Office of Regulations EPA-440/.;
£ nvironnwnttl Protection and Standards Monitoring December 1986
Agtncy a"d Data Support Division pin»!
IWH-553)
Washington, DC 20460
Wmr
oEPA Technical Guidance
Manual for Performing
Waste Load Allocations
Book IV
Lakes, Reservoirs
and Impoundments
Chapter 3
Toxic Substances Impact
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U.S. Environmental Protection Agency
Monitoring and Data Support Division
Washington, DC
Under Subcontract to:
Arthur D. Little, Inc.
Cambridge Massachusetts
TECHNICAL GUIDANCE MANUAL FOR
PERFORMING WASTELOAD ALLOCATIONS
BOOK IV LAKES, RESERVOIRS AND IMPOUNDMENTS
CHAPTER 3 TOXIC SUBSTANCES IMPACT
Prepared by:
HydroQual, Inc.
1 Lechbridge Plaza
Mahwah, New Jersey 07430
December 1986
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CONTENTS
Section 2SS.
FIGURES .................................................. iv
TABLES ...... ..... ...................... v"
1.0 INTRODUCTION ........ '. .................................... J
1.1 Relacion to Other Books and Chapters ................ 1
1.2 Scope of the Chapter *
1.3 Organization of the Chapter .................
2.0 BASIC PRINCIPLES OF CHEMICAL MODELS ...................... j>
2.1 Chemical Partitioning- .............................. 6
2.2 Chemical Transfers and Kinetics ...................... 10
2.3 Transport and Bed Sediment .......................... |2
2.3.1 Transport Regime ............................. 1J
2.3.2 Bed Conditions ........ ; ...................... l^
2.4 Mass Balance for Chemicals .......................... 16
3.0 CHEMICAL MODELS FOR LAKES /IMPOUNDMENTS ................... 22
3.1 Simplified Steady-State Models ...................... 23
3.1.1 Sedimenting .................................. 24
3.1.2 Interactive Bed .............................. 35
3.2 Time to Steady-State ................................ f
3.2.1 Settling and Sedimenting ..................... *'
3.2.2 Bed Interacting .............................. 52
3.3 Complex Models ...................................... \*
3.3.1 Steady-State Models .......................... 58
3.3.2 Time Varying Models .......................... 60
3.4 Model Assumptions and Limitations ................... 60
3.4.1 Instantaneous Equilibrium .................... 61
3.4.2 First Order Reactions ............... - ........ 62
3.4.3 Settling, Resuspension and Sedimentation ..... 62
3.4.4 Water-Bed Diffusive Exchange ................. 63
3.4.5 Bed Characterization ........ i ................ 64
3.4.6 Particle Sizes ............................... 65
3.5 Criteria for Model Selection ........................ 66
3.5.1 State and Dimensionality ..................... 66
3.5.2 Transport and Bed Considerations ............. 67
3.5.3 Available Data and Purpose of Analysis ....... 68
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CONTENTS
(continued)
Section
4.0 MASS INPUTS TO LAKES JO
4.1 Point Source Inputs JO
4.1.1 Sediment Inputs 7l
4.1.2 Chemical Inputs J2
4.2 Non-point Source Inputs 79
4.2.1 Non-urban Runoff 80
4*2.2 Urban Runofi. 81
4,2.3 Phytoplankton Growth..............«»«»»«»»«»» 81
4.2.4 Atmospheric Loadings 82
4.2.5 Tributary Inputs........ 83
4.3 Data Sampling Requirements 83
4.3.1 Problem Time Scale 84
4.3.2 Sampling Frequency 8
4.3.3 Measurements of Chemical Inputs 87
5.0 DETERMINATION AND ASSESSMENT OF MODEL PARAMETERS 88
5.1 Problem Time Scales 89
5.2 Location of Sampling Stations "
5.3 Water Quality Measurements 90
5.3.1 Water Column .-V H
5.3.2 Sediment Layer 92
5.4 Sample Handling 93
5.5 Fluid Transport - *4
5.5.1 ..Flow Determinations 95
5.5.2 Geomorphological Dimensions 96
5.5.3 Evaluation of Detention Time 97
5.6 Particle Transport 99
5.6.1 Solids Concentration 99
5.6.2 Particle Classification 101
5.6.3 Particle Settling l°2
5.7 Water Column-Bed Interaction 105
5.7.1 Sedimentation, l08
5.7.2 Particle Resuspension HO
5.7.3 Sediment-Water Column Diffusive Exchange 113
5.8 Chemical Transfers. H*
5.8.1 Adsorption and Desorption 11*
5.8.2 Air-Water Surface Exchange 124
5.9 Chemical Kinetics of Degradation 132
5.9.1 Photolysis. 133
5.9.2 Hydrolysis...... 139
5.9.3 Biodegradation... 1*0
5.10 Sediment Capacity Ratio I*2
5.10.1 Equal Water Column and
Sediment Partition Coefficient 1*7
5.10.2 Particulate Ratio 150
5.11 Bioaccumulation of Chemical
ii
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CONTENTS
(continued)
Section
6.0 PRINCIPLES OF MODEL APPLICATION .......................... J52
6.1 Evaluation of Model Inputs .......................... J^Z
6.2 Calibration/Validation Procedures ................... 15*
6.3 Measures of Validation .............................. 158
6.4 Sensitivity Analysis ................................
6.4.1 First Order Uncertainty Analysis .............
7.0 EXAMPLE LAKE ANALYSIS SEDIMENTING CASE ................... 167
7.1 Chemical Partitioning ............................... l°°
7.2 Volatilization Rate ................................. l
7.3 Photolysis .......................................... };f
7.4 Overall Reaction Coefficient ........................ 1'*
7.5 Computation of Water Column Solids Concentration
m. and Sediment Solids Concentration m, ............. 175
7.6 Computation of Water Column Concentration
C_. and Sediment Concentration CT2 .................. |7jj
7.7 Time to Steady-State ................................ 7*
7.8 Sensitivity of Resuspension
7.9 First Order Uncertainty Analysis
7.9.1 Computation of Analysis ...................... I84
8.0 EXAMPLE LAKE ANALYSIS BED INTERACTIVE CASE.....' .......... 1J7
8.1 Overview of Quarry Experiment ....................... fj7.
8. 1.1.. Chronological Review of Important Events ..... la/
8.1.2 Discussion of Water Column
and Sediment Data °8
8.1.3 Chemical Budget ..............................
8.2 Evaluation of Model Inputs ..........................
8.2.1 Model Geometry ...............................
8.2.2 Fluid Transport ..............................
8.2.3 Particulate Transport ........................
8.2.4 Chemical Transfers and Kinetics ..............
8.2.5 Chemical Inputs .............................. 209
8.3 Results of Model Calibration Analysis ...... . ......... 209
8.4 Model Verification and Projections .................. 213
9.0 REFERENCES ...................................... ; ......... 2l7
APPENDIX A: DERIVATION OF STEADY-STATE AND TIME VARIABLE SOLUTIONS
APPENDIX B: OCCURRENCE OF PRIORITY POLLUTANTS IN
PUBLICLY OWNED TREATMENT WORKS
APPENDIX C: A PARTICLE INTERACTION MODEL OF
REVERSIBLE ORGANIC CHEMICAL SORPTION
APPENDIX D: BIOCONCENTRATION AND DEPURATION BY AQUATIC ORGANISMS
iii
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FIGURES
Paffp
Figure £=*£
2-1 SCHEMATIC OF CHEMICAL SORPTION ........ - .................. 7
2-2 EXAMPLE ISOTHERMS AND PARTITION COEFFICIENT .............. 9
2-3 SCHEMATIC OF CHEMICAL TRANSFERS AND KINETICS ............. U
2-4 TRANSPORT REGIMES AND BED CONDITIONS ..................... l4
2-5 ' FINITE DIFFERENCE SEGMENTATION AND TRANSPORT ............. 18
2-6 PARTICULATE FRACTION AS A. FUNCTION OF PARTITION
COEFFICIENT AND SOLIDS CONCENTRATION ..................... 20
3-1 SCHEMATIC OF SOLIDS AND CHEMICAL
PARAMETERS - SEDIMENTING CASE ............................ 26
3-2 SCHEMATIC OF SOLIDS AND CHEMICAL
PARAMETERS - INTERACTIVE BED CASE ........................ 36
3-3 SCHEMATIC OF INTERACTIVE BED MODEL FRAMEWORK
3-4 THEORETICAL TIME TO STEADY-STATE FOR
INSTANTANEOUS AND CONTINUOUS INPUTS ...................... 50
3-5 NORMALIZED TIME TO STEADY-STATE
IN WATER COLUMN SEDIMENTING CASE ......................... 52
3-6 EXAMPLE OF TIME VARIABLE BEHAVIOR
CONSERVATIVE SUBSTANCE ................................... 56
4-1 LAKE ILLUSTRATION SAMPLING FREQUENCY ..................... 86
5-1 EXAMPLE SAMPLING STATION LOCATIONS ....................... 91
5-2 LOG - PROBABILITY OF FLOW ................................ 96
5-3 LOG - PROBABILITY OF MEAN DEPTH .......................... 97
*
5-4 LOG - PROBABILITY OF DETENTION TIME ...................... 98
iv
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FIGURES
(continued)
Figure
5-5 LOG - PROBABILITY OF ESTIMATED
WATER COLUMN SUSPENDED 60LIDS
5-22 CONTOURS OF SEDIMENT CAPACITY FACTOR, B,
VERSUS DIMENSIONLESS SOLIDS CONCENTRATIONS
FOR H/H 1000, » - »
5-6 LOG - PROBABILITY OF ESTIMATED AREAL
HATER COLUMN SUSPENDED SOLIDS ....... ........... 100
5-7 ILLUSTRATIONS OF SEDIMENT TRAPS .......................... 104
5-8 SETTLING VELOCITIES BY STOKES" LAW ........................ 106
5-9 EXAMPLES SETTLING VELOCITIES FROM BENCH SCALE TESTS ...... 107
5-10 ADSORPTION/DESORPTION EXPERIMENTAL PROCEDURE ............. 116
5-11 LINDANE ADSORPTION/DESORPTION DATA
WITH INDIANA QUARRY WATER AND SEDIMENT ................... 118
5-12 VARIATION OF PARTITION COEFFICIENTS
WITH SOLID CONCENTRATION ................................. I23
5-13 GAS TRANSFER RELATIONS ................................... I28
,
5-14 DIFFUSIVITY (AIR) VERSUS MOLECULAR WEIGHT ................ 129
5-15 GAS PHASE CONTROL AIR/WATER TRANSFER COEFFICIENT ......... 129
5-16 DIFFUSIVITY (AIR) VERSUS MOLECULAR WEIGHT ................ 130
5-17 LIQUID PHASE CONTROL AIR/WATER TRANSFER COEFFICIENT ...... 131
5-18 EFFECT OF pH ON HYDROLYSIS RATE ..................... I41
5-19 DISSOLVED AND PARTICULATE FRACTIONS VERSUS », AND o
5-20 LOG - PROBABILTY OF SOLIDS MASS RATIO
5-21 CONTOURS OF SEDIMENT CAPACITY FACTOR, 3,
VERSUS ». AND m. FOR »-!.,
H/H - toOO, m 1007000 mg/1
6-1 STEPS IN MODEL APPLICATION ............................... 156
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Figure
FIGURES
(continued)
7-1 HYPOTHETICAL RESULTS OF
ADSORPTION/DESORPTION EXPERIMENT
8-1 TEMPORAL VARIATION OF DDE IN WATER ....................... 189
8-2 TEMPORAL VARIATION OF DDE IN SEDIMENT .................... 191
8-3 TEMPORAL VARIATION OF LINDANE IN WATER.... ............... 192
8-4 TEMPORAL VARIATION OF LINDANE IN SEDIMENT ................ . 193
8-5 MODEL GEOMETRY FOR ANALYSIS OF INDIANA QUARRY ............ 196
8-6 TYPICAL DDT AND LINDANE PARTITION COEFFICIENTS
VERSUS SEDIMENT SOLIDS CONCENTRATION ..................... 202
8-7 LINDANE ADSORPTION/DESORPTION DATA
WITH INDIANA QUARRY WATER AND SEDIMENT ................... 203
8-8 MODEL CALIBRATION FOR DDE ................................ 21°
8-9 MODEL CALIBRATION FOR LINDANE ............................ 211
8-10 LONG TERM MODEL VERIFICATION/ PROJECTION
FOR LINDANE AND DDE ...................................... 2l6
vi
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Table
TABLES
Page
1-1 ORGANIZATION OF GUIDANCE MANUAL
FOR PERFORMANCE OF WASTELOAD ALLOCATIONS 2
3-1 "STEADY STATE SOLUTIONS SEDIMENTING CASE 34
3-2 DEFINITIONS 43
3-3 GENERAL FORMCHEMICAL WATER COLUMN
AND SEDIMENT EQUATIONS 4°
3-4 CHEMICAL WATER COLUMN AND SEDIMENT EQUATIONS
DIFFUSION - 0 46
3-5 TIME VARIABLE SOLUTIONS FOR RECEIVING WATER SEGMENT 53
3-6 EQUILIBRIUM CALCULATIONS BED-INTERACTIVE CASE 57
3-7 SUMMARY OF* STEADY-STATE LAKE TOXICITY MODELS 59
3-8 SUMMARY OF TIME VARIABLE LAKE TOXICITY MODELS 60
3-9 SUMMARY OF MODEL APPLICATIONS 67
3-10 CONDITIONS FOR MODEL APPLICATIONS 68
4-1 WATER WITHDRAWALS FOR PUBLIC SUPPLIES
BY STATE AND BY SELECTED MUNICIPAL SYSTEMS, 1970 73
4-2 MUNICIPAL WASTEWATER TREATMENT SYSTEM PERFORMANCE 74
4-3 TYPICAL INDUSTRIAL DISCHARGE POLLUTANT CONCENTRATIONS.... 75
4-4 SUMMARY OF CURRENT AND PROJECTED WASTELOADS
IN ONE REGION 208 AREA 76
4-5 AVERAGE 1979 SUSPENDED SOLIDS LOADINGS TO SAGINAW BAY.... 81
4-6 ESTIMATED RANGE OF CONTEMPORARY TOTAL PCB LOADING 83
5-1 SUMMARY OF WATER QUALITY MEASUREMENTS 90
vii
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TABLES
(continued)"
Table Ml
5-2 STATISTICAL PARAMETERS FOR LAKE PHYSICAL PROPERTIES ...... 98
5-3 SUSPENDED SOLIDS SIZE DISTRIBUTIONS SAGINAW BAY .......... 102
5-4 PARTICLE SIZE CLASSIFICATION AND
WATER COLUMN SETTLING VELOCITIES SAGINAW BAY .............. 103
5-5 SEDIMENT PARAMETERS FOR VARIOUS LAKES .....................
5-6 SEDIMENT PARAMETERS FOR THE GREAT LAKES ................... H1
5-7 SUMMARY OF LAKE PARAMETERS ................................ 151
6-1 DATA REQUIREMENTS FOR CHEMICAL FATE MODELING ANALYSIS ..... 154
7-1 SUMMARY OF DATA COLLECTION PROGRAM ........................ I67
7-2 RESULTS OF ADSORPTION/ DESORPTION EXPERIMENTS ...... . ........ 169
7-3 DISSOLVED AND PARTICULATE CHEMICAL FRACTIONS .............. 170
7-4 VOLATILIZATION RATE CALCULATION SUMMARY ................... 173
.
7-5 OVERALL REACTION COEFFICIENTS
KL AND Kj AND COMPARISON WITH fd^ ....................... 1/5
7-6 CALCULATED CTI AND O^ CONCENTRATIONS; W - 100 LBS/DAY.... 178
7-7 TIME TO STEADY-STATE ...................................... l79
7-8 SENSITIVITY TO RESUSPENSION ............................... l81
8-1 MASS BALANCE CALCULATION FOR INITIAL CHEMICAL DOSAGE ...... 197
8-2 SUMMARY OF SOLIDS RELATED PARAMETERS
USED IN QUARRY ANALYSIS ................................. 2°l
8-3 SUMMARY OF DDE AND UNDANE DECAY COEFFICIENTS ............. 204
8-4 PROGRAM SOLAR INPUTS USED
TO COMPUTE DDE PHOTOLYSIS RATES ........................... 205
8-5 ESTIMATES OF LINDANE VOLATILIZATION RATE .................. 208.
8-6 SUMMARY OF SEDIMENT DDE DATA FROM JUNE 21, 1977 ........... 214
viii
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ACKNOWLEDGMENTS
This report was developed by HydroQual, Inc. under subcontract to JACA
Corporation in response to Work Assignment No, 39, EPA Contract No.
68-03-3131 and under subcontract to Arthur D. Little Corporation, Task No.
17, EPA Contract No. 68-01-6951. Charles Oelos, Monitoring and Data
Support Division, was the Work Assignment Manager for the U.S.
Environmental Protection Agency.
The basic simplified technology toward which much of the report is
focused was developed by Dominic M. DiToro and Donald J. O'Connor of
HydroQual, who served as Project Consultants and provided technical input
and review. Charles L. Dujardin served as Project Manager, organized and
prepared the technical material and example cases, and wrote most of che
report. John P. 'St. John served as Principal Engineer, developed the
report outline and provided text. Our office services staff is also
gratefully acknowledged. Karen J. Klein for her word processing and Audrey
E. Czyzewski for her editing of the report. Joseph H. McDonald drafted the
figures for the report. Certain technical material was abstracted from the
literature and is duly cited as appropriate.
Charles Delos, Larry E. Fink of Remedial Programs Staff, and Elizabeth
Southerland of Monitoring and Data Support Division reviewed the Draft
Report and provided many detailed and valuable comments which are
acknowledged and appreciated.
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SECTION 1.0
INTRODUCTION
This document is one of a series of manuals whose purpose is to provide
technical information for the preparation of technically sound wasteload
allocations (WLAs). The objective of such allocations is to ensure that
acceptable water quality conditions are achieved and/or maintained so that
designated beneficial uses are practical. The purpose of this specific
manual is to present applicable technology for analysis of the face of
toxic substances when released to lakes and impoundments. The methodology
incorporates a number of transport, transfer, and transformation
characteristics specific to lakes and toxic substances and ultimately may
be used to define the relationship between toxic waste inputs and receiving
vater concentrations. Once a target concentration is established for a
particular toxicant, the methodology may be used to determine WLAs.
1.1 Relation co Other Books and Chapters
Table 1-1 summarizes various publications which make up the set of WLA
guidance documents. It is intended that this and other technical chapters
be used in conjunction with each other and with material presented in Book
I, which provides general information applicable to a variety of
situations. The information presented in Book I applies to all types of
water bodies and to all contaminants which must be addressed by the WLA
process. It is not the intention of this chapter to reiterate information
which has appeared elsewhere except when the principles of certain topics
are important for comprehension of this text.
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BOOR I
BOOK II
BOOK III
BOOK IV
BOOK VIII
TABLE 1-1. ORGANIZATION OF GUIDANCE MANUAL FOR
PERFORMANCE OF WASTELOAD ALLOCATIONS
procedures, and
GENERAL GUIDANCE3
(Discussion of overall WLA processes,
considerations)
STREAMS AND RIVERS
Chapter I - BOD/Dissolved Oxygen Impacts
2 - Nutrient/Eutrophicationalmpacts
3 - Toxic Substance Impacts
ESTUARIES
Chapter 1 - BOD/Dissolved Oxygen Impacts
2 - Nutrient/Eutrophication |mpacts
3 - Toxic Substances Impacts
LAKES, RESERVOIRS, AND IMPOUNDMENTS
Chapter 1 - BOD/Dissolved Oxygen Impacts a
2 - Nutrient/Eutrophication Impacts
3 - Toxic Substances Impacts
A SCREENING PROCEDURE FOR TOXIC AND CONVENTIONAL POLLUTANTS'
aBooks or chapters particularly pertinent to this manual
1.2 Scope of the Chapter
Chemicals are present in varying degrees in all phases of the
environment. The benefits derived from the use of these substances are
evident in many facets of society, particularly with respect to increased
food production. The demand for these materials, more specifically the
benefits derived from their use, continuously increases. However, care is
warranted to make certain that any undesirable effects of the chemicals in
the environment are ascertained and controlled. This concern prompts the
use of certain chemicals which may be safely assimilated in the environment
co such levels as to yield the benefits without deleterious effects.
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This goal necessitates the development of assessment mecaoud »...
permit an- evaluation and ultimately a prediction of environmental
concentrations. An understanding is therefore required of the transport,
transformation and exchange of chemical substances in and between the
various media of the environment and the incorporation of this information
into a practical assessment methodology.
In the water environment, toxic materials may be discharged to all
manner of waterways, streams, rivers, estuaries, lakes, and reservoirs.
The purpose of this document is to present applicable technology by which
to calculate ambient water quality concentrations resulting from the
discharge of toxicants to lakes, reservoirs, and impoundments. The manual
has been prepared to achieve the following objectives.
1. Review the basic principles of chemical water V««ty modeling
frameworks-in sufficient detail to permit physical understanding of the
problem and the fundamental basis of mathematical representation of
natural systems, particularly lakes.
2. Define the assumptions and limitations of such modeling frameworks and
indicate criteria for application.
3. Specify in detail the type of information, both field and laboratory,
which is required for practical application of modeling frameworks and
how these data are evaluated and prepared for use in the models.
4. Illustrate the application of modeling frameworks in a step by step
manner through the use of examples.
It is noted that a substantial number of water quality modeling
programs have been developed which are applicable to the analysis of the
fate of toxicants in the water environment, many of which can be applied to
lakes and impoundments. It is beyond the scope of intent of this document
to review all such frameworks and to provide detailed guidance on the
application of specific programs to particular problem settings. Those
functions are properly provided by individual program documentation and
user's guides for the individual modeling programs. Rather, the intent of
this document is to present fundamental technology so that the reader gains
physical as well as a mathematical understanding of the behavior of
toxicants in aqueous systems, particularly in impounded settings.
3
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In order co accomplish this goal, the emphasis of this document is
placed on simplified modeling frameworks, that is, those which are obtained
by direct solution of basic equations developed from a mass balance for
partitioning toxic substances in completely mixed systems. It is felt that
this procedure, imparts to the user a physical appreciation and under-
standing of the problem at hand which is not easily gained by application
of large scale computer programs. Further, the technology presented,
though simplified, is directly applicable to many practical problem
settings. It is anticipated that once the user has a physical under-
standing of the problem at hand from review of the material presented in
this section, the relevant analysis framework, whether simplified desk top
calculations or complex computer program, can be selected for the
particular problem setting.
1.3 Organization of the Chapter
The remainder of this document is organized into seven pares as
summarized as follows:
.
Section 2.0 outlines basic principles which are applicable to chemical
fate models. The fundamental transfer and kinetic characteristics of
chemicals are reviewed and expressed in mathematical form. These
expressions are then combined with other relationships which account for
how a material is transported through an aqueous environment.
Section 3.0 presents the development.of simplified mathematical models
for treatment in lakes with assumptions and limitations. Formulations are
presented for different types of chemicals (i.e., heavy metal, organic) and
for various physical assumptions. These equations may be solved through
desk top calculations or currently available programs. Other areas covered
in this section include time to steady-state calculations, a summary of
available complex models and a discussion regarding the criteria for model
selection.
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Section 4.0 discusses the types of mass inputs to lakes from pome ana
non-point sources.' Time scale considerations for evaluating mass discharge
rates are also discussed.
Section 5.0 describes key model input variables with an emphasis on how
such values are measured or estimated. Sampling procedures and laboratory
analysis are discussed. Time and spatial considerations are addressed for
both water column and sediment measurements. Fluid transport, particle
transport, water column-bed Interactions, chemical transfers, and chemical
kinetics are areas covered in this section. Also, key mathematical
expressions (sediment capacity factor and chemical particulate ratio) are
evaluated for the purpose of providing guidelines to estimate these
parameters.
Section 6.0 provides a recapitulation of the procedures for obtaining
model input data and presents an overview of the general principles of
model application.
Sections 7.0 and 8.0 present examples for analyzing chemical fate
problems involving a sedimentating and interactive bed case, respectively.
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SECTION 2.0
BASIC PRINCIPLES OF CHEMICAL MODELS
The procedure for developing realistic mathematical models for chemical
fate is similar to the approach used historically for other measures of
water quality such as biochemical oxygen demand (BOD) and dissolved oxygen.
The fundamental transfer and kinetic characteristics of a wide variety of
chemicals are reviewed and expressed in mathematical form. These
expressions are then combined with other relationships which account for
how any material is transported through the aqueous environment. The
principle of conservation of mass is ' then used to develop generalized
expressions of.mass balance of chemical. These expressions are then either
solved to a direct algebraic solution which oay be used for desk cop
calculations in the case of physically simple situations, or they are
solved by digital computation in the case of more complex problem settings.
2.1 Chemical Partitioning
One of the major characteristics which differentiates many chemicals
from classical water quality variables is an affinity for adsorption to
particulate material. Figure 2-1 schematically illustrates the principle.
If a mass of soluble chemical is placed in a laboratory beaker of water, an
initial concentration of dissolved chemical, c, will result. If parti-
culate material is then added to the beaker and stirred, a portion of
dissolved chemical will be sorted onto the particulates and some of the
chemical concentration will then be in particulate form, p. If Chis
process is monitored with time, as shown on the diagram, the dissolved
chemical will be reduced and particulate chemical will increase in a
-------
cr
j-
z
UJ
o
z
o
o
EQUILIBRIUM
PHASE
REACTIVE
PHASE
TOTAL CHEMICAL
PARTICIPATE
CHEMICAL -P
DISSOLVED
CHEMlCAL-c
TIME
FIGURE 2-1. SCHEMATIC OF CHEMICAL SORPTION
reversible reaction until an equilibrium is achieved at some point. The
total chemical concentration at any time is equal to the sum of the
dissolved and particulate concentrations:
. . ^ . ' (2-1)
in which C- is total chemical concentration and i 1 represents the water
column concentration while i 2 represents the concentration in che
sediment*
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The race with which this reaction takes place and the relative
relationship between the dissolved and particulate chemical, that is, the
water-sediment partitioning, are both chemical specific. In most cases,
reaction between the dissolved chemical and participates occurs very
rapidly, minutes to hours, and equilibrium is achieved quickly relative to
Che time characteristics of the environmental setting. The tendency to
sorb is highly chemical specific, especially in the case of materials with
low water solubility.
The affinity of a particular chemical to sorb' can be quantitatively
expressed by a solids-water partition coefficient, ». A series of
experiments of the type schematically indicated on Figure 2-1 may be
conducted with differing initial dissolved concentrations of a specific
chemical. After equilibrium is achieved, the particulate chemical
concentration, r, expressed as micrograms of chemical per gram of
particulate material (ug/g), may be plotted as a function of the dissolved
chemical remaining, c, expressed as microgram per liter of water (ug/1).
Figure 2-2 schematically illustrates the results of the previously
described laboratory experiment. A specific chemical will produce one of
the lines shown on the logarithmic diagram, the relative position of which
determines the partition coefficient. For a particular dissolved
concentracion, greater particulate concentrations yield larger partition
coefficients as shown schematically by the various distributions. Data
from chemicals which can be plotted and correlated, as shown on Figure 2-2,
behave according to the Freundlich isotherm defined as:
in which n is a constant characterizing the slope of the relationship. If
the slope is near 1 indicating a linear relationship, the partition
coefficient is defined as:
Ci
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10.000
l.OOO
o»
*^
o»
= 100
z
Ul
u
z
o
o
UJ
cr
<
0.
0 s
c
r» ire, I/B
TI PARTITION COER
I 10 '00
DISSOLVED CONCENTRATION -C-, ( /ig /
FIGURE 2-2. EXAMPLE ISOTHERMS
AND PARTITION COEFFICIENT
i COO
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As indicated, a specific chemical will yield one of the relationships
indicated schematically on Figure 2-2 for a specific type of sorbing
particulate material. However, different relationships, and therefore
different partition coefficients, may be observed for the same chemical
with various types of sorbants. For example, organic particulates or silty
materials may attract a certain chemical more strongly than sandy
materials. Further, different size classes of particulate material, in
that they may reflect different classes of particulates as sands, silts,
clays etc., may exhibit differing affinities and partitioning, for a
specific chemical. In principle, it is most advantageous, therefore, to
perform experiments and determine a chemical's partitioning characteristics
with the type of particulate material (suspended and bed sediment) to which
it will come in contact in the natural environment.
Another useful relationship is the definition of particulate chemical
concentration on a volumetric basis:
(2-4)
p rm
in which p is particulate chemical concentration on a bulk volume basis
(e g iig/1). r is chemical sorbed to particulate material (e.g., ug
chemical/g suspended sediment) and m is the volumetric concentration of
particulates (e.g., g of suspended sediment/1 bulk volume). As chemical
concentrations may exist in both dissolved and particulate form, the
modeling framework must track both forms of chemical, ct and PI, as well as
the particulates, m, to which a fraction of the chemical is sorbed.
2.2 Chemical Transfers and Kinetics
The mathematical models developed herein are based on a mechanistic
framework for the transport, transfer and reaction of chemical in the
aqueous environment. Figure 2-3 is a schematic diagram which shows the
various transfers and kinetic decay mechanisms (transforms) included in the
models. The diagram represents -the water column in any receiving water
body bounded by bed sediment and atmosphere. In the water column, both
. ' 10
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dissolved, Cj, and particulate, pjf chemical concentration are considered
to exist, each of which may be caused by direct inputs of chemical, either
dissolved, Wd, or particulate, Wp> from industrial, municipal, and/or
diffuse sources.
K
^^^^^
a
Ul
o
Ul
CD
1
^4=^-
VOD
*,
DISSOLVED
DEC At
0
E
»i
DISSOLVED
DECAY
II
II
1TILIZATION ^
C.
K«t«
SSOLVEO
XCMANviE W,
1 | Kv. SCO
i '
*
W»
1 AIR-WATER
~=~ INTERFACE
Ki
P| PAHTICULAT6
DECAY
SETTLING
UR WATER -BED
?/WA' INTERFACE
1 * I PftflTICULATE
OCCAT
SEDIMENTATION
FIGURE 2-3. SCHEMATIC OF CHEMICAL TRANSFERS
AND KINETICS
Due to the characteristic of chemical partitioning, a reversible
reaction is shown between the dissolved and particulate forms. If Che
equilibrium between these fractions, as shown on Figures 2-1 and 2-2, is
disturbed in some manner, as by addition of dissolved chemical or decay. of
the particulate fraction, for example, a reaction will commence either
toward sorption or desorption until a new equilibrium is achieved between
dissolved and particulate chemical. The rates at which sorption-desorption
reactions occur are denoted by K^ and Kdeg on the diagram.
11
-------
Dissolved chemical may undergo volatilization and be exchanged from the
water column to the atmosphere through the air-water interface at a rate,
K . Once in the atmosphere, it may also be sorbed onto participates which
Jy then fall back to earth and be a source of chemical input to receiving
waters. Caseous chemicals in the atmosphere may also diffuse back into
solution through the air-water interface. These sources, however, are
likely to be of significance only to the largest of water bodies and for
the mes* nMnuifms of chemicals.
In a similar manner, the chemical associated" with particulates may be
removed from the water column to the bed sediment by a settling mechanism,
denoted by the rate, w^ Under certain hydraulic characteristics,
particulate chemical in the bed sediment may be resuspended back into Che
water column by scour' at a rate, w^. Once a particulate chemical is
introduced into the bed sediment, a desorption may take place so that some
chemical is dissolved into the interstitial waters of the bed. This is a
reversible reaction as In. the water column governed by the partitioning
characteristics of the chemical and solids. Dissolved chemical may also be
exchanged, at a rate 1^, between the water column and bed sediment in
accordance with the laws of diffusion, that is, from an area of greater
concentration to one of lesser.
In all cases, dissolved and particulate chemical forms in both wacer
column and sediment may undergo various decay transformations, KJ> and K2,
depending upon the nature of the compound. Such mechanisms may include
hydrolysis, biological degradation, and photodegradation under the
influence of solar ultraviolet radiation. This latter factor is not
usually of significance in the case of bed sediment.
2.3 Transport and Bed Sediment
As described previously, the distribution between dissolved and
particulate components of the chemical, as well as transfers and kinetic
interactions, are both essential- factors common to all types of models.
What distinguishes various models, however, are transport components of a
12
-------
specific water system and the characteristics of the bed with which ic
interacts. Thus, the differences of various models lie, to some degree, in
the transport regimes of the lakes, but more significantly they rest on the
transport characteristics of the bed itself, and the magnitude of the
water bed interaction.
2.3.1 Transport Regimes
Each of the general types of natural water systems may be classified in
accordance with a characteristic fluid transport regime and the interaction
of the water with the bed as shown on Figure 2-4. The components of the
transport field are the advective (U) and dispersive (E) elements which, in
general, are expressed in three-dimensional space. The transport in lakes
may be approximated frequently" by one- or two-dimensions (A) in which the
vertical -is the major component, and by a spatially uniform condition,
completely nixed (B), whose transport coefficient is the dPtencion time,
c
0
2.3.2 Bed Conditions
The bed conditions, which are relevant to the analysis are shown also
on Figure 2-4. They may be classified as inactive (stationary); or active
(exchanging). The latter may be further subdivided: with and without
horizontal transport. A further characteristic of bed conditions relates
to the phenomenon of sedimentation. All natural water bodies accumulate,
in varying degrees, materials which settle from the water column. In
freshwater systems, reservoirs and lakes are repositories of much of the
suspended sediment which are discharged by the tributary streams and direct
drainage. Bed conditions in these systems are subject to seasonal and
possibly daily variations, but tend to accumulate material over long time
scales. The increase in bed depth and concentration is expressed in terms
of a sedimentation velocity, measured in terms of centimeters/year, by
contrast to the settling velocity of the various solids in suspension,
measured in terms of meters/day. .
13
-------
B
WINO-ORIVgN
Q-,
f MIXED
r
£-/* -
n
(.AXES ANO
COASTAL WAT2RS
U- HORIZONTAL VELOCITY
«-VERTICAL MIXING
0-PLOW RATE
V-VOLUME
t0» V/0-DETENTION
(A) TRANSPORT REGIMES
WATER
BCD
. \
STAT'QNARY
SEOiMENTiNG 3E3
> »i«eo
u*»e»
MIXED LAYgfl
O W
unco
STATIONAMY
aeo
9S3 TRANSPOR"!
MIXED LAYER
SEOIMENTING aea
CO
w,
SEDIMENTATION VELOCITY
LIST Q? SYMBOLS
w, SETTLING
W2, RESUSPENSIQN
W SEDIMENTATION
U8 MIXING
(B) BcD CONDITIONS
FIGURE 2-4. TRANSPORT REGIMES AND BED CONDITIONS
14
-------
The different bed conditions depicted on Figure 2-4 are further defined
as follows:
Type I; Stationary Bed. A stationary bed is basically characterized
by negligible horizontal motion. This condition is most commonly
encountered in lakes and reservoirs of relatively great depth, with minimal
winds.
The essential characteristic of this type of system is the relatively
low degree of vertical mixing in the fluid. The hydrodynamic environment
is one which permits the gravitational force to predominate and suspended
particles of density greater than that of water to settle. The accumula-
tion of this material in the bed causes an increase in the thickness of the
benthal layer, the rate of increase being referred to as a sedimentation
velocity. The bed is also characterized by minimal or zero particle mixing
in the layer in contact with the water.
Type II; Exchanging Bed. This condition, which is probably more
common, is characterized by some degree of particle mixing in the active
layer of the bed. The mixing may be due to either physical or biological
factors; increased levels of shear, associated with horizontal or vertical
velocities and gradients or bioturbation attributable to the feeding
behavior of benthic organisms. It exists, therefore, in Lakes where the
wind effects extend to the bottom.
In such cases, the shear exerted on the bed is sufficient to bring
about mixing in the interfacial layer, but not sufficient to cause
significant erosion and bed motion. The net flux of material to the bed is
the difference between the settling flux and that returned by the exchange
due to the mixing. Thus, the bed thickness may increase or decrease and
the sedimentation velocity nay be positive or negative. This type of bed
condition is usually associated where water depths are sufficiently shallow
to permit wind effects to be transmitted to the bed.
15
-------
T ill: fach-T- '«* *** Transport. This bed condicion possesses
both mixing and advective characteristics. The shearing stress exerted by
the fluid is of sufficient intensity to cause erosion and resuspension of
the bed and the fluid velocity of sufficient magnitude to induce horizontal
motion of either or both the resuspended material and the interfacial bed
layer. This phenomenon involves the complex field of sediment transport,
which has been greatly developed in streams, but much less in estuaries and
lakes. The bed system may now be envisioned as three distinct segments: a
moving interfacial layer, a mixed zone and a stationary bed beneath. There
is vertical .exchange between the moving and mixed layers and the vertical
transport in the bed is characterized by the sedimentation velocity. This
cype of bed condition is rarely associated with reservoirs or lakes.
2.4 Mass Balance for Chemicals
Conservation of mass is the fundamental principle which is used as the
basis of all mathematical models of real world processes. All aaterial
must be accounted for whether transported, transferred, or transformed. A
rate equation which conforms to the requirements of mass balances is
written as follows:'
v *£ . j + rr + ZR + iw (2"5)
dt
A
in which
c
J
T
R
W
V
t
concentration of the chemical
transport through the system
transfers within the system
transformation reactions within the system
chemical inputs
volume
time
Equation 2-5 states that the rate of change of mass of chemical with time
at any location in the system is due to the net effect of the various
fluxes, transfers, reactions, and-inputs.
16
-------
The-various terns on Che right side of Equation *-j *c* *******
appropriate mathematical form as described in previous publications. An
equation may be written for each of the chemical forms, dissolved and
particulate, for both water column and bed sedinent. In physically simple
systems, these four equations may be solved simultaneously to yield a
direct algebraic solution for each chemical form. The spatial distribution
of chemical, dissolved and particulate, in water column and sediment is
calculated as a function or chemical input, freshwater flow and advection,
and the various transfer and decay rates. The algebraic solutions are
programmed for convenience of calculation.
