  of these
 are a result of  the assumptions  already discussed.  For example,  the  plumes  are
 assumed to  be  round,  whereas  some evidence Indicates  substantial  deviation from  this
 Idealization (Abramovich,  1963).   Other important  limitations  are listed below:
        t   Dlffuser parallel  current:   The model does not predict plume  dilution
             for cases  of  current flowing parallel to the  diffuser pipe.   This is  a
             severe limitation  especially in some  ocean applications  because this
             case  may be  expected to  result 1n the lowest  Initial  dilutions.
        •   Surface  entrainment  Interference:   The model  does  not properly  account
             for Interfacial  boundary  conditions.   Dilutions near the surface  or
             bottom may be  overestimated  because entrainment will  be  assumed where
             water Is unavailable for  entrainment.
        •   Horizontal homogeneity:   The model  assumes  homogeneous horizontal
             current  although  bottom topography, internal  waves,  or other  factors  may
             cause considerable spatial flow variations.   This  1s  in  addition  to
             temporal variations  which are excluded by  virtue of  assumed steady-state.
        •   Uniform  discharge:   It is assumed that an  infinitely  long diffuser  exists
             for which there is no port-to-port  variation  in effluent  characteristics.

 6.5.2.3   Similarity
      The  success of a set of tables in describing  an  infinite number  of possible
 diffuser, effluent, and ambient flow configurations depends on the principles
 of  similarity.   Basically,  similarity theory states that model and prototype will
 display equivalent  behavior if a  limited  number of similarity conditions or parameters
 are preserved.    Equivalent  behavior means   that relative to appropriate measures the
 behavior  will be equal.  For example, if  all similarity parameters are preserved,
 then  the  height  of  rise predicted by the model  and observed in the prototype will be
 equal when measured in terms of the initial diameters of the corresponding  plumes.
      The  number  of  similarity conditions  is determined by the difference between  the
 number of Independent variables and primary variables involved in the  problem (Streeter,
 1961).  Primary  variables must include mass, time,  and distance.  The  present problem
 involves  eleven  independent variables implying  eight similarity conditions.  The
 independent variables, corresponding symbols,  units, similarity parameters, and their
 names are listed in Table VI-20.  As the dilution tables are based on  a linear
equation  of state,  the effluent and ambient densities  p  and p  ,  respectively,
replace four independent variables:   the effluent and  ambient  salinities  and  tempera-
tures. 'This effectively reduces the number of  similarity conditions by two to  six.
                                         -237-

-------
                                               T«b1e,,Vl-20.
                            PLUME VARIABLES,  UNITS,  AND SIMILARITY  CONDITIONS
     Variable
Density stratification
Current velocity

Kinematic viscosity
Port spacing
Symbol
Units
Oimensionless Sim.  Parm
dpa/dz
 ML
 LT
                                                   -4
                 -I
  V
  S.
                                 u,/v
                   Vdo
Name
Eflluent density
Effluent velocity
Effective diameter
Ambient density
Reduced gravity
Pe
V
do
Pa
9'
ML'3
IT'1
L
ML'3
LT"2
none— primary variable
none— primary variable
none— primary variable
Pe/Pa
v/VcTiL
none
none
none
density ratio
denslmetrlc Froude
                                   number:   Fr
                               stratification parm.
                               current to effluent
                                velocity ratio:  k
                               Reynolds number: Re
                               Port spacing parm.:
                                      PS
Notes:
1.
2.
3.
9,' " ((Pa-Pe)/Pe)9 where g is the acceleration of gravity (9.807 msec"2).
In the present application a composite stratification parameter, SP, is used
lieu of the density ratio and the stratification parameter. SP * (pa-p€)/(dc
The diameter, d is taken to be the vena contracta diameter.
in
                                                          -238-

-------
      It 1s advantageous to further reduce the number of similarity conditions to
minimize the number of tables necessary to represent the flow configurations of
Interest.  From experimental observations, 1t Is found that plume behavior ts basic-
ally  Invariant for large Reynolds numbers reducing the number of similarity conditions
to five.  Finally, the ratio Pe/P, and the stratification parameter can be combined
in a  composite stratification parameter, SP, where:
        SP " (Pa-P
     This is a satisfactory similarity parameter providing that differences 1n
model and prototype densities are not too great.  The assumption 1s valid for
discharge of municipal waste water into estuarine or coastal waters.  Figures
VI-28 and VI-29 demonstrate the effectiveness of this parameter.  The same similarity
conditions are shared for both cases.  The two figures show rise and dilution to be
within about a percent of each other even though the stratification and Initial
buoyancies are much different.  With only four similarity conditions to be satisfied,
the problem can be represented by considerably fewer model runs than 1f six similarity
conditions were required.

6.5.2.4  Table Usage
     To use the dilution tables to estimate dilutions, 1t 1s necessary to calculate
trie appropriate similarity parameters and know the depth of the outfall.  Calculation
of the -*)ur similarity parameters Fr, SP, Ic, and PS, given In Table VI-20 requires
knowledge of all the variables except v.  The dilution tables are shown In Appendix G.
     The>depth used 1n the dilution tables 1s expressed in terms of the diameter
of the ports; that is, the vena contracta diameter.   For bell-mouthed ports, this
diameter is approximately equal to the physical  diameter of the port.  Thus, 1f the
actual  depth of water Is 10 m and the port diameter  1s 10 cm, then the depth of water
is 100-port diameters.
     The dilution tables are numbered from 1 through 100 and are grouped by port
spacing as listed below:

        Tables      Port  Spacing (PS)  (Diameters)
         1-20                       2
        21-40                       5
        41-60                      10
        61-80                      25
        81-100                   1000 (effluent  from each  port
                                       acts  as a  single plume)
                                        -239-

-------
c»»e
t»»»«   TUT or  COMPOSITE •TMTIMCATIOII
IHPUT DAT* PSCUOO-CC-MO
U » A T 3
7.0200 O.OOOO 0.1(40 O.OOOO 0.0000
HOP 1TC* IfHO Nkk Hk« MAC IDEM*
2 1000 73 0 0 0 |
(If IDCNJM'I THEM PtNlltt VE'IION UICD--UIC 2HD HERAT
AHIICNT STHkTIFICkTIOH (k«0 CALCULATED (ICHkt)

DEPTH(H) TC«P(C) *AL(0/00) CUM(M/S) S1CHAT
0.000 0.000 0.000 0.000 -0.09)
10.000 0.000 0.000 9.000 •0.01)

• SPC
•.0300 IOO.OOOO
COL)


SICXATIOCM «CR)
o.ooo
27. MO

HT rr»
•.»•••
CMLUI TO rUKDINT •ATIO(«) . . .

DEPTH AVC STHATiriCATlOU PA««, .





•1199.0
<1. 1
0.033
1701.7
10.0
7.02
0.000
0,030*
1*0.00

                                       MOOCL OUTPUT kfTfH -J- ITrPATtONS (*Kt  UBITJ)
0 NOM COIH I) OIP1HC) OliMCTm VOL OIL HOD VCUU) Vf* »EtfO TOTAL VCL DtN OlFf TlMC CUUPMT
1 O.OOt 10.000 0.100
2S 0.040 tO. 000 0.1)1
SO 0.017 tO. 000 0.140
7b 0.14J 10.000 O.lbl
too o.jio 10.000 o.i««
m o.ito i
iso o.)«»
US 0.4»7
700 0.432
J/S O.J9J
7SO
7/S
100
12S
ISO
)7S
400
475
4SO
•OM1NAI T0»
469
»75
SOO
SH
.*•)
.701
.417
.7*7
.1"
.»7«
.1*3
.7*7
.SM
Pt«C LCVCL
.11*
.40«
.«57
.407
.000 0.71S
.9«« 0.779
.»«•» 0.112
.««• O.H5
.19* 0.4«»
•»»J 0.5S«
.Ml O.ttl
.'•t «.7»»
.»»' O.»l»
.*M l.lll I
.»07 t.m l
.007
.104
.40]
.(64
.»n
.M7
,7*0
.701
.»2t
.447
.514
.57^
.115
.70*
.047
.IJT
.972 0.000 4.972 24.113
.90} 0.001 5.101 72.704
.*44
.114
.SJO
.952
.417
.017
.7S5
.*'*
.741
.00) 4.944 t9.0»7
.004 4. 174 14.054
•0»4 3.510 IJ.500
.001 7.9S2 11.15!
.010 2.401 •.34}
.012 2.007 I.07S
.015 1.753 4.744
.Oil 1.474 5.441
.021 1.741 4.740
.044 0.024 1.044 J.99I
.171 0.011 O.|7| J.1J4
.7U «.0)7 0.7)1 1. 772
.470
,»»2
.MS t.S*l IS.»0» 9.4M
.74) I.I5» I0.5S5 O.JH
.401 2.102 27.044 t.JIO
CACHCO
.454 J. 30* 75.149 0.1T2
.401 7.4J5 24.7)1 0.241
.in i.iio 11.304 t.iif
.1)1 J.^<2 )S.CO» O.HJ
.04) 0.422 2.214
.031 0.314 |.|22
.051 0.44) I.JI7
.045 0.173 0.92»
,000 0.000
,00k
.013
.017
.043
.070
.103
.133
.114
.»2»
,4U
.4bl
.131
.132
.117
.713
.111
,«I4
.047 O.Jll 0.417 7.424

.047 0.271 -0.001 ».«77
.031 0.241 -0.1)5 10.710
.Oil •.]>] >«.«2T 13.DT
.000
.00*
.000
.000
.000
.000
.(too
.00*
.000
.000
.000
.000
.000
.000
.000
.000
.oo«
.•00

.000
.000
,0»0
.Oflf ».m -0.74* 1«.7|* f.OO*
                               FIGURE VI-28   EXAMPLE OUTPUT OF  MERGE  -  CASE  1
                                                          -240-

-------
C»»t NUMtC*    I

••«••   Tt»T Of CONPOSITC ITMTIMCAT10N PAHAMCTCN
INPUT OAT* PICWOO-CCMO
        V
    3.MOO
    V
0.0000
    A         T         3         6       IOC
0.11*0    0.0000     0.0000 i   9.0100  100.0000
                                                                       ALT OCH
                                                                        O.MIO
  • DP ITrfl IMO  NAA  HAI  MAC  IOCNSM
    7 1000   35    0    •    0     I

(IF 10CNJM-I TNCH OCNIITT VERSION  OitO-'Vtt 2ND SICHAT C0t»
AHHICNT  ATNATIMCATION  (AND CALCULATIO (1CNAT)

  DCPTHm    TCHPIC)  •ALCO/00)  CU»(M/S>    «IC*AT
     0.000      0.000      0.000     0.000    -0.09)
    10.000      0.000      0.009     0.00*    -0.09)
                                                     SICMATCDCN »C"J
                                                      0.000
                                                      1.000
                                                                       TO CUNP.CMT  KATIOdO  .  .
                                                                            rnouoc NO .....
                                                                       rtux(H**)/s) ......
                                                                DCPTN AVC «TMT1MC*TION PAN*.
                                                                OCPTH(N) ...........
                                                                OISCHAKCC
                                                                CUMCNT s
                                                                POPT SPACIMG(N)
                                                                                               .0
                                                                                             4).I
                                                                                            0.010
                                                                                          lliii.l
                                                                                             to.o
                                                                                             2.)4
                                                                                            0.000
                                                                                           0.0500
                                                                                           100.00
                                          NUOLL OUTPUT  AfTC* -J-  ITF.IIAflONI (HHS  UNITS)
J HOD COH(I)
1
35
50
75
100
1 25
150
1 75
300
375
750
775
100
175
150
175
400
435
450
in«lNA
461
475
500
517
0.001
0.041
0.0*9
0. 146
0.714
0,295
0.797
0.506
0.6*1
0.105
0.99*
1.777
1.500
1 .174
7.709
7 .666
1.706
).*4)
4.5*7
t, TRAPPING
5.211
5.476
6.5)7
7.1*1
OCPTHtn DIANCTC*
10.000
10.000
10.000
10.000
10.000
10.000
9.999
9.999
9.99*
9.996
9.991
I.It*
9.910
9.9«6
9.142
9.907
9.11*
9.716
1.1*5
ICVCL PCACHCO
1.441
1.1*3
1.177
I.IVT
0.100
O.I II
0,141
0.167
0.11*
0.3)7
0.7*7
0.115
0.19*
0.47)
0.561
0.669
0.794
0.946
1.174
1.116
1.515
l.*79
2.225

2.511
2.644
1.1*7
1.5*1
VOL OIL HOf) VEL(U) VCH »CL(») TOTAL »CU














1
i
.007
.1*9
.411
.6*0
.9*7
.174
.12)
.156
.991
.746
.64)
.710
.979
.4*11
.70
.417
15.955
11.97)
22.561

25.561
26.1)2
11.101
15.960
3.124
1.16*
1.655
1.191
1.170
0.9*4
0.137
0.6*6
0.515
0.497
0.414
0.14*
0.3'*
0.746
0.707
0.174
0.144
0.17)
9.101

• .Oil
0.017
O.OD
• .065
0.00*
0.10*
0.001
0.001
0.007
0.001
O.OB)
0.0*4
0.0*5
0.0*4
0.007
0.009
0.011
0.01)
0.015
0.017
0.07*
0.037
• .•71

• .031
0.070
9.010
».*»•
7.J74
1. 16k
1.6*5
I.J91
1.170
0.1*4
0.177
0.6*6
0.515
0.4*7
0.414
O.)4l
0.39)
0.344
0.307
0,175
0.14*
0.135
0.106

0.0*4
0.0*1
0 .074
0.045
pen oirr
7.171
2.57)
2.131
1.714
1.500
1.741
1.041
0.197
0.749
0.6)0
0.571
0.44)
0.170
0.10k
0.757
0.701
0.157
0.100
0.04)

•0.007
-0.019
•0.07)
•9.0*1
TIHC
0.001
0.011
0.046
0.014
0.1)1
0.214
0.177
0.474
0.4*9
0.114
1.475
1.014
7.195
4.117
5.1)0
1.754
11.666
16.450
31.149

79.56)
13.575
45.1)1
5I.J7*
CUNSfNT
0.000
0.000
0.000
• .000
n.ooo
0.000
0.000
0.000
0.000
o.ooo
0.000
O.ftOtt
0.000
o.ooo
0.000
0.000
n.ooo
o.ooo
0.000

0.000
o.ooo
«.o°o
o.ooo
                                 FIGURE  VI-29
                                     EXAMPLE  OUTPUT OF  MERdE - CASE 2
                                              -241-

-------
Each group of 20 1s further subdivided by current  velocity to effluent  velocity
ratio  (k). I.e.:

                   Current Velocity to Effluent
                       Velocity Ratio (k)
                                 0.1
                                 0.05
                                 0.02
                                 0.00 (no current)
Each subgroup of five tables 1s comprised of tables of varying composite density
stratification (SP):

                   Composite Stratification Parameter (SP)
                               200 (high stratification)
                               500
                              2000
                             10000
                          Infinity (no stratification)
Finally, each table Includes densimetrlc Froude number,  Fr - 1,  3, 10, 30, 100,
and 1000 tg represent cases ranging from highly buoyant  plumes to almost pure
jets.  The 411 utIons are tabulated with plume rise.  The following examples demonstrate
how the tables may be applied.
j-	EXAMPLE VI-11	
i
                         Calculation of Initial Dilution

;        Example A.  This example demonstrates many of the basic features of the
{   dilution tables and their usage.  It also Includes a method for estimating
I   the plume diameter Indirectly using Information derived from the tables.  The
|   method Is used In cases of unmerged or slightly merged plumes and 1s necessary to
j   better estimate plume dilution when the plume  Is shown to Interact with the water
j   surface.
        Given that waste water 1s discharged horizontally at a depth of 66 m from a
!   simple pipe opening and that:
           ua     • the current velocity  • 0.15  m/s
           v      • the effluent velocity  » 1.5  m/s
           pe     - the effluent density  • 1000  kg/n3
           Pa     • the ambient density at discharge depth  • 1015 kg/m
           I      « the port spacing  • infinite
                                         -242-

-------
           d      - the port discharge vena contracta diameter  « 1.7 m                 I
           dp /dr » the ambient density stratification  « 0.0441 kg/«                   |
    The  four similarity parameters necessary to use the tables are:                      j
           Fr « the densimetrlc Froude number « 3.0                                     |
           k  • the current to effluent velocity ratio « 0.1                            j
           SP • the composite stratification parameter « 200                            j
           PS « the port spacing parameter • Infinity.
     The  infinite port spacing indicates that the dilutions will be found in the last   .
    20 tables of the dilution tables 1n Appendix G, I.e., Tables 81-100.  These tables   j
    are  appropriate because merging does not occur with PS » Infinity.  The current to   I
    effluent velocity ratio of 0.1 indicates that the appropriate dilutions are among    |
    the  first five of these 20 tables.  The stratification parameter 200 Identifies      j
    the  first of these five tables as the correct reference location.  Finally, the      •
    densimetric Froude number of 3.0 isolates the second column as the one containing
    the  information of Interest.
        The column of dilutions  contains  a wealth  of information about the plume        J
   whose overall behavior Is described in Figure VI-30.   After rising one diameter      |
    (1.7 m), the average plume dilution (expressed  in terms of volume dilution) is       |
   2.8.  In other words,  a given amount of plume volume  has  been diluted with 1.8       j
   times as much ambient  fluid.   After rising 2 diameters  (3.4 m),  the average          J
   dilution is- 3.7,  and so on.   At  15 diameters  rise,  the  dilution  1s 21.4.   The next
   entry.follows in  a line headed  by "T",  Indicating that  the Initial  trapping level     .
   has  been peached.   This means  that the  plume  and  ambient  densities are equal  at       J
   this teve1.  and momentary equilibrium has  been attained.   The "trapping" level         I
                                                                                        i
   dilution is 26.2  and the corresponding  plume  rise,  set  off in parentheses  to the     |
   right of the dilution,  is 17.0  diameters.   The  parentheses are a  mnemonic  for        j
   indicating  trapping  while values  set off  in  square  brackets are merging level         j
   plume rises.                                                                          •
        When  a plume  intercepts  the  water  surface,  it  is deprived of some of  its
   entraining  surface  and  consequently  the dilution  is less  than that  indicated  1n       \
   the  tables.   For well-diluted,  unmerged or slightly merged plumes,  w1h  k not  equal    I
   to zero, the  plume  diameter, d, may  be  estimated:                                    I
                                                                                       i
                                                                           (VI-61)

!   In dimensionless units,  or diameters:
I                                                                                       I
I                                    d/d  - v/DA                           (VI-62)     I
'                                       **                                               i
I                                                                                       I
|   In the  present  case, the diameter  at maximum  rise calculated  in this way is          j
                                         -243-

-------
                                              .-' _|_-IYP'C«'         v
                                                 ' '     'trapping l«v«i
     ^,^              ..                        ^ ...»                ..     ....


    . '•'.•'.'• .".'•*'•'•'.'."• ••^7>TS-r--<{-.'^ ;'.*''.""•.•• •"••' .'.'.••"•".•.'»'T.T''.*"•••."• .'•'.'•*•';"•  '  '•".'••'  •'". • "• •' •'.'•*.
    FIGI*E VI-50   SCHEMATIC  OF PLUME  BEHAVIOR  PREDICTED  BY  MERGE  IN
                     THE  PRESENT USAGE
25.2 diameters (42.8m).  Thus the top of the plume  1s  34.8 diameters (22.2 +
12.6) above the level of the outfall. I.e.  12.6 diameters  above  the plume centerline,
and 4.0 diameters below the surface.  Therefore,  surface  interaction does not occur.
     For the sake of comparison, the plume  diameter calculated by  the program at
maximum rise 1s 23.5 diameters which compares  favorably with the simplified
estimate made above.
     Example B.  Suppose that all the conditions  given 1n  Example  A apply here
except that the depth of water is only 29.7 diameters  (50.5 m).   Table 81 is
again used to provide dilution estimates; however,  surface interaction does
occur.  A conservative estimate of  initial  dilution is obtained  by assuming
that entrainment stops as soon as the top boundary  of  the  plume  intersects
the surface.  In reality, some additional ambient water could be expected to
enter through the sides of the plume.
     When the centerline depth of the plume 1s 20 diameters, its dilution 1s
37.3 and Us approximate diameter 1s 19.4 diameters (33 m).  Consequently,
the top boundary of the plume is 29.7 diameters above  the  level  of the outfall and
1s equal to the depth of water.  Thus the dilution  of  37.3 provides a conservative
                                        -244-

-------
   estimate of initial  dilution 1n this case.
        Example C.  Suppose the following data apply:
u,
a
V
pe
pa
Sl
d
0
dpa/dz
- 0.15 m/s

• 1.5 m/s
• 1000 kg/*
- 1015 kg/m
• 0.34 m
- 0.17 m
• 0.0441 kg/m4
I
i
I   Then,  Fr  -"9.5.  k  •  0.1.  SP  -  2000,  and  PS  •  2. and Table  3 1n Appendix G
|   is  the appropriate source of dilution  information.  As the Froude  number  is           |
j   almost equal  to  10,  column 3 information can  be used without modification  although    j
j   interpolation may  be  appropriate  In  some applications.  The plumes merge almost       j
•   immediately  at a dilution of 2.1.  The initial trapping level 1s encountered  after
!   the  plume  rises 89.4  diameters  (15.2 ra).  The maximum dilution is  76.2 after
I   rising 125 diameters  (21.3 ).                                                         !
I       For  closely spaced plumes, the  diameter may be estimated from the relationship:  I
i                                                                                        |
j                                  d/d0  «  (irD)  (4 k PS)                       (VI-63)     j
i                                                                                        1
       Tfre maximum diameter estimated  in this way 1s 299 diameters (50.9 m).            j
.   In contract,  the program  gives  a value of 268 diameters (45.S n).  Ho surface
j   interaction  occurs In deep water.  In very  shallow water,  a conservative estimate
I   of dilution  may be made by dividing  the total flow across  the length of the           J
|   diffuser by  the flow  through the diffuser.  It is conservative because no aspira-     I
   tion entrainment is included in the  estimate.                                         |
       Table 3 contains a blank entry  in the second column of the 90-diameter           i
•   rise line.   The previous  entry  in the column Indicates trapping.  This means          j
.   that trapping and the 90-diameter rise level occurred in the same iteration.          •
•   Therefore, the dilution of 41.3 is the appropriate value for this blank.
I       Example  D.  The methods given in Examples A and C for estimating the plume       '
|   diameter are  not accurate when  intermediate degrees of merging exist.  If surface     I
|   interaction  is important, 1t may be necessary to run the model  to obtain accurate    |
   plume  diameter predictions.                                                          i
       Example  E.  Sometimes outfalls or diffusers are located in  water only a few'     j
•   port diameters deep and, as a result, initial  dilutions may be expected to be        j
,   quite  small.  However, after the plumes reach the surface, they  still have sub-
'   stantial horizontal velocity  and continue to entrain ambient  water more vigorously   !
|   than a plume whose trajectory is unhindered by surface constraints.  The worxbook    j
|   by Shirazi and Davis   (1976) may be consulted to estimate additional  dilution.         I
                                         -245-

-------
I        Example F.  Strong stratification Inhibits plume rise.  As stratification
j   weakens, plume rise and dilution tend to Increase.  Predicting large dilutions
j   and plume rises can require more program Iterations than used to develop the
j   tables 1n Appendix G.  On the other hand, very large dilutions are usually of
>   lesser Interest.  Consequently, the number of Iterations 1s arbitrarily limited to
!   1000 and rise to 300 diameters.  Table 94 provides examples In which the runs for
j   each dens1metr1c Froude number are United by the permitted number of Iterations.
I   The final dilutions listed are underlined to remind the user that larger dilutions
|   and plume rises occur.  When the rise limitation criterion has been reached, a
j   rise of 300 diameters or slightly more will be Indicated.
i        Example G.  Many dlffusers have horizontally discharging paired ports
   on each side of the dlffuser.  In cross current, the resulting plume behavior
   appears somewhat like that shown 1n Figure VI-31.  The upstream plume 1s bent over
!   the counterflowing current and ultimately may be entrained by the downstream
I   plume.  The entrainment of pollutant laden fluid will  reduce the overall dilution
|   1n the merged plumes.  Estimates of the magnitude of this  effect may be made If 1t
|   may be assumed that:
j           o    The interaction occurs
:           o    There 1s merging of adjacent plumes to assure cross dlffuser merging
           -    end not  Interweaving of plumes
!           o    The opposite plumes have similar rise and overall  entrainment
I           »    There are no surface constraints
|           o    The actual  (not permitted)  rise 1s  provided 1n the tables.
I   The fina4 dHytion of the merged plumes,  0., 1s  approximately:
j
j                                  Of -  (D2)/(20 - Oe)                         (VI-64)

!   where D is the dilution at maximum rise of the downstream  plume as  given in
{   the tables and D  Is  the dilution of the  downstream plume  upon  entry  into the
I   bottom of the bent over upstream plume (see Figure VI-31).   D  1s  estimated  by
|   finding the distance  in diameters, Z ,  between the depth at entry  and the port
j   depth.   The  dilution  at  this  depth  is read  from the appropriate line  1n the
   dilution  tables or  Interpolated.   The maximum radius of  the plume Is  added to the
   depth  at  which maximum rise occurs.   The difference between the port  depth and the
   depth  so  calculated is Z  .
                           <
        Given that Fr  •  3,  PS •  25,  SP  • 2000,  and k  • 0.1, and that Identical
   plumes  are injected Into the  ambient water  from both sides of the dlffuser.
   From  Table 63, 1t  Is  found that the  dilution  1s 270 and  the rise 1s 55.1 diameters.
   The width of  the plumes  may be  estimated:
            d/d0 -  (»270)/[4(0.1)(25)]  •  85
                                         -246-

-------
  •.  .• •  .-.:-..	•!  • .  ••.;. ;.•77. •  ...-..." ••. •.• • . • •" • u  t "...  -.••••.  ?.  .;  •
 :••'...',"•'*.•• •• •.;•••.••  .-.'••..•• •'.•' .'•*•• *• .'«.••••••••.•'••'.- • •• :...'.-».':••.'.'.••'•
 t .•.., .-•••.*.:•.•  ':*.-••. •.', .«•••• •••••.••.••"••.	.'..	 •..•...•.*.  ...••• .,  •••..••••••
 • . ...',•'• •-•..'  	••/.•.•••.•.••..•.•...-••••.•-•  .-•-•..•	1 •!.'•••  ••',•-,. •	
                    FIGURE VI-51   CROSS DIFFUSED MERGING
(cf. ti» computer  calculated  width of 83 diameters).  Therefore, the  vertical
distaffoe between the  ports  and  the plume entry level Is 55.1-85/2  «  12.6  diameters,
and D    15.5 as estimated  from the table at rise equal to 12 diameters.
D, may now be calculated:
        Df * 270/[2(270)  -  15.5] « 139
This result may have  been anticipated:   the dilution is effectively  halved.
This is the outcome whenever  the entry level, I , is small.  In many  cases,
halving the dilution  provided In the tables gives an adequate estimate of the
overall dilution achieved by  the cross diffuser merging plumes.
     Example H.  Given that PS  » 25, SP • 200, k - 0.0, Fr - 10, and  that  an
estimate of the center line  dilution at maximum rise is required.   By  consult-
ing Table 77, it is found that  the average dilution at maximum rise  1s 26.0.
Since there Is no  current and virtually no merging, this value can be divided  by
1.77 to obtain the centerline dilution (based on a gaussian profile,  see  Teeter
and Baumgartner, 1979).   The  centerline dilution 1s 14.7.
     With Identical conditions  except for port spacing of 2 instead  of 25,
Table 16 shows that the dilution at maximum rise is 11.6.  The centerline  dilution
is again smaller but  not  by the same percentage amount.  For the 3/2 power profile,
similar to the gaussian,  the  peak-to-mean ratio in stagnant ambient and complete
merging is 1.43 (Teeter and Baumgartner,  1979).  Thus the centerline dilution  may
be found to be 8.1.
                                       -247-

-------
 I       The peak-to-mean ratios given above are flow-weighted and are obtained          I
 j  through a straightforward integration.  Unfortunately the problem Is not as          |
 j  simple when current 1s present because the gaussian or other arbitrary profiles of   |
 [  velocity are superimposed onto a non-zero average velocity.  Hence, in high          j
 •  current, the peak-to-mean ratio for single plumes assuming the 3/2 power profile     •
 !  is 3.89.  For merged plumes, the ratio is lower.  For Intermediate currents, the
 |  ratio  is between the  corresponding extremes depending on the degree of merging  and   j
 |  the  actual  current  velocity.                                                         I
 |       Fortunately, many standards and  regulations - for example, the Federal          (
 j  301(h)  regulations  -  are written in terms of average dilutions.   Also, repeated      j
 j  measurements  in the field are  likely  to provide estimates of average concentrations  |
   before  estimates of maximum concentrations are possible.  Thus, the user of HERGE
 !  1s normally not concerned with centerline dilutions.  It is useful to remember
 I  that estimating average dilutions using centerline models Involves not only the      {
 I  use  of  variable peak-to-mean ratios but also variable aspiration  coefficients.       I
 :	EHD OF EXAMPLE ¥1-11
 6.5.3  Pollutant Concentration Following  Initial Dilution
     The concentration of a conservative  pollutant at the completion of initial
 dilution is. exprfssible as:
                                                                             (¥1-65)
where
        C   »  background concentration, mo/1
         a                                *
        C   «  effluent concentration, mg/1
        Sa  «  initial dilution (flux-averaged)
        C|  «  concentration at the completion of initial dilution, mg/1.
When the background level, C , is negligible Equation Vl-65 simplifies to:

                                       Cf • £                               (¥1-66)

This expression can be used to predict the increased pollutant concentration above
ambient, as long as the effluent concentration greatly exceeds the ambient concen-
tration.   It is interesting to note that when the effluent concentration is below
ambient, the final pollutant concentration is also below ambient.
      Since water quality criteria are  often  prescribed as maximum  values not to be
exceeded  following initial dilution, 1t  is useful to rearrange Equation Vl-65 to
                                         -248-

-------
express the maximum allowable effluent concentration as follows:
where
        (C )     -  maximum allowable effluent concentration such that
                    water quality criteria are not exceeded
        CG       •  applicable water quality criterion
        (Sa)m1n  •  minimum expected Initial dilution.
Since initial dilution is a function of discharge and receiving water character-
istics, as discussed in detail in Section 6.5.2, finding an appropriate "minimum"
initial dilution 1s not a trivial problem.  Host often,  Initial dilutions are
lowest when density stratification 1s greatest.  For a given stratification profile,
dilutions  generally decrease at lower ambient current speeds and higher effluent flow
rates. Based on expected critical conditions 1n the vicinity of the discharge, the
tables in  Appendix 6 can be used to predict
                                  EXAMPLE VI-12
        Analysis of the effluent wastewater from a treatment plant discharging         1
   Into a large west coast estuary revealed that the effluent contained a number of    ;
   priffffty pollutants.  A few of the pollutants and their measured concentrations     I
   are shown below.                                                                    |
                                                                                       i
                                   Concentrations (fig/1)    Criterion Level             j
           Priority Pollutant     Dry Weather  Met MeatheF       (t*g/l)                \
                copper              32.3          61.9              4.0                I
                zinc                33.0         180.0             58.0                j
                mercury          not detected      3.5              0.025              j
                lindane              8.6       not detected         0.16               j
   The critical initial dilution has been determined to  be 30.   If the criterion       j
   levels are designed to be complied with at the completion of  initial dilution,
   determine if the criteria for the four priority pollutants are contravened.          !
        A cursory  review  of  the  tabulations  above shows  that all  detected effluent      .'
   pollutant  concentrations  (I.e.,  undiluted concentrations) exceed  the criteria       I
   levels,  other than  zinc during  dry weather flow conditions. Hence 1f initial         |
   dilutions  were  to become  low  enough,  each of  the  four priority  pollutants could      j
   violate  water quality  criterion  for either dry or wet weather  conditions.
        Using  the  minimum initial dilution of 30,  the final  pollutant  levels can be
   predicted  using  Equation  VI-66,  by  assuming background  levels are  neglible.   The
   final  pollutant  levels compared  with  the  criterion  levels  are shown  below.
                                        -249-

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                                 Final Concentrations  (ng/1) Criterion  Level
            Priority  Pollutant    Dry Weather     Wet Weather      (^g/1)
                 copper               1.1             2.1           4.0
                 zinc                1.1             6.0          58.0
                 mercury              -               0.1           0.025
                 Undane              0.3             -             0.16
   Both mercury  and  Undane violate the criteria while copper and zinc do not.
   However, copper levels are sufficiently close to the criterion of 4.0 Kg/1 to
   warrant  further attention.
                              END OF EXAMPLE VI-12
6.5.4  pH Following Initial Dilution
     The pH standard governing wastewater discharges into estuarlne or coastal
waters 1s usually quite strict.  Typically, state standards require that the pH
following initial dilution not deviate by more than 0.2 units from background.
A step by step approach Is presented here that can be used to determine whether
a discharge will comply with a standard of this type.
     Steft j^.  The following Input data are required:
              Sa           • Initial dilution
              Alkfl         • alkalinity of receiving water, eq/1
              Alk
                           » alkalinity of effluent wastewater, eq/1
              pH&          « pH of receiving water
              pH           » pH of effluent wastewater
              K     CK
               *'!'   a*l   • equilibrium constant for dissociation of carbonic acid
                             in wastewater and receiving water, respectively (first
              „,     c         acidity constants)
               a'2'   *'2   « equilibrium constant for dissociation of bicarbonate  1n
                             wastewater and receiving water,  respectively  (second
                             acidity constants)
              *w, Cjf       • ion product for wastewater and receiving water,
                             respectively.
Table VI-21 shows values of the equilibrium constants and 1on product of water.  For
seawater, typical values of pH and alkalinity are 8.3 units and 2.3 meq/1,  respectively,
     Step 2.   Calculate the total  inorganic carbon concentrations  in the effluent
              wastewater (Cte)  and receiving water (Cta):
                                                                             (VI-68)
                                      (a, +  2a2)e

                                        -250-

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                                    TABLE VI-21

                 VALUES OF EQUILIBRIUM CONSTANTS AND ION PRODUCT OF
                 WATER AS A FUNCTION OF TEMPERATURE FOR FRESHWATER
                                   AND SALT WATER
-log Ka i -log
Temp.,*C Freshwater Seawater Freshwater
5 6.52 6.00 10.56
10 6.46 5.97 10.49
15 6.42 5.94 10.43
20 6.38 5.91 10.38
25 6.35 5.84 10.33
and
C • a
"*a (a,+2a,)a
where
' r T2
2 [H*]2 * [H+] K +
«.i
Note: cr and cr are used 1n a. and
a 1 a 2 *
' 3. Calculate {he akallnfty (Alkf) and total
at the completion of Initial dilution:
A1lc . Au ^ Alk* '
a
c - c ct ' ct
Ltr <-t + -le l
Ka ? -log Kw
Seawater Freshwater Seawater
9.23 14.63 14.03
9.17
9.12 14.35 13.60
9.06 14.17 13.40
8.99 14.00 13.20
\
l\i\ 7f>\

K»M K«.2
<*2 tl> calculate C .
Inorganic carbon {C -)
Alt
a l\i i T>\
{Vl-ie.)
i (VI-73)
Step 4.  Express the final  alkalinity  as:



                        '  Ctf <«i * 2-2>f *   n?T.   '   tM*3f           tVI-74)



                                        -251-

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     Rather than solving for [H ]^ directly 1n Equation VI-74, 1t 1s easier
to calculate Alk- In equation VI-72 for a range of [H ] values, until the
alkalinlties computed from equations VI-72 and VI-74 match.
     In most cases pK, will not differ from the ambient pH by more than 0.1 to
0.3 units.  Consequently 1t 1s usually most expeditious to begin by assuming pHf
• pH .  If pH >pH , then each subsequent calculation should be at 0.1 pH
    &        Co
units higher than pH .  If pH 
-------
                   TABLE  VI-22
  ESTIMATED pH VALUES AFTER INITIAL DILUTION
StMUr
TOT *C
S.*-Ur

7.5
7.7
1.0
I.J

7.S
7.7
1.0
1.5
7.5
7.7
f 0
1 J
1.5
7.0
7.5
1.0
I.J
I.I
7.5
7.7
1.0
I.J
| |
7 0
7.5
7.7
1.0
1.)
1 5
7.0
7.5
7.7
1.0
I.J
1.5
7.0
75
7.7
1.0 1
13 1
1.5 1
7.0 )
7.5 7
7.7 7
10 1
1.3 1
1.5 1
7.0 7
7.5 7
7.7 7
1.0 1
I.J 1
IS 1
s-c
I*1t14l 9
-------
!   The total  inorganic  carbon of the wastewater 1s:
                                            0.000398 mole/1
             e          0.137  + 2 x .863

   The dissociation constants for the ambient water are:

                                   io"83 x 8  + 10" 7
                                                                         0.909
               (10~83)2 +  10"63  x 8 x  10"7  + 8  x  10"7 x  4.68 x 10" I0

   •«*
       *, • 0.085
   The  total  Inorganic  carbon  content  is:
                          6.3  x 10-"
                 0.0023 -- — - + 10" B-3
                            10" 8-3
           c^   »  - . .00212 mole/1
            a          .909 +  2 x 0.085
   The  f1n»l  alkalinity and Inorganic  carbon are:
                           0.002  - 0.0023
           AU   - 0.0023 + - go -  "  °-00229
           *   --            0.000398 -  0.00212
           Ctf    0.00212 * - jo - "  °-0020
   Using  Equation VI-74, the alkalinity  is calculated for the  range of pH values        j
   tabulated below,  beginning  at  8.3 and incrementing by 0.1 units.

                    £H                 Alkalinity, eg/1                               j
                    8.3                    0.00217                                     I
                    8.4                    0.00222                                     I
                    8.5                    0.00228                                     j
                    8.6                    not  needed                                  j
                    8.7                     not  needed                                  •
                    8.8                    not  needed
   The  actual and calculated aUallnlties match  at a pH barely exceeding 8.5.  Since    !
   this slightly  is  more than  0.2 units  above ambient, the pH standard is violated,     '
   The  pH problem that  results  from this discharge could be mitigated in a number of    I
   ways,  such as  increasing  initial  dilution, or by treating the wastewater in orler    j
   to lower the effluent pH.
                             END Of EXAMPLE VI-13 -•

                                        -254-

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 6.5.5   Dissolved  Oxygen Concentration Following  Initial Dilution
     Dissolved  oxygen  standards  1n estuarlne and coastal waters can be quite  stringent.
 For  example, the  California Ocean Plan  (State Hater Resources Control Board,  1978)
 specifies  that:
             "The dissolved oxygen concentration shall not at any time be
         depressed more than 10 percent  from that which occurs naturally.
         as the  result  of the discharge  of oxygen demanding waste materials."
 Since dissolved oxygen concentrations can naturally range as low as 4.0 to 5.0 mg/1
 at certain times  of the year In  estuarlne or coastal waters, allowable depletions
 under these conditions are only  0.4 to  0.5 mg/1.
     The dissolved oxygen concentration following Initial dilution can be predicted
 using the  following expression:
                           D0f
                                        DO  -  IDOD - DO
                                                                             (VI-75)
where
         DO.    •   final dissolved oxygen concentration of receiving water at the
                  plume's trapping level, mg/1
         CO"    •   ambient dissolved oxygen concentration averaged from the
                  dlffuser to the trapping level, mg/1
         10     *   dissolved oxygen of effluent, mg/1
         H)OD-  •   Immediate dissolved oxygen demand, mg/1
         Sa   *-•   Initial dilution.
Thf  immediate  dissolved oxygen demand represents the oxygen demand of reduced
substances which  are rapidly oxidized during Initial dilution (e.g. sulfides to
sulfates).  The procedure for determining IDOD is found in standard methods (APHA,
1976).   IOOD values are often between 1 and 5 mg/1, but can be considerably higher.
When the effluent dissolved oxygen concentration is 0.0 mg/1  and IDOD 1s negligible
(which 1s a common situation). Equation VI-75 simplifies to:

                               DO  . DO  (} --]                           
                                      O, ( 1 - —  )
                                       a V    Sa /
The ambient dissolved oxygen concentration which appears  in Equations  VI-75 and
VI-76 Is the concentration in the water column averaged between the location of
the dlffuser and the trapping level, while the final  dissolved oxygen  concentra-
tion is referenced to the plume's trapping level.
     The dissolved oxygen concentration can change significantly over  depth, depending
on the estuary or coastal system as  well  as on seasonal  Influences  (e.g.   upwelUng).
As the plume rises during Initial  dilution, water from deeper  parts of the water
column is entrained Into the plume and  advected  to the plume's trapping level.   If
                                         -255-

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the dissolved oxygen concentration 1s much lower In the bottom of the water column
than 1n the top, the low dissolved oxygen water 1s advected to a region  formerly
occupied by water containing higher concentrations of dissolved oxygen,  and then  a
"pseudo" dissolved oxygen depletion results,  solely caused  by  entrainment  and  advec-
tion and not consumption of oxygen-demanding  material.   The following example  illus-
trates this process.
                               •-EXAMPLE  VI-14	1
                                                                                       I
        Puget Sound,  located in the  northwest  corner  of the  state of Washington,        j
   is a glacially carved, fjord-type estuary.   The  average depth of water  is about      :
   100 m (330 ft).  (Hiring periods  of upwelling,  low  dissolved  oxygen water enters
   the estuary at depth and produces a vertical dissolved oxygen gradient  throughout
   much of the estuary.  In Commencement  Bay,  near  Tacoma, dissolved oxygen profiles    {
   similar to the one shown in Table VI-23 have been  observed.  Suppose the trapping    I
   level is 43 ft (13 m) above the  bottom and  the minimum initial dilution is 28.       |
   Find the final dissolved oxygen  concentration  and  calculate  the percent depletion,   j
                                                                                       i

                                    TABLE VI-23
               DISSOLVED OXYGEN PROFILE IN COMMENCEMENT BAY, WASHINGTON

           Depfti ft(m)	Temperature, °C	Dissolved Oxygen,  mg/1               j
               ,                                                                        (
               0  (0)              14.0                      7.8                        j
               3  (1)              12.0                      7.7                        j
               7  (2)              12.0                      7.6                        j
                                                                                       i
              10  (3)              11.7                      7.4                        I
              16  (5)              11.7                      7.2                        !
              23  (7)              11.7                      7.0
                                                                                       I
              33  (10)             12.5                      6.8                        j
              49  (15)             13.5                      6.5                        j
              66  (20)             11.5                      6.1                        j
              98  (30)             11.5                      5.3                        I
                                                                                       *
              108  (33)             11.5                      5.0                        I
                                         -256-

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I         The  dissolved  oxygen  concentration  varies  significantly  over  depth,  from  5.0    I
j   mg/1  at the  bottom  to  7.8  mg/1 at the water's surface.  The average concentration    |
j   over  the  plume's trapping  level  1s:                                                  |

j           5'°  *  6'1 - 5.6 mg/1                                                         !
!   Using Equation VI-76,  the  final  dissolved oxygen concentration at  the trapping
I   level  1s:                                                                            !
           DO, » 5.6 [ 1	J « 5.4 mg/1
             f       \     28 /
    Compared to the ambient concentration at the trapping level  (6.1 mg/1). the         j
    percent depletion  1s:

           6'1"5-4  x 100 - 11 percent                                                \
I    Compared to the average over the height of rise, the percent depletion 1s only:     I
'5654                                                                   '
              sTfi    x 100 • 4 percent
,                                                                                       i
I                                                                                       I
	  £ND OF £XAMPLE VI-14	

      In-contrm to the deep estuaries on the west coast of the United States,
those on the east coast are quite shallow.  In the Chesapeake Bay. the largest
east  co*«t ettuary, water depths are often 1n the 20- to 30-ft (6 to 9 m) range, with
channels as deep as 60 to 90ft (18 to 27 m) 1n places.  Because of the shallow water
depths. Initial dilution Is often limited by the depth of the water and can be 10  or
less at times of low ambient current velocity.

6.5.6  Far Field Dilution and Pollutant Distribution
     After the Initial dilution process has been completed, the wastefield becomes
further diluted as it migrates away from the ZID.  Since concentrations of coHform
organisms are often required not to exceed certain specified values at sensitive
locations (e.g. public bathing beaches), a tool  is needed to predict collform (or
other pollutant) levels as a function of distance from the ZID.   This can be accomp-
lished by solving the following expression:
                                        cy       -   kC
where
         C  «  pollutant concentration
         u  -  current speed
                                         -257-

-------
         f   •  lateral  turbulent diffusion coefficient
          k  •  pollutant decay rate.
 Figure ¥1-32 shows now  the sewage field spreads laterally as a function of distance
 fro* the ZID.  The concentration within the wastefleld,  C(x,y),  depends on both x and
 y,  with the maximum concentrations occurring at y • O.for any x  value.
      It 1s the maximum  concentration C(x,y - 0) which  1s of  Interest here.  Solving
 Equation VI-77,  the maximum concentration as a  function  of distance  x 1s:
                              C - Cfl +—	exp|. ^-J                   (VI-7B)

where
         D    •   dilution  attained  subsequent to the  Initial dilution and  1s  a
                function  of  travel  time
         All  other  symbols have  been  previously defined.
The  subsequent  dilution  1s  unity  when x •  0 (I.e.,  at the completion of  Initial
dilution), so C  •  C   at  x •  0,  as  required.   In many Instances, the background
concentration is negligible,  so that Equation ¥1-78 simplifies to:
                                       Cf
                                   C • jji- exp (-let)                          (¥1-79)
                                        s

     Subsequent dilution gradually Increases as the wastefleld travels away from the
ZID  and  depends- on mixing caused by turbulence, shear flows, and wind stresses.
Often, dildlior caused by lateral entrainment of ambient water greatly exceeds that
caused by vertical  entralnment.  This 1s assumed to be the case here.
     In  open coastal areas, the lateral dispersion coefficient 1s often predicted
using the so-called 4/3 law  (Brooks, 1960), where the diffusion coefficient increases
as the 4/3 power of the wastefield width.  In mathematical form:
                                     Eo
where
        CQ  •  diffusion coefficient when L - b
        L   »  width of sewage field at any distance from the ZID
        b   •  initial  width of sewage field.
The Initial diffusion coefficient can be predicted from:


                                   E  • 0.001b4/3
                                         -258-

-------
                 Line source
                                                                 Sewage
                                                                 field
             FIGURE  VI-32  PLAN VIEW OF SPREADING SEWAGE  FIELD
 where
        eQ  •  Initial diffusion coefficient,  ft2/sec
        b   -  Initial width of sewage field,  ft.
 Based on Equation VI-80, the center-line dilution.  0    1s given by:

erf


/ 1.5 \

)3
. j

\ /
'*



MM
                                                                            (VI-82)
where
        t    •  travel time
        erf  *  error function.
     The 4/3 law 1s not always applicable  and  in  confined estuaries might overesti-
mate the diffusion coefficient.  Under these circumstances, it 1s wore conservative
to assume the diffusion coefficient is a constant.  Equation VI-81 can be used to
estimate the constant diffusion coefficient, unless the user has better data.  Under
these circumstances, the subsequent dilution 1s expressible as:
                                  erf
                                       16 E
                                                     -1
                                                                            (VI-83)
     Equations  VI-82 and  VI-83 are cumbersome to use. especially 1f repeated applica
tions are needed.   To facilitate predicting subsequent dilutions,  values of 0
are tabulated in Table VI-24  for different Initial widths (b) and  travel ti«es  (t).
                                        -259-

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                TABLE VI-24

SUBSEQUENT DILUlIUNb  FOR VARIOUS INITIAL
      FIELD,WfDTHS AND TRAVEL TIMES
Travel Time(hr)
0.5
1.0
2.0
4.0
8.0
12.
24.
48.
72.
96.

10
2.3/ 5.5
3. 1/ 13.
4.3/ 32.
6.17 85.
8.5/>100.
10. />100.
15. />100.
21. />100.
26. 7>100.

50
1.5/ 2.0
2.07 3.9
2.77 8.5
3.77 21.
5.27 53.
6.37 95.
8.9/>100.
13. 7>100.
15. 7>100.
Initial Field
100
1.37 1.6
1.6/ 2.6
2.27 5.1
3.07 11.
4. I/ 29.
5. I/ 50.
7. I/ 100.
10. />100.
12. />100.
29. 7>100. 18. />100. 14. />100.
Width (ft)
500
l.O/ 1.1
1.2/ 1.3
1.4/ 1.9
1.9/ 3.5
2.57 7.3
3.07 12.
4.27 30.
5.97 80.
7.3/>100.
8.4/>100.

1000
l.O/ 1.0
1.17 1.1
1.2/ 1.5
1.5/ 2.3
2.0/ 4.4
2.47 6.8
3.47 16.
4.77 41.
5.87 73
6.6/100.

