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
-------
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
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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
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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
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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
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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
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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
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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
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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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
•Ml
JtK
1
j
i
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a.
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i
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^^
^^
10 70 3
TEMP. C
;
/
10 fO 1
TEMP, c
0
IO
^
o 60c
0
20-
£
O.
UJ
0 C
10 20 3
Tenr. c
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TEMP. C
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10 70 3
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TEMP. C
20-
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°.o.
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TEMP. C
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WICMITR. KRNSR5 1
200' [NiriPL MOXJMUM OEfTH 1
INFINITE MYO«. RES- TlnE j
nRxinun n]x[NG j
I
I
i
10 70 30
TEMP. C |
1 PIRURE V-4 THERMAL PROFILE PLOTS "SED IN EXAMPLE V-] I
i I
i !
i i
i i
-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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10 20 3
TEMP. C
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10 20 3
TEMP. C
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tic
10 tl it 0 10 t'a 3
TEMP. C TEMP. C
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RTLRNTR. GEORGIR j
20' INITIBL MHXIMUM DEPTH |
INFINITE MYOR. RES- TIME j
MINIMUM MIXING
1
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• FIGURE V-5 IHERMAL PROFILE PLOTS APPROPRIATE FOR USE IN F.XAMPLE V-2 :
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run (V PYiuoi c u_o _._ J
-18-
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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-
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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-
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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-
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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-
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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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10 »
10
^'p' Jf
./I
10'
\
10
10'
-2
IO'3 10-2
10'
10
102 103
Valuts of R*
vd
FIGURE V-8 PLOT OF C./R AND rP2 vERSus " (CAMP, 1968)
-25-
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10 3
u
C to2
o
U
o
w
O
10
10'
\
LEGEND'
A - StokM' tt«
B - Spheres
C - Cylinders, L *
0 - Discs
K
2
I 10 K>2 IO3 tO4 K)9 IO*
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-
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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
I.U
0.9
0.8
>|> 0 7
£ 06
(J
0
u.
0.5
C
o
0 04
•
5 °>
0.2
0 1
n
X
X
V^v
v^
\
«
v^
s^
\
^
"^
^
X
vA
4-
>
^
>s
LEGEND:
A - Red Blood Ctll*
B - Lucite Spheres, d<0.0l8lcm., P, « 1.194
C - Round Sand Graint, d «O.OI67 cm., f, * 2.66
^
X
^^.
^<
X
^*-
^0>
>
^
^
^
k.
•^^.
^s^
^^>
^>-
'^-^
^
(Ci
^^^ <
0.05
010
015
0.20
0.25
O.SO
0.35
Volumetric Concentration, C f
FIGURE V-ll VELOCITY CORRECTION FACTOR FOR HINDERED SETTLINS (FROM CAMP, 1968)
-27-
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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-
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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-
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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-
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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-
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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-
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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-
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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-
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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-
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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-
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FIGURE V-18 LAKE OWYHEE AND ENVIRONS
-41-
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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-
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-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-
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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-
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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-
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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-
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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-
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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-
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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-
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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
i
i
i
*
i
i
*
i
i
•
i
i
i
i
i
i
*
i
i
i
i
*
i
4
1
i
i
i
*
'
i
i
i
i
i
i
i
i
*
i
i
i
-59-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
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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-
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"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-
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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-
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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-
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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-
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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-
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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-
-------
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-
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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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1
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10 70 M 0 10 70 30 0 10 70 30 '
TCHP.
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c TEMP, c Tcnr. c :
If . tCl '
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TEMP. C TEMP. C TEMP. C 1
10
TEMP
j FIGURE V-33
i
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t
i
tt
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\
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t
£
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BURLINGTON. VERMONT j
20' IN1TIHL MPXtMUH DEPTH j
IMF1NHE MXOR. RES. TIME
niNinun nixiNC !
|
i
i
„
i
THERMAL PROFILE PLOTS FOR USE IN QUIET LAKE EXAMPLE I
i
*
i
*
i
-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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
OATA
INI IT ICUVVOI* IT,
f»u»*o
V,. U.. ..,.«.« r,,.. ..
- ** _ f
V* MIW • 1
».l •». •»!.. .. .. ».
V4» I..-..H U._ 1.14 .»
4» • ••>
— to. _...to~
"" _-Tto. .--to-
44 4««4>M •. ^ toiiBnin
Vl» *rl»4«l|»l« 1. (IrlfklM 1.1- HiMMt
to .--.to--
<•• (W.4.1-. l.ltl.C.