In the case of physically complex systems, such as large lakes, the
study area is subdivided into a series of segments, in one-, two- or
three-dimensions, as schematically indicated on Figure 2-5, as required by
the expected distribution of chemical. For each water column segment, a
mass balance equation may be written in finite difference form for each
chemical fraction, dissolved and particulate. Similar equations are also
written for bed sediment segments. The equations for each segment interact
with equations written for all adjacent segments through physical inter-
actions caused by" chemical transport and transfer among the various
adjacent segments. The result is a matrix of equations which are solved by
digital computation. The solution is the calculated chemical concentra-
cions, dissolved and particulate, for each water column and bed sediment
segment.
A simplification may be made. in the case of those chemicals where the
partitioning reaction shown on Figure 2-1 occurs very rapidly compared to
other time constants in the system. If the time to reach equilibrium
between dissolved and particulate forms occurs .within minutes or hours, a
common circumstance, it is possible to write the foregoing mass balance
equations in terms of total chemical, CT, rather than in dissolved and
particulate forms. This reduces the number of equations which must be
solved -ry half. Then, dissolved and particulate forms can be determined
from the total chemical concentration at any .location using the partition
coefficient and local suspended sediment concentration as follows.
17
-------
V7
WATER
COLUMN
s EDI we NT
LAYER.
U_
E
//*///
Us AOVECTION
£= DISPERSION
FIGURE 2-5. FINITE DIFFERENCE SEGMENTATION
AND TRANSPORT
The total chemical concentration Is the -sum of the dissolved and
.
particulate fractions:
CT Cl
(2-6)
The particulate chemical concentration is defined by Equation 2-4:
Pi " ri
(2-7)
However, the chemical concentration,' r, sorted to particulaces may be
determined from Equation 2-3, re-expressed:
r
(2-3a)
Substitution of Equation 2.3a into 2.7 yields:
(2-8).
18
-------
Then:
*ri ' et * <* ci 1> (2"9)
Rearranging the terms in Equation 2-9, the fraction of total chemical which
is in dissolved form is then defined as:
_ *! 1 (2-10)
Ed C 1 + n.
Ti
Similarly, ic can be shown that the fraction of total chemical which is in
particulate form can be defined as:
pi
Hence, for the conditions of nearly instantaneous local equilibrium, the
dissolved and particulate fraction of total chemical are determined by:
'i ' V =1,
where the fractions are calculated from the chemical's partition
coefficient, », and local suspended or bed sediment concentration, m.
Figure 2-6 shows the fraction of particulate chemical -which may be
calculated from Equation 2-11 as a function of various partition
coefficients and solids concentrations.
19
-------
i.O -
z
o
u as
y o.*
a:
a.
0-2 h"
/
00
NOW-
enoc'ic
sriauf
seo
"7" ,'>''" /
/ /"'' /
7 A'*// /
*7 ^V/' *j
y / y /
- / >
AULUVI*!.
X ^ X
UNITS OF TT* l
' '''*' S -"'
\ . ,0' 10* "O1 10* . I09
SOLIDS CCNCSNT3ATION (mg/ I)
FIGURE 2-6. PARTICULATE FRACTION AS A FUNCTION OF
PARTITION COEFFICIENT AND SOLIDS CONCENTRATION
It is appropriate to note that the local suspended or bed sediment
concentration is required in the analysis. Hence, a mass balance equation
is also required for suspended sediment and is established in a similar
manner as for chemical. In addition to the calculation of the local solids
concentration, the suspended sediment balance, performed independently,
helps to define the rates of particle settling and resuspension.
The basic purpose'of the mathematical models for chemical fate is to
calculate the dissolved and particulate chemical fractions, ^ and ?L in
both the water column and bed sediment from known chemical inputs. The
various reaction coefficients specific to the chemical compound for
sorption-desorption, partitioning, volatilization, and the various decay
transformations are ideally determined in the laboratory for input to the
mathematical model. Settling and resuspension rates are normally evaluated
20
-------
using field data and a mass balance of suspended sediment, as subsequently
discussed. Once these rates are defined, the rates of chemical discharge
are input to the model for calculation of the dissolved and particulate
chemical in water column and sediment. These values are then compared with
observed data, if available, and reaction rates may be adjusted within
prescribed limits for fine-tuning.
21
-------
SECTION 3.0
CHEMICAL MODELS FOR LAKES/IMPOUNDMENTS
The basic principles presented in Section 2.0 sets the format for model
development of chemicals in lakes and reservoirs. There are, however, many
approaches and assumptions which may be incorporated in the mathematical
representation of a natural lake system. The complexity of a final
solution is dependent on the approach and assumptions initiated at the
outset of the model development. Since there are many conditions and
variables that may be considered in a chemical fate model, the complexity
and practicality of a model will vary greatly.
The approach adopted for this manual is to emphasize the simplified
formulation of chemical models. The purpose for this approach is twofold:
(1) a detailed description of the simplified approach gives the non-
specialist an understanding of the basic principles of chemical models and
allows him to use desk top calculations or simplified programs for
computation, and (2) in most allocation studies, the data are not available
co evaluate a system using complex formulations so that the simplified
approaches may be less time consuming and probably just as useful. It is
also noted that most of the major complex steady-state or time varying
models currently available are equipped with documentation of the
respective formulations and input requirements. It would not be necessary
or practical in the context of this manual to discuss in detail each
program's derivation.- Rather, summaries are provided regarding the
available model's structure and general application.
The following sections discuss in detail the simplified steady-state
model approach with assumptions and limitations. Other areas covered in
the section include time to steady-state calculations, a summary of
22
-------
available complex models and a discussion regarding cue c**.=--« ---
selection.
3.1 Simplified Steady-State Models
The physics, chemistry, and biology of lakes is a subject with an
extensive literature and a number of reviews are available (e.g.,
Hutchinson, 1957; Wetzel, 1975). The historical focus has been primarily
biological and the chemicals of concern have been those which interact with
biological processes, e.g., forms of carbon, oxygen, nitrogen, phosphorus
and silica. The fate of these chemicals is strongly affected by biological
interactions, and the computational frameworks that have been developed to
analyze their behavior can be quite complex. These detailed analyses are
supported by the availability of large data sets and extensive laboratory
and field scale experimental experience.
The situation is quite different for heavy metals, organic chemicals,
and radionuclides. Very few comprehensive data sets exist and the
frameworks for the calculation of chemical fate are necessarily simplified.
As a consequence',' Che discussions given below are limited to those
processes which are currently believed to be of principal importance and
for which information is presently available.
The simplified steady-state framework assumes complete mixing
throughout the water body. It is recognized that a characteristic feature
of lakes and impoundments is thermal stratification during the summer
months. The vertical mixing is inhibited due to the density gradient
between epilimnion and hypolimnion. Hencer distinct volume segments
characterize the water column (the epilimnion -and hypolimnion). A more
refined analysis should take this into account. Most lakes (the exceptions
being very deep lakes) do mix vertically on an annual time scale, and the
water columns vertically are homogeneous. Hence, the assumption of a
completely mixed water column is reasonable on an annual time scale and
less so for shorter time scales.
23
-------
Two types of bed conditions are considered for the simplified
steady-state approach. They are classified as the sedimenting and
interactive bed. The sedimenting bed condition assumes negligible particle
mixing between the bed and water column and thus, offers the simplest
solution for calculating chemical distributions. Only the solids settling
velocity and the bed sedimentation velocity are required for the transport
description.
The bed interactive condition by contrast considers- the resuspension of
particles from the mixed layer interface to the water column. The rate of
resuspension, therefore, must also be defined for this type of evaluation.
3.1.1 Sedimenting
The basic principles of chemical models are discussed in Section 2.0.
One of the major characteristics which differentiates many chemicals from
classical water quality variables is an affinity for sorpcion to
particulate material. The total chemical concentration at any time in
either the water; column or the bed is the sum of the dissolved and
particulate concentrations. The ratio of the chemical concentration on the
particles to the total concentration (f ) is a function of the concentra-
tion of particulate material -(suspended or fine grain sediment solids) and
the partition coefficient. In order to calculate the particulate chemical
concentration in the water column, therefore, the suspended solids
distribution must first be evaluated.
The following sections present the mathematical solutions for the
expected .concentration of suspended solids and the chemical of concern for
three chemical categories. The three categories considered are non-
reactive/non-volatile, non-reactive volatile, and reactive volatile. In
general, these categories may be associated with metals, volatile organic
chemicals and reactive volatile organic chemicals, respectively.
Suspended Solids. The concentration of suspended solids in a reservoir
or lake depends on the physical characteristics of the incoming sediment
24
-------
and Che hydraulic features of Che system and inflow. The important
characteristic of the * solids is che distribution of settling velocities
reflecting their size, shape, and density. The detention time and the
depth of the water body are the significant hydraulic and geomorphological
features. The following analysis assumes steady-state conditions in a
completely mixed system, in which the concentration of solids is spatially
uniform*
Consider a body of water whose concentration is spatially uniform
throughout its volume, V., receiving an inflow, Q, as shown on Figure 3-1.
Under steady-state conditions, hydraulic inflow and outflow are equal. The
mass balance of the solids takes into account the mass input by the inflow,
that discharged in the outflow and that removed by settling. The mass rate
of change of solids in the reservoirs is the net of these fluxes:
v dr-Qni Qrai Vsmi (3"°'
in which
n. - concentration of solids in inflow
m. - concentration of solids in water body
w settling velocity of the solids (L/T)
A » horizontal area through which seeding occurs
The flux, Qm., equals the rate of mass input, W. Dividing through by the
volume, V., the above equation becomes:
dmi u i
_i.H.-mtI_+Kl (3-2)
in which
r detention time V/Q (T)
K , - settling coefficient w /H (1/T)
SH mean depth V/A (L) . L
25
-------
N*
SOLIDS
LEGEND*
UNITS
w
0
V
H
m
c.
10
*P
w,
wt
Ky
Kd
Kp
MASS INFLUX RATE
FLOW RATE
VOLUME
DEPTH
SOLIDS CONC.
TOXIC -TOTAL CONC.
DISSOLVED FRACTION
PARTICULATE FRACTION
SETTLING VELOCITY
SEDIMENTATION VELOCITY
EVAPORATION COEFFICIENT
DISSOLVED DECAY RATE
PARTICULATE DECAY RATE
M/T
L»/T
L»
L
M/L1
M/L"
L/T
L/T
I/T
I/T
I/T
TOXIC
FIGURE 3-1. SCHEMATIC OF SOLIDS AND CHEMICAL
PARAMETERS-SEDIMENTING CASE
-------
Under the steady-state condition., aquation j-i *.~j -«= s.»r--= '
W/Q (3-3a)
Division by W/Q yields
_1 1 (3-3b)
W/Q ' I* K9lco .
which is the fraction of the incoming solids remaining in suspension and,
with the assumption of complete mixing, is also the concentration in the
outflow. The fraction removed from the water column is simply
C3-4)
KslCo
It is apparent from the above development that conditions in che bed
have no effect on the concentration in the water body, because, of the
assumption that there is no resuspension of the bed material. The increase
in bed sediment mass and volume on che other hand, is due directly to the
influx of the settling solids. The rate of change of solids mass in the
bed is therefore:
dM2 (3-5)
dT' + Vl"!
The bed mass, MZ, equals the product of the bed volume V2, and bed
concentration, m* Thus:
dM, dCV m ) dV dm
_ 2 Z Z m _ * a. « = * A w m,
dT " "d^ -- "2 dc * V2 dt Vl'l
Dividing by the area, and expressing the results dH2/dt as Wj, the final
result is:
(3_6b)
"2
27
-------
where:
w- sedimentation velocity
Ac steady-state (when dm2/dc - 0), the relationship between particle
concentrations and settling and sedimentation velocities is given by:
Non-reactive/Non-volatile Substances (Metals). The distribution of
non-reactive toxic substances, such as metals, is established by
application of the principle of continuity or mass balance, in a manner
similar to that employed in the case of the suspended solids. Each phase,
the dissolved and participate, is analyzed separately, taking into account
the adsorption-desorption interactions. For the dissolved component, che
mass balance includes the sorption terms in addition to the inflow and
outflow. The basic differential equation for the dissolved concentration
is:
. .K . e > K D
" V~ " T *«Umlcl * Kdespl
1 o
in which:
,3.
V
w
c
1
1
c
reservoir volume (L )
rate of mass input of the dissolved component (M/T)
dissolved concentration in water^body (M/L )
-
x . the adsorption rate, constant (L /l£- .
- suspended solids concentration (T _J
the desorption rate coefficient (T ) 3
particulate chemical concentration (M/L )
*
For the particulate concentration:
d"i \ »i
28
-------
in which:
W rate of mass input of thf particulate adsorbed chemical (M/T)
K J settling coefficient (T )
Adding Equations 3-7 and 3-8 cancels the adsorption and desorption
terms and yields the rate of change of the total concentration CT:
"* * T1 / 0_Q \
WT ' V Wc
Since the rate at which sorption equilibrium is achieved between the
two phases is very rapid by contrast to the rates of transfer and decay the
sorption coefficients. Kadg and Kdes are usually orders of magnitude
greater than the decay and transfer coefficients of the dissolved and
particulate concentrations. Thus, liquid-solid phase equilibrium can be
assumed to occur instantaneously. The particulate concentration, pr in
Equation 3-9 may be replaced by *plCT1 given in Equation 2-11.
Under steady-state conditions, the above may be expressed, after multi-
plying through by CQ and replacing p^ith fplCT1 as:
V« _ (3-10)
where:
Vl
Note that Equation 3-10 is identical to Equation 3-3a with the exception
that the dimensionless settling parameter K§lto is multiplied by the
particulate fraction f ..
29
-------
The bed concentration may be described by constructing its mass
balance. Influx is due to the toxic substance associated with the settling
solids and the volumetric accumulation is accounted for by the sedimenta-
tion velocity, as in the bed solids analysis Equation 3-6c. Thus:
2
-' Vivn
<3-u)
at steady-state
in which:
(3-12)
P2
particulate fraction in the water column
particulate fraction in the sediment
m »./(! + m »,) '
secEling velocity
sedimentation velocity
Since m2 »2 ». 1 for most metals in bed sediments, it is often
reasonable to approximate:
d2
so chat:
- p,
w2 pl
Equations 3-10 and 3-12, given above, are the key solutions for
analysis of a non-reactive/non-volatile substance, such as metals, assuming
sedimentation. The following sections consider volatilization and decay of
a chemical.
Non-reactive Volatile Substances (Organic Chemicals). Certain organic
chemicals will transfer to the atmosphere at the surface of the lake. The
30
-------
transfer of organic chemicals from the water body co the atmosphere is
known as the volatilization. Section 5.0 of this manual discusses in
detail the various mechanisms of the air-water surface exchange.
The volatilization rate coefficient, Ky (I/day), only affects the
dissolved portion ftfl, of the chemical concentration in the surface layer.
The differential equation for the total 'concentration in the surface layer
becomes :
.
dCTl WT _ fll. . f C'R _f rv (3-14)
IT" *7 ~ fpicTiKsi fdi SriS .
at steady-state:
(3-15)
Co
-------
The mathematical expresions which describe the decay process represent
the sum of the first order decay coefficients for these reactions such
that:
K - f K + f K (3-l7a)
- . + K + K (3-17b)
Kdi KdPi KdHi * KdBi
ir .v + K + K (3-l7c)
Kpi ' KpPi * KpHi * *pBi
where:
K total decay rate (I/day) for dissolved portion in water
di- column (i 1) or sediment (i " 2)
K - total decay rate (I/day) for particulate portion in water
P* column (i - I) or sediment (i -.2)
K , (K BJ- photolysis rate (I/day) of dissolved (of particulace) in
"SiPi PPi; J;acer £oiumn (i , l} or bed (i - 2)
hydrolysis rate-(I/day) of dissolved (of particuiace) in
(i I) or bed (i 2).
K (K )- biodegradation rate (I/day) of dissolved (of particulace)
dBi pBi in water column (i - I) or bed (i - 2).
The differential equation which includes the degradation processes in
the water column is:
dCTl WT °T f CK -frtC (3-18a)
dT" ' v~ ' T V SAi '
o
fdl-CTlKdl " fplCTlV
At steady-state, solving for
(3-l8b)
fdlco (Kv * Kdl> * fplCo (Ksl *
32
-------
or
« In
(3-18c)
" l * co UplKsl * fdlKv * V
Similarly, the differencial equation describing the chemical
concentration in the sediment is as follows:
3T1 - VlCTl/H2
at steady-state, solving for
CT1 fol VI/H2 (3-19b)
fp2
-------
TABLE 3-1. STEADY-STATE SOLUTIONS SEDIMENTING CASE
(RESUSPENSION AND DIFFUSION ASSUMED NEGLIGIBLE)
Water Column __ Sediment
w/q
Solids «! - i + K c
o
Metal C,l -
Non-reactive Volatile CTJ i + e (f ,K . * fjiK.J
Organic ° *l 81
VQ c Si fPi VH2
Reactive Organic CTJ - I * to U ^ * faiKv * V ** *p2 Ks2 * K2
where:
...» +fK (i-lfor water column, I 2 for sediment)
*i pl pi di <!
K total docay rate for particulate portion
P '
K toenl decay rate for dissolved portion
llf resuspcnslo,, or diffusion Is significant, these eonntions are not applicable. The
general form of cite solutions (Table 3-3) must be used.
evaluated directly; cogecher wich Che solids concencracion ic yields che
dimensionless parameter m^. Alternately, given measurements of the total
and dissolved concentrations of the toxicant (or contaminant) the term m^
may be calculated. With such information, Che removal efficiency is
readily computed for those metals and chemicals which are non-volatile and
non-reaccive.
As indicated above, certain chemicals may be subjected Co additional
transfer or transformation. The fundamental properties of the constituent
are indicative of Che potential magnitude of these routes, e.g., the vapor
pressure and solubility are properties which permit assessment of the
evaporative transfer. Laboratory experiments may be necessary to determine
the chemical and biological routes, e.g., the biodegradabilicy of the
substance. In any particular case, an assessment, either analytical or
experimental, should be made to establish the degree to which transforma-
tion or transfer may be significant.
34
-------
The sedimenting case analysis assumes steady-state conditions in a
completely mixed system and does not consider exchange between the bed and
the water through the interstitial water diffusion or particle resuspen-
sion. For many applications, these assumptions may be adequate for
determining the impact on a lake or reservoir. Also, the data' necessary
for a more sophisticated analysis may not be available in many cases so
that these types of analyses may provide the same level of insight as other
techniques. On the other hand, for sensitive circumstances, these analyses
may not be adequate. The purpose, scope, and the availability of data for
a particular application must all be weighed carefully and evaluated in any
investigation.
3.1.2 Interactive Bed
The type of analysis described in this section is identical to that of
the previous, with the addition of a resuspension term in both the solids
and toxic mass balance equations. The physical structure of the system is
shown on Figure 3-2, from which it is apparent that a mass balance equation
must be developed for both the water column and the bed, since they are
interactive.
Suspended Solids. The mass rate of change of solids in the water
column is:
dm.
Vl dt~ " Qmi " Qml " WlAsml * W21As°2 (
in which
w,. resuspension velocity - L/T
w. settling velocity - L/T 3
mf concentration of solids in the bed - M/L
and the remaining terms are as previously defined by Equation 3-1.
35
-------
LEGEND'
UNITS
SOLIDS
W MASS INFLUX RATE
0 FLOW RATE
V VOLUME
H DEPTH
m SOLIDS CONC.
Cf TOXIC -TOTAL CONC.
ld DISSOLVED FRACTION
Ip PARTICULATE FRACTION
W, SETTLING VELOCITY
W,, RESUSPENSION VELOCITY
W, SEDIMENTATION VELOCITY .
KM EVAPORATION RATE COEFF.
Kd DISSOLVED DECAY RATE
Ka PARTICULATE DECAY RATE
M/T
L»/T
L*
L
M/L*
M/L*
L/T
L/T
L/T
I/T
I/T
I/T
TOXIC
FIGURE 3-2. SCHEMATIC OF SOLIDS AND CHEMICAL
PARAMETERS-INTERACTIVE BED CASE
-------
Expressing the input flux of solids Qro^ as W and dividing through by
the volume V^, yields:
dm
in which
H. average depth of the water column
A mass balance of the bed solids includes the influx of the settling
solids from the water and mass outflow from the bed due to the resuspension
and sedimentation:
dm, w m. w,,»5 W2m2
- - - - - °-22)
in which
H- average depth of the bed
w. - sedimentation velocity - L/T
i
At steady-state conditions, doij/dt - 0, the concentration in the bed
may be expressed in terms of the concentration in the water from Equacion
3-22:
(3-23)
in which
Wl
W21 * W2
Substitution of which into Equation 3-21 under steady-state yields:
' B [
21 2
37
-------
Solving for m., after simplification, gives:
W/Q (3-24b)
ml
The bed concentration follows from substitution of Equation 3-24b in
3-23:
"2
b W/Q (3-25a)
Algebraic simplification yields
W/Q (3-25b)
B2 w
i 1 2
+ * t
b Hj co
It is noted that in most practical applications, the solids concentra-
tions («! and «j) are parameters that are fixed by measurement since *2 and
w,. are difficult to measure.
Chemical Substances. The equations Cor the toxic substances are
developed in an identical fashion as in the sedimenting analysis. Each
phase In the water column, the dissolved, d, and the particulate, p, is
analyzed separately with adsorption and desorption kinetics in addition to
the input, outflow and settling terms. Furthermore, allowance is made for
the exchange of the dissolved component between the water and the bed,
.expressed in terms of the difference in the dissolved concentrations.
Addition of the two equations cancels the adsorption-desorption terms and
yields:
dCTl WT CT1 VoICTl , W21 £P2CT2
--- - H
(3-26)
38
-------
where:
2
K- diffusive mass transfer coefficient (L /T)
Ki ' fai (Kdi * V * fPi KPi
K the sum of the hydrolysis and photolysis and biodegradation race
dl constant of dissolved chemical
K - the sum of the hydrolysis and photolysis and biodegradation rate
pl constant of particulate chemical
K - volatilization rate constant of dissolved chemical-
The bed equation is developed in a similar fashion:
K C -.C (3'27)
K2 CT2 H CT2
where:
K
K - the sum of the hydrolysis, photolysis and biodegradation race
constant of dissolved chemical
» the sum of the hydrolysis, photolysis and biodegradacion race
p2 constant of particulate chemical
Adding the water column and sediment equations at steady-state gives:
vyQ
CT1
The results (which are not a final solution) show that che general form
of che solucion can be cast into a form which is analogous to the simplest
case discussed above (Equation 3-iO). That is:
39
-------
. . C3-29)
Si 1 + C.Kj
where:
is the cocal apparent removal, and:
An alternate expression for the total apparent removal rate on a total
mass basis can be obtained since volumes and depths are related via
interfacial areas.
K_ is re-expressed as:
vi Si
* * "
Hence, the total apparent removal rate is the weighted average of the
water column, Kj, and sediment, KZ * Kg2, removal rates, where the total
mass of chemical in the water column is 'V^, and in the sediment is
V C_2. The effectiveness of each segment's removal mechanism is in
proportion to the total mass of chemical in that segment, an intuitively
reasonable result*
Equation 3-28 given above, gives insight to the form of the solution
and an understanding of the apparent total removal rate, but is not a
solution since CTI, and C^2 are contained in the equation. The complete
derivation for the apparent total removal rate Kj is shown in Appendix A
and the solution is given by the following equations:
(3-31)
40
-------
(3-32)
where:
- «i * i T:
-------
'1 V
'PI "ri'l ' (>35)
As shown in Appendix A,
£
d2 (3.36)
Although this expression is somewhat formidable, it has some properties
that are informative and useful. The equation for ^/^ is determined by
the particulate transport parameters: the resuspension velocity, w21; the
sedimentation velocity, Wj, each of which is modified by the particulate
fraction in the sediment layer, fp2; the diffusive exchange coefficient,
1L , modified by the fraction dissolved in the sediment layer, fd2; and the
total sediment decay rate-sediment depth product, KjHj, which expresses
this process as an equivalent loss velocity. These are all sediment
related parameters. (Note that the subscripts all relate to the sediment
compartment.) The only water column parameter involved is »j, vhich
appears as a ratio 'ty^. Therefore, r^ is determined entirely by the
relative magnitudes of the particulate and diffusive mass transfer
coefficients, the sediment decay rate, and the partition coefficient ratio.
It is surprising which parameters are not part of the expression: the
discharge rate of chemical, WT; the aqueous decay reaction rate, ^ , and
the hydraulic detention time, tQ. Hence, r^, is not dependent upon
these water column parameters.
Application of Simplified Steady-State Bed Interacting Equations. The
general form of the solution with an Illustration of the mechanisms is
shown on Figure 3-3 and the parameters are defined in Table 3-2. The
general solution for many cases may be reduced to a simpler form depending
upon the type of chemical of concern and the assumptions which may be valid
for a particular case. As in the sedimenting case, the key parameters
within the general form of the solution are defined given three categories
of toxics; the categories presented are metals, conservative organic
42
-------
TABLE 3-2. DEFINITIONS
Parameters
Chemical/Biological
Loading Rate (kg/day)
Sum of Hydrolysis, Oxidation,
Biodegradation, Photolysis (I/day)
Volatilization Rates (/day)
Partition Coefficients (I/kg)
Physical
Solids Concentration (mg/1)
Depths (m)
Volumes (m )
Flow Rate (m3/day)
Detention Time (day)
Settling Velocity (m/day)
Resuspension Velocity (mm/year)
Diffusion Exchange Coefficient (cm/day)
Sedimentation Velocity (mm/year)
(Sedimentation Rate Coefficient (I/day)
Concentrations
Total Dissolved + Particulate (ug/D
Particulate (ug Chemical/g Solids)
Fractions
Particulate f
Water Column
W
H
Ce
'Pi
'dl
Sediment
H
'21
s.
w-
*T2
43
-------
INFLOW
MECHANISMS
LOADING
OUTFLOW
Q,[" *r[ °i
A
WATER COLUMN REACTIONS K,
ADSORPTION -OESORPTION m, IT,
SETTLING
RESUSPENS1C
SEDIMENT REACTIONS K2
AOSORPTION-OESORPTION n\2
SEDIMENTATION
W2
IN} DIFFUSION
W2.
*2
"C
SOLUTIONS
'01
CT2=CT1b
fp. r2
TOTAL APPARENT REMOVAL RATE
KTsK, + /3 -jr (K2 * fp2 KS2)
SEDIMENT CAPACITY FACTOR
m2H2 fpl
m, H, f.p2
h
m,
m.
W.
W2I 4- W2
RATIO OF PARTTCULATE CONCENTRATIONS
d2
W
2,
f
K2H2
FIGURE 3-3. SCHEMATIC OF INTERACTIVE
BED MODEL FRAMEWORK
44
-------
chemicals and non-conservative organic chemicals. The parameter rj/rl can
also be evaluated"assuming diffusion to be negligible. Tables 3-3 and 3-4
show the equivalents for Kp 14 and r2/rl for the various assumptions and
demonstrate that the solutions become considerably more manageable when the
diffusion rate is negligible.
Many of the parameters contained within the general solution will not
have been measured and are difficult to measure. The key to understanding
the behavior of the steady-state solution is an appreciation of the
mechanisms which control the sediment capacity factor, 8, and the
particulate concentration ratio: r2/rr The necessity to understand these
parameters should be obvious; if estimates of these parameters can be made
using accessible data, the general solution becomes an easily adaptable
tool. The detailed discussions on the sediment capacity ratio and the
particulate concentration ratio, r^, along with methodologies for
estimating these factors are presented in Section 5.0 of this manual.
3.2 Tine to Steady-State
An assessment of the fate of toxicants in lakes must consider the -time
scale of the problem. In some cases, an investigation may be initiated as
a result of an accidental spill or an instantaneous discharge of a
chemical. In the case of a continuous discharge, the time scale of concern
may be when steady-state is reached, which may take a significant period of
time. The time to steady-state depends on all the physical and chemical
parameters of the system.
The simplified approach to the time varying problem presented in the
'following sections assumes complete mixing in the lake. Although this
assumption may seem crude for short time scales, the approach does give
order of magnitude estimates for the time to steady-state. The critical
aspect of these calculations is to determine the time frame of the problem
and not necessarily to pinpoint chemical concentrations at a particular
45
-------
TABLE 3-3. GENERAL FORM CHEMICAL WATER COLUMN AND SEDIMENT EQUATIONS
Metal
r2/rl
d2
Hon-re.cclv« Volatile .
Organic Chemical *» f«ll
W.) f , * K. (",/",
2 2 L
<"21 * V fp2 * 'S. fd2
. * w.) f. * K, <,/,)
Si- Si "777
(K2 * fp2 K.2
"2 wl
b
l W2t * W2
TABU 3-4. CHEMICAL WATER COLUMN AND SEDIMENT EQUATIONS
DIFFUSION - 0
Metals
Non-reaccive Volatile
Organic
0
0
f2/r,
Restive Organic
Chealeal
d,
* Rdl> » f a K , fd2 K,,2 * ',
*.w J f ll.
« P* *
46
-------
time. For example, Che question to be answered is whether the 'wash-cue
period for an instantaneous discharge or the time to steady-state for a
continuous discharge is on the order of days, months or years.
The following sections address two simplified cases. The first,
settling and sedimentation, assumes that diffusive exchange and resuspen-
sion are negligible. The second, includes interaction between the bed and
the water column through resuspension and diffusion. In both cases, ic is
assumed that the solids are constant at the steady-state concentrations.
3.2.1 Settling and Sedimenting
Consider an instantaneous mass discharge (M) into a lake of volume V.
The dynamic mass balance equation for the water column is:
d°Tl m _fli . ,K \ f K ) c (3-37)
~dT ~ ( I Pi "I1 Tl
where:
Kl " fpKp * fdKd * fdKv
K " Wl/Hl * Secclin8 coefficient
K parciculate chemical reaction race
K. - dissolved chemical reaction rate
d
K - volatilization rate
The mass balance for the bed is given by:
°-38)
dt
where :
K , - w_/H7 - sedimentation coefficient
92 ' 47
-------
The solution for an instantaneous discharge is then given by:
CT.
and
/» « * f«.' K-'lc "K2e
r £ w. /H- o p* » *
CT2 *ol Wl/tt2 - v - e ] (3-40)
' ll/to * fplKslJ
where:
CL - M/V. the initial concentration at t 0.
To
The solution for the continuous discharge is developed similarly and is
given as follows:
-[1 * (Kj * f ! Ksl) co] C/Cfl
IS.. I [1 -e ' ' 1(3-41)
CTo l * ( 1 * pi al; o
and for the bed:
fS- A. II -e ^ 1 -Aj [e ^ "9l °-e' " ] (3-42)
b
where:
f
pl
Ks2 U * CK1 * fpl
fpl Ksl))[i * (K! * fpl
fpl W1/H2
CTo '
48
-------
The solution behavior can be understood by inspection of Equation 3-41.
At t - 0~t" the exponential is unity and the bracketed term is zero, and,
therefore, so is C^ (0). For large times the exponential approaches zero
and the solution approaches its steady-state value, the leading term.
The solution to the equation for an instantaneous discharge and a
continuous discharge are demonstrated on Figure 3-4. As shown, the water
column concentration rapidly changes with time after the initial release
until steady-state is met. For an instantaneous release the chemical will
eventually settle, react, or wash out of the water column. A continuous
discharge will cause a buildup of the chemical to its steady-state
concentration. In the bed, there is an initial rapid rate of buildup
followed by a slow sedimentation loss for an instantaneous release or a
slow buildup rate for a continuous release. In the bed, the time to
steady-state is. approximated by the time of the slow buildup rate.
The time to reach steady-state is theoretically infinite since che
exponential (Equation 3-41) never actually becomes exactly zero. However,
for practical purposes, it is usual to define the time to steady-state as
that time for which the solution has reached a certain percent of the
steady-state solution, say 90 percent. It can be shown from Equation 3-41
that:
-"".*«!* ',t *.!>«
where:
C , » steady-state concentration
TCss)
At 90 percent of steady-state:
-Cl/t0 + V f i K9l
_..__. _ (3-44a)
CT(ss)
49
-------
INSTANTANEOUS INPUT
CT./CTX,
WATER
T/t,
BED
CT2/CTQ
SLOW NATC-SCOl"CITATION
CONTINUOUS INPUT
TO
WATER
T(SS)
^
TO
t/t0
FIGURE 3-4. THEORETICALTIMETO STEADY-STATE
FOR INSTANTANEOUS AND CONTINUOUS INPUTS
so
-------
so that
+ K+fK)t: <>44b)
or
2.303 (3-44c)
C90 ' l/co * Kj + fpl Ksl
where 2.303 - -In (0.1). Other percenciles simply alter the numerical
constant, but not the fora of the equation.
Finally, Equation 3-43 nay be expressed as:
^. . Wl + (Kl + fpl K3l)t0] U (i . ^ ) (3-*S)
o
so that the ratio tgs/to may be calculated for a given CT/CT(SS) ratio as a
function of (^ + Kfl> Figure 3-5 shows Cg3/tQ versus (^ * KSI)CQ for
various VCT(ss) r"iOS' Note" ChaC Che Css/Co rati° levels °ff " Che
lower values of (Kj * K§I)CO- This Bcaas chac Che naximum clme "
steady-state can be easily estimated. For example, the maximum tsg/tQ
ratio with a CT/CKgg) ratio of 99 percent is approximately 4.8. In other
words, after 4.8 hydraulic retention times, a steady-state condition will
be approximated in the water column for almost any system regardless of
settling velocities or reaction rates.
51
-------
10
LAKES » HESEBVQIUS
TIME TO STEAOV-STATE
1000
FIGURE 3-5. NORMALIZED TIME TO STEADY-STATE
IN.WATER COLUMN SEDIMENTING CASE
3.2.2 Bed Interacting
The cine varying solutions which include resuspension and diffusion are
considerably more complex than those of the sedimenting case. The time
variable solutions for the mass balance equations for the receiving water
segment are derived in Appendix A. The results are:
T1
. c (.,
CtlC J
(3-46)
(3-47)
where C..C) and C_2C) are the steady-state solutions, gt and g2 are the
roots of the characteristic equation. The formulas are given in Table 3-5.
52
-------
TABLE 3-5. TIME VARIABLE SOLUTIONS FOR RECEIVING HATER SEGMENT
-g,
. « i
'2VS2
tl -
where :
i/c
i Ki * (wi£pi * Vdi)/Hi
1*w2) f2* Vd21/H2
ST ' Sl * S2
and:
W./Q
Hl
ag is computed using the plus sign
g is computed using the minus sign
53
(ST
-------
It is easily seen that t - 0, the bracketed terns cancel and Ccl(0) -
C (0) - Q\ the assumed initial conditions. The form of the solutions is
analogous to the case discussed above. The constant terms are the
steady-state solutions and the time variable behavior is specified by the
exponentials. There are two exponentials in each solution, corresponding
to the tvo coupled differential equations representing the water column and
sediment volumes, which interact to produce the resulting time variable
behavior .
The time to steady-state is governed by the magnitudes of the two
characteristic roots: gj and g2, which are given by the equations in Table
3-5, as wen as the coefficients of the exponentials. Hence, no simple
expression is available for tgQ.
However, approximations are available which give an insight into the
magnitude of BI and g^ The approximation depends upon the observation
that for physically reasonable magnitudes of the parameters, the expression
in the radical (Table 3-5) is small relative to one. This leads co the
approximations:
*
where:
ai Ki * (wifpi * Vdi)/Hi
si * S2
and K_ is the total apparent reaction rate. The expressions Sj and s2 are
the sum, respectively, of the water column and sediment segment reaction
rates and transport terms expressed as equivalent reaction rates. Hence,
in this approximation, g^ is the-sum of all the water column'and sediment
reaction and transport rates.
54
-------
The ocher race, g2, Is, in tnis approximation, cu. - ........
apparent 'reaction- rate, 1^, and outflow rate, l/tQl> modified by the ratio
s, (ST + l/Col)« « 9l is large relative to s2, S2 is significantly less
than ie + l/col' Since *T iS Mually nuch smaller chan sl * S2 (the laccer
contains the sum of the transport terms), it is always the case that:
a > r +--> z
gl > S t > g2
Hence, relative to the simple water column example, the effect of
sediment-water interaction is to produce two characteristic roots, one
larger and one smaller than K^ *
The time to steady-state may be approximated through the discussion
presented above. Certain practical situations occur when g{ » g2> i.e.,
for which:
This can occur if X. is small (due to small degradation rates, ^ and KZ,
and small sedimentation rate, Xs2) or where sediment-water particle
exchange and/or diffusive exchange is large.
In " this case, the time variable solution behavior has two distinct
phases as illustrated on Figure 3-6; the solution rapidly rises to a
plateau concentration as e"gl decays to zero.
This occurs at a time on the order of t « 1/gj. However, the second
exponential is e"g2/gl which 'is still approximately unity since g1 » gj.
Hence, the solution rises to a plateau concentration which can be expressed
as:
55
-------
1 * 'ol 8I
(3-52)
4QO
300 1200
TIME (days)
I6GO
2000
FIGURE 3-6.'EXAMPLE OF TIME VARIABLE BEHAVIOR
CONSERVATIVE SUBSTANCE
Noce chac s_ Is ehe sum of all waeer column and sediment reaction and
transport rates. Hence, the solution is behaving as if all reaction and
transport rates remove chemicals from the water column. The reason for
this behavior can be understood by considering the state of the sediment
during this time period. For gl » g2, the sediment concentration is
approximately zero since g2/g2 - gj » 0, e~*2e » 1, and g^Cgj - «2} ' l
for t » 1/g, (see Equation 3-47). Hence, transport by settling and
diffusion to the sediment is a sink and resuspension brings uncontaminated
solids to the water column which provide a further sink. The result is
that all the transport processes are acting as sinks while the sediment is
being contaminated.
56
-------
After the Initial plateau is reached, the water column and the sediment
proceed toward equilibrium at approximately the same rate. This phase of
the process is controlled by the first exponential e"g2C and can be much
longer than the first plateau time scale. The time to about 95 percent
equilibrium completion can be estimated by 3/g2 since e » .05.