5000
l.O/ 1.0
l.O/ 1.0
l.O/ 1.0
l.l/ 1.2
1.4/ 1.7
1.6/ 2.3
2. 1/ 4.4
2.8/10.
3.4/17.
3.9/24.
*
The dilutions are entered in the table as NI/NJ,
where N| is the dilution assuming a constant diffusion
coefficient, and N2 is the dilution assuming the 4/3 law.
                                   -260-

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The Initial sewage fi'eld widths  range from 10 to  5,000 feet  and travel  times  range
from 0.5 to 96 hours.
     The dilutions presented in  the table reveal  that as the initial  field width
increases, the subsequent dilution decreases for  a given travel time.   For a wider
wastefield, a larger time 1s required to entrain  ambient water into the center of the
wastefield, so dilutions are lower.  This Illustrates that a tradeoff exists between
large diffusers where initial dilution is high but subsequent dilution  low, and small
diffusers where initial dilution is low and subsequent dilution high.
     The table also reveals that the predicted dilutions are significantly different,
depending on whether Equation VI-82 or VI-83 is used.  In many cases  likely to be
evaluated by users of this document, the 4/3 law might overestimate subsequent
dilution, even if the outfall is in coastal  waters.  To attain the subsequent dilu-
tions predicted by the 4/3 law at large travel times, a significant amount of dilu-
tion water must be available.  Since many outfalls, particularly small ones, are
often not too far front shore, the entrainment rate of dilution water can be restricted
by the presence of the shoreline and the depth of the water.  The  wastefield from
diffusers located further offshore might entrain water at a rate corresponding to the
4/2 law for an Initial  period of time.   As  the wastefield widens significantly, the
rate of entrainment could decrease,  and  the  4/3 law no longer be obeyed.
    Wbin travel  times  are small (e.g.,  12  hours or less),  there is less discrepancy
between.rthe two methods of calculating  subsequent  dilution, except for the very small
initial wastefield widths.
 	EXAMPLE  VI-15	-\

                                                                                       \
   Figure VI-33 shows  an  outfall  which  extends about  one  mile  offshore.   At  the  end     j
   of tne outfall  is a  multiport  diffuser,  800 feet  in  length.   Occasionally,  fecal
   coliform bacteria counts  as  high  as  10,000 MPN/100 ml  have  been  detected  in the
   effluent of  the treatment  plant.                                                     \
        The allowable  fecal  coliform level  at the  shellfish  harvesting area  inshore     I
   of the diffuser is  70  MPN/100  ml.  Typically, the  ambient current  is  parallel  to     |
   shore so that effluent is  not  carried onshore.  However,  when wind conditions  are    j
   right,  onshore  transport  has been  observed, and the  sustained transport velocity     j
   is 4  cm/s«c  (0.13 ft/sec).   Determine whether the  coliform  standard is likely  to
   be violated  or  not.  Other information needed is:
           Coliform decay rate •  1.0/day                                               j
           Minimum  initial dilution  - 35                                               I
        The width  of the  diffuser is 800 feet and will be used as the initial          |
   field width.  Note, however, that the diffuser is not exactly perpendicular         j
   to shore, so that the  initial  field width is probably less than 800 feet  in
   the travel direction.  Using 800 feet is conservative because subsequent  dilution

                                        -261-

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FIGURE Vl-55  OUTFALL  LOCATION, SHELLFISH  HARVESTING  AREA,  AND  ENVIRONSJ
 will  be -somewhat lower under this assumption.
      The coHform count following Initial  dilution 1s, using Equation VI-66:
             10000
           - 290 MPN/100 ml
 The  travel time to the shore 1s:
           5280
                      11 hours
                      -1 *
.U I I I
 ul
 »J
        O.LJ x  3600
Interpolating from Table VI-24, the subsequent  dilution is about 2.6.
Using Equation  VI-79, the coliform concentration  at the shoreline is:
            290
        C "E?
          • 70  MPN/100 ml
The predicted col1 form count 1s equal  to the  water quality standard. Since the
subsequent dilution was conservatively estimated, 1t 1s possible that actual
collforn counts will be less than 70 MPN/100  ml.  However, the prediction does
Indicate that careful monitoring of col1 for*  levels at the shoreline 1s needed  to
                                     -262-

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I   see that the standard 1s not violated.  Since shoreward transport of effluent is     I
j   Infrequent, sampling has to be conducted at times when the transport Is shoreward;   |
j   otherwise detected coHform levels might not represent worst-case conditions.        j

1	END Of EXAMPLE VI-15  	

6.5.7  Farfleld Dissolved Oxygen Depletion
     Oxygen demanding materials contained 1n the effluent of wastewater treatment
plants can produce dissolved oxygen deficits following discharge of the effluent into
receiving waters.   A method will be presented here to  predict the depletion  following
discharge from a marine outfall.  The most critical  cases occur when the plume  and
wastefield remain submerged, so that reaeratlon does not occur.  The analysis presented
here is applicable to submerged plumes only.  When the wastefield is mixed uniformly
across the estuary, the methods presented earlier in Section 6.4.5 are  applicable.
      The oxygen-demanding materials  In the wastewater are the sum of the carbonaceous
and nitrogenous materials (CBOD and  NBOD. respectively).  It is possible that the
nitrogenous demand night not be exerted  if a  viable background population of nitrifiers
1s absent from the receiving water.  Under these circumstances, the wastefield is
likely *o be dlsoersed before the nitrifying population can increase to numbers
capable of oxidizing the NBOO.  The user can perform analyses with and without NBOD
exertion ana then determine whether NBOO is significant or not.  If it is, it is
suggested that some sampling be conducted to find out whether nitrification  is
occurring.
      The dissolved oxygen concentration in the receiving waters can be  expressed
as a  function of travel time as follows:
                             DO, -  DO
                               «      d
               D0( t)  *  DO  *
                         d
                                D
                                 s
—  [l-exa(-Kt)]
(VI-84)
where
        D0(t)  •  dissolved oxygen concentration  in a  submerged  wastefield  as  a
                  function of travel  time t,  mg/1
        DO     «  ambient dissolved oxygen concentration,  mg/1
        D0f    •  dissolved oxygen concentration  following initial  dilution
                  (see Equation VI-75)
        k      «  BOD decay rate
        Lf     •  ultimate BOD concentration  above  amoient at the  completion
                  of initial  dilution
        DS     -  subsequent  centerline  dilution.
Equation VI-84 expresses  the  dissolved oxygen  deficit  which  arises  due  to an initial
deficit at the completion of  initial  dilution  (DO -DO  ) plus that  caused by
                                                 '   A
                                        -263-

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elevated BOD levels In the water column (Lf).  The elevated BOD level 1s either
the CBOO or sum of CBOD and MBOO.  The Initial  dissolved oxygen deficit tends to
decrease at longer and longer travel tines because subsequent dilution increases.
However, BOO 1s being exerted simultaneously and tends to cause the dissolved oxygen
level to drop.  Depending on the particular case being analyzed,  one Influence can
dominate the other over a range of travel  times so that a minimum dissolved  oxygen
level can occur either Immediately following Initial  dilution,  or at a subsequent
travel time.  The following example Illustrates both  cases.
                                  EXAMPLE  VI-16
        A municipal wastewater treatment plant discharges Us effluent through
   an  outfall  and  dlffuser  system.  The maximum dally CBOD  value 1s 270 mg/1.
   and the critical Initial dilution  Is 114.  Limited analyses have been performed on
   IDOO and the  results  vary widely,  from 0 to 66 mg/1.  The length of the dlffuser
   Is  500 n (1,640 ft) and  can be used as the Initial sewage field width.  Determine
   the dissolved oxygen  deficit produced by the discharge, assuming the wastefleld
   remains submerged  and the ambient  dissolved oxygen concentration 1s 7.0 mg/1.
        Tfie BOD  concentration at the  completion of Initial dilution 1s:
            • 2.4 «g/l,BOD5
            ' 3.5 mg/1,  BOD-ultimate
The dissolved oxygen concentration at  the completion  of  initial  dilution
is (from Equation YI-75):

                      0.0  -  66.  -
                                . - 7.01
                                       J
              « 6.4 mg/1, wnen IDOD - 66
or
                    " 0.0 - 0.0 -
        D°
                                    7.0*1
                                       J
          f  	   L     114
            •6.9 mg/1,  when  1000 •  0


Note that the IDOD of 66 »g/l produces a deficit  of 0.6 mg/1.
     Since values of IDOO vary widely due to the  limited analyses,  the  far  field
oxygen depletion curves  will  be calculated for the following three  IDOD's:   0,  40,
and 66 mg/1.  A BOD decay rate of 0.2/day 1s used. When IDOO •  66 mg/1,  the
                                        -264-

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I   following  oxygen  depletions are predicted:
           Travel  Time(hr)
Ds (Table VI-24)
O0a-D0t  (Equation  VI-84)
1
4
8
12
24
48
72
96
1.
1.4
1.9
2.3
3.2
4.6
5.5
6.3
0.6
0.5
0.4
0.4
0.4
0.4
0.4
0.4
   These results are plotted in Figure VI-34  (Curve A), along with the cases for IOOD

   •  40 mg/1  (Curve B). and IDOO • 0.0 mg/1  (Curve C).
                      i.O-


                      0.9-


                  _   0.8-
                  o

                  =   07 -|
                  u
                  "Z
                  •o   0.6 H
                  «
                  a
                  *   0.5 H
                  o
                  •o
                  5   0.4 H
                  o

                  I   0.3 H


                      0.2-


                      0.1-


                      0.0
Curve
A
B
C
BOOt lullim»i«)
35
3.5
3 5
IDOO. mg/l
660
40.0
00
                                  1        2         3

                                    Travel time; days
                 FIGURE VI-3^  DISSOLVED OXYGEN DEPLETIONS
                                 VERSUS  TRAVEL TIME
                                       -265-

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 I       When the  IDOO 1s  66 tng/1, the maximum  dissolved  oxygen  deficit  is  0.6 mg/1
 j  and occurs at  the completion of  Initial dilution  (a travel time  of 0.0  hr).   Thus,
 j  the processes  which occur during initial dilution are more significant  than the
 j  subsequent BOD exertion.  Curve C (IDOO • 0.0 mg/1) shows the opposite  situation:
   farfleld BOD exertion  is primarily responsible for the maximum oxygen depletion of
   0.3 mg/1.  The middle  curve (Curve B) shows the case when the oxygen depletion
   remains relatively constant over time and both the near field and farfield processes
 I  are important.
 |       In summary, when  the IDOO 1s above 40 mg/1. in this example the maximum
 j  oxygen depletion 1s controlled by the processes occurring during Initial dilution.
   When 1DOD is below 40 mg/1, BOD exertion in the far field is primarily responsible
   for the oxygen depletion.  For primary treatment plants, IDOD values of 66 mg/1
   are atypical;  values from 1 to 10 mg/1 are much more common.  Depending on
   whether the state dissolved oxygen standard is violated  by Curve A,  the user might
   need to make further IDOD determinations to firmly establish the true range of
   IDOD values.
                                  OF EXAMPLE Vl-16

6.6  THERMS. POCLUTION

6.6.1
     The presence of one or more major heat sources can have  a significant  impact  on
Both the local  biotic community and local  water quality.  As  a result,  consideration
of significant  thermal discharges by the planner is essential  in any comprehensive
water quality analysis.  Thermal power plants account for the  vast majority of  both
the number of thermal discharges and the total  thermal  load.   However,  some industrial
processes generate significant amounts of  excess heat.
     The most important of the impacts of  heat  discharge are:
        •    Ecological Effects:  water temperature increases  change the productivity
             of planktonic anfl many oenthic species.  As  a  result  local  community
             structures are altered.  Many of the species benefited by  warmer con-
             ditions (e.g., blue green algae) may be  considered  to be undesirable.   In
             addition, many species can perform certain life cycle functions only
             within a limited  temperature  range.   Elevated  temperatures may prevent
             some species from completing  one or more life  stages, thus disrupting
             the reproductive  cycle and destroying the  stability of the population.
        •    Water Quality Effects:  Figure VI-23 showed the relative effect of
             salinity and ambient temperature on oxygen saturation.  From this
                                         -266-

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             figure, note that •  10*C* rise  1n temperature decreases  the  oxygen
             saturation concentration by 1.5 to 2.0 mg/1.
        •    Sediment Effects:  Estuarine sedimentation rates are increased by
             increasing local water column temperature.  The significance of this
             increase was discussed by Parker and Krenkel (1970).  They concluded
             that not only are sedimentation rates Increased, but vertical particle
             size distribution, particle fall velocity, and thus bottom composition
             are also affected.
        •    Beneficial Effects:   The effects of thermal discharges are not all
             negative.  It has been shown for example, that marine biofouling is
             substantially reduced 1r warmed waters (Parker and Krenkel, 1970).  In
             fact, the recirculation of heated discharge through the condenser has
             proven to be a less  expensive and equally effective method of biofouling
             control than chlorination for several California coastal  power plants.
             Estuarine contact recreation potentials are increased by  increasing
             local water temperatures, and extreme northern estuaries  have reduced
             winter ice coverage  as a result of thermal discharges.

6.6.2  Approach
     A number of the algorithms which appear in this section  were originally prepared
by Tetra Tech,  (1979) for the Electric Power Research Institute.  The  thermal  screening
approach /or estuaries is composed of procedures  that can  be  used to evaluate  the
following standards:
        A    Ifae AT Criterion: The increase in temperature of  water passing through
             the condenser must not exceed  a specified maximum.
        t    The Maximum Discharge Temperature Criterion:   The  temperature of
             the heated effluent  must not exceed  a specified  maximum.
        •    The Thermal  Block Criterion:  The cross-sectional  area  of an  estuary
             occupied t>y temperatures greater than a specified  value must  not  exceed
             a  specified percentage of the  total  area .
        •    The Surface Area Criterion:   The surface area  covered by  isotherms
             exceeding a specified temperature increment (above ambient) must
             not exceed a specified maximum .
        •    The Surface Temperature Criterion:   No discharge shall  cause  a  surface
             water temperature rise greater than  a specified  maximum above the
             natural temperature  of the receiving waters at  any time or place.
     Table Vl-25 presents a summary of the  information needed to apply the thermal
screening procedure.  Data needed for the  T criterion and  the  maximum discharge
temperature criterion were included earlier in the thermal  screening section for
•Such a rise is common  near power  plant  thermal  plumes.
                                        -267-

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                                     TABLE  VI-25

                DATA MEr-tfD  FOR ESTUARY THERMAL SCREENING
variable
4T(
°P
"P
Qp
*'tb
*«
««
1
u
»,
o,
Criuru tffctre
Wrlltlt 1M«
All
All
THcrwl
surface
All
Thermal
TMrMl
TMrMl
TMTM1
surface
TlterMl
Surface
TMrMl
iMrMl


block.
ire«

block
block
block
block.
are*
block.
ero*
block
block.
DtflMlttt* Dtf4ult V*lu*
TOBMrttitr* rite ecrwt tM oxinier (*f) 20
• ItCMrfe UMl (•)
Litt velocity of MerMl tfttcMrfe (m/l)
Flex nu of «ucMre« |»3/»)
Teaeeriture rise i" ttUtlry cross section Uttt
constitutes « UWTM) block (*F) &
Portion of estiMMM croti-tectioiwl »r«4 tMt 2S1 of the estu*rin«
constitutes « tiwrMl block (a2) crast-section4l ire4
Avertfe oeeth of estuory frx» tticMro* location to
Average fresMMter flo« rite f loving in UM esuiry 7Q
Mil tit* poMr plant lite I*3/ 1) lu
ui«ui of esuory at mw plant site (•)
Crass-sectional area at po«er plant lit* (*2)
lonfitudiKal dispersion coefficient i»2/s) see Uit «iscusnon
TMTM! block.       Surface tMrMl  transfer coefficient  (ltu/o^-« •  *F)
TMrMl block,
       block.
        block.
surface  area

TnerMl  block,

TnerMl  block,
turfac*  area

TnerMl  block,
turftct  area

Surface  are*

Surface  area
Surftce «rM
                    A*«r*ot Mil Onilltjr Of IMtr«' **Ur *t poinr pUnt
                    lit*  (kg/»J)
Specific  Mat of Mter (lu/kg • *F)


          I crost-sectionally averaged salinity
(PPl

Manntng'i « (• '6)
                   oyartvhc riOHM ( croit-lKtloiul  •» leoally alloi^bl*  surface teapcraturt producM by
                     CF)
                    n*ii geniity of Mter *t oeptA of luoaergea «ucn«rfe
                    (kQ/»3)
             ature  Linear oenstly graotent over «»ur coluan oeptn
                                                             1000 I tins  n Unity)
                                                                                        22
                                                                                 0.016 - 0.06
                                                                                       91
                                                                                       1000
                                          -268-

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 rivers  and  are  not  repeated here.   That  the  maximum discharge temperature criterion
 for  rivers  can  be applied  to estuaries assumes  the  intake temperature Is near ambient,
 and  that  tidal  action  does  not  cause  significantly  elevated temperatures near the
 Intake.

 6.6.3 Application
      The  AT criterion  and the effluent temperature  criterion  can be evaluated
 first following the  procedures  outlined  1n the  river thermal  screening section.
 The  maximum allowable  flow  rate through  the  plant, which  needs to be  Identified
 for  use 1n  evaluating  those  criteria, may not always have a readily determinable
 upper limit, unlike  plants  sited on rivers.  For estuaries that are essentially
 tidal rivers, a fraction (say 20%) of the net freshwater  flow rate might be used as
 an upper  limit.
     The  remainder of  the estuary physical screening procedure consists of evaluating
 the  following three  criteria:  the thermal block, the Isotherm surface area, and the
 surface water temperature criteria.  Because of the complexity of the flow field In
 estuaries,  slack tide  conditions have been chosen as a basis  for computations when
 possible.   It 1s during these conditions that the effects of plume momentum and
 buoyancy  re propagated the  greatest distance across the estuary from the discharge
 site.  It is also during slack tide that the thermal block 1s most likely to occur
 because o£  the absence of an ambient current that normally enhances plume entrainment
 of ambient  water.
     As tP» plume spreads across the estuary, the methodology assumes it to be
 vertically mixed.  Although most plumes do not generally exhibit this behavior due to
 such effects as buoyancy and stratification,  this approach will  roughly estimate the
 capacity of the estuary at  the power plant location  to assimilate the excess  heat.
     In  some instances, when the estuary  is  relatively narrow, the plume may  extend
across the estuary's entire width.   In these  cases  {guidelines are given later to
determine when this  occurs) the  near field momentum  approach can be used.  By  using
the well  mixed assumption (even  1f  the actual estuary is stratified)  a lower  limit  on
the expected temperature elevation  across the estuary is obtained.
     Slack tide conditions  will  also be used  to evaluate the maximum surface  tempera-
 ture produced by a  submerged discharge.  Both vertically homogeneous and linearly
 stratified conditions can be evaluated.

6.6.3.1   Evaluating  the Thermal  Block  Constraint
     Based upon momentum considerations,  the  relationship  between  the  AT
                                         -269-

-------
Isotherm and the distance  (y) H extends from the discharge point is given by
(Ueigel, 1964):
                                         \ *y
                            y "T (^ )    '  fory-yc                     (VI'85)

where
        AT   •  temperature rise across the condenser (*F)
        AT   •  temperature excess at a distance y from the discharge outlet (*F)
        y    •  distance measured along the jet axis originating at the discharge
                point (m)
        y    «  virtual  source position (m).
     The virtual source position is usually about two to ten times the diameter
of the discharge orifice.  The equivalent diameter of a discharge canal Is the
diameter of a circle whose cross-sectional  area 1s the same as that of the discharge
canal.
     Brooks (1972) has shown that for round orifices, the virtual source position 1s
approximately six times  the orifice diameter.  At the virtual  discharge position (y •
y ) the average excess temperature 1s approximately  70 percent that at the
discharge location.
     Sines one of the assumptions used in developing Equation  VI-8S 1s that  momentum
is conserved along the jet axis, an upper limit on y must be established to  prevent
the user from seriously  violating this assumption.  The  upper  limit  can be chosen to
be where the plume velocity has  decreased to 1  ft/sec or 0.31  meters per second.
This implies that the minimum A'  that can  be evaluated  using  the equation is:
where
        U         «  exit velocity  of thermal  discharge  (m/s)
        (AT )      -  minimum excess temperature that  can  be  evaluated
           y mi n
                     using Equation VI-86 (*F).
This constraint  generally does  not  restrict  practical  application  of Equation
VI-85.
     Using the value estimated  by Brooks (1972) for the  virtual  source  position.
Equation VI-85 can be rewritten as:
                                                                            (VI-87)
                                         -270-

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 The  distance,  then,  to  the AT    Isotherm  (the  Isotherm  establishing  the  thermal
 block)  1s  given  as:
                                /AT.   \2
                                                                             (VI-88)
      The  cross sectional area to the AT.. Isotherm 1s (assuming the plume
 remains vertically nixed):

                                     Ac B *tb *tb                             (VI'89)

where
                                                                        2
        AC   «  cross sectional  area measured out to the distance y,b (• )
        
-------
6.6.3.2  Surface Area Constraint
     The surface area constraint can be evaluated employing the same approach
used to evaluate the thermal block constraint.  Before beginning, Equation VI-86
should be evaluated to ensure that AT$a exceeds (^Ty)mifl. since (ATy)mtft
establishes the minimum excess Isotherm that can be evaluated using these methods.
     The distance offshore to the &T   Isothenn (the Isotherm associated with the
legal surface area constraint) can be found as:
        y    «  distance offshore at AT   Isotherm (m).
The surface area enclosed by that &T   Isotherm can be estimated as:
where
               2
        "•'  T-.
     When the estuary depth drops off rapidly from the outfall  location, an appropri-
ate average depth would be the depth to the bottom of the discharge orifice.  If
A  < A    «»>en the surface area constraint is not violated.
 S    So
     When v   exceecs the width of the estuary, Equation VI-92  should not
            o
be used to find A .  Instead, a surface area based on steady  state, well mixed
conditions, is moi* appropriate and can be found from the following expression:
                               As .W|J-« J- I   In  [^ )                (VI-93)

wnere
        W      «  width of estuary (m)
        C     - 1/2 |R/(AtD,) *VW*tD,)2 * (AHL/(oCpAtD  •  24 •  3600))

        C2    - 1/2 [R/(AtD,) *V
-------
 should approximate  conditions  under wmen  rne  lowest  maximum surrace  water tempera-
 ture excess  1s  attained.
      When  the ambient  water  density 1s  constant  over  depth  the  following  two  dimension-
 less parameter  groups  are  needed:
and
                                              1.07 U
                          F  (Froude Number)
                                                                              (IV-94)
                                                                             (VI-95)
After  calculating G and F, Figure VI-35 can be used to find S , the centerline
dilution  relative to the virtual source position.  From this information, the maximum
surface temperature elevation can be estimated as:
                                                ATc
                                   ^surface " ITiS                          W'W
 If ^Surface < ATst (the legal allowable surface temperature excess), the surface
 temperature constraint is not violated.
      In cases where the estuary is stratified more often than not at the power
 plant Stte, the maximum surface temperature calculation would more appropriately
 be performed under stratified conditions.  If the stratification is substantial,
 it is possibTe" the discharge may be prevented from reaching the surface entirely.
 A procedure is given here for a linearly stratified environment.  Under stratified
 conditions the maximum height of rise of the thermal  plume can be estimated by
 (BrooKS, 1972):
                                      3.86
                                                                             (VI-97)
where
                0.87
                          -  Pp)
        max
       dz
                maximum height of rise of thermal plume (m)
                linear density gradient (kg/m3/m).
                                         -273-

-------
               3  -
               FIGURE  VI-35
CENTERLINE  DILUTION OF  ROUND  BUOYANT
JET  IN STAGNANT  UNIFORM ENVIRONMENT
(AFTER FAN, 1967)
Using Equation  VI-97, the maximum rise of  the thermal plume can be estimated.
If 1t 1s less than the depth of water, the  plume remains submerged.   If.  however,
zmax **ceeds the water depth, the plume will surface.  In this case  the methods
given previously for the nonstratified case can be used to estimate  the maximum
surface  temperature where the ambient  water density should be  chosen to be the
depth-averaged  mean.

6.7  TURBIDITY

6.7.1  Introduction

     Turbidity  1s a measure of the optical  clarity of water and  1s dependent upon the
light scattering and absorption characteristics of both suspended  and dissolved
                                       -274-

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material  in  the  water  column  (Austin,  1974).   The  physical  definition  of  turbidity is
not yet  fully  agreed upon, and  varies  from equivalence  with the  scattering  coefficient
 (Beyer,  1969), to  the  product of an extinction coefficient  and Pleasured pathlength
 (Hodkinson,  1968), and to the sum of scattering and absorption coefficients  (VandeHulst,
 1957). Turbidity affects water  clarity and apparent water odor,  and hence Is of
aesthetic significance.  It also affects light penetration, so that Increased turbidity
results  1n a decreased photic zone depth and a decrease 1n  primary productivity.
     Turbidity levels  in an estuary are likely to vary substantially In both temporal
and spatial dimensions.  Temporal variations occur as a function of seasonal river
discharge, seasonal water temperature changes. Instantaneous tidal current,  and wind
speed and direction.  Spatially, turbidity varies as a function of water depth,
distance from the head of the estuary, water column biomass content, and salinity
level.  Much of the complexity  in the analysis of turbidity results from different
sources of turbidity responding differently to the controlling variables mentioned
above.  As an example, increased river discharge tends to increase turbidity because
of increased inorganic suspended sediment load.  However, such an Increase curtails
light penetration,  thus reducing water column photosynthesis.  This, in turn, reduces
the biologically induced turbidity.
     Methods employed to monitor turbidity Include use of a "turbldimeter".  Light
extinction measurements are commonly given in Jackson Turbidity Units  (JTU) which  are
based off the turbidity of a standard clay suspension.  Once standardized, this
arbitrary scale* can be used as a basis to measure changes  in turbidity.  The turbid-
ity calibration scale  is given  in APHA (1980).  From a measured change in turbidity a
relative change in water quality may be inferred.  Estuarine water is almost always
extremely turbid, especially when compared to ocean or lake waters.
     The JTU scale is not the only available turbidity scale.  In 1926 Kingsbury
and Clark devised a scale based on a Formazin suspension medium which resulted
in Formazin Turbidtty Units (FTU's).  More recently volume scattering functions
(VSF) and volume attenuation coefficients have been proposed (Austin, 1974).
However, JTU's are still  most commonly used as an indicator of estuarine turbidity
levels.
     As a rough indication  of the wide variations possible in turbidity.  Figure
VI-36 shows suspended solid concentrations for the various sub-bays of San Francisco
Bay for one year (Pearson,  et^ al_,  1967).   The solid line shows annual  mean concentra-
tions while the dashed lines  indicate concentrations  exceeded by  201 and  80S of the
samples taken at each station over the one year time  period.  These variations  at
stations located near bay heads  (left and right extremities  of Figure VI-36) typically
exceed 3001 of the  annual  20th percentile values.  Use of extreme high/low values
would produce correspondingly larger annual  variations.
•The JTU scale is an arbitrary scale since it cannot  be directly  related to physical
 units when used as a calibration basis  for turbidimeter measurement.
                                        -275-

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                          £9. i
                          3L
                          *£.
                          JSL
                         to

                         «_
                         c
                                      -•01*
                                            «yrr» I su> MMLO I         I
                                            tA" J  XT  1  SUHUXMT I
           FIGURE VI-36  MEAN SUSPENDED SOLIDS  IN SAN FRANCISCO BAY
                           FROM:   PEARSON £i Ai..,  1967,  PG  V-15

6.7.2  Prgceaure to Assess Impacts  of Wastewater Discharges on Turbidity  or Related
     Numerous States have enacted  water quality  standards which  limit the allowable
turbidity increase due to a  wastewater discharge In  an  estuary or  coastal water body.
The standards, however, are  not  always written  In terms  of  turbidity, but are  sometimes
expressed as surrogate parameters  such as  light  transmittance or Secchi disk.  The
following three standards provide  illustrations:
 For class AA water  in  Puget Sound, State of Washington:
   Turbidity  shall  not exceed 5 NTU over background turbidity  when the  background
   turbidity  is 50  NTU or less, or have more than a 10 percent  increase in
   turbidity when the  background turbidity is more than 50 NTU.
 For class A water in the State of Hawaii:
   Secchi disk or Secchi disk equivalent as "extinction coefficient"  determinations
   shall not be altered more than 10 percent.
 For coastal waters  off the State of California:
   The transmittance of natural light shall not be significantly reduced
   at any point outside of the initial dilution zone.   A significant  difference
   is defined as a  statistically significant difference in the  means  of two
   distributions of sampling results at the 95 percent confidence  level.
                                         -276-

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 These standards Illustrate the need for developing Interrelationships between turbidity
 related parameters, since data night be available for one parameter while the state
 standard is expressed in terms of another.  Based on these considerations methods
 will  be presented  to:
         •    Predict the turbidity 1n the receiving water at the completion of
              initial dilution
         •    Predict the suspended solIds concentrations  1n the receiving water at
              the completion  of Initial  dilution
         •    Relate turbidity and light transmittance data
         •    Relate Seech 1  disk and turbidity  data.
      By treating turbidity  as a conservative parameter the turbidity  in  the receiving
 water at the completion  of  initial  dilution can be predicted as:

                                    Tf - Ta * -^	                         (VI-98)

 where
         Tf   •   turbidity  in  receiving water at  the completion of  initial  dilution
                (typical  units:   JTU)
         T   «   ambient or background turbidity
         Te   •   effluent  turbidity
         Sa   •   initial dilution.
      InJtiaJ dilution can be  predicted  based on  the methods  presented earlier  in
 Sectiw 6.5r2.   Equation  VI-98  can  be used, then,  to directly evaluate those standards
 written  in  terms of  maximum  allowable turbidity  or turbidity Increase.
     An expression similar to Equation  VI-98 can be used to evaluate the suspended
solids concentration in an estuary following  completion of initial dilution.
Specifically:

                                              SSe ' SSa
                                  SSf - SSa + —^	                      (VI-99)

where
        SSf  •  suspended solids concentration  at completion of initial  dilution,
                mg/1
        SSfl  »  ambient  suspended solids concentration, mg/1
        SSft  »  effluent  suspended solids concentration, mg/1
        S,   «  initial  dilution.
         O
     Consider now a situation where light transmittance data have been  collected
but the state standard is expressed in terms of turbidity.   A relationship between
the two parameters  would  be  useful.  Such a relationship can be  developed by first
                                         -277-

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 considering the Beer-Lambert law for light menu it 1 on:

                                       T^ - exp(-od)                          (VI-100)

 where
         T^  •  fraction of light transmitted  over a depth d,  d1men$1onless
         0   »  light attenuation, or extinction coefficient,  per meter
         d   *  vertical  distance between two  locations  where  light  1s  measured.
                meters.
 Austin  (1974) has  shown that the attenuation  coefficient  Is expressible 1n terms  of
 turbidity as:

                                        a - k  •  JTU                            (VI-101)

 where
         JTU  «  turbidity, 1n Jackson turbidity units
         k    •  coefficient ranging  from 0.5  to 1.0.
 Combining Equations  VI-100 and  VI-101 the turbidity Is  expressible  as:

                                   JTU  » - ~ In  Td                          (VI-10Z)
The increased turJsidlty (JTU) 1s expressible as:

                                 AJTU -    -  In                               (VI-103)
where
        TH   -light transmlttance at the final  turbidity
          2
        T^   «  light transmlttance at the initial  turbidity.
  	 EXAMPLE VI-17 	'
                                                                                       t
        Vertical  profiles of several  water quality parameters,  including percent        ;
   light transmlttance, have been collected in the vicinity  of  a  municipal  wastewater  I
   discharge in Puget Sound.  Figure  VI-37 shows  each of  the three profiles.   If  the    I
   maximum allowable turbidity increase is 5 NTU,  does the discharge,  based on the      |
   light transmlttance profile shown  in Figure YI-37  violate this requirement?         j
        It 1s known that the wastefield is submerged  between about 10  to 20 m          •
   below the water's surface.  Light  transmlttances at these depths are about          >
   18 to 20 percent.  Deeper within the water column  light transmlttances are          J
   at background values of about 55 percent. Note  that in the top few  meters  the        I
                                         -27&-

-------
                                • - % Light  transmission
            0      10     20     30     40     50    60     70     80     90     i?C
                                     • -Density OT
           14.0    15.5    170    18.5   200    215    23.0    245    260   275    295
                                    A - Salinity %o
17



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                         NEAR  A MUNICIPAL OUTFALL  IN PUGET SOUND,
                         WASHINGTON
J   light transmittances are between 0 and  10 percent.  These low transmittances are
I   not due to the wastefield,  but rather are caused by a  lens of '.urtia freshwater.
|   Consequently, the following data will be used  here:
j          k    -  0.5
j          d    •  1 m (I.e.,  percent transmittance measured over i m)
:          T^   •  18 percent
               "  55 percent.
I            2
;   The turbidity increase 1s:
          £JTU
                 (0.5] TIT
                                        -279-

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I   Assuming JTU and NTU units are equivalent (EPA, 1979), then the increased turbidity
j   is  less than the 5.0 NTU allowable.
i         It is of interest to calculate the percent light transmittance within the
1   plume that would cause a 5 NTU Increase in turbidity. Using a typical background
   light transmittance of 50 percent found in central Puget Sound, the minimum light
'   transmittance (T^ ) Is computed to be:
I           y   m  ("4 percent for k » 0.5
I            °2    *«."•' PerceR* f°f « = !•"
I   Light transmittances as  low  as  C.5 to  4 percent  have  been  found due to  causes
|   other than  the  plume (e.g.   plankton blooms  and  fresh water  runoff),  but  the
i   lowest light  transmittances  associated with  the  plume have been  about 18  percent
:   per meter.
                              END  OF  EXAHPLE  VI-17
Secern disk and turbidity can be related to each other in the following manner.
Assume that the extinction coefficient of visible light (a)  Is directly propor-
tional to turbidity (T) and inversely proportional  to Secchl  disk (SD), or:

                                       a  •  k,  T                           (VI-104)

and

                                      Q  •    -                             (VI-105)
       ^ and kg are constants which have not  yet  been specified.   These  two  rela-
tionships have theoretical  bases,  as discussed in Austin (1974)  and Graham (1968).
Combining those two expressions,  the relationship between Secchl  disk  and  turbidity
becomes:

                                      T  •  4r  sr                        (VI-1061

Typical values of kj and k? are:
        kj  •  0.5 to 1.0,  where  T is expressed in JTU's
        k2  «  1.7 where Secchl disk is  expressed in  meters.
Thus Equation Vl-106 provides a method of correlating turbidity  and Secchi disk
data.
     When state standards are written in terms of Secchl  disk, 1t  1s convenient
                                         -280-

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to combine Equations VI-98 and VI-106 to yield:
                                               1     1
                              1   -   i   *   SDe " *°a~                      (VI-107)
or
                           so.  -   M--^r)s, *^r                    (vi-ios)
where
        SDf  -  minimum allowable Secchi  disk reading 1n  receiving  water  such
                that the water quality standard 1s not  violated
        SDfl  •  ambient Seech1 disk reading
        Sa   •  minimum Initial dilution  which occurs when the plume  surfaces
        SDe  -  Secchl disk of effluent.
Since Secchl disk measurements are made from the water's  surface  downward,  critical
conditions (1n terms of the Secchl disk standard) will  occur when the Initial  dilution
Is just sufficient to allow the plume to  surface.  It 1s  notable  that maximum  turbidity
or light transmlttance Impacts of a wastewater plume  will  occur when  the  water column
Is stratified, the plume remains  submerged, and Initial dilution  1s a minimum.   Under
these s"«e conditions, however, Secchl  disk readings  might not be altered at all.  1f
the pluflfe 1s trapped below the water's  surface at a depth  exceeding the ambient
Secchl d"1sk depth.
                              •-  EXAMPLE  VI-18
        A municipality  discharges  Its wastewater through an outfall and dlffuser
   system Into an embayment.   The  state  standard specifies that the minimum allowable
   Secchl disk Is 3m.   Determine whether the discharge 1s likely to violate the
   standard.   Use these data:
           SD   •  5 to 10m, observed range
             *
           5^   -  75,  minimum Initial dilution when the plume surfaces
        One method of approaching  the problem  Is to assume that violation of the
   water quality standard  is Incipient (I.e.   SDf  « 3m).  Under these conditions
   the effluent Secchl  disk would  have to be:
                                             • 0.1  m
                                             •  4  inches
                                        -281-

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   Thus,  1f the Secchl  disk  of  the  effluent  exceeds  4  Inches,  the  standards  will  not
   be  violated even under these critical  conditions.  It would  be a simple  matter  to
   measure the Secchl disk of the treated effluent to  see whether  the  standard  could
   be  violated or not.
                              END OF EXAMPLE VI-18--
6.8  SEDIMENTATION

6.8.1  Introduction
     Like turbidity, sedimentation Is a multlfaceted phenomenon In estuaries.  As
in rivers, estuaries transport bed load and suspended sediment.  However with the
time varying currents in estuaries, no equilibrium or steady state conditions can be
achieved  (Ippen, 1966).  Additionally, while any given reach of a river has reasonably
constant water quality conditions, an estuary can vary from fresh water (1 ppt.
salinity) to sea water (30 ppt. salinity), and from a normally slightly acidic
condition near the head to a slightly basic condition at the mouth.  The behavior of
many dissolved and suspended sediments varies substantially across these pH and
salinity gradients.  Many colloidal particles* agglomerate and settle to the bottom.
In genera-Is all estuaries undergo active sedimentation which tends to fill them in.
It is also-tru* for essentially all U.S.  estuaries that the rate of accumulation of
sediment 4« Iim4-ted not by the available sources of sediment but by the estuary's
ability to scour unconsolidated sediments from the channel floor and banks.

6.8.2  Qualitative Description of Sedimentation
     Before presenting what quantitative information 1s available concerning sediment
distribution in an estuary, a qualitative description of sediment sources, types and
distribution will  be helpful.  Sediment sources may be divided into two general
classes:  sources external to the estuary and sources internal  to the estuary (Schultz
and Simmons, 1957).  The major sources of sediment within each category are shown
below.   By far the largest external contributor 1s the upstream watershed.
     1. External:
        •    Upstream watershed
        «    Banks and stream bed of tributaries
        •    Ocean areas adjacent to the mouth of the estuary
        •    Surface runoff from land adjacent to the estuary
 •Colloidal  particles  are  particles  small  enough to  remain suspended by the  random
  thermal motion  of the water.
                                         -282-

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        •    Wind borne sediments
        •    Point  sources  (municipal and Industrial).
      2.  internal:
        •    Estuarlne marsh  areas
        •    Wave and current  resuspenslon of unconsoll dated bed materials
        •    Estuarlne biological activity
        •    Dredging.
      General characterizations of U.S. estuarlne sediments have been made by Ippen
 (1966) and  by  Schultz and Simmons (1957).  Many Individual case study reports are
 available for  sediment characterization of most of the larger U.S.  estuaries (i.e.
 Columbia River, San Francisco Bay, Charles Harbor, Galveston Bay, Savannah Harbor,
 New  York Harbor. Delaware River and Bay, etc.).  In general, estuarine sediments
 range  from  fine granular sand  (0,01 1n. to 0.002 in. in diameter) through silts and
 clays  to fine  colloidal clay  (0.003 1n. or less 1n diameter) (Ippen, 1966).  Very
 little, If  any, larger material (coarse sand, gravel, etc.) 1s found in estuarine
 sediments.  Sand plays a relatively minor role In East Coast. Gulf Coast and Southern
 Pacific Coast  estuaries.  Usually 1t constitutes less than 51 by volume (251 by
 weight) of  total sediments  for these estuaries with most of this sand concentrated
 near the estuarlne mouth (Schultz 4 Simmons, 1957).  By contrast, sand 1s a major
 element rn  estuarlne shoaling for the north Pacific estuaries (1 .e., Washington
 and  Oregaft  coasts).  These  estuaries are characterized by extensive oceanic sand
 intrusion into, the lower estuarlne segments and by extensive bar formations near the
 estuarina mouth..  The relative distribution of silts and clays,  of organic and
 inorganic material  within different estuaries, and, in fact, the distribution of
 shoaling and scour areas within estuaries, varies  widely.

 6.8.3  Estuarlne Sediment  Forces  and Movement
     As sediments enter the lower reaches of a river and come under tidal  influence
they are subjected to a wide variety of forces which control  their movement and
deposition.  First, net velocities 1n the upper reaches of estuaries are normally
lower than river velocities. Additionally, the water column comes  under the influence
of tidal action and thus is subject to periods of slack water.   During  these periods
coarse sand and larger materials settle.  The scour velocity  required to resuspend a
particle is higher than that required to carry it in suspension.   Thus, once the
coarser particles settle out 1n the lower river and upper estuarlne areas,  they tend
not to be resuspended and carried farther into the estuary (U.S.  Engineering District,
San Francisco,  1975).  Exceptions to this principle can come  during periods  of
extremely high  river discharge when water velocities can hold many  of these particles
in suspension well  into or even through an estuary.  Table Vl-26  lists  approximate
maximum allowable velocities to avoid scour for various sizes of exposed particles.
                                         -283-

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                                 TABLE VI-26
       MAXIMUM ALLOWABLE  CHANNEL VELOCITY  TO AVOID BED SCOUR (FPS) (KING, 1954)
Original material excavated
Fine sand
Sandy loam
Silt loam
Alluvial silts
Ordinary firm loam
Volcanic ash
Fine gravel
Stiff clay
Graded, loam to cobbles
Alluvial silt
traded, silt to cobbles
Coarse gravel
lobbies and shinqles
ShalJs and hardpans
Clear
wa ter ,
no
detritus
1.50
1.75
2.00
2.00
2.50
2.50
2.50
3.75
3.75
3.75
4.00
4.00
5. 00
6.00
Water
trans-
porting
colloidal
silts
2.50
2.50
3.00
3.50
3.50
3.50
5.00
5.00
5.00
5.00
5.50
6.00
5.50
6.00
Water trans-
porting non-
colloidal silts,
sands, gravels
or rock
fragments
1.50
2.00
2.00
2.00
2.25
2.00
3.75
3.00
5.00
3.00
5.00
6.50
6.50
5.00
Values ore approximate and are for unarmored sediment (sediment not protected by a
covering of larger material).
     Sediments are subject to gravitational forces and have size-dependent settling
velocities.  In highly turbulent water the particle fall velocities can be small
compared to background fluid motion.  Thus gravitational settling occurs chiefly 1n
the relatively quiescent, shallow areas of estuaries or during periods of slack
water.  As mentioned earlier, particle settling attains a maximum in each tidal cycle
during high water slack and low water slack tides.  During periods of peak Uoal
velocity (approximately half way between high and low water) resuspension of unconsoll-
dated sediment may occur.  Thus during a tidal  cycle large volumes of sediment are
resuspended, carried upstream with Hood flow,  deposited, resuspenoed, and carried
downstream on the ebb tide. Only those particles deposited in relatively quiescent
areas have the potential  for long term residence.  Compounding this cyclic movement
of sediments are seasonal river discharge variations which alter estuarine hydro-
dynamics.  Thus, sediment masses tend to shift  from one part of an estuary to
another (Schultz and Simmons, 1975).
                                         -284-

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      As fresh waters encounter areas of significant salinity gradients extremely
 fine particles (primarily colloidal clay minerals) often destabilize (coagulate)
 and agglomerate to form larger particles (flocculate).  The resulting floe (larger
 agglomerated masses) then settles to the bottom.  Coagulation occurs when electrolytes,
 such as magnesium sulfate and sodium chloride, "neutralize" the repulsive forces be-
 tween clay particles.  This allows the particles to adhere upon collision (flocculation}
 thus producing larger masses of material.   Flocculation  rates are dependent  on the
 size distribution and relative composition  of the clays  and electrolytes  and upon
 local boundary shear forces (Ippen, 1966, and Schultz  and Simmons,  1957). Flocculation
 occurs primarily  1n the upper central  segments of an estuary 1n the areas of rapid
 salinity increase.
      Movement of  sediments  along the bottom of an estuary does  not  continue  in a net
 downstream direction as it  does In the upper layers  and  In stream reaches.   In all
 but a very few extremely well  mixed estuaries  upstream bottom currents predominate  at
 the mouth  of an estuary. Thus, upstream flow  is greater than downstream  flow  at the
 bottom.  This 1s  counterbalanced by Increased  surface  downstream  flow.  However,  net
 upstream flow along the bottom results in a net  upstream transport  of sediment along
 the bottom of an  estuary near  the  mouth.  Thus,  sediments  and floes  settling  into the
 bottom layers of  an estuary near the mouth  are often carried  back into the estuary
 ratner itan being carried out  Into the open sea.  Consequently,  estuaries  tend  to
 trap,  or to conserve sediments  while allowing  fresh water  flows to  continue on out  to
 sea.   At^some point along the  bottom,  the upstream transport  is counter-balanced  by
 the downstream transport from  the  fresh water  inflow.  At  this  point, termed the
 "null  zo«e,"  there  is essentially  no net bottom  transport.   Here  sediment deposition
 is  extensive.   In a stratified estuary this  point is at the head of the saline
 intrusion wedge.  In a partially mixed estuary it Is harder to pinpoint.   Nonetheless,
 sedimentation Is a useful parameter to analyze and will be handled in a  quantitative
manner beginning with Section 6.8.4.
     To this point,  flow in  a fairly regular channel  has  been assumed.   However,
 1n  many estuaries geomorphlc Irregularities  exist.  Such  Irregularities  (e.g.,
narrow headlands)  create eddy currents on their lee sides.  These  eddy  currents,
or  gyres, slow the sediment  movement and allow local  shoaling.  Additionally,
 large shallow subtidal or tidal flatlands exist in many estuaries.  Such areas  are
usually well out of  the Influence of primary currents.  As a result  local  water
velocities  are usually low and Increased shoaling Is  possible.
     Wind and waves  also have a major influence on estuarine sediment distribution.
Seasonal wind driven currents can significantly alter water circulation patterns and
associated  velocities.  This in turn determines,  to  a large extent,  the areas  of net
shoaling and scour throughout an estuary.  Local  wind driven and oceanic waves  can
create significant scour forces.  Such  scour,  or  particle resuspension, is particularly
                                        -285-

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 evident  in  shallow areas  where  significant  wave energy 1s present  at the sediment/
 water  interface.   Local wind  driven waves are a major counterbalancing force to low
 velocity  deposition In many shallow estuarlne areas  (U.S.  Engineering District,  San
 Francisco,  1975).
     Finally,  oceanic  littoral  currents  (long shore  currents)  Interact with  flood  and
 ebb  flows 1n the area of  an estuary mouth.  Particularly  1n  the Pacific Northwest,
 sandy  sediment fed from such  littoral drift  1s  a aajor source  of estuarine sediment,
 and  the  Interference of littoral drift with  normal flood  and ebb flows Is the major
 factor creating estuarine bars.
     Figure VI-38  shows the schematic flow of annual  sediment  movement through
 San  Francisco  Bay. WHh  the  exception of the magnitude of  annual dredging,  this 1s
 typical  for most U.S. estuaries.  The most Important  thing  to  observe  1s the dominance
 of resuspension and redeposltlon over all other elements  of sediment movement Includ-
 ing  net  Inflow and outflow.   Also note that  there Is  a net  annual accumulation of
 deposited sediment in the bay.  This figure  1s  also helpful in  conceptualizing the
 sediment  trap  or sediment concentration  characteristic of estuaries.   In any year,
 8-10 million cubic yards  flow Into  the estuary  and 5  to 9 million cubic yards flow
 out.   However, over 180 million cubic yards  are actively  Involved in annual  sediment
 transport within the estuary.
     Figure VE-39  is an idealized conceptualization of the  various sediment-related
 processes*in an estuary.   It  oust be remembered that  these  processes actually overlap
spatiall>nnuch more than  1s shown and that the processes active at  any given  location
wary consfderably  over time.
     From thls.qualttative analysis, there are some  general  statements  which  can be
made.  Ippen (1966) drew  the following  conclusions on the  distribution  of estuarine
sediments:
        t    Tne major  portion of  sediments  introduced Into  suspension  in an  estuary
             from any source (including  resuspension)  during normal  conditions is
             retained therein, and  if transportable by the existing  currents  is
             deposited  near the  ends of  the  salinity  Intrusion, or at  locations  of
             zero net bottom velocity.
        •    Any measure  contributing to  a shift of the regime  towards  stratification
             causes increased  shoaling.   Such measures may be:   structures to reduce
             tne tidal  flow and  prism, diversion of additional  fresh water into  the
             estuary, deepening  and  narrowing of the  channel.
        •    Sediments  settlinu  to the bottom of  an estuary  are generally transported
             upstream and  not  downstream. Such sediments may at some upstream point
             be resusoe-xled into tHe upper layers and  carried back downstream.
        •    Segments  accumulate near tne ends  of the Intrusion zone and form
                      inoals also form where  *he  net bottom  velocity  Is zero  (in the
                                        -286-

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        FIGURE VMS
SEDIMENT  MOVEMENT IN  SAN  FRANCISCO BAY SYSTEM
(MILLION  CUBIC  YARDS),  FROM:  U,S, ENGINEERING
DISTRICT,  SAN FRANCISCO,  1975)
             The Intensity of  shoaling  1s most extreme near the end of the intrusion
             for stratified estuaries and 1s lessened in the well mixed estuary.
             Shoals occur  along  the banks of the main estuarine channel  where
             •water 1s deep enough to prevent wave induced scour and where velocities
             are reduced from  main channel velocities sufficiently to allow settling.
     Schultz and Simmons (1957)  made similar conclusions but added the presence
of shoaling at the mouth where flood and ebb currents intercept littoral  drift.

6.8.4  Settling Velocities
     As was stated in the  previous section, settling velocities do not play  a
great role in controlling  sedimentation patterns in estuaries  as they do  in  lakes.
However, 1t is informative to  assess settling rates for various size particles.   The
possible size classifications  of particles and their general inclusive diameter sizes
are shown in Table VI-27.   Table Vl-28 lists terminal settling velocities  for each
particle size assuming spherical particles and density of 2.0* in quiescent  water.
From this table it can be  Inferred that particles of the medium sand class  and
coarser probably settle to the bottom within a very short time after entering an
estuary.
The density of many  inorganic suspended particles is approximately  equal to that of
sand (2.7 gm/cm ) while that of biomass and organic detritus  is  usually much closer
to that of water and can be assumed to be about 1.1 gm/cm  .
                                       -287-

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                PLAN VIEW
                         MAJOR EDDY DEPOSITION
                        | CM ANN EL BANK DEPOSITION
                         AREA Of LOW ENERGY DEPOSITION
                PROFILE
                                   .r-FLOCCULATION
                AREA OF MAXIMUM  /
               "SALINITY GRADIENTS/     /-SEDIMENT TRAP AREA
                                                            HEAVY
                                                            PARTICLE
                                                            SETTLING
                      NULL ZONE
                     "SETTLING
   •SEDIMENT MOVEMENT (NET)
•WATER COLUMN MOVEMENT
              FIGURE  VI-39   IDEALIZED ESTUARINE  SEDIMENTATI
                                          ON
     Turning to the other end of the particle size scale of Table  VI-28, particles
with a diameter of 10~6 mm fall only 3.1  x  10"7 inches per hour in the most
favorable  environment (calm waters). Such a settling rate is  not significant in the
estuarine  environment.  Figure VI-40 shows the quiescent settling  rates for particle
sizes in between these two extremes  since this intermediate size group is of real
significance in estuarine management (primarily silts).   For  particles smaller than
those shown  in  Figure VI-40, gravitational settling is not a  significant factor in
controlling  particle motion.  Particles substantially larger  than the range shown in
Figure VI-40 tend to settle above, or  at, the head of an estuary.
     Combining  Figure VI-40 (fall per  tidal cycle)*  with known segnent flushing
• Based on a 12.4 hour tidal  cycle.
                                       -288-

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                                      TABLE VI-27

                   SEDIMENT PARTICLE SIZE RANGES (AFTER HOUGH,  1957)
PARTICLE SIZE RANGE
Inches

Derrick STONE
One-man STONE
Clean, fine to coarse GRAVEL
Fine, uniform GRAVEL
Very coarse, clean uniform SAND
Uniform, coarse SAND
Uniform, medium SAND
Clean, well -graded SAND AND GRAVEL
Uniform, fine SAND
Well -graded, silty SAND AND GRAVEL
Silt* SAND
Uniform SILT
Sand/ CLAY
Silty CLAY
CLAT 130 to BOS clay sizes)
Collodal CLAY (-2u>50*)
max.
120
12
3
3/8
1/8
1/8
--
—
--
—
--
--
—
--
--
min.
36
4
1/4
1/16
1/32
1/64
—
--
--
--
«
—
—
--
—
Millimeters
max.
..
--
80
8
3
2
0.5
10
0.25
5
2
0.05
1.0
0.05
0.05
0.01
min.
..
--
10
1.5
0.8
0.5
0.25
0.05
0.05
0.01
0.005
0.005
0.001
0.001
0.0005
ID'6
times (in tidal cycles) the size of particles tending to settle out 1n each segment
can be estimated.  If such predictions reasonably match actual mean segment sediment
particle size, then tMs method can be useful in predicting changes 1n sediment
pattern.  Anticipated changes in river-borne suspended sediment load by particle size
can be compared to areas where each size of particle would tend to settle.  This
would then identify areas which would either be subject to increased shoaling or
reduced shoaling and increased scour.  This type of analysis has been more successful
when applied to organic detritus material  than for inorganic suspended loads.
     A number of simplifying assumptions have gone into this settling velocity
analysis.  The most significant  of these are:
        •    Water column density changes  have been ignored. Inclusion of  this
                                        -289-

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                              TABLE VI-28
                    RATE OF FALL IN WATER OF SPHERES OF
                 VARYING RADII AND CONSTANT DENSITY OF 2a
               AS CALCULATED BY STOKES1 LAWb'°(MYSELS,1959)
Radius
inn.
10
1
0.1
0.01
10-3
10"*
10-5
10'6
io-7
Terminal
cm. /sec.
(>D
(>D
(>D
2.2x10-2
2.2x10'4
2.2x10-6
2.2xlO'8
2.2x10'10
{2.2x10-12)
velocity
cm. /min.