Vt TW... 4— U.. to-
VII V>~(. tt— 0- «.-..•!
jj _
••>- * 4*
Wtl .W*. We. *1I. 1*. l-rt oV*.
«, 4*
V| •,.«•_ IL. »>~«l «.M, .~
"""" JT.^ »^ JT
- — •- —to-
y •»! MtlMptl t**4ft«>*}4 l*»t «»** •»» ***.» ••). •*.
t»|« »)VM «•* ••«« t« i** t*4( ««lt«l»llW«».
V/ *W*I**4 •f»«» IW1 •*»*•?.
& C*M**MM««II**> •» •«4ll*MNt (Ml mtf.
p •••••) *M *>tl|lMl •*>ltt«f «r**4 *|»*«I|M 04 r
r***lll*>« '»— « I• •' «»•.
Hllfl Iff A HUT TOWN CNUOTAGC AftCA
I9QUARI HLtt)
TOTAL ] MCT
MfOWC, •ftPMM.MkA, MM. M* t
HI*.** it*** — rm« o»*»>. H. u.f u.)
4MMMI. ll.w lll~ tfrl««. •• n.l H.tT
!-,..£,-..--. fc— ..H. *l |»/.l» .Tt
-»
_._to-: " H
-.-to.
„. e-»~i.~ . ». u iyt
» M H.I
— ii«-^.«. «.. imo IM.U
*«• Ml
' ' '
~"'~^ " ""
9VM*. M«*1*C, ttt, fttVU. •« C4ff F»M I
** 'fc
4 C.^.M^.. i. e. ni Ti.4
r* _
1 I* IHI. * tMlMBI
t>cnoo
CAM Of MtntH
WlTVIT M/tVITI
ITCAM)
r*fi
ITOtACt J«
CAfAOTf ™'J
(ACtf -Ft , ™"
Itl
ACM
»«i turn mm
M>. 1*11 - t/*!*1'
1*. KM »ll tt.TM
4^. itii it.i y>.*t>
»». l«7» - I.IM
!•». KM M !.!»>
• | KM - III
«r. KM T.I tt
I.I, Kit - IM
• •». KM l.t IM
k<. Itll K.I III
/•. ItM 10. 1 U/lil
l««. K»l ~ Ml
>... IHI U ITI
J«M IHT II. 1 IM
l«, KM ~ 1 Ml
4«. KIT T.I 4 IM
J~. IHI - U/» III
•rl. ItM 1.) 10 Mt
»•»• ItM l.t K III
4>(. ItM l.t K Ml
to**. Itl) _ ) in
4fl. ItM M.I 1 004
Mr. If)) - T HI
•n. IHI I.I T IH
*>r. Itt) — » Ml
ll.r. ItM I.I M Ul
to.. ItM — • MO
4^. KM M.4 M Wt
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to., itw u.i tor.*
»•»«. itM ~ itt.tr
4^! ItM it III.TI
i«u Him
— K»1 - IM
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"»J KM 111 1.1
• to. KM •- ».«W
U,. KH U.I >.tH
M.. KM .. I.IM
4>«. KH I.I I.IM
•»>. KM I.T1 4,*»
ItM.
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l«4cl tiiltoMl to talk *Mto* Uk* MH •«•
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"" «0»IC
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ACCIMUaTTO*)
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•.m *M i.ti ii. in
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. »>4 H* I.W I.HI
.IH —
.•II -
H* .IU IM
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IT l.ll I.IM
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ill! HO l!tl l'.tn
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MT*
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on
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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-
-------
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-
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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)
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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
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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
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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
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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.
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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:
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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
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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
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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
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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}.
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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
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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)
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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
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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
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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.
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Transported by Urban Runoff. JWPCF 48:580-591.
Dean, J.D., R.J.M. Hudson, and W.B. Mills. 1979. Chesapeake-Sandusky: Non-designated
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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
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Hudson, R.J.M., and D.B. Porcella, 1980. Selected Organic Consent Decree Chemicals:
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&A. In Press.
Hutchinson, G.E. 1957. A Treatise on Limnology, Volume I. John Wiley ft Sons, New
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Hydrologic Engineering Center (HEC), Corps of Engineers. 1974. Water Quality
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Jones, J.R., and R.W. Bachmann. 1976. Prediction of Phosphorus and Chlorophyll
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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.
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Lorenzen, M.W. 1978. Dhosphorus Models and Eutrophication. In press.
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Lund, J. 1971. Water Treatment and Examination 19:332-358.
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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
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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
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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
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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.
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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
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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
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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.
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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
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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
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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.
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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.
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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
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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.
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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-
-------
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
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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
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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.