Although the time varying solutions are quite complex, it is shown that
the time to steady-state calculation is readily obtainable. The time to
the first plateau is estimated as l/g1§ and the time to steady-state is
approximated by 3/gj. Approximations of gj arid g2 are functions of the
water column and sediment reaction rates and the transport term. Table 3-6
summarizes the time to first plateau, the time to steady-state and the
approximations of gj and g2«
. TABLE 3-6. EQUILIBRIUM CALCULATIONS BED-INTERACTIVE CASE
Time to First Plateau -
Time to Steady-State (95 percent) - 3/g2
where :
«1 ' Sl * S2 * l/Col - St * 1/Col
sl Kl * fp2
ST - 9l * S2
3.3 Complex Models
The methodologies described in previous sections simplify the
mechanisms and processes that effect the fate of a toxic. The application
of these methodologies have a two-fold advantage over more sophisticated
analyses: (1) the equations are easy to use and can be solved through
57
-------
desk top calculations, and (2) data requirements are reduced; the data
necessary to do more sophisticated analyses are not available for most
applications.
The simplified methodologies assume complete mixing, stationary bed,
equilibrium partitioning and linear transformation kinetics. In an
investigation for a wide or deep lake perhaps the most critical of these
assumptions is complete mixing. These lakes may tend to have water quality
gradients over depth and width. A completely mixed assumption, therefore,
may tend to show the results in either a positive or negative direction
depending on the location in the lake. This is not to say that the
simplified methodologies cannot be used to make screening or order of
magnitude estimates, but if a stratified condition exists over the problem
time scale or if longitudinal gradients are severe, a more sophisticated
analysis may be warranted.
Besides the spatial limitation inherent in available toxic models,
other restrictions may also exist. The transport, transfer and trans-
formation processes, may be handled differently ' between models. In
addition, the interaction between the bed and water column as well as bed
movement are conditions which will vary between models. The user must be
aware of these differences as well as the restrictions and limitations
before model selection.
Three major sources of information have summarized the complex models
available. The reader is referred to Book II, Chapter 3 (USEPA, 1984);
Book III, (USZPA, 1984); and Book IV, Chapter 2 (USEPA, 1983), for the
detailed discussions. The following sections summarize some of these
discussions which are particularly pertinent to lake analyses.
3.3.1 Steady-State Models
The number of steady-state models currently in the public domain and
applicable to lakes are limited to four. The four available models
include: CTAP and SLSA developed by HydroQual for the Chemical Manufac-
58
-------
curers Association, EXAMS aevelopea oy c.£A ^wiiciio
Laboratory (ERL), and MEXAMS developed by Battelle Pacific Northwest
Laboratory for Athens ERL. SLSA uses the simplified approach described
earlier in this section.
Table 3-7 summarizes some of the key differences between these models.
The three-dimensional models listed all have the capability of simulating
stratified systems or near-shore analyses. The stratification and near-
shore definition are both a function of the lake size and the compartment
number limits. In very deep lakes, multi-layered models may"be desired to
reproduce the observed stratification. The greater number of layers,
however, may restrict the longitudinal definition if the number of
compartments are approaching the model's 'limits. Likewise, the compartment
definition desired near an outfall may restrict the definition for the rest
of the lake.
TABLE 3-7. SUMMARY OF STEADY-STATE LAKE TOXICITY MODELS
Steady-State
Model
CTAP
EXAMS
MEXAMS
SLSA
'Dimension
3D
3D
3D
CM
Maximum Number
Compartments
Bed Type
Load
425
100
100
1
S or M
S
S
S
Multi
Multi
Multi
Single
S Stationary
M Moving
CM - Completely mixed
In general, CTAP uses' first order kinetics and sums the various transforma-
tion and degradation rates into one decay coefficient. EXAMS is capable of
handling second-order kinetics and transformation processes that convert
chemical to daughter products. MEXAMS, linking EXAMS and MITEQ can
calculate speciation, and dissolved, adsorbed and precipitated metal
concentration.
59
-------
3.3.2 Tine Varying Models
There are currently six eime-varying models that are applicable to
lakes or reservoirs.' These include CHNTRN, HSPF, TOXIC, TOXIWASP, and
WASTOX. The chemical and sediment capabilities as well as dimensionality
and numerical solution techniques will vary for each model. Table 3-8
briefly summarizes some of the key aspects of these models.
TABLE 3-8. SUMMARY OF TIME VARIABLE LAKE TOXICITY MODELS
Dimension
CHNTRN 3D
HSPF 1D
TOXIC 3D
TOXIWASP 3D
WASTOX 3D
As mentioned above, the reader is referred to other EPA manuals for
more detailed discussions of these models.
.
3.4 Model Assumptions and Limitations
The models for the analyses of organic chemicals and metals are similar
to those developed for constituents which are natural components of
.ecological cycles. The terms relating to the particular form and its
interactions with the dissolved component are the additional components to
be incorporated. The reaction and transfer mechanisms are incorporated
with the transport phenomena and input functions to define the temporal and
spatial distribution of toxic substances in natural systems. By virtue of
their interactions with the solids in these systems, it is also necessary
to analyze the distribution of the various types of solids. Furthermore,
the exchange between the suspended and the bed constituents may be taken
into account. The resulting models describe the distribution, accumula-
tion, and transfer of solids and chemicals in the water column and the bed.
60
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1C Is not within the scope of this manual to describe the assumptions and
limitations of each available model. The following sections describe the
assumptions and limitations for the simplified approaches as well as some
discussion pertaining to the uncertainties.
3.4.1 Instantaneous Equilibrium
Certain chemical substances have a strong affinity for sorptiou to
particulate materials, and the subsequent transport of such particulate
chemical forms may be markedly different than for the soluble chemical
phase. It is known that -soluble materials will be sorbed onto particulate
surfaces in a reversible reaction at some rate until an equilibrium is
achieved. Once equilibrium is established, the relationship between sorbed
and soluble material can be described by various isotherms such as
Langmuir, Freundlich, and others. In linear portions of these functions,
the relationship between particulate and soluble forms of the material can
be accounted for in a simple manner by use of a solid-liquid partition
coefficient.
The dissolved and particulate fractions may exist in a state of dynamic
equilibrium where the rate of sorbing to particles is equal to the rate of
desorbing from particles. The rates at which chemicals sorb to or desorb
from particles is generally fast in relation to other phenomenon such as
lake- detention time or kinetic transformation reactions. Because the
adsorption-desorption mechanisms occur rapidly, the basic equations in the
simplified approaches assume this phenomenon occurs "instantaneously and
that soluble and particulate chemicals in the water column and sediment are
in a state of local equilibrium.
*
The validity of the instantaneous equilibrium assumption may be tested
by comparing the time scale for chemical equilibrium to be established with
the time scales for the other kinetic reactions: photolysis, hydrolysis,
and biodegradation. Generally, equilibrium is established on a time scale
of minutes to hours while the other transformation and removal reactions
have time scales on the order of days, months or years. As long as this
61
-------
constraint is fulfilled, instantaneous equilibrium is a reasonable
assumption." For those chemicals whose sorption-desorption mechanisms
proceed more slowly in comparison to their transformation/decay reactions,
Che simplified approaches based on instantaneous equilibrium, may not be
adequate for evaluation of their environmental behavior.
3.4.2 First Order Reactions
In the simplified modeling frameworks, the reactions which remove
chemicals from natural water systems'are approximated as first order
kinetics as shown by Equation 3-53.
dc m (3-53)
dt KC '
in which dc/dc is the time rate of change of a chemical with concentration,
c, and K is the decay race. This equacion states chaC Che chemical loss
race is proportional Co Che amount of chemical available in a reaction che
speed of which is defined by che constanc, K. Individual values for K are
required for each of the -transfers and removal mechanisms as discuss'ed in
Section 7.0. Values are determined from laboratory and field daca. The
transfer mechanisms are discussed in che following sections.
3.4.3 Seeding. Resuspension. and Sedimentation
Transfer mechanisms for chemical substances bound to particles may
involve settling, resuspension and sedimentation, and perhaps bed
transport, compaction and diffusion to the deeper sediment. These transfer
processes become more or less important depending on the receiving wacer
context as discussed above. In deep lakes, the principal particulace
chemical transport mechanisms are likely to be settling and subsequent
burial. In shallow lakes settling and resuspension may be the principal
sediment transport mechanisms of concern.
62
-------
In general, Che simplinea approacned
effects of'settling, sedimentation and resuspension. The problem, however,
is obtaining the measurements representative of these parameters.
Definition of these transfer mechanisms, particularly resuspension, are
difficult and may be critical to the evaluation.
3.4.4 Water-Bed Diffusive Exchange
Another basic transfer mechanism is diffusive exchange of dissolved
substances between water column and sediment. To some degree, the process
is analagous to the water-air exchange. Once a chemical substance is
introduced into the water column of a water body, a diffusive exchange will
take place to transfer dissolved substances to the interstitial water in
bottom sediment. The process will continue until an equilibrium is
achieved between dissolved material in water column and sediment
interstitial waters as affected by all transport, transfer, and kinetic
processes. If the equilibrium is disturbed in any manner, for example, by
continual deposition of particles with sorbed chemical which then cends co
desorb on the bottom, diffusive exchange may continue with soluble chemical
being transported from sediment interstitial waters to the overlying water
column. This process is controlled by concentration gradients which
develop in thin films at the water-sediment interface. The rate at which
transfer occurs is a function of diffusivity, film thickness and
geometrical characteristics of water column and sediment. Therefore,
quantification of this transfer- process requires a value for the molecular
diffusivity of the chemical and an estimate of the film thickness. Each
factor may vary by an order of magnitude such that the overall process may
have a range of two orders.
At present, the diffusive exchange coefficient is a parameter that is
difficult to measure by direct field testing. This parameter is usually
evaluated through the model calibration analyses.
63
-------
3.4.5 Bed Characterization
Sediment layers are characterized as sedimenting, exchanging, or moving
beds. Stationary beds are sediments which increase in depth due to
settling of solids from the water column and virtually no resuspension of
sediment layer solids. These sediments can possess significant chemical
concentration gradients over depth. Mixed beds are subject to both
settling and resuspension, but tend to be completely mixed over the top few
centimeters. It is assumed that both stationary and mixed sediments
undergo no movement in the direction of flow. Moving 'beds are subject to
both settling and resuspension. They are, however, subject to shear forces
at the sediment-water interface which tend to move a dense layer of
sediment solids along the direction of flow.
The simplified approaches are designed for chemical evaluations in
lakes which contain either mixed or stationary bed. More complex models
would be necessary for provision of a moving bed. CHNTRN, and HSPF are
models that have the capability to simulate sediment transport.
While much is Known about the fluid transport in most natural water
systems, the understanding of bed transport is minimal. It is appreciated
that while much work has been done in both the laboratory and field in
elucidating the factors affecting the transport of sands and gravel,
comparatively little has been accomplished with respect to clays, silts and
detrital material. Due to their affinity to adsorb many constituents, it
is this latter category which is of major importance In the analysis of
chemicals in natural systems. Theoretical formulations as well as reliable
field data is particularly lacking in the littoral zones of lakes.
Other questions of paramount importance are related to the concentra-
tion, depth, velocity and dispersion of mixed and moving bed layers. Rates
of scour and entrainment are only now being addressed. The effect of
agglomeration and flocculation on the settling and resuspension of these
solids have not been fully clarified.
64
-------
The above considerations reiace primarily co w*ic i»«
of the chemical. In addition, the characteristics of the bed which affect
the dissolved component must also be addressed more fully. The diffusion
of the dissolved chemical through the interstitial waters and the
interaction with other constituents, both dissolved and particulate,
requires further study.
3.4.6 Particle Sizes
The total chemical concentration at any time is equal to the sum of the
dissolved -and particulate concentrations. The tendency for a chemical to
sorb to particulate material is highly chemical specific and will range
from very weak to strong. The amount adsorbed per unit mass increases with
increasing concentration of solute and usually approaches a limit as the
capacity of the solid to accumulate Is reached. The affinity of a
particular chemical to sorb can be quantitatively expressed by a
sediment-water partition coefficient.
The partition coefficient is not only dependent on the cy?e of
chemical, but different partition coefficients may be observed for the same
chemical with various types of sorbants. For example, organic particulaces
or silty materials may attract a certain chemical more strongly than sandy
materials. Further, different size classes of particulate material, in
that they may reflect different classes of parciculates as sands, silts,
clays, etc., may exhibit differing affinities, and partitioning, for a
specific chemical. In principle, it is most advantageous, therefore, to
perform experiments and determine a chemical's partitioning characteristics
with the type of particulate material (suspended and bed sediment) to which
it will come in contact in the natural environment.
The simplified steady-state and time variable approaches allow for
different partition coefficients between the water column and the sediment.
Partition coefficients may not vary for different particle characteristics
within the same system. The., coefficient must reflect the overall
partitioning behavior for all types of particles. More complex models
65
-------
(SERATRA, CHNTRN and HSPP) can model three particle sizes and provide the
ability to vary the adsorption/desorption rates as a function of particle
characteristics.
3.5 Criteria for Model Selection
Discussions of model selection are presented in Book II, Chapter 3
(USEPA, 1984), Book IV, Chapter 2 (USEPA, 1983), and Book III (USEPA,
1984). The reader is referred to these reports for this information.
These discussions are directed towards the general considerations which
must be evaluated. The major concerns of model selection are presented;
these concerns are both technical and practical in nature. These
discussions, however, are not specific to the fate of toxics in lakes.
The steady-state and time varying models represent two levels of
complexity for the modeling analysis of chemical fate in receiving waters.
At the outset of an analysis, an evaluation should be made to determine
which type of model is consistent with the problem characteristics. The
state and dimensionality of chemical distributions, transport character-
istics, the purpose of the analysis, and availability of data are all to be
considered in this regard.
3.5.1 Scate and Dimensionality
Two basic criteria which must be evaluated in selecting a model for
chemical impact analyses are state and dimensionality of the systems. The
state refers to the time domain to which a particular model can be applied
while dimensionality refers to the spatial dimensions over which the model
can simulate concentration gradients. The analysis can be one-, two- or
three-dimensional with time domains of either steady-state or time varying.
For a proper analysis, the model applied should be consistent with both the
time and space scales of the chemical concentration gradients in the water
body. Therefore, before analyses are initiated, it is appropriate that.
in situ chemical data are reviewed to determine both the temporal and
spatial scales of chemical concentrations.
66
-------
In many analyses suincienc cnemicsj.
directly" assess 'the above domains. When this is the case, other
conventional pollutant data such as total dissolved solids, chlorides,
temperature, dissolved oxygen, nitrogen, or phosphorus may be available to
assess water quality space and time scales. Other factors such as the
variability of influent flow, depth, and the variability of chemical inputs
may also help to define temporal and spatial dimensions.
Guidelines for the temporal state and spatial dimension for which
available models are applicable are presented in Table 3-9. In general,
SLSA, CTAP, and EXAMS are applicable to steady-state problems with CTAP and
EXAMS applicable for multi-dimensional analyses. The SLSA is also
applicable for time varying analyses but is limited to completely mixed
impoundments. The more complex problem settings may require the use of one
of the following time varying models: HSPF, CHNTRN, TOXIWASP, and WASTOX.
TABLE 3-9. SUMMARY OF MODEL APPLICATIONS
State
Dimension Model
Steady-state " completely mixed SLSA
multi-dimensional CTAP, EXAMS, MEXAMS
Time varying completely mixed . SLSA
one-dimensional HSPF
three-dimensional CHNTRN, TOXIWASP,
WASTOX
3.5.2 Transport and Bed Considerations
Water column and sediment layer transport should also be considered as
criteria for model selection. Transport in the water column consists of
both advective and/or dispersive transport. Bed conditions include
sedimenting, exchanging, and moving beds. Table 3-10 presents water column
transport and bed sediment conditions included in available models.
67
-------
TABLE 3-10. CONDITIONS FOR MODEL APPLICATIONS
Model
SLSA
CTAP
EXAMS
WASTOX
TOXIWASP
TOXIC
CHNTRN
HSPF
Water Column
Advective transport
Advective and
dispersive transport
Advective and
dispersive
Advective and
dispersive
Advective and
dispersive
Advective. and
dispersive
Advective and
dispersive
Advective
Bed Condition
Completely nixed;
sedimenting;
exchanging
Completely mixed or
stationary; multi-
dimensional;
exchanging
Completely mixed;
simplified exchange
Sedimenting; three
sediment size
fractions; unequal
partitioning,
advective sediment
process
Multi-dimensional;
advective and
exchanging
Completely mixed;
sedimenting;
exchanging
Mulel-dimensional;
sedimenting;
exchanging
Completely mixed
sedimenting;
multi-sediment size
Application
Completely mixed
lakes
Steady-State
Unmixed lakes
Steady-State
Non-tidal lakes
Steady-State
General
Time Varying
General
Time Varying
Reservoirs and
impoundments
Time Varying
General
Time Varying
Unstratified lakes
Time Varying
3.5.3 Available Data and Purpose of Analysis
Two additional factors to be evaluated when selecting the model are the
amount of data available and the purpose of the analysis. These factors
help to define the complexity of the model required for the impact
analysis.
68
-------
If only limited data exist and no additional data are to be collected,
application of a simple modeling framework la recommended. If a complex
model is applied in such a situation, certain model input parameters may
remain as unknowns resulting in a weak technical analysis. A preferable
approach in this situation is to apply a simpler modeling framework and to
recognize that the analysis is preliminary.
Similarly, if the purpose of an impact analysis is to obtain initial
estimates of chemical levels in a lake after introduction of a new source,
it is better to use a less complex model if applicable within the foregoing
guidelines. If, however, the problem under evaluation is to develop a
mixing zone for chemicals discharged to a lake then it may be necessary to
use multi-dimensional, time varying models. Finally, if an analysis is to
be performed for WLA purposes, it is appropriate to collect laboratory and
field data; select the model which is most physically realistic for the
problem setting (simple to complex); and calibrate and validate the model
prior to allocation determinations.
69
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SECTION 4.0
MASS INPUTS TO LAKES
Chemicals are introduced to natural water bodies by point sources such
as municipal or industrial discharges and by non-point sources such as
combined' sewer overflows, storm sewer inflows, direct urban runoff,
tributaries, groundwater, or non-urban overland runoff. The purpose of
this section is to introduce these sources and to illustr.ce data
requirements necessary to define chemical inputs.
Book VIII, Part i, Chapter 3 (USEPA, 1982) thoroughly outlines
wasteloading calculations. This .manual will not attempt to duplicate
information in other reports but will highlight certain aspects which are
pertinent to toxic analyses. This section will address sediment and
chemical mass inputs from both point and non-point sources. Data sampling
requirements to generate mass inputs is also discussed.
4.1 Point Source Inputs
Mass loadings must be developed for each industry and/or municipality
discharging a chemical of interest to the water body under consideration.
In many instances, the discharging entity may be the best source of
information as many states require dischargers to conduct a self monitoring
program. Daily chemical loading and/or effluent chemical concentration
data are usually part of this information. Additional sources of effluent
data for certain chemials may be the state regulatory agency and perhaps
the USEPA Surveillance and Analysis Division. If mass input data are
available from these sources, field sampling may be conducted to generate
data necessary to perform the analysis. Section 4.3 presents details of
actual field sampling.
70
-------
The principal, parameters of concern for a toxics analysis are the
suspended solids mass discharge rate and the chemical mass discharge rate.
The point sources are categorized by municipal and industrial discharges.
Municipal effluent strengths will vary by geographic location, degree of
industrialization and community size. Industrial effluent strengths is
largely dependent on the type of industry.
4.1.1 Sediment Inputs
The discussion of sediment inputs is divided into two categories:
municipal and industrial. The following sections briefly discuss the
information available and the methodologies used for estimating these types
of sediment inputs.
\
Municipal Suspended Solids Inputs. The best available estimate of
municipal suspended solids mass discharge rate is from the records of a
self monitoring program that Is required by most states or from the state
or federal agency which issued the discharge permit. If, for one reason or
another, monitoring, data is not available, the mass input of suspended
solids may be approximated through literature values, treatment type, and
community population. The mass discharge rate is given by:
W - Q x P x Ce x (I - e)
ss xp P ss
where:
U mass discharge rate of suspended solids (M/T)
S3
Q - flow per capita per day (L /T)
P
P population served by municipality
C concentration of suspended solids in raw domestic sewage
c removal efficiency based on treatment type.
71
-------
The concentration of suspended solids in raw domestic sewerage usually
ranges from 100 to 350 mg/1 with a median of about 220 mg/1. Table 4-1
shows average water withdrawals per capita (Qp) of public supplies by
states and selected municipal systems; the average withdrawal nationwide in
1970 was 166 gal/capita/day (Book VIII, Part 1, USEPA, 1982). Table 4-2
gives typical treatment plant performance with removal efficiencies (e) for
various treatment processes. These three sources of information, along
with community population, provides the' data to make a first cut estimate
of the suspended solids mass discharge rate.
Industrial Suspended Solids Inputs. Industrial waste discharges are
extremely difficult to generalize due to the wide variety of processes and
treatment schemes. The user is advised to obtain as much data as possible
from on-site measurements. If local data is unavailable, the best sources
of information on industrial waste characterization is the "Effluent
Guidelines" series of reports by the USEPA. A report is available for each
of the USEPA point source categories. These reports contain typical waste
characteristics for various processes within the point source category as
well as process water usage and are listed in the references at the end of
che chapter. Effluent limitations are also given which can be used as
upper bound concentrations in water quality assessments.
Table 4-3 contains some typical pollutant loads which might result from
the industries shown. Table 4-4 also presents loads for some industries
with expected treatment efficiency from best practicable treatment. These
wastewater treatment processes are representative, though not exhaustive,
of techniques which may be used. Values in Tables 4-3 and 4-4 are for
comparison only. They should' not be used for load projecting in other
areas.
4.1.2 Chemical Inputs
The priority pollutants which appear in municipal wastewaters come from
three main sources: (1) industrial effluents, (2) non-point source runoff,
and (3) domestic uses. The proportion from each category will also vary
from location to location as' well.
72
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TABLE 4-1 IMTEK WITHDRAWALS FOR PUBLIC SUPPLIt STAfE AM.I BY SELECTED MUNICIPAL SYSTEMS. 1970
LI
State | til ty ***«pi »
Alabama 806
Birmingham 576
Alaska 1790
Anchorage 769
Arizona . 787
Phoenix 864
Arkansas 501
Little Rock 784
California 685
Los Angeles 686
San Francisco 1424
Colorado '46
Denver 955
Connecticut 541
Hartford 564
Delaware '00
Florida 617
Miami 1208
Georgia 946
Atlanta 564
Hawaii '46
Honolulu '80
Idaho 897
Illinois "2
Chicago 871
Indiana 514
Indianapolis 508
Iowa 466
Des Mo 1 nee 514
Ksnsas 587
Wichita 508
Kentucky 114
Louisville
Louisiana
Shreveport
655
5*5
519
Gal/
213
152
471
203
208
228
133
207
181
181
176
19'
252
143
149
85
163
319
250
149
197
206
23'
. 204
210
141
114
123
141
155
134
81
171
144
117
t /
*/
State. Clly C«plta-d
Main
Portland
Maryland
Baltimore
Massachusetts
Boston
Michigan
Detroit
Minnesota
St. Paul
Mississippi
Jackson
Missouri
Kansas City
Montana
Billings
Nebraska
Omaha
Nevada
Los Vegas
New Hampshire
New Jersey
Elizabeth
New Mexico
Albuquerque
New York
New York City
Rochester '
North Carolina
Greensboro
North Dakota
Fargo
Ohio
Akron
553
580
515
648
510
883
616
671
473
515
507
412
485
587
826
754
616
742
1154
1018
415
526
314
772
746
609
1046
663
644
492
477
515
594
492
Gal/
L/
Caplta-d State, City Caplta-d
146
151
116
171
140
211
168
177
125
116
114
114
128
155
219
199
168
196
105
274
128
119
81
204
197
161
276
175
170
no
126
116
1 JO
Oklahoma
Tulaa
Oregon
Portland
Pennsylvania
Pittsburgh
Rhode Island
South Carolina
Charleston
South Dskota
' Sioux Falls
Tennessee
Memphis
Texas
Dallas
Houston
Utah
Salt Lake City
Vermont
Virginia
Richmond
Washington
Seattle
West Virginia
Morgsntown
Wisconsin
Ml Iwsukea
Wyoming
Chenne
District of Columbia
Puerto Rico A
United States
492
595
712
1129
685
485
462
916
652
549
587
488
549
587
610
947
till
523
553
420
644
1200
1091
568
549
587
659
746
841
'99
326
628
Gal/
C*plta-d
110
157
188
298
181
128
122
242
172
145
155
129
145
155
161
250
294
118
146
III
170
117
288
150
145
155
174
197
222
211
86
166
Note: L x 0.2642 gal.
Source: Metcalf and Eddy. 1979.
-------
TABLE 4-2. MUNICIPAL WASTEWATER TREATMENT SYSTEM PERFORMANCE
Influent: -Raw-Medium Scrength Domestic Sewage" see Scheme Number 0 for
Characteristics.
Effluent Concentrations (mg/1^,
(Z Total Removal Efficiencies )
Scheme Number
Raw wastewater
1
2
3
4
5'
6
7
BOD
2°°(OZ)
130(35Z)
40(80Z)
25(88Z)
18(91Z)
18(91Z)
13(94Z)
\ m *w »
COD
5°°(OZ)
375(25Z)
125(75Z)
100(80Z)
70(86Z)
70(86Z)
60(88Z)
SS P.*
2°°(OZ)
l°°(25Z)
3°(85Z)
12(94Z)
7(96Z)
7(96Z)
l(99'.5Z)
(mgP/1)
l°(OZ)
9(10Z)
7(55Z)
7(30Z)
l(90Z) .
l(90Z)
l(90Z)
N_TJ (men/11
40
(OZ)
32
26
(20Z)
24
22
(35Z)
(40Z)
(45Z)
'(90Z)
S(99Z)
15
(97Z)
1
(99.5Z)
L(90Z)
(95Z)
c for waatewater treatment are for the approximate concentration
range, as measured by BOD5, of 100 < BOD5 <. 400, («g/l).
Scheme No.
0
1
2
3
Process
No treatment
Primary
Primary, plus Activated Sludge (Secondary Treatment)
Filter (High
5
6
7
Primary, Activated Sludge, plus
Efficiency or Super Secondary)
Primary, Activated Sludge. Polishing Filter, plus Phosphorus
Removal and Recarbonation
Primary, Activated Sludge, Polishing Filter, Phosphorus Removal,
plus Mitrocen Stripping and Reearbonation
Primary Activated Sludge, Polishing Filter, Phosphorus Removal,
Nitrogen Stripping Recarbonation, plus Pressure Filtration
Primary, Activated Sludge, Polishing Filter, Phosphorus Removal,
Nitrogen Stripping Recarbonation, Pressure Filtration, plus
Activated Carbon Adsorption
Source: Meta Systems, 1973
74
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TABLE 4-1. TYPICAL INDUSTRIAL OISCHAtMIK POLUiTANT CONCENTRATIONS
Induatry
Primary Metal £
CH. Braaa RodH
Roof Inn Material*
Steel Plate. Ulrec fc
Petroleuai (General)
Oil Production ( ID-
oil Production ('2 )c
oil Production (11)
Paiter (General)
Pupurboaril
Paper fe
Primary Inorganic
Alky Lead Fluoro
Hydrocarbon* £
Inorganic Acid*.
Prliaary Organic
Cauatlc Cheat ca la
Plant Food
PIlMJ
g/MOO Ib*
.2-1.6
0.04
0.01
0.004
0.0115
O.OOJ
0.001
0.001
0.015
0.017
0.024
0.002
0.002
0.004
0.002
0.021
0.001
BOD
Ib/IOOO Ib
O.I
11.6
0.56
1.1
0.57
0.4S
0.4S
18
19.6
12.6
0.2-1.5
0.19
0.08
1-1.9
1.24
0.01
CO»
Ib/IOOO Ib
.
0.5
25.7
2.7
1.7
2.1
1.1
2.9
55
64.8
41
0.89
0.52
4.9
1.41
TSS
Ib/IOOO Ib
0.02
14.2
5.1
O.5U
0.86
0.65
28
U. V
11. 1
5-10
0.15
5.37
19.9
0.01
Total N
Ib/IOOO Ib
12
0.07
0.14
0.04
0.4
0.11
0.16
0.24
"
0.05
0.01
0.01-0.7
0.01
0.04
1-7
1.27
1.17
Total P
Ib/IOOO Ib
15
-o
-0
0.01
0.01
0.01
0.01
0.8-9.0
0.02
0.15-0.1
0.1
0.14
Heavy
Hetal
Ib/IOOO Ib
55-242
0.11
1.2
0.001
0.05
0.01
0.04
0.05-0.1
0.11
0.01-0.02
1.69
0.02
Oil and
Creaae
Ib/IOOO Ib
_
0.68
0.12
0.15
0.14
0.09
0.11
0.06-2
O.I
0.06
0.05-0.08
0.24
0.02
'llnlta ara nllllon galIana of pollutant par 1000 Ib. of flnlahed product
.liaiaer Engineer a. 1969
^Puaraun. Storm. Sal lech. 1969
-------
TABU 4-4. SUMMARY OF CURRENT AND PROIECTED UASTELOAOS IN ONE REGION 208 AREA (BY SIC CODE)
Bust Practicable Waste Reduction Technology
Current Loadings
U-
NO*
301
202
204
20)
208
J 211
22-
226
251
265
27-
28-
32-
35-
36-
379
9999
SIC Group
Neat Products
Dairy Products
tiraln Hill Prods.
Bakery Proda.
Soft Orlnka
Tobacco Man.
Textile Hill
Dying & Pin.
Furniture
Paperboard Con.
Print. & Pub.
Chen. 4 Allied P.
Stone, Clay P.
Machinery
Elect. Eqlp.
Tranap. Equip.
Non-Manuf .
Hun. UUTP
HflD
(Ib/day)
Sewer
1523
973
IBO
915
130
2024
2530
0
0
245
0
64
0
32
659
100
1374
0
ss
Expected Projected
Reductions
(Ib/day)
Sewer Description
1059
40U
50
910
40
1750
2173
0
0
150
0
29
0
79
402
100
170
0
Anaerobic Lagoon to Stabilisation Pond
Anaerobic Digestion & Clarification
Oxidation Ditch 4 Clarification
Rotating Blo-Fllters 4 Clarification
Fixed Activated Sludge-
Activated Sludge (E.A.) & Clarification
Activated Sludge 4 A Inn- Aided Clarlf.
Carbon Adsorption & Clarification
Screening. Ext. Aeration. Clarification
Activated Sludge 4 Clarification
Stilling Ponds. Water Recycle
Ollt Crease Traps
Ion Exchange (for Plating Process)
Oil 6 Crease Traps
See Text
Upgrade Six Largest Plants
BOD
9O
85
85
85
84
85
85
75
35
85
30
50
10
5O
70
BUU
SS (Ib/day)
(X) Sewer
85
90
75
65
»s
/S
60
65
75
70
65
90
65
90
152
71
27
140
53
304
380
159
10
16
593
5O
412
Loadings
(Ib/day)
Sewer
117
40
11
119
14
418
541
51
18
oa
to
40
17
Varies for
Each Plant
Totals
10469
7312
2367
1690
-------
In 1978, the OSEPA Initiated a project to systematically study the
occurrence and fate of the 129 priority toxic pollutants in 40 publicly
owned treatment works (POTWs). The scope of the project included extensive
sampling at geographically distributed POTWs representing a variety of
municipal treatment technologies, size ranges and industrial flow
contributions. The results of this project are reported in "Fate of
Priority Pollutants in Publicly Owned Treatment Works," (USEPA, 1982), and
project summaries are shown in tables in Appendix B of this manual.
Tables B-l and B-2 summarize the occurrence of priority pollutants in
POTW influents and effluents. A total of 102 priority pollutants were
measured at least once above detection limits. However, only 40 of these
were detected in 10 percent or more of these samples and likewise, 24
pollutants were measured in SO percent or more.
The results of the effluent sampling indicate chat 90 priority
pollutants were detected; 30 were detected in 10 percent or more 'and only
12 were detected'in 50 percent or more of the samples. In both the
influent and effluent samples, copper, cyanide, and zinc were the most
commonly measured pollutants.
Table B-3 shows the average and median influent concentrations for che
priority pollutants detected in more than 50 percent of all influenc
samples. The first column is the average of the average from each of the
40 POTWs. In other words, an equal weight is assigned to each POTW. The
second column gives the median value from the same data base. In Table B-4
percent removals are presented for two subgroups of analytical data:
removals where the priority pollutant average influent concentration was
greater than zero, and removals when the plant average influent concen-
tration was significantly above the pollutant's detection limit,, For the
purposes of Table B-4, "significantly above the detection limit" was
defined as four times the most frequent detection limit. This minimizes
the effect of the detection limit on calculating percent removals. The
number of data points for each subgroup is indicated by N.
-------
Table B-4 shows chat 50 percent of the POTWs sampled achieved minimum
priority pollutant metal removals ranging from 35 to 97 percent. For the
selected organic priority pollutants 50 percent of the POTWs achieve
minimum removals of 51 percent to over 99 percent. Many of the organic
removal rates that are close to 100 percent occur primarily because the
average pollutant concentration in the influent was - slightly above that
pollutant's detection limit and the pollutant was not detected in the
effluent sample. This is illustrated in Table B-4 by cocparl«.S the number
of sample points between the two different subgroups. For many of the
organic pollutants, there were an insufficient number of meaningful data
sets to draw accurate conclusions about pollutant removal rates.
Table B-5 summarizes the median removals for selected conventional and
priority toxic pollutants by the various types of treatment plants sampled
tn the 40 POTWs study. The types of treatment plants are activated sludge,
trickling filter, pure oxygen activated sludge, and rotating biological
contactors (RBC) plants; an aerated lagoon, and four treatment plants that
have both activated sludge processes and trickling filters in parallel
modes.
.
Table B-5 shows that among the treatment plants examined, trickling
filters, activated sludge, the RBC, and the pure oxygen systems achieved
good removals of conventional pollutants and most of che measureable
priority pollutants. At those plants that had activated sludge and
parallel trickling filtration plants, the activated sludge plants appeared
to remove slightly more priority pollutant metals and organics than the
trickling filter plants. However, for some parameters the trickling filter
plants achieved higher removal rates.
Primary treatment was less effective than any secondary treatment for
conventional and priority pollutant removal. It should be noted that the
primary effluent samples from this study may not be representative of
primary treatment plants. The major reason is that secondary treatment
plants generate a much greater -volume of sludge than primary treatment
plants, and many of the sludge processing side streams are returned to the
78
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primary tanks. This often causes the influent to the primary tanks to be
ouch higher in organic loading than the influent to a typical primary
treatment plant. Nevertheless, primary treatment removed from 10 percent
to 57 percent of priority pollutant metals, from 0 to 57 percent of
priority pollutant metals and from 0 to 56 percent of the priority
pollutant organics. Tertiary treatment was slightly more effective than
average secondary treatment for removing conventional and priority
pollutants based on eight plants that had either mixed media filtration or
polishing ponds.
The mixture of priority substances found in municipal influent will
depend primarily on the mixture of industries contributing flow. Table B-2
contains 42 of the 129 priority pollutants categorized by the industrial
effluents in which they will likely be found. This table is based on
screening data provided by the USEPA (Neptune, 1980). The 42 which appear
are those which most frequently appeared in the screening data. The intent
of the table is not to imply that these chemicals are necessarily the most
problematic (i.e., carcinogenic, toxic) but only that they are the aosc
common. If data for a particular priority pollutant is necessary, sampling
of the influent and effluent of the muicipal or industrial plant is
recommended.
4.2 Non-point Source Inputs
i
There are many non-point sources of sedment and chemicals in both
non-urban and urban areas. Suspended solids, for example, may originate
from tributaries, phytoplankton growth, shoreline erosion, or atmospheric
loadings. In addition, agricultural runoff may be critical in rural areas
while combined sewer overflow may be critical in urban areas. Again, the
reader is referred to "Water Quality Assessment, A Screening Procedure for
Toxic and Conventional Pollutants," Part I, page 239 for detailed
discussion of the non-urban and urban processes. The following section
briefly describes the major waste sources and the available methodologies
to evaluate non-point source inputs.
79
-------
In recent years, there has been extensive Investigations, research and
reporting"of non-point source waste inputs. These methods, however, have
been primarily directed towards evaluation of conventional pollutants mass
loadings such as BODs, nitrogen and phosphorus, suspended sediment and
coliform bacteria. Limited methodologies have been developed for
assessment of chemical movement.
4.2.1 Non-urban Runoff
In many cases, it may be unlikely that specific chemical compounds
exist in the non-point sources. Hence, it is appropriate to evaluate the
potential for the chemical of concern to be detected in these non-point
sources. Where there is a potential, then specific field sampling is
recommended. Where no potential exists, the analysis may proceed using
only point source inputs.
Agricultural runoff may be a major source of -solids and/or chemical.
Perhaps Che raosc widely known no-urban waste inpuc equation is che
Universal Soil Loss Equation (USLE) (Wischmeir and Smith, 1960). This
equation Is applicable to a wide variety of land uses and in many instances
data has already been collected for factors included in the equation. This
equation is'particularly applicable for estimating sediment loading through
an agricultural environment. Parameter values for silviculture,
construction and mining are less documented and the user may find the USLE
equation more difficult to use for these environments.
The primary group of coxic chemicals that are of concern in agricul-
tural or forested settings are the pesticides. The key processes which
control the volume of washoff from the field surfaces include the rate of
accumulation at the watershed surface; the loss rate due to leaching,
runoff or reaction; and the partitioning characteristics between the
dissolved and sorbed phases. One methodology for assessment of chemical
movement through agricultural lands is developed by a USEPA model, the
Agricultural Runoff Model (ARM). .-Other models Include Simulation of Water
Resources in Rural Basins (SWRRB), and Hydrological Simulation Program -
80
-------
Fortran (HSPP). However, some of these models and others of the same type
can be very complex and require a substantial committment of work resources
to use effectively.
4.2.2 Urban Runoff
Toxic pollutants and solids loading rates in urban watersheds are
introduced by a variety of mechanisms. The loading of metals and solids to
street surfaces is estimated in the same manner as conventional pollutants.
In these cases, some' well documented stormwater runoff models, such as SWMM
may be utilized.
4.2.3 Phytoplankton Growth
Phytoplankton growth may be a significant source of solids in a lake or
impoundment. As an example, Table 4-5 shows the estimated suspended solids
loading to Saginaw Bay in 1979. In this case, the phytoplankcon component
accounts for 44 percent of total solids loadings.