1.3
0.013
1.3x10-4
1.3x10'6
1.3X10'8

          To apply to other conditions, multiply the u value
          by the pertinent density difference and divide it
          by the pertinent viscosity in centipoises.
          Values in parentheses  are calculated by Stokes'  law
          under conditions where this law is not applicable.
        c  Stokes lav* states  that the terminal  velocity 1s  nro-
          portional  to  the particle radius  squared,  the differ-
          ence  in  density  and  Inversely proportional  to the
          liquid viscosity.
     factor would slightly reduce the settling velocity with increased
     depth.  This effect will be more significant for organic natter because
     of Us lower density.
•    Dispersive phenomena and advective velocities have not  been  considered.
•    Table VI-27 and Figure Vl-40 are based  on the fall  of perfectly  spherical
     particles,  (ton-spherical  particles have lower sattUng velocities.
•    Interference between particles has not  been  considered.  However,  in  a
     turbulent, sediment-laden  estuary such  Interference Is  possible  (hindered
     settling).  The analysis of the effect  of interference  on settling  veloci-
     ties was  covered 1n Chapter V for lakes.   This analysis 1s also  basically
     valid for estuaries.  The  effects Introduced there can  be applied to
     Figure Vl-40 velocities  to adjust for particle Interference.
                                 -290-

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                             0    5    10   15   20   25   30
                           FALL DISTANCE PER TIDAL CYCLE (FT.)
                FIGURE  VMO    PARTICLE DIAMETER vs  SETTLING
                                  FALL  PER TIDAL  CYCLE  (12,3  HRS)
                                  UNDER QUIESCENT CONDITIONS
                                  (SPHERES WITH DENSITY  2.0 GM/CMJ)
 6.8.5  TCi 11 Zone Calculations
     U was previously mentioned that substantial shoaling occurs 1n  the area of the
 null zone.   It 1s possible to estimate the  location of this zone, and hence the associ-
 ated shoaling areas, as a function of water depth and river discharge.   In addition
 to the Importance of the null zone to shoaling, Peterson and Conomos  (Peterson, et^ aj_.,
 1975) established the biological and ecological Importance of this area 1n terns of
 planktonic  production.  The null zone,  therefore, 1s both an area of  potential
 navigational  hazard and an area of major ecological  Importance to the planner.
     Silvester (1974) summarized the analysis for estimating the  location of the null
 zone with respect  to the mouth of an estuary. The basic  equation  used 1n this analysis
 is:
                                     1000
                                                                     (VI-109)
where
               mean salinity  (averaged vertically and over a tidal
               cycle) at the  null point (n), (ppt)
                                       -291-

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          5    •  ocean surface salinity adjacent to the estuary in parts per
                  thousand (ppt),
          Ur   •  fresh water flow velocity (ft/sec)
          g    »  gravitational acceleration • 32.2 ft/sec ,
          d    «  estuaHne depth, (ft)
          F    -  dens1«tetr1c Froude number at the null zone where F  1s
           n                                                        n
                  defined by:
where
                                            (Ao/on)gd
       &p/Pn  •  difference between fresh water density and that at the the null
                  zone (averaged over the depth of the water column) divided by the
                  density at the null zone.  This value may be approximated for
                  estuarlne waters by:
Combining Equations VI-109 and VI-110 and solving for  £f   yields
                                                       "~
                                     A£    0.7  .
                                     cn    T550"  bn

     This formulation is particularly good for channels which are either maintained
at a g1verv*depth (dredged for navigation) or are naturally regular, as "d" represents
mean cros"S sectton channel depth at the null zone.
     The use of these equations first requires location of the present null zone.
This can most easily be done by measuring and averaging bottom currents over one
tidal cycle to locate the point where upstream bottom currents and downstream river
velocities are exactly equal, resulting in no net flow.  This situation is schematic-
ally shown in Figure VI-41.
     When this point has been established for one set of river discharge conditions,
Equation VI-111 can be substituted into Equation VI-110 to calculate Fn>  This
Fn value is an inherent characteristic of an estuary  and  can be considered to be
constant regardless of the variations in flow conditions  or null  zone location
(Silvester, 1974).
     With this information and a salinity profile for the estuary (S  plotted
against x from x • 0 at the mouth of the estuary to x • L at the  head) the location
of future null zones may be calculated.  Given the new conditions of U  (changes
in river discharge) or of d (changes in channel  depth, as by dredging activity),
Equation VI-109 will allow calculation of a new I .  This My be
                                                 n          '
plotted on the salinity profile to calculate the location of a new null zone position.
Even though these changes will produce a new estuarine salinity profile, the use of
                                         -292-

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          U0.9
                                                     NULL ZONE
                                                     NULL ZONE
                        J0.9
»  tidally averaged velocity at  a  depth  equal
   to 0.9 of the water column depth.
=   river  flow velocity
               FIGURE  VM1   ESTUARINE  NULL  ZONE  IDENTIFICATION

Equation VI-109 and the old (known)  salinity profile will produce reasonably good
estimates of longitudinal  shifts  in  the  location of the null zone.  Salinity profiles
for appropriate seasonal  conditions  should  be used for each calculation (e.g.,  low
flow profiles for a new low flow  null  zone  calculation).
                                 EXAMPLE VI-19
                        Estimation of Null Zone Location
f        An  estuary  has the tidally averaged salinity  profile  shown  in the Salinity
I   Table below.   Mean channel depth \n the area of the existing  nuU zone is 18 feet
                                        -293-

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I   and  the  salinity  at that  point  1s  10 parts  per  thousand  (ppt).   Current  (low  flow)    I
j   river  discharge velocity  1s  0.5 ft/sec.   Norwal winter  (high  flow)  velocity Is  1.8    |
j   ft/sec.   It  1s desired to know  where the  null zone will  be  located  1n  summer  and      j
•   winter If  a  30 ft  deep channel  Is  dredged up to 70,000 feet from the aouth.           j

'                         SALINITY DATA FOR  EXAMPLE VI-19                                !
j                                                                                        !
i           Distance from mouth  (1000ft)   5  15  25  35  45  55  65  75  85              I
j           Salinity  (ppt)	30  28  25  20  13   8   6   4   1              j
i                                                                                        i
           From Equation Vl-110 and Equation VI-111:                                     ;
                                         (g) (d)
                  • 0.5 ft/sec/V(7xlQ~4) (10 ppt)  (32.2 ft/sec2) (18 ft)             I
                                                                                       j
          or   Fn - 0.248                                                              j
       From equation VI-109 the null zone salinity with • deeper channel  will          j
  be:                                                                                  j
               $Q 1000 U2                                                              !
               Se 0.7 F2 gd
             • 11000) (0.5 ft/sec)2/0.7 (0.248)2 (32.2 ft/sec3) (30 ft)                !
               •                                                                        i
I             « 6.0 ppt                                                                 I
I       From- the -previous tabulation this will occur approximately 65,000 ft from the   I
j  mouth of the estuary.                                                                 |
j       Under winter flow conditions:                                                   j
               Sn 1000 U2
,          I  .  °   .   r                                                              I
               0.7F^gd                                                               |
!             « (1000) (1.8 ft/sec)/0.7 (0.248)2 (32.2  ft/sec2)  (30 ft)
!          *n ' 77.9 ppt                                                                 !
        This  ?n is greater than ocean  salinity  and  will  not actually be
.   encountered.  Thus, null zone shoaling  will  occur at  the mouth  1f it occurs at
j   all.  This condition  is common for  rivers  with  seasonally  variable flow  rates.
                              END OF  EXAMPLE  Yl-19
                                         -294-

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Frick, W.E., and L.D. Winlarski. 1980.  Why Froude Number  Replication  Does  Not
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Graham, J.J.  1968.  Secchi  Disc Observations  and  Extinction  Coefficients in
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Green,  J.   1968.  The Biology of  Estuarine Animals.  University of Washington
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Hansen, D.V., and M.  Rattray.  1966.   New Dimensions in  Estuarine Classification.
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Hardy.  C.D.   1972. Movement and  Quality  of  Long  Island Sound Waters, 1971.
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Harleman,  D.R.F.  1964.   The Significance of Longitudinal Dispersion in the
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Harleman,  D.R.F.  1971.   Hydrodynamic  Model  -  One  Dimensional Models.  Estuarine
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     No.  16070 DZV 02/71.  pp.  34-gQ.
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 Hodkinson, J.R.  1968.  The Optical  Measurement of Aerosols.  In:   Aerosol
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 Hydroscience, Inc.  1974.  Water Quality  Evaluation for Ocean  Disposal  System -
      Suffolk County,  New  York.   Bowe, Walsh and Associates Engineers, New
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 Ippen, A.T.  1966.  Estuary and Coastline Hydrodynamics.  McGraw-Hill,  New
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 Jirka, G., and D.R.F.  Harleman.   1973.  The Mechanics  of  Submerged Multiport
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'O'Brien,  M.P.   1969.   Equilibrium Flow  Areas  of  Inlets  on  Sandy  Coasts.
      Journal of the Waterways  and Harbors  Division,  Proceedings  of  the American
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      Physical,  and Biological  Constituents.   Estuarine Modeling-:  An Assessment,
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      Thermal Pollution.   Chemical Rubber Company Press, Cleveland, OH.

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                                       CHAPTER 7
                                     GROUND WATER

7.1  OVERVIEW
     Ground water now serves as a source of drinking water for over 100 million people
In the United States, including an estimated 95 percent of the rural population.
Ground water is also used for irrigation, industrial process water, and cooling water.
Along with its increased usage has come an awareness of the need for protecting its
quality.  Recent legislation and policy decisions, including the Resource Conservation
and Recovery Act, its amendments, and the U.S. EPA's Ground Water Protection Strategy,
attempt to minimize the impacts of waste disposal on ground water quality.  Predictive
methods are needed to determine the hazards associated with existing sites and proposed
waste disposal activities.

7.1.1  Purpose of Screening Methods
     The purpose of this chapter is to discuss approaches and hand calculation methods
which can be used to predict ground water contamination for common waste disposal
techniques and hydrogeologic settings.  The screening methods can answer questions such
as how loofi it jrill tfrke contaminants to reach a downgradient location.  For example,
are the cajtaminants likely to reach a water supply well in 1 to 2 days or 10 to 20
years? In addition, an initial assessment of the hazard involved can be made.  For
example, a?e ttre predicted concentrations below detectable levels or several times
greater tnan the drinking water standards?  Based on such results, decisions can be
made to improve the estimates by collecting additional data, to proceed to more
detailed analyses including numerical simulation models, or to proceed to other more
critical problems.  Guidance is included at the end of this chapter suggesting when
numerical simulation models should be used.
     The hand calculation methods presented in this chapter have been selected based on
a series of criteria similar to those used for the surface water methods presented in
earlier chapters.  The two primary criteria are 1) that, although the method can be
simplified, it must be technically defensible and 2) that it require limited data which
can be easily estimated or obtained.  One simplification in all the methods presented
is the use of spatially and temporally averaged data.  To do otherwise requires a grid
system, a computer, and most importantly—extensive data.  Through careful selection of
parameter values and the use of sensitivity analyses, results for both worst case and
typical conditions can be obtained.  The other criteria are 3) that the method be
applicable to a range of waste sources and 4) that the method be applicable to a
variety of hydrogeologic settings.
     The emphasis of this chapter is on prediction of contaminant migration in porous
media.  Specific methods for handling solute migration in fractured formations have not
                                         -300-

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 been Included in this chapter.   While fractured formations are Important in some parts
 of the country, predictions of contaminant behavior in such systems are typically not
 amenable to screening methods.   For porous media,  the hand calculation methods
 presented can predict the time for specific concentrations to occur at downgradient
 locations, the time for contaminants to reach a specified distance, the concentration
 at a given time and location,  or the maximum likely concentration at any location.

 7.1.2  Ground Water vs.  Surface Water
      To orient readers who are  more familiar with  surface water  than ground water,  the
 major differences  in both physical  and  chemical processes are presented before
 proceeding to the  remainder of  the  chapter.   Host  of the  differences stem  from the  fact
 that surface  waters occur 1n surface depressions exposed  to the  atmosphere, while most
 ground water  occurs in porous media typically Isolated from the  atmosphere.  Flow
 velocities in ground water are  much slower,  on the order  of meters  per month rather
 than meters per second.   A consequence  of  the low  velocities  is  that flow  in porous
 media is  generally  laminar,  with  the exception of  flow in cavernous  limestone
 formations or volcanic formations with  lava  tubes.   The presence  of  laminar flow
 simplifies the flow calculations  as  will be  discussed 1n  more  detail  in Section  7.3.
 The  low velocities  also  mean that travel times must  be carefully  considered in
 selecting sampling  well  locations and in Interpreting previously  collected  data.  The
 lower velocities of ground  water  have several  important Implications with respect to
 chemical  processes.   At  low  velocities, very  slow  chemical  reactions can become
 important  snd faster  reactions  often  can be  treated  as equilibrium processes.
      Mixing or-tiispersion  in ground  water  is  more difficult to quantify than in  surface
 water.  Estimation  of  the  extent  of  a mixing  zone when contaminants  enter an aquifer  is
 hard  to determine and  depends on  local heterogeneities, particularly with respect to
 hydraulic  conductivity.  The extent  of vertical dispersion can be critical  when
 interpreting  data obtained from wells screened over different intervals.
      Another  factor which  1s different 1s that there is far less temperature
 fluctuation in most ground waters so that rate coefficients do not have to be
 continuously  adjusted  for short-term temperature changes.   Except in geothermal waters
 or where a  waste discharge has  increased the  temperature  In its immediate vicinity,
 ground water  temperatures are likely to be between  5 and 15°C.
      In addition to the above differences, there are differences in the solution
 characteristics which  influence the behavior of contaminants in subsurface  waters.   The
 important  solution characteristics are total dissolved solids, dissolved oxygen, pH,
 redox potential, partial pressure of carbon dioxide, and  solid/liquid ratio.  Total
dissolved  solids (TDS) concentrations in ground water typically range from  100-1000
mg/1, ionic strengths are generally close to 0, and activity coefficient corrections
 are usually not necessary for screening calculations.  If  the TDS concentrations are
                                         -301-

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greater than 1000 mg/1 and the contaminants are metals,  the  need  for activity
corrections should be considered.  Dissolved  oxygen  (DO)  had traditionally been
considered to be absent  in ground waters.  However,  measurements  in  the  last  10 to 15
years have shown levels  up to 4 mg/1 in some  systems  (Wilson and  HcMabb,  1981).   The
presence or absence of DO can determine whether certain reactions will occur.   For
example, dehydrochlorination of trichloroethylene into the dichloro  isomers and  vinyl
chloride can occur under anaerobic conditions but not aerobic conditions.
     The presence or absence of dissolved oxygen along with  other redox species  also
determines the redox potential.  Reducing conditions  (no DO, presence of  dissolved
iron) are common in ground water.  Speciation of metals partly depends on  redox
conditions.  The pH of the ground water influences the degree to which metals adsorb
onto the permeable media.  The occurrence of reducing conditions complicates  sampling
and can cause metals to  precipitate when the ground water is brought to the surface and
is exposed to the atmosphere.  Another factor which causes problems  in sampling,
particularly for metals, is that the ground water is typically supersaturated with
respect to atmospheric levels of carbon dioxide.  When samples are brought to the
surface, the weak acid CO. may be lost.  This causes the sample pH to rise and may
thereby change the speciation of metals and allow some to precipitate.
     The high solid to liquid ratio in ground water is a major difference  from surface
water.  l*terf«cial phenomena such as adsorption can be important cnemical attenuation
processes*  Example problems presented in later sections clearly show that solutes with
strong affinities for the solid phase do not travel  far in porous media.  Unlike  in
surface wzfters,  the particles to which the contaminants adsorb are usually immobile.
Because t*> particles are in continual  contact with  the flowing water the sorbed
contaminants can act as secondary sources and may desorb when the concentrations in the
ground water decrease.   Desorption can occur in rivers but is less important since
most of the sorbed contaminants become part of the bottom sediment.
     A final difference between surface and ground waters is in the screening methods
themselves.  As  will be discussed in more detail, considerably more analysis  is
required prior to the use of a particular screening  method to determine the flow paths
of the contaminants in  ground water.   Flow paths for  rivers  ere easily determined by
visual observation, whereas in ground water they are  based on limited data and
calculations.

7.1.3  Types of  Ground  Water Systems  Suitable for Screening Methods
     The screening methods presented  in this chapter  are applicable to porous media
where the capacity to transmit water  is due to primary permeability (connected pores)
rather than due  to secondary permeability (e.g.,  fractures,  lava tubes).   If fractures
in a formation are relatively uniform in size  and spatially  distributed over the area
of interest, these formations could  be  analyzed using the  screening methods by
                                        -302-

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 substituting  an equivalent permeability from pump  tests.   More  complex  fractured
 formations  (e.g., when  the fractures  are  predominantly  1n  one direction)  are not
 amenable  to screening methods.
      Major  types of aquifers  1n the United States  are shown  in  Figure VIM.  The
 divisions shown are unconsolidated and consolidated formations, alluvial  aquifers  along
 major rivers, and areas where aquifer yields are less than 0.2 m /min (50 gpm)  to
 individual  wells.  The  stratigraphy 1n an area can range from a layered system  such  as
 on  Long Island (Figure  VI1-2} to a complex system  of unconsolidated glacial  formations
 overlying several different types of consolidated  rock formations such as occur  in New
 Jersey  (Figure VII-3).  In such complex hydrogeologic systems,  some aquifers  may be
 confined  (i.e., not open to the atmosphere).  In the arid western part of the country,
 additional  complications can occur.  Examples include closed basins where
 evapotranspiration is the only outflow and highly  faulted basins which can have  large
 changes in  permeability over short distances (Figure VII-4).  Infiltration in such
 basins typically occurs along the basin boundaries, primarily from runoff in  the
 mountains,  instead of directly through the valley floor.  There are also more likely to
 be  thick  unsaturated zones.  Screening methods are presented in this chapter  which
 predict the migration of contaminants in both the unsaturated and saturated zones.

 7.1.4  Pathways for Contamination
      Th«  usual-division of waste sources into point and nonpoint sources can  be  used
 for ground  water but this kind of division does not indicate the variety of ways in
 which co*tarnloants can enter ground water systems.   Waste can enter the ground water
directly,  through recharge of contaminated surface  water, or through leakage from one
 aquifer to  another.   In some cases, recharge of contaminated water may not be
 considered  because of the inferred presence of an impermeable layer or confining bed,
when  in reality the  impermeable layer or bed is discontinuous and contamination of an
underlying  or overlying aquifer has occurred.
     Examples of point sources of importance to ground water include surface
 impoundments, landfills, spills and leaks, and injection wells.   The largest number of
 impoundments are associated with the oil  and gas  industry,  although  larger volumes  of
waste are  disposed by  the paper, chemical, and metals  processing industries  (U.S. EPA,
 1979).  The relative number of impoundments  by state  is  shown in Figure  VI1-5.
Landfills  are used to  dispose of sludge from municipal  waste treatment plants, ash and
flue-gas desulfurization sludge from coal-fired  utilities,  and wastes  from other types
of  industries.  The  wastes can contain high  concentrations  of metals,  organic
chemicals, and acids.   Spills  and  leaks,  particularly  from  underground storage tanks,
have recently been recognized  as a  major  source of  contamination,  especially  with
respect to organic chemicals  (e.g., trichloroethylene  and gasoline).   Injection  wells
have been  used primarily for  oil  field brines  and the  associated "produced waters', but
                                         -303-

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  a«« MMI • «• ***** *» •*•••« «M •• (MM
  r>M • —» •• *» m» » «•
FIGURE VII-1   MAJOR AQUIFERS OF THE  UNITED STATES,   REFERENCE:   THOMAS (1951)
                                             -304-

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 FIGURE VI1-2
GEOLOGIC  SECTION IN WESTERN  SUFFOLK COUNTY,  LONG  ISLAND,
SHOWING BOTH CONFINED  AND  UNCONFINED AQUIFERS.
REFERENCE:   TETRA TECH (1977)
 some ma*vfactur1ng process wastes  and mining wastes have also been injected into deep
 aquifers or tnto dry wells in areas with  deep unsaturated zones.  Contamination from
 wells cah also occur from migration from  one zone or aquifer to another along abandoned
 or  improperly plugged casings.
     Nonpoint sources,  which  result in contaminants being spread over large areas,
 include seepage from residential areas with septic tank systems, infiltration of
 runoff, and application of pesticides and fertilizer to agricultural  and residential
 land.  The methods presented  in  this chapter are oriented more towards point sources
 but can be used to estimate the  overall effect on an aquifer of a wide-spread
 contaminant.

 7.1.5  Approach to Ground Water  Contamination Problems
     The initial  step 1n analyzing a ground water problem is the selection  of the
 spatial and temporal framework for the problem.  The spatial representation 1s
 determined from the disposal  system configuration (i.e., a large pond or landfill
 versus a leak or  an injection well) and the type of question being asked.   For  example,
 if the need is to predict the concentration at the water table of a contaminant spilled
 at the surface, a one-dimensional vertical transport method  may be most  appropriate.
 If the need is to predict the areal extent of a ground water plume, a two-dimensional
method for flow in the  saturated zone would be preferred.  The temporal  representation
 of a problem must consider  whether a waste source should be  considered as a one-time
                                        -305-

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        UWNfr
FIGURE VI1-3
DETAILED QUATERNARY GEOLOGIC MAP OF MORRIS COUNTY  (AFTER GILL  AND VECCHIOLI,  1965)
                                     -306-

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            A) VALLEY IN BASIN AND RANGE AREA SHOWING
               THICK UNSATURATED ZONE OF COARSE SAND
               AND GRAVEL
      B) FAULTED BASINS WHICH  CAN BE  CLOSED,   RECHARGE  is
         MOSTLY FROM RUNOFF  IN MOUNTAINS  NOT  RAINFALL
         DIRECTLY ON VALLEY  FLOOR
FIGURE VIM
GENERALIZED CROSS-SECTIONS SHOWING FEATURES COMMON
IN ARID WESTERN REGIONS OF THE UNITED STATES,
REFERENCE:  EAKIN, PRICE, HARRILL (1976)
                             -307-

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Totdl Impoundments
  Figure Vll-5   Nunber of Waste  Impoundments by State (after U.S.  EPA,  1979a)
                                         -308-

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 discharge (slug),  as  a continuous  discharge,  or otherwise.   This distinction does not
 have  to be made in absolute terms  but instead can be made relative to the time scale of
 the problem.   For  example,  if waste had been  discharged to a pond for a one-month
 period and the objective was to predict concentrations at a downgradient well five
 years later,  the waste source could be considered to act as a slug discharge.  Examples
 of  how problems should be proposed (set-up) are given in Section 7.5.

 7.1.6  Organization of This Chapter
      The remaining sections describe the specific screening methods,  how to estimate or
 obtain the necessary  data,  and how to interpret the  results.   Section  7.2,  Aquifer
 Characterization,  is  intended as a reference  section for those readers who  may  not be
 familiar with ground  water  terminology.   Parameter nomenclature which  may be
 encountered in the literature is explained, and typical  values are provided.
 Information is also included on methods  for estimating the  parameters  and for
 quantifying them either in  the laboratory  or  in the  field.   Section 7.3,  Ground  Water
 Flow  Regimes, describes detailed procedures for estimating  seepage velocities and
 travel  times  for conservative constituents and  includes  example problems.   Section 7.4,
 Pollutant Transport Processes,  discusses  the  major physical  and chemical  transport
 processes.  A practical approach is  provided  for  estimating dispersion and  diffusion.
 This  section  •also  discusses  pollutant-soil interactions  and the chemical  and  biological
 processes-which  are pertinent to subsurface problems.  Methods  are described for
 estimating  the  necessary  rate  coefficients and  for incorporating  them  into  the
 screening methods.  Section  7.5, Methods  for  Predicting  the Fate and Transport of
 Conventional  and Toxic  Pollutants, presents five  different calculation methods.  The
 methods  predict  migration of  solutes  from a contaminated aquifer  to a  well,  from an
 injection well out into an  aqu-ifer, from the  surface down to the  water table, and  from
 a one-time  or  continuous  discharge downgradient  in the saturated  zone.  For each method
 selected  the  following  information is provided:
        •    Uses of the method
       «    Brief description of method and its theoretical basis
       •    Assumptions and simplifications required
       •    Types of input data needed
       •    Worked-out  example problems
       •    Limitations of the method.
 Finally, Section 7.6,  Interpretation of Results, discusses reference criteria which may
be of interest, and methods  for estimating the uncertainty associated  with the results.
Buidelines are discussed for suggesting when  more detailed analyses, including use of
nwnerical simulation models, are warranted given the  relative hazard,  the uncertainty
associated with the screening results, data availability, and time and budget
constraints.  Section  7.7, References, includes  the references cited in the  chapter and
a list of additional material which may be helpful, particularly with  respect to  field
sampling.
                                         -309-

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7.2   AQUIFER  CHARACTERIZATION

      This  section  1s  Intended as  a  reference section for those users of the manual who
may  not  be  familiar with  the  parameters  used in  ground  water  investigations.   It is
anticipated that most  readers will  use this  section  only as needed to obtain  a typical
value for  a given  parameter or to review methods for measuring the parameters.
      Before the transport of  contaminants  in ground  water can  be  predicted, estimates
of key properties  of  the  porous media are  needed.  Section 7.2 discusses  the  definition
and  use  of  these parameters in the  screening methods.   The key parameters have been
grouped  into  those characteristic of the porous  media (Section 7.2.2).  those  used to
estimate flow in the  saturated zone {Section 7.2.3),  and those used to  estimate flow in
the  unsaturated zone  {Section 7.2.4).  Tables of average and typical  values for a wide
range of geologic  formations  have been Included.  The specific parameters are listed in
Table VII-1.   Additional  parameters, also  shown  in this table, are discussed  in
Appendix 1.   The parameters given in Appendix I  are  not generally needed  for  the
screening methods  presented later in this  chapter but may be encountered  in the ground
water literature.  Methods for measuring the parameters in the field  or laboratory or
estimating  them from other parameters are presented in Section 7.2.5.  A discussion  has
also  been  included in this section on sample  size and confidence  levels.

7.2.1  Physical Properties of Water
      For t*e  vast majority of  problems of interest, the concentration of dissolved
solids in the ground water is  so low that it does not affect the  physics of fluid  flow.
Hence, the  phystcal properties of the transport fluid such as  density, viscosity,
compressibility, etc. are assumed to be  independent of  the solute concentrations and to
be equal  to those  of pure water.  Situations where this assumption may not be true are
when  the solute concentrations are very high, (e.g.,  brackish  aquifers or where  large
quantities of pure solute with a density  different than water  have been mixed with
ground water  (e.g., oil, gasoline)).  The principal physical  properties of water that
are of interest in ground water flow are  density, viscosity,  and compressibility.    In
most  situations these properties can be considered constant as shown below:
       Compressibility of water at 1 atm  and 4°C:  4.96X10"11  cm sec2/g
       Density of water at 1 atm and 4°C:  1.000 g/cm
       Viscosity of water at 1 atm and 4°C:  0.01567  g/on sec
Values for these properties as a function of temperature are  included in Appendix  I.

7.2.2  Physical Properties of Porous Media
      The physical  properties of porous media can be described  by the relative state of
its three phases or primary components.   These are the solid,  liquid, and gaseous
phases.  A schematic representation  of a  soil's three phases  is given in Figure VII-6.
                                         -310-

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                                 TABLE VII-1

                    AQUIFER PARAMETERS AND THEIR RELATIVE
                     IMPORTANCE AS SCREENING PARAMETERS
Symbol
pw
V
6w
"s
Pb
de
P
0
Sr
S
°s
S?
S
b,m
K,T



x.y.z
#(«>)

0-0
h
VVHg
pp.'/'p.Hp
Wo
I
Parameter
density of water
viscosity of water
compressibility of water
particle density
bulk density
particle-size distribution
porosity
water content
specific retention
specific yield
compressibility of soil
specific storage
storativlty
aquifer thickness
hydraulic conductivity
and transmissivity:
saturated media
unsaturated media
anistropy
soil-moisture
characteristic curve
hysteresis
water level elevation
gravitational potential
pressure potential
osmotic potential
hydraulic gradient
Section
Where
Discussed
1-1
1-1
1-1
1-1
7.2.2.1
7.2.2.2
7.2.2.3
7.2.2.4
1-1
1-1
1-1
1-1
1-1
7.2.3.2


7.2.3.2
7.2.4.3
7.2.3.2

1-1
1-1
7.3.2
1-1
1-1
1-1
7.3.1
Relative Importance As
A Screening Parameter
Low* Highb
X
X
X
X
X
X
X
X
X
X
X
X
X
X


X
X
X

X
X
X
X
X
X
X
"Parameter is not essential  and/or  Us  value  can  be  easily  obtained from
 tables given in  Section 7.2 and  Appendix I.

 Parameter is essential.  Estimates  or  measurements  of  its  value are used in
 the methods  included in this chapter.

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                                                            AS SPACES
                                                          WATER
                                                         SOLIDS
       Figure VI1-6   Schematic  Showing the  Solid,  Liquid  and Gaseous

                        Phases In  a Unit  Volume  of Soil
The solid  0hase is made up of soil particles that represent the granular skeleton  of


the
     A volume of soil V is equal  to the sum of the volume  of solids V , the volume  of
water V ,  and the volume of gas  (vapor phase), V •
       w                                      y
                                 v ' v
(VIM)
The volume of  voids or pores V  in a soil is defined as  the sum of the water and  gas


volumes:
                                  V  « V  * V
                                   v    w    g
(VII-2)
hence
                                    V . vs * Vy
IVI1-3)
     The total mass M of these three phases in a volume of  soil  is the sum of the mass


of solids M ,  the mass of water M , and the mass of gas M  (which is negligible):

-------
                                   H . M  * M  + M                             (VII-4J
                                        »    w    y

     The quantltafive relationship between the three phases can  be  characterized  by
 such variables as the bulk density of the soil, the particle-sue distribution  and  the
 porosity or water content.

 7.2.2.1  Bulk Density
     Bulk density is used in describing the phenomenon of sorption  and  retardation  in
 contaminant transport equations  (see Section 7.4.2.1.1).  The dry bulk  density  of a
 soil (>*(9/cii?) is defined as the mass of a dry soil M (g) divided by  its bulk or  total
           3
 volume V(cm ):

                                       PK • M /V                              (VII-5)
                                        b    s

     The bulk density 1s affected by the structure of the soil (e.g., its looseness or
 degree of compaction) as well as its swelling and shrinkage characteristics which are
 dependent upon its wetness.  Loose, porous soils will have low values of bulk density
 and more compact soils will have higher values.  Bulk density values normally range
 from 1 too 2 g/on .  Soils with high organic matter content will generally have  lower
 bulk dejjslty values.  Very compact subsoils, regardless of texture, may have bulk
 densirfes higher than 2 g/on .   Moreover,  there is a general tendency for the bulk
 density to increase with depth.  The range and mean value of bulk density for various
 geologtf materials are given in Table VII-2.

 7.2.2.2  Particle-Size Distribution
     Soil type can be used to estimate porosity, hydraulic conductivity, and specific
 surface area available for sorption.  The  texture of a soil  is usually determined by
 the relative proportions (by dry weight)  of sand, silt and clay present  in the soil.  A
 soil-texture trilinear diagram is then used to determine the soil class  (Figure VI1-7).
Alternatively, soil  classification can be  characterized  on the basis of  particle or
 grain-size distribution.  Particle-size distribution curves  (Figure VII-8)  are obtained
 by plotting the cumulative percentage (by  dry weight)  of soil  particles  in a soil  as a
 function of their particle size.  Table VII-3 lists the range  of  particle sizes for
 various soil  classifications.
     An effective particle size, d , is defined as the grain diameter for which "e"
 percent of the particles (by dry weight)  is equal  or smaller in diameter.   Normally  "e"
 is set to 10 percent for Hazen's effective  grain  size  d.Q but  d20 will often be  used to
 characterize coarse  materials.   Hence,  if d.- •  0.6mm  (uniform, coarse sand),
then 101 of the soil particles  of this  material  (by  dry  weight) will have  a  grain
diameter less  than or  equal  to  0.6mm.   A list of  d.. effective  grain sizes  is  given  for


                                        -313-

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               TABLE VII-2
RANGE AND MEAN VALUES OF DRY BULK DENSITY
Material
clay
silt
sand, fine
sand, medium
sand, coarse
gravel, fine
gravel, medium
gravel, coarse
loess
eollan sand
till, predominantly silt
till, predominantly sand
till, predominantly gravel
glacial drift, predominantly s1U
glacial drift, predominantly sand
gladaV Jrlft, predominantly gravel
sandstone, fine grained
sandstone, medium grained
siltston*
claystone
shale
limestone
dolomite
granite, weathered
gabbro, weathered
basalt
schist
Reference: Morris and Johnson (1967).
Range
(a/on
1.18
1.01
1.13
1.27
1.42
1.60
1.47
1.69
1.25
1.33
1.61
1.69
1.72
1.11
1.36
1.47
1.34
1.50
1.35
1.37
2.20
1.21
1.83
1.21
1.67
1.99
1.42

- 1.72
- 1.79
- 1.99
- 1.93
- 1.94
- 1.99
- 2.09
• 2.08
- 1.62
- 1.70
- 1.91
- 2.12
- 2.12
- 1.66
- 1.83
- 1.78
- 2.32
- 1.86
- 2.12
-1.60
- 2.72
- 2.69
- 2.20
- 1.78
- 1.77
- 2.89
- 2.69

Mean,
(g/cuT)
1.49
1.38
1.55
1.69
1.73
1.76
1.85
1.93
1.45
1.58
1.78
1.88
1.91
1.38
1.55
1.60
1.76
1.68
1.61
1.51
2.53
1.94
2.02
1.50
1.73
2.53
1.76

               -314-

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                              too
                         PERCENT BY WElCKT SAND
Figure VII-7    Soil  Texture Trllineor Diagram Showing Basic Soil
                Textural Classes,   Reference:  Hlllel  (1971)
       o
       a
         SO
                                                Montmontonitt
                  MfM
10' e
2  10* ew'
                                   zw'w'&w* 2«r»
                            PARTIO.E
   Figure VII-8    Typical Particle-size Distribution  Curves
                   for Various Soil  Classifications.
                   Reference:  Bear  (1972)
                             -315-

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                                      TABLE VI1-3
                       EFFECTIVE GRAIN SIZE AND THE  RANGE  OF  SOIL
                          PARTICLE SIZES FOR VARIOUS MATERIALS
Material
colloidal clay
clay (30 to 501 clay sizes)
silty clay
sandy clay
uniform silt
silty sand
well-graded, silty sand and gravel
uniform, fine sand
clean, well-graded sand and gravel
uniform, medium sand
uniform, coarse sand
very coarse, clean, uniform sand
fine uniform gravel
clean, fine to coarse gravel
onejan stone
derrick stone
Effective
Grain Size
V"1 dio((WI)
—
—
—
—
—
—
—
—
—
—
—
1.5
3
13
150
1200
40A*
.0003
.0015
.002
.006
.01
.02
.06
.1
.3
.6
—
—
—
—
—
Particle Size
(«")
10A-.01
.0005-. 05
.001-. 05
.001-1
.005-. 05
.005-2
.01-5
.05-. 25
.05-10
.25-. 5
.5-2
.8-3
1.5-8
10-80
100-300
900-3000
                            -8
      *A « angstrom « 1 x 10   cm.
      Reference:   Hough (1957).
various materials in Table VII-3.   The d.Q value can be used to predict Intrinsic
permeability, as shown in Section 7.2.5.2.1.

7.2.2.3  Porosity
     Porosity is an important screening parameter 1n saturated aquifers used in
computing the velocity of contaminants in the ground water (seepage velocity.
Section 7.3.3.1.2) and the sorption and retardation of contaminants (see
Section 7.4.2.1.1).  Soil porosity "p" (unltless) 1s defined as the void or pore volume
Vy(cm3) of the soil divided by the bulk volume V(on3} of the soil:

                                      P - V¥ / V                              (VI1-6)
                                         -316-

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 The porosity 1s expressed as either a decimal fraction or as a percent.  The void
 volume of a soil 1s defined 1n Equation VII-2 as the sum of the gas and water filled
 voids or interstices.   Typical values of porosity for various geologic materials are
 given 1n Table VII-4.
      The term effective porosity pe (unitless)  1s sometimes used but Its meaning
 depends upon Its usage.  It can equal the specific yield of a water-table aquifer which
 1s defined as the volume of water obtained under a unit drop in head from a unit area
 of the aquifer.  Alternatively, 1t can refer to that portion of the porous  medium
 through which flow actually takes place.   The last definition is  important  when  the
 porous matrix includes  a large number of  dead-end pores and hence  part of the fluid in
 the pore space 1s Immobile (or practically so).   In either  definition, the  effective
 porosity is always less than or equal  to  the total porosity (p *  p).   The  porosity of
 consolidated materials  depends mainly on  the degree of  cementation of  the grains.   The
 porosity of unconsolldated materials  depends on  the packing of the grains,  their shape,
 arrangement and size distribution.

 7.2.2.4  Water  Content
      Water  content in the  unsaturated  zone 1s 1n  some ways  analagous to porosity in the
 saturated zone  of an aquifer.   The  water  content  is  used  in  the computation of seepage
 velocity and the  sorption  and  retardation  of contaminants.   The water  or  moisture
 content -«t  a so41  1s the amount  of  water  in  a given  amount  of  soil.  It  is  a
 dimensioniess -quantity  and  can  be expressed  on either a gravimetric  (mass)  or a
 volumetr4«  (vo4time) basis.  The  gravimetric  water  content Q   (unitless)  is  defined  as
 the mass  of  water  M  (g) divided by the dry  mass of  the soil H  (g)  (oven dried  at  105-
The  volumetric water content  (unitless)  is defined as the volume  of water V   (cm3)
divided by the volume of the  soil V (cm3):

                                       0' Vw / V                               (VII-8)

     These two expressions for water content are related as follows:
where ^(g/cm3) is the dry bulk density of the soil and P (g/on3) is the density of
water.  The ratio ^/^^ is often called the apparent specific gravity of the soil
(unitless).  Values for Pfa can be found in Table VII-2 for different geologic
materials.
                                         -317-

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           TABLE VII-4
RANGE AND MEAN VALUES OF POROSITY
Material
clay
s1H
sand, fine
sand, medium
sand, coarse
gravel, fine
gravel, medium
gravel, coarse
loess
eolian sand (dune sand)
till, predominantly silt
till, predominantly sand
till, predominantly gravel
glacial JCm, predominantly silt
glacial a*"1ft, predominantly sand
glacial »r1ft, predominantly gravel
sandstone fin* grained
sandstones medium grained
siltstone
clay stone
shale
limestone
dolomite
granite, weathered
gabbro, weathered
basalt
schist
Reference: Morris and Johnson (1967).
Range
(percent)
34.2
33.9
26.0
28.5
30.9
25.1
23.7
23.6
44.0
39.9
29.5
22.1
22.1
38.4
36.2
34.6
13.7
29.7
21.2
41.2
1.4
6.6
19.1
34.3
41.7
3.0
4.4
- 56.9
- 61.1
- 53.3
- 48.9
- 46.4
- 38.5
- 44.1
- 36.5
- 57.2
- 50.7
- 40.6
- 36.7
- 30.3
- 59.3
- 47.6
- 41.5
- 49.3
- 43.6
- 41.0
- 45.2
- 9.7
- 55.7
- 32.7
- 56.6
- 45.0
- 35.0
- 49.3
Mean
(percent]
42
46
43
39
39
34
32
28
49
45
34
31
26
49
44
39
33
37
35
43
6
30
26
45
43
17
38
             -318-

-------
      In general,  at saturation the volumetric water content 0$at equals the porosity
 (i.e.,  e  t • o)-   for unsaturated conditions, 6 1s always less than the porosity.
 However, for swelling, clayey soils,  the volume of water at saturation can exceed the
 porosity of the dry soil.
      The volumetric water  content  1s  the most used and probably the most convenient
 method  of expressing water content.   It  is  more directly adaptable to the computation
 of fluxes and water quantities added  or  subtracted by seepage through ponds and
 landfills,  irrigation or evaporation.

 7.2.3  Flow Properties of  Saturated Porous  Media
      Saturation of  a porous  medium means that all  of the soil  voids or pores are filled
 with  water.   Complete saturation,  however,  is not  always possible  since some gas may be
 trapped between soil  particles.
      In an  unconfined aquifer the  upper  surface of the saturated zone is open to the
 soil  atmosphere.  This  surface Is  called the  water table or phreatic surface.   In a
 well  penetrating an  unconfined aquifer,  the water  will  rise only to the level  of the
 water table  (i.e., when the  ground water flow 1s predominately  horizontal).   A
 schematic of  an unconfined aquifer is shown in  Figure  VII-9.  Changes  1n the level of
 water in such  a well  result  primarily from  changes  in  the  volume of water  in storage.
      In * confined aquifer,  the saturated zone  is  underlain  and overlain by  relatively
 impermeable  strata.   The ground water 1n  a  confined  aquifer  is  under a  pressure greater
 than  atmospheric.  In a well  penetrating  a  confined  aquifer, the water  may  rise above
 the bottom of  the overlying  confining stratum.  The  water  level 1s  called  the
 piezometfic or-potentiometric  surface.   A schematic  of a confined aquifer  is also shown
 in Figure  VII-9.  Changes in  the level  of  water in  such a well result  primarily from
 changes  in pressure  rather than from changes  in storage  volumes.  If the piezometric
 surface  lies above the ground, a flowing well  will  result.  In a leaky  or semiconfined
 aquifer, the saturated zone  is underlain or overlain by a semipervious  stratum.
      In order to describe flow through saturated porous media, the hydraulic
 conductivity  (or transmissivlty) and storativity of the medium must  be  characterized.

 7.2.3.1  Saturated Hydraulic Conductivity
      Hydraulic conductivity K  (cm/sec) expresses the ease with which a  fluid can be
 transported through a porous medium.   Hydraulic conductivity is an  imporant parameter
 used  in computing seepage velocity.  It is also one of the most difficult parameters  to
measure accurately and is relatively expensive to obtain.  Usually 'point' values are
measured but large variations can occur within short distances, even in apparently
uniform geologic formations.   It is a  function of properties of both the porous medium
and the fluid.  The range of values for saturated hydraulic conductivity and intrinsic
permeability are given in Table VII-5  for various geologic materials.
                                         -319-

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         ^S (7 B'/*^  .\«'v*»-
         rafo3o--.Q-:--<
         •Lv?'*/»:6'-CS-0-
         DKTO'rvAO
         fc//A •. ' r\ -.•_•. »

^•O«

             UNCOHf WED
                                     fffhpffQ^
                                  S§^

             COnrtNCO

              ViI-9   SCHEMATIC CROSS SECTION  SHOWING BOTH A  CONFINED
                       AND AN  UNCONFINED  AQUIFER
     These properties can ideally be  separated  by  expressing hydraulic conductivity as
follows:
                                      K  - K
               .2,
                                                                             {VII-10}
-here ^ is the intrinsic  permeability  (cm2). 9 is the gravitational acceleration
(980.7 cm/sec ). PW is  the density of water  (g/cm3) and n is the viscosity of water
(g/cm sec).  Values of  PW  and  v  are  given in Table 1-1 in Appendix I.  The
intrinsic permeability  is  only a function of porous medium properties such as the
particle-size distribution,  grain or pore shape, and tortuosity.  However, the
expression  in Equation  YII-10  for saturated hydraulic conductivity assumes that the
water and solid matrix  of  the  soil do not interact in such a way as to change the
properties  of either.   In  most soils there is no matrix-water interaction.   In
addition, the intrinsic permeability may vary with time as a result of chemical.
physical and  biological processes.  These may include structural and textural  changes
                                        -320-

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                                      TABLE  VII-5
                  TYPICAL VALUES OF SATURATED  HYDRAULIC  CONDUCTIVITY
                              AND INTRINSIC  PERMEABILITY

                                               Hydraulic             Intrinsic  *
                                               Conductivity *       Permeability
       Material                                 K(cm/sec)             If  '-*'

clean gravel
clean sand
silty sand
silt, loess
stratified clayb
glacial till
unweathered, marine clay
karst limestone
permeable basalt
fractured igneous and
metamorphic rocks
limestone and dolomite
sandstone
4*5 le
breccia, granite
uafractured metamorphic and
igneous rocks

.1 -
10-4-
io-5-
io-7-
io-7-
io-10 -
io-11 -
io-4-
io-5-
io-6-
io-7-
io-8-
lo-11 -
ID'11 -
ID'12 -

100
1
.1
ID'3
io-4
io-4
io-7
1
1
ID'2
ID'4
ID'4
io-7
io-9
io-8
-6
10 -
io-9-
io-10 -
ID'12 -
io-12 -
io-15 -
ID'16 -
io-9-
io-10 -
lO'11 -
io-12 -
io-13 -
io-16 -
ID'16 -
io-17 -
_3
10 J
io-5
io-6
ID'8
ID'9
io-9
ID'12
io-5
io-5
io-7
ID'9
ID'9
io-12
io-14
ID'13
       a Reference:  Freeze and Cherry (1979).
       b Reference:  Bear (1972).
due to subsidence and consolidation, the development of solution channels, clay
swelling, and clogging due to biological growth and by precipitates carried by the
water.
     If the aquifer properties (e.g., hydraulic conductivity) are independent of
position within a geologic formation, the formation is called homogeneous.  If the
properties are dependent on position within a geologic formation, the formation is
called heterogeneous.  Heterogeneity is caused by the presence of interlayered
deposits, faults, or other large-scale stratigraphic features (such as overburden-
bedrock contacts), large scale changes 1n the sedimentary formations (particularly
those which are part of deltas, alluvial fans, and glacial  outwash  plains) and small-
scale layering in an otherwise homogeneous formation.
                                         -321-

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      If hydraulic conductivity  1s  Independent  of the  direction of measurement in a
geologic  formation, the  formation  1s  called  Isotropic.   If the hydraulic conductivity
varies with the direction of measurement,  the  formation  Is called anisotropic.   The
primary cause of anlsotropy on  a small scale 1s  the orientation of clay minerals in
sedimentary rocks and unconsolldated  sediments.   Anlsotropy of consolidated geologic
materials  is governed by the orientation of layers, fractures,  solution openings or
other structural conditions which may not  have a horizontal  alignment.   Fractured rocks
can also be anisotropic because of directional variation  in  joint  aperture  and  spacing.
     The horizontal saturated hydraulic conductivity  Kh  (cm/sec)  in  some materials
(e.g., alluvium) is normally greater than  the vertical conductivity  Ky  (cm/sec); hence
KL/K £l.   Ratios of *h/*v usually fall in  the range of 2  to  10  for alluvium and  glacial
outwash (Weeks, 1969) and 1.5 to 3 for sandstone  (Plersol  et aJL.  1940)  but  it  is not
uncommon to have values of 100 or more occur where clay  layers  are present  (Morris  and
Johnson, 1967).

7.2.3.2  Transmissivlty
The transmissivity or coefficient of transmisslbility T  (on /sec)  is defined  as:

                                        T • Kb                                (VII-11)

where K Vs the saturated hydraulic conductivity  (cm/sec) and b  1s  the aquifer thickness
(cm).  Traj»smissiv1ty has traditionally been expressed in units of gal/(ft day)  but
this can -h« comrerte<
1.438 x 10~3.  Thus:
                                            2
this can -h« concerted to the cgs units of cm /sec by multiplying the gal/(ft day) by
                         1 gal/(ft day) • 1.438 x 10~3 cm2/sec                (VII-12)

     Transmissivity can be estimated by multiplying the saturated hydraulic
conductivity K(cm/sec) given for various geologic materials in Table VII-5 by the
aquifer thickness b(cm).  Because pumping tests can provide values for transmissivity,
this type of data may be more available than saturated hydraulic conductivity.

7.2.3.3  Storativlty
     Storativlty or storage coefficient, S, is defined as the volume of water that is
released from storage per unit horizontal area of aquifer per unit decline of hydraulic
head. It is a dimensionless quantity.  This parameter is obtained in addition to
transmissivity from pumping tests.  It is used to compute aquifer yields and to compute
drawdowns of individual wells.
     For confined aquifers, storetlvity 1s due to water being released from the
compression of the granular skeleton and expansion of the pore water.   S is
                                        -322-

-------
 mathematically defined as  the product of the specific storage, S$ (cm" ) and the
 aquifer thickness,  b(cm):   S  «  S$b.
      The value of the  storativlty  for confined  aquifers 1s generally small, falling
 between the range of  .00005 to  .005  (Todd,  1980).   Hence,  large pressure changes over
 an  extensive area of aquifer  are required before substantial  water  1s  released.

 7.2.4  Flow Properties  of  Unsaturated Porous Media
      The term unsaturated  means that  the voids  or pores of  a  porous  medium  are only
 partially filled  with  water.  Under these conditions,  the  pressure within a soil  pore
 becomes less than atmospheric because water  Is  under  surface-tension forces.  These
 surface-tension forces  Increase as the water content  decreases.   Hence,  the flow
 properties  of a porous  medium (such as hydraulic conductivity)  are functionally
 dependent on the  water  content.  These functional relationships  are  a  characteristic  of
 the particular porous medium.