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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-
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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-
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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
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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-
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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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
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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-
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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-
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.-' _|_-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-
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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-
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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-
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•. .• • .-.:-.. •! • . ••.;. ;.•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-
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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-
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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 -•
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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
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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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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.
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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
»
IB 0-
to
u>
u
0'
u
r . -
0 16
T
\
..__ u
.5 2C
^r:
Kj
1.0 21
=^
>•
)
/_
^x_
~f
"M
5 2C
—
^
1.0 24
•*•
^\
"X
.5 2
-^
\
\
k
s\
i
? \
BO 27
^-^
r
5
1
I
(
2S
^
r
1.0
\
I
^
^
3C
,
)5 3;
I 5
I
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
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).
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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
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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
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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.
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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
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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.
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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)
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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
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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-
-------
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
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Glenne, B. 1967. A Classification System for Estuaries. Journal of the
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Graham, J.J. 1968. Secchi Disc Observations and Extinction Coefficients in
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Harleman, D.R.F. 1971. Hydrodynamic Model - One Dimensional Models. Estuarine
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Harleman, D., and C.H. Lee. 1969. The Computation of Tides and Current in
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Hodkinson, J.R. 1968. The Optical Measurement of Aerosols. In: Aerosol
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Hydroscience, Inc. 1971. Simplified Mathematical Modeling of Water Qual ity.
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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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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
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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
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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
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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
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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.
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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.
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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.
-------
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
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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
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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)
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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.
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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-
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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-
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(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-
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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-
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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-
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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-
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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-
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(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-
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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-
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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
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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
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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.
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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
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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
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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.
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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.
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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).
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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
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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)
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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)
-356-
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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
-358-
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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
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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)
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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
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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
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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$:
D • Om * D* (VII-45)
Molecular diffusion D* 1s a microscopic and molecular scale process that results
from the random thermal induced motion of the solute molecules within the liquid phase.
This process is Independent of the advective motion of the ground water and can be of
significant importance at low flow velocities and very near solid surfaces. Duursma
(1966) reported experimentally determined molecular diffusion coefficients that ranged
between 2 x 10~ and 6 x 10" cm /sec for trivalent and monovalent ions (both positive
and negative) in fine sand. However, molecular diffusion is generally specified
(Sudicky, 1983; Gillham et al_., 1984) as:
D* - 1 x 10"6 cm2/sec (VI1-46)
Mechanical dispersion 0 occurs predominately on a macro and megascopic scale and
HI
is due to the "mechanical mixing* of the solutes. Such mechanical mixing is caused by:
a) variations in the velocity profile across the water filled portions of a pore, b)
variations in the channel size of the pores, c) the tortuosity, branching and
interfingering of pore channels.
7.4.1.2 One-Dimensional Flow
7.4.1.2.1 Introduction
For one-dimensional flow, mechanical dispersion D^cn^/sec) is generally expressed
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^mmw/////////////^^^^^
MILLIM
MICROSCOPIC SCALE
MACROSCOPIC SCALE
SOLUTE MIGRATION
PATHWAY
FIGURE VI1-20 SCHEMATIC SHOWING THE EFFECT OF SCALE ON
HYDRODYNAMIC DISPERSION PROCESSES
as a function of the seepage velocity v (cm/sec) witn the relationship:
Vs
(VII-47)
where «1 (cm) is the longitudinal dispersivity of the porous medium. Upon substitution
of Equation VII-47 into Equation VII-45, the hydrodynamic dispersion coefficient D
(cm /sec) becomes:
+ D"
(VII-48)
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where the molecular diffusion D* (c»2/$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.
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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)
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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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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-
-------
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
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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-
-------
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-
-------
=H= J~£I^
/X^ii C^ "SK"01"
*••*»•!•**• »»•*»•
:'/-'-'.--.'--:-'.'-.'
•/•':.:V.V.:.:'.: -"•'-•.'
• :-•:••:••:••:•/
•.'•'.•/•'.•/•V.'-V.V.V
»»*» ,*• * * * » ^ » •*•
.",.* »•*»**• »*»»
• '. '.V ' " • • ' '.'.'• •'*' •-'"'•''." '-''
'•/.•.-.'•'.••.•!• "'.•••; :•'.•'.'•.• '•'••'
• :: ;: :.•:.••'.• :».'.-'•' •'•;•;'•
a
M
• *'»•*»•••*•**'»** •**%**»**«**«"'^'*t'*H**«* '»**»"•,
' •'••'••'. •'*•'* ••*"•"*"!. '.'•'••'. '••'." ,"••"•• '"''"'••
' "1' 'I*'"'.*''* "1 "'*"'''?• '*"Z "*"'."', ••'.'•'.••'••'*
»•*••**•»* *»*'.*'***»*****«*'r*'t* *•*"*"***"***»****•
"*•*••*•» **1*'*»'***"*'»»*^'»^»'"**^''» •»"•»*«•**•*
• •*••*• *t*'»****'t*****»*****»**»***"*»**" *•*»»*•*"••
*,.*•, "•*l'"%********»**«'*»**t*'"**'*'"***'<**'***%
.'.':'.'•:.'•;.'';''••'•'•:•'•''•'••'•'•:•'• aoimif mi SHALE .'.';V
•'.?•'
•'•V-.i-
>'•.'.