TABLE 4-5. AVERAGE 1979 SUSPENDED SOLIDS LOADINGS TO SAGINAW 3AY
Source Kilograms/day
Saginaw River 351,500
Other Tributaries 89,700
Shoreline Erosion 129,000
Atmospheric 37,800
Phytoplankton 473.300
Total. 1,081,300
One method for estimating solids concentration due to phytoplankton
growth is to construct a nutrient/eutrohication model. This type of
analysis can be complex and could require considerable effort. For a
81
-------
detailed discussion of the types of methodologies available, the reader is
referred to Book IV, Lakes, Reservoirs and Impoundments, Chapter 2 -
Nutrient/Eutrophication Impacts.
An estimate of the suspended solids concentration due to algal activity
may also be made from chlorophyll-a measurements. Typically, in a natural
environment, there exists a carbon to chlorophyll-a ratio which ranges from
30 to iO ug/1-c/ug/l-chl-a. Also, typically, the ratio of suspended solids
to carbon usually ranges from 1.4 to 2.5. Therefore,. the range of the
suspended solids to chlorophyll-a ratio is approximately 85 to 250. An
easy estimate 'of the suspended solids concentration due to algal activity
can be calculated. For example, if the chlorophyll-a concentration is 40
ug/1, then the suspended solids concentration due to algal activity is
estimated to be between 3.4 and 12.5 pg/1.
If the settling rate (W.) is assumed, then a loading rate'of solids (W)
due to algal activity may also be estimated through Equation (3-3a).
Typical phytoplankton settling rates range from 0.5 to 1.0 meters/day.
*
4.2.4 Atmospheric Loadings
Many organic pollutants are emitted into the atmosphere and eventually
settle out directly onto water or watershed surface, where chey become
available for transport. The mass discharge of organic pollutants
delivered to the receptor is calculated by first determining the settling
velocity from the atmosphere to the watershed and then the dry deposition
loading.
Atmospheric loadings may be a significant component of the total
chemical loading to a lake. As an example, Table 4-6 shows the estimated
range of PCB loadings to the Great Lakes. As indicated, the atmospheric
loadings range from 7 to 92 percent of the total load depending on the lake
and assumptions.
82
-------
TABLE 4-6. ESTIMATED RANGE OF CONTEMPORARY TOTAL PCB LOADING (kg/yr)
Lake
Superior
Michigan
Huron
Erie
Ontario
.
Atmospheric
755-7550
530-5310
340-3410
230-2290
180-1830
b
Tributary
630-1890
460-1380
680-2040
230-690
330-990
Municipal
and e
Industrial
5-60
70-700
10-130
220-2180
130-1260
Atmospheric
Load as
Total
1390-9500
1060-7390
1030-5580
680-5160
640-4080
Percent of
Total
28-92
20-91
14-83
7-84
7-80
aAtmospheric loading. ranges: precipitation, 10-100 ng/1; dry deposition,
1.2*10"6 to 1.2" 10^ g/m -yr.
tributary loading <§ 10-30 ng/1, except Saginaw Bay (#10) where tributary
input data were directly available.
Municipal and industrial direct point source loading <§ 0.1 to 1.0 ug/1 9
municipal direct point source flows.
4.2.5 Tributary Inputs
Data for tributary inputs may be gathered from the USGS or state
agencies which maintain routine monitoring stations on many water bodies.
As chemical Input data for other sources are usually not available, wich
the possible exception of pesticides in overland runoff, they must eicher
be estimated from desk top procedures or develped from field sampling.
4.3 Data Sampling Requirements
As discussed, effluent sampling should be conducted when data on
chenical nasa inputs are not available. In addition, if it is suspected
that several point or non-point sources contribute significantly to the
chemical compound of interest in the water body, they should be sampled
concurrently with any water quality field studies.
83
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4.3.1 Problem Time Scale
Before sampling is initiated, the characteristics of the problem must
be defined so that sampling logistics can be developed consistent with the
problem time scale. The problem time scale is generally related to the
time scale of water quality impacts.
In most situations, Ihfc effl-ant chemical load should be specified
within and throughout a period of time equal to the time to steady-state.
The time to steady-state is a function of the lake's physical properties
and the kinetic characteristics of the chemical. Section 3.2 presents a
simplified approach to estimate the time to steady-state which then governs
the duration of sampling.
.It is appropriate to note, in this regard, that for strongly sorbing
chemicals which are refractory, the time to steady-state in bed sediments'
may be quite long. Hence, an analysis of an existing situation, estimates
of mass inputs of chemical over a lengthy period may be required. In such
situations, the time scale in the sediment governs the problems rather than
.
that in the water column.
When practical, chemical inputs should be specified within the
characteristic time scale. If chemical loadings are relatively steady,
only a few measurements may be required. If chemical loadings are highly
variable, then more samples within a characteristic time scale are required
to develop a representative input value.
4.3.2 Sampling Frequency
The number of samples to be taken within a given period is a function
of the accuracy required for the analysis. It can be shown that the
standard error of the mean from a set of samples is inversely proportional
to the square root of the number of samples and is given by:
a a/ /n
A
84
-------
where:
a standard error of the mean
0 standard deviation of sample set
n number of samples
This means that for a sample size of n - 16, the measured variance of
the mean is probably within 25 percent of the true variance (I/ 15 - .25).
yor comparison purposes, a sample size of n - 4, the measured variance is
probably within 50 percent of the true variance.
An illustration is presented for two hypothetical lakes shown on Figure
4-1. Lake A and Lake B have hydraulic retention times of 60 days and 240
days, respectively. The same type of toxicant is discharged to each.
Assuming conservative behavior of the toxicant, the problem time scale as
well as the recommended sampling duration is equal Co the time co equili-
brium. The recommended frequency of sampling, assuming 35 percent accuracy
(n - 8), Is weekly for Lake A and monthly for Lake B. Figure 4-1
demonstrates both the frequency and duration of the monitoring for the wo
lakes. As shown, a discharge monitoring program is largely dependent upon
lake characteristics and perhaps less dependent on the discharge Itself.
The necessity of periodic monitoring of the load with time as opposed
co relying on single grab or composice samples Is shown by the effluent
load data by Lake A. It is observed chat the last load characterization
shows an effluent chemical load to the lake of approximately 1.2 Ibs/day,
much less than the daily average load of 18 Ibs/day. If a grab sample had
been collected during this period, the modeling analysis would be based on
an effluent load equal to approximately 60 percent of the average load to
which the majority of the lake is responding. In addition, if a composite
were collected over Che entire day, rather than periodic sampling, the
analysis would be based on the correct average daily load. What would be
missing, however, is the definition within the day which may add to the
understanding of possible receiving water variability in chemical
conoentration data.
85
-------
LAKE A
LAKES
0:
V = I.6xl08ft3
Q.sQgs 30cfs
tQs 60 days
V= 2.5 x I09ft3
Qs 120 cfs
t0s 240 days
Q
O
UJ**
z
30
«0
30
20
10
.SO
O
<
UJ
Z
u
30
20
10
S/l 4/1 9/1 /! 7/1 /!«/! IO/I
3/1 */i 9/1 /1 r/i a/i «/< 10/1
t0= 60 days
/. 2 MONTHS OF WEEKLY SAMPLING
t0= 240 days
A. 8 MONTHS OF MONTHLY SAMPLING
FIGURE 4-1. LAKE ILLUSTRATION SAMPLING FREQUENCY
86
-------
4,3.3 Measurements of Chemical Inputs
During field sampling of effluents or tributary sources, samples should
be analyzed for total chemical, including dissolved and particulate
fractions and suspended solids concentration. In addition, flow rates are
also required for calculation of mass inputs.
Mass input loads are determined from chemical concentration and
associated flow rate data in accordance with the following:
W-QC <4'l)
in which W is the mass input of chemical (total, dissolved or particulate),
Q is flow rate and c is chemical concentration (total, dissolved or
particulate) as measured at the indicated flow rate. For most model
applications, mass inputs are usually expressed as total chemical although
dissolved and particulate forms should be measured.
87
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SECTION 5.0
DETERMINATION AND ASSESSMENT OF MODEL PARAMETERS
In many cases, it is advantageous to conduct water quality field
studies for the collection of physical, chemical and biological data that
are required for modeling analysis. The .basic objectives for conducting
such field studies are:
to determine the distribution of chemical in the water column and
sediments of a natural water body;
to measure existing effects of point source loads and background
influences on water quality and water uses;
to collect sufficient data on chemical inputs, water quality, and
lake characteristics to permit the calibration and validation of a
mathematical model for problem evaluation;
.
to facilitace che projection of probable wasteload impacts ac
ambient conditions different Chan those prevailing during the
field study with the validated model; and
to support the determination of allowable chemical discharges and
WLAs which will maintain applicable ambient standards and
beneficial water usage.
In order to achieve these objectives, a plan of study must be developed
which includes the following tasks:
definition of problem scales;
location and magnitude of chemical inputs (Section 4.0);
selection of sampling stations;
determination of measurements to be obtained; and
identification of sampling procedures, frequency and duration.
88
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5.1 Problem Time Scales
The appropriate cime scale of che problem is again approximated by the
time to steady-state calculations presented in Section 3.2. Sufficient
data should be collected on inputs and water quality responses during this
period so that reasonable average values can be used for the steady-state
analyses.
The time scale of chemical build-up in bed sediments can be highly
variable. The chemical build-up in bed sediments is caused by diffusion of
chemical from the water column into the bed and by the initial exchange of
particulate chemical between water column and bed by settling and
resuspension. In situations where the chemical has weak partitioning
characteristics and is primarily in the dissolved state in the water
column, chemical build-up in the sediment will be controlled primarily by
diffusive exchange, a relatively slow process. For strongly partitioning
chemicals, chemical build-up in the sediment nay be dominated by
parciculace exchange through settling and resuspension.
Guidelines for time scales in sediments are approximate at best. In
lakes, time scales may be in the order of months to years. From a water
quality field survey standpoint, practicality dictates that the problem
time scale as defined for the water column will be used as a s?uide for nose
intensive field work. However, as the time scale for bed sediments may be
substantially longer, it would be desirable to obtain chemical loading
information periodically over a roughly equivalent period of time.
5.2 Location of Sampling Stations
In lakes, concentration gradients are likely to be a function of depth
and width as well as flow and time of season. Sampling locations in lakes
should therefore be oriented around the sources so that gradients will be
measured. This usually calls for closely spaced sampling stations near
outfalls and more widely spaced-stations at distances from the outfall.
When appropriate, it may be advantageous to perform a dye or tracer study
89
-------
to determine Che mixing characteristics of the lake or Impoundment. This
type of study win also give insight to the appropriateness of a completely
mixed assumption.
Figure 5-1 shows three different lake configurations; one which is
completely mixed throughout its volume and two which do not mix rapidly
enough to be completely mixed throughout. Potential sampling locations for
each lake are also shown on Figure 5-1. For slowly mixing Lakes A and C,
samples can be collected at each station and at various depths from surface
to bottom. In Lake B, which is mixed over depth and width, samples are
required only at a single point in the water column, .perhaps mid-depch.
5.3 Water Quality Measurements
For calibration purposes, water quality data are required in boch water
column and sediment as shown in Table 5-1 and discussed below.
TABLE 5-1. SUMMARY OF WATER QUALITY MEASUREMENTS
WATER COLUMN
I. dissolved chemical
2. particulate chemical
3. suspended sediment
4. particulate organic carbon
5.
. BED SEDIMENT
Supplemental
1. conservative tracer
- total dissolved solids
- chlorides
- conductivity
2. temperature
3. pH
4. light intensity wich depth
(ultraviolet penetration)
particle size distribution
Required
1. dissolved chemical
2. particulate chemical
3. solids concentration
(fine fraction)
4. porosity
5. particulate organic carbon
Supplemental
1. measure with depth
2. particle size distribution
3. pH
90
-------
CHEMICAL
LOAD
(A) NON-MIXED
LAKE
CHEMICAL
LOAD
/ybout
Qin
Q our
(B)MIXED LAKE
LffffMO'
$ SAMPLING STA.
LOCATIONS
(C) NON-MIXED LAKE
VERTICAL PROFILE
FIGURE 5-1. EXAMPLE SAMPLING STATION LOCATIONS
91
-------
5.3.1. Water Column
Analyses should be performed for che chemical of concern in both
dissolved and participate form. The concentration of suspended solids at
each sampling location should also be determined for subsequent use to
estimate settling and resuspension rates. Particulate organic carbon
(f ), which may strongly influence organic chemical partitioning should
also be measured. in more advanced modeling applications, the fQC should
be evaluated for various particle size categories. Additional data which
may be useful are measurements of conservative tracers in the water column.
These tracers are useful to evaluate the mixing characteristics in lakes.
Temperature and pH measurements may be required to modify laboratory
reaction kinetics to lake conditions. For photosensitive chemical, data
should be gathered on surface light intensity and the depth distribution of
sunlight in the water column.
5.3.2 Sediment Layer
Dissolved and particulate chemical measurements are also required in
the sediment layer to perform the impact analysis. For many chemicals,
most of che chemical mass is adhered co sediment in the bed. In this case,
measurements of cocal chemical in che sedimenc layer as grams of chemical
per gram dry weight sediment solids, together with bed sedimenc solids
concentration and porosity, are sufficient to estimate the total mass of
chemical in the bed. Again, fQC should be measured to help determine
organic partitioning characteristics. The dissolved concentration in the
interstitial water, cd2» should also be measured for the purpose of
estimating the partition coefficient in the sediment layer. Bed sediment
chemical concentrations are usually measured in the top few centimeters of
che bottom material, or the mixed layer, as discussed in Section 2.0.
However, measurements of chemical at various depths in the sediment (i.e.,
core samples) may be useful co more accurately define the well mixed layer
and total mass of chemical in the-sediments. In cases where the partition
characteristics of the chemical are dependent on che size of each
92
-------
sediment particle, particle size distributions should be developed for both
water column suspended solids and bed sediments.
5.4 Sample Handling
Proper sample collection, handling, and preservation of water column
and bed sediment samples are important for successful completion of the
chemical impact evaluation. Volatile chemicals may be lost through gas
transfer to the atmosphere while highly partitioning chemicals will adhere
to collection vessel walls and caps. Light.sensitive chemicals a.ay undergo
photodegradation, while others may be lost through hydrolysis or biological
decay. Chemical characteristics and special handling requirements should
be determined as part of the preparation for the field programs. The
following excerpt from Book III (USEPA, 1984) summarizes some of the key
principles for toxic sampling.
...Samples to be analyzed for coxic- substances require
special qualicy control procedures beyond those necessary for
conventional water qualicy parameters. The quality assurance plan
for a toxics monitoring program, should include a description of
the following special quality control procedures:
1. Extra care should be taken in sampling, handling, and preser-
vation because coxics generally occur in trace concentrations
and are frequently unstable.
2. Toxic samples should be stored in Che dark Co avoid phoco-
chemical decomposition and at reduced temperatures co
minimize the rate of chemical reaction.
3. Samples should be exposed to the atmosphere as little as
possible co avoid the loss of volatile compounds.
4. Sample bottles must be clean and made of materials that will
not contaminate the samples, either plastic or glass,
depending upon the analyses to be performed on the sample.
5. Replicate samples should be taken and analyzed to assess the
variability of measurements caused by sampling technique and
site heterogeneity.
93
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6. One sample spiked with each of the routinely aonicored
toxicants (except dioxin) should be analyzed with each group
of samples. A blank should also be analyzed along with each
group of samples.
In addition to this information on sample handling and analysis, the
analytical detection limit for each toxic pollutant should be included in
the quality assurance plan (Book XI, Chapter 3, USEPA, 1984).
Finally, the documentation of all field ana laooratory procedures is a
necessity to assure the defensibility of the toxics monitoring data. A
sample observation sheet should be filled out for each station providing
observations on surface conditions. For each sampling period, a sample log
book should be kept with a record of the in situ results and the numbers
and times of water column measurements. All samples should be properly
labeled and numbered with preprinted forms and labels. Additionally, a log
book should be kept in the laboratory in order to record each sample as ic
arrives in the laboratory and to document the analytical results.
Additional information on quality assurance programs can be found in
the following publications:
1. Test MethodsTechnical Additions to Methods for Chemical Analysis of
Water and Waste, EPA 600/4-82-055, USEPA Office of Research and
Development, 1982.
2. Guidelines and Specifications for Preparing Quality Assurance Project
Plans, USEPA Office of Research and Development, Municipal Environ-
mental Research Laboratory, 1980.
3. Standard Methods for Che Examination of Water and Wastewater, 15th
Edition, American Public Health Association, 1980.
4. Methods for Chemical Analysis of Water and Wastes, EPA-600/4-79-020,
USEPA Environmental Support Laboratory, 1979.
5. Handbook for Analytical Quality in Water and Wastewater Laboratories,
EPA-600/4-79-019, USEPA Environmental Support Laboratory, 1979.
5.5 Fluid Transport
The fluid transport for a simplified modeling approach can be easily
defined by the flow rate through the lake or impoundment along with the
94
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volume and depth. The flow race and volume define che retention time of
the lake whicis a'critical physical characteristic that is required. The
flow rate is simply the sum of the flows into or out of the system;
therefore, it is determined by data collected from the discharges which
empty into the lake.
5.5.1 Flow Determinations
The flow rate is a fundamental parameter required as input when
performing chemical impact analyses in lakes. Flow and dispersive
transport dilute and move chemicals through the water body. The basic
source of information on stream flow to lakes is USGS, which maintains flow
measuring gages on many streams throughout the country. In many instances,
the USGS will have a network of flow gaging stations throughout a study
area. These data can be combined with point source input flows to
construct a flow balance around an impoundment.
In order to provide a range of expected flow rates for lakes in
general, a log-probabilty plot of lake outflow is shown on Figure 5-2. The
plot is based on "a comprehensive investigation of United States lakes
conducted as part of the National Eutrophication Survey (NES) (USEPA, 1975,
1978). A total of approximately 400 lakes have been sampled and
characterized physically and chemically. The probability shows che 10th
and 90th percentile flows to be 8 to 3000 cfs with a median (50ch
percentile) outflow of 160 efs.
When flow information is not available from the USCS, field survey
measurements -may be required to monitor flow during the chemical sampling
surveys.
95
-------
I*
X
u
K
o
NATIONAL EUTROPHICATION STUDY LAKES
1000 -
100 -
10
0.
*
M
SO 40 90 60 TO 80 90 93
PERCENTILES
99
FIGURE 5-2. LOG-PROBABILITY OF FLOW
5.5.2 Geomorphological Dimensions
Methods for determining the physical characteristics of Lakes are
discussed in other manuals (Book IV, Chapter 2, USEPA, 1983). The basic
information necessary for the simplified analyses are the average depth and
surface area. From this information the volume of the impoundment is
calculated.
There are many existing sources of information which may possess
physical characteristics. Some of these include the USCS, National Oceanic
and Atmospheric Administration (NOAA), NES, and State Lake Classification
Surveys.
96
-------
A log-probability plot of lake mean depth measured as part of the NES
is shown on Figure 5-3. The 10 to 90 percent range for the water column
depth is 1.5 to 17 meters with a median depth of approximately 5 meters.
NATIONAL EUTROPHICAT10N STUDY LAKES
IQO -
w
a
z
4
10
'MM*
20 JO «0 30 SO 70 80 90 99
FIGURE 5-3. LOG-PROBABILITY OF MEAN DEPTH
5.5.3 Evaluation of Detention Time
The detention time is the critical physical parameter necessary to
calculate the fate of a chemical using a simplified^ technique. The
detention time (V/Q) dictates the tocal mass accumulacion of solids to che
bed as well as the percent removal of a chemical through transfer or
reaction. As the retention time increases the solids will have more time
to settle to the sediment layer and the chemical will have more time to
react through photolysis, hydrolysis or biodegradation. In other words,
water column concentrations may be less with larger retention times, but
sediment chemical concentrations may be greater.
97
-------
The log-probability of detention times is shown on Figure 5-4. The 10
to 90 percent range is 10 to 1000 days with a median of about 100 days.
NATIONAL CUTROPHICATION STUDY LAKES
.. MUOOO
I
i
100
10.0
1.0
I I I
I I
10 10
10 «o so to ro
peRceNTii.es
FIGURE 9*4. LOG-PROBABILITY OF DETENTION TIME
A summary of the statistical parameters for lake physical characteristics
is shown on Table 5-2.
TABLE 5-2. STATISTICAL PARAMETERS FOR LAKE PHYSICAL PROPERTIES
Variable Symbol
Discharge Q,
Rate
Detention t
Time
Mean Bench H.
Unit Median 90Za
(cfs) 157.0 3170.0
(days) 144.0 1870.0
Cm) 5.22 17.2
10Zb
7.78
11.1
1.5
Ratio
902 10%
407.0
168.0
11.4
fvalue which is not exceeded in 90 percent of the lakes.
Value which is not exceeded in 10 percent of the lake (i.e., it is
exceeded by 90 percent of the lakes).
98
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5.6 Particle Transport
Transport of suspended sediment is an important aspect of an impact
analyses as many chemicals partition strongly to suspended sediment. It is
important, therefore, to develop information on the transport of
partlculate materials.
5.6.1 Solids Concentration
Although no measurements from the NES of water column solids is
available, secchi disk depth, Zs, is reported. This can be used to roughly
estimate water column solids concentration. The extinction coefficient,
K , is related to secchi disk depth via the empirical correlation (Beeton,
1958):
111 (5-1)
e"Zs
and the relationship between dry weight of suspended solids, n>1 (mg/1) and
extinction coefficient. K is K /m. - 0.1-0.4 ng/m2 for algae and K-/»l -
1
0.05 - 0.25 ng/m for other suspended particles (Di Toco, 1978). Hence a
reasonable ratio is:
K_ n i _ \5~Z/
» 0.2 m,
and water column suspended solids concentration can be estimated from
secchi disk depth. A probability plot of «lt computed in this way, is
shown on Figure 5-5. The 10 to 90 percent range is 2.0 to- 25 ag/1, with
readings near 100 mg/1 at the 99th perentile. The variation of total
solids mass, m.H. is shown on Figure 5-6. The range is from. 10 to 100
g/m2, a tenfold variation. This variation is smaller than that observed
for detention time and outflow. It suggests that individual site specific
values for detention time and outflow parameters are critical for the
analysis rather than representative values, whereas m1H1 is less variable.
99
-------
NATIONAL EUTROPHICATION STUDY LAKES
?
o
i
M*
I
a 10 to to «o ao *o ro «o «o
FIGURE 5-5. LOG- PROBABILITY OF ESTIMATED WATER COLUMN
SUSPENDED SOLIDS
NATIONAL EUTROPHICATION STUDY LAKES
I
M
I
WO -
S
I
M
.J
J 1 L
*o so M
ao «o
M
FIGURE 5-e. LOG-PROBABILITY OF ESTIMATED AREAL WATER COLUMN
SUSPENDED SOLIDS
100
-------
5.6.2 Particle Classification
The physical characteristics of a particle of suspended sediment, such
as its size and organic content, are known to affect the degree to which it
will adsorb a chemical. The explanation for stronger chemical adsorption
onto finer particles is that these materials have a higher surface area per
unit weight than do larger particles. The suspended solids concentration
and partition coefficient are also inversely related. Although the
underlying cause of this phenomenon is not completely understood, it is a
factor which appears to be a characteristic of the interaction between
solids and chemicals. Organic carbon content also influences partitioning
characteristics. The combined effects of the particle size, surface area,
weight fraction and sorption characteristics all define the mass of
chemical associated with sediment particles.
To perform a simplified analysis it is not necessary to classify
sediment particles by size, as only a single type of sediment particle is
considered. Where sediment transport is a significant feature of lake
dynamics and particle organic content changes significantly wich particle
size, the use of one' particle size may introduce significant error into che
representation of chemical fate processes. When performing more detailed
chemical fate evaluations for such systems, it is possible and may be
necessary to include the effects of up to five different particle types.
Inclusion of more than one sediment particle type in an impact analysis
requires information on the weight fractionation, settling and resuspension
characteristics and chemical sorption for each different particle type.
Weight fractionation of particles is generally performed by sieve analysis
for particles greater than 75 microns and by hydrometer evaluations for
smaller particles. Particles greater than about 400 microns are considered
sands; between 75 and 400 microns, fine sands; and less than 75 microns,
silts and clays. An example of particle size distributions found in
Saglnaw Bay is shown in Table 5-3. The following discussion is applicable
to the various size classes of particul'ates. However, the complexity and
amount of data necessary to perform a chemical modeling analysis with more
101
-------
than one particle type Increases substantially with the number of size
classes considered. As a result, most evaluations will consider only a
single class or type of suspended sediment.
TABLE 5-3. SUSPENDED SOLIDS SIZE DISTRIBUTIONS
SAGINAW BAY
Area
^^^^^^
i
2
3
4
5
Average
Number
of
Stations
3
9
3
5
5
25
Number
of
Data
Points
12
39
12
19
15
97
0.7-39
81.8
71.6
76.3
63.8
62.3
70.5
Percent
urn 37-74
'l2.3
16.3
17.2
21.6
23.0
18.0
in Each Size
urn 74-210
4.9
10.5
5.4
12.0
12.5
9.8
Class
urn 210-1000 urn
1.0
1.6
1.1
2.6
2.2
1.7
5.6.3 Particle Settling
The fate of particulate chemical is strongly influenced by the fate and
movement of sediment. In accordance with Figures 2-3 and 2-4, the two
terms which must be developed to define particle motion are the water
column particle settling velocity, w^ and the sediment layer resuspension
velocity, w... These terms fix the rate at which particles move from the
water column to the sediment layer or from the sediment layer to the water
column.
It should be recognized that each of these phenomena are difficult to
measure with a high degree of accuracy. General approaches to establish
the suspended solids settling velocity are to use sediment traps, to employ
estimating equations, to evaluate quiescent settling rates, and to use
suspended solids data.
Sometimes, it may be advantageous to use different settling rates for
different particle size classifications. In an analysis of suspended
102
-------
solids In Saginaw Bay, for example, three particle size classifications
were established with different settling velocities for each category.
Table 5-4 presents the various classifications and settling velocities used
in Saginaw Bay.
TABLE 5-4. PARTICLE SIZE CLASSIFICATION AND
WATER COLUMN SETTLING VELOCITIES
SAGINAW BAY
Settling Velocity
Classification (m/day)
light . 0-2
heavy l 5
organic °»l
Sediment Traps. Sediment traps are devices which are either suspended
in the water column or set on che lake bottom to collect suspended solids
which settle to the bottom over a period of time. Traps are designed co
collect solids, Co prevent solids washout and to permit che flow of lake
water across the trap Itself. Examples of four types of sediment traps are
shown on Figure 5-7. Design "of the vessels in the sediment crap has been
shown (Blomquist and Hackanson, 1981) co influence che amounc of oacerial
crapped. Figure 5-7B shows vercical cylindrical vessels cend uo yield che
most accurate results.
The settling velocity can be calculated using data from sediment craps:
w - -
1 At
where:
wfl - settling velocity in ft/day
M mass of sediment crapped (mg)
m. « average water column suspended solids (mg/1)
1 2
A surface area of trap (ft )
Ac » time of trap incubation
103
-------
CAI SAMPLE TRAP SCHEMATICS
Rtf LOMQVlSf AND II«**NSOU
|BI TRAP EFFICIENCY
lOOOf--.
00
o
a
00
_J 400
O
«t
b.
O
j? »00
100
O
90
FIGURE 5-7. ILLUSTRATIONS OF SEDIMENT TRAPS
-------
Scokes Equation. Some estimate of the particle settling velocity can
be obtained using Stokes Law. As this formulation was developed for
quiescent settling of discrete spherical particles, caution must be used
when applying the velocity in natural settings. Because of turbulent
motion in most water bodies, Stokes velocity should be considered an upper
limit of the particle settling rate. As a first estimate, the Stokes
velocity may be employed directly in deep, non-turbulent lakes. When a
Stokes velocity is used in an analysis, it should be considered a
preliminary value and be subject to change through calibration of suspended
solids. Figure 5-8 presents information and techniques to be employed in
estimating the Stokes settling velocity.
Bench Scale Tests. Laboratory bench scale testing can also be employed
to evaluate discrete quiescent settling on a site specific basis. The
process used to develop the settling rate on a laboratory scale Involves
the introduction of mixed lake water to a laboratory settling column
(Figure 5-9A) and the evaluation of percent removal at various depchs with
time (Figure S-9B). These data are then used (Figure 5-9C) co develop
settling velocity as. a function of the percent of material.
*
5.7 Water Column-Bed Interaction
The following simplified cases were developed co introduce different
bed conditions that may be encountered in lakes. The cases presented are a
stable bed, net sedimentation and net scour.
Case I: Stable Bed. During periods of stable bed conditions, the
surface of the bed is neither accumulating solids nor scouring away. Under
this condition, particle settling and scour may be occurring but water
column suspended solids remain relatively constant, and there is no net
flux of material between the water column and sediment.
Case lit Net Sedimentation. This condition frequently occurs in
natural water bodies and is characterized by a net flux of suspended solids
from the water column to the sediment.
105
-------
(A)
E
o
O
O
Ul
O
2
UJ
10
10
IO~* 10"' I 10
DIAMETER (cm)
PROCEDURE'
STEP I-ESTABLISH i
la I MEDIAN PARTICLE DIAMETER
J b J PARTICLE SPECIFIC GRAVITY
STEP2-FROM FIGURE A SELECT |W,|
STEP3-FROM B CALCULATE
REYNOLDS NUMBER (Rl
STEP 4-| o ) IF R < I CONTINUE
(b I IF R > I CANNOT USE
STOKES VELOCITY
STEP9-USINGC MODIFY W, FROM
IO°C TO AMBIENT TEMPERATURE
(B)REYNOLDS NUMBER (Rl
R> W,-J
V
WHERE* R« REYNOLDS NUMBER
W,* SETTLING VELOCITY
(C">/tec. )
d« PARTICLE DIAMETER
(cm |
V* KINEMATIC VISCOSITY
(C«n«/»tC.)
(C) wi AT TEMP, s W, AT IO» (
V AT TEMP
t.si«io-§
FIGURE 5-8. SETTLING VELOCITIES BY STOKES LAW
-------
(A) LABORATORY SETTLING
COLUMN
T
2'
00.
tO.
-*v.:
°\\
1_-ana
%
*.*
4::
'LL
(8) SETTLING PROFILE
(C) DATA EVALUATION
200 400 800 300 e
£ ,5
o c
* a °-'
1!
^ ^
H- &
|t I ^^
y* ^2
5
^\
\
\
\
0
N
s
s
N
>tl^-
f30% SCT1XS 4T »
4 .OI3J1. 0» 22 _!!_
/ mm. dot
i i i i T* o_ .3 \ '
0 iO 20 30 *O 30 60 ?0 SO 90 'C
PERCENT OF PARTICLES WITH VELOCITY
LESS THAN
FIGURE 5-9. EXAMPLES SETTLING VELOCITIES FROM
BENCH SCALE TESTS
107
-------
Case III; Net Scour. This condition is observed when there is a net
flux of material from the sediment layer to the overlying water and an
increase of suspended solids mass in the water column.
The term in the chemical models which describes net bed accumulation or
scour in lakes is the net sedimentation rate, w2, the rate of change of the
elevation of the sediment surface per unit time. In principle, this rate
is the dirierence between the solid fluxes due to particle settling, m^,
and particle resuspension, m^. A stable bed condition (Case I) means
that the net sedimentation rate is equal to zero. For Cases II and III,
the rate is non-xero and can be evaluated from direct field measurement, or
evaluation of instream suspended solids data. The following sections
discuss sedimentation, resuspension, and diffusive exchange.
5.7.1 Sedimentation
The sedimencacion of lakes is the process by which lakes gradually fill
with sediment. Particles which settle, to the sediment-water interface and
become incorporated into the sediment, gradually accumulate and fill the
lake. The result is a net flux of particles to the sediment, Jg> in units
of gm dry solids/m2/day. The sedimentation velocity is defined as w2 -
J / and it can be thought of as the velocity at which the sediment-water
s 2
interface is moving vertically upward. Since the active sediment layer of
depth, H-, is fixed relative to the sediment-water interface, the sedimen-
tation velocity is also the velocity at which particles leave the bottom of
the active sediment layer and enter the deep sediment. Chemicals adsorbed
by these particles are lost from the active sediment layer and are presumed
to be buried. Hence sedimentation provides an ultimate sink for the
chemical.
Direct field measurement of sedimentation is performed by developing
benchmarks in the lake with marked survey stakes driven into the lake bed.
Observation of sediment levels on the calibrated stakes over time will
108
-------
yield a net sedimentation rate. This method, although accurate and direct,
is time consuming,' as rates may be on the order of 0 to +50 millimeters per
year*
Net sedimentation rates can also be estimated using tracers in the
sediment. The radiochemical methods used rely either on the naturally
occurring radionuclide , lead-210, which is continually produced in the
atmosphere, or the man-made nuclide cesium-137 from the atomic weapons
tests. For the lead-210 method, the vertical profile is measured and using
the known half-life the age of the sediment layers is obtained. The
cesium-137 method gives an estimate of both the depth of the well-mixed
layer and the sedimentation rate.
The more traditional methods involve finding a layer in che sediment
where the concentration of some material either abruptly terminates or
abruptly begins. 'Pollen grains associated with the onset of agriculture
and the clearing of the forests are employed. Since the dates of these
events are known, the sediment depth co the transition layer divided by che
known elapsed time yields the sedimentation velocity.
The concentration of solids in the well-mixed sediment layer, n>2, can
be obtained by direct measurement. It is normally expressed as porosicy,
*. which is che volume fraction of interstitial water. If dry solids have
a density, o , then the solids concentration in the sediment layer is:
where * is the average porosity of the well-mixed layer. Tables 5-5 and
5-6 present examples of this type of analysis with the solids concentra-
tions, the active mixed layer depth and sedimentation rates.
109
-------
TABLE 5-5. SEDIMENT PARAMETERS FOR VARIOUS LAKES
(After Krishnaswami and Lai, 1978)
Lake
India
Tansa
Tulsi
France
Pavin
Leman
Montcynere
Lagodiville
USA
Mendota
Trout
Tahoe
Washington
UK
Windermere
Lowe s water
Blelham Tarn
Japan
Shinji
Belgium
Mirwart
Sedimentation
Velocity
w« (mm/yr)
4.0
2.6
1.3
1.2
1.5
0.7
6.0
6.3
1.0
3.8
2.4
2.0
2.0-3.6
0.8-9.0
1.2-2.7
1.5-1.8
Sedimentation
Flux2
(J_ mjj/cra /yr)
280
160
13
72
21
13
18
60
21
.
60
-
-
-
13-71
64-104
Sediment
Solids
nu (mg/1)
£
700 ,000
615,000
100 ,000
600,000
140,000
186,000
30,000
95,200
210,000
250,000 '
'
-
.180,000
.510,000
Porosity
0.714
0.749
0.959
0.755
0.943
0.924
0.988
0.961
0.914
* *
0.898
-
-
0.927
0.792
5.7.2 Particle Resuspension
The estimation of the resuspension velocity is a difficult part of this
analysis. The difficulty is related to the time scale implicit in the
chemical fate analysis. What is required is the resuspension velocity
averaged over the characteristic time scale of the chemical response to the
input. As discussed previously, there are two time scales, the time to
reach the first plateau (»l/g,) and the time to reach equilibrium (»3/g2).
The former can be quite short (910 days) and the latter can be quite long
(>100-1000 days).
110
-------
TABLE 5-6. SEDIMENT PA. .lETERS FOR THE GREAT LAKES
Lake
Sediment
Sedimentation Sedimentation Solid ' Well-Mixed
Velocity Flux » Concentration Porosity Depth^
(w« (nn/yr) J (mg/cm /yr) m. (rog/1) ±
2 * 8 *
Michigan
Station 11
29
31
17
100 A
103
105
Ontario
KB
UB
Erie
M32
G16
U42
Huron
14
18
4
0.4 -1.0
2.8
0.5 -0.7
0.78-0.66
1.08-1.34
0.74-0.80
0.53-0.83
4.7 -5.2
2.3 -6.6
15.3-25.0
8.6 -9.8
1.6 -3.2
0.97
1.10
15.82
102.2
22.8
15.41
27.5
15.5
13.7
57 - 63
27 - 78
270 - 440
73 - 83
47 - 96
21.0
51.0
266.000
365.000
.380.000
214.000
227,000
201.000
201.000
122.000
119.000
176.000
85.100
296.000
216.000
464.000
0.891
0.851
0.845
0.913
0.907
0.918
0.918
0.950
0.951
.0.928
0.965
0.879
0.912
0.811
'£.
0 - 1
3.4 - 4
2.0 - 0
0.2 - 0
1.0 - 1
-
_
^"
-
6.0
3.0
.0
.8
.0
.0
Reference
Bobbins et al. 1975
Bobbins et al. 1978
Bobbins et al. 1977
-------
Resuspeasion In lakes Is a sporadic process which occurs when
sufficient turbulence is generated at the sediment-water interface to
resuspend bed sediment. This typically occurs during high winds. Some
estimates of these resuspension fluxes have been made. What is required,
however, is an estimate of the average resuspension velocity which is not
the same as the intermittent resuspension velocities.
Direct measurement techniques have not beer rf«v«lop«d for practical
application in an impact analysis. A method to evaluate this coefficient
uses estimates of the particle settling velocity, w^ from Section 5.6.3
and the particle sedimentation velocity, w2, from Section 5.7.1.
. (IL\ - w <5~5)
W21 Pm.; 2
in which w21 is the resuspension velocity, Wj is the settling velocity, «2
is" the sedimentation velocity, mj is the average water column suspended
solids concentration, and m2 is the sediment layer solids concentration. A
limitation of this technique is that the method is not independent and
depends on two other particulate transport rates.
A method of estimating the upper bound for resuspension velocity is co
employ the following reasoning: the settling velocity of particles in the
water column can be estimated from Stokes Law. It can be shown that the
Stokes settling velocity will be greater than the actual settling velocity,
w., in lakes due to vertical dispersion. If the sedimentation velocity is
assumed to be zero, the maximum resuspension velocity is given by:
« /« - w
21 B2/ml wi
Stokes settling velocities for natural particles range from 1 to 20 m/day.
If m./m. is on the order of 10,000, then the maximum w21 is approximately
750 mm/year. A reasonable range for the resuspension velocity, therefore,
is about 0 to 750 mm/year.