 7.2.4.1   Soil-Water Energy
      To describe  the movement and behavior of ground  water, the  relative  energy  state
 of the  soil  water must  be known.  This 1s necessary because flow will  occur in the
 direction of decreasing energy and the soil water tends to equilibrate with Its
 surroundings.  As stated above, the relative amount of energy contained  in  the soil
 water is  important and  not  the absolute amount of energy (i.e.,  relative  to a standard
 refererm state).  Generally, the standard state is defined as a  hypothetical reservoir
 of free water, at atmospheric pressure, at the same temperature  as that of  the soil
 water,  and at-a given and constant elevation.
     The  total energy £ of  the soil water 1s equal  to the sum of  its kinetic E.   and
 potential E   . energies:

                                     E • Ek * Epot                             (VII-13)

     Kinetic energy Efc  is that energy which the soil water has by virtue of Its motion.
 However,  under most typical ground water situations, the kinetic energy will be
 negligible compared to potential energy by virtue of the low velocities generally
 encountered  in subsurface flow.
     Potential energy is that  energy  which  soil  water has  by virtue of Its position.
Technically the potential  energy of soil  water is the amount of work that must be done
per unit quantity  of pure water  in order  to transport reverslbly and isothermally an
 infinitesimal quantity of water  from  a pool  of pure  water  at a specified elevation at
atmospheric pressure to the soil  water at the point  under  consideration.
                                        -323-

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     The potential energy, EDOt> of soil water can be separated  into  at  least  three
components:  gravitational, E ; pressure, E  ; and osmotic, EQ.   The total  potential
energy 1s the sum of these three:
     The three components of the potential energy are considered below.

7.2.4.1.1  Gravitational Potential
     Gravitational potential energy is the potential for work resulting from the force
of gravity acting on a quantity of pure water located at some point in space that  is
vertically different from a reference point.  The strength of this potential energy
E (erg) depends on the strength of the gravitational force gfcm/sec ), the density of
 g           i
water P (g/on ) and the vertical elevation of the water from a reference point z(cm).
       w                                                          3
Hence, the gravitational potential energy acting on a volume VW(CBI ) of water is
mathematically defined as:

                                      Eg " W                             (VI1-15)

This potential energy is a positive quantity If the unit volume of soil water is
located above the reference level and negative if located below.

7.2.4.1.2''Pressure Potential
     Pressure potential energy E  (erg)  is that potential energy due to the pressure of
the surrounding fluid acting on it.   Mathematically, this can be represented as follows
for the case of constant density p (g/on ):
                                   Ep • PMw/Pw - PV^                          (VI1-16)

where P is the relative or gage pressure (dyne/on )  acting on a unit volume V (cm) or
unit mass M^ (g) of soil water.

Note that P is the relative or gage pressure and not the absolute pressure.  Hence:

                                      p ' Pw - P0                             (VII-17)

where PW is the absolute pressure at the point under consideration and p  is the
absolute pressure at the reference elevation (usually taken to be atmospheric
pressure).  Thus, pressure potential is a positive quantity under a free-water surface
                                         -324-

-------
 (saturated  zone),  a zero  potential  at the  water  surface  and  a  negative pressure
 potential  in  the unsaturated zone.
      In the saturated zone, the pressure potential  is  a  direct result of the weight of
 overlying water.   Hence,  the pressure potential  at  any point in the  system is
 determined  by the  depth that the point  lies below the  water  table.   The  relative
 pressure P  (dyne/cm ) can thus be expressed as:

                                        P - p gh                                (VII-18)

 where h (cm)  is the depth below the water  table.  The  pressure potential  is  measured  in
 the field with a piezometer.  In a confined aquifer, the piezometer  head  h  is  measured
 as the distance between the point under consideration  and the  free water  level  in  the
 piezometer.
     In the unsaturated zone,  the pressure potential is a negative quantity  and is
often given a special  symbol such as t//and a special name such as the mafic potential,
capillary potential, matric suction or tension.  By convention, suction and  tension are
considered positive quantities,  hence:

       
-------
        •MATRC POTENTIAL U»«uc»led toil)
•OSMOTIC POTENTIAL
                                             w
                                   ADSORKD
                                   VMTER
                                                                   MEMBRANE
                                                (Tl*£ • 0)
        FIGURE VI1-10    SCHEMATIC  OF MATRIC  AND  OSMOTIC SOIL-WATER
                           POTENTIAL.   REFERENCE:   BRADY  (1974)

Note that plants cannot obtain water from soil  at  pressure  potentials less  than  the
wilting coefficient and water will not  move  in  liquid form  below the  hygroscopic
coefficienVlevel.

7.2.4.1.3  Psmotic  Potential
     Osmotvc potential  energy is that potential  energy attributed to the  attraction  of
solutes for water.   Attractive forces arising from the polar  nature of  water  tend  to
orient water around ions.   Hence,  osmotic potential  refers  to  the work required to
pull water away from these attracted ions.
     In the absence of  a semipermeable  membrane, soluble ions will diffuse  Into  a  soil
solution until the  ions are uniformly distributed.   With the  presence of  a
semipermeable membrane  between two solutions, water  molecules will move through  the
membrane to the side with   the higher solute concentration  (see  Figure  VII-10).  Water
will continue to pass through such a membrane until  the  hydrostatic pressure  difference
between the two sides balances the effect of  the ion-water  attraction forces.  Hence,
one can measure the osmotic potential of  the  solute  solution  by  measuring the
hydrostatic pressure difference  across  the membrane.  The osmotic potential is a
negative quantity because  the presence  of solutes  lowers the  vapor pressure and  free
energy of the soil  water and hence lowers the potential  energy.
     Clays can act  as a leaky semipermeable membrane, allowing water to pass  more
easily than salts.   This is sometimes referred to  as  salt sieving  (Nye  and Tinker,
1977).  Thus in sedimentary basins,  osmosis can  cause significant pressure
differentials across clayey strata (Freeze and Cherry, 1979).  The osmotic potential
                                         -326-

-------
 can also be important 1n saline soils of arid and semlarid regions  (Brady,  1974).   In
 addition, the osmotic potential 1s important to the uptake of water by plant  roots  and
 the movement of water vapor.  Both the soil-root and water-gas interfaces act as
 semipermeable membranes.  Except for the above cases, however, the contribution of
 osmotic potential to the mass movement of water is negligible in most soil  systems.

 7.2.4.2  Soil-Moisture Characteristic Curves
      Consider a sample of soil that is maintained at saturation and is exposed to
 atmospheric pressure.  By definition, the pressure potential  of the soil  water in this
 soil sample would be zero.   Now consider the case of applying a slight suction or
 subatmospheric pressure across the soil sample.   No water will flow out until a certain
 critical suction (called the air-entry suction)  is reached.   At this point, the largest
 soil pores start to empty.   As the suction 1s further increased,  additional water flows
 as progressively smaller pores empty.  Finally,  at very high  suctions, only the
 micropores remain filled.  As the  soil becomes increasingly  dry,  a nearly exponential
 increase in suction is required to remove additional water.
     The functional relationship between the moisture content and matric or  suction
potential  is a characteristic of a particular soil.  This relationship  is called the
soil-moisture characteristic curve, the soil-moisture retention curve or simply the
characteristic curve.  The soil-moisture characteristic curves for three different
textured soils are shown  in Figure VII-11.  As previously stated,  the absolute value of
the mat«=*c or suction potential increases as the moisture content decreases.   In
addition  for a given matric potential, a coarse soil (e.g.,  sand) generally has less
water reaainiog in the soil  and has a steeper slope to the curve than a fine soil
(e.g., clay).  The slope of the soil-moisture characteristic  curve (i.e.,  the change of
water content per unit change-of matric potential) is called  the specific  water
capacity.
     In a coarse, saturated soil, the pores are predominately  large and drain quickly
under a slight suction.  A high suction is required to remove  the  last water from the
remaining, small pores.  In a clayey soil, the pore-size distribution is more uniform,
so that a more gradual decrease in  water content occurs with  an increase in suction.
In addition, at low suctions (for example, between 0 and 1000  cm H.O) the  amount of
water remaining in a soil depends primarily on soil structure  (i.e., pore-size
distribution and particle aggregation).  At higher suctions,  however, water retention
is due increasingly to adsorption and thus is influenced more  by the particle-size
distribution and specific surface of a soil.
     Unfortunately, the water content and matric  potential  arc not always  uniquely
related to each other because of hysteresis.   Hysteresis means that the characteristic
curves are different, depending on  whether the soil is being wetted or dried.  The
characteristic curve during  a drying cycle is called  the drying, desorption  or drainage
                                         -327-

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             NOTE:  1 ATM • 1033 CM
                    .1        a        3       .4
                  VOUJMCTfllC MOISTURE CONTEKT.6
FIGURE VII-11
CHARACTERISTIC  CURVES OF MOISTURE  CONTENT AS
A FUNCTION  OF MATRIC POTENTIAL  FOR THREE
DIFFERENT SOILS,   REFERENCE:  BRAESTER (1972)
                             -328-

-------
curve; during wetting  1t  is called the wetting,  sorptlon or imbition curve.   A soil
which  is partially wetted, then dried or vice versa  will  follow an  intermediate
characteristic curve called a scanning curve, which  lies  between  the envelope formed  by
the wetting and drying curves.
     Figure VII-12 shows an example of hysteresis  in a sandy soil.   The hysteresis
effect may be attributed to the inkbottle effect (geometric nonunifortuity of  individual
pores), the contact-angle or rain drop effect (differences  in the contact angle  for
advancing and receding fluids), entrapped air, and changes  in soil  structure  (e.g.,
swelling, shrinking or aging phenomena) caused during the wetting or  drying of  a  soil.

7.2.4.3  Unsaturated Hydraulic Conductivity
     In Section 7.2.3.1, the saturated hydraulic conductivity was stated to be affected
by an intrinsic property of the solid matrix of a soil and by fluid properties.   For
unsaturated porous media, the hydraulic conductivity is also a  function o* the energy
state of the soil water (i.e., the water content or pressure potential).
     The hydraulic conductivity of three different soils  is shown in  Figure VII-13 as  a
function of moisture content.  The hydraulic conductivity decreases  exponentially as
the moisture content decreases.  The large pores of  a porous media  are the most
conductive, their relative conductivity being proportional  to the square of the  pore
diameter- and their volumetric discharge rate being proportional to  the fourth  power of
the poca diameter.  As a soil dries out, the large pores empty  first, forcing  flow to
be conducted through a diminishing cross-sectional area.
     Si»ce UK moisture content is related to the matric or suction  potential,  through
the son-moisture characteristic curve (see Section 7.2.4.2), the hydraulic
conductivity can be expressed as a function of either the moisture  content, K(«), or of
the matric potential, K(u>).  Just as with moisture and pressure, hydraulic conductivity
is also not a single valued function.   Figure VII-12 showed hysteresis in the  hydraulic
conductivity of a sandy soil.  At a given suction, the hydraulic conductivity  is
generally lower in a wetting soil than in a drying soil.  This  is because the wetting
soil contains less water than the drying one (for a given suction).

7.2.5  Data Aquisition or Estimation
     In Sections 7.2.2 to 7.2.4, the physical and flow properties of porous media were
discussed in detail.   Tables were included to show what values are typically found in
aquifers of various geologic materials.   In this section, laboratory and field methods
are briefly discussed to show how the  properties of a particular aquifer or porous
medium can be estimated or measured.   Finally,  in Section 7.2.5.4 the effect of sample
size on measurement precision is discussed from a statistical  point  of view.
                                         -329-

-------
                   UNSATURATED
                 TENSION-SATURATED-
                            •SATURATED'
                                           SATURATED
                                           MOISTURE
                                           CONTENT
                                           •POROSITY
                                            OF SOIL.
                                           p.30%
                                         30
                                                      20
                                                      10
                             I
                             X
                             *
                             «
                                                           UJ

                                                           §
             -300
         -200
-100
                                                100
                                           SATURATED  _Q03
                                           HYDRAULIC
     -4OO
-300      -2OO     -TOO       0

    PRESSURE HEAD. * (cm of water)
             (b)
FIGURE VI1-12
    CHARACTERISTIC  CURVES OF (A) MOISTURE CONTENT
    AND (B) HYDRAULIC  CONDUCTIVITY  AS  A HYSTERETIC
    FUNCTION OF MATRIC POTENTIAL FOR A NATURALLY
    OCCURRING SANDY SOIL,  REFERENCE:   FREEZE AND
    CHERRY (1979)
                                -330-

-------
           KT'H
           KH-
I
I
X
           Kr»-
        2
        O
        o
        Q
                                   QLAT LOAM
                                VOLO CLAY
FIGURE VII-13
        VOLUMETRIC MOISTURE CONTENT. 6

        HYDRAULIC  CONDUCTIVITY AS A FUNCTION OF
        MOISTURE CONTENT FOR THREE DIFFERENT
        SOILS.  REFERENCE:  BRAESTER  (1972)
                            -331-

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7.2.5.1  Methods to Measure the Physical Properties  of  Porous  Media
      In Section 7.2.2, the physical properties of bulk  density,  particle-size
distribution, porosity and water content were discussed.  Methods  to measure  and
estimate these properties are reviewed below.
     Bulk density P  (g/c*3) of s niteris!  Is measured by taking an undisturbed sample
of the material in the field, using a sampler of known volume.  The sample is then
dried to a constant weight in an oven at 105-110°C.  The bulk density of a sample is
thus calculated as its ever, dry weight divided by the sample volume (see Equation
VI1-5).  Other methods of measuring bulk density Include 1n-situ measurement by gamma
radiation and microscopic methods using paraffin fixation.  These methods are discussed
in detail by Fox and Page-Hanify (iS59), Baver e_t in. (1S72) and Taylor and Ashcroft
(1972).
     The determination of particle-size distribution is carried out by mechanical or
sieve analysis for particles larger than approximately 0.0625 mm, and hydrometer or
sedimentation analysis for smaller particles.  In the mechanical analysis, the soil
sample is shaken on a sieve with square openings of specified size.  Successively
smaller and smaller screens are used.   For  particles less than 0.0625 mm, a
sedimentation analysis is done.  In this method, the size of a particle is defined as
the diameter of a sohere that settles  in water at the same velocity as the particle
(Morris aafl Johnson, 1967; Taylor and  Ashcroft, 1972).
     Soil torosTty can be measured directly in the laboratory by either an air-
pi en ometer* technique, a porosimeter, mercury displacement or a gas expansion method
((Clock et VL ,*t969; Bear, 1972; Baver et aj_., 1972).  Porosity, p {unitless), can also
be estimated based on typical values for a  given soil or rock type (see Table VII-4).
     Soil water content in the laboratory is usually measured by the gravimetric method
of determining the soil's moist and dry (oven dried at  105-110°C) weights and then
using Equation VII-7 to get the gravimetric water content $   (unitless).  The
volumetric water content 6 (unitless)  can be found from $  through Equation VI1-9.
Other methods of measuring water content are neutron scattering, gamma ray attenuation,
electromagnetic techniques, tensiometric techniques and hygrometric techniques.  A
summary of the  relative advantages and disadvantages of these methods, is given in
Table VI1-6.  For screening calculations, an estimated  average water content based on
grain-size is usually adequate.  If necessary, this estimate could be checked by
collecting a few samples and measuring the  water content gravimetrically.

7.2.5.2  Methods to Measure the Flow Properties of Saturated Porous Media
     The flow properties of saturated  porous media are  discussed in Section 7.2.3.
These properties include specific yield,  specific storage, storatlvlty, saturated
hydraulic conductivity and transmissivity.   The measurement  of those properties related
to the quantity of water that an aquifer can release or take up (I.e.,  specific yield,
                                         -332-

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                                             TABLE  VI1-6

                                SUMMARY  OF  METHODS  FOR  MEASURING
                                         SOIL  MOISTURE (0)
   Netted
             Advantages
                                                         Disadvantages
                                                                                      References
 gravimetric     easy to take saaplts                destructive sampling

                •011 accurate of available  methods   provides a point value
                                                              Black (1965)

                                                              Reynolds (197Q*.t>]

                                                              Taylor and Ashcroft  (1972)
 neutron
 >catt*r1ng
•easurei moisture 1n-sltu
regardless of Us physical  state

can determine ff versus  depth

nondestructive

can detect rapid changes  1n t
depth resolution
+0.5 ft below a depth
of 6 In. below land
surface

tip*nslve and requires
a radioactive source
Gardner and Klrkham (1952)

van lave) (1961. 1962)

Rawls and Asmussen (1973)

Vachaud et • !_. (1977)
 ga«M ray
 attenuation
can determine 0 versus  depth
In-sHu

easy to obtain temporal changes

very good depth resolution
(2-3 em)

nondestructive

automatic recording  e periods

                rapid response time (with tr«ns-
                ducers)

                adaptable to freezing and thawing
                conditions
                                    but an  Indirect Mature
                                    of 0

                                    Instruments  can be
                                    broken  during  Instal-
                                    lation

                                    soae electronic drift
                                    in pressure  transducers

                                    srtsltive to teaptr*.
                                    ture ch«nges
                         S.J. Richards (1965)

                         Rice (1969)

                         Taylor ind Ashcroft (1972)

                         Ullllaas (1978)
Reference:   after Schaugge el_ al^. (1980)  and  Wilson  (1981)
                                                -333-

-------
specific storage and storatlvlty) are discussed  1n Appendix  I.  Those  properties  that
describe the rate at which water can move  1n the aquifer  (I.e., hydraulic  conductivity
and transmissivity) are discussed below.

7.2.5.2.1  Laboratory Methods of Measuring Hydraulic Conductivity
     There are two major ways of assessing saturated hydraulic conductivity K in the
laboratory:  particle-size analysis and permeaweter tests.
     In particle-size analysis, soil samples are characterized by their particle-size
distribution, and then empirical formulae are used to estimate K.  For example,
consider the following empirical formula developed by Hazen for intrinsic  permeability
   (cm2)-.
                                      Ki • C d0                              (VI 1-19)
where C is a dimensionless coefficient and d10(mm) 1s the effective particle diameter
obtained from the particle-size gradation curve (see Section 7.2.2.2).  The intrinsic
permeability is related to hydraulic conductivity through the relation of Equation
VII-10.  Harleman et al. (1963) found good agreement with experimental values of K.
                  ~~~e.~~                                  2
using C « 6.54 x 10   (where d.g is 1n mm and K^ is in cm ) .  Krumbeln and Monk (1943)
found C to equal 6.17 x 10.  Hazin's approximation for intrinsic permeability in
Equation ¥11-19 was originally determined for uniformly graded sand, but it can give a
rough estimate for soils in the fine sand to gravel range (Freeze and Cherry, 1979).
     Hyc«ul1c conductivity can also be determined in the laboratory by a permeameter,
in which flow is maintained through a soil core that is held in a metal or plastic
cyl inder irhile-measurements of flow rate and head loss are made.  Either a constant
head or a variable head permeameter method can be used (Todd, 1980; Morris and Johnson,
1967).  The constant head permeameter is generally used for samples of medium to high
permeability and the variable head permeameter for samples of low permeability.
     However, permeability results from the laboratory may bear only limited relation
to values obtained by in-situ methods in the field.  Supposedly uniform deposits, for
example clays, more often than not contain thin seams or lenses of silt or fine sand.
These thin layers may occur as continuous laminations or be randomly dispersed and
discontinuous.  As a consequence of this stratification, hydraulic conductivity values
calculated in-situ in the field for clay or clay/silt deposits are generally several
orders of magnitude larger than those derived from laboratory tests (Milligan, 1976).
An order of magnitude difference generally occurs  for sand and silt deposits.   The
greater the heterogenity in a formation, the greater the discrepancy between laboratory
and field measured values of saturated hydraulic conductivity.   Hence,  the most
reliable methods are the in-situ or field methods.
                                        -334-

-------
 7.2.5.2.2   Field  Methods  of Measuring  Hydraulic Conductivity
      Field  or 1n-s1tu  determination  of saturated hydraulic conductivity can be made by
 a  wide variety of methods.   These methods  include the auger-hole method, piezometer
 method, pumping tests, tracer  tests, packer  tests and the point dilution method.
 Mllligan (1976) reviewed  these various 1n-s1tu  methods  as summarized In Table VII-7.
 Many  authors. Including Todd (1980)  and MilUgan (1976),  feel  that  the most reliable
 1n-s1tu method for  estimating  hydraulic conductivity  1s the  well  pumping test.  When
 such  a test 1s not  practical,  borehole slug  tests can be  used  to provide adequate
 estimates for screening calculations.   Values of transmissivity T are obtained  from
 pumping tests by  superimposing a  plot  of nonsteady-state  drawdown on a family of  type
 curves. Transmlssivity is  converted to hydraulic conductivity by dividing  T by tfie
 aquifer thickness.  Worked  out examples using the various pumping and slug  tests  are
 given  by Lohman (1972)  and  Fetter (1980).  A detailed discussion  on designing the
 geometry or layout  of  pumping  tests  can also be found in  Kruseman and deRidder  (1970)
 and Stallman  (1971).

 7.2.5.3 Methods  to Measure  the Flow Properties  of Unsaturated Porous Media
     The methods  of measuring  soil-water potential, such  as  the gravitational,  pressure
 and osmotic potentials  will  be discussed in  Section 7.2.5.3.1.  Measuring the
 characteristic curves  of soil-water retention and unsaturated  hydraulic conductivity
 will be-discussed in Section 7.2.5.3.2.

 7.2.5.3.1  Measuring Soil-Water Potential
     Gravitational potential is easy to measure  since only the  vertical  distance  z(cm)
 between  the reference  point  and the point under  consideration  has to  be measured.   If
 the point under consideration  is  above the reference  point,  the gravitational potential
 is positive and negative if  it lies below the reference point.
     Pressure potential is that potential  in the soil water due to  the  pressure of  the
 surrounding fluid acting on the soil water.  It  is the relative or  gauge pressure that
 is measured (i.e., relative to atmospheric pressure).  Hence,  the pressure  potential  is
 zero at a water surface (e.g., water table) exposed to atmospheric  pressure.  Pressure
 potential is positive at any saturated point below a water surface  and  is generally
measured with a piezometer.  A piezometer  consists of a small diameter  casing which has
 a short section of slotted pipe or well screen at the bottom and  is open to the
 atmosphere at the  top.  The pressure potential or hydraulic head in  a water  table
 aquifer or a confined aquifer  is calculated as the distance between the well  point and
the free water level in the piezometer.  Under unsaturated conditions,  the  pressure
 potential or matric potential  is negative  and is measured  with a tensiometer. A
 tensiometer generally consists of a  ceramic porous cup attached through an airtight,
water filled tube  to a  manometer.   The  vacuum created in the tube is a measure of  the
matric potential of the soil water surrounding the porous  cup and is measured by a

                                        -335-

-------
(I)  tort ho It Sluf
                                                      TABLE  VII-7

                           TECHNIQUES  FOR MEASURING SATURATED HYDRAULIC CONDUCTIVITY
«. Direct Ittllftt ol iM-tllv p«rM«»fl(ty 1* tolli
Ntttotf T*ch«lqu«
Shi DM unctiH holt In
uniitvrittd Mtcrttl
(A) Opt* A«9«rhol* »bo*t Mttr 1t«il
Tttt Pit Squtrt or rtctinfuUr
tut pit (*qul»«l««t to
circular holt *bo*t)
•c*«rkt on Method
«pallc«tlo« R«tl««
Difficult to MlftUU Poor
Mt*r lt»el» In cotrtt
Poor
t«f«r«iK«
USM HIM)
Ucroli (1NO)
  I) fjllldf/rltUj h«td,
     Ah In c*iln( •*«fnrt4
     »J tlM

 II) Conitint h«t4 m»\n-
     ttlnttf In cttlnt.
     ewtfloo M
     Q «t tlM
                                                         Soretalf «w»t W
                                                         Potflblt fines c)of b*tt
                                                                 (rltUf Ad)
                                                         M. loMtrri tictMlvtly
r»lr to
                 H««r»o(lt(/pUcH In
borlMf.  i**IH ctitiif •Itfc-
                 of borlMf.
                         VtrttoU ht«4t «Uo
                         POttUlt.
rotjlklt tip 'tmttr'
     I.  Ak ttt «p It
       «•
                                                         frcctwt
                 C1»to«
                 M«Ut« (1*74)
                 «»or«»«» (IM1)
                         tt •}.. (IW?)
(0)  Htll pw*l*« tttt
Dr**tevn l« ctntril veil
Muttered In obi*r*ttlon
••III on «t I**it  t«o
•0° r«4UI 4
-------
                                                  TABLE  VI1-7  (continued)
        Method
             b.  Direct testing of In-sllu permeability  In reck

                                         Remarks  on
         Technique                       Application
                                  Method
                                  Rating
                                                                                                                   Reference
(A)   lorehole  (simple
     tests)
  I)  Miter pin/loss In
      drilling

 II)  Staple variable/
      constant head tests
      In  open boreholes
 I) Gives possible
    Indication of
    previous tones.
   Must be supple-
   mented by detailed
    eiamtnatlo« of cor*.

II)  Similar  to borehole
    si49 tests
                                                                                                Poor
                                                                                                 Poor
                                                                                                              USIR  (IHB)
(8)  Borehole packer
(C)  Permeameters/
     Inserts
                             I) Single packer tests
                                (during advance of
                                boring)
                                  Eipandlng I eat her/rubber
                                  packers My provide
                                  Inadequate seal
                               I)  fair
Variable head  tests  In:

  I) Sealed Individual
     pleioaeters
     (local lone)

 II) Continuous  borehole
     pleiometers
                                                                                  USSR (1MB)
                                                                                  Sherard. et al. ()H3)
tests
II) Double packer tests
( In completed bore-
holes)
PneuMtlc packers superior
to other types, but
llslted to pressures
od)
(0)  Hell popping test
Normally carried  out  In
open central  veil .
Observation veils at  radii.
                                  Screen/perforated
                                  casing often not
                                  required
                                                                                            [icellent
                                                 lodd (1980)
                                                                              -337-

-------
                                                  TABLE  VII-7 (continued)
c. Indirect assessment of in-sltu premeabll Ity 1n tods and rocks
Method Technique
1) Partlcte-slte distribution
(A) Tests on samples II) Laboratory I
1) Multi-electrode
II ) Single point
(1) Geophysical Logging resistance potential
III) fluid conductivity.
temperature
Remarks on Method
Application Ratlig
1) 0.0 applicable to fair
uniform sands
II) Often Inapplicable Poor
to field conditions
Continuous profiling of fair
borings can be carried Future
out at Ion cost development
(Requires further good
correlation with In- situ
direct testing)
Reference
Colder, 6*11 (1HJ)
Cuyod (1*M)
(C)   Obtervatloni  of
     natural or Induced
     »eep*«e
HtttvreMnt and analytlt
of data  froa:

  I) Obtervatlon veils

 II) Ptetoaeteri

III) Oyei, tracers,
      radloictlre Isotopes
Provides Method of
assessing i*r»e«M)lttei.
In-sltv
ficellent          Malker  (IMS)
                  Tert««k< (IMO. IH«)
                  Colder, tan (1H3)
                  Sharp (l»70)
Deference:  Hllllgan  (I97»).
                                                           -338-

-------
 manometer, a vacuum gauge or a transducer.  A detailed description of the design and
 use of tensiometers can be found In Kirkham (1964) and S.J. Richards (1965).
 Additional discussion is included 1n Table VII-6.
      Osmotic potential is that potential of the soil water due to the physical
 separation of free water from soil  water solutes by a semlpermeable membrane.  Separate
 measurement of osmotic potential 1s not necessary for screening calculations.  It is
 difficult to measure but can be measured with a psychrometer (Richards and Ogata, 1961;
 Campbell et aj.,  1966; Taylor and Ashcroft, 1972) or a ceramic conductivity cell
 (Kemper, 1959).

 7.2.5.3.2  Measuring the Characteristic Curves of Soil-Water Retention and Hydraulic
            Conductivity"
      The soil-moisture characteristic  curve can be obtained 1n the laboratory by a
 combination of measurement techniques.   The hanging water  column or tension plate
 method is generally used to measure the wet range (0 to 100 cm H.O suction) of the
 characteristic curve and a pressure plate  or membrane apparatus 1s generally used for
 the  dry  range (100 to 5000 on H.O suction).   For suctions  greater than 5000 cm H_0, the
 soil-moisture characteristic  curve  can  be  determined by a  psychrometer  or vapor
 pressure technique using saturated  salt solutions (Taylor  and  Ashcroft,  1972).
      There are several  methods  of obtaining  the  characteristic  curve  of  unsaturated
 hydraulic  conductivity.   These  include  direct  laboratory methods  and  quasi-empirical
 metnods,  such as the  instantaneous  profile and  capillary model  techniques.   The usual
 laboratory method  of  measuring  unsaturated hydraulic  conductivity is  to  apply a
 constant  hydraulic  head  or  pressure difference  across  a  soil sample and  then measuring
 the  resulting steady  flux  of  water.  This  pressure  difference  can be  created by
 applying  a vacuum  in  a  tension  plate or pressure  chamber device or by creating  a  fixed
 evaporation  rate (Taylor  and  Ashcroft,  1972).  Measurements  are made  at  successive
 levels of  suction,  so  as  to obtain  the  characteristic  function  K(0) or K(i/>).
 Additional  laboratory methods are described  in detail  by L.A. Richards (1965),  Klute
 (1965) and  Bouwer  and Jackson (1974).
      Various  empirical equations  have been proposed to relate hydraulic  conductivity
 with  matric  potential or with percent saturation.  The most  commonly employed empirical
 equation  is  of the  following  form:

                                    K • a/(b « 0m)                             (VII-20)

 where a, b and m are empirical  constants,  0  is the absolute  value  of the matric or
 suction potential  and K  is the unsaturated conductivity.  The empirical constants a, b
 and m are  found experimentally for each soil by best fit.
     The instantaneous profile method can be applied to either  laboratory flow columns
or to field situations {Klute, 1972).  In this method, the  unsaturated hydraulic

                                         -339-

-------
 conductivity  1$  calculated  from th« measured moisture content profile of a draining
 soil  by  averaging  the  value of  the time  derivative of the moisture content between
 successive  depths.   However,  the Instantaneous  profile method can only determine
 hydraulic conductivity  1n the relatively wet range (suctions  less than 1000 cm H20).
 In  addition,  1t  1s  experimentally difficult  to  carry  out  this method and generally many
 duplicate measurements  are  necessary  to make the  conductivity-water  content
 relationship  reliable.
      Another  method  of  calculating the unsaturated hydraulic  conductivity  1s  to  combine
 the water retention  characteristic with the capillary  pore-size  distribution.   This
 approach, called the capillary  model, is based  on  the Kelvin  equation which relates  the
 surface  tension  and  soil water  energy to pore radius.   A  capillary model with a  closed
 form  solution for hydraulic conductivity 1s  given  by  van  Genuchten  (1980).  A review of
 previous theoretical capillary  models 1s given  by  Mualem  (1976) and  a comparison
 between  six recent models 1s  given by Simmons and  See  (1981).

7.2.5.4  Measurement Precision and Sample Size
     Many of  the methods given in Section 7.2.5 will give an accurate measurement  of  an
aquifer property but this information usually consists of one or two  values that are
taken at one  point in the aquifer.  Because of heterogeneity within an aquifer,  one  or
two measurements may not be representative.   In this section, a brief discussion is
given on how  to achieve a specified level of precision and confidence level when
estimating aquifer properties.
     The number of measurements  necessary to reasonably characterize the mean value of
an aquifer property or parameter can  be  determined after some initial data collection.
For the methods discussed below, several  assumptions must be made.  First, the sample
mean of an aquifer parameter is  assumed  to  be normally distributed.  This means that  if
random measurements are made of  an aquifer  parameter,  the deviation of the sample mean
from the "true population" mean  will  be  normally distributed.  Secondly, the variance
or  standard deviation of the aquifer  property will be assumed to be known or
measurable.    Based on these assumptions,  the number of measurements needed to obtain a
specified precision and confidence level  of an aquifer parameter can be prescribed.
However, the  number of measurements  and  tests which can be made is often dictated by
time and budget constraints.  Comparison  to the sample sizes given below indicates the
level  of confidence which should be placed  in the data obtained.  For screening
calculations,  the number of measurements  collected will most likely be small.
     The precision or margin of  error that  can be tolerated in measuring the mean value
of  a variable  X with n samples and with  confidence level y is:
                                  Px
                                         -340-

-------
where  P   is  the  precision of measuring variable X, tyn_j  is  the student's t-
distributlon percentile with confidence y and n-1 degrees  of  freedom, $x  is the
standard  deviation of the sample:
                                                                              (vn-22)
X,  is the  i-the observed value of variable X, n* is the number of data measurements or
observations used to find an estimate of the sample standard deviation, X Is the sample
mean of variable X:
                                     X •   >  Xn*                           (VII-23)
     The precision PX can also be written as a percent of the sample mean:

                                    Px » |X d/10o|                            (VII-24)

where d  is the allowed deviation of the sample mean from the true mean, expressed as a
percent of the true mean (I.e., d can range between 0 and 100).
     Upon rearranging Equation VII-21, 1t is possible to determine the number of
measurements necessary to obtain a specified precision and confidence level:

                                   n i (t  n_j /e)2                           {VII-25)

where the variable "e" is defined as:

                              e « PX/SX • |Xd/(100 Sx)                         (VI1-26)

The variable "e" is related to the inverse of the coefficient of variation  and is
dimensionless.
     Equation VII-25 has been solved for various confidence levels and tabulated in
Table VII-8 as a function of 'e*.  It  is quite clear from this table that  the sample
size "n* grows dramatically as the numerical value of precision decreases  and as the
desired  confidence level increases.
     If some value of "e" is desired other than that given in Table VII-8,  then  an
iterative solution is necessary to solve Equation VII-25.   This is because  the
student's t-distribution percentile tyn_j is  also a function of the number of
measurements minus one,  n-1.  As an initial  guess to the  size of n,  the  standard normal
deviate Zy can be used in place of the student's t-distribution 1n Equation VII-25.
                                        -341-

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                                    TABLE  VII-8

                  SAM>LE  SIZE FOR VARIOUS  CONFIDENCE LEVELS  USING
                            THE STUDENT'S  t-DISTRIBUTION
Confidence Level X(t)
e
.01
.05
.10
.15
.20
.25
.30
.40
.50
.60
.70
.80
.90
1.00
1.25
1.50
1.75
2
3
4
5
6
7
29
50
4549
182
46
21
12
8
6
4
3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
Values of Zy are given 1n
first guess to

determining

80
16424
657
164
74
42
28
20
12
8
6
5
4
4
3
3
3
2
2
2
2
2
2
2
2
Table VII-9
the sample
n
90
27055
1062
271
120
70
45
32
19
13
10
8
7
5
5
4
3
3
3
3
2
2
2
2
2
as a function
size (called
1 • (Zy/e)2
95
38414
1537
384
173
99
64
45
26
18
13
10
9
7
6
5
4
4
4
3
3
3
2
2
2
of confidence
n'), solve:

99
66349
2654
663
295
171
110
78
45
30
22
17
14
12
10
8
7
6
5
4
4
3
3
3
2
level. Thus, as a

(VII-26
With n' from Equation VII-26a, calculate  the student's  t-distr1but1on  ty  ,    and
substitute into Equation VII-25.   Values of ty B,_j  are given  1n  Table  VII-10 as  a
function of confidence  level  and  degrees of freedom  df, where  df  »  n'-l.  The correct
                                        -342-

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                             TABLE  VII-9

                STANDARD NORMAL  DISTRIBUTION FUNCTION
Confidence Level
y(«)
50
80
90
95
99
Deviate
Zy
0.67449
1.28155
1.64485
1.95996
2.57583
                                           2
                    where  Y -  100 f  e ~y /Z dy
      Reference:   after Abramowltz  and  Stegun (1964).
                      Table VII-10

  PERCENTAGE POINTS  OF  THE STUDENT'S t-DISTRIBUTION
                         t,. ^
Degrees pf
Freeoom
Of-
n-1
1
2
3
t
5
10
IS
20
25
10
40
60
120
Infinite
Confidence Level (1)
SO
1.000
0.816
0.76S
0.741
0.727
0.700
0.691
0.687
0.6*4
0.683
0.6S1
0.679
0.677
0.674
80
3.078
1.886
1.638
1.S33
1.476
1.J72
1.341
1.32S
1.316
1.310
1.303
1.296
1.28?
1.282
90
6.314
2.920
2.353
2.112
2.01S
1.812
1.7S3
1.725
1.708
1.697
1.684
1.671
1.658
1.645
95
12.706
4.303
3.182
2.776
2.571
2.228
2.131
2.086
2.060
2.042
2.021
2.000
1.980
1.960
99
63.657
9. 925
5.841
4.604
4.032
3.169
2.947
2.845
2.787
2.750
2.704
2.660
2.617
2.576
n • niMw of •etsurwents.
Reference: tfter AfirtwMitz tnd Sttgun
                             -343-

-------
sample  size  *r\" can be determined after one or  two  Iterations  (I.e.,  iterate until

      Hence,  in order to determine the correct sample  size,  the precision  and confidence
level have to be specified and an estimate made of  the standard deviation.   The  latter
can  be  made  from historical data or by making a rough estimate from previous  sampling
or from a pilot survey.  If no data are available,  then a two  step sampling  procedure
would be needed.  First, a sample of size n* from the initial  data set  (where n*  Is at
least 2 or more)  is made from which the standard deviation is estimated using Equation
VI1-22.   Then. Equation VI1-26 and Table VII-8 can be used to find a total sample size
"n".   This and other sampling strategies are  discussed in detail by Cochran (1977) and
Nelson and Ward (1981).
     An  example of  a two step sampling problem 1s  shown  below.   In this example,  the
proper sample size  for  measuring hydraulic conductivity  will be determined.   The
aquifer  consists  of alluvial  sand.   The drawdown versus  elapsed time method of Theis is
used  to  evaluate  the horizontal  hydraulic  conductivity at various  observation wells.
                                      EXAMPLE  VII-1
      Initially,  six  texts  were  conducted.  The  results are  shown  below:
            Field Data                                  Data Summary
            Saturated,  Horizontal                       existing data  size:   n*  •  6
            Hydraulic Conductivity                      confidence level:      y«  95i
                  (cm/sec)                              allowed deviation:     d  *  10*

            0.13    0.12     0.18
            0.13    0.13     0.15

   Based on  these six initial measurements, a 95 percent confidence level, and a 10
   percent deviation  or precision in estimating  the  true mean, the following
   parameters  were calculated.   The sample mean  X was calculated using  Equation  VII-
   23  to give  X » 0.14  cm/sec, the sample standard deivation  S  from Equation  VII-22
   gives Sx  •  0.022 cm/sec,  precision P  from Equation VII-24 gives P   « 0.014 cm/sec
   and variable e was calculated from Equation VII-26 to give e «  0.64.  Finally,  by
   using either Equation VII-25  or Table VII-8,  it was determined  that  a total of  12  '
   tests would have to  be done (i.e., sample size n  • 12).   Since  six  tests had
   already been done, six additional drawdown tests  would have to  be performed to
   obtain the  desired degree of  precision and confidence level.
                                         -344-

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I            Note  that  this  precision  and  confidence refer to the uncertainty or
I    variability of  a single site  1f all  12  drawdown tests are done using the same
j    observation well.   Using 12 different observation  wells  will show the variability
•    of  the  aquifer  over the region  measured.

!	END  OF EXAMPLE  VII-1	
      Before  leaving this  section on  sampling  size,  one additional  consideration  needs
to  be considered: cost.   Virtually all of the field tests used  to  measure  the  flow
properties of aquifers, such as transm1ss1v1ty or hydraulic  conductivity are costly  to
perform.  Typically, most ground water studies use  only a few pumping  tests per  site or
per study area.  It 1s clear from Table VII-8 that  two tests can only  give results with
a low confidence level and/or poor precision  and one test provides no  Information about
precision.   But a few tests can give an 'order of magnitude" value to  an aquifer
characteristic, such as hydraulic conductivity.  An order of magnitude value is
adequate for most screening calculations.  For detailed investigations more data are
needed to provide a greater level of confidence and precision.

7.3   GROUND WATER FLOW REGIME
7.3.1  Approach To Analysis of Ground Water Contamination Sites
      The recommended approach to analysis of  ground water contamination problems is  to
first  use existing data and screening methods  such as presented in this chapter to gain
a basic understanding of the site hydrogeologlc characteristics and the relative hazard
associated with the particular problem.  The  steps  Involved are to first characterize
the waste sources in terms of. type of waste,  quantities disposed, disposal  method, and
dimensions of the disposal area.  Next, hydrogeologic data for water levels, hydraulic
conductivity, and porosity or moisture content  are obtained.  The water level data are
plotted as ground water elevation contour maps  from which flow directions are then
determined.   The remaining hydrogeologlc data  are used to estimate vertical and
horizontal seepage velocities.   Next, these velocities are used to estimate travel
times  for conservative solutes  to nearby wells  or surface water bodies.  These
estimates are compared to observed solute concentration data which can also be plotted
as contour maps.  The effects of additional  processes  including dispersion  and chemical
attenuation are then considered using the methods discussed in Section 7.5.  Finally,
estimates of uncertainty associated with the predictions  should be made.   At this point
information  is available to determine whether additional  field sampling or  detailed
investigations are warranted.
     The procedures for conducting the hydrogeologic portion of the analyses are
discussed in detail in the following sections.  Section 7.3.2 discusses measurement of
water  levels and determination  of flow directions.   Section 7.3.3 presents  methods for
calculating  seepage velocities  and travel  times.

                                        -345-

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 7.3.2  Hater Levels  and Flow Directions
 7.3.2.1  Introduction
      Water  level  data  can  be found  In  ground  water Investigation reports or well  logs,
 by  talking  to the owners of  nearby  wells,  or  by making water  level Measurements at
 existing  wells.   Also,  water surface elevations of nearby  streams, ponds,  lakes,
 springs,  marshes,  gravel pits, etc. can be used to estimate water level  elevations
 since these are areas where  the ground water  table Intersects the land surface.   (Care
 should be taken,  however,  to be sure that  these water bodies are not perched.)
      In the field, the  presence or  absence of vegetation common  to wet soils and  salt
 tolerant  plants (e.g.,  willow, cottonwood, mesqulte, saltgrass,  greasewood) may be
 Indicative  of discharge areas and hence can be used to locate areas where  the ground
 water table is near  the surface.  In arid  regions,  a thicker than normal cover of
 vegetation  or salt outcrop (e.g., saline soils, playas, or salt precipitates) may
 indicate  a  discharge area.   Field mapping  of  such  occurrences can be valuable in
 obtaining an  initial idea  of  the depth to water.   However, relatively impermeable
 layers  of even small area! extent may result  1n perched waters, which in turn yield
 wetlands  or  ponds.  The unforeseen presence of a perched water table may lead to
 misinterpretations of surface observations.
      The  following general observations for unconflned water table aquifers in humid
 areas  can be made:
        •    Ground water  discharge zones  are in topographic low spots
        t    Ground water  generally flows  away from topographic high spots and toward
             topographic low  spots
        •    The water table may have the  same general shape as the land surface.
 From  the  above, it might seem reasonable that the  hydraulic gradient (i.e., the change
 in ground water surface elevation per unit distance) of water table aquifers should
 vary  in a direct relationship with the slope of the land (I.e., the hydraulic gradient
 is steepest where the land slope is steepest).  However, the presence of formations
with  low hydraulic conductivity, subsurface geologic inhomogenelties and man-made
 influences  (e.g.,  pumping wells, landfills) can have a profound effect on both the
direction ano magnitude of ground water flow.   Care should be taken in assuming that
the direction of the local  ground water flow is the same as that of either the surface
topography or regional  ground water flow directions.  For example, the presence of an
unknown buried stream channel can cause the local  flow to be in the opposite direction
of the  regional flow.  Obtaining reliable water level  data from observation wells  is
 indispensable, even in the screening stage of a ground water study.

 7.3.2.2  Water Level  Measurement
      One of the most important measurements 1n ground  water Investigations  1$  the
determination of water level  elevation.   Mean  sea  level  1s  generally  taken  as  the

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 reference or datum from which water level elevations are measured.  Water level
 elevation is best measured as the height of water in a piezometer or observation well.
 Such a well has a short, screened interval in the aquifer (confined or unconfined) and
 is open to the atmosphere at the top.   Water level elevation represents the average
 hydraulic head H at the location of the well screen.
      Most measurement techniques involve measuring depth to water (i.e.,  depth to water
 from land surface or from the top of the well casing).   Depth to water is converted to
 water elevation by subtracting depth to water from the  elevation of the ground surface.
 Serious errors  in data  interpretation  can occur  if the  reference point  from  which  the
 depth to water  was measured  (I.e.,  land  surface  or well  casing  top)  was not  noted.
      To convert depth to water  table to  water level  elevations,  the  land  surface
 elevation  (or well  casing  elevation) needs  to be known.   The  required  accuracy in
 measuring  or knowing  surface  elevation  depends in  part  on the ultimate  use of  the  data
 and  on  the scale of the  problem.   Individually surveying  each well  is  the best method.
 However,  for screening purposes,  an estimate  based on topographic maps  and the height
 of the  casing above the  land  surface may  be  adequate in  some cases.
      Water level  elevations are  usually  measured by means of a  chalked  steel tape  or  an
 electric water-level probe, but  air lines, pressure transducers  and  sound reflection
 methods may also be used.
      Great care should be  taken  when measuring water level elevations,  particularly
 when  the hydraulic  gradient or  aquifer slope  is  small.   In general though, an  accuracy
 of +3 centimeters  in measuring water level elevation should be sufficient for  most
 ground  water applications  and is easily obtained.

 7.3.2.3  Sources  of Error  in Water Level Data
      There are  many possible sources of error and misinterpretation when taking water
 level data.  Some of the most serious errors are those caused by vertical flow  in the
 aquifer, water  level fluctuation, unknown screen locations and unknown  or excessively
 long  screened intervals.  These sources are described in more detail in this section.

 7.3.2.3.1  Vertical Flow
     Under most conditions, flow in a homogeneous formation  is predominately
 horizontal.  Under this  assumption, the equipotential (equal energy) lines are
 vertical.  Hence, water  will  rise to the same level in piezometers that are located
 side-by-side but which penetrate the aquifer to different depths.  However,  if flow is
 not horizontal, such as  near a discharge or recharge area, the water will  rise to
different  levels.  This  is schematically shown in Figure VII-14.  The observed water
 level in a piezometer will decrease as  the well tip of the piezometer is located at
 lower and lower depths in a recharge area (compare wells "a" and "b" in Figure VII-14).
The water level  will increase in a discharge area (compare wells "d" and "e"  in
Figure VII-14).   This same phenomenon  can occur near large pumping wells.   Hence,  a

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            RECHARGE AREA
                                                                   SCREENED
                                                                   INTERVAL
         FIGURE Vll-m
CROSS-SECTIONAL DIAGRAM SHOWING THE WATER
LEVEL AS MEASURED BY  PIEZOMETERS  LOCATED
AT VARIOUS DEPTHS,  THE WATER LEVEL IN
PIEZOMETER c  is THE SAME AS WELL  B SINCE
IT LIES ALONG THE SAME EQUIPOTENTIAL LINE
piezometer will only indicate the approximate water table in an  unconflned aquifer  with
vertical flow.  What the  piezometer does indicate (assuming a short screen length is
used)  1s the exact hydraulic or piezometric  head at the point of the well screen.  In
fact,  the vertical flow component of ground  water velocity can be determined by placing
several piezometers at various depths so that the vertical hydraulic gradient can be
measured.  This vertical  gradient is then multiplied by the vertical hydraulic
conductivity to obtain the  vertical flow velocity (see Section 7.3.3.1).
                                       -348-

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      Fortunately,  the  vertical  hydraulic  gradient  1n most aquifers is small enough that
 the component  of vertical  flow  can  be  ignored.   Care must be taken, however, to
 properly  Interpret water  level  data near  recharge/discharge  areas  of the aquifer and
 near pumping wells.  During  pumping tests,  only  short well screens should be used in
 observation wells  to avoid integrating or averaging  ground water heads  in the  vertical
 direction.

 7.3.2.3.2 Water Level  Fluctuations
      Water levels  in wells are  usually not  static  but are constantly  fluctuating.
 The water levels 1n wells that  monitor confined  aquifers  generally fluctuate more  than
 those in  unconfined or  water table  aquifers.  Short  term  fluctuations in  confined
 aquifers  can be  caused  by many  factors, including  earthquakes, ocean  tides,  changes  in
 atmospheric or barometric pressure,  changes  1n surface-water  levels and  in  surface
 loadings  (e.g.,  a  passing train), recharge  from  precipitation and  from drawdown  of
 nearby pumping wells.   Water levels  1n unconfined  or water table aquifers are  affected
 by  recharge from precipitation  (including air entrapment  In  the unsaturated  zone),
 evapotranspiratlon, nearby pumping  wells  and atmospheric  pressure  changes.
      These fluctuations can  be  observed by maintaining a  continuous record  of  measured
 water levels over  a period of time  and then plotting water level as a function of  time.
 The best  way to  reduce  the effect of such fluctuation  is  to take water level
 measurements from  all observation wells within a 1 to 2 day period.  Generally,  it  is
 the relative spatial difference in  the water level that is the most important
 information desired (see Section 7.3.3),  rather than  the absolute  water level  value.

 7.3.2.3.3  Screen  Length and Location
      Additional  interpretation  errors may occur when either screen length or screen
 location of the  observation wells are unknown.    In addition,  excessively  long  screens
 (such as used in large production wells and open boreholes) can give conflicting
 information on water level.  Long screens allow flow between  different formations
within an aquifer  and may even  penetrate more than one aquifer.  Invalid  conclusions
 can  also be reached if wells tapping different aquifers are compared.  It is important
 that  accurate information be obtained as  to screen length and depth.  If  such
 information is not obtainable,  the water  level  data  should be interpreted most
cautiously.