• iv'-::.':^v • •••: 'V^;i->;'V--::':^ :'-;>-:'- •**<»ro»i« >v;:i:
v?^/®:^-? ^ !• ^'^^ ^^^ •v:^-''-/:
:'::'''.:*'--'.'.':''" •.':••••.'••::••.•:'•.'.•': :>'••• : • .•'.•: •.".•'•:vX::;''.-::i': -.'••> •;"•".
.••••'• .••"••.'..'•:'.••'•.-•.•.'•.':••'. .7.'-.-'.'.'.':-' ' ••:••••.•.•••.•••.••.•:•:•:!•••• •
•^
••
a
H
MONTTOAlNC
wfu
*•; x
• - 1
» * *
* » •
K>* ; .'
•. *. "'.'* *- .'•'•'.
•• '*•"'"! .* '•". •*?
'«••*.• ^ ••-
•'••,'••••-••'. •".'.'•' •'•"•'.'•'.'•'."•"•''•" ^ •'• ' •• ' •'- • •'• ••".•."'•'*'•"•'," -V '•"•"'•'* 1"! •*• '•'•'•'
1 •• j ••;•••.".•/.• • ."•'."•'.'•',"••,'."'••;•-'••'.'.•.*.•,*.•.' . *.•'.*•"."•""••"•*""**•".'••*•"••
• •; •'•*.".•.",•/.•"•*."•','•*• ^ v •''* "I "* •'•••'••.'.".'.•.' '' * ;••'••*••'•'•'•".•.'.
'-•,•••/'. •'••• •'• :•'•'•'.'.'•'.•.'•'.•.'.'.•'.• •' v' v '•.-* •'- : •'• .'•'- • .'. • •***"MeA*L£ SHALE • >- *•*-.••'- :•'- .-.'. ;
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-
-------
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-
-------
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-
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. . (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
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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.
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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).
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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.
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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)
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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
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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?
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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.
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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.
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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-
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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
-------
REFERENCES
References Cited
Abramowitz, M. and I.A. Stcgun. 1964. Handbook of Mathematical Functions with
Formulas, Graphs and Mathematical Tables. Applied Mathematics Series No. 55, National
Bureau of Standards, 1046 p.
Bachmat, Y., B. Andrews, 0. Holtz and S. Sebastian. 1978. Utilization of Numerical
Ground Water Models for Uater Resource Management. EPA-60G78-78-012, U.S. EPA, Robert
S. Kerr Environmental Research Laboratory, Ada, Okalhoma.
Basak, P. and V.V. Murty. 1979. Determination of Hydrodynamic Dispersion Coefficients
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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-
-------
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.
-------
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
-------
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
-------
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
-------
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
-------
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
r o
x
H
a
40
60-
eo
s
f
*
/
»f
/
£/
•f
I
r
1 • Simula
-rrotet
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
-------
Legend' o ii MAv-26 w*r IMS 0 » JUNE- 25 JUNE r*es A TJULV - ZIJULY 19*5
X 26 MAY-9 JUNE '969 O 23 JUNE-7 JULY 1965
IU.U
a.o
6.0
40
2.0
1.0
.8
.6
4
2
. i
8
06
C*
02
m
A •
u
C
i
(T
c
<
A^
3U
i
I
i
,
A
.r....
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a
o
o
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^
A
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-»T
0
A
u
-
(J
— «.
A
°
o oo
X
\
A
t^f.
^ "Cl
<>
I
Jo t?
<£°
Q ^
k
\
>
c
x)07
. Op
.
o
k
L«^J' "
0 o
V
6
— •^
s
X
•
^
V
JO
i
V
Upper
.Envelope
^'
X.
I /x(
o
1
"x lo
A ^>
v
\
i
X
f o<
7
X
X
Lower
Envelope'
^
>-N
^'
\
D
N
N
V
\
N
0 \
S. "•
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' A
^
X
>^\
'XN
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u
.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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
------- |