112
-------
5.7.3 Sediment-Water Column Diffusive Exchange
The diffusive exchange of dissolved chemical between che wacer column
and Che sediment interstitial water can provide an Important .transfer
mechanism either to or from the sediment. The rate of transfer is
formulated as a mass transfer coefficient, 1^ (cm/day), by analogy co the
volatilization transfer coefficient, Ky. It can be shown that:
where the numerator is the apparent sediment diffusion coefficient, DL, and
the denominator accounts for the length of the vertical concentration
gradient in the sediment, *2'
The apparent sediment diffusion coefficient may be estimated by
empirical .correlations found for natural sediments. The relationship
between the molecular diffusion coefficient, 0, and the apparent sediment
diffusion, D^, is:
B. -
u
where 8 is che tortuosity: . the ratio of the length of the actual diffusion
path to the linear length of Che sediment. It has been found empirically
that:
where F is the formation factor: F - R/%, the ratio of the electrical
resistivity of the bulk sediment to the pore fluid and * is the porosity.
Analyses of actual sediments yield the relationship:
(5-10)
113
-------
where n - 2.8. .If n 2, this relationship is known as Archie's law
Thus:
DT - D t'
L
Unfortunately, the diffusion coefficient is difficult to measure directly
so that the magnitude of K, itself is only known from calibration results
(HydroQual, 1981 and 1982) or empirical relationships. It appears that 1^
» 10-100 cm/day is the reasonable range.
5.8 Chemical Transfers
This section presents some of the methods and procedures for evaluating
the rates and magnitudes of chemical transfers between dissolved chemical
and (1) suspended particles (adsorption and desorption); and (2) the
atmosphere (air-water transfer).
Chemical transfers refer to mechanisms that transfer chemical mass
between various phases in the environment. The phases to be considered are
suspended particles and the atmosphere. Chemical transport via particle
exchange between the sediment and the water column is discussed in Section
5.7. The following sections only highlight some of the key considerations
pertaining to these mechanisms. The reader is referred to Book VIII
(USEPA, 1982), for more detailed discussions and information. Also, USEPA
documents entitled, "Water-Related Fate of 129 Priority Pollutants," and
"Aquatic Fate Process for Organic Priority Pollutant," present laboratory
rates and field measurements for various transfer mechanisms.
5.8.1 Adsorption and Desorption
All chemicals, to a greater or lesser degree, tend to associate with
suspended particles. The extent of this association depends upon the
nature of the chemical, principally its solubility, and the physical and
chemical properties of the particles, primarily their surface area and
organic carbon content.
114
-------
The mechanism, is conceived of as a reversible reaction between the
dissolved chemical concentration: ^ (mass of chemical/ liter of water) and
sediment-bound chemical, r (mass of chemical/leg of particles). That is:
(5-12)
where K . is the rate of adsorption and Kdes is the rate of desorption.
AO3
If these reactions are first order, then the kinetic equations are:
Cl K e + K r
dl --- Kads Cl * Kdes r
dr m _ e _ . ' (5-14)
dT Kads Cl
At equilibrium, dc^dt and dr/dt are zero and:
(5-15)
where
- K/K (liters of water/kg of particles) is the partition
adsdes
S
as
coefficient? S A number of studies have been completed which develop
empirical relationships for partition coefficients. The reader is referred
co Book II. Chapter 3 (USEPA, 1984), and Book VIII (USEPA, 1982) for
elaboration of these relationships.
Experimental Procedures. The experimental procedure for basic
adsorption-desorption measurements are illustrated on Figure 5-10. The
aqueous phase, sediment, and chemical stock solutions are combined to
achieve the desired concentrations in the reaction vessel. The vessel is
capped and agitated until adsorption equilibria is achieved. A sample of
the sediment-aqueous phase mixture is removed and analyzed for chemical
concentration, cT(ads). After centrifuging, a sample of the aqueous phase
is removed and analyzed yielding the dissolved concentration at adsorption
equilibrium, cl(mda). The particulate concentration at: adsorption
115
-------
AQUEOUS PHASE
(A) "ADSORPTION
SEDIMENT (ADSORBENT)
CT {ad's)
CHEMICAL
(AQSORBATEl
SHANE
'ads
CENTRIPUGE
ci laai)
REMOVE AQUEOUS
PHASE
~l
(Bl OESORPT10N
AOO UNCONTAMiMATED
AQUEOUS PHASE
SHAKE
des
cT(ats)
EXTRACT CLASS
CSMTRIPUGS
,
k
REMOVE AQUEOUS
ft SEDIMENT
V
A
MASS BALANCE
FIGURE 5-10. ADSORPTION/OESORPT10N
EXPERIMENTAL PROCEDURE
116
-------
equilibrium is calculated by difference: r(adg) - ^T(ads)-ci(ads)]/m>
where m is the adsorbent concentration. This completes the adsorption
step.
For the desorption step, the contaminated aqueous phase is carefully
removed leaving the sedimented solids in the vessel, and uncontaminated
aqueous phase is added (to achieve a total volume that produces the same
adsorbent concentration as initially present at adsorption). The capped
tube is agitated until desorption equilibrium is achieved. A sample of
sediment-aqueous phase mixture is removed and analyzed yielding cT(deg).
After centrifuging an aqueous phase sample is removed and analyzed for
c The particulate concentration is obtained by the difference:
rl(deS . [- - c1(des)]/m. The remaining sediment and aqueous phase
issuer discarded or sa^ed for further analysis. The centrifuge tube is
extracted, and the chemical which was adsorbed to the tube itself is
measured. A mass balance calculation is. made to insure the integrity of
the experiment. ' '
Various quantities of chemical stock solution and aqueous phase are
employed so that 'a range of dissolved and sediment-bound chemical
concentrations are observed. Ideally, these concentrations should be at
environmentally realistic levels so that minimal extrapolation is required.
The data are displayed in terms of an isotherm: a plot of the sediment-
bound chemical concentration, r, versus the dissolved concentration, cr
An example is shown for lindane on Figure 5-1i. Log-log plots are normally
used in order to check the linearity of the isotherm (the line on the
figure has unity slope). The partition coefficient is calculated by
choosing any dissolved concentration, c, and using the diagonal line to
obtain a sediment-bound concentration, also called a particulate
concentration, r, and forming the ratio r/c - » as shown. Deviations from
unity slope isotherms (Freundlich isotherms) are sometimes observed. The
data in the concentration region of interest is approximated by a unity
slope line and the partition coefficient is evaluated as shown on Figure
5-11.
117
-------
10.000
1.000 -
Ul
z
4
a
Z
UJ
-------
and the particl.es being considered. The properties that govern the
partitioning of inorganic metal and other ions are different chan those
that apply to organic chemicals. For heavy metals there exist models of
sorption to pure oxide phases (Westall, 1980) but a general theory of the
partition coefficient for naturally occurring particles is not available.
Thus, partition coefficients are either measured for each situation or
representative values can be used (USEPA, 1984).
For organic chemicals the important distinguishing feature is whether
the chemical ionizes in water. If it does not then the partitioning is
dominated by hydrophobic effects only and a general model for sorption is
available. For organic acids and bases, both the hydrophobic and the
electrostatic forces can be important (Bailey and White, 1970). For this
reason, no general model is available, although as a first approximation
the methods presented below for neutral hydrophobic chemicals can be used
(Lyman ec al., 1982).
Reversible Equilibrium Partitioning. The partitioning of neutral
hydrophobic chemicals to natural soils and sediment particles has been the
focus of numerous investigations. A useful synthesis and review of the
major features of neutral organic chemical sorption (Karickhoff, 1984)
indicates that the partition coefficient can be calculated, from the
octanol-wacer partition coefficient of che chemical, KQW, a property chac
has been measured or can be estimated (Lyman et al., 1982} for most
chemicals of environmental interest, and the organic carbon concent of the
particle. The degree of hydrophobicity of the chemical is parameterized by
K and the quantity of sites available for sorption on the particle is
proportional to the organic carbon content.
Karickhoff et al. (1979) examined the sorption of aromatic hydrocarbons
and chlorinated hydrocarbons in natural systems. They found it convenient
to relate the partition coefficient directly to organic carbon content of
the solids as follows:
, - K f <5-16>
oc oc
119
-------
where :
K - partition coefficient expressed on an organic carbon basis
oc
f » mass fraction of organic carbon in fine solids fraction
oc
A number of equations have been proposed for the relationship of KQC
to K . Karickhoff et al. (1979) were also able to relate KQC to the
octanol-water partition coefficient and to the water solubility by the
following relationships:
it - 0 63 K (5'17)
K - 0.63 K
where:
K - octanol-water partition coefficient (concentration of chemical in
ow octanol divided by concentration of chemical in water, at
equilibrium)
and
KQC -0.54 log Stf + 0.44 (5-18)
where:
S » water solubility of sorbate, expressed as a mole fraction,
w
The water solubilities of the compounds examined ranged from 1 ppb to
1000 ppm.
Thus, for organic hydrophobic compounds which obey a linear isochenn
relationship, the partition coefficient » can be predicted. First, KQC is
predicted based on either water solubility or the octanol-water partition
coefficient. Then based on an estimate of organic carbon fraction, i can
be estimated from Equation 5-16.
120
-------
This empirical relationship appears to extend from essentially entirely
organic carbon particles (sludges) to particles with greater than 0.5
percent organic carbon (fQ<. >0.005).
This remarkably simple and powerful model of hydrophobic chemical
sorption is, unfortunately, not a complete description of the phenomena.
As shown below, however, it is entirely descriptive of the reversible or
labile component of sorbed chemical at low suspended solids concentration.
The two factors that complicate the sorption problem are kinetic and
particle concentration effects. These are discussed below.
Reversiblity of Sorption. It is a common finding (Karickhoff, 1984 and
the review in Appendix C) that the partition coefficient found from a short
time (hours) desorption is larger than the adsorption partition coeffi-
cient. This suggests that the kinetics of desorption are slow. Thus, the
assumption that the particulate and dissolved chemical concentrations are
ac Che equilibrium determined by the partition coefficient, Equation
(5-11) may not be the case in all situations.
A two component' model has been proposed (Di Toro and Horzempa, 1982;
see Appendix C) which separates the sorbed chemical into a reversible
component which achieves equilibrium rapidly and a resistant component chat
does not appreciably desorb during the time scale of most laboratory
experiments (hours co days). It has been shown through the use of gas
purging experiments that all the sorbed chemical can be removed eventually,
but the desorption time scale for hydrophobic chemicals can be months to
years (Karickhoff and Morris, 1985).
From a practical point of view, the question of the impact of the
extent of short term reversibility on WLAs is best approached using
sensitivity analysis. At one extreme the chemical can be assumed to be
entirely reversible sorbed. At the other extreme a large fraction can be
assumed to be entirely associated with the particles. In this way the
importance of this phenomena can be investigated.
121
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Particle Concentration Effects. Ie has been found experimentally that
the sediment concentration, .. . can affect the observed partition
coefficient. An .experimental design which eliminates isotherm nonlinearity
effects is to manipulate the initial mass of chemical employed so that the
dissolved concentration at equilibrium is constant for each concentration,
m, of suspended particles employed. Typically the partition coefficient
decreases as adsorbent concentration increases. Ie has been found
(O'Connor and Connolly, 1980) that a relationship of che form:
«b
o
describes the data in which »Q is some reference value and b is an
experimental constant. Figure 5-12 presents examples of chis relationship.
While Che mechanism which is responsible for this behavior is a matter of
speculation at present, ic is consistently observed and must be taken into
account .
A number of mechanisms have been suggested to explain the particle
concentration effect. One class of suggested mechanisms ascribes che
observation to the chemical complexing to some particle associated
component, either dissolved organic carbon (Voice and Weber, 1983) or some
other unspecified component (Curl and Keolelan, 1984) desorbing from the
particles, or the colloidal fraction of the particles which is not
separated during the particle separation procedure (Gschwend and Wu, 1985).
All these "third phase" explanations depend on the assumption that the
operationally measured dissolved concentration, whether in the laboratory
or the field, cannot distinguish between the truly dissolved chemical
concentration, whose partitioning is not dependent on particle concentra-
tion, and the chemical complexed to the third phase (dissolved organic
carbon or colloids), which increases with particle concentration since the
»
third phase is assumed to be present in proportion to the particles that
are present. Thus, when the operationally measured dissolved concentration
is divided into the particulate chemical concentration to calculate the
partition coefficient, Equation (-5-11), it appears to decrease as particle
concentration increases .
122
-------
10"
DATAi O'CONNOR AND CONNOLLY
z
bJ
O
U.
U.
1U
O
H
tt
I0a
10*
I01
10'
LEGEND:
-DOT
O - HEPTACMLOR
A -LINOANE
A-KEPONE
-MANGANESE
0-CADMIUM
A-COBALT
0- CALCIUM
«--STRONTIUM
I03
10'
SE OJ ME NT CONCENT.RAT SON, m. (mg/l)
FIGURE 5-12. VARIATION OF PARTITION COEFFICIENTS
WITH SOLID CONCENTRATION
-------
There is no .doubt chat these mechanisms would appear to make che
partition coefficient decrease with increasing particle concentration. The
question is whether this is the explanation for all or most of the
observations of this phenomena. A series of experiments have been
conducted for which the third phase mechanism cannot be invoked as an
explanation. These resuspension and dilution experiments (Di'Toro and
Horzempa, 1983; Mcllory et !.. 1986; Di Toro et al., 1986) continue to
exhibit a decreasing in partition coefficient with increasing particle
concentration. In addition, experiments with particles (2 micrometer glass
spheres) that cannot introduce a third phase clearly show the effect (Di
Toro et al., 1987). Hence,'the experimental information appears to suggest
that the effect is real and is independent of whatever third phase effects
are present.
A model has been proposed (Di Toro, 1985, Appendix C) which attributes
che effect to particle-particle interactions that cause a desorption. The
resulting model fits the available laboratory data for six orders of
magnitude in partition coefficient (Appendix Cf Figure 5). At the low
solids concentration limit the Kow-foc relationships apply as given above.
However, as the solids concentration increase the particle concentration
becomes the dominant parameter that determines the partition coefficient.
A recent variation of the model which assumes a specific type of
particle-particle interaction: complete desorption upon collision, can
explain the observed constancy of the particle interaction parameter (v»x)
(Mackay and Powers, 1987). Thus, for neutral hydrophobic organic chemicals
the reversible component partition coefficient can estimated from KQW, foc,
and the particle concentration, m (Equations 14 and 15, Appendix C).
5.8.2 Air-Water Surface Exchange
All chemicals, to some degree, are transferred between the surface of a
water body and the atmosphere. This process is variously described as
volatilization, evaporation, and reaeration. For the applications of
chemical fate in natural waters 'considered in this report the atmospheric
concentration of chemical is negligible and the process is a one-way
124
-------
transfer of chemical from the water body to the atmosphere, which is
assumed to"be an infinite sink. The rate at which this process occurs, K,
(I/day), must be evaluated for each setting and chemical of concefn. The
volatilization rate, Ky, is related to the mass transfer coefficient,
if bv K - K /H, , where H. is the water depth.
air-water' y v air-water' 1' 1
The conventional methods employed are based upon the two film theory of
air-water surface exchange. Two mass transfer coefficients are required:
the liquid phase mass transfer coefficient, K£l and the gas phase transfer
coefficient, Kg. These are related to the overall mass transfer rate,
K . via the reciprocal relationship:
air-water*
1 m I_ + _L_ (5-20)
air-water * g
where H is Henry's constant for the chemical. The units of these mass
transfer coefficients are typically meters/day.
One method of measuring Henry's constant is to perform an experiment
using filtered water from the location in question and enclosing it within
a vessel which has a gas phase overlying the liquid phase. If Cj is the
measured liquid phase dissolved chemical concentration (mass of chemical/-
liter of liquid phase) and cg is the measured gas phase concentration (mass
of chemical/liter of gas phase) at equilibrium then the Henry's constant
is:
H . _i (1 Of water/1 of gas)
cl
(5'21)
which is referred to as the -dimensionless" form of the constant. Note its
similarity to the partition coefficient » - r/Cj. In fact, it is the gas
phase-liquid phase partition coefficient.
Another reliable method of estimating Henry's constant is to use the
water solubility and vapor pressure of the chemical. Since both of these
125
-------
concentrations represent equilibrium concentrations between a pure chemical
phase (solid or liquid) and an aqueous or gas phase respectively, they
should also represent the equilibrium condition in the tvo phase experi-
ments described above. Unfortunately it is usually not clear what is the
reference state of the pure chemical phase for these measurements so that
care must be taken in their use.
If p is the vapor pressure (in mm Hg) and cg is the water solubility
(mg/1) and I is temperature (°C), then it is convenient to convert cg to
units of mg/1:
o (mm Hg) 1 mole gas _ MX IP3 mg ^ 273 * (°C) (5_22)
cg " 760 (mm Hg) 22.4 1 gas mole chemical 273
where p/760 Is the saturated partial pressure which, for ideal gases, is
the mole fraction of chemical in the gas phase. At 0°C and I atmosphere of
pressure, a mole of gas occupies 22.4 liters. Finally, M is the molecular
weight (gm/mole) of chemical and 103 converts to milligrams. An equivalenc
calculation giving the same answer uses the gas constant, R, and assorted
conversions. Note" that this calculation assumes that the solubility is
measured at 25°C. For different temperatures both the solubilicy, the
vapor pressure, and the volume of ideal gas/mole changes (the latter via
the Ideal gas law). The importance of these corrections depend on che
relative magnitude of the gas and liquid phSase transfer coefficients.
henry's constant, in dimensionless form, is then calculated by:
(5-23)
cs
It is useful to delineate three basic cases: (1) when K£ « Hkg, then
K in Equation 5-20 is essentially equal to K (liquid phase
air-water ^ *
controlled); (2) when ^ » Hkg, then fcair.wacer t» essentially equal to
HK (gas phase controlled); and (3) when Kt and Hkg are of the same
magnitude, then both contribute-significantly to Kair_water'
126
-------
A
As the chemical-to-chemical variability of H is greater than the
site-to-site variability of Kt and Kg, the value of the H is generally more
important than the environmental conditions in determining whether the
liquid or gas phase resistance controls the volatilization rate.
graphical presentation of Equation 5-20 is shown on Figure 5-13 for various
ratios of the transfer coefficients. For substances with-Henry's constant
greater than 1, the liquid film controls and less than 0.001, the gas film
controls.
Gas Phase. The movement of air causes a mixing of the air surface film
which results in an increase in Kg. Because the evaporation of water is
controlled by K , and because this process has considerable engineering
importance, data are available relating Kg (for water vapor) to the ambient
windspeed. Such data are presented by O'Connor (1980) and HydroQual
(1982). By including theoretical effects of diffusivity and viscosity, the
result is:
K - 0.001 WI (D 7v )°'67 (3-24)
g & &
where:
D diffusivity of substance in air (cm /sec)
K 2
v » kinematic viscosity of air (a 0.15 cm /sec)
g
WI - wind speed (L/T)
As the expression is dimensionally correct, consistent units will
result in kg having the same units as WI. Average windspeeds tend to be in
the neighborhood of 5 m/sec. Although transient periods of no wind are
common in many localities, such periods are not long. Consequently, use of
a steady-state condition of little or no wind may not produce a realistic
result. Figures 5-14 and 5-15 show the empirical relationships between the
diffusivity in air, D , with molecular weight and gas transfer coefficient,
K , as a function of windspeed.
127
-------
-I
o
£
-------
0,20
aio
COS
OT
ao2
aoi
10 20
AIM, 29*C
I
©CALCULATED
. I I
90 100 200
MOLECULAR WEIGHT
900
1000
FIGURE 5-14. DIFFUSIVITY (AIR) VERSUS
MOLECULAR WEIGHT
e
x
6
2
u
U.
UJ
8
vt
2
90OO
400O
3000
~ 2000
-CMAM86RLAIM (1966)
10 20 30 '0
WX-WI'NOSPEEO (m
90
60
FIGURE 5-15. GAS PHASE CONTROL AIR / WATER
TRANSFER COEFFICIENT
129
-------
Liquid Phase. In Impounded waters and other slow moving water bodies,
water turbulence"may be generated by wind. O'Connor (1980) and HydroQual
(1982) summarized data relating K^ to windspeed, WI. These data suggest a
relationship:
- 0.17
WI
,2/3
(5-25)
where:
r m Drag coefficient (unitless), and 2
« - Kinematic viscosity of water (-0.0100 cat /sec.)
The units of all other parameters must be chosen to be compatible.
also appeari to. vary with windspeed, WI, but may maintain a value around
0.001 for WI less than 10 m/day. As with using Equation. 5-21, sustained
periods of little or no wind are not common; k^Oj) values substantially
less than about 0.5 m/day are not usually expected. Figures 5-16 and 5-17
6
u
i
O
tf)
a
0.1
WATER,29°C
2.0 - &
1.0
0.9
0129
0.2
O
& EXPERIMENTAL
O CALCULATED
10
20
90 100 200
MOLECULAR WEIGHT
900
(000
FIGURE 5-I6.-DIFFUSIVITY (AIR) VERSUS
MOLECULAR WEIGHT
130
-------
.004
K .003 -
UJ
3
O
(9
<
IT
O
.002
.001 -
.000
3 iO '3
WI-WINOSPEEO (m/sec)
2
O
O
u
e
IU
u.
2
O
a
10 19
WI-WINOSPEEO (m/sec)
FIGURE 5-17. LIQUID PHASE CONTROL
AIR/WATER TRANSFER COEFFICIENT
131
-------
show the empirical relationships between the diffusivity in water as a
function of molecular weight and the liquid transfer coefficient (Kt) as a
function of windspeed.
Equation 5-20 can be examined in light of the observed relationships of
Kt and K versus windspeed. If H < 10"4," then Kg will control ^r^atar
in all aquatic environments, even standing waters. This is because HKg
will increase much more slowly than ^ as a function of windspeed. In this
case, the analyst need not consider the turbulence of the water body at
all. Furthermore, surface transfer will be slow for substances of this
type, and the rate will decrease as H decreases.
If H > 1, then Kt will control Kalr_wacer *n a*1 aquatic environments
except possibly those with extraordinarily turbulent flow. Under this
condition the analyst need not consider the air phase.
5.9 'Chemical Kinetics of Degradation
The rates at which a chemical transfers between various phases in the
environment controls ics relative distribution within the water body and
sediment layers. In previous sections, chemical transfer and transport
have been discussed. Chemicals, however, may degrade in Che envirorimenc
through physical or biological processes. The predominate processes, which
are addressed in this section, are photolysis, hydrolysis and biodegra-
dation.
These kinetic processes have been extensively discussed in other USEPA
manuals (Book II, Chapter 3, USEPA. 1984 and Book VIII, USEPA, 1982). The
reader is referred to these documents for detailed discussions and
information. The following sections will highlight the basic principles of
each process and discuss available techniques for measuring the key
reaction rates or coefficients.
132
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5.9.T Photolysis
One of Che Important mechanisms by which organic chemicals may be
transformed in the environment is by photolysis. It is defined as the
chemical degradation or disassociacion of a compound by the action of the
radiant energy of light. Only light that is absorbed, which is a quantum
process, can produce a photochemical change. A significant number of
organic chemicals absorb sunlight most strongly in the ultraviolet region.
The photolytic decomposition of a chemical is brought about by the
absorption of the light energy, which may be acquired by the molecule in
any one of the three following ways: direct absorption, indirect
(sensitized) adsorption or reaction with a photochemicalljr excited
molecule. The first, as the name implies, refers to the decomposition of
the organic chemical by direct absorption of light. The second is a
photolytic reaction, which is accelerated by the presence of other organic
compounds which transfer the energy to the chemical. The third is the
reaction of the organic chemical with a photosensitized compound. All
mechanisms may be effective in natural waters. Direct photolysis is most
significant in systems with low concentrations of photosensitizes such as
humic acids.
In view of the presence of phocosensitizers in all natural wacer
systems, it is probable that most organic chemicals are subjected to both
direct and sensitized reactions. Furthermore, adsorption to suspended
solids may alter the maximum absorption wavelength and photoreactivity of a
molecule, thus changing the energy required for photodecomposition. At
this stage in the development of the field, it is difficult to distinguish
between the various mechanisms. Although it is possible and desirable to
conduct laboratory experiments to do so, the extrapolation of these
findings to prototype conditions is tenuous. Consequently, it is
preferable to carry on such experiments in water samples from the actual
system under study using various concentrations of solids to cover the
range encountered in the actual system.
133
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The kinetic expressions, presented in the following sections, describe
the suggested framework for evaluating laboratory data and for correlating
the rate coefficients. The means, by which the reaction coefficient thus
determined, may be extrapolated to prototype conditions is described. The
extrapolation is presented taking into account the relative significance of
direct and photosensitized photolysis.
Kinetic Expression. The rate of photochemical reaction may usually be
expressed as a first-order reaction
*£.-*< (5'26>
dt p
The reaction coefficient, Kp, is a function of the quantum yield and
the light absorbed in the reaction. The quantum yield, *, a characteristic
quantity of a photochemical reaction, is the ratio of the number of
molecules changed to number of light quanta absorbed. The light absorbed
depends on the available light in direct photolysis and on the lighc
absorbed by the intermediate sensitizers.
.
The most direct determination of photolysis is through field
measurements. Ultraviolet transparent vessels and dark vessels as controls
are suspended at various depths. The first order degradation of chemical
is observed in each container. The overall photolysis race can be
calculated by depth averaging the various rates. This procedure yields an
unambiguous estimate of field photolysis rate and requires no further
assumption.
Laboratory experiments can also be performed in which the chemical is
irradiated in an ultraviolet transparent vessel and degradation is
observed. The first order rate at which degradation occurs is the
laboratory photolysis rate, Kp (lab). If Kp (lab) reflects the same
ultraviolet solar radiation as the field site, then the site specific rate
can be computed using the expression:
134
-------
K- (field) - (Rab) t1 ex* ('Ke ' H)lf (5"27)
P *aH e
where K is the diffuse attenuation coefficient of ultraviolet radiation,
H is the water column depth and f is the fraction of daylight hours.
The extinction coefficient can be measured directly using an
ultraviolet irradiance meter, or it can be estimated from the secchi disk
transparency depth, Z^t and an empirical relationship
K Zm - 5 to 42
e s
(5-28)
with a median value of 9.2. Note that this relationship correlates the
secchi disk depth to the extinction of ultraviolet light which is the most
significant catalyst of photolysis. Since this coefficient is quite
variable accurate estimates require in situ measurements of the vertical
distribution of ultraviolet radiation for the wavelengths chat cause
photolysis.
Light and Quantum Yield. The reaction coefficient, Kp, may also be
expressed as:
K - K I (5-29}
Kp Va
in which K is a functon on the light absorption characteristics and the
o
quantum yield of the chemical and Ia is the average available light. The
rate of change of light per unit depth is proportional to its intensity and
may be expressed as:
4! . -K I (5-30)
dZ V
which integrates to
Ke ' Z) (5-31)
135
-------
in which
I intensity at depth, Z
I - intensity at the surface, z-o
o -i
K extinction coefficient, L
The average value of light in the vertical is obtained by integrating
over the depth and dividing b« the depth:
<.-f "-«>
If the magnitude of KeH » 1, as in deep turbid systems, which is represen-
tative of many natural waters, Equation 5-30 reduces to:
T . «_ (5-33)
* KeH
Conversely if KftH « I, as in clear shallow systems representative of
laboratory conditions, Equation 5-30 becomes:
<5-34)
and obviously approaches I as a limit.
o
The extinction of light, as measured by the magnitude of the
coefficient, K , is due to the physical processes of absorption and
scattering. The first component, absorption, occurs when a photon of light
is taken up by the compound. The energy induces excitation and either
transformation of the molecular structure or decay back to the ground state
by liberation of heat arid light. Both dissolved and particulate matter
absorb light. Scattering occurs when a photon of light has its direction
of propagation changed due to collision with a particle in the water.
136
-------
In order Co characterize Che extinction coefficient completely, it is
also necessary to know the angular distribution of the light scattered by
the particles. The volume scattering function specifies the angular
distribution of scattering as a function of the angle between incoming and
outgoing photons. It is composed of forward and isotropic components. The
former, expressed as a fraction, T, is scattered in the incident: direction
and the latter, 1 - y» ia the isotropically scattered fraction.
For a wide range of conditions in natural water systems, it has been
demonstrated Chat the extinction coefficient may be approximated by:
Ke - a
(i-r)b <5-35)
in which:
a absorption coefficient
b scattering coefficient
1-T isotropically scattered fraction
It is possible to estimate the magnitude of T from readily measurable
quantities. From a'series of such measurements, its range is 0.91 Co 0.98,
with a reasonable average of 0.95. Thus, (i-Y) 0.05.
Similarly, the absorption and scactering coefficiencs, a and b, may be
correlated to the concentrations of both dissolved and oarticulace solids.
The particulate solids, in Cum, may be subdivided into the organic and
inorganic components, each of which have distinct effects on the absorption
and scattering. Since the majority of the light attenuating components in
natural systems are in particulate form, Che cocal extinction coefficient
may generally be expressed as the "sum of the organic and inorganic
fractions of the parciculace solids plus the absorpcion due co che chemical
undergoing photolysis:
K - oc + 3m + 6m (5-36)
e o i
137
-------
in which:
m concentration of organic particulate solids
o
m. concentration of inorganic particulate solids
c dissolved concentration of chemical
a,8,9 constants
In the vast majority of cases, the first term is insignificant with respect
to light extinction, due to the relative concentrations of particulate and
chemical.
The dependence of the rate of reaction on characteristics of the
chemical is specified by KO in Equation 5-29. This constant is a function
of the quantum yield, *, which is the fraction of the light absorbed by the
chemical that produces a photoreaction and the extent of light absorption,
a . Assuming that the concentration of chemical is small, as is the common
condicion in natural water systems, the coefficient, KO, is defined as
follows:
(5-37)
in which
+ » quantum yield at wavelength \
a. extent of light absorption
1 J a conversion factor to transform light to concentration units
_ 2.6 X 104 _ .langleys,
X (nm) X HCgrms molecular weight) mg/l-m
The sum is taken over all active wavelengths. Values for $x and *x may be
obtained from laboratory experiments.
138
-------
Substitution of Equations 5-29 and 5-32 in 5-26 and integration yields:
(5-38)
K and K are further identified by Equations 5-36 and 5-37, respectively.
e o
The above relations are most appropriate for direct ohotolytic
reactions. They may also be used as a preliminary framework for sensitized
photolysis in many cases. Zepp (1980), provides a more complete discussion
of this process.
Since many chemicals absorb most strongly in the ultraviolet region,
the factors affecting penetration in natural waters of light in this
wavelength region deserves particular attention. Fresh inland waters
contain various quantities of dissolved and particulate maccer. The
dissolved organic matter,. which is derived from detrital or decaying
vegetative natter, appears to have a substantial effect on the attenuation
of ultraviolet light. The necessity of measuring prototype condicions and
using samples from'these waters in conjunction with pure water is evident.
5.9.2 Hydrolysis
Hydrolysis is a reaction in which a cleavage of a molecular bond of the
compound occurs and the formation of a new bond with the hydrogen and
hydroxyl components of the water molecule results. Hydrolytic reactions
are usually catalyzed by an acid or base and are identified in that
fashion. To a more limited degree, there may also be a neutral reaction
with water. By its nature, the rate of the reaction is a function of pH
and, as with most chemical reactions, temperature.
The reaction equation is fundamentally second order, containing the
product of the concentration of the chemical and either the hydrogen ion or
hydroxide ion concentration, and in general, may be expressed ass
139
-------
in which:
K - K [Hj* for acid hydrolysis
- Kv [OH]" for alkaline hydrolysis
B
K [H-0] for neutral hydrolysis
The effect of pH on the reaction may be quite pronounced. ' Data are
available from laboratory experiments at relatively low chemical
concentrations, representative of natural water systems. These data
demonstrate the effect of pH on the first order rate coefficient as shown
on Figure 5-18. On the upper figure, the more pronounced effects are
presented and on the lower, the less pronounced. For those pesticides
whose rates are pH dependent, the patterns appear to be reasonably
consistent and in accord with theoretical hypothesis. Due to the acid and
base catalytic action, greater reaction coefficients are observed at the
acid and alkaline pH extremes and minimum values in the neutral zone, as
shown on the' figure..
For most substances there is no alternative to a direct measurement of
this rate since at present, theoretical methods for estimating the
hydrolysis rate constant do not exist. A straightforward laboratory
experiment in which the. rate of degradation of the chemical is observed at
various pH levels is the conventional method. The hydrolysis rate appears
to be dependent upon the composition of the aqueous phase so that site
specific measurements are preferable. The laboratory experiment should be
performed within the range of pH observed in the system.
5.9.3 Biodegradation
Microbial degradation of organic chemicals is a common occurrence in
many situations. Classical dissolved oxygen depletion problems are
associated with this mechanism". The degree of persistence of many
140
-------
10
10
>
<
a
UJ
o
O
10
10
UJ
2
-------
chemicals is ultimately controlled by this rate. Initially the biodegrada-
bility of a chemical is investigated in laboratory experiments in which the
chemical is exposed to large concentrations of bacterial biomass and
degradation is monitored. If no significant degradation is observed, then
it is assumed that no degradation will occur in the environment since the
biomass of degradation organisms Is certain to be less than that used in
the laboratory reactors. If degradation does occur, then the rate at which
it can be expected to occur in the field must be estimated.
Essentially there is no alternative to well conceived experimental
procedures that evaluate the rate of microbial degradation In situ for both
the water column and sediment. General designs are difficult to suggest
and site specific factors often dictate the required experiments. It has
been suggested that the rate of microbial degradation is directly
correlated to the biomass of bacteria as measured via plate counts. While
evidence exists that this relationship can be used' for certain chemicals
that undergo degradation mediated by enzymes that are common co many
microorganisms, it is aot known a priori that the relationship will apply
to a specific .setting for a specific chemical. Thus, some experimental or
,
field calibration work is required.
5.10 Sediment Capacity Ratio
The effectiveness of sediment removal mechanisms (decay and sedimenta-
tion) as sinks of chemical is determined to a large extent by the magnitude
of the sediment capacity factor, B. Therefore, its variation as a function
of the relevant physical and chemical parameters is an important component
in the understanding of chemical fate. The capacity factor is given by the
expression:
_ » £
(5-40)
where m and m. are the particle concentrations in the water column and
sediment respectively; H. and H2 are the water column and sediment depths;
142
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f and f - are the partlculate fractions of total chemical concentration
in the water column and sediment. These latter fractions are given by:
e l (5-41)
rpl I + rnT
c (5-42)
Cp2 I + mjij
Hence the sediment capacity factor is a linear function of the depth ratio
H /H ; and a more complicated function of the water column and sedimen
solids concentrations, m^ and m2, and partition coefficients, »j and »2.
Consider first the sediment parameters, m2 and »2, which determine the
particulate fraction f -. The relationship is shown on Figure 5-19. With
the exception of weakly partitioning chemicals, »2 < 10 I/kg, and
unrealistlcally low sediment solids concentrations, ra2 <' 10 mg/L, fp2 is
approximately one and »2 is not a significant factor in determining 3.
Note, however, that m2, the sediment solids concentration, is directly
involved: 6 is linear with respect to m2.
The effect of water column parameters, m^ and »l§ can be highlighted as
follows. The capacity factor can be expressed as:
and by cancelling the o^, the result is:
% v. %
where
f * (5-45)
zdl I » m
143
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10001
1,000,000
i,000.000 E
100,000
10,000 =
l,00'0
i i imm i i M i
tO ICO
m, (mq/I)
1000
FIGURE 5-19. DISSOLVED AND PARTICULATE
FRACTIONS VERSUS IT, AND m
144
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The water column solids concentration enters into the expression ror cne
dissolved fraction, £dl, and its variation as a function of mL and »L is
also shown on Figure 5-19. If m^ < 0.1, then fdl « 1. That^is fdl is
approximately one for ^ < 105 I/kg and n^ - 1 mg/1, or Vj < 10 I/kg and
m. » 10 mg/1. Therefore, for the intermediate range of partition
coefficients and water column solids concentration, fdl 1 and 6 becomes:
.-Vi 10 and g becomes:
, . fp2 . I. Vl > 10 (5-7,
and the partition coefficients are not involved at all but the water column
solids concentrations now assume a role in determining 3.
Since sediment data are not available that complement the available
water column data ic is not possible to construct a probability plot for
the sediment capacity ratio which takes the variation of sediment
properties into account. However, if constant values are assigned to &2
and H-, then an estimate of the probability can be constructed. The
probability is illustrated on Figure 5-20 for the ratio m^/m^. The
range of m-Hj/m.Hj is about 10 to 100 for an assumed value of m^ - 1000
g/m .
It must be emphasized that the probability plot presented (Figure
5-20), is constructed only to give insight to the solids mass ratio.
Since, the m2H2 value is assigned arbitrarily, the results are not
necessarily representative of actual conditions.
145
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NATIONAL EUTROPHICATION STUDY LAKES
1000
CM
M
E
-------
Additional guidelines for estimating the sediment capacity factor are
given in the following sections. The first section assumes the water
column partition coefficient to equal the sediment partition coefficient
while the second investigates the effect of variable partition coeffi-
cients.
5.10.1 Equal Water Column and Sediment Partition Coefficient:
A number- of relationships can be developed if »j is assumed equal to
»,. The sediment capacity factor for ^ - TZ becomes:
B.!l "*V> -*>
8 Hj (1 + m^)
The first relationship shown on Figure 5-21 assumes typical values for
both H./H, and m2 of 1,000 and 100,000, respectively. The figure presents
the sediment capacity factor as a function of. m^ and ». Note thac the
partition coefficient Is the dominant factor for Low solids concentrations
m < 10 mg/1. For the intermediate range (10-100 mg/1) the partition
coefficient controls for t, < 10* I/kg and the solids concentration
4 l
controls for v1 > 10 1/kg.
Since the sediment capacity factor, S, is inversely proportional to
H./H-, the contours shown on Figure 5-21 can easily be transposed for other
values of H./Hj. If,"for example, the Hj/Hj ratio is 100, a tenfold
decrease, the values of B would simply increase by a factor of ten.