7.3.2.4  Determination of Flow Directions
      After water level   information has  been  collected, the data should be plotted as
water level  elevation contours and used to determine the  ground water flow directions.
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 7.3.2.4.1  Mater Level Elevation Contours
      A contour map of the water level elevations 1s prepared fro* wells screened  In the
 same aquifer.  Water level elevation data fro* the observation wells nust all be
 measured during the same time period (best If measured within a few days) and In the
 same portion or zone of the aquifer (e.g., upper, middle, lower).  A contour map of the
 water levels can be constructed using the following five steps:   1}  plot the spatial
 location of each well on a map and label  each point;  2) write the water level
 elevation value on the nap for every well measured during the same specified time
 period and in the same aquifer;  3)  decide which contour values  are  desired (e.g.,
 every meter or decimeter change 1n elevation):   4)  locate points on  the map
 corresponding to the contour values  chosen 1n step 3 by interpolating between all  of
 the measured values;  5)  draw a line connecting  all  points of equal  value.   These  lines
 are drawn so that no two lines ever  cross.  This process 1$ repeated for each time
 period and for each  aquifer.  An example of these steps  1s shown  1n Figure VII-15 for a
 water table aquifer  underlying a series of waste ponds.
      There are,  of course,  more sophisticated methods of constructing contour plots,
 such as  contained in several  computer  programs.   SURFACE II  is a recent FORTRAN
 computer  program developed  by the  Kansas  Geological  Survey (Olea,  1975; Sampson, 1978).
 This program uses  regionalized variable theory or Krlglng to  perform automatic
 contouring of  point  observations.  This and many  other  programs  (Davis, 1973)  are
 available but  usually  hand  contouring  is more than adequate for  screening purposes.

 7.3.2.4.2  Mater  Flow  Directions
      It was  stated in  Section  7.2.4.1  that water  flows  in  the direction of decreasing
 potential  energy.  In  the case  of  saturated ground water,  the potential  energy is  equal
 to  the water  level elevation,  as measured  by  piezometers  or wells  screened  in  either
 confined  or  unconfined aquifers.
      It can  be shown that ground water in  an  isotropic aquifer not only  moves  in the
direction  of decreasing water  level elevation but also perpendicular to  the
 equipotential  lines.   Isotropy means that  the hydraulic  properties (e.g., hydraulic
 conductivity) of  the aquifer are equal in all directions.  Hence, 1f a  contour plot of
 the  water  level elevation is available and if the horizontal and vertical scales that
are  used  in constructing the contour plot  are the same, then the ground water flow
direction  can easily be found as follows:   1) pick any point along a water level
elevation  contour or equipotential line;  2) draw a line  (called a flow  line) from this
 initial contour line to the next smaller valued contour line, going Initially in a
direction perpendicular to the first contour line;  3) extend the flow line  until 1t
reaches the next contour, making sure that U crosses this new contour line
perpendicularly;   4) extend this flow line to as many contour lines  as desired,  always
crossing the contour  lines at right angles.  Any  number of flow lines can be
                                         -350-

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                                                                   *
                                                                   N
                                                 ••u*
                                                             SCALE
                                                           0  250 300
                                                              FEET
         FIGURE  VII-15
AN  EXAMPLE  OF A  CONTOUR PLOT  OF WATER LEVEL
DATA  WITH  INFERRED FLOW DIRECTIONS,
REFERENCE:   TETRA TECH,  1985
constructed  in this manner.  The direction  of  ground water flow is along these  flow
lines.   An example of constructing flow directions  is shown in Figure VII-15,  using  the
water level  data shown in the figure.   An extensive discussion of graphical  methods  for
constructing flow lines and flow nets  can be found  in OeWiest (1965).
     As shown in Figure VII-16, the graphical  construction of flow lines are made  by
crossing the equipotential lines at right angles.  This is always true for  isotropic,
homogeneous  aquifers when the plotted  contours are constructed using equal  horizontal
and vertical scales.  However, additional complications or modifications arise  if  these
                                        -351-

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conditions are not met.  Van Everdlngen (1963)  discusses  the  problem of drawing flow
lines when the horizontal and vertical scales are not  equal as  1n cross-section
diagrams.  Uakopoulos  (1965) provides theoretical principles for constructing flow
lines in homogeneous, anlsotroplc media (when the hydraulic conductivity varies
according to the  direction of flow).  Fetter (1981) gives a simple graphical method
(using a permeability tensor ellipse)  to account  for an 1sotropy.  Comparison of flow
directions in an  isotropic aquifer and anlsotroplc aquifer 1s shown in Figure VI1-16.
     The effects  of anlsotropy and heterogeneity  are Important but they are difficult
to take into account with data generally available during the screening phase of  s
project.  The construction of equlpotential  and flow lines should be done  first
assuming a homogeneous and isotropic aquifer.  The flow directions could then be
adjusted if additional detailed data show this to be necessary.
                                                    FLOW LINES
                                   FLOW LINES FOR
                                   ANISOTROPIC AQUIFERS (K »K )
                                                         *   y
                                   FLOW LINES FOR
                                   ISOTROPIC AQUIFERS (K »K )
                                                       *  y
       FIGURE VI1-16
SCHEMATIC  SHOWING  THE  CONSTRUCTION  OF FLOW
DIRECTION  LINES  FROM EQUIPOTENTIAL  LINES
FOR  ISOTROPIC AQUIFERS  AND ANISOTROPIC AQUIFERS
                                       -352-

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  7.3.3  Flow Velocities  ant^ Travel  Times
  7.3.3.1   Ground  Water Flow  Velocities
       The  direction of ground water flow  is  discussed  in  Section  7.3.2.4.2  in  terms of
  water level  elevations  and  hydraulic gradient.  To  determine  the magnitude  of ground
  water flow,  Oarcy's  law is  used.   Section 7.3.3.1.1 presents  Darcy's  law for  both
  saturated and unsaturated flow situations.  The various  forms of representing  flow
  velocity  are discussed  in Section  7.3.3.1.2 and the applicability or  range  of  validity
  of Darcy's  law 1s reviewed  in Section 7.3.3.1.3.  Finally, methods of measuring or
  estimating ground water flow velocities are discussed in Section 7.3.3.1.4.

  7.3.3.1.1  Darcy's Law
       In 1856, Henri  Darcy discovered by experiment that the flow rate through a
  saturated porous  medium was proportional  to the change in head across the medium and
  inversely proportional  to the length of the flow path.  Darcy's  law can be expressed
 as:
                                  Q - -KA AH/AL - -KAI                          (VI 1-27)


 where K is  a proportionality constant (the hydraulic conductivity,  cm/sec), A is the
 flow cross-sectional  area (cm2)  of the  soil  (measured  at a right angle to the direction
 of  flow), AH 1s  the change in hydraulic head (cm H20)  across  the soil, AL is the
 distance or  length  (on)  across the soil  (measured parallel  to the flow),  I  1s the
 hydraulic gradient  (cm/an)  and Q Is  the volumetric discharge  rate (cm3/sec).  The
 negative sign  in Equation  VII-27 indicates that  water  flows in  the  direction of
 decreasing  head  or potential  energy.
      Schematics  of the experimental  set-ups  to demonstrate Darcy's  law can  be  seen  in
 Figure  VII-17.   In Figure Vll-17a. flow occurs along an  inclined, saturated   soil
 column.  The flow  is  from left to right, going from the  upper to the  lower  reservoir of
 water.   The  change  in  hydraulic  head AH across the soil  column  is simply:

                                   AH * "out ' Hin                             (VII-28)

 where H.fl is the hydraulic  head  (cm) at the  inlet  and  H    is the hydraulic  head  (cm)
 at  the  outlet.
      Darcy's law is also valid for unsaturated flow, the only difference being that the
 hydraulic conductivity is now a function of pressure potential H  or ^

                                  Q • -*((£) A AH/AL                           (VI 1-29)

An example of a demonstration of  Darcy's law  for unsaturated  flow can  be  seen in
Figure YIM7b.  This  example is  the  same as  shown in Figure VII-17* but  now the  soil
                                        -353-

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           a.  Flow in an inclined  saturated column of soil.
      M»M£TTUK
                                                 KlATt
                                                      T
                                          Li.. i« ^ O     '



                                     CW>TLIM      J——L.     1    	
     b.   Flow in an inclined,  unsaturated column of soil.   Note
         that the Mariotte reservoir maintains a constant  reference
         level at atmospheric  pressure, even when the  inlet water
         column is under negative  pressure.
FIGURE VII-17   SCHEMATIC  DIAGRAMS SHOWING PERMEAMETERS TO
                  DEMONSTRATE DARCY'S LAW
                              -354-

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is subject  to a negative pressure (or a positive suction) potential at both ends  of
the soil sample by hanging water columns.  The hanging water columns will exert  a
negative pressure potential as long as points "a" and "b" are located below the  inlet
and outlet, respectively.  In general, both the pressure potential and hydraulic
conductivity will vary along the soil column.  As the absolute value of the pressure
potential increases, the hydraulic conductivity will decrease.  However, a constant
hydraulic conductivity can be made by making the pressure potential H .   equal to
Hpouf
     The total head or potential at any given point 1s due to the sum of the
gravitational and pressure potentials:
                                         ". -
                                                                              (VIJ-30)
The minus sign was put in front of the absolute value of the pressure potential to
avoid any confusion as to the contribution of the pressure potential to the total head
in unsaturated soil.  Upon substitution of Equation VI1-30 into Equation VI1-28 and
VII-29, Darcy's law for the unsaturated flow case illustrated in Figure VII-17b can be
described by:
                         -K*A(H
                               gout
                                       H
                                        pout
- H
   gin
where all of the H terms are expressed in units of length (cm).  Since unsaturated
hydraulic conductivity is a nonlinear function of pressure potential (see
Section 7.2.4.3), the K* (cm/sec) used in Equation VII-31 represents the hydraulic
conductivity for the average matric or pressure potential ^   (cm)  In the soil column:
                                                           o VQ

                                *avg - '"pin * Hpout>/2                       

Hence, the hydraulic conductivity used in Equation VII-31 becomes:

                                                                              (VII-33)
7.3.3.1.2  Darcy and  Seepage Velocities:
     If the volumetric  discharge rate 0  (cm3/sec)  from Darcy's  law 1s  divided by the
                                                                               d
cross-sectional  area A (cm2),  then the ratio Q/A has the  units of a velocity,  v
(cm/sec).   This  "velocity"  is  called  the  Darcy  velocity  or  specific  discharge:
                               v
                               d
                                    Q/A  .  -KAH/AL  •  -KI                        (vn-34)
                                        -355-

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 where I (cm/cm)  1s defined as the hydraulic gradient.  However, the Oarcy velocity is
 not the 'true'  velocity at which the water moves through the pores of a medium.  It is
 both impractical  and unnecessary to determine the actual microscopic velocities through
 the pore spaces.   A more useful  macroscopic quantity is called the seepage velocity.
 Since solutes do  not migrate across the  entire pore space,  we need only consider the
 water filled portion of it.  To  take this  into account, the Darcy  velocity vd is
 divided by the  volumetric  moisture content to  yield the seepage velocity, v$:

                                       v$ • v^/0                               (VI1-35)

      Since e is less than  one, the seepage velocity 1s  greater than  the Darcy velocity
 (usually by  a factor of 2  or more).  The seepage velocity is also  called the  average
 interstitial or pore-water velocity.
      For saturated flow,  like in Figure VII-17a,  the volumetric water  content equals
 the porosity p  (unities*  ratio).   Upon substitution of  p into Equation V1I-35 and  v
 into Equation VI1-34,  the  seepage velocity for saturated conditions  becomes:

                                       -K AH
                                 vs "  ~iiT " "K1/p                          (VII-36)

where I  (cm/cm)  is the hydraulic  gradient.   For unsaturated  flow,  the seepage velocity
 is:

                                   vs * 7 f ' -«'«                         (VII-37)

 where the  hydraulic conductivity  K  is now a function of the  moisture content  6.
      In  general, the Darcy velocity vrf is used in the computation  of ground water flow
problems and the seepage velocity, v , is used in the computation  of contaminant or
solute transport problems.  Great care must be used when obtaining  velocity data from
published  reports  since many authors do not state which velocity formulation they are
using.

7.3.3.1.3  Applicability of Darcy's Law
     Darcy's law is only valid for those  conditions in which the flux Q is a linear
function of the  hydraulic gradient I (i.e., AH/AL).  This generally corresponds to  the
condition of laminar flow and when resistance to flow is dominated  by viscosity.
However, at very high velocities, the flow  becomes turbulent and inertial forces become
dominant.  The Reynolds number Rg is a dimensionless number  that expresses the ratio of
the  inertial  to  the viscous forces during  flow:

                                     % "  Vwvd/M                            (VI1-38)

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where P   1s the density of water  (g/on3),  jiis the viscosity  (cm /sec) and d$  is  some
characteristic length  (cm) representing the intergranular flow channels.  Bear  (1972)
suggests  using d5Q  (I.e., the average or mean grain size diameter) for d$ but sometimes
d1Q  1s used (See Section 7.2.2.2).  Values for p^ and ^ are given 1n Appendix I.
     Darcy's law has been shown experimentally to be valid for those conditions for
which the Reynolds  number is less than 10 when using d5Q (the average grain-size
diameter)  for d .   This covers virtually all natural ground water situations, except
perhaps for flow through extremely coarse materials, and in areas of steep hydraulic
gradients  (gradients greater than 1, such as close to pumping wells).  On the other
extreme,  Darcy's law may also be  invalid for extremely low hydraulic gradients and flow
through dense clay.

7.3.3.1.4  Methods  to Estimate Flow Velocities
     There are several ways of estimating the ground water flow velocity.  A review of
these methods is shown in Table VII-11.  The Oarcy-based method, as discussed in
Sections  7.3.3.1.1  and 7.3.3.1.2, is probably the least expensive and quickest method
of estimating flow  velocities.  From Equation VII-34, the horizontal Darcy velocity v.
(cm/sec)  can be calculated between any two points spaced a distance Ax (cm)  apart as:

                                vdh' -KhAH/A* • -Vh                       (VII'39)

where L  (cm/cm)  is the horizontal hydraulic gradient, AH is the hydraulic head change
and  K.  (cm/sec) is  the horizontal hydraulic conductivity.  The vertical Darcy velocity
v    (cm/sec) can be calculated between any two depths spaced a distance Az (cm)  apart
as:

                                vdy - -K  AH/Az -  -Kyly                        (VI1-40)

where Iy  (cm/cm)  is the vertical  hydraulic gradient,  K  (on/sec)  is  the vertical
hydraulic conductivity and AH (cm) is the change  in  hydraulic  head  across the  points  of
measurement.  Mote that in  the case of saturated  flow (confined  or  unconfined),  AH is
simply the difference in water level  elevations between the  measurement points.
     The major disadvantage of using  the  Darcian  method for  calculating flow  velocities
is that the hydraulic conductivity needs  to be known.   Methods of measuring  hydraulic
conductivity are  given in  Section 7.2.5.2.2 but  large uncertainties  are usually
associated with these methods.   Despite these  uncertainties, Darcy's  method  is  best
suited for the screening phase of a ground water  study.
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                                          TABLE VI1-11

                        METHODS  FOR  MEASURING  GROUND WATER FLOW VELOCITY
    Technique
     Advantages
    Disadvantages
       References
Darcy-based
•ethod
Inexpensive

simple to calculate

can measure horizontal
or vertical velocity
need to Measure hy-
drautlc conductivity
separately
Freeze and Cherry (1979)
Fetter (1980)
Direct tracer
Method
stuple In principle

only travel tine
needs to be
•easured
expensive

Must adjust for dis-
persion

Must know direction of
flow and approximate
velocity to design well
saMplIng prograa

long tlMes are typically
required to obtain data
Knutson (1966)
Brown et al. (1972)
Gaspar aniTOncescu (1972)
Point dilution
Method
a down-hole Method

short tlMes needed

single observation
can only Measure hori-
zontal velocity
Htlevy et al. (1967)
Orost et aIT (1968)
GrlMlfct al. (1977)
Klotz eF«T7 (1978)
                  single
                  well Is
        needed
Flow Meter
a down-hole Method
for directly Measuring
horizontal velocity

quick, real-tlMe
Method
under development

significant Interference
froM well screens and
gravel packs does occur
Kerfoot, 1982
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 7.3.3.2  Ground Water Travel Times
      The distance traveled by an object moving at a  constant  velocity is:

                                  Al « (At) (Velocity)                          (VII-41)

 where Al  is  the distance  traveled and At  is  the  time of  travel.   If  the  transport  of a
 non-reactive and non-dispersive solute or  contaminant  is considered,  the "velocity"  in
 the above  equation  becomes equal to the seepage  velocity v$  (which was discussed  in
 Section 7.3.3.1.2).  The  seepage velocity  is used because  solutes only travel  through
 the water  filled portion  of  soil pores.  The travel  time At  can  now  be solved  from
 Equation VII-41 to  give:

                                      At -  Al/vs                               (VII-42)

 If  the seepage velocity is calculated from Darcy's law,  then  Equation VII-36 can  be
 substituted  into Equation VII-42 to yield the travel time  for  saturated  flow
 conditions:
                                      At - =•                               (VII-43)
where At (sec) is the travel time, Al (cm) is the travel distance, p (unitless ratio)
is the porosity, K (cm/ sec) is the hydraulic conductivity and I (cm/ cm) is the
hydraulic gradient.   Estimated values of porosity are given in Table VII-4 for a
variety of geologic  materials.  Note that the porosity used in Equation VII-43 is to be
expressed as a ratio or decimal fraction and not as a percent.  For unsaturated flow,
the volumetric moisture content 6 (unitless ratio) is substituted in place of porosity
"p" in Equation VII-43.
     It should be remembered that travel times computed from Equations VII-42 and
VII-43 are for non-reactive and non-dispersive, conservative solutes moving at a
constant velocity.  Retardation by sorption and attenuation by other solute-soil
interactions may substantially decrease the velocity  of solute movement and increase
the travel  time.  Conversely,  dispersive processes can either substantially increase or
decrease the velocity that a portion of the solute molecules move and hence change the
travel time.  The processes of sorption and dispersion will be discussed in greater
detail in Section 7.4.
     In many situations,  the flow velocity may vary in both direction and  magnitude Tn
an aquifer.   Variable velocity and/or variable soil properties can easily  be
incorporated into the calculation of solute travel time by  assuming that solute flow is
a constant  over a series  of finite subregions.  If these properties vary by less than
20 percent,  discretization is  not necessary for screening calculations.  Figure VII-18
                                         -359-

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                                              ASH/FCO SLUDGE
                                                       SATURATED ZONE  '
                                    (a)
   B
                                                            FLOW LINE
FIGURE VI1-18
                                   (b)
SCHEMATIC SHOWING HOW TRAVEL  TIME  CAN B£  CALCULATED
FOR SOLUTE TRANSPORT WHEN THE  FLOW VELOCITY VARIES:
A) ORIGINAL PROBLEM, B) DISCRETIZED REPRESENTATION
OF THE FLOW LINE.  REFERENCE:  TETRA TECH (1984)
                                 -360-

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shows such a discretization process.  Equation VII-43 1$ applied  over  each  "constant"
subreglon and then all travel times are summed, such that the total travel  time  Tt  is:


                               Tt • Z At, - -Z  K                         (VII-44)
                                t   1-1   1    1-lL *IJ1

where the subscript "1" refers to the 1-th subregion and n is the total number of
subregions, p (unltless ratio) 1s the porosity, Al (cm)  1s the travel  distance, K
(cm/sec) is the hydraulic conductivity and I (cm/cm) 1s  the hydraulic gradient.  For
unsaturated flow, the volumetric moisture content & (unltless ratio) is substituted for
porosity p.  The parameters p,Al, * and I can be different for each subregion "1".
Obviously, a small number of subregions should be chosen at first, and the number
increased as more data become available.
     Consider the following example illustrating the computation of travel time for
ground water from a holding basin to a nearby river.
                                    EXAMPLE VI1-2
       A burled  stream channel 1s suspected of being beneath the holding basin
   shown in Figure  VII-19.  The aquifer underlying the holding basin and the
   surrounding area 1s a water table aquifer (unconfined).  The hydraulic
   conductivity measurement from a pump test at well Bl was 0.4 cm/sec and the
   hydraulic conductivity from a pump test in well B2 was 0.6 cm/sec.  The water
   level elevations in wells Bl and 82 were 2.82 x 104 cm and 2.8140 x 104 cm,
   respectively.  The estimated porosity is 0.3.  Calculate the seepage velocity and
   travel time for sulfate from the edge of the holding basin to the river using the
   above data.  Assume the sulfate does not interact with the soil.
   Consider the following steps:

       1)  Obtain the average hydraulic conductivity from the two pumping tests,

           K • (0.4 * 0.6J/2 • 0.5 cm/sec

       2)  Calculate the hydraulic gradient between the basin and the river, where
           the distance between wells Bl and 82 is 4 x 104 cm,

            I . AH „ (VH2)  m (2.8200 x 1Q4 - 2.8140 x ID4)
                ff    ~*^               4 x 104
              • 0.0015 (cm/on)
                                        -361-

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      PLAN
         VIEW
                      HOLDING
                      BASIH FOR
                      PLAT IWG
                      WASTE
            Scale
                   600
            teterz
      VERTICAL CROSS-SECTIOlt (not to scale)
                           Ground Water Flow
      Parameter
         H
         C
         P
                              Dau
 Weil Ho PI
2 02 x I04cm
  04 cm/sec
     03
  Well MQ-P2
2.A 14 X 104 cm
  0.6 cm/sec
     0.3
FIGURE VI1-19  EXAMPLE  PROBLEM:   CALCULATION  OF TRAVEL TIME FOR
              SULFATE  FROM HOLDING BASIN TO  RlVER
                           -362-

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        3)  Calculate the seepage velocity using Equation VII-36,
                .  tt . (0.5) (0.0015) . 0>0025
              s    p        (0.3)
\        4)  Estimate the travel time to the river using either Equation VII-42  or
'            VII-43, where the distance between the basin and the  river  is  6  x
I             104 cm,
   or
                                10*)
                    Al    (0.3H6  x  104)  _  . .  , In7
                •  P TcT  B  (o.siio.oois)   '  2-4  x 10  sec
        Hence, the travel time for sulfate, from the basin to the  river  1s  280  days
   or  approximately 9 months.
   	 END OF EXAMPLE VII-2 	
7.4  POLLUTANT TRANSPORT PROCESSES
     The basis for ground water transport of contaminants is discussed in this section.
First, the processes of dispersion and diffusion are reviewed in Section 7.4.1.  This
section includes both the definition and the estimation of these parameters for the
one-dimensional and then the two-dimensional case.  Finally, chemical and biological
processes that affect contaminant transport are discussed in Section 7.4.2.  This
section discusses how sorption and rate processes can be represented in screening
methods.

7.4.1  Dispersion and Diffusion

7.4.1.1  Hydrodynainic Dispersion

     Up until this point, the migration of dissolved solutes through porous media was
assumed to be only related to the seepage velocity of ground water (see Section 7.3.3).
Under this assumption, an Injected solute or contaminant would travel through the
aquifer by plug flow (e.g., piston-like motion).  The concentration profile would
resemble a step function.  However, experience has shown that solutes do not exhibit
true plug flow.  Instead, solutes gradually spread out from their initial point of
introduction and occupy an ever increasing volume of the aquifer, moving far beyond the
region that it would be expected to occupy based on the average seepage velocity alone.
This spreading or dispersing phenomenon 1s called hydrodynamlc dispersion.
     Hydrodynamic dispersion constitutes a nonsteady, irreversible mixing process.
Bear (1972) states that hydrodynamic dispersion 1s the macroscopic outcome of the
                                         -363-

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solute's movement due to Microscopic, macroscopic and megascopic  effects.   Or the
microscopic scale, dispersion  1s caused by:  a) external  forces acting  on  the ground
water fluid,  b) macroscopic variations 1n the pore geometry,  c) molecular diffusion
along solute concentration gradients, and d) variations 1n the fluid properties,  such
as density and viscosity.
     In addition to 1nhomogene1ty on the microscopic scale (I.e., pores and grains),
there may also be 1nhomogene1ty 1n the hydraulic properties (macroscopic variation).
Variations 1n hydraulic conductivity and porosity Introduce Irregularities  in the
seepage velocity with the consequent additional mixing of solute.  Finally, over  large
distances of transport, megascopic or regional variations 1n the hydrogeologlc units or
strata are present 1n the aquifer.  The effect of scale on the mechanisms of
hydrodynamlc dispersion are shown schematically 1n Figure VI1-20.  Since the magnitude
of dispersion varies significantly with the scale of the physical system, care must  be
taken to properly define which scale is to be used 1n any given problem.
     The hydrodynamlc dispersion coefficient D (cm /sec) may be mathematically
expressed as the sum of two dispersive processes:  mechanical dispersion D_ (cm /sec)
                              2
and molecular diffusion D* (cm /sec).  Thus, the sum 1$:

                                      D •  Om  * D*                             (VII-45)

     Molecular diffusion D* 1s  a microscopic  and  molecular scale process that results
from the random thermal  induced motion of  the solute molecules within the liquid phase.
This process is Independent of  the advective  motion  of the ground water and can be of
significant importance at low flow velocities and very near solid surfaces.  Duursma
(1966)  reported experimentally  determined  molecular  diffusion coefficients that ranged
between 2 x 10~  and  6 x 10"  cm /sec for  trivalent  and monovalent ions (both positive
and negative)  in fine sand.   However, molecular diffusion  is generally specified
(Sudicky, 1983; Gillham et al_., 1984) as:

                                 D* - 1  x  10"6 cm2/sec                        (VI1-46)

     Mechanical dispersion 0  occurs predominately on  a macro and  megascopic scale and
                            HI
is due  to the "mechanical mixing*  of the solutes.  Such  mechanical mixing is caused by:
a) variations in the  velocity profile across  the  water filled portions of a pore,   b)
variations in the channel size  of the pores,   c)  the tortuosity,  branching and
interfingering of pore channels.

7.4.1.2  One-Dimensional Flow
7.4.1.2.1  Introduction
     For one-dimensional flow,  mechanical  dispersion D^cn^/sec)  is  generally expressed

                                         -364-

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                           ^mmw/////////////^^^^^
                                                      MILLIM

                                                   MICROSCOPIC SCALE
                    MACROSCOPIC SCALE
                                                   SOLUTE MIGRATION
                                                       PATHWAY
        FIGURE VI1-20    SCHEMATIC SHOWING THE  EFFECT OF SCALE ON
                           HYDRODYNAMIC  DISPERSION PROCESSES
as a function of the seepage velocity v  (cm/sec)  witn  the relationship:
                                          Vs
(VII-47)
where «1  (cm)  is the longitudinal dispersivity of the  porous medium.  Upon  substitution
of Equation VII-47 into Equation VII-45, the hydrodynamic dispersion coefficient D
(cm /sec)  becomes:
                                            + D"
(VII-48)
                                       -365-

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 where the molecular diffusion D* (c»2/$ec)  1$ given by Equation VII-46.
      Unfortunately, dispersivlty «1  1s not  a constant but rather appears to depend on
 the mean travel  distance or scale at which  the •easurements were taken (Fried, 1975;
 Pickens and Grisak, 1981 a, b; Sudlcky, 1983).  For example, laboratory experiments
 give values of d1spers1v1ty 1n the range of 10   to 1 on, while field determined values
 range from about  10  to 10  cm.

7.4.1.2.2  Estimating Longitudinal D1spers1v1ty
     A rough estimate of longitudinal d1spers1v1ty  1n saturated porous media may be
made by setting QI  (cm) equal  to 101 of the mean travel distance x (cm) (Gelhar and
Axness, 1981):

                                       a1 • .lx                               (VII-49)

     In Figure VI1-21, 48 values of longitudinal d1$per$1v1ty are plotted as a function
of scale length of the experiment for saturated porous media (Lallemand-Barres and
Peaudecerf, 1978).  Note in Figure VII-21 the  line predicted by Equation VII-49.
Lallemand-Barres and Peaudecerf  (1978) concluded that field-scale dispersivlty was
independent of both the aquifer material and Its thickness.  In addition. Equation
VII-49 and Figure VII-21 suggest that longitudinal dispersivlty Increases indefinitely
with scale length.
     More recently, Gelhar e_t a_l_. (1985) reviewed the available literature and obtained
77 values of longitudinal dispersivlty from saturated field studies and 13 values of
longitudinal dispersivity from unsaturated field and laboratory studies.  The saturated
media results are shown in Figure VI1-22 and the unsaturated media results in
Figure VII-23.  These data also show that longitudinal dispersivity increases with
scale length.  However, a critical evaluation of saturated site data in terms of
reliability (as indicated by the size of the circles in Figure VII-22) led Gelhar
et a_l_. (1985) to suggest that no definite conclusion could be reached concerning scales
greater than 100 meters.  Longitudinal dispersivlty probably approaches asymptotically
a constant value for very large or megascopic scale lengths (Gelhar and Axness, 1983;
Sudicky. 1983).  In addition, the 10 percent rule of thumb expression for longitudinal
dispersivity given by Equation VII-49 does not hold in the unsaturated zone.    Rough
approximations of longitudinal dispersivity  for unsaturated flow can be made by using
Figure VII-23, where scale means the mean travel distance or simply the distance from
the origin of the contaminant.
     To estimate longitudinal dispersion, an appropriate distance is determined
(typically the distance from the contaminant source to the furthest point of Interest).
The dispersivity is then selected for the chosen distance from either Equation (VII-44)
or Figure VII-22 for the saturated zone or Figure VII-23 for the unsaturated  zone.
                                        -366-

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           100  -
       _§
       >
       ^

       CO

       £
       CO
       o
                                        O LIMESTONE
                                        V CHALK
                                        D GRANfTE
                                          SCHIST
                                        • CLAY. SAND
                                           OR GRAVEL
                                        • SANDSTONE
                                        A DOLOMITE
                                           Of)  BASALT
                                   100
                                 DISTANCE (m)
                              WOO
FIGURE VII-21
FIELD MEASURED  VALUES OF LONGITUDINAL DISPERSIVITY
AS A FUNCTION OF  SCALE LENGTH  FOR  SATURATED POROUS
MEDIA,   REFERENCE:   LALLEMAND-BARRES AND
PEAUDECERF  (1973)
                                  -367-

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            1000
        —   100
        a.
        CO
        e?

        o
              10
             1.0
             .10
           .me)
                                           a- .1 7
   O
        O  "   W       KY:
O &?&          O      2*~
                         MlttbllU; of dJU 1ncr«i>es
   O'   o                 "1th ^crMSinq tyWMl stzt:

  'O                       « low

    n                   °

 •  o°                  O
o
                        10       100     1000    10.000  100,000


                                      SCALE (m)
   FIGURE  VI 1-22    A PLOT OF  LONGITUDINAL DISPERSIVITY  vs, SCALE LENGTH

                     FOR SATURATED POROUS  MEDIA,   REFERENCE:  GELHAR
                     EJ AL, (1985)
Dispersion 1s then calculated using Equation (VI1-48) or Equation (VII-47)  for one-

dimensional flow.



7.4.1.2.3  Solute  Transport Equation


     In order to better visualize  the concept of dispersion,  a brief discussion is

given concerning the equation describing one-dimensional solute transport in ground

water flow systems.  The partial differential equation describing the one-dimensional,

advective-dispersive transport of  non-reactive solutes in saturated (or unsaturated) ,

homogeneous porous media 1s given  by:
«•»&••, if
                                                                         (VII-50)
                                      -368-

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                  1.00
             £    o.io
             V)
             c
             Ul
             Q.
             CO
             5
o
o
             o
             o
                0.001
                      X
                    X X

                      X
                 X

                O*
                                              O LAB EXPERIMENTS
                                              X FIELD EXPERIMENTS
                                              A ENVIR. TRACER
0.1
                                                       10
100
                                          SCALE (m)
   FIGURE VII-23
 A  PLOT OF  LONGITUDINAL DISPERSIVITY vs.  SCALE LENGTH
 FOR  UNSATURATED  POROUS MEDIA.    REFERENCE:   GELHAR
 ET AL,. (1935)
where c (g/ml)  is  the  solute concentration at time  t  (day) and distance x (m),
    2
D (m /day)  is the  hydrodynamic dispersion coefficient  and v   (m/day)  is the ground
water seepage velocity.
     If the aquifer  is  initially assumed to be solute  free and if the D and v
parameters  are constant over the distance of interest,  then a solution to Equation
VII-50 for  a step  function input (i.e., the initial concentration goes from zero to a
value c  at t « 0} can  be obtained (Ogata and Banks,  1961; Ogata, 1970).  The analytic
solution and a  worked  out example using an integrated  form of Equation VII-50 are given
in Section  7.5.4.  Note that a constant hydrodynamic dispersion coefficient D was used
when solving Equation  VII-50 in Section 7.5.4.  Yet, Equation VII-49 and Equation
VII-50 indicate that D  is a function of distance or scale.  Unfortunately, no simple
analytic solution  exists for the general case of a  spatially varying dispersivity term.
Hence, the  distance or  scale of the problem is used to  compute the longitudinal
dispersivity.
                                       -369-

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      Consider the analytic solution to Equation VI1-50 from Section 7.5.4, shown
 schematically In Figure VI1-24.   The solute concentration 1s plotted as a function of
 distance  In  Figure VII-24a at  times t.  and  t«.  where t? 1$ greater than tj.   The solute
 concentration 1s plotted as a  function of time  1n Figure YII-245.   The solute
 concentration versus  tine plot 1s also known as a breakthrough  curve.   Each  plot 1n
 Figure  YII-24 also shows the solution  to Equation VI1-50 for plug  flow (I.e., no
 dispersion).
      A  comparison between plug flow and dispersive flow 1n Figure  VII-24 shows an *S*
 shaped  curve  when dispersion 1s considered.   As time  or distance Increases,  the S shape
 flattens  out.   Remember that solutes  1n plug flow move  at  the seepage  velocity and as a
 sharp front.   Hence,  solutes 1n dispersive  flow are spreading out  and  the  leading
 portion of the solutes  are moving faster than the seepage  velocity and the trailing
 portion are moving slower than the seepage  velocity.  At the point C/CQ •  0.5, the
 solutes move  at  a rate  approximately equal  to the seepage  velocity.
      In Section  7.3.3.2,  the question  of travel  time  was addressed but only  for non-
 reactive, non-dispersive,  plug flow.   It should now be  obvious  from the above
 discussion that  Ignoring the effect of  dispersion can considerably overestimate the
 travel  time of a  contaminant.  The leading  front  of a contaminant  plume may  reach a
 given location as much  as  an order of magnitude faster  than  that predicted by plug or
 non-dispersive flow.  Plug flow only predicts the travel  time for  the  center  or
 centroid of solute mass of  the contaminant plume.  The travel time estimates  given by
 plug  flow in Section 7.3.3.2 are  still  useful in  that It gives  a time  reference  for
 contaminant transport.  What plug  flow considerations alone cannot do  is to predict
 time  of arrival for the  leading edge of a contaminant plume.
      Unfortunately, there  is no simple, algebraic way to incorporate the effect of
 dispersion into calculating  time of travel  and solute concentration profiles.
 Equation VII-50 has to be solved repeatedly  for different times  and distances.  The
 example given above plus four other examples of solute transport are discussed with
 additional detail  1n Section 7.5.

 7.4.1.2.4  Measuring Longitudinal  Dispersivity
      In Section 7.4.1.2.1, several figures  and equations were given as a means of
 estimating longitudinal  d1spers1v1ty.  These methods  of estimation  are more than
 adequate during the screening phase of a ground water project.
     A great  deal of controversy still exists as to  the true meaning of hydrodynamic
dispersion,  its correct mathematical representation  and the proper  method to measure   H
 in the  field.  In Equation VII-49, longitudinal  d1spers1v1ty was estimated as a linear
 function of scale distance.  However, many  other representations are possible {Pickens
 and Grisak,  1981 a. b).   Even stochastic representations are available (Todorovic,
 1975; Smith  and Schwartz, 1980; Gelhar and Axness, 1983).
                                         -370-

-------
   o
  o
  O
  UJ
  O
  U
  LU
                              PLUG FLOW (no dispersion)
                                                        FLOW DIRECTION
                 EFFECT OF
                 DISPERSION
                                                        DISTANCE
  o
  o
  cr
  u
  o
  o
 UJ
 cr
       i. -
        J»LUG FLOW (no dispersion)

                r-
                            EFFECT OF
                            DISPERSION
                              (b)
                                                          TIME
FIGURE VI1-24
SCHEMATIC  SHOWING THE  SOLUTION OF EQUATION VI1-50
AND THE  EFFECT OF DISPERSION:   A) SOLUTE
CONCENTRATION AS A FUNCTION OF DISTANCE  AT TIMES
TI AND T2,  B) SOLUTE CONCENTRATION AS  A  FUNCTION
OF TIME  (THE  BREAKTHROUGH  CURVE)
                                -371-

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     The typical field method to measure longitudinal d1spersiv1ty consists of
Injecting a tracer Into the porous medium and then monitoring the arrival  time of  the
tracer concentrations.  The experimental data are then fitted or calibrated (using
either an analytical or numerical solution of the dispersion equation) to  obtain the
longitudinal d1spers1v1ty or dispersion coefficients.  Many analytical methods of
fitting the solute breakthrough curve are available, such as those given by Elprlnce
and Day (1977) and Basak and Hurty (1979).   An extensive discussion on field methods to
determine dispersion coefficients is also given by Fried (1975).

7.4.1.3  Multi-Dimensional Flow
7.4.1.3.1  Introduction
     In any real ground water system, the point release of a solute or contaminant Into
the aquifer will produce an expanding, three-dimensional  ellipsoid.  The concentration
profile of such a plume will be approximately Gaussian in shape in the transverse
directions (both across and down).   The concentration profile will also be
approximately Gaussian in shape along the longitudinal direction if the point release
is instantaneous (i.e., a slug or short pulse).   The component or contribution of
dispersion will generally be greatest along the direction of flow (longitudinal)  and
less in the transverse directions.   The longitudinal direction is Implicitly taken to
be along the principal direction of ground  water flow.  The transverse directions t and
v are perpendicular to the longitudinal but t (lateral-transverse) is in the same plane
as that of ground water flow.  The v or vertical-transverse direction is perpendicular
to the 1-t plane but 1t is not necessarily  in the same direction as gravity.  The
vertical-transverse direction is only along the direction of gravity when  the ground
water flow is in the horizontal direction.
     In a layered, unconsolidated aquifer with horizontal flow, the effect of vertical
dispersion will generally be significantly  less than from horizontal  dispersion.
Vertical mixing is a slow process and solute will often remain confined to a narrow
horizontal zone in the aquifer.  Hence, most analyses, including those of the screening
methods, consider one- or two-dimensional analyses of solute transport.  If the source
of the solute or contaminant is very wide compared to the distance of interest, then
one-dimensional analyses (such as is given  in Section 7.4.1.2) are adequate.
     As in Section 7.4.1.1, the coefficient of hydrodynamic dispersion 0 is defined as
the linear sum of mechanical dispersion and molecular dispersion D*.   However, for an
anisotropic, three-dimensional medium, Scheidegger (1961) and Bear (1972) define 0 as a
fourth-rank tensor, containing 81 components.  If the coordinate axes are chosen so
that they coincide with the principal axes  of dispersion, then virtually all of the
off-diagonal terms of the tensor are zero.
                                         -372-

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      In a two dimensional,  horizontal,  1sotrop1c  medium,  the hydrodynamic dispersion
 coefficient becomes:
                             Dxx • Vsx/vs  * Vsy/vs  * D*
                             Dyy  ' Vsx/vs  * °lvsy/vs  * D*

 where the magnitude  of  the  seepage velocity v   (cm/sec) 1s given by:

                                    vj - v*x *  v^                             (VI 1-52)
                 2
 and  where D*  (cm /sec)  1s molecular dispersion  (see Equation VII-46); a,  (cm)  and a.
 (cm)  are  the  disper$1v1t1es  1n the longitudinal and transverse directions,
 respectively;  v    (cm/sec)  and v,  (cm/sec) are the longitudinal and transverse  seepage
               sx                sy            2
 velocity  components, respectively; 0  , 0   (cm  /sec) are the principal  components of
                                    xx   yy      2
 the  hydrodynamic dispersion  term; and D  ,  0  (cm /sec) are the off-diagonal components
 of the  hydrodynamic dispersion term.
      If the Cartesian coordinate system 1s  chosen so that the longitudinal  (i.e., the
 x) axis coincides with the direction of the average seepage velocity v  , then D  reduces
 to:
                                                                              (VII-53)
                                    0* * atv
            2                2
where D, (cm /sec) and D. (cm /sec) are the longitudinal and transverse hydrodynamic
dispersion terms, respectively.  This orientation of the Cartesian coordinate system is
used in most of the problems in Section 7.5.  The molecular dispersion term D*
   2                                -6       -5  2
(cm /sec) ranges In value between 10~  and 10" cm /sec.   The computation of th
velocity v$ is discussed in Sections 7.3.3.1, the longitudinal  dispersivity term
(cm) is given in
discussed below.
   2                                -6        -5   2
(cm /sec)  ranges  In  value  between  10~   and  10" cm /sec.  The  computation  of  the  seepage
velocity vs is  discussed  in  Sections 7.3.3.1, the longitudinal  dispersivity  term a^
(cm) is given in  Section  7.4.1.2.2 and  the  transverse  dispersivity  term a.  (cm)  is
7.4.1.3.2  Estimating the Transverse Dispersivity Components
     Whitaker (1967) predicted that for uniform flow in an isotropic, saturated porous
medium, that dispersivity would be dominated by the longitudinal  dispersivity component
o^ and that a^ would be exactly three times the value of the lateral-transverse
component a..  Hence:

                                      a1/at - 3                               (VII-54)
                                        -373-

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     The estimate of Equation YII-54 agrees with the field data  analyzed  recently  by
Gelhar et al. (1985) for unconsolldated materials.  The a^<»t ratio  ranged  between 2.1
and 5 for alluvial and glacial deposits (sand and gravel), the average being  3.5.   The
ratio of a,/ot for limestone was 3.2.  The vertical transverse component  of
d1spers1v1ty o  was generally two orders of magnitude smaller than that of  the
horizontal components.  The o1/oy ratio ranged between 30 and 860 for alluvial/glacial
deposits, the average being 400 (Selhar et al_., 1985).
     The d1spers1v1ty components can be estimated for screening purposes  as follows:
a) use the 10 percent rule of thumb from Equation "VII-49 to estimate the  longitudinal
a, component for saturated media and Figure VII-23 for unsaturated media,   b) then use
either Equation VII-54 or the above ratios to estimate the transverse dlsperslvlties afc
and/or o .

7.4.1.3.3  Alternative Dispersion Formulations
     Before leaving this section on dispersion, one additional comment should be made
concerning spatial variability.  In both the one-dimensional  and two-dimensional
representations of solute transport, it is conveniently assumed that the seepage
velocity v  could be averaged and expressed as a constant.  However, the seepage
velocity may have substantial variations in space.   Consider  Figure VII-2S which
schematically shows how the horizontal  seepage velocity v$(z)  may vary dramatically
with depth.  Such stratification or variations are quite common  in aquifers and are
caused by the variations in the hydraulic conductivity and porosity  in the medium
(Sudicky et aj., 1983; Gillham et a_1_. •  1984).  Recently, several researchers  such  as
Molz £t a_U (1983). Sudicky (1983), Gillham et al_.  (1984), etc. have suggested that the
primary physical mechanism that causes  the spreading of solute in the longitudinal
direction is due to the vertical variation in the seepage velocity v (z).  Hence,  they
argue that, the phenomenon of scale-dependent dispersivity and hydrodynamic dispersion
is an artifact.  They suggest that more emphasis should be placed on the accurate
determination of hydraulic conductivity and aquifer inhomogeneities.
     Artifact or not, the use of hydraulic dispersion algorithms 1s currently the  only
practical method, short of direct measurement, to account for dispersive solute
transport.  Those who are in the screening phase of a ground  water project are unlikely
to have access to a detailed survey of  the hydraulic conductivity and seepage
velocities of the aquifer.  The analytic and heuristic methods presented here and  in
Section 7.5 are the best that are currently available.

7.4.2  Chemical and Biological Processes Affecting  Pollutant  Transport
     Pollutants in ground water can be  affected by  a number of chemical and biological
processes as shown in Figure VII-26.  Volatilization generally does not have to be
considered in ground water screening problems unless the pollutant is within a few
inches of the land surface and the media is highly  permeable.   Of the remaining

                                         -374-

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                                                              VERTICALLY
                                                              AVERAGED SEEPAGE
                                                              VELOCITY
                                                      Ai'
                                                      itf
    FIGURE VI1-25
SCHEMATIC  SHOWING HYPOTHETICAL VERTICAL  VARIATION  IN
THE  GROUND WATER FLOW VELOCITY
processes shown in Figure Vll-26,  some  can  be  incorporated directly  into the analytical
methods to be presented  later  in  this chapter.  These processes are sorption-desorption
and ion-exchange,  hydrolysis,  and  biodegradation.
     Other chemical processes  can  be considered separately from the analytical methods.
Processes which can be evaluated  include acid-base  reactions, speciation, complexation,
oxidation-reduction reactions  and  precipitation-dissolution.  For example, to determine
if sorption is important and if so, an  appropriate  coefficient, the metal speciation
must be determined for the pH  and  redox conditions  present in the ground water.  This
can be done based  on Eh-pH diagrams or  equilibrium  geochemical models.  At this point,
the transport of the metals can be estimated using  the analytical methods discussed in
Section 7.5.   Next, the  extent of  precipitation-dissolution can be determined using
methods similar to those described in Chapter 4 of  this manual.   If the calculations
snow that some metal  could precipitate,  the transport calculations can be revised using
the new dissolved  concentration.   In most surface and ground waters, revised transport
calculations  will  not be necessary because  sorption is the dominant process at typical
metal  concentrations.  However, within  a waste naterial and immediately downgradient of
it, metal concentrations can be high so  solubility  limits should be checked.
7.4.2.1  Sorption
     Sorption can  be  defined as the accumulation of a chemical in the boundary region
of the soil-water  interface.  Sorption-desorption processes are an important
                                         -375-

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                                                 PROCESS
               PHYSICAL TftANSPQrVr
                                            Pbpersion - Ptffuaion
   CHEMICAL REACTION  &(,* *roc«s«s)
Fbrttfloning                    eqcrti&na
             -tl—*-
            aorpon
            ion-«xcK
            volatilization
                    speualion
                    computation
                        PrCOOH •» M«* *=* frCOOM*
            Microbially Mediated
            ox idot ion- reduction
            rvydroiy its
            Conjugation
            ring +i5S*On. etc.
           o-oc
                   Other
                    prcapttahon-dis&olution
                      (cncmicai weathering)
                    -logC
     FIGURE VII-26
MAJOR  EQUILIBRIUM AND  RATE PROCESSES  IN NATURAL
WATERS.   REFERENCE:  SCIENCE APPLICATIONS, 1982
determinant of pollutant behavior  in the subsurface environment.  Because of the much
higher  solid to liquid ratios in ground waters than in surface waters, the
concentration of even a moderately-sorbed pollutant can decrease  significantly with
distance as it migrates in the ground water.   In  addition to decreasing the aqueous
concentration, there are several other implications of sorption.  Volatlzation, even in
the uppermost soil  layers, is diminished.  Rates  of reactions such as microbial
degradation can be  different for the adsorbed pollutant and the portion remaining in
solution.  Unlike in surface waters where the adsorbed pollutant  may still be advected
                                      -376-

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downstream associated  with  suspended  sediment,  1n  ground water  the  adsorbed  pollutant
1s not  ususally  transported by advectlon or dispersion  (the solid phase  is  immobile.)
However,  when  the  concentration gradient changes,  the pollutant  can  be desorbed  over
tine  at the same or a  different rate  than  1t was sorbed onto  the soil particles.   This
has important  Implications  for handling waste disposal problems  1n that when  "clean"
water flushes  an aquifer which previously  contained water contaminated with metals or
organic chemicals, the concentrations of the pollutants may remain relatively high
until the reservoir of adsorbed pollutants has  been depleted.   In one case of high TCE
contamination, the downgradient concentration was  predicted to be 80 percent of  the
existing  level even after the aquifer was  flushed  once with distilled water.

7.4.2.1.1   Retardation Factor
      If sorption 1s modeled as a linear, equilibrium process, it can be incorporated
into  the  analytical methods presented 1n Section 7.5 as a retardation factor.  This
factor  is  defined as follows:

                                   Rd - 1 * {*dpb/p)                          (VI1-55}

where

        Rd • retardation factor (unltless)
       Kd • distribution  coefficient (ml/g)
       P.  • bulk  density  (g/ml)
       p  « porosity  (decimal fraction).

The term,  Kfl is  used in most ground water literature, but 1t is synonymous with K  , the
partition  coefficient, which is more common in chemical  and surface water literature.
If a  pollutant is not  sorbed, the retardation factor equals 1 which shows that the
pollutant moves  at the same speed as the ground water.   If the retardation factor is
greater than 1,  say 2, the pollutant will  move  half as fast as the water.  Typical
values  for bulk density and  porosity for  different  types  of  soil  materials were
included in Table VII-2 and  VII-4,  respectively.
     The Kg term  is an  empirical  coefficient  for a  specific  constituent under  a
particular set  of conditions.   For  linear,  equilibrium sorption,  K   can be measured in
the  laboratory  as:

                                    K   • C*]/[c]                              (VII-56)
                                        -377-

-------
where  K^   « distribution coefficient, «l/g
        d
       [$]  « concentration of pollutant sorbed on  soil,  g/g
       [c]  • concentration of pollutant in solution, g/nl.

K . may be  a function of the concentration of the  sorbing chemical species Itself,  the
concentration of any competing species (usually major ions affect trace constituents
but not vice-versa), concentrations of any complexlng species present (e.g., Cl,
organics), pH of solution, the amount and type of adsorbent (e.g., clays. Iron oxides,
aluminum oxides), and the amount of organic matter associated with the solid phase.
Figure VI1-27 shows the effect of pH and organic matter on typical adsorption curves.
When obtaining values for a pollutant of Interest, these and other factors should be as
similar as possible to the conditions in the problem being addressed.  Selected K.
values  for metals have been Included An Chapter 4.  Available values for M, Sb, As,
Ba, Be. B, Cd. Cr, Cu, F, Fe. Pb. Hn, Kg. No. N1. Se, Na. S04. V. and In have been
compiled from the literature for a variety of conditions (Ra1 and Zachara, 1984).  The
values  are reported along with characteristics of the absorbent (i.e., type of
material,  cation exchange capacity, and surface area), concentration of species of
interest,  and solution characteristics (i.e., composition, molar concentration of
adsorbing  species and pH).
     For organic chemicals, the adsorption coefficients are usually referred to as
partition coefficients K .   The partition coefficient can be calculated from the
octanol-water partition coefficient KQW (unitless) and estimates of the organic
fraction of sand and silt plus clay (see Section 2.3.2).  The octanol-water partition
coefficient can also be calculated from solubility data using an empirical
relationship.   Typical values for solubility and K   are included in Tables II-S
through II-9 for the 129 priority pollutants.  Additional data on pesticides including
EDB and DBCP are included in Zalkin et al_.(1984) and Bowman and Sans (1983).  Partition
coefficients and sorption In general  are discussed in more detail  in Section 2.3.2.
                              -- EXAMPLE PROBLEM VI1-3
j        Calculate  the  retardation factor for  anthracene  in a silty-clay formation
I   where the  organic carbon content of the silty-clay is about 0.01.
|        From  Table  II-9, the octanol-water partition coefficient  1s found to be
j   28.000 (unitless).  The organic carbon partition coefficient is first estimated
j   from  Equation 11-18 as follows:

!          K   • 0.63 K
I           OC         OW
1              • (0.63)(28,000)
I              • 17,640 ml/g
                                         -378-

-------
              100
    Percent
    Adsorption
    by Soil
               SO
1 - /
/ Shift due 1
to presence 1
I of soil organic 1
j Matter /
.
1 1
/^-Typical adsorption I
' curve for heavy 1
/ Metal x. on silica /
I or alMrinuM silicate I
surface coated with /
/ soil organic Matter /
/ 1
' S
.' 	 s
F

*)s Typical
adsorption
curve for
heavy Metal
x, on a clean
silica tr
aluMlnuM
silicate
surface


[CT] • const
t^ • const

                              pH of  the Soil  Solution

    a) Generalized Heavy Metal Adsorption Curve for Cationic Species

                          (e.g., CuOH4)
100
Percent
Adsorption 50
by Soil
n .

Typical adsorption
curve for heavy
metal species, x,
on iron hydroxide
-r\
\
\ a
\Shift \
\ due to \
\ presence \
\ of soil \
^ organic \
v matter \
" 	 	 V
pH of the Soil Solution
b) Generalized Heavy Metal Adsorption Curve for Anionic Species
(e.g., CrO^'J
FIGURE  VI1-27    HYPOTHETICAL ADSORPTION CURVES FOR  A)  CATIONS AND
                  B)  ANIONS  SHOWING  EFFECT OF  pH AND  ORGANIC  MATTER
                                 -379-

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I    where the conversion  coefficient 0.63  has  units of «l/g.

j    The partition  coefficient,  K .  1s calculated next using Equation 11-17 as
•    follows:
    where
                 mass  of  silt  and  clay
           f    "
                 mass of  silt,  clay an  sand

                                 of **nd
•           Xox  "  Or9anic  fr»ct1on of silt-clay  (OiX^iO.l)

I   Substituting  the above data yields the following expression:
i
j           K  • 17,640 [0.2(1-1)0 * 1(0.01)]
j             « 176 ml/g

'   Finally, the  retardation factor is calculated as follows using Equation YII-55,
I   where the bulk density and porosity of this formation are 1.6 g/ml and 0.3
I   (unities*), respectively:
!           *»  •  '
              .  l  .  (176 m1/q)(1.6 q/ml)
j              -940

    The  relative amounts of anthracene  in the dissolved and sorbed phases can be
|    estimated  using  a modified  form of  Equation  11-22 as follows:
I
i           ^ -      c       „ i
•           ct   (c * $VP)    Rd

i      where c  • total  dissolved pollutant  concentration
I            ct • c * $Pb/p
j            s  - mass of sorbed pollutant  per unit mass of soil
            R  - retardation  factor
                                         -380-

-------
I  hence,
i              ,                                                                         !
i       r'm  •  °-m                                                               !
i                                                                                       !
j  Thus,  0.1  percent  of  the  anthracene  is  in  the  dissolved  phase  and  the  rest  is         |
;  associated with  the solid phase.                                                      |
 I
                            END  OF EXAMPLE  PROBLEM  VI1-3
                                                                                       I
7.4.2.1.2  Effect of Sorption on Seepage Velocity and Travel Time
     A solute subject to sorption will travel at the following average velocity:

                                     v* • vs / Rd                             {VI1-57)

where v* (cm/sec) is the velocity of the solute, v$ (cm/sec) is the seepage velocity of
the ground water and Rrf (unitless) is the retardation factor accounting for sorption.
Since the retardation factor Rrf is equal to one for no sorption and is greater than one
with sorption, the solute velocity v  will always be less than or equal to that of the
seepage velocity.
     Ground water travel time At was defined in Section 7.3.3.2 as the average time
that it takes ground water to travel a specified distance.   In the case of a solute
subject to linear, equilibrium sorption, its travel time will  be:

                                     dt* « Rddt                             (VII-58)

where 4t* (sec) is the travel time of the solute, 4t (sec)  is  the travel  time of ground
water and K. (unitless)  is the retardation factor accounting for  sorption.  Hence,  the
travel time of a solute will  be greater than or equal  to that  of  the ground water.   (An
insignificant exception  may  exist  for solutes like chloride, which  because of  anion
exclusion by negatively charged soils, may move slightly faster than the  ground water
itself.)

7.4.2.2  Other Processes
     Processes such as biodegradation and hydrolysis can be represented in some of  the
analytical methods by first-order decay rates.  The actual  rate constant  used  should be
the sum of the individual  first order decay rate for the specific pollutant.
Hydrolysis rates are given in Section 2.5.3 for organic chemicals.   Biodegradation  is
presented in Section 2.5.1.   Biodegradation for some compounds  may  be  more important in
ground waters than in surface waters due to the slow velocities,  and hence long  travel
                                         -381-

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times, and the common occurrence of anoxic  conditions.   Figure  VI1-28 shows  the
degradation of tetrachlorethylene and the resulting products  of the  series of
dehydrochlorination reactions which occur under anoxic  conditions.   Biodegradation
rates in ground water for selected organic  chemicals are available from Wood et a_L,
1981 and Wilson and McNabb, 1981.

7.5  METHODS FOR PREDICTING THE FATE AND TRANSPORT OF CONVENTIONAL AND TOXIC POLLUTANTS
7.5.1  Introduction to Analytical Methods
     In this section, five analytical  models are presented which can  be used to  predict
the extent of contamination in ground  water.  A summary of these models is given in
Table VI1-12,  For each model, the types of contaminant sources, flow situations,
source release characteristics and spatial dimensions are briefly described.   A
discussion of the assumptions and the  mathematical expression for each model  is given
in Figures VII-29 to VII-33.  Finally, a more complete presentation of the derivation
and use of each model, plus one or more worked out examples or applications are given
in Sections 7.5.2 to 7.5.6.   Each model  has  been  programmed for solution on micro-
computers (Mills  et a_L ,  1985).
     Obviously, there exist far more than five analytical models that describe ground
water contamination.  These five were  chosen because they represent many of the  typical
ground water contamination problems for which solutions could be obtained with hand-
held calculators.  A more comprehensive collection of one-dimensional analytical
transport models  is given by van Genuchten and Alves (1982) and multiple-dimension
analytical models by Yeh  (1981) but these are primarily suitable for solution with
large desk-top or main-frame computers.   The models chosen in this section are
relatively simple to use, yet are powerful  in their range of applications.
     Analytical methods  allow prediction of  contaminant concentrations in the aquifer
at given times and locations as a result of  an individual contaminant source.  The
simplest methods  are based on the theory of  flow to a pumping well (see Section 7.5.2).
Most analytical methods,  however, involve solving some form of the equation of flow in
porous media.  The complexity of the solutions varies greatly, depending on the number
of dimensions included and the simplifying assumptions made.   The equations range from
simple, one-dimensional  advective-transport  equations to those simulating contaminant
dispersion, diffusion, sorption and decay in two dimensions.
     Analytical techniques are based on a number of simplifying assumptions.   A key to
using and interpreting the results of  these  methods appropriately, therefore, is
understanding the assumptions which need to  be made about the aquifer system and the
various hydrogeologic parameters.  Common assumptions include steady and uniform ground
water flow in the saturated zone, aquifer isotropy (equal hydraulic conductivity in all
directions), and  constant contaminant  concentration or mass loading rate from the
contaminant source.
     The reliability of the predictions generated depends on  the inherent limitations

                                        -382-

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                       200
                       150
                       100
                        BO
                                                         Tyltm
                                                         Vinyl cMoridt
                                                         1.1 DkJik»rocthy««n«
                                                         trww. DichlorocthytiM
                                                         ..
                                                            I
                                   10
                                        D»v«
      FIGURE VI1-28    DEHYDROCHLORINATION  RATE  OF TETRACHLOROETHYLENE
                         AND  THE  PRODUCTION  RATE OF ITS  DECHLORINATION
                         PRODUCTS  (AFTER WOOD ET AL,,  1931)

of the equations used,  the  assumptions made, the  data used, and the complexity of field
conditions.  It  is critical for  the  user  to understand how reasonable the assumptions
of a particular  technique are  for  the aquifer and site being examined.  For example, a
technique assuming aquifer  isotropy  may not be well suited for predicting contaminant
transport through  an aquifer with  a  we 11-developed fracture system.  In addition,
mathematical constraints  due to  functions  used in the algorithms sometimes limit the
usefulness of the  analytical techniques,  restricting them to relatively narrow ranges
of input values.  Predictions  for  a  number  of times and  locations in the aquifer can be
used to detect aberrant values stemming from those mathematical factors.
     Solving the flow and transport  equations of analytical methods requires a limited
amount of field  data.  Typically,  these data needs include:
        •    Contaminant  concentration (or mass  loading  rate) at the source
        •    Effective  porosity  of the aquifer
        •    Aquifer thickness
        9    Soil  bulk  density
        t    Ground water velocity
        t    Hydraulic  conductivity
        •    Dispersion coefficients in longitudinal and transverse directions
        t    Distribution coefficient (Kd) or retardation factor (R )
        t    Solute decay rate constants,  1f appropriate.
                                        -383-

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                                      TABLE VII-12

                               SUMMARY OF SOLUTION METHODS
Solution
Method
Section 7.5.2
Figure VII-29
Section 7.5.3
Figure VII-30
Section 7.5.4
Figure VII-31
Contaminant
Source

Migration of contaminant to
pumping well
Migration of contaminant from
injection well
Migration of contaminant from
surface to ground water table.
Contaminant
Release
continuous
and constant
continuous
and constant
continuous or
Intermittent
Spatial
Dimensions
and Coordinate
System
1-D
radial
1-D
radial
1-D
cartesian
    Section 7.5.5
    Figure VII-32
    Section 7.5.6
    Figure VII-33
such as from:  spills or
dumping, leaky ponds or tanks,
landfills, surface sites or
deposits

Migration of contaminant
in saturated zone, such as
from:  leaky ponds or tanks,
spills, landfills

Migration of contaminant
in saturated zone, such as
from:  leaky ponds or tanks,
spills, landfills, surface
sites or deposits
release with
a constant or
exponential
source strength

slug
continuous or
intermittent
release with
a constant
source
strength
2-D
cartesian
2-D
cartesian
Techniques specifically for wells also require well pumping or injection rate and
duration of the pumping/injection period.

     Despite some limitations, the analytical techniques are extremely useful 1n the
assessment of aquifer contamination from point sources.  Once the necessary input data

are collected, contaminant prediction can be performed quickly and easily.  The

algorithms can be programmed on hand-held calculators or micro-computers.  Once they
are programmed, contaminant predictions for a number of times and locations can be
generated quickly.  In this way, maps of potential aquifer contamination can be

prepared.  When numerical  modeling of a site is being considered, use of analytical

calculations can indicate whether there is sufficient contamination potential to

justify a major modeling effort and,  if so, where the data collection efforts for the
model should be concentrated.

     Given their ability to address many types of problems,  their relative ease of
application and low cost,  analytical  techniques offer potential  uses for a variety of
                                         -384-

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                          CONTAMINANT TRANSFER TO DEEP  WELLS
                                 (SEE SECTION 7.5.2)
Reference:

Objective:


Assumptions:
Equation:


where



and


     co
     c

     Q

     t
     H

     P
     B
Phillips  and  Gelhar (1978)

Compute  concentration as a function of time  in a deep well drawing water
downward  or upwards from a contaminated  aquifer or layer.

 •   uniform, radial flow in saturated media
 •   no dispersion
 •   no adsorption or decay of contaminant
 •   screened interval of well is short  (screen-length/depth ratio  less
     than 1/5)
 •   screen interval is located considerably below or above the base of
     the  contaminant zone

     £ ,
     c.
                     30t
                   4»HpB
                            or t
  average concentration of the  contaminated layer (mg/1)
  concentration at well screen  (mg/1)

  pumping rate of well  (m /day)
  time  (day)

  distance from contaminated  layer to center of screen (m)
  porosity (unitless)
  anisotropy ratio • K  /K  (unitless)

  saturated  hydraulic  conductivity in the  horizontal  and  vertical
  directions,  respectively (m/day)
    FIGURE VII-29
          SUMMARY  OF MODEL DESCRIBING CONTAMINANT TRANSFER
          TO DEEP  WELLS
                                      -385-

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                         SOLUTE INJECTION  WELLS:   RADIAL FLOW
                                  (SEE  SECTION  7.5.3)


References:   Hoopes and  Harleman  (1967), Tang and  Babu (1979)

Objective:    To determine contaminant concentrations for a given tine and location from
             a continuously discharging, fully penetrating  injection well.   Regional
             flow 1s negligible compared to flow induced by injection well.
Assumptions:
uniform, radial  flow in  a  confined aquifer
contaminant enters  the aquifer as a line source over the saturated
thickness of the aquifer at r « rQ
linear equilibrium adsorption of contaminant
first-order decay of the contaminant
concentration of contaminant at well is constant
                        c(r,t)


where                       ,
                           (rV2 -
                                     (* A\''      °     /          r\
                            V •  ¥ )             (tf • "•  r)
     r    *  radial distance from center of well (meters)

     r    *  radius of well casing (meters)
     t    •  time  (days)

     a    •  dispersivity of aquifer (meters)
     A    -  Q/(2*bp)
      *                                      2
     D    «  molecular diffusion coefficient (m /day)

     c    *  contaminant concentration in the aquifer  (mg/1)

     c    *  contaminant concentration in the injection well  (mg/1)

     Q    *  volumetric rate of injection by the well  (m /day)

     b    «  saturated thickness of the aquifer (meters)
     p    "  porosity of the aquifer (unitless)

     R^   «  retardation coefficient for linear adsorption  (unitless)
     k    «  total decay rate constant  for the  contaminant  (I/day)
      FIGURE VI1-30    SUMMARY  OF MODEL DESCRIBING RADIAL  FLOW  FROM AN
                         INJECTION WELL
                                       -386-

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       CONTAMINANT RELEASE ON THE SURFACE WITH 1-D VERTICAL, DOWNWARD  TRANSPORT
                                 (SEE  SECTION 7.5.4)

Reference:      van Genuchten and Alves  (1982)
Objective:      Compute solute  concentration as a function of  time and distance for a
               continuous surface  contaminant release  with subsequent  vertical,
               downward transport.
Assumptions:    •    uniform,  steady, vertical, downward flow
               •    first-order decay  and  linear,  equilibrium  adsorption of  the
                   contaminant in  the  aquifer
               •    constant  or first-order decay of the contaminant source at the land
                   surface
               •    one-dimensional  transport in unsaturated or  saturated media
where
               e(x.t)

                        «rf£
                         erfcf- ax/t  * -£=
     c   «  initial concentration of the contaminant  source  (mg/1)
     c   -  concentration of  the contaminant at a specified  time and depth (mg/1)
     v   »  seepage velocity,  positive vertically downward (m/day)
      5                                                    y
     Q   *  dispersion coefficient in the vertical  direction (m/day)
     x   «  vertical distance,  positive downwards (m)
     Rd  »  retardation coefficient for linear adsorption (unitless)
     k   *  total decay rate  constant for the contaminant in the aquifer (I/day)
     Y   •  decay rate of the  contaminant source at the land surface (I/day)
    FIGURE  VII-31
SUMMARY OF  MODEL DESCRIBING ONE-DIMENSIONAL,
VERTICALLY  DOWNWARD TRANSPORT OF  A CONTAMINANT
RELEASED ON  THE SURFACE
                                      -387-

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                  TyO-QIMENSIONAL HORIZONTAL FLOW WITH A SLUG SOURCE
                                 (SEE SECTION 7.5.5)
Reference:      Wilson  and Miller (1978)
Objective:      To  determine contaminant concentration  for  a given time and location for
               an  Instantaneous  discharge  from a fully penetrating  line  source.
               Contaminant transport is dominated by regional flow.
Assumptions:    •   uniform, steady regional flow in the x direction
               •   contaminant enters  the aquifer over the full saturated thickness of
                  the  aquifer at x • 0, y • 0
               •   linear, equilibrium adsorption of the contaminant
               t   decay of the contaminant in the aquifer  is first-order
               •   mass loading rate of contaminant is  Instantaneous
              c(x.y.t)
                            co°'
                      exp -kt -
                                                 40xtRd
where
      o
     0'
     b
     P
     t
initial  concentration of discharged contaminant (mg/1)
volume of contaminant being discharged (m )
aquifer  saturated  thickness (m)
porosity (unitless)
time (days)
dispersion coefficients (m /day)
seepage  velocity of  the regional flow (m/day)
spatial  coordinates  (m}
total  decay rate constant for the contaminant  (I/day)
retardation coefficient for linear adsorption  (unitless)
       FIGURE  VI1-32
           SUMMARY OF  MODEL  DESCRIBING TWO-DIMENSIONAL
           HORIZONTAL  FLOW WITH A  SLUG SOURCE
                                       -388-

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          TWO-DIMENSIONAL HORIZONTAL  FLOW WITH CONTINUOUS SOLUTE  LINE SOURCES
                                 (SEE  SECTION 7.5.6}
Reference:     Wilson and Miller (1978)
Objective:
Assumptions:
To determine contaminant concentration for a given time  and  location from
a continuously discharging,  fully penetrating line source.  Contaminant
transport  is dominated by the  regional flow.

   uniform, steady regional  flow in the x direction
   contaminant enters  the  aquifer over the full  saturated thickness  of
   the  aquifer at x • 0, y • 0
   linear, equilibrium adsorption of the contaminant
   decay of the contaminant  1n the aquifer is first-order
   mass loading rate  of contaminant is continuous and  constant over the
   time period of interest
                      c{x,y,t)
exp
                                  (EM-0
where
     W(-)   - the leaky well  function of Hantush
     B     « 20 /v
                         (unitless)

     a    « 1 + 2BR.k/v   (unitless)

     0     »   volumetric  rate of discharge of  the line source (m /day)
     t     • time (days)

     (x,y) » spatial  coordinates (m)
                                     2
     OX,D  - dispersion coefficients (m /day)

     v^    « seepage  velocity of the regional flow (m/day)

     p     - porosity of the aquifer (unitless)
     b     » saturated thickness of the aquifer (m)
     k     « total  decay rate constant  for  the contaminant  (I/day)

     Rd    » retardation coefficient for linear adsorption  (unitless)

     c     • concentration of contaminant being discharged  (mg/1)
     FIGURE  VI1-33
         SUMMARY  OF MODEL DESCRIBING TWO-DIMENSIONAL
         HORIZONTAL FLOW  WITH CONTINUOUS SOLUTE LINE
         SOURCES
                                       -389-

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 ground  water management  activities.   Analytical  techniques can be used to predict the
 migration  of plumes  and  to  determine  the  extent  of contaminant mixing 1n ground water.
 Four  specific questions  can be  addressed:   (1)  In what  direction will a contaminant
 plume travel  and  how will Us shape change  as  1t travels?   (2) To what extent will
 concentrations of contaminants  be  reduced as a result of dispersion,  sorption and
 decay?   (3)  How far  will the plume migrate  over  time?   (4) Where should  wells to
 monitor the  plume's  movement be located?
      Other applications  of  analytical methods  Include estimating "worst  case"
 concentrations at a  site as  a conservative  estimate of  a site's  hazard,  guiding the
 collection and analysis of  field data to test hypotheses,  checking the results of more
 sophisticated numerical models, determining design requirements  for pump tests and
 tracer  studies, and  designing and  evaluating the effectiveness of plume  control
 options.   Because analytical techniques are relatively  quick and Inexpensive  to apply,
 they  are useful in many  phases  of  ground water activities—facility siting and
 permitting,  site  inspection  and enforcement, monitoring, estimating the  extent and
 significance  of known contamination, and evaluating plume management  options. A
 reliable "worst case" evaluation of a known ground water contamination problem may show
 that  the site poses  little  near-term risk to the  public and that a low-level  monitoring
 program is an  appropriate management strategy.   Alternatively,  an  evaluation  may
 indicate significant health  or  environmental risks, 1n which case  Intensive monitoring
 and/or  use of  a sophisticated numerical model may  be warranted.
      An overall summary of analytical methods is given below:
        •     Provide quantitative  estimates of potential contamination at a specific
              lc-  :ion and time
        t     Require limited field data
        f     Predictions can be made quickly using hand calculators
        •     Require simplifying assumptions
        •     Cannot handle complex field conditions.
 In the  remaining  portion of  Section 7.5, the five  analytical models are  presented along
 with  worked out examples of  their  use.

 7.5.2  Contaminant Transport to Deep Wells
      Many  regions of the country obtain their freshwater supply  from deep well systems.
 However, many  of  these deep wells are now in jeopardy because of the contamination of
 shallow ground water aquifers from cesspools, septic tanks  and overuse of crop and lawn
 fertilizers.    Subsurface sanitary disposal  systems discharge wastewaters high in
nitrogen and  bacteria to the unsaturated zone.   Nitrogen and pesticides from
fertilizers and herbicides  may  migrate to the saturated  zone where water-supply wells
may intercept them.  Our objective  is  to predict  the increase  in contaminant
concentration at a water supply  well  and to  determine  how long  it would take  for  a
                                         -390-

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specified concentration to be reached.  Phillips and 6elhar  (1978)  presented  an
equation for solving these types of problems.  The Phillips  and  Selhar  equation  is
appropriate when the well  is either far below the existing contaminant  zone or  far
above the contaminant zone.  One other restriction is that the length of the  well
screen must be less than about one-fifth of the well depth.  The flow to the  well can
then be represented as three-dimensional radial flow as shown 1n Figure VII-34.
     For the example shown in the figure, there 1s an unbounded radial flow system with
a contamination zone initially a distance H above the center of the well screen.  The
equation to represent the movement of the contamination zone is based on fluid
displacement in a homogeneous anisotropic porous medium.  The effects of dispersion are
not included in Phillips and Gelhar's equation.  However, Hoopes and Harleman (1965)
have shown that dispersion is a secondary effect in such local flow systems.
     The analytic solution for the contaminant concentration at the well screen as a
function of time is given by:
                                              - T"1/3))/2                     (VII-59)
where

                                            30t
                                         	T-                              (VII-60)
                                          4fHJpB
or


                                     t -  ^3^  T                           (VII-61)

and where
        c(t}  • concentration at the well  (mg/1)
        c     - average concentration of the contaminated zone (mg/l)
         0                                          •>
        Q     • constant pumping rate of the well  (m /day)
        t     • time (day)
        T     « dimensionless time (unitless)
        H     « distance from the contaminated zone to the  center of the screened
                interval of the well (m)
        p     « effective porosity of the  saturated portion of the aquifer (unitless-
                decimal  fraction)
        B     - anisotropy  ratio of the aquifer -  K^/K  (unitless)

        Kx'*z * saturated hydraulic conductivity in the horizontal and vertical
                directions, respectively  (m/day)
                                         -391-

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    FIGURE  VII-34
SCHEMATIC  OF FLOW TO A  WELL  BENEATH A CONTAMINATED
ZONE
     Equation VI1-59 has been solved  for  various values of T.  The results  are  shown  in
Figure VII-35.   Equation VII-60 and VII-61  can be solved to answer several  questions:
        •    When will shallow contaminated ground water reach a deep pumping well?
        t    When will the percentage  of  the contaminant concentration in the well
            exceed a given value, say 20 percent?
            What is the effect  of  changing the pumping rate?
                                        -392-

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    o.s
     .3
c/c.
T«k
t/C»
.0
.0001
.0005
.001
.004
.01
.OS
.1
.IS
.2
l« 1
T
1.
1.0004
1.0030
1.0060
1.030*
1.0*75
1.3717
l.tS31
I.91S4
4.WH
                                    TltXMtNSWHUSS IIME)
      FIGURE  VI1-35   NORMALIZED SOLUTE CONCENTRATION vs.  DIMENSIONLESS  TIME
                                                     -393-

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                                •-EXAMPLE  VI1-4
     The nitrate concentration  in a town's ground water has  been  increasing  for    |
     the last several years.  The following  Information is available.   A            j
schematic of the problem is shown in Figure  VII-36.                                 j
     The aquifer is unconfirmed with fine to •tedium grained quartz sand  deposited
originally as. sand dunes.  The storage coefficient is about 0.2 and the ratio
of the horizontal to the vertical hydraulic conductivity 1s 10.  This anlsotropy    '
is caused by localized cementation and horizontal bedding in the dunes.  The        I
municipal well is pumping 3000 m /day.  The  lower tip of the municipal  well         |
screen is located 50 meters below the surface of the land.  The well is screened    j
over 4 meters.  Analysis of the water samples showed that the municipal well had    j
a nitrate-nitrogen concentration of 7.2 mg/1 on January 1, 1984.  A series of
shallow monitoring wells indicated that the upper part of the aquifer has an
average concentration of 26 mg/1 of nitrate-nitrogen and that the zone of           •
contamination extends down to 20 meters below the surface of the land.              I
     The city council wants to know when the nitrate-nitrogen concentration in      |
the community well will equal or exceed 10 mg/1 (the primary drinking water         |
standard).                                                                          j
     The steps required to answer this question are given below:                    j
                                                                                    i
     1.  Determine the current dtmensionless  time,  T , where c/c  •                 }
         (1 - TQ"1/3)/2 « 7.2/26 • 0.28
         From Figure VII-35 we find that TQ « 11.7.                                 j

     2.  Determine the dimensionless time when the well concentration equals 10     1
         mg/ 1 :                                                                      j
         c/co - (1 - TlQ')/2 « 10. /26 - 0.38

     From Figure VII-35 we find that TIQ • 72.3.

     3.  Real time is related to dimensionless time by Equation VII-61:
         Hence, the estimated time when the concentration at the pumping well
         reach 10 ing/1 is given by the difference between t.  and t  :
                                     -394-

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         FIGURE  VI1-36
SCHEMATIC  OF EXAMPLE  PROBLEM FOR  FLOW
TO  WELL  FROM A  SHALLOW CONTAMINATED
ZONE
    Calculate  H and then substitute H,  p,  B, 0, TQ and TIQ into the above
    equation.  Note that H and Q must b« expressed in the same units.   Also
    note that  H is measured as the distance between the center of the  well
    screen  and the bottom of the contamination zone.  In this example, H
    « (50-20-4/2) • 28 meters.  The data can now be tabulated as follows:
    H - 28 meters
    B « 10
p - 0.2
Q • 3000 m3/day
    Substituting the above data into the  expression for t.Q-t , results  in
    the following:

    (tin-tJ '
                             3(3000)

            « 3715 days » 10.2 years
Hence,  the  concentration of nitrate-nitrogen  is expected to reach 10 mg/1  in
the municipal well in about ten years.
                   •END OF EXAMPLE  PROBLEM  VI1-4 -•
                                    -395-

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7.5.3  Solute Injection Hells:  Radial Flow
     Because of the Interest  In underground  Injection, the  following  analyses  will  be
presented to show how Injection wells can be modeled analytically.  With  the model
given below, the concentration of solute from an Injection well can be predicted as  a
function of time and space.  This Information can then be used to estimate the  Impact
of an Injection well on the ground water quality.  A schematic view of a  typical
Injection well 1s given in Figure VII-37.
     Both shallow and deep wells have been used for Injection of waste Into subsurface
strata.  Storm water, spent cooling water, and sewage effluent have been  Injected
through relatively shallow wells.   Sometimes these wells are completed in the
unsaturated zone; however, they often penetrate the saturated zone and thus
contaminants are discharged directly Into the ground water.   In addition, large volumes
of brine produced by chemical Industries, geothermal energy production, and other
sources have been Injected through deep wells Into saline-water aquifers.  Adds, spent
solvents, and plating solutions containing heavy metals have also been Injected.
     The following assumptions will be made concerning the Injection well system to
permit the analytical solution given below to be used.  A solute with a constant
concentration c  w11l be discharged at a constant rate Q Into a homogeneous, non-leaky,
isotropic aquifer.  The aquifer 1s assumed to be confined by two parallel. Impermeable
formations and spaced a distance "b" apart.  The Injection well 1s screened over the
entire thickness of the confined aquifer.  The density and viscosity of the injected
solute are the same as those of the native water In the aquifer.  There 1s negligible
regional flow in the aquifer and the flow field near the well 1s dominated by the waste
being discharged. A schematic view of the problem is given 1n Figure VII-37.
     The seepage velocity, v  , at any specified radius from the well can  be computed
from the continuity equation:

                                     0 • Zirbv$p                              (VII-62)
where 0  is the volumetric rate of Injection by the well (m /day), r 1s the radius to -a
point in the aquifer measured from the center of the well (m), b 1s the saturated
thickness of the aquifer (m), p is the porosity of the aquifer (decimal percent,
unitless), and v$ is the radial seepage velocity of the fluid from the well (m/day).
     The seepage velocity can thus be expressed as:

                           vs • *  with A • Q/(2*bp)                          (VII-63)
                                         -396-

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                               ?L
                                                 CONFINING STRATA
                                      RADIUS
                                                  of
        FIGURE VI1-37    SCHEMATIC VIEW OF A WELL  INJECTING SOLUTE
                           INTO  A CONFINED  AQUIFER
     The governing equation  describing the spatial and temporal distribution of  a
dissolved substance introduced  into the saturated zone is:
                                                  - kcR
(VII-64)
                        Q ic^L     s vf   T* <9r"  r 
-------
                        C(P.T) • CQ expj—5-^- kT|C *ff(s)f                 (VII-66)

where t'^w is the inverse Laplace transfers operator and f(s) is the Laplace solution
to Equation VI1-64:

                                                  (KM * 1/4)]
                                                  •-*-	—-J-              (VI1-67)
where s 1s the transformed variable of time; A^[:] is the Airy function; k  is the
dimensionless decay rate, where k « kta2; ris the dimensionless tlwe, r« t/(Aa );p
is the dimensionless radial distance from the center of the well, P- r/ct; and PQ is
the dimensionless radius of the well casing, pfl * rQ/tt.
     Equation VII-66 has been solved analytically by Tang and Babu (1979) but their
solution involves integrating four different types of Bessel functions of fractional
order (order 1/3) over three different integrals.  Alternatively, one can numerically
compute the Laplace inverse of Equation VII-66 by the Stehfest algorithm (Moench and
Ogata, 1981).  However, if one uses Equation VII-67 in the numerical  inversion, a great
deal of care must be used in computing the Airy functions to avoid numerical roundoff
problems in the solution.
     Because of the difficulties in obtaining numerical values from Equation VII-66,
several authors have suggested approximate solutions.  The method of  Raimondi e£ aj.
(1959) assumes that at some distance from the source, the influence of dispersion and
diffusion on the concentration distribution are small in comparison to the total
dispersion that has taken place up to that po^nt.  Thus the spatial gradient on the
right-hand side of Equation VI1-64 is ignored and is substituted by the temporal
gradient:
     The solution to this approximation  was  originally  given  by  Tang  and  Babu  (1979)
Their solution has been modified to allow for  retardation  and is shown  below.
                           c  "  co
                                  -••-•-0'

where erfc(:)  is the complimentary error  function (see  Appendix  J)  and
                                        -398-

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                           a0«  ^	S*-*u                               (VII-70>
                                                                              (VII-71)
When the radius of the well casing, rfl, 1s negligible, then erfc(a0) 1s set equal to 2
and Equation VII-69 reduces to:
                                 erfc(a) exp      - - *-                     (VII-72)
Equation VII-72 1s the same as Hoopes and Harleman (1967)  when k • 0 (i.e., the
exponential term drops out).  Equation VII-69 and VII-72 satisfy the boundary
conditions c * c  at r • t  and c • 0 at distances far from the well but they do not
satisfy the Initial condition c « 0 at t • 0 near the well.   Equations VII-69 and VII-
72 predict a finite amount of mass In the media at t « 0.   However, Equations VII-69
and VII-72 are approximately true away from the immediate  vicinity of the source.
Hoopes and Harleman (1965) carried out an extensive series of laboratory investigations
in a sand-filled box and concluded that Equations VII-69 and VII-72 are a good
approximation of dispersion 1n radially diverging flow for distances larger than
20 particle diameters from the well.
     A table of the complimentary error function 1s given  In Table J-l of Appendix J.
                                    •EXAMPLE  VI1-5
        A local  electronic  component  factory,  called  "The  Chip  Works',  was  recently
   constructed in town.   It produces  electronic  circuit  boards  and  micro chips.   As
   part of the manufacturing process, various  acids are  used  to etch  and plate  the
   electronic circuits.   These  acids  leach  various heavy metals,  including  cadmium
   from the metal components and hence must be disposed  of.   Because  of the high
   toxicity of the plating  waste,  the local sewer authority will  not  allow  The  Chip
   Works to discharge  Its waste into  the  domestic sewer  line  without  pretreatment.
   After much negotiation,  it was  finally decided to  inject the plating waste
   directly into a deep  aquifer.   The following  analyses were done  to determine  If
   solute injection into the aquifer  would  allow the  drinking water standards to  be
   met in the aquifer  without pretreatlng the  plating waste.

                                         -399-

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 I       The sandstone aquifer 1s about 30 meters thick.   It  1s  confined  above  and
 |  below by impermeable shale.  The aquifer lies about 300 meters  below  the  surface
 j  of the ground.  The velocity in the aquifer 1s negligible.   The plating waste is
 j  to be Injected at a volumetric rate of 550 m /day through a  well screened over
 '  the entire depth of the aquifer.  The casing radius 1s 0.1 meters. The plating
 •  waste contains an average concentration of 50 ug/1 of cadmium and has a pH of
 .  about 5.5.  The dispersivity of the sandstone 1s about 50 meters, the effective
 I  porosity about 0.2 and the molecular diffusion coefficient about 8.7 x 10"
 I  m /day.  The cadmium concentration 1s below solubility limits.  To be
 |  conservative, adsorption is assumed to be negligible,  thus the retardation factor
 j  is set equal to 1 (see Equation VII-55 of Section 7.4.2.1.1).
 j       The injection well is located 1n the center of the property of The Chip
 •  Works and the nearest property boundary is 450 meters  away.   The local pollution
   agency has specified that the cadmium concentration in the aquifer never exceed
 !  10 ug/1 at the property boundary.   It is known that the background concentration
 I  of cadmium is negligible.  A series of monitoring wells have been installed at
 |  the property boundary to verify compliance.  Will the  standard be exceeded and if
 I  so, when?  A schematic of the above problem is given in Figure VII-38.
 j       He want to know when the cadmium concentration will  equal or exceed 10 ug/1.
 •  The data can be summarized as follows:

I           r   • 0.1 m                           R. • 1
             o                                     d
I           r   • 450 m                           k  • 0/day
|           o   • 50 m                            b  « 30 m
j           0*  « 8.7 x 10"5 m2/day               p  - 0.2
j           Q   • 550 m3/day                      CQ • 50 yg/1

        The only missing variable is  time,  t,  which  can be estimated.   The well
.  casing radius rQ is  negligible in  comparison to  the distance of interest,  r, and
J  time t is not extremely short (i.e. less than  0.001  days), so Equation VII-72 can
I  be used (i.e.,  erfc(aQ) « 2).  This expression is first solved for  "a":
I
j           erfc(a)  • 2c/cfl • (2>(10}/50 «  0.4

•  Interpolating the complimentary  error  function in Table J-l  of Appendix J, one
.  can see that the  above  corresponds  to  a  value  of  a » 0.59.  From Equation  VI1-71,
'  one can solve for time  as a function of  'a':
                                         -400-

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=H= J~£I^
/X^ii C^ "SK"01"
*••*»•!•**• »»•*»•
:'/-'-'.--.'--:-'.'-.'
•/•':.:V.V.:.:'.: -"•'-•.'
• :-•:••:••:••:•/
•.'•'.•/•'.•/•V.'-V.V.V
»»*» ,*• * * * » ^ » •*•
.",.* »•*»**• »*»»
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'•/.•.-.'•'.••.•!• "'.•••; :•'.•'.'•.• '•'••'
• :: ;: :.•:.••'.• :».'.-'•' •'•;•;'•

a
M
• *'»•*»•••*•**'»** •**%**»**«**«"'^'*t'*H**«* '»**»"•,
' •'••'••'. •'*•'* ••*"•"*"!. '.'•'••'. '••'." ,"••"•• '"''"'••
' "1' 'I*'"'.*''* "1 "'*"'''?• '*"Z "*"'."', ••'.'•'.••'••'*
»•*••**•»* *»*'.*'***»*****«*'r*'t* *•*"*"***"***»****•
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• •*••*• *t*'»****'t*****»*****»**»***"*»**" *•*»»*•*"••
*,.*•, "•*l'"%********»**«'*»**t*'"**'*'"***'<**'***%
.'.':'.'•:.'•;.'';''••'•'•:•'•''•'••'•'•:•'• aoimif mi SHALE .'.';V
•'.?•'
•'•V-.i-
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• iv'-::.':^v • •••: 'V^;i->;'V--::':^ :'-;>-:'- •**<»ro»i« >v;:i:
v?^/®:^-? ^ !• ^'^^ ^^^ •v:^-''-/:
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MONTTOAlNC
wfu
*•; x
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» * *
* » •
K>* ; .'
•. *. "'.'* *- .'•'•'.
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'«••*.• ^ ••-
•'••,'••••-••'. •".'.'•' •'•"•'.'•'.'•'."•"•''•" ^ •'• ' •• ' •'- • •'• ••".•."'•'*'•"•'," -V '•"•"'•'* 1"! •*• '•'•'•'
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FIGURE VI1-38   SCHEMATIC OF THE EXAMPLE PROBLEM SHOWING RADIAL
                FLOW OF PLATING WASTE FROM AN INJECTION WELL
                              -401-

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I   where                                                                                !
i                                                                                        !
j                                      A - Q/{2»bp)                             (VII-74)  |
i                                                                                        i
   Upon substitution of the data Into Equations VII-73 and VII-74, we can solve  for     :
!   time, t.  Thus:                                                                      ;
I                                                                                        I
                                                                    Vfr
                 (1)(4SO)2   (0.59) /4(50){450)3 ^ (8.7xlO"5)(450)4\
                 2{l4.6)  " (14.6) \I                        14.6 /
              • 3780 days or about 10 years
   Hence, the cadmium concentration will equal 10 ug/1 at the monitoring well after
   about 10 years of continuous injection.  It appears from the calculations that
   pretreatment of the waste will be necessary prior to disposal.
                                END OF EXAMPLE YII-5 ••

                               — EXAMPLE VII-6	
        This example problem considers another metal, zinc, which is present in
   smaller quantities in this waste.  Zinc is weakly adsorbed at a pH of 6.0.  The
   adsorption coefficient K. for zinc is about 2 ml/g at a pH of 6.0.  The bulk
   density, Pfc, of sandstone is 2.3 g/ml.   Hence, the retardation factor for linear
   equilibrium adsorption can be calculated using Equation VII-55.
        Calculate the concentration of zinc at the property boundary after 3780
   days.  Assume the waste has been pretreated to a pH of 6.0.   The data can now be
   summarized as follows:
             o
     0.1 m                       pfa « 2.3 g/ml
r  - 450 m                       p  « 0.2
a  - 50 m                        Q  - 550 m3/day
0* • 8.7 x 10"5 m*/day           b  • 30 m
            K^ « 2 ml/g                      c   « 5 mg/1
            k  » 0                           t   • 3780 days

        Step 1.  Calculate the retardation  coefficient  using Equation  VII-55:
                                         -402-

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I         Step 2. Calculate A using  Equation  VII-74:
j               Q        550
                                   14<6
                     2i(30)(0.2)

        Step 3. Calculate "a"  using  Equation VII-71:

                                           - (14.6)(370)
             „ ~T°^V'
             |j «r  .-,
                                                        )
                                                 12«J_^	.  30.5
                                   /4(50)(450)3 « (8.7xlO~5) {450)4\
                                   (l                  TTT^T       I
        Step 4. Calculate erfc(a)  {see Table J-l of Appendix J):
            erfc(a)  - erfc(30.5) »     0
        Step 5. Calculate c:
            c . ^ erfc(a)  -    (5)(0) - Q mg/1.
I
|   Hence, the zinc concentration will be zero at the property boundary after 10
j   years.   The difference between  the behavior of cadmium and zinc 1s due to
|   sorption.  Without sorption, cadmium moves with the same velocity as does the
   injected water (I.e.,  the  seepage veil
!   times slower than the  injected water.
   injected water  (I.e.,  the seepage velocity v ).  With adsorption, zinc  moves  24
                                                                                      I
                               END OF EXAMPLE VII-6	'
7.5.4  Contaminant  Release on the Surface with 1-D Vertical  Downward Transport
     A surface  release  of a contaminant can be treated in many instances  as  a one-
dimensional  flow problem with the contaminant moving vertically downward  through  the
soil as shown in Figure VII-39.  This case can be greatly simplified by considering the
velocity,  moisture  content, retardation and dispersion coefficient as constant  over a
given depth.   If the  soil has several distinct layers, calculations can be performed
for each layer  separately.  Flow can occur through either saturated or unsaturated
soil, as long as the  moisture content is assumed to be a constant throughout the  soil.
     To understand  how  the analytical method may be used, the governing equation  should
be briefly reviewed.  The equation describing one-dimensional advective transport with
dispersion,  adsorption  and first-order decay is as follows:
                                                  - kcRd                     (VII-75)
                                        -403-

-------
                 Iftraaagxart
                       o: o
                      0  0 0
                     9-
                         T
f net rate of
    mass
fmass flov>
    by
f^
\
^
                                mass
                                   by
       R
       R
                     d2c
rmass depletion^
     by
.   reactions  ,
              Wast* Pon
-------
 where
         c    «  concentration  of  contaminant  In  the  soil  solution  (mg/1)
         v    •  seepage  velocity,  positive  downward  (velocity  of fluid  flow through
                Interstices  of the soil)  (m/day)
         t    •  time  (days)
         x    -  distance down  the  soil  (positive downward)  (m)
         D    »  dispersion coefficient  of the contaminant  1n solution  in  the soil  (m
                /day)
         R,    »  retardation  factor for  linear, equilibrium  adsorption  (unitless)
          o
         k    -  first-order  decay  constant  of the  contaminant  in the aquifer (per  day)
      The terms  in Equation  VII-75 from left  to right represent the time  rate of change
 in  the  concentration of the contaminant, transport  due to  dispersion,  transport due  to
 advection,  and  last, a  term accounting for adsorption by the  soil matrix and chemical
 reaction (Figure VII-39).
      As presented in Equation  VII-75,  the  first-order decay rate, k, assumes that
 solute  in its liquid and solid phases  decays at the same rate {i.e., k •
 k   I1d).  The  liquid phase refers to solute  1n the aqueous phase and the solid phase
 refers  to solute that has been adsorbed.  If the liquid and solid phase decay rates
 are not the  same, the following substitution needs to be made:
                                             kso1id b*d
                                                                              (VII.76)
wnere Kd  Is the distribution coefficient (unitless) for linear, equilibrium sorption,
P&  is the soil bulk density (g/ml) and 8 is the volumetric moisture content (unitless
fraction).
     The  initial concentration of the contaminant is assumed to be zero in the soil
solution:
        c(x,t) » 0   for xiO and t » 0

     At the upper boundary,  x  » 0, the concentration of  the  contaminant  (source)  is
either held constant or allowed to decrease exponentially  with  a  rate  constant  >  (for  a
source concentration which does not change  with  time,  setY-0):
        c(x,t) • c e~n   for  x « 0   and  t >  0
     At large distances from the upper boundary, both  the  concentration  and the
gradient of the concentration  become negligible:
          c, — •  0  when  x  is very large and t > 0
                                         -405-

-------
     Equation VII-75 can be solved with the above Initial  and  boundary  conditions by
 either the  Integral transform or Laplace transfer* techniques.  A  solution  1s given by
 van Genuchten and Alves (1982) as:
                     ,.„. -f. if • '}{,•
                                    (•"•*)!
c(x,t)  • ^. e ?v       f  fe "u erfc ( -t^t * -^|*         (VII-77J

             erfc
where
        erfc(:)  «  the  complimentary error function (Appendix JJ.

|	EXAMPLE VII-7	
        A farmhand  has  just finished spraying a field of potatoes with the
   insecticide endrin.   He then returns the spray rig back to a livestock water well
   where he washes  out  the spray tank.  After carefully hosing out the Inside  of  the    ;
   spray tank with  fresh water, he opens the tank valve and allows the rinse water      I
   to run out on  top  of the ground.  A total of about 0.5 m  of rinse water             |
   contaminated with  endrin drains and forms a pool about 10 m  in area.  This pool     |
   takes about four hours to  seep into the ground.  Upon draining the spray tank,       j
   the farmhand drives  back to the ranch.                                              j
        When the  farmhand tells the boss of his activities, the boss becomes
   furious.  Apparently, the  well used to clean out the spray tank is also used to      !
   water the milk cows.  If endrin contaminates the well and then the cows, the cows    {
   may have to be destroyed.  The boss, his son, and the farmhand quickly drive out     I
   to the well site.  The son has recently completed a course in contaminant            |
   transport and  wants  to try out some of his new knowledge.  Along the way, the  son    j
   explains to his  father he  thinks a one-dimensional model of contaminant transport    j
   with a constant  surface concentration would be sufficient to model the spill.
   The analytical method would predict the contaminant concentration for any depth
   and time.  To  use  the method, the following parameters would have to be              j
   calculated: vertical pore-water velocity, dispersion coefficient and retardation    I
   factor for linear, equilibrium adsorption.  Upon arriving at the well site, the      |
   following information 1s estimated from well data and their experience 1n farming    j
   the area.  A schematic of  the example problem 1s shown 1n Figure VII-40.  Data       '.
                                        -406-

-------
           FIGURE  VI1-40    SCHEMATIC  OF EXAMPLE  1-D  PROBLEM
are listed below:
         Soil  type:   silty  sand with gravel
         Soil  fraction  silt and clay
         Percent  organic  carbon in sand
         Percent  organic  carbon in silt and clay
         Soil  bulk density
         Volumetric  moisture content
         Dispersivity coefficient
         Saturated hydraulic conductivity
         Depth to water table
         Decay rate  in the soil
         Decay rate  of the source
         Time  since  start of spill
         Contaminant
         Partition coefficient
sat
9
a
K
x
k
y
t
endrin
0.1
0
0.10
1.8 g/ml
0.15
0.22 meter
 0.5 m/day
2 meters
0/day
0/day
1 day
                                     -407-

-------
I              for endrln  1n  octanol-water                  K^ « 4 x 10
j            Surface  concentration  (rinse water)            CQ  • 200 ppb
j        To calculate the  retardation factor R. for linear, equilibrium  adsorption,
1   one must first calculate  the partition coefficient K  using Equation 11-17  and
•   11-18:

I            Kp "  *oc(0'2(1'f)Xoc * fXoc)

            Koc * (°-63M4 * l°5) m 2-5 x 1(j5 ml/8
!            K   «  2.5  x 105(0.2(1-0.1)(0) * (0.1)(0.1))  -  2500  «l/g
I            P
i   Therefore,
                                   30001
   One next  needs to compute the vertical  Darcy velocity and then the vertical
   seepage velocity.  For the case of a large spill  into unsaturated medium, the
   following procedure can be used to estimate the Darcy velocity:
v
Y
                                             Sp1T?              fn/dav)       fVII-78) I
                                                               l"¥aaJr'       lfil f0>
                                .
                 d   {area of spill) (time to completely drain)
                                                                                     I
   Substitute the above data Into Equations  YII-35  and VII-78 to get:                 j
            vd
           •.-8*-'
I
I        To  calculate tne dispersion coefficient,  dispersion  is assumed to oe a         i
j   linear  function of the seepage velocity and molecular diffusion is                  I
j   considered  to be negligible (Equation VII-47).  Thus:                               j

I           0  • ovs  (m2/day)                                                         \
.   where a  is  the dispersivity coefficient (meters).
j        Substituting the data yields:                                                  f
I                                2                                                     I
'           D - (0.22) (2)  •  .44 mVday
I                               '                                                     I
j       The concentration  of  endrin  as a function of time and depth  can  be              j
•  calculated from  Equation VII-77.  Upon  rearranging terms,  Equation VII-77
.  becomes:
I                                                                                     I

1                            cfle"xVAi             s         \                       !
I                   e(x,t) •  -J-    Ie  l  erfc(A2)  *  e J erfc(A4)l             (VII-79)   |
                                        -408-

-------
   where

                                        X  S  o.u                           tvr i an\  '
                                  Aj  -V-Zab                           (VI1-80) .'
                                  A2 •  -aVT+ -7--                      (VI1-81)  I
 j                                                                                 I
 !                                 A3 • jjji * 2ab                          (VII-82)  !
                /             ,2      V
           a  - ( 0-0 +  . ^	.,..,_     I  » o new
                \u  u    (30001M4)(0.44)/    u'uus

           >-l(^)*     -2"
           Al •  (ffiu^) - (2)(0.009)(261)  - -0.15
           A, •  -  0.009VT* *^L  - 261
            2                VT

           A3 "  (ffiu^) * (2)(0.009)(261)   - 9.2
I           A. -  0.009VT+ ^g_  . 260
j                           vr
I   Hence,
I
 |                                 A4 -   aVt+ ^_                       (VII-83)
 I
 I  and where a and b are  as defined previously 1n Equation VII-77.
 |       For this problem, the concentration of endrln at the water table  (I.e., x *
 i  2 meters) 1s needed for a time period of one day since the spill started (i.e., t   j
 j  • 1 day).  The data needed for this problem are sumnarlzed below:                   j
 j          0   • 0.44 m  2/day               CQ - 200  ppb
           v$  • 2 m/day                   FL • 30001
 !          x   • 2 m                       k  - 0/day                              !
 I          t   - 1 day                     X  • 0/day                              I
 j                                                                                 !
 j       Substitute all of the data Into Equation VII-79 to get:                        j
                                      -409-