The magnitude of 6 is also proportional to the sediment solids
concentration, m2< Since this concentration is directly related to
sediment porosity, its probable range is i^ - 50,000 to 500,000 mg/1, so
that B can vary over another order of magnitude. Hence the magnitude of S
is quite variable and should be calculated for each location of interest.
A dimensionless plot of B versus m^^ and m^ is shown on Figure 5-22 for
the case that ». ».. This figure can be used to estimate B directly
since for any other depth ratio, t^/Hj, B changes linearly.
147
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SEDIMENT CAPACITY FACTOR CONTOURS
OB
o
oc
H
z
a
z
o
o
o _
Ul g
z
2
o
o
DC
1000 pr
100 -
IO
IOO
I.OOO IO.OOO
Vt (I/kg)
WATER COLUMN PARTITION COEFFICIENT
lOO.OOO
I.OOO.OOO
FIGURE 5-21 CONTOURS OF SEDIMENT CAPACITY FACTOR, £. VERSUS
t FOR1T2= fti H^Hg- 1000, m2= 100,000 mq /I
irtAND
-------
SEDIMENT CAPACITY FACTOR CONTOURS
10'
10'
io' io- io'
SEDIMENT SOLIDS CONCENTRATION-PARTITION COEFFICIENT
FIGURE 5-22. CONTOURS OF SEDIMENT CAPACITY FACTOR, 0, VERSUS
DIMENSIONLESS SOLIDS CONCENTRATIONS FOR Hj/Hp" 1000, irg= Uj
-------
5.10.2 Particulace Ratio
The ratio r2/rl is the ratio of particulate chemical concentration in
the sediment, r2 to that in the overlying waters, ^ in units of chemical
per unit mass of solids. The particulate ratio r2/rL has -a direct effect
on the sediment removal mechanisms of sediment decay and sedimentation
since :
Kl + 8 (K2 * fp2 Ks2> - <5
Through mass balances, the ratio can be shown to be a function of sediment
decay, sediment depth, diffusive exchange, sedimentation, resuspension,
water column and sediment partition coefficients and. solids concentrations.
The full algebraic expression is given as follows:
r? <«,.*».> go2 * ~L *-2'-I' -dl (5.30)
Estimates for all these mechanisms have been approximated in the
appropriate sections of this manual. These estimates are summarized in
Table 5-7.
Based upon these results it appears that the probable range for rj/^
is O.I - 1.0 for K2 < O.I/day. Combining this information with the
probable range of 8 - 0.01 - 100 suggests that the range of 8 r2/rlt which
is the parameter group that directly determines the importance of the
sediment removal mechanisms, Kj + KS, is in the range Br2/rl - .001 to 100,
150
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TABLE 5-7. SUMMARY OP LAKE PARAMETERS
Variable
Water Column Solids
Concentration
Water Column Depth
Sediment Solids
Concentration
Active Sediment Layer
Depth
Sediment Capacity
Factor
Interstitital Water
Diffusion Coefficient
Characteristic
Diffusion Length
Diffusive Exchange
Coefficient
Sedimentation Velocity
Resuspension Velocity
Particulate
Concentration
Ratio
Symbol
Hl
"2
H2
3
VYV
W21
r2/rl
Probable Range Information Base
2.0-20.0 (mg/1) Good
0.5-20.0 (m)
50,000-500,000
(mg/1)
0.01-100.0
0.3r3.0
(on /day)
0.1-1.0 (cm)
1-100 cm/day
(mm/yr)
0.5-50 (mm/yr)
1-750 (mm/yr)
0.1-1.0
Excellent
Good
0.1-10.0 (cm) Fair
Strong Function of
H./H-* 1*2' ff 1
Good
Poor
Poor
Good
Poor
This Is Che likely
for all but very
reactive chemicals,
K2>0.1/day
5.11 Bioaccumulation of Chemical
The bioconcentration and depuration of chemical by aquatic organisms
can' be a primary factor for formulating the guidelines of a WLA. That is,
the desired level of chemical may be a function of the impacts on the
aquatic food chain. However, it is not the intention of this document to
develop chemical criteria or guidelines. Therefore, the reader is referred
to Appendix D for a technical discussion of bioconcentration and depuration
by aquatic organisms.
151
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SECTION 6.0
PRINCIPLES OF MODEL APPLICATION
Sections 4.0 and 5.0 of this manual describe in decail the daca
requirements for performing an evaluation of chemical fate, including a
review of techniques of analyzing the data to extract the requisite model
input information. The actual application of the model to the analysis of
field data requires the systematic utilization of this information in such
a way as to obtain an improved understanding of the problem being
investigated. This section includes a recapitulation of the procedures for
obtaining the model input data and presents an overview of the general
principles of model application.
6.1 Evaluation of Model Inputs
The previous sections described in detail the procedures for collecting
data and estimating chemical loading rates, fluid and particulate transport
parameters, and chemical transfer and decay rates. Each of these icesis
represents an essential aspect of the model calibration analysis and the
reliability associated with the various parameter estimates will have a
direct bearing on the credibility of the analysis as a whole.
The importance of reliable measures of the upstream, tributary and
wastewater chemical loading rates both before and during the period of the
field surveys is emphasized. At a minimum, waste samples should be
collected for a period approximately equal to the detention time of the
system. Further, some estimates of the long term (three to six month and
yearly average) chemical loading rates should also be available, as
152
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sediment concentration levels are probably more closely related to long
tern average loading rates than the short term values measured during a
survey period.
The transport characteristics of the receiving water must, also be
determined for the model analysis. Stream flow rates to a lake are usually
obtainable from a nearby OSGS gaging station. The volume and retention
time are also required. This information is available from a number of
sources, but may be most readily obtainable from the USEPA as part of the
NES.
An important element in the calculation of the environmental
distribution of those chemicals moderately or strongly absorbed to sediment
is the settling and resuspension rates of particulates. The effective
particle settling velocity can be measured with sedimentation traps or
bounded by either Stokes Law or settling ' test data. Resuspension and
sedimentation rates are then determined from an analysis of'observed
suspended solids distributions.
.
The final information which must be obtained for problem analysis and
WLA is concerned with reactions and transfer rates. Certain of these
reaction rates are characteristic of the chemical by its nature and can be
determined in the laboratory and modified to field conditions.. Solids-
water partition coefficients should be determined for the wide range of
solids concentrations to be expected in water column to sediment. Such
tests are best performed with samples of the particulate material obtained
from the study area. Hydrolysis is a characteristic of the chemical
substance and can be determined in the laboratory using samples of the
receiving water. Photolysis and volatility are similarly determined in
calibrated laboratory experiments and converted to field conditions
observed or expected during surveys. Biodagradation, if any, should be
assessed in laboratory experiments using samples from the site containing
acclimatized organisms as a first approximation.
153
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.Table 6-1 presents a summary of information required for the modeling
analysis.
TABLE 6-1. DATA REQUIREMENTS FOR CHEMICAL FATE MODELING ANALYSIS
FIELD DATA
Water column concentrations (dissolved and particulate)
Sediment concentrations (diaswl^cd and particulate)
Suspended solids concentration and de.pth of penetration
Sediment -solids concentration and porosity
Chlorides or conservative tracer for flow balance
Light intensity and penetration (for photolytic chemicals)
LOAD INPUTS
Dissolved and particulate mass discharges from point sources
Upstream, tributaries and non-point sources
Suspended solids mass discharges from all sources
TRANSPORT INFORMATION
Flow balance
Volume and depth
Active-sediment depth
Suspended sediment settling rate
Sediment resuspension rate
Sedimentation rate
REACTIONS AND TRANSFERS
Solids-water partition coefficients for range of solids concentrations
Hydrolysis data
Photolysis rate
Volatilization rate
Biodegradation rate
Sediment diffusion rate
6.2 Calibration/Validation Procedures
The calibration and verification of a water quality model should be
performed in a systematic manner in order to achieve all of the potential
benefits of the modeling effort. Although it is not possible to prescribe
a detailed step by step approach that is applicable to all problem
154
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settings, there are certain features of the calibration/validation
procedure which are common to most situations. The preferred approach is
to calibrate the model with one or more sets of data, and then validate the
resulting calibrated model by applying it to an independent set of data.
The purpose of the calibration step is. to evaluate the parameters which are
included in the model formulation. The model is then applied to the
validation data set using a consistent set of model parameters. If the
calculated model results are in good agreement with the independent set of
data, the model is validated and can be considered for use in evaluating
alternative control strategies which are proposed and making WLA analyses.
The initial attempt at model validation often identifies areas where
the model calibration was inadequate and adjustments are made accordingly.
In such a case, where feedback from the model validation is used to refine
the results of the original calibration of the model, the distinction
between the two steps is less rigorous. In any event, the ultimate
objective Is to arrive at a consistent set of parameters which will result
in acceptable agreement between the calculated model results and- observed
data for a range of.environmental conditions.
A schematic diagram which summarizes the principal features of the
model calibration procedure is presented on Figure 6-1. First, the model
segmentation and system geometry must be specified. With simple,
completely mixed models, this step of the analysis defines the water column
and sediment volumes, ^ and Vj, and depths, ^ and HZ, for constant
geometry reaches of the receiving water. Other complex models may provide
greater flexibility and the study area may be segmented into a number of
compartments. Additional segments should also be established at locations
where point source loads or tributaries enter the lake.
The flow balance is determined on the basis of the gaging station and
plant flow records, or from field measurements of flow at the time of the
survey. The flow balance should be checked by modeling the distribution of
a conservative substance, such as total dissolved solids or chlorides, to
insure that a reasonable flow balance has been determined.
155
-------
MODEL
CALIBRATION
DEFINE LAKE GEOMETRY
AND
DETENTION TIMg
DETERMINE FLOW DISTRIBUTION
AND CHECK WITH CONSERVATIVE
SUBSTANCE ANALYSIS
ANALYZE SUSPENDED SOLIDS DATA
TO EVALUATE PARTICLE SETTLING
ANO RSSUSPENSION RATES
ANALYZE CHEMICAL DISTRIBUTION
IN WATER COLUMN ANO SEDIMENT
APPLY MODEL TO VERIFICATION
DATA SET
USE OF MODEL AS AN
EVALUATIVE TOOL
POSSIBLE
RESVAUUATIQN
OP ANALYSIS
FIGURE 6-1. STEPS IN MODEL APPLICATION
Once the model geometry and flow balance have been established,
suspended solids data should be analyzed Co evaluate che parameters
controlling the solids concentration profile in the lake. The particle
settling velocity, Wj, should be assigned the basis of field measurements
with sedimentation traps or, if such measurements are unavailable, it may
be bounded using estimates based on Stokes Law and particle size
distributions. The net flux o-f solids between the water column and
sediment, which is directly related to the change in mass of solids in the
156
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water column, establishes the magnitude of the sedimentation velocity, w^
The particle resuspension velocity, w2l, can then be directly determined
from the water column suspended solids profile, BI, provided the sediment
solids concentration, m^t is also known.
The total chemical profile can be modeled using estimates of the total
chemical loading rate, WT. 'from each of the known sources of chemical to
the receiving water. Preliminary estimates of the water c«iuo.n anH
sediment partition coefficients, ^ and «2 respectively, are specified at
this time on the basis of field observations or values obtained from the
literature. Chemical decay rates are also assigned. If there are no
losses of chemical from the system, the partition coefficient will noc
affect the calculated spatial distribution of total chemical, but only the
partitioning of total chemical betw.een the dissolved and particulate
phases. If chemical is lost from the system, however, such as by decay or
sedimentation, the partition coefficient would have an effect on the total
chemical concentration in the water column, and an iterative approach would
be required. A comparison of calculated results and observed data will
indicate whether or not it is necessary to make adjustments to jny of che
model parameters, 'if adjustments are required, they should be Limited to
che range of uncertainty associated with the various inputs.
Once the model has been calibrated, it should be validated by
calculating che receiving water and sediment response during an alternative
set of environmental conditions. Chemical inputs would also be changed to
reflect the load which preceded the verification survey period.. Kinetic
coefficients used in the model calibration should be adjusted for
differences in temperature or light intensity, as appropriate, but should
otherwise be consistent with the values used for calibration purposes.
After making the necessary input modifications, the computed model results
are compared with the verification data set and, if agreement is
acceptable, the model can be considered to have been verified. Inconsis-
tent results, however, may indicate aspects of the data analysis which
should be reviewed, and where modifications should be made. The intent of
the analysis should be to arrive at a reasonable and consistent set of
157
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model parameters which will allow the model to calculate the essential
features of the water column and sediment distributions. Within limits,
differences between calculated model results and observed data are to be
expected and are not necessarily unacceptable. The extent of such
discrepancies will affect the measure of validation, which is described in
Section 6.3.
In certain instances data limitations may prevent a rigorous
calibration and/or verification analysis. When this is so, the available
data may still be utilized to arrive at a preliminary model 'calibration
which may be useful for planning and assessment purposes. The preliminary
model calibration will also aid in the rational design of subsequent water
quality field surveys which are performed for the purpose of obtaining daca
*
for validating the model.
.The methodology of model calibration and verification which has been
described represents a generalized approach which can be followed when
evaluating almost any receiving water system. Although the details of Che
analysis will undoubtedly vary with the specific problem setting and
availability of data, the general direction is to proceed with the analysis
in a systematic manner. Each step in the analysis should eliminate an
additional degree of freedom and, as much as possible, be independent of
subsequent tasks. This will facilitate the achievement of a realistic
model for chemical fate.
6.3 Measure of Validation
Measure of validation refers to the degree to which the calibrated
model is capable of reproducing observed water quality data over a range of
environmental conditions. It addresses questions concerning the validity
and utility of the water quality model and will directly affect the level
of confidence placed in the accuracy of water quality projections.
Numerous measures of validation have been proposed. Qualitative measures
are probably the most direct and readily understood indication of model
performance, and are generally obtained by comparing data and calculated
158
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model results by eye. Other measures make use of more formal statistical
techniques such as regression theory, calculation of relative error, or
comparison of means to quantify the goodness of fit of the data by the
model. Each of these approaches has its advantages and disadvantages. At
present, no single measure of validation is generally agreed upon as the
best measure of a model's credibility. A detailed review of model
verification in general and measures of validation is presented elsewhere
(USEPA, 1980).
6.4 Sensitivity Analysis
The sensitivity analysis is an important aspect of the model
application. It provides a sense of those model parameters which are most
important in determining the fate of the chemical being investigated, and
leads to a better understanding of the significance of the interactions
between the mechanisms which are included in the model. A sensicivicy
analysis is performed by independently or concurrently adjuscing selected
model parameters of interest over a reasonable range of values. If Che
computed chemical distribution is insensitive to the perturbations of a
particular model parameter, it is an indication chat the parameter is
adequately defined for modeling purposes. Alternatively, if che computed
results are very sensitive to changes in a particular model parameter, it
focuses actention on Chat particular parameter in subsequent investiga-
tions.
The model sensitivity analysis also provides a means of assessing Che
degree of confidence which should be placed in model projection results.
For example, consider a hypothetical situation where a model projection
shows that a proposed permit load will result in a maximum water column
concentration that is 25 percent less than the maximum allowable receiving
water criterion. The volatilization rate of the substance is not well
defined, however, and thus the projection may or may not be accurate. If a
sensitivity analysis shows that the criterion would still be achieved even
with the conservative assumption of a zero volatilization rate, the
uncertainty in Che volatilization rate would be of much less concern.
159
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Alternatively, if the standard was exceeded when the volatilization rate
was decreased by 50 percent, the importance of an accurate determination of
the volatilization rate would be evident and future efforts could be
directed to this area of study.
Another type of uncertainty analysis which may be applicable, is the
First Order Uncertainty Analysis. This type of analysis differs from a
sensitivity analysis in that it provides the ability to combine sensitivity
functions. The idea is to characterize the parameter uncertainty in
probabilistic terms. If the variability of a state variable can be
expressed as a linear function of the uncertainty parameters, a propagation
of variance formula can be applied. The major impediment to using First
Order Uncertainty Analysis, is the fact that it results from a lineariza-
tion of the state equations. Thus, if the equations are outside che region
of reasonably linear behavior, inaccurace results might be expected.
There is another method, the Monte Carlo, technique, chac dispenses che
need for linearization, but at the expense of greatly increased computa-
tional burden. The Monte Carlo method randomly selects parameter values
from parameter probability density functions to solve a series of scace
variable equations. An estimate of the uncertainty covariance is Chen
computed.
Monte Carlo methods can be quite powerful since they
-------
computational demand, but it is unlikely to result in rawer ca-n
simulations. This, then, sets the bound of practicality for this method.
Di Toro ( 1984) reviews statistical methods for estimating - and
evaluating the uncertainty of water quality parameters. The reader is
referred to this reference for further information concerning the First
Order Uncertainty Analysis and the Monte Carlo technique. The following
section discvsses the theory and framework for performing first order
uncertainty analysis.
6.4.1 First Order Uncertainty Analysis
Water quality and ecological models are normally formulated as sees of
mass conservation equations for the concentrations of concern. They
express the interrelations between transport, kinetics, and mass discharges
to the system being considered. Let c(t) be the vector of concentrations
ordered in some convenient way. For example, let c be the vector ordered
by location and concentration type: c^x^t), c^x^e),.... c^xn» = );
C2(xl§t)f C2
-------
The parameters of I, W and the reaction expressions, r, are usually
functions of time 'as well. In accordance with normal systems analysis
notation, we win express this equation in state variable form:
-g (x.e.u.t) (6-2)
where :
x(t) vector of state variables
8 vector of all uncertain parameters
u - vector of all forcing functions
g - vector function expressing the relationships In the right hand
side of Equation (6-1)
Two alternate forms of this differential state variable equation will
be used subsequently. Numerical integration schemes for che differencial
equations result in difference equations of the form:
x(t * 1) -.F(x
where x(t + i) is the state vector at time t » 1, as a function, F, of che
state and forcing functions at time t. The notation t + I is used instead
of the more precise t + At for convenience.
Since numerical integration of the differential equations produce the
solutions, x(t), at any time, we can adopt the point of view that the state
vector is given as a function (actually a functional) of the forcing
function, u, from. t - 0 to t, the parameters, 8, and time so that:
x(t) - f(9,u,t) (6-4)
where f is now some complicated expression involving the initial
conditions, x(o), the parameters, 8, the forcing function history up to
time t, and time itself. This point of view is quite useful since varia-
162
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tlons in f due to changes in parameters can be computed by Just rerunning
the computer program that integrates the model equations with the altered
parameter values. Thus, although f is not expressible analytically, its
behavior can be easily computed.
These three state equations correspond to, within the numerical
accuracy of the integration schemes, the same system viewed from three
points of view, the differential, difference, and integrated form of the
fundamental state variable equation. As shown subsequently, the point of
view adopted affects the form of the methods available for quantifying
uncertainty.
The difficulties with sensitivity analysis can be greatly mitigated by
combining the sensitivity functions together with an estimate of parameter
uncertainty to obtain directly the resulting model uncertainty. The idea
Is to characterize the parameter uncertainty in probabilist Lc terms.
Consider two parameters, e^ and 9^ as random variables with means at
their calibrated values, and with variances, V^] and V[«2K If -^ and J2
are two nonrandom functions, and if 6 l and 9 2 are uncorrelated, then:
VtVl * J292] - Jl2 V[ei1 * V VI92] (6"5)
Thus, If the variability of a state variable can be expressed as a linear
function of the uncertain parameters, the propogation of variance formula
can be applied directly. Again, the different system points of /lew yield
different computational methods.
Let 6* be the calibrated parameters which yield the model solution:
»*
-------
and expanding the first term in a Taylor series yields:
«x(t) - f(8*,u,t) + |f |
If only ehe first order term is retained, then:
«x(t) « |j | * «8
It is for chis reason chat the analysis is termed "first order" uncertainty
analysis. Mote chat the Jacobian matrix, af/ae is just che matrix of
sensiCivicy coefficienes compuced using ehe calibrated parameters, 6 :
j .11. [J (t)] C6"10)
38 ij
which is the reason we used the notation Jy as the sensiCivicy coefficient
inscead of che more convencional Stj. Hence, che firsc order uncertainty
equation is:
«x(t) - J(t) 48 (6"L1)
We now calculace the uncertainty cbvariance matrix of the states:
I (c) - Cov
where the prime denotes .the transpose. Note that the diagonal elements of
I (t) are the variances of the states, which is ultimately of interest.
That is, for the first state, element 1.1 of IgCt) is:
Ux(t))u - E Ctejf-* *" '-''I (6'13)
i
- E Ux ,
- V (x
t
164
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Computing tfte scace uncertaincy
(6-12) and Che first order approximation Equation (6-11) yields:
ECi.Ce) ' -«8Jt«e') (6-14)
- EU(t) «8 68'
- J(t) E{68 58'} J(t)1
so that, in covariance notations:
r(t) - J(t) r J'(t)
x
where I9 is the parameter uncertainty covariance I9 - EU8 68'}. The
fundamental roles played by the sensitivity functions J(c). which we shall
now call the Jacobian matrix, and the parameter uncertainty covariance is
clear. Methods of computing J(t) have been discussed above. The parameter
covariance is more difficult to obtain .the available methods are discussed
below.
The common approach is to specify the diagonal elements using
intelligent guesses 'of the probable parameter variability. The parameter
coefficient of variation:
v(9t) - a(81)/61 (6'16)
expressed as a percent is specified and it is used to compute a'C^). the
diagonal elements of I,. Since there is no obvious way to guess the
off-diagonal elements, they are invariably set to zero. Thus, with only
che diagonal elements of Z9 nonzero, the state variance is:
VCx^t)} - I J*k a2(8k) <6-l7>
which is the direct analogue of the propagation of error formula, Equation
(6-5). The covariance Equation (6-15) is the generalization of this
formula for general parameter covariance, Zg.
165
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The uncertainty variance of the individual states, VCx^t)), are the
quantities of interest and they can be used together with the state
solution Itself, x^t), to quantify the state uncertainty due to parameter
uncertainty. A common form is to use the standard error formulation and
express the state uncertainty as:
More precise probabilistic statements require additional assumptions or a
different approach as discussed below.
The real value of uncertainty analysis is to assess the uncertainty of
projections made wich the model. Let up(t) be the forcing functions under
projected conditions. The projected states are:
XpCt) - f(9,t,up) ' (6'19)
Evaluating Che Jacobtan matrix tor these conditions by che difference or
differential mettiod yields J (t). The model projection uncertainty is:
...
from which che standard errors of the projection follows:
x (t) + [diag elements of Cov(x (t))ll/2 (6-21)
p P
Applications of this technique have also been made to the analysis the
effect of instrument errors on the uncertainty of evaporation models
predictions (Coleman and DeCousey, 1976). for groundwater flow models
(Fluhler et al., 1976) and dissolved oxygen balance models for streams
(Chadderton et al., 1982). A detailed discussion of the use of these
methods tn designing experiments is also available (Moffat, 1982). An
interesting analysis of total lake mass balance errors and the design of
sampling programs using first order uncertainty is available (Lettenmaier
and Richey, 1979).
166
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SECTION 7.0
EXAMPLE LAKE ANALYSIS SEDIMENTINC CASE
The impacts of DDT, pyrene, naphthalene and carbon tetrachloride
discharges'to a hypothetical lake are to be evaluated. Resuspension and
diffusion are considered negligible. The hypothetical results of field
studies, laboratory experiments and physical characteristics are shown in
Table 7-1. The following sections step'through the various components of
t
the computation.
TABLE 7-1. SUMMARY OF DATA COLLECTION PROGRAM
A. Physical Characteristics - 3
Volume, V - 1.3 x 10 ft
Water Column Depth, Hj 5 meters
Plow, Q -150 cfs
Wind Speed, WI - 5 ra/sec. 2
Drainage Area, D.A. - 40 mi
Sediment Yield "1.22 tons/acre-yr
B. Field Measurements
Settling Velocity, v{ - 1.0 m/day
Sedimentation Velocity, w2 - 3.7 cm/yr
Percent Organic Carbon Content, £ - 10 percent
Sediment Active Later Depth, HZ - T cm
Secchi Disk Depth, Zg 0.7 m
C. Laboratory Experiments Results (biodegradation, photolysis, hydrolysis)
.
Chemical K^Q KpHOT *HYD
DDT "
Pyrene 0.5 0.105
Naphthalene 0.2 10.5
Carbon Tetrachloride 0.5
167
-------
7.1
Partitioning
Adaorption/desorpcion laboratory analyses were performed on che four
chemicals using lake water as the media. Figure 7-1 shows the results of
napthalene and carbon tetrachloride experiments.
iSOO
100
u
-------
Table 7-2 summarizes the results of all four chemicals analyzed.
TABLE 7-2. RESULTS OF ADSORPTION/DESORPTION EXPERIMENTS
Partition Coefficient:
Chemical <*
DDT 100,000
Pyrene 12,000
Naphthalene
Carbon Tetrachloride
It is noted that the partition coefficient can also be approximated
from the octanol-water partition coefficient, KQW, and the fraction of
organic carbon in the solids, f^. Karlckhoff et al. (1979), relates the
partition coefficient to organic carbon content of solids as follows:
and
.
K » 0 63 K (7"2)
KQC - 0.63 KQW
where K Is the partition coefficient expressed on an organic carbon
basis. °FCor example, if the KQW for DDT is 106'2 or 1,550,000,. ::hen:
KQC - 0.63 (106-2)
« 975,000
and for £Qe - 0.1:
» - 0.1 (975,000)
- 97,500
This type of analysis should only be used when no other data is
available. When planning the sampling program and laboratory analysis for
169
-------
a WLA study, the adsorption/desorption experimental analyses should be
included*
The next step is to calculate the fraction of dissolved chemical (fdl>
and fraction of particulate chemical in both the water column (i - .1)
and sediment (i - 2) from the following relationships:
di
pi
so that for DOT in the water column
f.. - i/Cl + W - 100,000 ' 10"6)
dl
- 0.5
The results are shown in Table 7-3.
TABLE 7-3. DISSOLVED AND PARTICULATE CHEMICAL FRACTIONS
(7-3)
(7-4)
DDT
Pyrene
Naphthalene
Carbon Tetrachloride
gpi
.50
.11
.001
0.0
-------
and
1 _ 1 . _L. (7-6)
r"^"~"~""~" IT if H
'air-water *l g
where:
K volatilization rate (I/day)
v m mass transfer coefficient (a/day)
air-water
K liquid phase mass transfer coefficient (m/day)
K - gas phase mass transfer coefficient (m/day)
H - Henry's constant (dimensionless)
The liquid phase mass transfer coefficient, KI§ may be approximated by:
Kt - 0.17 C0 (Dt/vt)2/3 WI <7-7>
where:
.
(I. - drag coefficient (dimensionless)
v - kinetic velocity of water (.01 cm /sec)
2
D - chemical diffusivity in water (cm /sec)
WI - wind speed
The chemical diffusivity, Ot, may.be approximated from Figure 5-19 or
the following empirical relationship:
Dt - 22 (MW)'2/3 dO'5) (7-8)
so that for DDT with a molecular weight of 355:
171
-------
Dt - 22 (355f 2/3 00~5)
-6 2,
- 4.4 x 10 on /sec
and Chen from Figure 5-20:
-A 2/3
Kt - 0.17 (.001X4.4 x i
-------
Henry's constant for DDT is given as 3.9 x 10* atm-m /mole. At 20°C
H(dimensionless) 41.6 H(atm-« /mole) (7~1]
so that:
- 41.6 (3.9 x 10'5)
- .0016
For DDT. the volatilization rate is calculated from Equations 7-5 and
7-6:
1 1,1
K~~ 0.42 172C.0016)
air-water
Kair-«ater ' °-17
Ky - 0.17/5
0.033/day
Table 7-4 summarizes the volatilization rates of the four chemicals of
concern.
r.ABLE 7-4. VOLATILIZATION RATE CALCULATION SUMMARY
J» *.*«lo"t -*2 .0378 171 .0016 .2732 .17 .03
DBT J» *.*« - . . .
7.3 Photolysis
The laboratory photolysis rates are given in Table 7-1. From Equation
5-25, the site specific rate can be computed as follows:
173
-------
Kp(field) - -%*₯* Cl * -'---"* <7"12)
where K U/m) is the diffuse attention coefficient and f is the fraction
of daylight hours. Normally, Kg should be measured directly using an
ultraviolet irradiance meter. However, Ke can be estimated from the secchi
disk depth, Za, and the empirical relationship:
Z - 5 to 40
9
with a median value of 9.2. For a secchi disk depth equal to 0.7 meters
and using the median value, K. - 13.1. the field photolysis rate is thus
calculated for pyrene.
« .0008 /day for pyrene
and for naphthalene
K 0.08/day
P
7.4 Overall Reaction Coefficient
Assuming the particulate reactions are equal e» the dissolved
reactions, the overall reaction coefficient reduces to the following
equations:
K2
174
-------
Table 7-5 summarizes the overall coefficients, ^ and 1^, for the four
chemicals.- For 'comparison purposes, the effective volatilization rate
f jr is also shown in the table.
TABLE 7-5. OVERALL REACTION COEFFICIENTS Kj AND Kj
AND COMPARISON WITH fd^
^^^^^H
^
DDT
Pyrene
Naphthalene
Carbon Tetrachloride
7.5
Computation of Water
and Sediment Solids
BY
0
0
0
0
D
.0
.0
.0
.0
s
0
0
0
0
10 !
.0 0
.5
.2
.5 0
PHOT
.0
.0008
.08
.0
^^M
0
0
0
0
mm^^^^
.0
.5008
.28
.5
fdl*v
.015
.004
.12
.12
K
^^M
0
0
0
0
2
^MMM
.0
.5
.2
.5
Column Solids Concentration m^
Concentration nu
Since resuspension and diffusion are considered negligible, che
equations to solve for m]> and m2 are found in Table 3-1 and are given as
follows :
U/Q (7-14)
K c
-I "1/-2
o
where
C . v/Q
1.3 x 109/150 . 86400
100 days
175
-------
and
1.0/5.0
0.2 /day
The average daily solids loading race w is calculated from che sediment
yield and basin drainage area as follows:
171,100 Ibs/day
The water .column solids concentration, n^, and the sedimenc solids
concentration, i»2, are then calculated
171. 000/150. S. 4
l " I » 0.2(100)
10 mg/1
100,000 mg/1
7.6 Computation of Water Column Concentration
C.. and Sediment Concentration C^
The equations to solve for CTI and CTZ are found in Table 3-1. For
reactive organic chemicals the equations are:
Co(fplKsl * fdlKv * Kl
176
-------
VH2 (7-19)
where:
e - 100 days
Kgl - 0.2/day
a»d rearranging Equation 7-15
-2 ' -, -1/-2 C7-M)
1.0 10/100,000
- .0001 m/day
and
K - w /H (7-21)
Ks2 W2/H2
.00017.01
0.01 I/day
Since the loading rate, WT, is directly proportional to the water
column and sediment concentrations, 100 Ibs/day of chemical mass discharge
rate is arbitrarily assumed for the computation. Then substitution of the
proper parameters for DDT into Equations 7-18 and 7-19 yields:
, 1007(150 * 5.4)
CT1 Cmg/1) " 1 + 100[0.5(0.2) * 0.5(0.03) + 0.0]
.0099 mg/1 DDT in water column
and
.... .0099(0.50) (1.07.01)
T2 lBg/l' " l.O(.Ol) + 0.0
49.4 mg/1 DDT in sediment
177
-------
Although 100 Iba/day of DDT is not a practical loading rate, it is used
for comparison purposes with the other three chemicals evaluated. Table
7-6 summarizes the results for the four chemicals.
TABLE 7-6. CALCULATED CTI AND C^ CONCENTRATIONS; W LOO LBS/DAY
DDT ' 49'4
-0023 0.05
-0030 0.0
Carbon Tetrachloride .0020 0.0
Note that for' DDT with a high partition coefficient and low reaction
rate, there is a large build-up of chemical in the sediment. On the other
hand, naphthalene and carbon tetrachloride with very low partitioning
characteristics and high reaction rates have negligible concentrations in
Che sediment. Pyrene, with a relatively high reaction race, still has some
build-up in the sediment due to a moderately high partition coefficient.
7.7 Time to Steadv-Stace
The time Co reach 90 percent steady-scate in the water column assuming
negligible tnceraction between the bed and water column is estimated using
Equation 3-44c given by:
2.303 _ ( 7-22 )
C90 ' l/to * Kt * fpl
and:
Kl * £pl Kp * fdlKc * fdlKv
Assuming the particulate chemical reactions are equal to the dissolved
chemical reactions, K, becomes:
178
-------
«,»* *" (7'24)
Thus for naphchalene:
K - 0.0 « 0.2 + .08 + .12
- 0.4/day
and
f , K . - tt.OOl (0.2)
pi s i
- .00027day
The time to reach 90 percent steady-state for naphchalene is:
2.303
Ce " I/100 * 0.4 * .0002
5.6 days
The results for the. four chemicals are shown in Table 7-7.
TABLE 7-7. TIME TO STEADY-STATE
^^^M^^^^^^^^^^
Time to 90 Percent
Chemical
Steady-State
DDT «
Pyrene *[
Naphchalene 5.6
Carbon Tecrachloride 3»7
MOM that the time to reach steady-state U shorter lor the more
reactive substances.
179
-------
7.8 Sensitivity of Resusnension
In order to evaluate the effect of resuspension on chemical concentra-
tions, the equations developed for the bed interactive case must be
utilized. The equations are shown In Table 3-3 and are given by:
(7-25)
«. f K ) <7'26)
. "2 H2 fpl (7-27)
BlHlfp2
(W21 * W2} V * *L (*2/T^ £
-------
The total reaction rate in the water column, KI§ is expressed by:
*1 ' fpl Kp * fdlKc * fdl*v (7
For DDT, the only reaction in the water column is due to volatilization
so that:
Kj 0.5 (.03)
- ,015/day
Since the reaction rate for DDT in the sediment, 14, is ecual to 0.0,
the total apparent reaction rate is calculated as follows:
1^ .015 * 10 (1X0.0 + .01)
- .115/day
then:
1007(150 x 5.4)
Si " 1 + ,115-UOO)
- .0099 mg/I
Table 7-8 compares the calculated concentrations in the water column
for the case with resuspension co the case wichouc resuspension.
TABLE 7-8. SENSITIVITY TO RESUSPENSION (*2/ri " U0)
Si CT1
Resuspension Sedimenting
Chemical
Kl K2 *T Case Case
DDT 10 0.015 0.0 0.115 0.0099 0.0099
PvTene 2.2 0.5004 0.5 1.62 0.0008 0.0023
Naphthalene 0.021 0.4 0.2 0.404 0.0030 0.0030
Carbon Tetrachloride 0.0 0.62 0.5 0.620 0.0020 0.0020
181
-------
NotB.ehae for.chree of the four chemicals, the concentrations have not
changed. Examination of Equations 7-20 through 7-23 can explain this
phenomenon. Naphthalene and carbon tetrachloride have low partitioning
characteristics such that fpl approaches 0.0, and the total apparent
removal rate, fcy, is approximately equal to the water column reaction race
K . Bed interaction, therefore, has a small effect on chemicals with low
partitioning characteristics. DDT, on the other hand, is highly
partitioning, hut in this case resuspension stili had no effect on the
water column concentrations Cjj. Examination of Equation 7-24 shows that
if diffusive exchange is negligible and the decay rate In the sediment, KZ,
is 0.0, then the particulate ratio r^ equals 1.0 regardless of the
resuspension velocity. Therefore, the calculated total apparent removal
rate, 1^, does not change. The water column concentration, C^, for pyrene
decreases with increasing bed interaction because of the decay of pyrene in
the bed, itself.
7.9 First Order Uncertainty Analysis
A simplified .first order uncertainty analysis is presented co
demonstrate the nethod of application. The theory presented in Section
6.4.1 will be the basis for the calculation. The state variables (x) co be
evaluated are CTI and C^ calculated for pyrene in Section 7.5 and the
uncertain parameters (9) are assumed to be KL and K2-
The quantity to be evaluated is the standard error of the state
variables (x ) given by Equation (6-21). At steady-state the projected
conditions for CTI and GJJ, plus or minus the standard error is given as
x » [diagonal elements of Cov
-------
so that Che parameters to be evaluated are the Jacobian matrix, Jp, the
transpose of the Jacobian matrix, Jpf, and the parameter uncertainty
covariance, Zg«
If x is the vector of state variables, and e is the vector of uncertain
parameters, then:
"(§g)
-(Si)
The Jacobian, J is given by:
l£ m( ** *
" 39 "\ 3C_2/3K.
and the transpose of the Jacobian, J ' is
JP
A common approach to obtain the parameter covariance 3^ is co compute
the variance of the uncertain parameter (V^ (the diagonal elements of I.,)
from the parameter coefficient of variation v9 ^0 V
2 183
-------
therefore:
and
JV
\
'
Only the diagonal elements are presented since they are the only elements
'of concern. From Equation (7-31) the standard error of Crl is equal Co the
first element of the diagonal and the standard error of CT2 is equal to the
second element of the diagonal.
7.9.1 Computation of Analysis
The products to be evaluated in order to calculate the standard errors
of CTI and ^ are as follows:
2. ^ (SCTI/3K2)2
3. Vicl
4. 7K2
The variances C7^ and VK2) are calculated from Equations (7-37) and
(7-38). If the coefficient of variation of the uncertainty parameters are
assumed to be 50 percent (0.5) and from Table 7-5 ^ 0.5008 and K2 -
0.50, then:
VKt - [0.5008 (0.5)]2
0.0627
184
-------
and
VK2 - [0.50 (0.5)]2
0.0625
The partial differentials (i^/H^. aC^/ai^, etc.) are estimated by
calculating the state variables at incremental changes with the uncertainty
parameters. For example; the differential 3CTl/3Kl may be estimated by:
icn/3K
where:
CTI
CT1
*i
Ki
concentration calculated at K^
concentration calculated at Kj
best estimate of KI or calibrated
K. ^ an incremental change in Kj
If K. is incremented by 10 percent, then:
Kj - 0.5008 -f .5008 (0.10)
- 0.5509
and
0.05008
In the example case for pyrene, ^ is calculated as follows:
CT1
(1007(150.5.4)
1 + 100(0.11X0.2) * .004 + 0.5509
0.0021
185
-------
Thus, the. approximation for
0.0021 - 0.0023
0.05008
0.004
In a similar fashion, the other differentials are estimated given, the
example conditions:
3CT2/3K1 " °*0877
The projected concentrations and standard errors of C^ and C^ are Chen
calculated as follows:
C p 0.0023 vVo.0627(-.004)2 * 0.0625(0.0)
Tl
0.0023 + 0.001
CT2
p - 0.050 ±-/0.0627(-0.0877)Z » 0.0625(0.106)
0.050 * 0.0344
186
-------
SECTION 8.0
EXAMPLE LAKE ANALYSIS
BED INTERACTIVE CASE
The data which will be analyzed in this section is from an experiment
in an Indiana quarry. The quarry experiment was initiated in 1972 by
Waybrant and Hamelink as part of a research study of the factors
controlling the distribution and persistence of DDE and lindane in lentic
environments. An abandoned flooded limestone quarry was used to trace the
time history of spike releases of DDE and lindane in the biotic and abiotic
sectors of the flooded quarry. The experiment was performed under
relatively controlled conditions, not subject to the usual complications of
a variable inflow, outflow, or loading history. Measurements of chemical
levels in the water, sediment and biota were made for a period of.
approximately one year after the initial spike release.
8.1 Overview of Quarry Experiment
The following sections review the application of DDE and lindane along
with significant rainfall events and sampling frequency. The results of
the sampling program are also presented.
8.1.1 Chronological Review of Important Events
The quarry experiment was conducted from May 29, 1972 through June 22,
1973. During this period of time several events transpired which are
pertinent to the interpretation of the quarry data. Equal mass inputs of
2.77 grams of both DDE and lindane were uniformly distributed over the
surface of the quarry on June 27, 1972, and on the following day samples
were collected for analysis of the post release "initial conditions" in the
187
-------
water column, sediment and biota of the quarry. Subsequent samples were
collected'on days 3. 10, 21, 42 and at progressively longer intervals over
the course of the next year.
An intense rainfall of 3.5 cm in 45 minutes occurred on the day after
the addition of chemicals to the quarry. Based on the accumulation of
solid material in sedimentation traps between days 0 to 21, it was
estimated that 2.9i x 103 kilograms of solids (dry weight) entered the
quarry and settled from the water column as a result of runoff from this
storm. The observed rapid rate of decrease of DDE in the water column was
attributed to the adsorption of DDE onto these solid particles which
settled to the bed. Undane, which has a much lower affinity for solids,
was not nearly as sensitive to the influx of solids, and hence it persisted
In the water column for a much longer period of time.
At the start of the quarry experiment the water body was thermally
stratified, and hence .nixing between the epilimnion and hypolimnion was
significantly impaired. The fall overttfm occurred on about day. 144, and
after this time vertical concentration gradients -in the water column were
effectively eliminated. The experimental monitoring was terminated on
about June 22, 1972, 360 days after che initial input of chemical to che
system.
8.1.2 Discussion of Water Column and Sediment Data
As part of the quarry experiment data collection program, the water
column and sediment were sampled with depth in order to detect the
existence of vertical gradients of chemical. A qualitative review of this
chemical data prior to a discussion of the modeling analysis is included as
a preview to the model application.
Figure 8-1 summarizes the water column DDE data that was collected
during the quarry experiment. As shown on the upper chronological plot of
DDE concentration, the initial input of 2.77 grams of DDE on day 0 resulted
in a depth averaged concentration on day 1 of about 44 ng/1 in the water
188
-------
_ lOOO
z
ui O
§5
K
H
Ul
OH
1 1 '
.1 i.O iO 'CO 1C
ION ( pp'r )
too
0
DATA:
WAT8RANT, 1973
0
20
40
60
0
OAT 81
Mi
M0»
H3t
m
\ \ \
0
20
40
an
OAT 173
- KH
HM
- K*
HD<
1 [ 1
i iQ >0 "GO 1000 0.1 I.O '0 '00 'G
OOE CONCENTRATION (pprr)
00
FIGURE 8-1. TEMPORAL VARIATION OF DOE IN WATER
189
-------
column. -This concentration was reduced to less than 10 ng/1 by day 10 and
then gradually decreased to 1 ng/1 by day 100. A DDE concentration of
about l" trg/1 persisted for the duration of the monitoring effort, although
an increase to 3 ng/1 was reported on day 360.
The lower graphs on Figure 8-1 illustrate the DDE water column profile
with depth on "selected days during the experimental monitoring program.
Some vertical stratification is exhibited on day 1, with average
concentrations of 50 ng/1 up to a. depth of 30 feet and about 10 to 20 ng/1
at depths of 40'and SO feet." Even though, the fall overturn did not occur
until day 144, a relatively homogeneous vertical water column concentration
profile developed by day 21, when Che average concentration was 3.5 ng/1.
The uniform vertical profile was also prevalent on days 81 and 173, when
the average concentration was at or near 1 ng/1.
Sediment DDE data for the upper 1.5 cm of bottom sediment, In units of
ug DDE/kg wet sediment, are summarized on the upper panel of Figure 8-2.
The sediment concentration on day I was quite low, but Increased sharply co
about 20 to 30 ug/Vcg by day 5 and this concentration'persisted for the
remainder of the first year. DDE sediment concentrations for depths of
0 to 1.5, 1.5 to 3.5, and 3.5 to 5.5 cm, presented for selected days on che
lower graphs of Figure 8-2, show that the DDE did not generally penetrate
beyond the upper 1.5 cm of the bottom sediment.
Several distinctly different characteristics were observed in the
temporal distributions of water column and sediment lindane which are
presented on Figures 8-3 and 8-4. Significantly higher concentrations of
lindane were observed throughout the study, with the minimum water column
concentration approaching 10 ng/1, an order of magnitude higher than the
corresponding DDE concentration, at the end of the study. The wide ranges
in the water column results in the chronological graph, and prior to the
fall overturn at day 144, reflect the vertical gradient of chemical between
the epilimnion and hypolimnion of the stratified water" body. The ranges
are reduced after day 144, when the water body was mixed by the fall
overturn.
190
-------
UJ
2 0>
uu 3.
UJ
60
40
20
0
^B
^m
_
,
^;
10 a
m
1
[I
«
. 1
MOTS
SAMPLE DEPTH
FPQM 0-i.Scm
i
(
t
1
i
i
<
i
L 2
I 1
1
SO 100 -SO 200 230 300 35O «oo
TIME AFTER RELEASE (days )
g
u
v-
Z
O
UJ
V)
OAT
NO OA7A
NO DATA
r r
OAT 21
NO DATA
| , r
,0 iQ iGO 1000 O.I '-0 "0 'CO .000
SEDIMENT OOE, r,
DATA:
WAY8R ANT, 1973
OAT 81
> I
> I
h- - T ~ ~ 1
. I
"00 lOOO
SEDIMENT DOE, r, (JLOOO
FIGURE 8-2. TEMPORAL VARIATION OF DOE IN SEDI MENT
191
-------
7
*
UlZ
ZO
<
§S
-cr
z
UJ
(J
z
o
IOC
10
I.O
1
"
1
_
l><
«
i
1 <
<
»
nO T ^P
d ^5 ^y ^P TP
J-
>
w 2.77 qramt
,1-11111
*' o 0 SO «00 "SO 200 2SO 500 320 «CO
TIME AFTER RELEASE Uays )
OATAi
0
. 20
r ^o
(X
LJW $C
i- -o
z
z
V-
0.
UJ
0 0
2C
«c
NT, 1973 *C
OAT 1
~ > OH ^
H^H
1 0 1
Kl
1 1 1
i i.O 10 100 1C
LINOANE CONC
OAT 81
u
B
Id
tei
I 1 1
>.l iQ IQ iOO 1C
c
20
40
30 C
^*H '
0
20
4Q
100 C
OAT 21
KH
KH
101 -
1 1 1
I 10 <0 iGO ICC
ATlON (pptrl
OAT ira
H-^ ^
B
B
- B
D4
1 1 1
).t i.O "0 iOO * 10
LINOANE CONCENTRATION ( ppfr)
FIGURE 8-3. TEMPOR.ALVARIATION OF LINOANE IN WATER
192
-------
8
Z
o *
Z 0»
« J«
J X.
K 0» 4
Z Jt.
5 w" 2
UJ
09
MB
V
-
EDy
i
i
-so o s
/vorr
SAMPLE DEPTH
FROM 0-1.3 em
_.
<
(
I
I .
> {
. 1 .
»
|
. 1 >o-»" I i
0 100 ISO 200 220 300 3SO *C
TIME AFTER RELEASE (days
E
u
a
UJ
en
vu
a
0
i
4
6
0
OAT i
sooxx
NO DATA
1 -r r
0
2
4
tf
OAT 21
>
NO DATA
- - -I- -T - "I
SEDIMENT LiNOANE, r, (^.g/hg)
DATA:
WAY BRANT, 1973
OAT 81
O.i >0 10 iOO lOOO
SEDIMENT LINOANE, r,
0
2
4
0
OAT 173
> O.S
1 I--T ~ ~
., |.0 10 100 1000
FIGURE 8-4 TEMPORAL VARIATION OF LINDANE IN SEDIMENT
193
-------
Sediment data for lindane are shown on Figure 8-4. Wich the exception
of the sediment concentration of about 7 ug/kg on day 1, the sediment
concentration averaged 1 to 2 ug/kg, an order of magnitude lower than the
sediment levels of DDE. Aa shown by the data on the lower graphs, lindane
did penetrate to the deeper sediment layer of 3.5 to 5.5 cm, and the
profile did not exhibit a strong vertical gradient. This is in contrast co
the DDE results which were an order of magnitude higher in the surface
layer, but at generally negligible levels at sediment depths greater than
1.5 cm.
8.1.3 Chemical Budget
The data analysis previously performed (Waybrant, 1973) included
estimates of the masses of DDE and lindane associated with the water
column, sediment, quarry walls, water surface film, fish, microcrustaceans
and plankton. Based on these results, it was concluded that essentially
all of the chemical which was recovered was in the water column and
sediment, while only a relatively small fraction was associated with che
other compartments. Thus, it was considered valid to neglect these other
compartments for the'purpose of the model testing analysis.
I
8.2 Evaluation of Model Inputs
The model analysis for the quarry is considerably simplified since
there was no continuous inflow or outflow, a known mass of chemical was
applied and the quarry has a relatively regular geometry. As is generally
the case, however, there were also certain aspects of the analysis where
data were lacking requiring the use of engineering Judgment. This section
will review the evaluation of model inputs and summarize the assumptions
which were required to calibrate the model.
8.2.1 Model Geometry
The initial step In the application of a chemical fate model is the
specification of the geometric configuration of the receiving water. The
194
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model geometry which was used for Che quarry analysis is illuscraced on the
upper panel of Figure 8-5. The water column volume, V^ and depth, Ep
were readily determined from the reported data which are shown on the lower
panel of the diagram. The quarry is rectangular in shape, 91.5 meters long
and 41.2 meters wide (300 ffeet x 135 feet), and has a total volume of Vj -
5.23 X 104 m3. These measurements correspond to an average depth of HX
13.9 meters (45 feet) which is in reasonably good agreement with the depth
profiles of Figure 8-5 which were measured at the tine of the quarry
experiment .
The depth of the active sediment layer, H2>. was a more difficult
parameter to evaluate. Fortunately, the chemical concentration data which
were measured with depth (Figures 8-2 and 8-4) provided some guidance about
Che selection of an appropriate value for Hj. DDE was observed to
penetrate at most the upper 1.5 cm of sediment, while lindane penetrated to
a depth of at least 5.5 cm. On this basis, chemical specific active layer
depths of H2 - 1.5 cm and 5.5 cm were used to characterize DDE and lindane
respectively. The use of different active layer depths is necessitated by
the simplified representation of diffusive exchange and che assumption oc a
completely mixed sediment layer which are incorporated in the modeling
framework.
Host modeling studies include the analysis of a conservative substance,
such as IDS or chlorides, as a means of verifying hydraulic balances where
tributary or point source loads enter the system. Although confirmation of
a flow balance is not applicable here, the initial concentrations of
lindane and DDE, ^(o). <=an be used to confirm the quarry geometry, Vj,
from the relationship
Table 8-1 summarizes the calculated initial concentrations of lindane
and DDE and the measured day I concentrations of both chemicals. Since
*
195
-------
(A) SCHEMATIC OF MODEL SEGMENTATION
0= 0
M,= 13.9 m
V, a 3.23 x 10 m'
WATER
COLUMN
ACTIVE
LAYER
OEE?
, SEDIMENT
H2= 1.9 cm FOR DOS
Ms 3.5cm FOR LINOANE
(B) DEPTH MAP OF QUARRY T
DATA:
,1973
FIGURE 8-5. MODEL GEOMTRY FOR ANALYSIS
OF INDIANA QUARRY
196
-------
equal mass loads of each chemical .were input co Che same volume of water,
the quarry, the initial concentrations of both chemicals should have been
equal. Using MT - 2.77 grams and ^ - 5.23 x 10 m3, the initial
concentration of both DDE and lindane was estimated to be 53.0 ng/L. The
calculated initial concentrations of both chemicals are higher but
reasonably close to the measured day 1 concentrations, and the lindane
concentration is less than the concentrations on days 5 to 21, thus it was
concluded that the water column volume of ^ - 5.23 x 10 . , provides a
reasonable estimate of the quarry geometry.
TABLE 8-1. MASS BALANCE CALCULATION FOR INITIAL CHEMICAL DOSAGE
Lindane
DDE
vu "r
(m ) (grams)
5.23 x 10* 2.77
5.23 x 10 2.77
Calculated
CT1(o) - MT/V1
53.0
53.0
Measured
cT1tn
47.3
44.4
8.2.2 Fluid Transport
The only inputs to the quarry are direct precipitation and runoff,
while water loss occurs as a result of evaporation. There Ls no infor-
mation available concerning quarry groundwatar inflow or oucflow, and chas
it has been neglected in this analysis. Since the average precipitation in
this region of the country is slightly more than 100 cm/year, and
evaporation is approximately 85 cm/year, the net input to the quarry
(neglecting runoff) over the course of a one year period is only about 15
on of water.' This amount is insignificant in comparison to the overall
volume of water in the quarry, which has an average depth of 13.9 m. Thus,
on a time scale equal to the duration of the quarry experiment, the net
inflow of water can be neglected.
197
-------
8.2.3 Participate Transport
The analysis of particulate transport in the quarry was complicated by
few field measurements of «l and m2, the solids concentrations in the water
column and sediment, respectively. The limited data which are available,
however, do provide some basis for characterizing the temporal variation of
01 . The key to solving the problem is the estimated mass of solids, MSS -
2\92 T 106 grams, which settled from La* qu-rry as a result of the influx
of solids at the time of the intense rainstorm. The mass of solids settled
can be represented by:
Mss
where the Initial suspended solids concentration, mu, is the sum of the
concentration which preceded the storm, *lb, and the concentration increase
resulting the influx of solids during the storm, d.p and c* Is che period
of sedimentation. Solving for the settling velocity, Wj, yields:
(8-3)
The background concentration may be estimated empirically from Che
extinction coefficient (8-3) as:
(8'4>
where K is given by the approximate relationship
Ke - 1.7/1. (8-5)
For a secchi depth of Zs - 6.1 m, Kg 0.28/m and from Equation 8-4, «lb >5
mg/1. The increase in BI due to the influx of solids with the storm is
obtained from
198
-------
such that for a water column volume of Vj - 5.23 x 10* a3, Arn^ .'56 mg/1.
Thus, «lt - mlb + *«! - 61 mg/1.
Although no suspended solids concentration data was available for this
analysis, it was assumed that the relatively rapid decrease of DDE in the
water column and buildup in the sediment (Figures 8-1 and 8-2) was due to
the adsorption of DDE on the solid particles which settled to the sediment
layer. Inspection of the DDE data would therefore indicate that t* - 10
days. Using this value in Equation 8-3 with the other previously estimated
parameters, yields Wj 3.2 m/d.
Assuming that removal of water column suspended solids is proportional
to the solids concentration BI. then the average concentration during days
1 to 10 is given by (HydroQual, 1982):
l
(8-7)
For ! - 3.2 m/d, HI - 13.9 .. «u - 61 mg/1 and t* - 10 days, ^ « 24
mg/1.
The secchi disk readings after day 21 were generally 6 to 7 oieters, and
aside from some initial variability which were attributed to algal effects,
che readings were essentially constant in time. From Equations 8-4 and
8-5, these readings indicate that ^ -5 «g/l characterized conditions in
Che quarry during this period of time. Since this low level of ^
persisted for the duration of the study, resuspension was probably
negligible, and as there were no other sources of solids to the quarry, the
data indicate that «L was much lower than the 3.2 m/d which was estimated
for the first 10 days. In view of these considerations, i^ - 0.1 m/d was
assigned for t > 10 days. This settling velocity essentially eliminates
particulate transport as a mechanism of chemical transfer after day 10.
Use of a variable settling velocity is not unreasonable since it is likely
L99
-------
that relatively coarse particles entered the quarry- as a result of the
intense storm on day 1, and these would settle rapidly. The remaining
particles are either settling much acre slowly or not at all.
It is important to. realize that the preceding estimates of suspended
solids concentrations from secchi disk depth readings by use of Equations
8-4 and 8-5 were made by necessity, since direct measurements of BI were
not available. When planning field surveys, however, BI should always be
measured, since these empirical correlations provide only approximate
estimates of m.
The sediment solids concentration is also required in order co perform
ehe modeling analysis. As reported, the 200 to 300 ml of wacer was
centrifuged from SOO to 600 ml of wet sediment. Using a liquid volume of
250 ml in a total sediment volume of 550 ml, the sediment porosity is
estimated eo be * - 250/550 - 0.45. Ic was also reported chat <>b, the bulk
density of Che sediment, was 1.2 g/cc. This information can be used to
estimate m_ from the following expression:
,->-*.
in which the density of water, Pa is close. to unity. Thus Equation 8-8
results in an estimate of m^ " 750 g/1.
To complete the specification of the requisite solids related para-
meters, ehe sedimentation velocity, w^ was set to zero for the calibration
analysis. This was done because the net chemical transfer to the deep,
inactive sediment was not considered as a loss of chemical from the system.
The solids related parameters which have been estimated thus far are
summarized in Table 8-2.
200
-------
TABLE 8-2 SUMMARY OF SOLIDS RELATED PARAMETERS USED IN QUARRY ANALYSIS
Dl
m.
t,
w.
5"
"2
(mg/1)
(g/D
(m/d)
(nnn/yr)
(mm/yr)
Days
0-10
24 '
750
3.2
0
0
Days
10-365
5
750
0.1
0
0
8.2.4 Chemical Transfers and Kinetics
The following sections describe the chemical partitioning, diffusive
exchange and chemical decay characteristics for lindane and DDE in the
quarry experiment.
Chemical PartitioningDDE. A limited amount of data was available to
characterize the partition coefficient for DDE. Estimates of the DDE
partition coefficient were therefore based on the partition coefficienc for
DDT. This is justified by the similarity of the octanol-water partition
coefficients of DDE and DDT and by the correlation between adsorption and
octanol-water partition coefficients (USEPA, 1979).
Figure 8-6 shows the DDT partition coefficients as a function of
suspended solids concentration for DDT on montmorillonite and illite clays
(O'Connor and Connolly, 1980). At solids concentrations on the order of 10
mg/1, as in the quarry, the data indicate a range of 50,000 I/kg on illite
clay to 275,000 I/kg on montmorillonite clay. Since DDE is a daughter
product of DDT, it would be expected to have a somewhat lower range of
partition coefficients than this range of DDT partition coefficients.
Figure 8-6 also illustrates the inverse relationship between partition
coefficient, », and the suspended solids concentration. It is expected
that this trend would also occur in the quarry, although the slope may be
different as a result of differences in the characteristics of the solids.
201
-------
1.000.000
100.000
U
fc 10.000
o
U
z
o
oc
£ 1.000
IOO
10
ODDT-ILLI1E
DOT- MONIMORILLONIIE
LINDANE-LAKE SEDIMENTS
J.
J.
REF.
O'CONNOR AND CONNOLLY
too 1.000 10.000
SEDIMENT CONCENTRATION (mg/l)
100.000
FIGURE 8-6. TYPICAL DDT AND LINDANE PARTITION
COEFFICIENTS VERSUS SEDIMENT SOLIDS CONCENTRATION
-------
Lindane. The partition coefficient for lindane is also shown as a
functloTrf' solids concentration on Figure 8-6. The data, which range from
i . 500 to 285 I/kg over a range of solids concentrations of approximately
500 to 20,000 .f/L. was measured using lake sediments. This difference in
solids cype may partially explain the less sensitive inverse relationship
with solids concentration of lindane in comparison to DDT. It is not
evident from these data whether or not the lindane partition coefficient
would increase at suspended solids concentrations less than 500 mg/1.
Figure 8-7 shows the lindane Isotherm data for water'and solids from
the quarry (Dickson, 1981). If a linear isotherm is assumed, a line having
a slope of unity on the log-log plot determines the partition coefficient.
As observed, an average partition coefficient of » - 250 I/kg provides a
good fit of these data. The difference between this value and those of
Figure 8-6 could readily be accounted for by differences in the character-
istics of the adsorbent materials which were used.
lOiOOO
X '00° T
CI»CIMMC»fAl MSUlM USIMO INOUNAOUAMT
WftTt* »«0
«OSO*'TIOM
a ocio«»"0«
ousouveo LINOANC
/ >
FIGURE 8-7. LINOANE ADSORPTION /OESORPTION DATA
WITH INDIANA QUARRY WATER AND SEDIMENT
203
-------
The previously reviewed DDE and lindane partition coefficient data
suggests that it will be difficult to estimate »2 at the estimated sediment
solids concentration in the quarry of »2 - 750 g/1. Thus, »2 Is not well
defined and should be viewed as a calibration parameter.
niffusive Exchange. Microcosm experiments (Dickson, 1981) with lindane
provided an alternate means of estimating ^ The data analysis resulted
in a value of K, - 50 cm/day. Since DOE and lindane have comparable
«olecular weights (352 and 291, respectively), a value of ^ - 50 cm/day
has been used for both compounds.
Chemical Decay. The DDE and lindane decay rates which have been used
in the modeling analysis of the quarry experiment are summarized in Table
8-3. As shown in this table, consideration was given to the following
types of chemical decay: oxidation, biolysis, hydrolysis, photolysis, and
volatilization. A brief description of the basis for assigning the race
coefficients in Table 8-3 follows.
TA8LZ 8-3 SUMMARY OF DDE AND LINDANE DECAY COEFFICIENTS (I/DAY)
Hydrolysis
Oxidation
Biolysis
Photolysis
Volatilization
Water
.0018 to .0257
.0
0.0 .
.00026*
.000 18C
Lindane
a .0018 to .0257a
On
0.0
Water
d
0.0
0.0
0.013!
0.0201
DDE
Sediment
0.0
0.0
0.0
*7 < pH < 9, (Dickson, 1981)
bQuIrry K (lab) - .00045/hr, Kex - US/.. ^ - 13.9 .. f - 0.5, (Dickson,
1981) P
^Average of 2 estimates in Table 10-5 .5
(1) £ aegr - 1.5 x 10 3 m/day using H - 1.5 x 10 ) and Kg - 100) HL
(ii) K^l^ej - 3-6 * l0"3 m/day (ItadMy, 1975)
dUSEPA, 1979
eProgram SOLAR (After Zepp)
fBased on lab data (Singmaster, 1975)
"204"
-------
DDE. The estimation of photolysis rates for DDE have been based on the
methods developed" by Zepp et al. (1977). This analysis makes use of the
USEPA computer program SOLAR to calculate site specific, seasonal, depth
averaged photolysis rates. Using the inputs which are summarized in Table
8-4, SOLAR was used to compute seasonal depth averaged DDE photolysis rates
for the quarry which ranged from .0034/day in winter to .0239/day in
Bid-summer and averaged .0130/day overall. The annual average rate was
used in the model calibration analysis.
TABLE 8-4 PROGRAM SOLAR INPUTS USED TO COMPUTE DDE PHOTOLYSIS RATES'
Quantum Yield J'j|
Depth (meters) «-°
Refractive Index J«8*
Latitude *°0
Longitude 85
UaV(S Water Extinction Molar Extinction
Coefficient (Ke.Q) Coefficient
( I/cm) ( liter /nole-en)
§ I
3 -S
-0078
320.0 -0078
S:S SS
volatilization rates for DDE were based on laboratory studies by
Singmaster, 1975. For these experiments, 900 ml of water containing about
I ng/1 of DDE was placed in a 5 liter flask. Air was passed through the
unoccupied volume (4.1 liters) overlying the water at a flow rate of 4.5
1/min. This corresponds to a wind velocity of 10 «/hr which is quite
small. Fortunately, however, the quarry is shaded on all sides and a low
velocity is probably realistic. 'The half life of DDE ranged from 1.2 hours
205
-------
to 1.9 hours, for three water samples from different natural systems. For
a half life of 1^3 hours, the" corresponding volatilization rate is \ -
11.I/day. Assuming an approximate depth of water in the flask of 2.5 cm,
this rate Is equivalent to a surface gas phase transfer coefficient of
r - 0.28 meters/day. The effective volatilization rate in the
air-water
quarry can be estimated as
K -K C8"9)
S air-water
Thus, for Hj - 13.9 m, 1^ - 0.020/day.
Although DDE is a product of the hydrolysis of DDT, DDE itself is
difficult to hydrolyze. Wolfe et al. (1977) reports a half-life of greater
than 120 years at a pH of 5 and 27°C. Other investigators (Eichelberger
and Lichtenberg, 1981) have observed less than a 2.5 percent decrease in
the inicial DDE concentration of 10 ppb over an eight week period of time.
This corresponds to a first order hydrolysis rate of K^ < 4.5 x 10* /day.
Since decay rates of DDE due to photolysis and volatilization were found co
be several orders of magnitude higher than this, the effects of DDE
hydrolysis have been neglected in this analysis.
No information could be found on the oxidation or biolysis rates of DDE
in natural water systems, although it appears reasonable to assume chac
they are small relative to the other decay rates considered, and can
therefore be neglected for the purposes of this analysis.
Lindane. The decay rates for lindane, which were considered in the
model analysis, are also summarized in Table 8-3. As shown, oxidation and
biolysis rates were neglected. The range of hydrolysis rates in Table 8-3
were estimated from laboratory studies (Dickson, 1981). The measurements
were made over a pE range of 5.0 to 9.3 and at lindane concentrations of
about 0.2 to 8.0 mg/1. These lindane concentrations are considerably
higher than the observed levels during the quarry experiment. Since the pH
of the quarry water was approximately 8.3, the test data which was
206
-------
considered was limited Co Che pH range of 7.0 to 9.0 and to lindane
concentrations of" less than 0.5 mg/1. The resulting range of hydrolysis
rates was K - 1.8 x 10'3 to 25.7 x 10'3/day.
The volatilization rate of lindane was estimated in two ways, as shown
in Table 3-5. The first approach makes use of Henry's constant for lindane
of H - 1.5 x 10"5 (dimensionless) and results in an estimate of the overall
.ass transfer coefficient of K^.^ - 1.5 * lO'3 m/day. This value is
in reasonably good agreement with the value of Kalr_wacer ' 3'6 x 10
«/day which was reported by Jorgenson (1979). Using the average value of
ic - 2 5 x 10~3 m/d and a water column depth H. - 13.9 m, Equation
air-water .4,
8-9 yields Kair^,ater - 1-3 x 10 /day.
The measured photolysis rate for lindane in quarry water is reported to
be K - .00045/hr. This value must be corrected to field conditions using
P
che expression:
K (field)
P .. el
where f is the fraction of daylight hours, Hj is the depth of che water
body and Ke is the diffuse attenuation coefficient for the range of
ulcraviolec Radiation responsible for photolysis. From the discussion of
DDE photolysis presented previously, Kfl - 1.5/meter (base ). Using HI -
13.9 meters and f - 0.5, Equation 8-10 yields a lindane field photolysis
rate of K. - 2.6 x 10* /day.
P
The photolysis and volatilization rates which have been estimated are-
more than an order of magnitude lower than the estimates of the hydrolysis
rate which ranged from 1.8 x 10'3 to 25.7 x 10~3/day. Since the hydrolysis
rate was assumed to effect both water column and sediment chemical
concentrations, it was clearly the dominant sink of lindane.
207
-------
TABLE 8-5. ESTIMATES OP LINDANE VOLATILIZATION RATE
i. Liquid phase transfer coefficient
K02 - 0.3/day (NTSU 3/6/81)
B1 0.333 a
Therefore K, - .333 a x 0.3/day - 0.1 a/day
Gas phase transfer coefficient
*H.O not measured as yet
Use *H20 @ wind speed - 0
Therefore K - 100 a/d
Henry's Constant H - 1.5 x 10~5 (dimensionleas)
1 - 1 ^ _
*air-water' Kl H
_
*l lOOxl.Sxlo"5
" Tools
Therefore K l.SxlO'3 a/day
15xJO_
L3.(
H. 13.9' a in Quarry thus
1.1 x I0"4/day
. R - i.SxlO"4 a/hr - 3.6xlO"3 a/d
air-water
2.6 x
Using average of above estimates: Ky - 1.8x10 /day
.208
-------
8,2.5 Chemical Inputs
The 'chemical mass loading rates of DDE and lindane to the quarry may be
well represented by an instantaneous release. At the start of the
experiment, Mj - 2.77 grams of both DDE and lindane were added uniformly
over the surface of the quarry and there were no other loads of either
chemical before or after this initial dosing.
8.3 Results of Model Calibration Analysis
The quarry geometry, particulate transport parameters, chemical
transfer rates, and chemical decay rate coefficients which were discussed
in the "previous sections of this report were used to compute the temporal
variation of DDE and lindane in the water column and sediment of che
quarry. The model results and observed data are compared on Figures 8-8
and 8-9 for DDE and lindane, respectively. The calculated and observed
total chemical concentrations in the water column and sediment, Cri and
C , are presented. The observed total sediment concentrations were
obtained by multiplying the reported sediment chemical concentrations in
units of ug chemical/kilogram wet solids by Che bulk density of 1.2 kg wee
solids/liter of sediment. Computed concentrations are also presence* in
cerms of the equivalent mass of chemical in the water column and sediment
in the upper panel of each diagram.
The DDE. calibration results of Figure 8-8 were obtained using partition
coefficients of ^ - 50,000 I/kg and *2 - 10,000 I/kg. The calculated
water column DDE concentrations are in very good agreement with the data.
During the first 10 days of the experiment the calculated and observed
water column concentration decreased from approximately 53 tig/1 to less
than 10 ng/1, while the total sediment concentration of DDE increased
sharply to more than 25 ug/1. The rapid decrease in the water column DDE
and the corresponding increase in the sediment DDE is due to adsorption of
DDE onto the water column solids which settle to the active layer. After
209
-------
CO
-30
1000
100 -
C 10 -
tu
o
o
o
o
DATA' 0
W At 8R ANT, 1973 -30
WATER COLUMN
f. -0.20
0 9Q 100 ISO 200 230300 330
TIME AFTER RELEASE (days)
i-O I
°^9P 0
ao
90 100 190
TFME AFTER RELEASE (days)
90 IQO ISO 200 290 300
TIME AFTER RELEASE (days)
y. .9.77,,.... WATER COLUMN
L
fiSUjLT, T T
1 1£ \ 3. *
1 1 1 1 I I 1
SEDIMENT LAYER
3 90 «00
FIGURE 8-8. MODEL CALIBRATION FOR DOE
210
-------
WATER COLUMN
fp,s.OOI
SEDIMENT LAYER, fP2v988
-90
1000
- ioo
UJ
Z
10
0.1
-30
8
6
o»
,3 4
DATA: 0
WAY9RANT.I973 -SO
SO 100 190 200 250 300
TIME AFTER RELEASE (doys )
WATER COLUMN
WT» 2.77gronn
I
90 100 190 200 290 300
TIME AFTER RELEASE ( days 1
3SO
0(8.9)
SEDIMENT LAYER
MEAN » STANDARD OEV
O-i. S cm
O 1.9 -3.3 cm
3.9-5.5 cm
90 <00 <90 200 290 300
TIME AFTER RELEASE (days)
390 «00
FIGURE 8-9. MODEL CALIBRATION FOR LINDANE
211
-------
day 10, there is a ouch more gradual decrease in the water column DDE
concentration, since the net flux of solids to the sediment is substan-
tially reduced*
The calculated sediment DDE concentration is a maximum of 34.5 ug/1 by
approximately day 40, at which time a local equilibrium condition between
Che water column and sediment concentrations is approached. After day 100,
.he calculated water column concentration of 1.3 ng/1 begins to decrease
slowly, while the sediment concentration of slightly more than 30 ug/1
begins to decrease at a rate which is in proportion to the water column
concentration. All of the removal of DDE occurs in the water column as a
result of decay due to photolysis and volatilization. As the water column
concentration decreases, DDE diffuses from the sediment (the resuspension
rate is zero) into the overlying water, and hence the sediment concentra-
tion decreases as well. As long as there is water column decay, equili-
brium conditions between the dissolved concentrations in the water column
and interstitial water cannot be established and the decrease of water and
sediment concentrations will continue until the DDE is depleted from the
system.
1C is of interest to note that on day 100, 70 percent of che inicial
2.77 grams of DDE remains in the water column and sediment layer of che
quarry. This is so in spice of che water column decay race of .033/day.
The persistence of DDE is due to the relatively high percentage of che
remaining chemical mass which is stored in the sediment layer, and hence
not available for photolysis or volatilization. The model calculations
show that more than 96 percent of the remaining 1.93 grams of DDE in Che
system at day 100 is in the sediment layer.
Lindane model calibration results are compared to the observed water
column and sediment data on Figure 8-9. The water column partition
coefficient of ^ - 250 I/kg, which was determined from laboratory studies,
was used in conjunction with a sediment value of »2 - 50 I/kg. A
hydrolysis rate of K^ - .0025;day, near the low end of the range of
laboratory measurements in Table 8-3, was also assigned. In contrast to
212
-------
the water column DDE concentration, the calculated and observed lindane
concentrations decrease at a much slower rate. The sediment lindane
concentration again increases sharply during the first 10 days as a result
of adsorption onto and net deposition of water column solids, but the
increase to between 2 and 3 ug/1 In ehe sediment is an order of: magnitude
lower than it was for DDE. This is due to the much lower partition
coefficient of lindane in comparison to DDE.
The mass of lindane in the quarry on day 100 of 2.07 grams, 75 percent
of the original dosage, was similar to the mass of DDE which remained at
this same point in time. In sharp contrast to DDE, however, more than 75
percent of the remaining lindane was in the wacer column. This observation
has important implications with'regard to the fate of each chemical,
lindane, which has a total effective removal rate coefficient of K, -
0.0036/day Is removed from the system over the next 100 days at an average
rate of 5.2 og/day. In comparison, DDE has a total removal rate
coefficient of K_ - 0.0330/day, an order of magnitude higher than the rate
coefficient for lindane, but is removed at the significantly lower average
rate of 1.9 mg/day. Thus by day 200, there is more DDE than lindane
remaining In the quarry, and as time goes on, DDE will continue to be che
more persistent of the two chemicals.
8.4 Model Verification and Projections
During the course of conducting the analysis of the quarry data, it was
discovered that several quarry sediment samples were collected and analyzed
for DDE approximately five years after the initial dosing of the quarry.
Although this followup sampling and analysis was of limited scope, it does
provide a suitable basis for what can be considered to be a preliminary
verification of the model. Thus, the calibrated model was used to project
the DDE and lindane levels in the quarry for the 12 year period of time
from June 27, 1972 to June 27, 1984.
The followup sampling of the .quarry sediment was performed on June 21,
1977-. The results are summarized in Table 8-6. As shown, two nethods were
213
-------
used for - sampling. In each case the depth of sample was only known to
within a rough approximation. The reported DDE concentrations on a solids
mass basis were converted to volumetric concentrations and then adjusted to
a concentration range which reflects the uncertainty in the sampling depth
and which corresponds to an assumed depth of DDE penetration of 1.5 cm.
These DDE concentration ranges, shown in the last column of Table 8-6, are
3.4 to 11.2 ug/1 for Sample A and 2.9 to 4.2 ug/1 for Sample B. These
concentrations represent almost an order of magnitude decrease in the
sediment DDE concentration since the time of the quarry experiment. The
DDE level in water column samples collected at the same time as the
sediment samples was less than the detection limit of the analytical
technique which was employed.
TABLE 8-6. SUMMARY OF SEDIMENT DDE DATA FROM JUNE 21, 1977
Sample
Designation
Approximate '
Description Depth DDE Concentration
of Sampling of Sample Reported CT
Technique (cm)
(ug/\cgw)
2.8
(ugh)
3.4
Depth
Adjusted DDE (
Concentration
(ug/1)
3.4-11.2
2.9-4.2
A Composite of £ 5 cm
3 samples
with an Ekman
dredge from
different
sites in
quarry
B Sample was 2-3 cm 1.8 2.2
manually
"scooped" from
sediment in
shallow gently,
sloping area of
quarry
*Based on previous sampling experience and visual observation
bSame analytical technique as original thesis data; may be used to make
direct comparison with Uaybrant data
CcT2 - [ug/(kg wet sediment)] x 1.2 kg wet sediment/liter
*Assumes DDE all in top 1.5 cm of sediment layer
Note: Water column DDE concentration was less than detection limit of 30
ng/1
214
-------
Model projections for DDE and lindane are shovn on Figure 3-10. These
projections are simply a continuation of the model calibration runs with
kinetic and transport parameters held constant in time after day 10. The
initial sharp decrease of DDE in the water column occurs during the first
year and is followed by an exponential rate of decrease over the next 11
years. The sediment concentration time history parallels the water column
profile, and at the time of the June 1977 sampling, the calculated sediment
concentration is 5.6 ug/1. Considering all of the simplifying; assumptions
in the modeling framework, the uncertainty associated with many of the
parameter estimates, and the precision of the data, the calculated and
observed concentrations at t - 5 years are considered to be in excellent
agreement. The fact that the calculated water column concentration of 0.2
ng/1 is less than the detection limit of the analytical procedure used to
measure the 1977 water column DDE concentration, gives further credence to
the validity of the modeling analysis. The model results also indicate the
projected DOE levels in the quarry sediment 10 years after the original
dosing, in June 1982, will be approximately 1 ug/1.