-------
                e(2tl,     .     e
    but
                erfc(261)  - 0
    Thus
                c(2.1)     • 0 ppb
        The model  predicted concentration of endrin two meters down and one day
   after  the spill 1s essentially zero.   Why?  Because of the extremely high
   retardation due to adsorption of endrin onto the soil particles.
L	END OF  EXAMPLE VII-7
7.5.5  Two-Dimensional Horizontal Flow With A Slug Source
     The previous three analytical models only considered one-dimensional flow.
Methods for two-dimensional flow will now be introduced.  The first 2-0 model that will
be considered calculates the concentration of a contaminant downgradient of the source.
The waste is considered to have been instantaneously discharged at a point.  The
resultant concentration 1n the aquifer is assumed to be uniform with depth at the point
of discharge.  The depth of mixing can be less than the full depth of the aquifer 1f
the contaminant is thought to be only in a particular part of an aquifer.  Vertical
dispersion is usually small as discussed earlier in Section 7.4.1 on dispersion.
Hence, only horizontal variations can be considered.  Such an Instantaneous discharge
is also called a slug source and can be caused by leaky ponds or tanks or by spills.
Instantaneous means that the duration of the discharge is very short compared to the
time since the discharge.  An analytical solution will be given below to model this
problem.  The solution can be used to answer the following questions:
        •    What is the maximum concentration of contaminants likely to be at a
             downgradient well?
        t    When does the concentration of contaminants at a downgradient well exceed
             a particular value or become negligible?
        •    At what distance will the concentration of contaminants remain at
             negligible concentrations?
        •    What is the approximate areal extent of the contaminant plume?
     Before the analytical model can be given, several additional assumptions need to
be stated.  These are as follows.  The saturated thickness of the aquifer is assumed to
be uniform and the hydraulic properties of the aquifer are relatively homogeneous.  The
density and viscosity of the Injected solute are the same as those of the native water
in the aquifer.  The regional flow in the aquifer is uniform and horizontal.  The
effect of the source on the seepage velocity is assumed to be negligible compared to
the uniform regional flow rate.
                                         -410-

-------
      The mass transport equation governing advection,  dispersion, first-order decay and
 linear, equilibrium adsorption 1n two dimensions in the aquifer for the above case is:


                •a ft * •, S • •
                                   a.         y

 The last term on  the right  side of Equation VI1-84  represents  the instantaneous
 discharge of mass at location x«0, y*0.   The fr{:)  represents  a  Dirac delta  function
 and m'  is the strength of the discharge,  where m1 - c  Q'/b  (i.e., the mass of
 contaminants injected divided by the thickness of the  aquifer).   A schematic  of  the
 problem is shown  1n  Figure  VII-41.
      As presented in Equation VII-84,  the first-order  decay rate, k, assumes  that
 solute  in the liquid and  solid phases  decays  at  the same rate  (i.e., k  «  k,,   id •
 k   iid)-   The liquid phase  refers  to solute in solution and the  solid phase refers  to
 solute  that  has been adsorbed.   If the liquid and solid phase  decay rates are not  the
 same, the k  value is corrected using Equation VII-76.
      The solution to the  equation  shown in  Equation VII-84, with  a zero initial
 condition and zero gradient  at large distances,  can be  found by means of  the  integral
 transform or Laplace transform techniques:

                              C00'           /     (xR  -v t)2
                                                                               (VII-B5)
where

        c     • initial concentration of contaminant being discharged (mg/1)
        Q1    « volume of contaminant being discharged (m )
        b     " saturated thickness of aquifer (m)
        p     • effective porosity (decimal percent, unitless)
        t     « time (days)
                                                                              2
        D ,0  « dispersion coefficients in x and y directions,  respectively (m /day)
         x  y
        v     « seepage velocity of the regional flow in the x  direction (m/day)
        x,y   « location of point of interest (m), where the source is located at x-0,
                y-0
        k     » first-order decay constant of the contaminant in the aquifer  (per day)
        R^    » retardation coefficient for linear, equilibrium adsorption (unitless)
Equation VII-85 is similar to the solution presented by Wilson  and Miller (1978)  but
linear, equilibrium adsorption has been added.
     The maximum concentration at any specified location occurs at time t   .   This
time is computed as:
                                         -411-

-------
          LOCATION
           Of LINE
      FIGURE VIMl    SCHEMATIC  SHOWING  A SLUG DISCHARGE  OF WASTE
                         INTO  A REGIONAL FLOW FIELD
(82-4AC)*)
                                                    /(2A)
where
                                             * v2Dy)
                                                                            (VII-86)


                               A »  (UD D R, * v'O )                        (VII-87)

                                                                            (VII-88)

                                                                           (VII-88a)

     Hence,  to calculate the maximum concentration that will occur at a point  (x,y),
substitute t(wx for t 1n Equation  VII-85.
I	EXAMPLE VII-8
        Consider  the problem of an accidental  spill  Inside a chemical warehouse  1n
   which a storage  drum of cMoromethane (methyl  chloride) leaks Into an Industrial
   sewer.  The Industrial sewer discharges Into an Injection well that 1s screened
   over the entire  saturated thickness of the  sandstone  aquifer.  About 0.1 m  of
                                        -412-

-------
1   chloromethane enters the aquifer at a concentration of 1600 mg/1.  The sandstone    "
I   aquifer has the following properties:                                               I
            Soil fraction silt and clay                     f   « 0.01
                                                            'U
Percent organic carbon In the sand fraction     X*  - 0.01
            Percent organic carbon 1n the silt and
              clay fraction                                 XQC  « 0.05
            Soil  bulk density                               Pb  « 2.5 g/ml
            Effective porosity                              p   • 0.12
            Saturated thickness                             b   • 15 m
            Dispersion coefficient                          DX  -4m /day
                                                            D   » 1 m /day
            Seepage velocity:                               vx  « 0.3 m/day
   In addition, chloromethane has the following adsorption  and degradation
   properties:
             Octanol-water partition coefficient            KQw  - 8 (unitless)
             Hydrolysis rate  (at a pH of 7)                 KR   - 0.0021  per  day
        At a distance of 35 meters downgradient of the injection well is a domestic
   supply well.  Uhat Is the maximum concentration of chloromethane expected  to
   reach the domestic well  and when will  the maximum concentration occur?
        To answer these questions,  several  parameters have  to be computed.
   Chloromethane  undergoes  both adsorption  and degradation  in the aquifer.
   Adsorption is  related to the soil  properties as described by  Equation 11-17  and
   11-18.
        Upon substitution of the data into  Equations 11-17  and 11-18, one obtains
   the adsorption coefficient K  as shown below:
             KQC  - 0.63(8)  -  5  ml/g
              Kd  • (5)(0.2(1-0.01)(0.01)  *  (0.01H0.05))  -  0.012 ml/g
i
I        If we assume adsorption can be  described  by a linear, equilibrium model,
|   then the retardation coefficient for chloromethane can be computed using Equation
j   VII-55 as shown below:
             Rd «  1  +  (2.5)(0.012)/(0.12)  •  1.25  {unitless)                             j

        In  addition  to adsorption, chloromethane  1n the aqueous phase  is subject  to     '
   hydrolysis.   Adsorbed  chloromethane does  not undergo hydrolysis.  The relation       I
   between  the  general degradation rate and  the 1iquid/adsorbed phase  rates  is given    |
                                         -413-

-------
t   by Equation VII-76.  Thus for this problem, k^   ^ would  equal  the hydrolysis
|   rate and k  .^ would be zero.  Upon substitution of the data Into  Equation  VII
   76:
               0.0021
                                         Q.0017 per day
                       (1-25)

        All of the soil and chemical  properties can  now be  given  for  the problem as
   follows:
          x  «  35 m                  c0 •  1600 mg/1
          y  - 0 m                    0' -  0.1 B3
          b  « 15 m                   v  •  0.3 m/ day
          P  " 0.12
          Rd-l.25                    Ox-4
          k   -  0.0017  per  day          D  «  1 m /day                                    '

        The time at  which  the maximum concentration  occurs  can  now  be  computed upon     {
   substitution of the above data into Equation VII-86 to VII-89:                       I
                               ,                                                        i
          A     " (k4DxDyRd *  Vyl  "  C°-ool7)4(4)ti)(1.25) * (0.3)Z(1) - 0.124         j
          B     " (40xDyRd)  "  4(4)(l)d-25) " 20                                       j

I          C     - -(x20^  * y2Dx)Rf,  -  -   (35)2(1) *  (0}2(4)   (1.25)2 • -1914            !
i                                                                                      !
I          'max  " (" B *  (Ej2-  4AC)H)/2A)                                               I

I                -  (-20* ( (20)2- 4(. 124) (-1914)m  /(2(.124))  »  67.5  days           j
i                                                                                      !
j       Hence, the maximum concentration will  occur at the domestic  well  68  days        |
j  after the spill.  The value of the maximum  concentration is  computed by              j
•  substituting t    and the other data into Equation VI 1-81:                          j
     co0'
                cxp rkt«"ax" "wn — r --- vn. — r        (vn-89)
b4nptmax(D D )^                 x max  d
                        (1600)(0.1)
                                                                 V2  \
                                                                 . — r ]
                                                                 max d/
               (15)4ir{0.12)(67.5)
                                        -414-

-------
1              ff3Sm.g5H0.3H67.5)) 2      (  (0) (1.25) J2)
j            "    4(4)(617.5)(1.25)        "    4(lj(67.5)(1.25) /

!             • (0.0524)exp(-0.524) - 0.031 mg/1
j
I        Hence, the maximum concentration of chloromethane that will reach the
|   domestic well 1s 0.031 mg/1 or 31 Mg/1.  This concentration will occur at the
j   domestic well 68 days after the spill.
                                END OF EXAMPLE VI1-8-
.	EXAMPLE VII-9	
i
I        Consider a large electric power company that has a coal-burning plant that
j   produces electricity.  Its fly ash 1s deposited as a slurry waste Into a large
   lagoon where the ash 1s allowed to settle.  The lagoon site 1s above a 2 meter
   thick water table aquifer that consists of glacial outwash.  A layer of
   Impermeable clay lines the bottom of the lagoon.  A large river flows nearby.
        Next to the lagoon, the electric company has been preparing the ground for
   another lagoon when a bulldozer accidentally breaches the benn surrounding the
   lagoon.  Very quickly, about 40 m  of supernatant spill out and form a pool on
   top of the ground.   The supernatant percolates Into the ground after a short
   time.  The greatest concern to the company is the level of boron in the spill
   water, which had a  concentration of about 10 mg/1.  They want to know what the
   maximum concentration of boron will be where the aquifer discharges to the river
   and when this will  occur.   The downgradient distance between the spill site and
   the river is 50 meters.
        Since the area of the spill site is very small  compared to the area over
   which the contaminant will travel and since the duration of the spill was short,
   a slug source model is selected.  This model  assumes complete vertical mixing of
   the source in  the aquifer.   This  seems  reasonable  considering  the relative
   thinness of  the  glacial  outwash  aquifer.
        After an  investigation  of  the  problem,  the  following  information  is
   obtained:

                x   «   50  m               c   »  10 mg/1
               y   - 0 m                 Q1  -  40 m3
                b   « 2 m                 v   •  2 m/day
                p   » .15
                Rd  - 17                  Dx  -  15 m3/day
                k   • 0/day               D   •  5 m3/day

                                         -415-

-------
I   Step 1.   The  time  at  which  the maximum concentration  of boron will  reach the        \
*
|            river,  t     can  now be  computed  by  substituting the above  data into        I
t                   nlflX
I            Equation  VII-86  to VI1-89:                                                  |



J            A    «  (k4D  D  R, * v2D  ) -  (0)(4)(15)(17) *  (2)2(5)  - 20                    j
|                      A J u    * /                                                     I
i                                                                                       '

!            B    -  (4DxDyRd) -  (4)(15)(5)(17) - 5100                                    !
I                                          ».                                             I

j             C    -  -(x20  +  y2OJR? • -((50)2(5) * (0)2(15))  (17)2 - -3.61xl06          I
|                         y               \                   /                            .


i             Snax '  ('B * (82-4AC)S)/(2A)                                                j



j                 •  {-5100 *  ({5100)2-4(20)(-3.6xl06))V(2(20)J • 316 days.


!        Hence, 1t will take  about 320 days for the maximum concentration of boron to    !

I   reach the river.                                                                     I

i                                                                                        i
j   Step 2.   The value of the maximum concentration of boron tnat will reach the         j

•             river is computed by substituting the above data Into Equation VII-85:      •


1                         c0Q'                                                           1

i             Snax	:	1 exp(9)                                              I
            where
                   /.kt
                   \   ""
                 _/-(0)(316)-((50)(17)-(2H316))2
                         (10)(*0)exp(-.15) _    .       mg/1
•   The maximum concentration of boron that will reach the river is about 0.03 mg/1

!   or 30
I ------------------ EMD OF EXAMPLE VII-9
                                         -416-

-------
 7.5.6  Two-Dimensional  Horizontal  Flow With Continuous Solute Line Sources
      In Section 7.5.5,  the problem of  an instantaneous waste discharge is considered.
 In this section,  a continuous  waste discharge  into  a  homogeneous,  isotropic  aquifer
 will  be considered.   The contaminant is  discharged  continuously  and  uniformly  with
 depth into the aquifer.   The density and viscosity  of the discharged  solute  are  the
 same  as those of  the  native water  in the aquifer.   The effect  of the  discharging solute
 on the seepage velocity  is assumed to  be negligible compared to  the  uniform  regional
 flow  rate.
      The mass transport  equation governing  advection,  dispersion,  first-order  decay and
 linear, equilibrium adsorption  in  two  dimensions in the aquifer  is:

                                     2        2
                  Rd at *  vx a*  ' Dx ^T  * °y 5y2 •  kRdc + SL   P                (VI1'90)

 The last term on  the  right-hand side of  Equation VII-90 represents the  instantaneous
 discharge  of  mass  by  a well  screened over the  entire  depth of  the  aquifer  at location
 x«0,  y«0.   The mixed  zone  can be set equal  to  the depth screened,  rather than  the full
 depth of the  aquifer, if vertical  mixing above and  below the screened zone is  thought
 to be small.   The  6 (')  is  a Dirac  delta function and  g. is the  strength of  the  line
 source,  where g,  » c  Q/b.
      As  presented  in  Equation VII-90,  the first-order decay rate,  k, assumes that
 solute  in  its  liquid  and solid phases decays at the same rate  (i.e., k « k, .    . . •
 ksolid''  The  lio-uid  Phase  refers  to solute in solution and the  solid phase refers  to
 solute  that has been  adsorbed.   If  the liquid and solid phase decay rates are not the
 same, Equation VII-76 needs to be  substituted.
      The solution to  Equation VII-90, with a zero initial  concentration and zero
 gradients at  large distances can be found by means  of the  integral  transform or Laplace
 transform techniques:

                                     cJ3           /v x\
                                  .   rnn
                                  4»rpb(D D )
                                        * "
where
        W(-)    •  the  leaky well  function of Hantush  (see Appendix J)
        B       »  2Dx/vx   (m)
        r       -  (8(x2 * y2D /D  ))'2(m)
                  -         *  y
                 r\
        u       "  WT
                                        -417-

-------
        0      - 1 *  2BRdk/vx (unUless)
        0      • volumetric rate discharge Into the aquifer by the line source (m /day)
        t      • time (days)
        (x.y)  * location of point of Interest (m) , where the line source is located at
                 x»0, y-0
        0 ,0   • dispersion coefficients 1n the x and y directions, respectively
                 («2/day)
        v      • seepage velocity of the regional flow 1n the x direction (m/day)
        p      * effective porosity of the aquifer (unities* , decimal percent)
        b      • saturated thickness of mixed zone (m)
        k      » first-order decay constant (per day)
        Rd     • retardation coefficient for linear, equilibrium adsorption (unUless)
        c      " concentration of contaminant being discharged (mg/1)
     Note that Equation VI 1-91 1s similar to the solution presented by Wilson and
Miller (1978).  However, Equation VI1-91 allows for linear, equilibrium adsorption.   A
schematic representation of Equation VII-91 1s shown 1n Figure VII-42.
     The leaky well function of Hantush W(u,r/B)  1s discussed in Appendix J. In
addition, a table of values (I.e., Table J-3) and several approximations are given for
the W(:)  function 1n Appendix J.
     For the special case of steady-state conditions (I.e., large times) and when the
ratio r/B 1s larger than one (I.e., far from the source), then Equation VII-91  reduces
to the following simplified form:
                c(x,y,steady-state) -        zTTT^   **P     " *           (VI 1-92)
 	EXAMPLE VII-10 	

       A small community had water from their municipal well checked for trace
  organics.  To their surprise, they found a concentration of 150 ug/1 of              '
  trichloroethylene (TCE).  After much Investigation, a local environmental            I
  organization found the only major user of TCE to be a semi-conductor                 |
  manufacturing plant.  However, the plant was located over 1000 meters away from      j
  the site of the municipal well.  At first, few could believe that the plant could    '
  be the source of the contamination because of the large distance Involved.
  Hence, a blue-ribbon committee was selected to Investigate the problem.   What         !
  follows are the results of the committee's work.                                      j
       The solvent TCE has been used continuously  by  the manufacturing plant for        I
  the last 25 years as a degreaser for their equipment.  All residual  TCE  1s washed    I
                                        -418-

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     LOCATION OF
     LINE SOURCE
     FIGURE VI1-42
SCHEMATIC  SHOWING A  CONTINUOUS  DISCHARGE  OF
WASTE INTO A  REGIONAL FLOW FIELD
out of the plant by a large  volume  of water, which  in turn is pumped to a small,
unlined pond.   The pond receives  about  500 m  of TCE contaminated wash water per
year and the concentration of  TCE in the  pond is 25,000 yg/1.  The wastewater
percolates through the bottom  of  the pond as quickly as it flows in.  The depth
to the water table is about  2  meters and  the underlying aquifer consists of
unconsolidated sand.   From well logs, observation wells and pumping tests, it was
found that the hydraulic conductivity in  the unconsolidated sand was 3640 m/yr,
the effective  porosity 0.2,  hydraulic gradient  in the aquifer 0.0022 m/m and
saturated thickness of the aquifer  20 meters.   The  unconsolidated sand is
underlain by a thick  impermeable  clay layer.  Dispersion tests showed that the
dispersivity along the direction  of ground water flow is about 50 m and
transverse to  the flow about 5 m.   The  background concentration of TCE upgradient
of the plant is below detection.
     As a first approximation, the  TCE  is considered to be vertically mixed in
the aquifer.  Since the dimensions  of the pond  are  small compared to the travel
distance, the  analytic solution of  Wilson and Miller (1978) can be used to
simulate the TCE transport.
     In addition to the other  information already given, the seepage velocity and
dispersion coefficients are  needed.  The  seepage velocity is calculated using
Equation VII-36:
                                     -419-

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I           vs(seepage)  «  (*sat)(hydraulic  grad1ent)/p
|                    vx  •  (3640){0.0022)/0.2  «  40 m/yr
t
I
j        Note that the transverse velocity  1s zero  because we have oriented the x
•   axis along the principal flow direction.   If hydrodynanlc dispersion 1s assumed
!   to be a linear function of seepage velocity, then dispersion can be computed as
I   follows from Equation  VII-53:
i
j          0  - oxvx • (50)(40) « 2000 m2/yr
i                                      2
j          Oy - cyx • (5) (40) - 200 mVyr

.   where a  and a  are  the longitudinal  and  transverse  d1spersiv1t1es, respectively.
I                 *
!        The committee further assumes that there is  negligible  adsorption  of  TCE and
I   that degradation (e.g., dehydrochlorination) Is zero because of the aerobic
I   conditions.   The amount of TCE entering the aquifer  through  the pond  bottom is
|   estimated to have been constant  over  the  past 25  years.
j   The information for  this  example  can  now  be tabulated  as  follows:

           t  « 25 yrs                CQ -  25000 ug/1
j           v  » 40 m/yr              Q  *  500  m3/yr
                      *)
t           QX « 2000 mVyr           b  •  20 m
|           0  • 200 m2/yr            p  -  0.2
i           x  « 1000 m                R . -  I
i                                      d
j           y  • 0 m                  k  »  0  per yr

        Determine the concentration  of TCE at  a distance  of  1000 meters  from  the
!   manufacturing plant  after  25  years.   This problem is mathematically described by
j   Equation  VII-90.  Equation VII-91  gives an  analytic  solution  to the problem.  To
I   predict the  concentration,  the committee  needs to first evaluate the  following
   terms:

          B   • 20 /v   «  (2)(200C)/40 •  100  m
                  A  A

          0   • 1 * 2BRdk/vx - 1 *  2(100)(1)(0)/40 • 1

          r   - (»,„* . f 'f}}" .  («>(UOOO)' .  <0>
                            y       \  \

          r/B • 1000/100  » 10
                                        -420-

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                  r Rd      (1000)2(
 j   With the above terms,  Equation VII-91 can now be evaluated:

 I                                           v   ,
                          c  Q          /vx* \  /    r  \
 !           c(x.y.t)  •	i^Pl^D"—)W\u*frJ
                      b4rrp(D D  )      \   x /   \      /
                            x y

            cdOOO.0.25) - (Z0)Jj?iffi^5fl881iao))H exP(iW00°)
 I
 |                       • (393.2)exp(10)W(5.10)
 i
 !       Unfortunately, the range of parameter values given  1n  Table  J-3  of
 j  Appendix J does not include the values needed to evaluate the  leaky well function
 I  of Hantush, W(5,10).   However,  since  the r/B parameter 1s very  large, one  can use
 |  the Wilson and Miller (1978)  approximation to W  given in Appendix J:
 i
 I
 i
|                       \       '                •                                       I

j           W(5,10)  - (0.40)exp(-10)erfc(0)                                            I
j      but erfc{0) « 1, thus                                                           |

I            W(5,10) « (0.4)(4.54 x 10"5)(1)  - 1.82 x  10"5                              !
|   Therefore,  upon substitution of W(5,10) back into our concentration solution        I
j   (Equation VII-91):                                                                  j


j        c(1000,0,25)  - (393.2)(22026.5)(1.82  x 10"5) « 158 ug/1                        j

!        If one does not  use the Wilson and Miller  approximation, the exact solution
I   is 154 ug/1.                                                                        !
I        As mentioned  earlier,  a concentration of 150 ug/1 of TCE was discovered in     [
|   the municipal  water well.   The manufacturing plant appears to be the likely         I
j   source of the  TCE  contamination.                                                    |
,                                                                                      i
I                                                                                      I
	END OF  EXAMPLE  VI1-10	'
                                        -421-

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                                     EXAMPLE  VII-11	,
          The previous  example showed  how  the  contaminant  TCE  decreased in              j
     concentration  with distance and time.   Biological  and chemical  degradation
     processes were assumed  to be negligible.   This  1s  true under  aerobic  conditions
     for  TCE  but  under  anaerobic conditions  degradation can take place.   It  is           ;
     difficult to provide  accurate rates of  degradation for field  type  situations        I
     because  many variables  (e.g., pH,  temperature)  «ay affect 1t.   The half life  of     |
     TCE  under anaerobic conditions ranges from 40 to 400  days (Wood et a_L, 1981).      j
 j    This corresponds to a decay rate  of 0.2 to 6 per year.                              '
 j         What is the concentration of  TCE at  a distance of 1000 m after 25  years  1f
     biodegradation at  a rate  of 0.2 per year  1s included?   The data needed  are
     summarized below:                                                                   |
 !                t   • 25 yrs               co  •  25000 ug/1                               I
 I                v   • 40 m/yr              Q   •  500  «3/yr                                \
 1                Ox - 2000 m2/yr          b   •  20 M                                    j
 j                0   » 200  m2/yr            p   •  0.2                                      j
 j                x   - 1000 m               R^  -  1                                        j
 j                y   » 0  m                  k-0.2peryr
 '                                                                                       i
 J  Step  1.  Calculate the following terms  in Equation VII-91:                            '
 j                                                                                       i
 |           8   • 20x/vx - 2(2000)/40  « 100                                              \

            A   . i * ZBR,k        2(100)(1)(0.2)   ,                                    !
 I           D   • j •» ^—-o    i +  '4(5 ''  ''	L •  (•                                    i

 '                    2    2        u                                                    I
 j           r   - (B(x   *  y   Ox/uy)p                                                    j
 '                                                                                       i
            r   • (2{(1000)2 * (0)2(2000)/(200))1* -  1414

 I           r/B • 1414/100 «  14.14                                                      I
 '                  2                                                                    '
 •                 _tQ             1                                                      i
                                     ,E1
                          4Z)(ZOOO)[25)
                     *                                                                 I
i                                                                                       i
•   Step 2.   Is r/B greater than 1?  If so.  use the Wilson and Miller (1978)
            approximation given in Appendix J to evaluate W,  the leaky well  function
!            Hantush.   If r/B is less than 1, then use Table J-3 to evaluate  W.   For     '
|            example,  to use the Wilson and  Miller approximation, proceed  as  follows.    I
I            Evaluate  the terms:                                                        I
                                         -422-

-------
                          . . (14.14-2(5)) . _0>g3
                                 2 VT"

            erfc /. i^tph. erfc(-0.93) - 1.81

   Note that erfc(-a)  - 2 -erfc(a)  «  2  -  0.188  •  1.81
I
I   Step 3.   Evaluate the final  computation  using  Equation  VII-91:
             W(5. 14.14)  -             cxp(-14.14)(1.81) - 4.36  x  10'7
                             x y
j            cdOOO.0,25)	L25000H50QJ	   fixp  140(1000|  (4.36 x 1C'7)
!                           4ff(0.2)(20)((2000)(200))S        t\a>™>
I
j            c(1000,0,25) - 3.8 ug/1

   With degradation over a 25-year period, the predicted concentration of TCE is
!   decreased from 185 ug/1 to 4 ug/1.  However, it should be noted that when TCE
I   undergoes degradation by dehydrochlorination, it produces incomplete degradation
I   products (e.g., the two isomers of dichloroethylene)  which are also hazardous.
I
;	ENO OF EXAMPLE  VII-11	'

7.6  INTERPRETATION OF RESULTS
     This section discusses the interpretation of results calculated using the
screening methods.  Section 7.6.1 reviews water quality  criteria which are pertinent to
ground water.    A brief analysis of uncertainty and methods  for quantifying it are
given in Section 7.6.2.  Finally, Section 7.6.3 provides guidance for determining  when
more detailed  analyses such as those involving numerical computer models are
appropriate.

7.6.1  Appropriate Reference Criteria
7.6.1.1  Introduction
     Federal and state regulations  applicable  to ground  water quality are currently
undergoing revision.   The trend is  toward more regulation at the state level  rather

                                         -423-

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than at the federal level.  Pertinent federal laws Include the Federal Hater Pollution
Control Act/Clean Water Act (1972/1977/1982), the Safe Drinking Water Act  (1974/1977),
the Resource Conservation and Recovery Act (1976/1984), and the Toxic Substances
Control Act (1976).  The U.S. Environmental Protection Agency recently made public its
policy regarding ground water protection In a document referred to as the EPA's Ground
Uater Protection Strategy (U.S. EPA, 1984).  Individual states are also in the process
of developing laws and programs related to ground water.  For example, Connecticut,
Florida, Wisconsin, and New Mexico have ground water classification systems and
numerical standards for each classification.  Maryland, New Jersey, and New York
specify effluent limitations for waste discharges to ground water.

7.6.1.2  Water Quality Standards
     The predicted results of the hand calculation methods should be compared to the
appropriate standards.  The federal standards for drinking water are currently being
reviewed (CFR Vol. 48, No. 194, October, 1983).   Numerical limits may change and new
parameters may be added as shown in Table VII-13.  The interim primary drinking water
standards are based on human health considerations.  The present standards cover ten
inorganic chemicals, bacteria, turbidity, organic chemicals and radioactivity.
     The interim seconoary drinking water standards (Table VII-14) mainly address
aesthetic and pragmatic factors rather than public health.  The secondary standards
cover parameters which affect taste, color, odor and the corrosive properties of water.
These standards are not federally enforceable but are considered guidelines for the
states.
     In addition to the federal drinking water standards,  each state may have its own
set of water quality standards, which may be equal or more stringent than the federal
standards.  These regulations may change so it is imperative to check with the local
state agencies regarding current values.
     The state may specify that standards apply  to the ground water at the waste
disposal site boundary, at a specified distance  downgradient of the site, at a property
boundary, or at the point of use.  In some states, ground  water downgradient of a waste
site may have to meet all federal drinking water standards.  In addition, if the ground
water discharges to a surface water body, surface water standards may apply.

7.6.2  Quantifying Uncertainty
     Uncertainty in ground water flow and contaminant transport has been implied
throughout this chapter.  Part of this uncertainty is due  to aquifer heterogeneities
and natural variability.  Additional uncertainty is introduced by sampling and
measurement errors and the assumptions on which  the hand calculation methods are based.
For numerical models used to compute ground water flow and contaminant transport,
uncertainty can also result from the numerical solution techniques.
                                         -424-

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                                        TABLE  VII-13

                            PRIMARY  DRINKING WATER  STANDARDS
                                       INORGANIC CHEMICALS
               Parameter
       Maximum Contaminant
          L«vtl  (-8/1)
                                                        Parameters Under Consideration
Arttnlc
UHuai
Cadmium
Chromium
Lead
Mercury
Nitrite (as N)
Selenlu*
Silver
Fluoride
0.05
1.0
0.010
O.OS
0.05
0.002
10. 0
0.01
O.OS
1.4-2.4
Aluminum
Antimony
Asbestos
•erylllum
Copper
Cyanide
Molybdenum



Nickel
Sodium
Sulfate
Thallium
Vanadium
Z1nc




                            HICR06IOLOGICAL CONTAMINANTS AND TURBIDITY
Parameter
Total Col 1 fonts
Turbidity
Level (mg/1)
1/1 00 •! Monthly Average
4/100 •! Single Sample
1-5 turbidity units
Parameters Under Consideration
Glardla. Leglonella, Viruses
Standard Plate Count (SPC)
                                        ORGANIC CHEMICALS
    Parameter
Mail at* Contaminant
    Level  (-9/D
                                                          Parameters Under Consideration
Endrln
LlneUne
Methoiychlor
Toxaphene
2.4-D
2,4. 5-TP Sllvex
Total Trlhaloaethanes








0.002
0.004
0.1
O.OOS
0.1
0.01
0.1








Aldtcarb
Chlordane
Dalapon
D1qu«t
Endothall
Glyphoiitt
Carbofuran
1.1,2-Trlehloroethane
Vydate
StHZlne
PAHS
PCBs
Atrazlne
Ptithalates
Acrylaalde
D1bro*ochloroproMne (OBCP)
1,2-Dlchloro pro pane
Pen tac More phenol
Pichloraa
Otnoseb
Alachlor
Ethyl ene dlbro«ide
Ep1cnlorohydr1n
OlbroeoBCthane
Toluene
Xyl ene
Adi pates
Hesachlorocyclopentadiene
2.3.7.8-TCDO (Dloxln)

              Parameter
Combined  radium  226 and radium 228
Cross  alpha  particle activities
Icta  particle and photon radioactivity
  from man-made  radlonuclldes
                 RAOIOACTIVITT

                  Maximum Contaminant
                     Level

                    5 PCI/1
                   IS pCI/1
                    4 minirem/year
Parameters  under Consideration

           Uranium
           Radon
Reference:  U.S. EPA (l»77a) and Code  of  Federal Regulations 40 CFR 141.11-141.16  (19S2).
                                            -425-

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                                     TABLE VII-14
                      INTERIM SECONDARY DRINKING WATER STANDARDS
                                                 Maxlmun Contaminant
                      Parameter                          Level
Chloride
Color
Copper
MBAS*
Iron
Manganese
Odor
PH
Sulfate
Total Dissolved Solids
Zinc
Corrosivity
250 mg/1
15 color
1 MQ/1
0.5 ng/1
0.3 ng/1
0.05 mg/1

units




Threshold Odor Number 3
6.5-8.5
Z50 mg/ 1
500 mg/1
5 mg/1
Non-Corrosive





               *Hethylene blue active substances
               Reference:  U.S.  EPA (1977b)  and Code of Federal
                           Regulations 40  CFR 143.3 (1982).
7.6.2.1  Sources of Uncertainty
     Uncertainty associated with measured values of a parameter may be due to
variability of aquifer characteristics, sampling error, and analytical error.  The
distinction between these sources can be made by collecting replicate samples,
splitting them, and performing at least duplicate analyses of the samples.  One common
sampling design involves collection of four replicates which are then each split four
ways.  The uncertainty can then be allocated using a 4 x 4 analysis of variance
(ANOVA).  The quality of laboratory analyses should also be checked by analysis of
blanks, standards, and unknowns.  Additional discussion of QA/QC procedures is Included
in Scalf et a_K (1981), U.S. EPA (1979b) and (1980).
     Uncertainty in the representation of the physical system may also create
uncertainty in the parameters used to describe the system.  For example, consider the
concept of hydrodynamic dispersion which was discussed 1n Section 7.4.1.  Several
figures and tables were given to provide estimates for d1spers1v1ty, which itself 1s
used to represent the dispersive characteristics of an aquifer.  However, current
research indicates that dispersion results from variations 1n the seepage velocity
profile.  These variations may not be adequately characterized by existing mathematical
formulations.
                                         -426-

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      Additional  uncertainty  and  errors  can be  introduced  by mathematical  solutions  in
 the form of overshoot,  numerical  dispersion, truncation and round-off errors.
 Overshoot and  numerical  dispersion  are  the most  important  errors  generated  by  finite
 difference and finite element models of  contaminant transport.  The  term  overshoot
 describes the  erroneously  high values computed near the upstream  side of  sharp  solute
 fronts  (undershoot  is the  analogous behavior on  the downstream side  of sharp fronts).
 Numerical dispersion, which  results from the incomplete approximation of  the
 differential equations,  can  smear a sharp front  and thereby produce  a solution
 indicative of  a  larger dispersion coefficient  (Pinder and  Gray, 1977).  Truncation
 errors  occur when only  a finite number of terms  are used to represent the original
 equations describing flow  and mass  transport.  Finally, round-off errors  result  from
 the finite accuracy of computer calculations.  It should be noted that  even analytic
 solutions can  be subject to  truncation and round-off errors.

 7.6.2.2   Methods of Estimating Uncertainty
      The  recognition of  uncertainty helps put predicted results in perspective.  For
 example,  if the time of arrival of a contaminant at a well is 300 *  10  days, then time
 is  available to design a plan of action.  However, if our  uncertainty  analysis
 predicted a time of arrival  of 300 + 200 days, a plan of action would have to be
 developed much sooner.
      Several methods are available for estimating the uncertainty associated with
 calculations.  Included are  sensitivity analysis, variance analysis,  interval analysis,
 and Monte  Carlo analysis.  Each of these methods is discussed briefly  below.
      Sensitivity analysis  is the process of determining the variation  in a model output
 variable  caused by a change  in one of the input parameters.  This can  be done using  a
mathematical approach or simply by making repeat calculations using different parameter
values.   The parameters which most influence the results can thereby  be identified.
      Consider a sensitivity analysis of the seepage velocity v  for saturated flow.
From  Section 7.3.3.1.2, it was shown that the seepage velocity is a function of the
hydraulic  conductivity K, the hydraulic gradient I  and the porosity p.  From Equation
VII-36 the seepage velocity was shown to be equal to:
      vs -  -KI/p
The total  uncertainty in the seepage velocity dv  can be expressed as:
                                    dk *  TT  dl  *-     "P                   (vn-93)
where (dv^/6K)t (ffv^/al) and (0vs/0p)  are the sensitivity coefficients and dK, dl and
dp are the uncertainties associated with these parameters (e.g., dK • tl x 10"5 cm/sec,
                                         -427-

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dl - ±0.001, dp « ±0.05).  Upon substitution of Equation YII-36 Into Equation VI1-93,
the uncertainty dv  becomes:
                                -    <* -     dl
The relative or percent uncertainty 1s found by dividing Equation VI 1-94 through by v .
Thus upon substitution:
In the case of the seepage velocity, the uncertainty can be due to K, I, or p.
However, the greatest source of uncertainty 1s generally the hydraulic conductivity
tern; Us value may vary over several orders of magnitude.  The above mathematical
procedure for computing the sensitivity analysis can in principal be done for any Input
parameter but 1t usually becomes too complicated except for simple expressions.  The
alternative "brute force" method 1s to repeatedly perform the calculations,
systematically varying the parameters, one at a time and 1n combinations, to determine
how the variations 1n parameter values affect the predicted result.
     Another mathematical technique used to quantify uncertainty 1s based upon
determining how the variance of individual equation terms Interact with each other.
Consider two variables, called X and Y.  Let the sum (or difference) of these two
variables be called Z.  If X and Y are considered as Independent random variables, then
the variance of Z can be calculated as:

                         Var[Z] • Var[X±Y] - Var[x] * Var[Y]                  (VI 1-96)

where Var [ ] is the variance of the variable.  (An estimate of the variance can be
obtained by squaring the standard deviation Sx<  $x is defined by Equation VI1-22 1n
Section 7.2.5.4).  If X and Y are multiplied together to get Z, then the variance of Z
for this product will vary as:

             Var[Z] - Var[XY]
                    • (E[x])2Varff] «. (E[Y])2Var[x] + Var[x]Var[Y]            (VI 1-97)

where E [ ] Is the expected value of the variable.  (An estimate of the expected or mean
value is given by Equation VII-23 1n Section 7.2.5.4.)  If Z is defined as X divided by
Y, the variance of Z for this quotient will vary approximately as:
                                                                              (VI1-98)
                                         -428-

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 From the above expressions, 1t Is obvious that if any independent variables have
 uncertainty associated with them, then the addition, subtraction, multiplication or
 division of these variables will  always increase the variance of the combined
 variables.  However,  if the variables are not mutually independent of each other, the
 effect on the variance is  not as  clear since covariance  terms need to be included in
 the above equations.   Procedures  for adding the covariance terms are included in Mood
 et a_K (1974).
      Interval analysis (Ross and  Faust, 1982) is similar to sensitivity analysis except
 that likely ranges  for the input  parameters of interest  are chosen and then  these
 values are substituted into the analytical  method to provide likely upper  and lower
 bounds for the desired output parameters.   For example,  the upper bound could be the
 predicted contaminant  concentration  in the  aquifer at  a  point 100 ft downgradient of an
 injection well  using as  input data   a low retardation  factor and minimal dispersion.
 The lower bound could  be the predicted contaminant concentration at this same location
 when the highest retardation factor  and dispersion are used in the calculations.   When
 limited field data  are available, this approach  can  provide at least an estimated range
 for the output  parameters.
      Monte Carlo analysis  involves solving  the ground  water flow and solute  transport
 equations using randomly chosen values as  input  parameters.   The random values  are
 selected  from specified  probability  density  functions  (pdf)  of key  parameters.
 Typically,  50 to 300 repetitions of  the  calculations would  be  performed with  different
 input  parameters.   Histograms  of the  predictions  are generated  and  used to calculate
 the probability of  specific  events (e.g., number  of  times  that  concentration  limits
 will  be exceeded  or time for  a  contaminant  plume  to  reach  a  given well  or  surface water
 body).   The  principal  limitations of  this approach are the  high  cost  of doing a  large
 number  of calculations, difficulties  in  estimating the pdf  for  each  of  the parameters
 and  the  need  to  include the  "worst cases" of  interest.  The  computer  program MACRO
 developed  by  Kaufman et aU  (1980) can be used to  calculate  pdf's of  predicted
 contaminant  concentrations.  MACRO works by  systematically making repeated model runs
 with regularly  spaced  values of the sensitive  parameters.  This program, however, has
 only been  used  for simple cases.

 7.6.3   Guidelines for  Proceeding to More Detailed Analysis
 7.6.3.1   Introduction
     There are typically four critical questions to be addressed in ground  water
 contamination studies:   a)  where are the contaminants; b) when will they arrive at a
 specific  location; c)  what  are the concentrations of the  contaminants; and  d) what
hazards are posed by the contaminants.  Answers to these  questions provide  a  concise
statement of the information needed  to evaluate the environmental consequences of
ground water contamination.  To address these types of questions, there are three
                                        -429-

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general types of assessment tools available:  site ranking methods, analytical (hand
calculation) methods, and numerical models.  These tools are useful for different
levels of analysis and thus offer complimentary rather than competing uses.  Up to this
point, the chapter has addressed only the hand calculation methods.  The three
approaches are briefly compared below:
        t    Site ranking methods allow  Initial assessment of a large number of
             existing ground water contamination problems.  With a minimum amount of
             Information and technical expertise, site ranking methods can be used for
             evaluating the relative hazard posed by a large number of contamination
             sources.  Because site ranking models do not provide quantitative
             estimates of contaminant concentrations, they will not be discussed
             further In this chapter.  A review of selected ranking methods 1s Included
             In Summers and Rupp (1982a).
        i    Analytical (or hand calculation) methods can predict the migration of
             contaminants 1n ground water from potential or existing waste sources.  As
             shown in Section 7.5, these techniques are based on simplified
             representations of the ground water system.  The techniques require
             limited field data and can be applied rapidly with hand calculators.
        •    Numerical models, like analytical methods, provide site-specific
             predictions by solving a series of equations.  These models can provide
             greater temporal and spatial resolution.  However, using numerical models
             generally requires large amounts of data and a computer.
     Numerical models will be briefly discussed below.  A method for determining when
numerical models are appropriate Is given in Section 7.6.3.3.

7.6.3.2  Numerical Models
     Numerical model results can help address the following questions pertinent to
ground water contamination problems:
        •    What is the maximum areal extent of a plume at a given site?
        t    What is the approximate time for a plume to reach a given well or surface
             water body?
        •    What is the maximum concentration of a contaminant that could occur at a
             given well or in the ground water discharging Into a surface water body?
        •    How much time would be required to flush contaminants from an aquifer?
        •    What control methods are technically feasible and cost-effective?
        •    Is it likely that a contaminant plume would form at a candidate waste
             disposal site?
        •    Where should monitoring wells be located?
                                         -430-

-------
      Flow and  solute  transport models vary  in  type and complexity  depending  upon  the
 system  being modeled  and  the extent  to which the model attempts  to fully  represent  that
 system.  Modeling contaminant movement in a homogeneous aquifer  is  significantly  less
 complex than attempting to model movement in a heterogeneous aquifer,  such as one with
 interbedded clay lenses.
      Data requirements for ground water flow and solute transport models are given  in
 Table VI1-15.  The amount of data needed increases with the number  of  dimensions
 modeled and the size  of the grid system.
      Along with the input data shown in Table YII-15, historical water level and ground
 water quality  data are needed to calibrate the model.  Model results are usually
 compared with  historical data and refined accordingly—a process known as calibration
 or history matching.  This does not  assure that a model will give accurate predictions
 for the  future when conditions may change (e.g., a confined aquifer could have been
 pumped  enough  to change it to an unconfined system).
      There are many mathematical models available for predicting ground water flow  and
 solute  transport in 1, 2, or 3 dimensions.  Numerical solution techniques to choose
 from  include finite difference, finite element, integrated finite difference, and
 method  of characteristics.  Detailed reviews of numerical models can be found in the
 following reports:  Kincaid e£ a_L (1983),  Bachmat e£ £l_. (1978),  van Genuchten
 (1978),  Oster  (1982)  and Thomas £t aU  (1982).  In addition, information and copies  of
 publicly available ground water models  may be obtained through the  International Ground
 Water Modeling Center (IGWMC) at the Holcomb Research Institute of  Butler University.
 The IGWMC has developed a computerized  data base of over 600 models called the Model
 Annotation Retrieval  System or MARS.

 7.6.3.3  Model  Selection
      In this chapter,  three different approaches to assessing ground water
 contamination problems have been briefly discussed, including site ranking,  analytical
 and numerical  models.   However, the question of which approach to use  is as  of yet
 unanswered.   Before a  method is selected, an assessment should be made of the
 complexity of the hydrogeologic system,  the type of information needed to meet the
 study objectives,  and  the present understanding of the aquifer system.  Figure VII-43
 shows a general sequence for determining whether a numerical  model   is needed and
 alternative approaches.   Numerical models should be applied when a detailed  assessment
of the extent  and significance of contamination is needed and when adequate  funding and
 trained personnel  are  available for the  required data collection and modeling effort.
The steps involved in  applying a model  are shown in Figure VII-44.   As this  figure
 shows, data collection,  interpretation  and model application  ideally should  be an
 iterative process.   Analytical  methods  should  be used at  each of these feedback  points
and to check final  model  results.
                                         -431-

-------
                                       TABLE  VII-15

                             DATA NEEDS FOR NUMERICAL  MODELS
       Flow Models
                 area!  extent  of  the  aquifer
                 grid  type  and spacing
                 aquifer thickness, by  node
                 boundary conditions  and  locations  of  assigned  nodes
                 hydraulic  conductivities  (or  permeabilities),  by node
                 specific storage or  specific  yield
                 initial  head, by node
                 net recharge  rate of the  aquifer
                 the locations and flow rates  of system  stresses
                 (e.g.  pumping wells)
                 relationship  to  surface water.  1f  present
                 water  level data for model  calibration  and  verf1c1at1on
       Solute Transport Models*

            •     longitudinal,  transverse,  and vertical  disperslvlty coefficients
            •     bulk  density of  permeable  media
            •     effective  porosity  of  the  aquifer
            •     initial  contaminant concentrations  1n  the  aquifer
            •     concentrations  and  flow  rates of waste  sources
                 (these may vary  by  location  and time)
            •     distribution coefficients  or retardation factors  for the
                 contaminants of  interest
            •     radioactive or biological  decay constants,  if  appropriate
            •     concentration  data  for model calibration and verification
       *The  flow  data  are  also  needed  to  run  solute  transport  models.
     The simplest models should be used first to determine sensitive parameters and to

identify significant data gaps.  Based on the predicted results of the simple models

and uncertainty analyses, a decision can then be made as to whether additional data and

more complex models are necessary.
                                         -432-

-------
          Determine Project Objectives
                      I
         Are Numerical Estimates Needed?
  Collect  Htniaal Data ind
  Use Site Ranking Metnods
          Dots Potential Hazard Justify
                Modeling Effort?
   Estimate Concentrations
      and  Travel TIMS
                        Yes
          Can MyOro^eolo^lc Syuw be
          Sufficiently Chtracttrized to
                a Model to be  Applied?
                                       .'to
             Data Available for Model'
Recotmend L in ted
   Mom to'inj
                 Field  Investigation
            if Hazard  Warrants it
          Determine  Soec'fic Objectives
              of Modeling Effort
            Determine Technical and
         Financial  Resources Available
          Determine Time Available for
                 Modeling Work
          Are Resources Adequate for
             Modeling Cbjectives'
   Refine Objectives or
Obtain Additional Resources
         Select and Apply Flow Mode'
        Do Flo- Model  Results Indicate
            Need  for Ground  .liter
               Dual it/  «od«>'
                       'es
        Select  ind ADO)? Cirouna uater
               Oual it/ "*odet
     Estinate Haiimun
    Concentrations  and
       Travel Times
      Note:  Steps marked with
                                    I use analytical techniques.
FIGURE  VIM3    GENERAL  SEQUENCE TO  DETERMINE  IF  A  MODELING  EFFORT
                       is  NEEDED,    REFERENCE:   SUMMERS  AND RUPP  (1932s)
                                          -433-

-------
                              Conoiie «no
                    NO
                               Oeveloo Conceotu*! »ooel o' Systtw
                                        S«l*et J
                                Collect Addition*! 0*U  if
                                             1
                                    Set-up «na Aoply
                                             I
                                Goes '•'OB*'  foTiuUt'on Adeau«tely
                                    Rep'ri*". >>**1
                                    C4' 'D
                                 Oo*s System Sf-*' -oot*r ts &«
                            Correct'./ Deicrisee o/ ^ooel
                                    ?reo'Cf'e
"ott   Stem «*•••?<) ait"
                                         "oo*l ACD • i cj: '
                               «n
-------
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Ra1mond1, P.G., H.G. Gradner and C.G. Petrlck. 1959.   Effect of Pore Structure and
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Rawls, W.J. and L.E. Asmussen. 1973.  Neutron Probe Field Calibration  for Soils in the
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Reynolds, S.G. 1970a.   The Gravimetric Method of Soil  Moisture Determination, I, A
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Reynolds, S.G. 1970b.   The Gravimetric Method of Soil  Moisture Determination, III, An
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Rice, R. 1969.  A Fast-Response, Fietd Tensiometer System.   Transactions of the
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Richards, L.A. and G.  Ogata. 196*1. Psychrometric Measurements of Soil  Samples
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Richards, L.A. 1965.  Physical Condition of Water in  Soil.   Methods of Soil Analysis,
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X 31> •

Richards, S.J. 1965.  Soil Suction Measurements with  Tenslometers 1n Methods of Soil
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                                         -440-

-------
Robinson,  V.K.  1974.   Low  Cost Geophysical Hell  Logs  for  Hydrogeologlcal
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Ross,  B. and C.R. Faust. 1982.  Analysis of Uncertainty 1n  Contaminant  Migration
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Rowe,  P.y. 1972.  The  Relevance of Soil Fabric to  SUe Investigation  Practice.  Twelfth
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Sampson, R.J.  1978.  SURFACE II Graphics System  (revised).  Number One  Series on
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Scalf, M.R., J.F. McNabb,  W.J. Dunlap, R.L. Cosby  and J.  Fryberger.   1981.  Manual of
Ground Hater Sampling  Procedures.  U.S. EPA Robert S. Kerr  Laboratory and National
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Scheidegger, A.E. 1961.  General Theory of Dispersion in  Porous Media.  Journal of
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Schmugge, T.J., T.O. Jackson and H.L. McK1n. 1980.  Survey  of Methods for Soil Moisture
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Smith, L. and F.W.  Schwartz. 1980.  Mass Transport:  Part 1, A Stochastic Analysis of
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Sudicky, E.A., J.A.  Cherry and E.O.  Frind.  1983.   Migration of Contaminants  in
Groundwater at a Landfill:   A Case Study,  Part 4.  A Natural-Gradient Dispersion Test.
Journal of Hydrology,  Volume 63,  pp.  81-108.

Summers, K.,  S. Gherini and C.  Chen.  1980.   Methodology  to Evaluate the  Potential  for
Ground Water  Contamination from Geothermal  Fluid Releases.  EPA  Report Number EPA-
600/7-80-117, 168 p.

Summers, K. and G.  Rupp. 1982a.   Assessment Methods for  Predicting Existence and
Transport of  Ground Water  Contamination.   Tetra Tech  Report. 47  p.


                                         -441-

-------
Simmers, K. and 6. Rupp.  1982b.  Selection and Use of Assessment Methods  for  Ground
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Ground Water Protection: Proceedings of the Sixth National Ground Water Quality
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Tang, D.H. and D.K. Babu. 1979.  Analytical Solution of a Velocity Dependent Dispersion
Problem, Water Resources Research, Volume 15, Number 6, pp. 1471-1478.

Taylor, S.A. and G.L. Ashcroft. 1972.  Physical Edaphology, W.H. Freeman and Company,
Sen Francisco, 533 p.

Terzaghi, K. 1960.  Storage Dam Founded on Landslide Debris.  Journal of the Boston
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Tetra Tech. 1977.  Stream-Aquifer Model of Carlls River Basin Long Island, New York.
85 p.

Tetra Tech. 1984a.  Ground Water Data Analyses at Utility Waste Disposal Sites.  EPRI
Research Project RP2283-2.  Electric Power Research Institute, Palo Alto, California.

Tetra Tech. 1984b.  Proceedings of First SWES Technology Transfer Seminar on Solute
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Thomas, A. 1963.  In-Situ Measurement of Moisture in Soil and Similar Substance by
Fringe Capacitance.  Journal of Scientific Instrumentation, Volume 43, p. 996.

Thomas, S.D., B. Ross and J.W. Mercer.  1982.   A Summary of Repository Siting Models.
NUREG/CR-2782, U.S. Nuclear Regulatory  Commission, Washington, D.C.

Todd, O.K. 1959.  Ground Water Hydrology.   John Wiley and Sons, Inc., New York, 336 p.

Todd, O.K. 1980.  Ground Water Hydrology,  Second Edition.  John Wiley and Sons, New
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Todorovic, P. 1975.  A Stochastic Model of Dispersion in a Porous Medium.  Water
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U.S. Environmental Protection Agency. 1977a.   National Interim Primary Drinking Water
Regulations.  U.S. Government Printing  Office, Washington, D.C.

U.S. Environmental Protection Agency. 1977b.   National Secondary Drinking Water
Regulations - Proposed Rules.  Federal  Register, Volume 42, Number 62.

U.S. Environmental Protection Agency. 1979a.   Draft Report to Congress: Water Supply-
Wastewater Treatment Coordination Study.  EPA Contract No. 68-01-5033.  375 p.

U.S. Environmental Protection Agency. 1979b.   Handbook for Analytical Quality Control
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U.S. Environmental Protection Agency. 1980.  Procedures Manual for Ground Water
Monitoring at Solid Waste Disposal Facilities.  Report No. SW-611.  2nd Edition.  269 p.

U.S. Environmental Protection Agency. 1984.  Ground Water Protection Strategy.
Washington, O.C.


                                         -442-

-------
 Vachaud,  6., J.M. Royer  and  J.O. Cooper.  1977.   Comparison  of  Methods  of  Calibration of
 a Neutron Probe by  Gravimetry on Neutron-Capture Model.   Journal  of Hydrology,  Volume
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 van  Bavel,  C.H.M. 1961.  Calibration and  Characteristics  of Two Neutron Moisture
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 van  Bavel,  C.H.M. 1962.  Accuracy and Source Strength in  Soil  Moisture Neutron  Probes.
 Soil  Science Society of  America Proceedings, Volume 26, p. 405.

 van  Everdingen, R.O. 1963.   Groundwater Flow-Diagrams in  Sections with Exaggerated
 Vertical  Scale.  Geological  Survey of Canada Paper 63-27, 21 p.

 van  Genuchten, M.Th. 1978.   Proceedings of the Fourth Annual Hazardous Waste Management
 Symposium,  Southwest Research Institute and U.S. EPA, San Antonio,  Texas, March 6-8,
 1978.

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 Conductivity of Unsaturated  Soils.  Soil Science Society of America  Proceedings, Volume
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 van  Genuchten, M.T. and  W.J. Alves. 1982.  Analytical Solutions of  the One-Dimensional
 Convective-Dispersive Solute Transport Equation.  USDA Agricultural  Research Service,
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 Walker, F.C. 1955.  Experience in the Evaluation and Treatment of Seepage from
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 Walton, W.C. 1970.  Groundwater Resource Evaluation.  McGraw-Hill Book Co., New York,
 664  p.

 Weast, R.C. 1969.   Handbook  of Chemistry and Physics, 50th Edition.  The Chemical
 Rubber Co., Cleveland,  Ohio, 2356 p.

 Weeks, E.P. 1969.   Determining the Ratio of Horizontal to Vertical  Permeability by
 Aquifer Test Analysis.   Water Resources Research, Volume 5, pp. 196-214.

 Whitaker, S. 1967.  Diffusion-and Dispersion in Porous Media.   Journal of the American
 Institute of Chemical Engineering, Volume 13, Number 3,  pp. 420-427.

Wilkes, P.F. 1974.  Permeability Tests in Alluvial  Deposits and the Determination of
Kg.   Geotechnique, Volume 24, Number  1.

Williams, T.H.L.  1978.   An Automatic  Scanning and Recording Tensiometer System.
Journal of Hydrology, Volume 39, pp.  175-183.

Wilson, J.T. and J.F. McNabb. 1981.   Biodegradation of Contaminants in the Subsurface.
 First International  Conference on Ground Water Quality Research, October 7-10,  1981,
Houston, Texas.

Wilson, J.L. and P.J. Miller. 1978.   Two-Dimensional  Plume in  Uniform Ground-Water
Flow.  Journal  of  the Hydraulic  Division,  ASCE, Volume 104, Number 4, pp.  503-514.

Wilson, L.G. 1981.  Monitoring in the Vadose Zone,  Part  1: Storage Changes.   Ground
Water Monitoring Review,  Volume  1,  Number  3,  pp.  32-41.

Wood, P.R., R.F.  Lang,  I.L.  Payan and J.  DeMarco. 1981.   Anaerobic Transformation,
Transport and Removal of  Volatile Chlorinated Organics in  Ground Water.   First
 International Conference  on  Ground  Water  Quality  Research, October 7-10,  1981,  Houston,
Texas.
                                         -443-

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Yeh, G. 1981.  AT123D:  Analytical Transient One, Two and Three-Oimenslonal Simulation
of Waste Transport 1n the Aquifer System.  Oak Ridge National Laboratory, ORNL-5602;
Publication Number 1439, Environmental Sciences Division, Oak Ridge, Tennessee, 79  p.

Zalkln, P., H. Wilkerson and R.J. Oshlma. 1984.  Pesticide Movement to Groundwater,
Volume II:  Pesticide Contamination in the Soil Profile at OBCP, EOB, Slmazine and
Carbofuran Application Sites.  Environmental Hazards Assessment Program, California
Department of Food and Agriculture, Sacramento, California, 168 p.


Additional References on ground Water Sampling

Barcelona, M.J., J.A. Helfrich, E.E. Garske, and J.P. G1bb,  A Laboratory Evaluation
of Ground Water Sampling Mechanisms.  Ground Water Monitoring Review.  4:32-41.

Barcelona, M.J., J.P. Gibb, and R.A. Miller.  1983.  A Guide to the Selection of
Materials for Monitoring Well Construction and Ground Water Sampling.  Illinois
State Water Survey Contract.  Report 327:78.

Claassen, H.C.  1982.  Guidelines and Techniques for Obtaining Water Samples that
Accurately Represent the Water Chemistry of an Aquifer.   U.S. Geological Survey.
Open-File Report 82-1 024, 49 p.

Ford, P.J., P.J. Turina, D.E. Seely.  1983.  Characterization of Hazardous Waste
Sites—A Methods Manual Vol II Available Sampling Methods.  EPA Report No. EPA-
600/4-83-040.  215 p.

Gibb, J.P., R.M. Schuller, and R.A.  Griffin.  1981.  Procedures for the Collection
of Representative Water Quality Data from Monitoring Wells.  Illinois State Water
Survey and Geological Survey.  70 p.

Gillham, R.W., M.J.L. Robin, J.F. Barker, and J.A.  Cherry.  1983.   Groundwater
Monitoring and Sampling Bias.  Department of Earth Sciences, University of Waterloo,
Ontario.  Prepared for American Petroleum Institute.  206 p.

Keely, J.F.  1982.  Chemical Time-Series Sampling.   Ground Water Monitoring Review.
2: 29-38.

Philip, J.R,  1957.  Evaporation and Moisture and Heat Fields in the Soil.  J.
Meteorology.  Vol. 14, No. 4.

Stolzenburg, T.R., D.G. Nicnols, and I.  Murarka.   1984.   Evaluation of Chemical
Changes in Ground Water Samples due to Sampling Mechanism.  Electric Power Research
Institute, Palo Alto, CA (In Press).

U.S. Environmental Protection Agency.   1983.  Ground Water Monitoring Guidance to
Owners and Operators of Interim Status Facilities.   (Draft).  USEPA SW-963.

U.S. Geological Survey.  1980.  Ground Water.  National  Handbook of Recommended
Methods for Water Data Acquisition.   Chapter 2.  Reston, VA.

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     Appendix A,  Monthly Distributor of Rainfall  Eros1v1ty Factor R, which
appears In the first two editions  of this manual.  1s now out of date and has
been deleted.
                                    A-l

-------
     Appendix B,  Methods for Predicting Soil Erod1b1l1ty Index K, which appears In the
first two editions of this manual. Is now out of date and has been deleted.
                                        B-l

-------
     Appendix C,  Stream and River Data, which appears 1n the first two editions of
this manual, 1s now out of date and has been deleted.
                                      C-l

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                                     APPENDIX 0

IMPOUNDMENT THERMAL PROFILES
     Thermal profile plots are provided  (on microfiche  1n  the  enclosed envelope for
EPA-publ1shed manual, or as Part 3, EPA-600/6-82-004c for  paper  copies purchased from
the National Technical  Information Service) for a variety  of Impoundment sizes and
geographic locations throughout the United States.  The  locations  are  arranged in
alphabetical order.  Within each location set. the plots are ordered by depth and
hydraulic residence time.  An Index to the plots 1s provided below, and the modeling
approach is described in Appendix F.
                                                                 Page
                       Atlanta,  Georgia
                          20-ft  Initial  Maximum Depth 	    0-4
                          40-ft  Initial  Maximum Depth 	  D-14
                          75-ft  Initial  Maximum Depth 	  D-24
                         100-ft  Initial  Maximum Depth 	  D-34
                         200-ft  Initial  Maximum Depth 	  D-44

                       Billings.  Montana
                          20-ft  Initial  Maximum Depth 	  D-54
                          40-ft  Initial  Maximum Depth 	  D-64
                          75-ft  Initial  Maximum Depth 	  D-74
                         100-ft  Initial  Maximum Depth 	  D-84
                         200-ft  Initial  Maximum Depth 	  D-94

                       Burlington,  Vermont
                          20-ft  Initial  Maximum  Depth 	 D-104
                          40-ft  Initial  Maximum  Depth	D-114
                          75-ft  Initial  Maximum  Depth 	 D-124
                         100-ft  Initial  Maximum  Depth 	 D-134
                         200-f.t  Initial  Maximum  Depth	D-144

                      Flagstaff, Arizona
                         20-ft  Initial Maximum  Depth	0-154
                         40-ft  Initial Maximum  Depth	D-164
                         75-ft  Initial Maximum  Depth  	 D-174
                         100-ft  Initial Maximum  Depth  	 0-184
                         200-ft  Initial Maximum  Depth  	 D-194
                                         D-l

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Fresno, California
   20-ft Initial Maximum  Depth	0-204
   40-ft Initial Maximum  Depth	D-214
   75-ft Initial Maximum  Depth	D-224
  100-ft Initial Maximum  Depth  	 D-234
  200-ft Initial Maximum  Depth  	 D-244
Minneapolis, Minnesota
   20-ft Initial Maximum  Depth	0-254
   40-ft Initial Maximum  Depth	0-264
   75-ft Initial Maximum  Depth  	 D-274
  100-ft Initial Maximum  Depth  	 D-284
  200-ft Initial Maximum  Depth  	 D-294
Salt  Lake City,  Utah
   20-ft Initial Maximum  Depth	D-304
   40-ft Initial Maximum  Depth  	 D-314
   75-ft Initial Maximum  Depth  	 D-324
  100-ft Initial Maximum  Depth	D-334
  200-ft Initial Maximum  Depth  	 D-344
San Antonio, Texas
   20-ft Initial Maximum  Depth  	 D-354
   40-ft Initial Maximum  Depth	D-364
   75-ft Initial Maximum  Depth  	 0-374
  100-ft Initial Maximum  Depth  	 D-384
  200-ft Initial Maximum  Depth  	 D-394

Washington, O.C.
   20-ft Initial Maximum  Depth	D-404
   40-ft Initial Maximum  Depth	0-414
   75-ft Initial Maximum  Depth	D-424
  100-ft Initial Maximum  Depth  	 D-434
  200-ft Initial Maximum  Depth  	 D-444

Wichita. Kansas
   20-ft Initial Maximum  Depth	D-454
   40-ft Initial Maximum  Depth	D-464
   75-ft Initial Maximum  Depth	D-474
  100-ft Initial Maximum  Depth  	 D-484
  200-ft Initial Maximum  Depth  	 D-494
                  D-2

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                                APPENDIX E

              MODELING THERMAL STRATIFICATION IN IMPOUNDMENTS

Figure E-l   Comparison of Computed and Observed Temperature Profiles 1n Kezar Lake

Figure E-2   Comparison of Computed and Observed Temperature Profiles 1n El  Capltan
             Reservoir

Figure E-3   Log of Eddy Conductivity Versus Log Stability—Hungry  Horse Data
                                      E-l

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E.I   IMPOUNDMENT THERMAL PROFILE MODEL:  BACKGROUND
      The model used for computation of Impoundment temperature profiles 1s based on
the Lake Ecologlc Model originally developed by Chen and Or lob (1975).  The model was
modified for this application to compute temperature alone.  The purpose of the model
application was to simulate the effects of mixing, Impoundment physical characteristics,
hydraulic residence time, and climate on the vertical profiles of temperature.

Physical Representation
      Each configuration simulated was Idealized as a number of horizontally mixed
layers.  Natural  vertical  mixing 1s computed by the use of dispersion coefficients In
the vertical mass transport equation.  Values of the dispersion coefficients for
different size lakes were estimated from previous studies (Water Resources Engineers,
Inc., 1969).

Temperature
     Temperatures were computed as a function of depth according to Equation (E-l):
where   T    »  the local  water temperature
        c    •  specific heat
        p    •  fluid density
        AZ   •  cross-sectional  area at the fluid element boundary
        t    •  time
        z    »  vertical distance
        DZ   «  the eddy diffusion coefficient 1n the vertical  direction
        Q    •  advection across the fluid element boundaries
        A$   -  cross-sectional  area of the surface fluid element
        n,x  -  coefficients describing heat transfer across air-water Interface
        e    »  sum of all  external  additions of heat to fluid  volume of fluid  element
        V    •  element volume.

Appli cat ion/ Verification
     The model has  recently been used  in a  lake aeration study (Lorenzen and Fast,
1976).   In that study,  the model was applied to Kezar Lake 1n New Hampshire and El
Capitan Reservoir  1n California to verify that artificial mixing could be adequately
simulated.
     Computed temperature profiles were compared to  observed values as shown 1n
                                          E-2

-------
 Figures  E-l  and  E-2.   The model performance was judged to be  good  for  the  intended
 purpose  of  providing  guidance  for  further  study.

 P.2   PREPARATION OF THERMAL PROFILES
      The thermal profiles 1n Appendix D of this report were prepared by inputting
 the  selected cllmatological  conditions, inflow rate. Impoundment physical  conditions,
 and  wind.  Of these, only wind warrants special discussion here.  Tne remaining model
 parameters are discussed In the text of Chapter 5.

 Wind-Induced Mixing and the Eddy Diffusion Coefficient
      Figure E-3 is a plot of the eddy conductivity coefficient versus stability.
 It was used to obtain coefficients for wind mixing for the model runs.   The
 upper envelope represents high wind mixing conditions and the lower envelope represents
 low  wind mixing conditions.   Note that the plot In Figure E-3 was developed for this
 model, and the model was then verified with data from Hungry Horse Reservoir, which is
 located on the South Fork of the Flathead River 1n northwestern Montana.  Accordingly,
 the  extremes of wind mixing  and the effects on impoundment stability are as found for
 Hungry Horse Reservoir.  The coefficients should be applicable elsewhere,  however,
 because the eddy diffusion coefficient is relatively insensitive to climate and location.
     The significance of the eddy  conductivity coefficient and its implications
 for wind mixing may be understood  by examining an  equation describing transport
 within the system.   Mixing implies the transfer of materials or properties  within a
 system from points  of high concentration to points of low concentration, and vice
 versa.  For a system which is  undergoing forced convection,  it has been observed that
 the  time rate of transport,  F,  of  a property,  S,  through  the system is  proportional
 (other things being equal) to  the  rate of change  of concentration of this  property with
distance, z.  In equation form, this rule is expressed  as:

                                      F  .  - D |i                                  (E-2)
                                               o 2,
where
        0  «  coefficient of proportionality.
The mixing process  as defined  by Equation E-2  is  variously called "effective diffusion,"
 "eddy diffusion," or the "diffusion analogy" because it  is identical  in form to the
equation describing the process of molecular diffusion.   The difference between the  two
processes, however, is that  for molecular diffusion, D  is constant,  while  for turbulent
transfer, D is a function of the dynamic character, or  the turbulence level, of the
 system.  In  general, D is a  temporal  and spatial  variable,  and thus  wi 11 be referred  to
here as D(z.t).   Equation E-2  rewritten  for heat  flow over the reservoir vertical  axis
 is:
                                         E-3

-------
            10
             TEMPERATURE (*C)

            20       0       10
   6


   9


   12


   15


   18


   21
Q.
UJ  ,
O  3
   12


   15


   18


   21


  24
        J JUL 1968
                         IS JUL. 1968
                  •Prototype
2O JUL 1968
t6 JUL 1998
 FIGURE E-l     COMPARISON OF  COMPUTED  AND OBSERVED
                 TEMPERATURE PROFILES  IN KEZAR  LAKE
                            E-4

-------
EL CAPITAN 1964 - NO Ml XING

     TEMPERATURE (*C)

     10   15  20   10   15   20   10   15   20  25

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     ISO DAYS    165 DAYS     ISO DAYS
EL CAPITAN 1966 - WITH AERATION

     TEMPERATURE <»C)

    JO   15  20  10  15   20   10   15   20  10  15  20   25   7
   80
  100
     6OO*rS     9ODAYS
ISO DAYS
      FIGURE E-2     COMPARISON OF COMPUTED AND OBSERVED

                     TEMPERATURE PROFILES  IN EL CAPITAN

                     RESERVOIR
                            E-5

-------
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         .02    .CV4 .06 .08.1    .2

     STABILITY Efx.f ),m-»« 10*
4  .6 .01.0   2.0   4.0 6,04.010   20   40 6O CO 100   2OO  400
    FIGURE E-3   PLOT  OF THE  EDDY CONDUCTIVITY COEFFICIENT, D(Z,T) VERSUS
                  STABILITY, E(z,T) FOR  HUNGRY  HORSE  RESERVOIR  DATA
                  (AFTER WATER RESOURCES,  INC,,  1969)
                                       E-6

-------
                                    H  - -pcD(z.t) fj                             


where   H       »  heat flux, HL"2!"1
        p       »  density of water, ML"
        c       •  heat capacity of *«ter, HM'V1
        D(z.t)  -  coefficient of eddy conductivity, L2!"1
        I       •  temperature, D
        z       •  elevation 1n the reservoir, L
        t       •  time T.
     From Equation E-3, therefore, 1t  may  be seen that the rate  of heat  flux  (H),  which
describes the rate of energy transfer  vertically In  an impoundment,  1s a function  of
the temperature gradient over depth (|y)  and the degree of turbulence (induced  by wind
and other factors) and Is characterized by the eddy  diffusion coefficient D(z,t) in  the
equation.  It is this coefficient, D(z,t)  which is plotted on the ordinate (stability
is on the abscissa) in Figure E-3.

Surface Heat Flux
The simulation of temperature involves the following steps:
     1. The heat transfer at the air-water Interface is evaluated for  all  surface  nodes
        as a function of the meterological  variables and nodal temperatures.
     2. The heat input due to shortwave solar radiation is distributed with depth
        according to the light transmissibility characteristics  of the water  (which  are
        a function of the suspended particulates).
     3. Heat 1s distributed within the water body by hydrodynamic transport (advection
        and dispersion) in the same manner as conservative dissolved constituents.
The net rate of heat transfer across the air-water interface is  computed according to
the following heat budget equation:

                         H ' "sn * "at '   
-------
        a    *  evaporative heat loss (Kcal/m^/sec)
        q    *  convectlve heat exchange between the water surface and the atmos-
                    phere (Kcal/m2/sec).
The heat transfer terms for long wave back radiation, evaporative heat loss, and
convectlve heat exchange depend on the water temperature In the surface nodes (\
values), while the solar radiation and atmospheric  long wave radiation (K values)  are
independent of water temperature.  Algorithms for the various terms  of Equation  E-2 are
used for separate computation and then summed as shown 1n Equation E-l.

NOTE:
     For a more detailed description of the model,  Its applicability,  and  the
eddy diffusion coefficient, the reader is referred  to a report entitled "Mathematical
Models for the Prediction of Thermal  Energy Changes in Impoundments."   (See  the  list of
references at the end of this  Appendix.)
                                         E-8

-------
REFERENCES FOR APPENDIX E


Chen, C.W., and G.T. Orlob.  1975.  Ecologic Simulation for Aquatic Environments
     in Systems Analysis and Simulation in Ecology.  Academic Press, New York, San
     Franciso, and London.  111:475-588.
Lorenzen, M.W., and A. Fast.  1976.   A Guide to Aeration/Circulation Techniques
     for Lake Management.  For U.S.  Environmental  Protection Agency, Corvallis,
     OR.
Hater Resources Engineers, Inc.   1969.  Mathematical  Models for the Prediction of
     Thermal  Energy Changes in Impoundments.  Water Quality Office, U.S.  Environmental
     Protection Agency, Washington,  D.C.
                                         E-9

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                                   APPENDIX F

                       RESERVOIR SEDIMENT DEPOSITION SURVEYS

     Summaries of data front known reliable reservoir sedimentation surveys made in
the United States through 1970 are presented 1n this Appendix, together with an
explanation of the summary table.  Additional  data from surveys made after 1970 are
included for some reservoirs.  The reservoirs  are grouped according to the 79 drain-
age areas into which the United States is divided in the publication:  "River Basin
Maps Showing Hydrologic Stations", compiled under the auspices of the Subcommittee on
Hydrology, Federal Inter-Agency River Basin Committee.  An Index map of these drainage
areas is shown on page F-78.  An Index to the surveys 1s provided below.  Appendix F
is available on microfiche in the enclosed envelope for the EPA-publ1shed
manual, or as Part 3, for paper copies purchased from the National  Technical
Information Service.

Drainage Area	Page

      1     St. John Machias, Penobscot,  Kennet>ec, Androscoggin and            F-6
            Presutnpscot River Basin
      2     Housatonic, Connecticut,  Thames, and Merrimack River Basin         F-6
      3     Hudson River Basin and St. Lawrence Drainage in New York           F-6
      4     Susquehanna and Delaware  River Basins                              F-6
      5     Potomac, Rappahannock, York,  and James River Basins                F-7
      6     Chowan,  Roanoke, Tar, Neuse,  and Cape Fear River Basins            F-7
      7     Pee Dee, Santee, and Edisto River  Basins                           F-8
      8     Savannah, Ogeechee,  and Altamaha River Basins                      F-9
      9     Satllla, St.  Mary's, St.  John's, and Suwannee River Basins         F-9
     10     Southern Florida Drainage                                          F-9
     11     Apalachicola  and Ochlockomee  River Basins                          F-9
     12     Choctawhatchee, Yellow, Escambia and Alabama River Basins          F-9
     13     Tombigbee,  Pascagoula,  and Pearl River Basins                      F-9
     14     Lower Mississippi  River Basin (Natchez to the Mouth):               F-9
            Calcasieu,  Mermentau, and Vermilion River Basins
     15     Lower Mississippi  River Basin (Helena to Natchez):   Yazoo,          F-10
            Big  Black,  and  Ouachita River Basins
     16     Lower Mississippi  River Basin (Chester to Helena):   St.  Francis     F-ll
            River Basin
     17     Ohio  River  Basin  (Madison to  Uniontown):   Uabash  River  Basin        F-12
     18     Tennessee River  Basin (below  Hales  Bar Dam):   Cumberland  and        F-13
            Green River Basins
    '19     Ohio  River  Basin  (Point Pleasant to  Madison):   Kanawha,  Big         F-13
            Sandy, Licking,  Kentucky,  Scioto,  and  Miami  River  Basins

                                          F-l

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                                      Page
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
Tennessee River Basin (above Hales Bar Oam)
Ohio River Basin (above Point Pleasant) and Lake Erie Drainage
Great Lakes Drainage (in Michigan) and Naunee River Basin
Great Lakes Drainage (in Michigan and Wisconsin)
Mississippi River Basin (Louisiana to Chester): Illinois,
Kaskaskla and Meramec River Basins
Upper Mississippi River Basin (Fairmont to Louisiana): Iowa,
Skunk, and DCS Moines River Basins
Upper Mississippi River Basin (Prairie du Chi en to Rock Island)
and Lake Michigan Drainage: Rock and Wapsipinicon River Basins
Upper Mississippi River Basin (St. Paul to Prairie du Chien):
Wisconsin, Root, Chippewa, and St. Croix River Basins
Upper Mississippi River Basin (above St. Paul)
Lake Superior and Lake of the Woods Area (1n Minnesota)
Red River of the North Basin
Missouri River Basin (Nebraska City to Hermann)
Smoky Hill and Lower Republican River Basins
Upper Republican, North Platte River Basins (Fort Laramle to
North Platte) and South Platte River Basin (Sublette to North
Platte)
North Platte River Basin (above Ft. Laramie) and South Platte
River Basin (above Sublette)
Missouri River Basin (above Blair to Nebraska City) and Platte
River Basin (below North Platte)
River Basin (Niobrara to above Blair), James, and Big Sioux
River Basins
Missouri River Basin (above Pierre to Niobrara): Niobrara
and White River Basins
Missouri River Basin (Mobridge to above Pierre): Cheyenne
and Belle Fourche River Basins
Missouri River (Williston to Mobridge): Moreau, Grand,
Cannonball, Heart, and Little Missouri River Basins
Missouri River Basin (Zortman to Williston): Milk and
Musselshell River Basins
Missouri River Basin (above Zortman)
Lower Yellowstone River Basin: Tongue and Power River Basins
Upper Yellowstone River Basin
Arkansas River Basin (Van Buren to Little Rock) and White
River Basin
Arkansas River Basin (Tulsa to Van Buren): Grand, Verdigris,
and Lower Canadian River Basins
Arkansas River Basin (Garden City to Tulsa): Middle Canadian,
Lower Cimarron, and Salt Fork River Basins
Arkansas River Basin (Lamar to Garden City): Upper Cimarron
and Upper Canadian River Basins
F-15
F-17
F-20
F-21
F-21
F-23
F-23
F-23
F-24
F-24
F-24
F-24
F-26
F-28
F-28
F-29
F-31
F-32
F-33
F-34
F-34
F-34
F-34
F-35
F-35
F-36
F-37
F-39
F-2

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Drainage
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
Area
R1o Grande Basin (above Espanola) and Arkansas River Basin
Red River Basin (Denison to Grand Ecore): Little and Sulphur
River Basins
Red River Basin {above Denison)
Sabine, Heches, and Trinity River Basins
Lower Brazos, Lower Colorado, Guadalupe, San Antonio, and
Nueces River Basins
Brazos River Basin (South Bend to Washington), Middle, and
Colorado River Basins
Upper Brazos and Upper Colorado River Basins
Rio Grande Basin (below Eagle Pass)
Rio Grande Basin (Fort Quitman to Eagle Pass) and Lower Pecos
River Basin
Rio Grande Basin (Espanota to Fort Quitman)
Upper Pecos River Basin
Colorado River Basin (below Hoover Dam): Williams and Lower
Gi la River Basins
Gila River Basin
Little Colorado and San Juan River Basins
Colorado River Basir (Hall's Crossing to Hoover Dam)
Colorado River Basin (above Hall's Crossing): Gunnison,
Dolores, and Fremont River Basins
Green River Basin
Great Salt Lake Basin
Sevier River Basin
Great Basin (northwestern part in California, Nevada, and
Oregon)
Great Basin: Humboldt, Carson and Truckee River Basins
Great Basin: Owens, Walker, and Mono Lake Drainages
Salton Sea and Southern California Coastal and Great Basin
Drainage
San Joaquin and Keen River Basins and Adjacent Coastal
Drainage
Sacramento, Eel, and Russian River Basins
Klamath, Rogue, and Umpqua River Basins
Lower Columbia River Basin and Pacific Coast Basins in
Page
F-40
F-40
F-41
F-43
F-44
F-45
F-47
F-47
F-47
F-48
F-48
F-49
F-49
F-51
F-52
F-52
F-56
F-56
F-56
F-57
F-57
F-57
F-57
F-69
F-71
F-72
F-73
       Northern Oregon

75     Columbia River Basin (Grand Coulee to Umatilla)  and Pacific        F-74
       Coast Drainage in Washington:   Yakima, Chelan,  and Okanogah
       River Basins

76     Columbia River Basin (International  Boundary  to  Grand Coulee)       F-75
       and Pacific  Coast Drainage in  Washington:   Pendorielle,
       Spokane. Walla Walla,  and  Lower Snake River Basins
                                     F-3

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Drainage Area	             Page
     77      Columbia  River Basin  1n  Canada                                      F-75
     78      Snake  River Basin  (from  Kings Hill to  Grande  Ronde  River)           F-75
     79      Snake  River Basin  (above Kings Nfll) and Salmon River Basin         F-7T
     80      Puerto R1co                                                         F-77
                                         F-4

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                                   APPENDIX 6

                             INITIAL DILUTION TABLES

     Appendix G consists of Initial  Dilution Tables.  Page 6-1 provides information
for choosing the appropriate table.   These follow 1n numerical order beginning on pp.
G-2 through G-101.  The Appendix  1s  available on microfiche in the enclosed envelope
for the EPA-published manual, or  as  Part 3 for paper copies purchased from the National
Technical  Information Service.
                                         G-l

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                  APPENDIX  H
EQUIVALENTS OF COMMONLY USED  UNITS OF MEASUREMENT
English Unit
•crt
•crt
•cre-ft
Btu
Btu
Btu/hr/sq ft
Btu/lb
eta
cfi
cfs/sq Biles
cu ft
cu ft
cu 1n.
cu yd
°F
°C
ft
ft-lb
9.1
9.1
gptf.cn
Other coancnly useC
Multiplier SI Unit
X4. 046. 724- B2
-2.471X10"*X
X0.405- M«
- 2.471X
XI .233. 5- m3
- 8. 11X10 X
XI. 055- kJ
-0.947SX
X0.252- kj-cal*
- 3.968X
-o'316J
X0.555- kg-cal/kg*
- 1.80X
X0.028- «3/«1n
- 3S.71X
XI. 7- • "'/•In
-O.S88X
X0.657- *3/Bln k»2
- 1 . S22X
X0.028- ii3
- 35.314X
English unit Multiplier SI Unit
9Pd/ft X0.0124- B^Vday «
-80.65X
gpd/sq ft X0.0408- *3/d
- 1.3709X , 2.6*X10"4X
0--»S( f-32)- CC rgd X0.0438- *2/i
* 1 8( C)»32 . - 22.82X
plus 273- X Bile XI. 61- km
- "inus 273 » 0.62U
X0.3048- B ppb HO'3- «,/!•
* 3 281 ; -i.ooox
XI. 356- J
- 0.737X
X3.785- !•
-0.264X
XO. 003785- «3
-2M.2X
X0.9365- n3/d«y k»:
- 1 .068X
conversions :
PP* appronBately ng/1*
equ«l to
sq ft X0.0929- «2
- 10.76X
sq In. X645.2- «*2
-0.00155
sq Biles X2.590- kK2
-0.3861X
1 MSO • l.SScfs , * .3.414 X I06 BTU/hr 1 BTU • 252 cil
YCp • 62.4 BTU/ftVf , ITU . 778 ft-lb ) Langley/day • 3.7 BTU/ft.2/d*y
•Hot an SI unU, but • terwi coM»nly used «nd preferred •! • M*stev«ter unit of expression.
                    H-l

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                                       APPENDIX I
                              ADDITIONAL AQUIFER PARAMETERS
 Physical  Properties  of  Water

      The  density  of  a fluid  1s  defined  as  the  mass  of  fluid  per  unit  volume.   The
 viscosity of a  fluid is a  measure  of  the resistance of the fluid to deform when  moving.
 The  kinematic viscosity v  is  defined  as the  viscosity  u divided  by  the  density of the
 fluid o  :
 Compressibility £   is  the  relative change  of  a  unit  volume  of  fluid  per  unit  increase
 in  pressure.  Thus  0   relates  the volumetric  strain  to  the  stress  induced  in  water  by  a
 change  in  fluid pressure.
      Upon  examining Table  1-1, the viscosity  u  is most  affected  by temperature  changes
 and u decreases by  about 3  percent per degree Celsius rise  in  temperature.  The
 properties of water are also a function of pressure, but they  are  even less sensitive
 to  changes in pressure than to changes in  temperature.  However, in  most situations
 that  are encountered in ground water problems,  the physical properties of  water are
 considered as constants.

 Particle Density
      Particle density, P (g/on ), of a soil is defined  as the mass of soil solids M  (g)
                        S                     •*                                     S
                        >                     3
divided by the volume of the soil solids V  (cm ):
      Ps ' VVs                                                                   .
     The particle density for most mineral soils varies between 2.6 and 2.75 g/cm  .
Table 1-2 gives a list of typical values for various materials.  Note that organic
matter has a much lower particle density, between 1.2 and 1.5 g/cm ,  Thus, surface
soils usually have a lower particle density than subsoils.
     Sometimes the density of a soil is expressed in terms of the specific gravity.
The specific gravity 6 (unitless) is equal to the ratio of the particle density
Ps(g/on ) of the material to that of water P (g/cm ) at 4 degrees Celsius and at
atmospheric pressure:
     G » PS/PW
However, since the density of water under these conditions is 1 g/cm3 (see Table 1-2),
the specific gravity is numerically (although not dimensionally) equal to the particle
density.
     The average particle density P  {g/cm )  of a soil  can be determined in the
laboratory by the picnometer method (i.e., water displacement test)  (Fox,  1959; Taylor
and Ashcroft, 1972).   Typical values for various materials are given in  Table  VII-3.
                                         1-1

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                                        TABLE i-1
                   PHYSICAL PROPERTIES OF PURE WATER AT ONE ATMOSPHERE
Temperature
°C
0
4
5
10
15
20
25
30
35
Density
(g/orf)
,99987
1.00000
.99999
.99973
.99913
.99823
.9970B
.99568
.99406
Viscosity
(g/cm sec)
,01787
.01567
.01519
.01307
.01139
.01002
.00890
.00798
.00719
Kinematic
Viscosity
(cm2/sec)
,0179
.0157
.0152
.0131
.0114
.01004
.00893
.00801
.00723
Compressibility
(on sec2/g)
5,098 x 10 ~1L
4.959 x 10 "U
4.928 x 10 "n
4.789 x 10 "H
4.678 x 10 ~11
4.591 x 10 ~11
4.524 x 10 "ll
4.475 x 10 "U
4.442 x 10 "H
 Reference:   Weast  (1969).
Specific Yield
     Specific yield can be used as an estimate of effective porosity.  Specific yield
is also used to predict the drawdown of the water table and the local velocity field
around a pumping well.   It is an essential parameter for the analysis of the
performance of a recovery well field.
     The specific yield S  (unities*) of an unconfined aquifer 1s a measure of the
"water-yielding" capacity of the porous medium.  The specific yield is defined as the
volume of water that will discharge per unit area of saturated porous medium under a
unit drop In hydraulic  head.  Specific yield can be expressed as either a ratio or as a
percentage.  That part  of the water retained by molecular and surface tension forces 1n
the void spaces of a gravity drained material is known as retained water.  The "water-
retaining" capacity of  porous media is called the specific retention Sr (unitless).
Hence, the porosity of  a saturated, unconfined aquifer 1s equal to the sum of the
specific yield and the  specific retention:
     P ' Sy * Sr
     Gravity drainage from most unconfined aquifers 1s not Instantaneous.  If the
hydraulic conductivity  1s low, the water-yielding capacity can increase up to the
                                          1-2

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                                        TABLE 1-2



                        RANGE  AND  MEAN  VALUES OF PARTICLE DENSITY
Material
clay
silt
sand, fine
sand, medium
sand, coarse
gravel, fine
gravel, medium
gravel, coarse
loess
eolian sand
till, predominantly clay
till, predominantly silt
till, predominantly sand
till, predominantly gravel
glacial drift, predominantly silt
glacial drift, predominantly sand
glacial drift, predominantly gravel
sandstone, fine grained
sandstone, medium grained
siltstone
claystone
shale
1 imestone
dolomite
granite, weathered
gabbro, weathered
basalt
schist
slate
Range
(9/cm5)
2.51 -
2.47 -
2.54 -
2.60 -
2.52 -
2.63 -
2.65 -
2.64 -
2.64 -
2.63 -
2.61 -
2.64 -
2.63 -
2.67 -
2.70 -
2.65 -
2.65 -
2.56 -
2.64 -
2.52 -
2.50 -
2.47 -
2.68 -
2.64 -
2.70 -
2.95 -
2.95 -
2.70 -
2.85 -
2.77
2.79
2.77
2.77
2.73
2.76
2.79
2.76
2.74
2.70
2.69
2.77
2.73
2.78
2.73
2.75
2.75
2.72
2.69
2.89
2.76
2.83
2.88
2.72
2.84
3.09
3.15
2.84
3.05
Mean,
(g/cmj)
2.67
2.62
2.67
2.66
2.65
2.68
2.71
2.69
2.67
2.66
2.65
2.70
2.69
2.72
2.72
2.69
2.68
2.65
2.66
2.65
2.66
2.69
2.75
2.69
2.74
3.02
3.07
2.79
2.94
Reference:   Morris and Johnson (1967)
                                          1-3

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                               TABLE  1-3
                RANGE AND MEAN VALUES OF SPECIFIC  YIELD
Material*
clay
s1H
sand, fine
sand, medium
sand, coarse
gravel, fine
gravel , medium
gravel, course
loess
eolian sand (dune sand)
till, predominately silt
till, predominately sand
till, predominately gravel
glacial drift, predominately silt
glacial drift, predominately sand
sandstone, fine grained
sandstone, medium grained
siltstone
shale13
1 imestone
schist
Range
(percent)
1.1
1.1
1.0
16.2
18.4
12.6
16.9
13.2
14.1
32.3
0.5
1.9
5.1
33.2
29.0
2.1
11.9
0.9
0.5
0.2
21.9
- 17.6
- 38.6
- 45.9
- 46.2
- 42.9
- 39.9
- 43.5
- 25.2
- 22.0
- 46.7
- 13.0
- 31.2
- 34.2
- 48.1
- 48.2
- 39.6
- 41.1
- 32.7
5
- 35.8
- 33.2
Mean
(percent)
6
20
33
32
30
28
24
21
18
38
6
16
16
40
41
21
27
12
14
26
Reference:   Morris and Johnson (1967)
bReference:   Walton (1970).
                                   1-4

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specific yield at a diminishing rate as  the time of drainage  increases.
     Values of specific yield depend on  grain size, shape and distribution  of  pores,
compaction of the stratum and time of drainage.  The range and mean  values  of
laboratory measured specific yields for  various geologic materials are given in Tadle
1-3.

Specific Storage
     The specific storage or elastic storage coefficient S  of a confined aquifer is
defined as the volume of water released  from storage per unit volume of aquifer per
unit decline in hydraulic head.  This release is due to the compaction of the aquifer's
granular skeleton and the expansion of pore water when the water pressure is reduced by
pumping.  S  has the units of cm"  and is normally a small quantity  (1 x 10~ cm~  or
less).  Typical values of specific storage S  are given for various geologic materials
in Table 1-4.

Storativity
     Storativity or storage coefficient, S, is also defined as the volume of water that
is released from storage per unit horizontal  area of aquifer per unit decline of
hydraulic head.   It is a dimensionless quantity.  This  parameter is obtained in
addition to transmissivity from pumping tests.   It  is  used to compute aquifer yields
and to compute drawdowns of individual  wells.
     For confined aquifers, Storativity is due  to water being released from  the
compression of the granular skeleton  and expansion  of  the  pore water.  S  is
mathematically defined as the product of the specific  storage, S  (cnT )  and the
aquifer thickness, b(cm):
     S « S$ b
     The value of the Storativity for confined aquifers is Generally small,  falling
between the range of 0.00005 and 0.005 (Todd,  1980).   Hence,  large pressure  changes
over an extensive area of aquifer are required before  substantial water is released.
     For unconfined aquifers, Storativity is  due to the release  of water  from gravity
drainage of voids (i.e., yield)  and from the  compressibility  of  the granular skeleton
(i.e., elastic storage).
     This is mathematically defined as:
     5 ' Sy + hSs
where S  is the specific yield (dimensionless),  h is the saturated thickness of the
       y                                                    i
water-table aquifer (cm) and 5  is the  specific  storage (cm  ).   The value of S  is
usually several  orders of magnitude larger than  hS  , except  for  fine-grained aquifers
where S  may approach  the value  of hS .   Storativity S  of  unconfined aquifers ranges
from 0.01 to 0.30.
                                         1-5

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                                      TABLE 1-4
                       RANGE OF VALUES FOR COMPRESSIBILITY AND
                    SPECIFIC STORAGE OF VARIOUS GEOLOGIC MATERIALS
                                                           Specific Storage
                                                                 Ss
              Material                                         (cm"1)

       plastic clay                                     2.0 x 10~4 - 2.5 x 10"5
       stiff clay                                       2.5 x 10*5 - 1.3 x 10"5
       medium-hard clay                                 1.3 x 10"5 - 6.9 x 10"6
       loose sand                                       9.8 x 10"6 - 5.1 x 10"6
       dense sand                                       2.1 x 10~6 - 1.3 x 10"6
       dense sandy gravel                               9.8 x 10   - 5.1 x 10~7
       rock, fissured, jointed                          6.9 x 10"7 - 3.2 x 10"8
       rock, sound                                      less than 3.2 x 10
       Reference:   Jumlkis (1962)  and Walton (1970).
Measuring Specific Yield, Specific Storage and Storat1v1ty
     Although most field methods determine specific yield directly, most laboratory
methods determine specific retention by the centrifuge-moisture method (Johnson e_t a_l.
1963), and specific yield S  (unitless) 1s found indirectly by subtracting the specific
retention 5  (unitless) from the porosity p (unitless):
     Sy ' P ' Sr
Other laboratory methods are discussed by Johnson (1967).  However, laboratory samples
may be disturbed or may not be representative of the aquifer.
     Several field methods are available to estimate specific yield, Including drawdown
tests, recharge tests, the neutron moisture methods and tracer methods.  Jones and
Schneider (1969) discuss the neutron moisture method and compare it to five other
methods for the Ogallala aquifer in Texas.  They concluded that pumping and recharge
methods underestimate the specific yield by 501 compared to the other methods.  Hanson
(1973) also concludes that pumping will underestimate the specific yield if the pumping
test is done over too short a period of time.  However, Todd (1980) believes that
methods based on an analysis of the time - drawdown data from well-pumping tests
generally give the most reliable results.
Specific storage S  is a function of the solid matrix and fluid compressibility.
Compressibility can be determined in the laboratory by means of a consolidation
                                         1-6

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apparatus called a  loading cell.  Either a fixed-ring or  a  floating-ring container  type
loading cell can be used  (Hall, 1953; Lambe, 1951).  In the  field,  specific  storage is
generally measured  indirectly as storativlty S by pumping tests.  If  the saturated
thickness b(cm) of the confined aquifer and storativlty S (unltless) are known, then
the specific storage S$ (cm  )  can be solved  as shown below:
     Ss - S/b
The contribution of specific  storage to storativlty in  unconfined aquifers is generally
negligible.
     Storativity can be determined directly from pumping tests of wells and from ground
water fluctuations in response  to  atmospheric pressure  or  ocean tide variations and
river level  fluctuations.   An extensive discussion of the  various types of pumping
tests and the procedures for  calculating the  storativlty from them Is  given by Todd
(1980), Walton  (1970),  and Lohman  (1972).
                                         1-7

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                                       APPENDIX J
                                 MATHEMATICAL  FUNCTIONS

Complimentary Error Function
      The complimentary error function  (erfc)  is defined as follows

                            erfc(x)  « -JL     e'z  dz
In addition,  erfc has the following  properties:
                            erfc(x)  -  1  -  erf(x)

                            erf(-x)  •  -erf(x)

                           erfc(-x)  «  2  -  erfc(x)

                            erfc(O)  «  1

                            erfc(-)  «  0
                          erfc(- «)  «  2
 where erf 1s the error function.   A 11st  of the  error function and
 complimentary error function for  various  values  of x are given 1n Table J-l.
 A method for numerically computing erfc Is shown 1n Table J-2.
      The following trick should be used when using erfc and exponential functions
 multiplied together:               ,
                                   e -erfc(x)  -  ?

                    when           a •* »
                                   x •* •
      Use the following solution:
                                                                  2
                ea.erfc(x) - (?1t  + a2t2 + a3t3  + a4t4 + a5t5)ea"x
 where a^-.a^ and t are given in  Table  J-2.  Note that the trick is to evaluate the
 combined exponential argument ea"x  rather than  es-e"x .  For example:

                             e100.erfc(9)  • 1.15  x 107

                             e100-erfc(lO) - 5.86 x 10'2

                             e100-erfc(ll) • 4.08 x 10"11

                                        J-l

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                                 TABLE  J-l

                TABLE OF THE ERROR  FUNCTION  (erf)  AND  THE
                   COMPLIMENTARY ERROR FUNCTION  (erfc)
X
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1.0
erf(x)
0
0.056372
0.112463
0.167996
0.222703
0.276326
0.328627
0.379382
0.428392
0.475482
0.520500
0.563323
0.603856
0.642029
0.677801
0.711156
0.742101
0.770668
0.796908
0.820891
0.842701
erfc(x)
1.0
0.943628
0.887537
0.832004
0.777297
0.723674
0.671373
0.620618
0.571608
0.524518
0.479500
0.436677
0.396144
0.357971
0.322199
0.288844
0.257899
0.229332
0.203092
0.179109
0.157299
X
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
infinite
erf(x)
0.880205
0.910314
0.934008
0.952285
0.966105
0.976348
0.983790
0.989091
0.992790
0.995322
0.997021
0.998137
0.998857
0.999311
0.999593
0.999764
0.999866
0.999925
0.999959
0.999978
1.000000
erfc(x)
0.119795
0.0896B6
0.065992
0.047715
0.033895
0.023652
0.016210
0.010909
0.007210
0.004678
0.002979
0.001863
0.001143
0.000689
0.000407
0.000236
0.000134
0.000075
0.000041
0.000022
0.000000
erfc(x)  • 1 - erf(x)
erfc(-x)  • 2 - erfc(x)
erf(-x)  - - erf(x)
Reference:   Crank (1975)
                                  J-2

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                                      TABLE J-2
                      NUMERICAL COMPUTATION OF THE COMPLIMENTARY
                                    ERROR FUNCTION
                       erfc{x)  «  Ut  + at2  + &t3  + »4t4  + at5)e~x   + c(x)
                           where   t
                                           PX)

                                                   -7
                      error term   |c(x)|  <_ 1.5  x  10

                             and   p   «  .3275911
                                  ^  -  .254829592
                                  a2  «  -.284496736
                                  a3  «  1.421413741
                                  a4  -  -1.453152027
                                  ac  •  1.061405429
          Reference:   page 299,  Eq.  7.1.26  of Abramowitz  and  Stegun (1964).
Leaky Uell Function of Hantush
     The leaky well function of Hantush is defined as follows:
     W(u,r/B)
               ~u   u   \       4Bct

where W(:) has the limits:
      W(o,r/B)  » 2K (r/B)  (modified Bessel function of zero order)
      W(u,o)    • E.(u)     (exponential integral)
      W(-,r/B)  - 0
      exp(:)    « exponential  function

The leaky well function has been extensively tabulated by Hantush (1956) and is given
in Table J-3.  For large values of r/B (i.e., r/B>l), Wilson and Miller (1978) have
developed the following approximation to W:
                                          J-3

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                                          TABLE J-3



                             THE LEAKY  HELL  FUNCTION OF HANTUSH



                                           W(u,r/B)
•
• MOW
t MMM
»MMI
• tuft
t M*l
f MM
• Ml
•  i mi
• I'M t «IW • tilt
< mi < ill » inr
> mi 4 mi • Mn
4 «m « tin i >it>
J or* r «>• I «
rx> ( •;« i twi i KM i MM t MM
rm » •;« « «n 4 iwi 4 4*«i i MM r »<«
11*1 t III* 4 (Ml • 4MI > MM 1 M«
•n » 4«) 4 n» • 4»«i i MM r MM
><*< t UK 4 •«/ 4 «« 1 MM r I44t
MM < Oil • >«M 1 Mil 1 «4I 1 Mft
tft 1 Mtl 1 4IM 1 tin 1 Mtt 1 MM
«I4 r MM 1 Mil t lilt Milt 1 »«l
•IM i un i m* i un i mi i.tiM
MM * «M« « «MI • «MI t Ml? * Mil
»)»> • lltl • MM 1 MM * lilt * >UI
Mil • Mil (Mil (Mil * Mil * Mil
II 4
mi
ir«i
mi
tm
ini
tni
ini
int
mi
wt
MM
MM
i fin
1 Mil
»
MM
.MM
MM
.MM
.MM
MM
MM
MM
MM
•HI
MM
turn
1 IMI
I.MII 1
• •
MM
HM
MM
HM
HM
.MM
KM
MM
MM
mt
Hit
MM
i rwi
>.MII
»' *.l •• I* i.l t.t I
»M I.IW ••>• «MJ» ».«!>* *.ltlt
HM I.IMI i»i» t.Mtt *.UM tnn
»M I.IIM tttm I.MN »H» t.ltl*
nn i.iw •!>• t.Mif t.wn 4).ttn
HM 1 >ml (.*!» »MN t.tlN t.ttM
.UM I.IW « tm *.Mf* IJ.IIM ttttt
»n I.IIM « tin  l»l 1 1'» • Ml* «.4fN t.nif
mt I.IIM t«M» *.*M» • «tn (.nit
Itl I.MM i.WW *.MM «.«fM (.lilt
.MM « 44M «.MM *.4tM ».MM t.MM
MM *.!•>» t.m< t.)4M «.IM* «.ltH
I.MII IMII IMII t.MII ».MW I.MM
.1
INI
\HI
INI
tut
.»NI
.INI
INI
.INI
.INI
.INI
IN»
.UN
I.MN
I.MH
N*flt«tl>
                                           J-4

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     W(u,r/B)

1n which erfc 1s the complementary error function (see Table J-l).  This expression for
W 1s reasonably accurate (within 10 percent)  for r/B > 1 and 1s very accurate (within 1
percent) for r/B > 10.
     Note that at large tines (I.e., as u goes to zero) the leaky well function reduces
to the modified Bessel function K :
                                 o

     W(0,r/B) - 2KQ(r/B)

If r/B is larger than one, the following approximation for  the Bessel  function  can  be
made:

     K0(r/B)
                                      J-5

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