It is unfortunate that no attempc was made to measure lindane at the
cime of the 1977 sampling. The model projections indicate that the lindane
concentration in the water was finally reduced to the same concentration as
DDE at about t - 5 years, while the sediment lindane concentration was 2 to
3 orders of magnitude lower than the sediment DDE concentration at chac
time. The estimated mass of lindane remaining in the quarry of 0.014 grams
is less than 5 percent of the mass of DDE in the system at that time (0.330
grams), even though the estimated water column decay rates for DDE were an
order of magnitude higher than the decay rates for lindane. This is
surprising considering that the lindane concentration in the water column
was much higher than the concentration of DDE during the first year,
thereby giving the appearance that lindane was the more persistent
chemical. These model results underscore the significance of chemical
partitioning on chemical fate and highlight the importance and utility of a
modeling framework which incorporates realistic mechanisms for water column
and sediment interaction.
215
-------
Ok
100
DOE
LINOANE
SAMPLE DESCRIPTION-
A. EKMAN COMPOSITE
"SCOOP"
024 6 8 10 12
UUNE'T2I IJUNEBZ'I
TIME AFTER RELEASE (YEARS)
DATA*
ZEPP AND STACEY, UNPUBLISHED
~ IOO
ZUI
UJZ
UJ -
cn-J
2
o
Ctt»O.I Ol
OOI
h ti L
"02 4 6 6 10 12
UUNE'721 |JUNE'B2I
TIME AFTER RELEASE (YEARS)
FIGURE 8-10. LONG TERM MODEL VERIFICATION / PROJECTION
FOR LINDANE AND DDE
-------
REFERENCES
-------
SECTION 9.0
REFERENCES
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Hydraulic Div. ASCE 110(6): 707-735, 1984.
Karickhoff, S.W. and K.R. Morris, "Sorption Dynamics of Hydrophobic
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218
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Karlckhoff, S.W. Brown, D.S. and T.A. Scott
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Krishnawami, S. and D. Lai, "Radionuclide Limnochronology," Chapter 6 in
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Lyman. W.J., Reehl, W.F. and D.H. Rosenblatt, "Handbook of Chemical
Property Estimation Methods," Environmental Behavior of Organic Chemicals,
McGraw-Hill Book Co., New York, 1982.
Mackay, 0. and P.J. Leinonen, "Rate of Volatilization of Low Solubility
Contaminants fro. Water to Atmosphere," Environ. Sci. Tech., 9:1178 to
1180, 1973.
Mackay, D.,,Paterson, S., Eisenreich, S. and M.S. Simmons, "Physical
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Mackay, tt...and B. Powers, "Sorption of hydrophobic chemicals from water: A
hypothesis for the mechanism of the particle concentration effect,
Chemo sphere, in press, 1986.
F.T. Manheim, "Earth Planet Science Letters," Yolume 9, p. 307-309, L970.
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heavy metals to suspended solids in the Flin-t River, Michigan, Environ-
mental Toxicology and Chemistry 5: 609-623, 1986.
D. Neptune, "Priority Pollutant Frequency Listing J^"1^
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Effluent Guidelines Division, USEPA, November .4, 1980.
D.J. O'Connor, "Physical Transfer Processes,' In: Modeling of Toxic
Substances in Natural Water Systems, Manhattan College (Summer Institute),
1980.
O'Connor. D.J. and J. Connolly, "The Effect qf Concentration of Absorbing
Solids on the Partition Coefficient," Water Research, Vol. 14, pp 1517 to
1523, 1980.
Robbins, J.A. and D.N. Edgincon, "Determination of Recent' Sedimentation
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Robbins. J.A., Krezoski, J.R. and S.C. Mozleyi "Radioactivity in Sediments
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219
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220
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-Methoxychlour and DDT Degradation in w««r' V? "1077 to 1081
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221
-------
APPENDIX A
DERIVATION OF STEADY STATE AND TIME VARIABLE SOLUTIONS
i
The mass balance equations for the water column and sediment
segments are:
- - =>
Wl m W21 £D2 CT2 i
* + ^^"^~~J^~~~~^~" * ^^
dt
W21
f e .f c
' "f P2 CT2 H f P2 CT2
H
H2 2
The tollowing definitions express the transport velocities in
terms of equivalent first order reactions rates (I/unit time)
.f
Ksl H. Cpl
M
K
=
s21 H p2
K - f (A5)
KS2 H £P2
-------
(A6)
The following ratios occur frequently:
(A7)
f /f (A8>
£dl/cd2
8 * »lHlfp2
The latter equation defines the sediment capacity factor that has
been discussed previously in the body of the report.
The sum of all- water column reaction rates is denoted by:
(A10)
a Kl * Ksl *
and if the outflow term is included a prime is used:
Similarly, the sum of all sediment reaction rates is denoted by:
-2 ' *2 *
-------
KS21
The complete suras are denoted by:
s
ST " Sl + S2
The solution of the differential equations is found using La
Place transform methods. Let
cT1- /«<«.-* dt is the La Place transform of CT]> (t). The La Place
transform for the derivatives are:
' ~- dt - PCT2 a °'
cT2(0) » 0. The -input load (actually a step function starting at
t » 0) becomes:
1
WT (A18)
-------
Use these expressions in the mass balance Equations (Al,A2)
yields:
+ zKd)CTi (A20)
The use of La Place transforms converts differential equations
into algebraic equations thus simplifying their solution. Ir
particular the sediment layer equation has the solution:
+ zKd (A21
CT2 ~ p * S CT1
and using this result in the water column equation yields:
(p + s1) - ("*s21 * "^dM^sl7" * ***d) C-, T (A22
1 P + S2P°lcol
so that the water column concentration becomes:
w P * s.
r a T 2 (A23^
Tl TS-S , * -!/ * s i - h(Kg21"- Kd)(Kgl/H + ZKd)
In order to find the solution in the time domain it i«
necessary to simplify the denominator of Equation (A23)
Expanding the terms in the denominator yields:
p2 + (s' + S2)p * S'S2 - h(Kg21 * Kd)(Ksl/h * 2Kd) (A24^
The coefficients of p2 and p.. are in their simplest form; however
the"constant term can be further simplified as follows:
*
31S2- h(Ks21 * Kd)(Ksl/h * 2Kd>
-------
KS21 * K»2*
The complete sums are denoted byi
ST - Sl
ST ' 4 * S2
The solution of the differential equations is found using La
Place transform methods. Let
CT1- =T1(t,e- = °'
cT2(0) *» 0. The input load (actually a step function starting at
t * 0) becomes:
1
WT (A18)
-------
Use these expressions in the mass balance Equations (Al,A2)
yields:
(A19)
- S C + (Ksl/h+ ZKd)CTl
'2
The use of La Place transforms converts differential equations
into algebraic equations thus simplifying their solution. In
particular the sediment layer equation has the solution:
Kal/h + zKd c (A21)
CT2 9 ~ P * S2 CT1
and using this result in the water column equation yields:
, ^ g.j . (hK321 * hKdHKsl/h * ZKd) CT1 - UT (A22)
1 P * S2 P0!^!
so that the water column concentration becomes:
^2 _ _ (A23)
Kd)(Ksl/h * ^d'
in order to find the solution in the time domain it is
necessary to simplify the denominator of Equation (A23).
Expanding the terras in the denominator yields:
^ * S2)p * S'S2 - h(K321 * Kd)(Kgl/h * «d)
(A24)
The coefficients of p2 and p.. are in their simplest form; however
the constant term can be further simplified as follows:
*
Sis2- h(Ks21 * Kd)(Ksl/h * 2Kd)
-------
(K1 * Ksl+ zhKd * '1/t:ol)(K2 * Ks21 * Ks2* Kd}
- h(Ks21* Kd)(Ksl/h * 2Kd)
(K1 + l/tcl] S2 * Ksl(K2 * Ks21J * KslKs21 * V^d (A25)
Kg2)
- KdKsl - zhKdKs21
- S2(K1 * a/tQ1)
where the underlined terras cancel. The denominator can now be
factored using the solution for the roots of a quadratic
equation. That is:
p2 + S.J.P + S1(K1 * l/tol)
U26)
* (K2 * Rs2)(s1 - KX) (p + gL) (P + 92)
where
, -
tl(
s, -* l»2(Kl * l/t01> * (K32 * Ks)(sl " K1)1.1/21(A27)
-
2
The" plus sign is used for g^ the minus sign for g2. Using these
roots the solutions for the water column and sediment concentra-
tions become:
W ^ * 32 -
CT1 - Q^I p(p + gi)(p * 92) (A28)
-------
f* «
CT2 Qt P
-------
The key to the simplified solution is to compute the ratio of
the particulate concentrations in the sediment, r2, to that in
the water column, r.. These concentrations are defined as the
mass 'of chemical on the particles per unit mass of particles.
The volumetric particulate- concentration in the water column,
c ,, is found from the total concentration by applying the
fraction of total chemical in the particulate phase, fpl« Then
dividing by the concentration of particles, n^, yields the
particulate concentration:
r , (A34)
1 "I
- , (A35)
2 n»
The ratio, r2/r^ is found using these equations and the steady-
state solutions Equations (A32,A33). The result is:
£P2 CT2/m2 * £P2 mi . (Ksl/h + 2Kd) (A36)
Cl
where Equation (A9) has been used for 8. Note that the loading
term (WT/01tQl) and the root product (g1g2) cancel in the
expression for the ratio: r2/r^.
It remains to simplify the terms in Equation (A36). The
settling velocity term becomes:
fsl . ^ f I'l' - i !l t (A37)
r
-------
The expression zh/s simplifies to:
QI n».,H..c |
1 2 2 pi
with the depth ratios cancelling. The ratios fp2/fd2 and fpl/fdl
are found from their expressions:
(A39)
f 3 1 (A40)
so tnat:
l
cdl A A
and, similarly,
'!* -»2.2 (A42)
Cd2 *
Using these Equations (A41,A42) in Equation (A38) yields the
remarkable simplification:
.zh.Il (A43)
And, finally, using Equations (A37,A43) in the expression for
f Equation (A36); yields:
-------
The key to the simplified solution is to compute the ratio of
the particulate concentrations in the sediment, r2, to that in
the water column, r,. These concentrations are defined as the
mass 'of chemical on the particles per unit mass of particles.
The volumetric particulate- concentration in the water column,
c ,, is found from the total concentration by applying the
fraction of total chemical in the particulate phase, fp]>. Then
dividing by the concentration of particles, n^, yields the
particulate concentration:
(A34)
. £P2 CT2 (A35)
2 m2
The ratio, r2/ri is found using these e2 mH« H m2 p2
sl =1 . o2 lf (A37)
~ £
-------
ii« , * 3lfd. ("2/'l)
'2 - «"» P2 "2 " (M4)
where all the equivalent reaction rates have been replaced by the
actual mass and decay transport parameters.
The properties of this simplified expression have been
discussed in the body of the report. As noted there, if the
particle mass balance condition is used:
wlml * (W21 * W2J m2 '
this ratio is further simplified to:
-w
The steady-state solution for the water column concentration
can now be simplified as follows. The solution, Equation (A32) ,
becomes
WT _ *2 __ _ _ ! - (A47)
CT1 ' 0 .l + lAol) * (K2 + Ks) Ua *
where the- product g^ is replaced by its equivalent expression,
Equation (A25) since g^ is the constant term in the quadratic
Equation (A24). Alternately" the product can be computed directly
using Equation (A.27). Dividing by s2 yields:
-------
CTI
S2
At this point it is necessary to make the key observation from
Equation (A36) that:
a _Z
rl
r2 Ksl + d (A49)
^ "-
so that the expression for the water column concentration
becomes :
CT1 ' Q 1 + 1A * 8 /rL IKS1 * K,2) (A50)
or:
WT i
CT1 S 0 1 * t K (A5i)
where
whicn is the final working form of the solution. Note that the
particle flux balance, Equation (A45), is not required to be true
for this solution to be valid. The general case, Equation (A46),
can be used for *2/rl in the solution-
The dissolved and particulate fractions in the water column
follow from the expressions:
*
=, f c (A53)
cdl fdl CT1
-------
(A54)
cpl " fpl ^1
The particulate concentration in the water column is:
. (ASS)
rl a cdl/nl
And using either Equation (A44) or (A46) for r2/r;, yields r2.
The dissolved concentration is the sediment segment follows
most directly by observing that:
(A56)
rl '1 cdl
so that the dissolved concentration ratio follows from the
particulate concentration ratio:
Cd2 a Ii II (AS7)
Cdl '2 Cl
Finally/
(ASS)
Cp2 ' W2r2
and:
Hence all the relevant steady-state concentrations follow from
the key expressions for CTI and ^2/'rl*
Time variable Solution - Approximation
NO useful simplified" exact expressions have been found for
the time variable solutions, for cT1(t) and c^U), Equations
-------
(A30,A31). The difficulty is that the characteristic roots, g]>
and g are given by a complicated expression, Equation (A27).
However, for most practical applications the magnitude of the
terms is such that a useful and quite accurate approximation is
available. Consider the terms in the square root of Equation
(A27) repeated here for convenience:
m
f32(*l + Xtan + (2 + .2)(l - l)l}l/2 (A60)
The denominator of the fraction is (s£) - (s{ + «2) , which is the
square of the sum of all the equivalent reaction rates in the
water column and sediment segments, including the outflow term,
1/t Hence if any of these terras is -large, then s^ will be
larye and its square will be larger still. This suggests that
the fraction will be small relative to one, thus the square rooc
can be approximated as:
(1- c)1/2 .1-$ (A61)
A numerical example illustrates this approximation: 1 -
(U.l)1^2 » 0.9487 whereas the approximation yields 0.9500, which
is an error of » 14%. Hence in this approximation:
1 m ^r [1 * (1 - -y)l (A62)
4
where
s K 1/t v. ,K, K ,i,K , _,_ zhK,.
4 t32(Kl * i/col)^ (R2 * 32) ( si + dj. (A63)
c
-------
Since t is assumed to be small, the large root, g^ becomes
(using the plus sign):
«1- ST a Si + S2a Sl * S2 * 1Xtol U64)
i.e., gx is approximately the sum of all water column and
sediment equivalent decay rates and outflow rate.
The small root, g2, is found using the minus sign:
ST
KK
32(K1 + l/tol) * <2 * s2)(sl > d) (A65)
ST
using the definition of c. Further, g2 can be simplified to
give:
, . ,.,. ,
Again, the key expression for Br2/rlf namely, Equation (A49), can
be used to express g2 as:
01^.K2>KS2)1
which yields the final form:
(A68)
-------
These Equations, (A64,A68) give the approximations that express
the characteristic roots as useful and comprehensible expres-
sions.
The First Plateau
The fact that g, is usually much larger than g2, since
£2 c (A69)
gl " 7
and c is usually small, leads to the following observation.
Consider a time, t , such that
t , !_ (A70)
P 91
After this time 'has elapsed, the first exponential term in the
time variable solution exp .1-Sj.tp) is quite small (exp(-3) =
0.05) whereas the second exponential term, exp (~(32t?) =
exp(-3e/4) » 1 is still approximately one for c small. Hence the
time variable solution, e.g. (A30), becomes:
, 2
e * o, e 1.
and
CTi.plateau . (_|. + -,,
Since y2 « glf (g2 - g^) - g± so that this expression becomes:
0
cT1-plateau - - * --,
-------
Using the approximation for gx, Equation (A64), yields
W 1
cT1-plateau = g- (A73)
or
cT1-pla»aU . Jjfc ^r^;
Hence after a time such that t » 3/g^ the solution has reached
this plateau concentration. The rate at which the solution
approaches steady-state is then determined by the magnitude of
g , the small root.
-------
Table B-l.
OCCMBEMCE OF Miami POILUIAMIO IN paiu INFIUCNIO
PIANIO i 10 40
PABAMMSO.
IIHC
CfAMIPE
coma
lOlUIHf
Cll» ON I UN
1C 1KACIU-OOOE IHVLEME
NflHIIfNC CMIOOIOC
M8I2-CIHILHCKVLI PNIMALAII
CHLOIIOFOkll
IftlCIUOMOCIMIlfNC
Ifl.l-HUCHlOROEINANf
CIIIUkfNICNE
NICKEL
PllfNOl
NEHCUfcV
OI-M-kUIIL PMIHAIAIE
I (All
.1.2- IfcANO-eiCUlOOOEIimCNE
f Nil IIC
UIVI ftEMIU PMIHAIAII
CAtMlUN
OIIIIIU rUIMAiAlf
HAFHIHALEMC
I . I -lUCHLOBOf IIIANC
PEMIACIILOROPIICNOL
OAHMA- SIIC
I . I -lilCHLOftOEIHIlENf
1.2-MCIIlOltatfMlCNE
PlirHAHIIIfcENC
4MIIM.ACENE
|.4-PICIILaROBCMIENE
AhSCHIC
1.2-MCIIlOROf INANE
ANIINOMV
ClllOKOHCMIfME
lllHfllllL PIIIHAIAlf
MCIIHL CIU.Ot.lliE
1.2.4- IMCULOhOkE NIf HC
1.4-PIMEIIIVLPIIENOL
CAEfcOM ICIfcACIILORIliE
I* Kill OaOFLUOROHCIIIAMf
6CICHIUH
P I CHI OfcOthONONC IHANC
I.I.2-IKICIUOBOCIHANC
|.2-l>ICIILOkpfkOfAMf
DI-M-OCIVL flllllALAlf
FlUOf.AHIIICHC
POllUfANia NOI 1 1 Sift" MEM NEVCA PCIfCICB
i occuKimcra AI.E aABtn ON Ait maiicm BAHi-iEa
^ P01IUIAHIB ftCPORlEP AB LEfia IMAM Ilir KCIECIIOM IINII
HI. nurnHriBHld fraflfllifB AKF A8SIIHCP HOI l-fllCiri<
NUNOEU OF
OAHPLEO
ANAim*
202
10 «
101
lao
IBI
laa
IBS
1B7
1BO
IBO
lao
100
102
200
101
101
202
iao
iao
2B7
101
1B7
IBO
107
200
280
207
207
207
207
201
100
101
207
200
207
200
200
200
202
200
200
200
200
207
207
NUNtC* OF
lines
OflfClEO
202
201
201
274
240
271
24A
243
211
140
114
111
124
120
100
1*4
IBS
174
I7ff
173
143
137
131
142
0*
04
73
74
47
37
32
4*
41
42
jf
14
11
11
20
20
23
23
24
24
22
21
21
20
20
PCRCCMI OF
BANPIEO UHEO.E
PCICCICO
100
100
100
4
3
3
1
1
1
0
03
00
7*
7*
71
70
44
Al
41
41
37
34
31
4*
11
Iff
14
14
11
20
10
17
13
13
14
11
II
II
10
10
7
7
7
7
MINIMUM
VALUE HAIIMUN
UNI 10 miEcico VALUE
UO/L 22
UO/l
UO/l
UO/L
UO/L
UO/L
UO/L
UO/l
UO/l
UO/L
UO/l
UO/l
UO/L
UO/L
UO/L
NO/I 20
UO/L
UO/L 1
UO/l
UO/l
UO/L
UO/L
UO/L
UO/l
UO/L
UO/L
NO/L 2
UO/L
UO/L
UO/l
UO/L
UO/L
UO/L
UO/L
UO/L
UO/L
UO/L
UO/L
UO/l
UO/L
UO/L
UO/L
UO/L
UO/l
MO /I
UO/l
UO/l
UO/l
110 /I
230
7300
2100
11000
1100
9700
4*000
470
410
1000
30000
710
3*70
1400
120
4000
140
1340
100
1340
340
1000
41
ISO
14
440
1*00
111
440
1
1
100
BO
74000
1*1
1300
110
1*00
4100
33
1*00
1*0
10
22
4400
1)3
2400
110
3
-------
Table B-l. (Continued)
occuumi or
roIM
2.4-lilCUlOCOrHfNOl
PIMM
1.1-PICIUOfcOkCMICMC
VlHll
rc»-iata
a .«. « - 1 a i cut oaorMCNOL
MflllVL
afftULIUH
ACCMAtUIIKNC
(III. V if Hi
|.a-MMIAMIIIftA«MC
»f||A-ailC
rAtACllLOIONCU
2-ctiiflLariiCMOL
.IIUtllUH
llfMAClliatOUNliNf
INOCMOII.3.1-C.OI
IkMIO
AIIUA-(Nl>0(UirAM
Clll flKOi IIIAHC
Qill-ClltaHOCIMVOIVI MIUAHE
l.«-»lNtOflUOI>«NIIUHC
11.12-bfNIOflUOkAMlllfNC
If kAClllOI.On MANE
2 -Clll OfcOHAl IIIIUICNC
llflACIIiaiflbUIABUNf
3.<-|i|HlIfi010IUCMC
HUMtCa Or MUHIfO Of f(
g Ann fa IIMIB a
aoa
aa> I*
aaa '
}ftg 19
2 ft!) 1 *
aaa H
aov H
aaa
aaa
ao»
aa>
aoa
aaa
aaa
aaa
aoa
aao
aaa
aaa
aa>
aa>
aa>
aav
aa*
aao
aa«
aa*
aaa
aaa
aaa
a?A
aao
aao
884
aa*
aa>
aa>
aa>
aaa
aaa
aaa
aa?
2fl»
307
207
aaa
lacfNi or
uirica UIICOE
iifcico uMiia
UO/L
bO/L
UO/L
UO/L
ua/L
MO/L
NO/L
UO/L
UO/L
UO/L
UO/L
« V
ua/L
UO/L
ua/L
MO/L
UO/L
ua/L
UO/L
ua/L
ua/L
UO/L
UO/L
UO/L
ua/L
UO/L
ua/L
MO/L
ua/L
UO/L
ua/L
MO/L
Ufi/L
MO/L
ua/L
UO/L
ua/L
UO/L
ua/L
UO/L
ua/L
MO /I
MO /I
NO/I
MO /I
i | ua/i
| | UOVL
| | UQ/l
I | ' na/L
IBB
MINIMUM
VALUE MAMMIII
BCICCIfO VALUf
i aa
1 04
a a»o
i aa
ao atoo
o aoo
aaoo 4tAoo
i n
i
10 IA4
i «
i ai
I »
I i«
100 1400
1 41
I a
i it
i a
1 01
4a 1000.
a too
a ai
1 H
i ao
i ao
10 aaoo
a a
a 10
a o
4»o ' avoo
1 10
«ao aaoo
a &
a ia
a a
a a
a a
A 11
1 >
110 "0
10 1000
10 40
310 aao
a a
a >
a »
a o
ai »>
101
D II
IfWI
rci
-------
Table B-l. (Continued)
OCCIMMMCC or Miomir roiiuiANis IN ioiy
ftAMI9 I 10 «
NUMMM or NUN*!* or risciMi or IHIHUN
SAHPlfC IIHCS SAHrLCS HIICM VALUC MAI I MUM
AMALVII* MlfCIf* ftCIICHk - ONUS II(CII» VALUE
VINI1 ilHfk > I HI V»ft I* I*
aas i il I UO/L 41 4«
ass i il I UO/L i f
«.«-frill 3M I il I MO/L IIO«
NO I ilBKU Ufhf NfVM PCIfClfD
t OCCUMfcCNCfl ARf MSIO OH All INftUfNI SANPLfe IAI>fN
roiiiiiAMif Mroaiio AS uss HUM HIE MirciiOH IIHII
AHIi UNCOHriKhCO IISIICIMS AM ASCUNrii HOI l
-------
Table B-2.
fABANfUR
1INC
corrco
MCIHUCNC CHLOMOf
UHUCHIOROCIMVICNK
MICKCL
101UIMC
IIIICIIlOIIOCIHVLfNC
OAHMA-IHC
rHCNOl
CAdHlUN
SILVCR
(IHVlMNICNf
fNICHI
LEAD
rtNlACHlOBOrMCMOL
PICMOHOIROHONCIMANC
OlflHVL fHIMAl»K
ANllHONI
ARSCHIC
UIVL MNIVL PHIHALAlf
iClCNIUII
l.l-OICIUOROdHfLCNC
CHI 0*OI> I mOMOWt IHANC
AlPHA-illC
HflHVL CULOIIIDC
CAtBOM
NAFIIIHAlfMC
.
M-N-OCIIL rillHAlAlf
U ICHl OKOriUOfcOHf I HANK
CHtOKOfrfHlfHf
MUHBfR Of
ANPlfB
AMAIV1CB
aoi
ait
loa
101
101
101
aii
101
101
101
101
101
101
aai
loa
101
aii
101
101
101
101
an
aii
loa
aii
101
101
101
141
101
101
101
101
101
loa
loa
loa
loa
101
loa
loa
101
loa
101
101
UNBCR Of
US!..*
fMMMI Of
»>
1
li
»
JJ
''
14
ai
ai
ai
ii
17
11
ia
13
ii
ii
it
to
10
I
t
;
"
«
»
s
i
!
a"
a«
11
ai
ai
M
it
o
SI
UMIIi
UO/L
UO/L
06/L
06/t
M0/t
oo/t
s
M
U0/t
U0/t
ua/t
uo/t
uo/l
UO/L
U0/t
uo/l
uo/l
UO/l
UO/l
UO/l
UO/l
UO/l
UO/L
NO/I
UO/L
UO/l
UO/L
UG/l
UO/l
ua.'i
UO/l
UO/l
UO/L
UO/L
UO/L
UO/L
UO/L
U«/l
MAKIHUH
VALUE
ai«o
1140
ass
A1000
170
07
iaoo
1100
7
1100
a 10
l«00
iaoo
01
oa
10
71
17
At
71
ISO
II
a
a7
11000
A
7«0
940
11
110
II
14
10
11
11
S
1
KOI
Ait *A«*
« PnillllAHIS
AB IfiB
fiieiiiiii LIHI.
. »..ni nrifflfD
-------
Table B-2. (Continued)
or luonii rouuiAMio IN roiu
ia «o
lild-IMICHlDMUIIMM
1.1.3.3-IEfftACIIlOftOEIHAHE
I 4 ft I CIU. OfcOM Mtf Nf
2-NIUOfHEHOL
4LI4.IN
MtlA-tllC
MMCtllVt FHIHALAIE
viHu nil at i PC
2-MHIAHIHftACENE
I 1-MCII1 OfcOfrCMZEME
»EIA-»HC
IIIAItlUM
ACEMAMIIIIENE
IIEflACHLOfc
iiEriACiiia* froiinc
4-NllfcOf HfNOL
SMItlUH
HIIHU MOMIM
rVftENE
rc»-i2«2
riUOfcANIIUHE
HEKACIILOfcOUNIENE
CkCSOl
3 ClllUlkOflllNOl
l.J'-MClllOfiOKNlllilHf
I>I3 MNIOfffKlCNI
CIU OfcOf IIIAHI
l«3-|>IIIICUVtllf|iMAIIIIf
NUNkiA or NUN»IA or rcRCtNi or
AHfiCS IIHC* SAHfiCI HUCRf
AHAlVUIt MUCIC* »CIICIC» UHIII
109
10>
101
101
101
101
109
103
109
103
101
101
3it
103
101
101
109
20t
109
109
101
103
109
103
103
102
101
2*4
102
103
103
103
103
2»S
9»«
101
103
102
101
101
101
UO/L
ua/L
ua/t
uo/t
NO/t
NO/t
uo/t
uo/t
ua/t
ua/t
uo/t
MO/t
ua/t
ua/t
MO/t
NO/t
uo/t
ua/t
ua/t
ua/t
NO/t
uo/t
ua/t
ua/t
ua/t
uo/t
NO/t
ua/t
uo/t
ua/t
ua/t
ua/t
ua/t
11 ua/1
1 1 ua/t
1 1 UC/l
1 1 00 /I
1 1 ua/t
i 1 HO /I
i 1 NO /I
1 1 HO /I
NININUN
VALUE
OCICCICft
1
1
1
a
1000
20
1
1
2
1
a
40
1
1
10
to
a
i
11
a
7SO
a
a
i
i
i
«o
«
ao
i
i
i
a
«
a
3
s
9
200
«0
300
NAHIMUN
VALUE
0
a
. t
i«
4000
1100
II
a
200
II
a
l>00
2
7
iaoo
aoo
230
12
220
a
2400
a
a
10
12
«
200
a
30
a
a
2
a
«
a
2
a
2
200
40
aoo
I fOIIUIAMIS NOI IISIIH HIM HI VIM PCIfClfK
t ocruMCNcrs AKE »ASEO ON AH SCCOHDAIH irriuiHi BANI-IIO
I fOUUIAHIS ICrOfclffi AS IliS IHAN HIE I'fllCIIOH IIHII
ANH UNCOMrikHEIi IfSIICIMS AftE ASSUIIfb MOI MIECICO
-------
Table B-3.
BUHMARV Or OBLBCTIO IMPUIIMT IOLUITAMT OONCntTRATIOH*
tOt fOIUa I THROUGH <0
no 1.,/u
TSS
Cldalue
ChicMlua
Coppef
Cyanide
uad
Mercury |ng/||
Michel
Silver
Slno
Btniena
l.i;i-Tflchloio«tlMMM
dilorofofa)
I.I-trana-Dlcltloroatkylan*
Ethylbentena
Methylana Oi|ocl4«
Tolucn*
Tr Ichlor o«thy l«n«
Phenol
N*phlb*l*n«
! |l-«lhyl hciyl)
Bulyl Baoiyl Vhihalak*
Ol-M-Bulyl Hilhlai*
OUthyl FhthaUta
Total Mela)*!*)
Total VblatlUa
Total Ac Ida
Total Baaa Heutrala
Avaraga o(
Haul Avaiaga Concanttatlona
III
III
II
III
ni
SIT
101
SSI
110
»
III
10
110
II
I
11
SOI
IIS
lit
It
SI
1
«s
II
t
I
IIM
Median of
»lant Avaraga ConcanltBHona
IIS
ISI
I
IOS
III
lit
SI
SII
S4
III
I
1
II
11
II
II
1
III
III
II
II
MOM Malytttad Awaiaqa of
ttant Avaiaga Concantiationa
111
aoi
II
Ml
as i
410
III
SII
1
I
140
II
141
II
4
11
Hi
III
an
«
10
SI
u
10
1
1161
III!
1C
101
UTAH imlta In 09/1 unlaea othacnUa noted.
HI Excluding Cyanide.
-------
Table B-4.
flUHHARY OF HINIHUH PBBCBHT REMOVALS*1» ACHIBVBD BV
SECONDARY TREATMENT
Paraaatar
BOD
TSS
Toluene
Tetrachloroethylena
Methylena Chloride
Bia |2-ethylhe«yl| Phthalata
Chloroform.
Trlchloroethylene
1,1 ,l-Trlchloroethana
Ethylbenzene
Phenol
Di-N-Butyl Phthalata
1,2-trana-Dlchloroethyiana
Benzene
Butyl Benzyl Phthalate
Diethyl PhthaUte
Napthalena
Zinc
Cyanide
Copper
Chromium
Nickel
Silver
Mercury'
Lead
Cadmium
Percent of
Mill
40
40
40
40
40
40
40
40
38
39
38
38
32
32
35
29
40
40
40
40
36
36
35
29
50
91
88
96
65
56
58
62
97
94
99*
99
51
99*
99*
99*
99*
99*
77
59
82
76
35 .
95
86
97
9)
75
82 .*
84
88
67
29
34
40
87
as
91
93
13
96
81
97
8i
99*
64
36
sa
66
ia
82
65
74
46 .
Planta
80
81
78
86
56
27
32
23
as
84
90
89
5
94
74
95
74
98
55
33
56
64
17
79
61
58
39
90
77
72
70
30
3
15
II
72
80
a6
46
4
79
66
40
67
85
. 44
5
46
48
a
66
25
35
4
N
40
»
40
25
21
24
27
a
25
23
12
9
4
4
5
1
1
4
40
40
40
35
22
2
9
3
12
percent
of Planta
50
91
88
97
87
55
63
62
97
91
97
99
97
97
99
97
'99
77
59
82
76
32
94
86
81
92
Lower
Ll.lt lug/!)111
Nona
Nona
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
80
4
a
20
40
20
800
200
a
<,) ~,movala baaed on average Influent and {""^K"?"'10'11
t »»« I ta M1 *e '.. ' ..-, 4 ea
me
.cl
-------
Table B-5.
MUlkM MOCOIff MMMUU Of OOLBCnO tatUlttMM
iMHMKMI iOtU BSSAmaUT KOCUOtt
BOQMBUY OBOOMD
tABAMBTBO MIMAOV
000
VOTAL OUOr. OOtlH
CAONIIM
ClIIUMIIM
COrtCB
CIANIOB
UAO ,
MOHCUlf
MICKBL
OILVEB
IMC
BIMIKMB
io(i-nn«iJ»B>i.| otfiuALAn
BUTVI BBMIVL nmUlATB
CMLOBOfOAN
Di-M-Burri. IUIMAUTB;
OIBTHVI. nRHLATB
MBI1IVLBMB QIUIBIOO
ruunk
VBIUCMUUOBTMVLIMB
TBICUUDKOmlVLBMB
1 . 1 . 1 -TBiaiUlBOniUMB
1.1-VBJUU-DICUtOBOKnlVUNi,
on
on
on
on
on
in
(41
01
on
on
in
HI
HI
on
on
141
on
on
in
10
IS
IS
ii
ii
ii
si
10
II
10
II
IS-
0
41
14
14
S4
II
If
1
1
10
10
14
ACT. OU10GB
on
on
HI
on
on
on
HSI
(SI
on
' HI
HI
HI
on
(41
HSI
on
KM
HOI
10
10
OS
14
04
01
11
14
01
01
11
11
01
41
10
01
00
40
11
10
01
II
10
10
00
IB*
IB. tlLIU
(M
HI
HI
HI
HI
HI
HI
HI
HI
HI
HI
HI
HI
HI
(M
(01
HI
HI
|0|
(01
(M
(M
HI
HI
l«l
11
10
II
40
40
SI
10
14
II
IS
41
40
14
10
IS
so
0
14
_
_
01
00
II
11
11
BBOOMOBBV
0, ACT,
in
in
HI
in
in
in
in .
IM
HI
in
in
HI
in
IM
HI
01
IM
HI
|0|
IM
IM
IM
in
IM
in
oiiinu
01
ll
01
11
II
10
11
II
II
10
II
1
II
41 '
10
0
II
11
-
II*
IS
II
41
40
It
OBOOI
UDABV OBOONOAOff tAMIUL Al/fff flAMM
MC AM lAOOOtf
in
in
III
HI
(0|
(01
HI
HI
(0|
(01
(0|
(o|
IM
HI
HI
IM
(01
(01
01
SO
01
01
01
04
-
I
-
-
Ol»
so
01*
01
~
HI
HI
in
HI
IM
IM
III
IM
IM
IM
' IM
(01
IM
III
HI
HI
IM
|0|
IM
HI
IM
IM
IM
IM
10
11
44
40
11
1
II
II
II
II
10
01
14
SO
II
10
11
1
10
A.I. 0100
01
141
01
01
OI
OI
(01
in
III
01
IM
HI
III
HI
IM
(0|
01
OI
|0|
01
HI
OI
HI
HI
(01
I
4
1
IS
00
44
1
14
11
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-------
A PARTICLE INTERACTION MODEL OP REVERSIBLE ORGANIC CHEMICAL
SORPTION
Dominie H. Di Toro
Environmental Engineering and Science Pr°9««» ,,
Manhattan College, Manhattan College Parkway, Bronx, H.Y. 10471, U.S.A.
INTRODUCTION
The sorption of hydrophobic organic chemicals onto soils, suspended, and
sediment particles is the reaction which distinguishes the environmental fate
of these chemicals from more conventional pollutants. The usual parameteriza-
tion of this reaction involves the use of a partition or distribution coeffi-
cient that determines the fraction of total chemical concentration that is in
the'particulate and dissolved phases. The typical assumption is that the
reaction is completely reversible.
Unfortunately there is a large body of experimental adsorption-desorption
data (1-54) which, in almost all cases, illustrates that complete reversibil-
ity is not commonly observed. Rather it is found that, for the usual time
scales of these experiments (hours-days) an apparent desorption steady state
occurs that is not in conformity with the particulate and dissolved concentra-
tion distribution predicted from the adsorption steady state partition coeffi-
cient, we employ an empirical model to quantify the partition coefficient of
the reversibly sorbed component and attempt to relate it to chemical and par-
ticle properties.
The most surprising and controversial of these is the particle concentra-
tion itself, whose effect on the adsorption partition coefficient has been
stressed by O'Connor and Connolly (55). He attempt to reconcile this effect
for reversible component partitioning by proposing a particle interaction
model that posits an additional desorption reaction. This model is shown
below to be in conformity with observations for a large set of adsorption-
desorption data (1-54). However the mechanism responsible for this desorption
reaction is still uncertain.
-------
METHODS
The reversible and resistant component model of sorption (38) assumes
that adsorbed chemical concentration, ra, is composed of two components; a
resistant component, rQ, that does not appreciably, desorb under the conditions
of the experiment, and a reversible component, rx- The key assumption is that
reversible component adsorption and desorption are both governed by the same
linear isotherm:
xc
(1)
where c is' the aqueous phase concentration at either adsorption or desorption
steady state.
Consider an adsorption experiment which yields an adsorbed concentration
r at aqueous concentration cfl. Then since ra " ro * rx*
*xca
(2)
If, for. a desorption into uncontaminated aqueous phase, the resulting sorbed
concentration is rd at aqueous concentration, cd, then
rd - ro
*xcd
(3)
since only the reversible component is affected. Thus the reversible compo-
nent partition coefficient can be estimated by subtracting eq. (3) from eq.
(2) yielding:
(4,
Consider, now, an adsorption isotherm comprised of i-l,...,Ma concentrations
r(i,o), c(i,o), the zero denoting the adsorption cycle. If, for each adsorp-
tion vessel a sequence of desorption cycles, J-l,...,Hd are performed, yield-
ing r(i,j), c(i,J), then the component model predicts that the slopes of the
consecutive desorption isotherms:
4i
'3'
c(i,3 -
(S)
are all constant, independent of the isotherm index, i, or the desorption
cycle index, j. Measurement errors and the idealized model assumptions will
yield variations in each estimate. The geometric mean, ignoring any negative
values of « (i.J), is used as the best estimate of «x for each isotherm ana-
lyzed.
tion:
Resistant component concentrations,
r0(i),
are estimated by subtrac-
(6)
-------
and for each isotherm the geometric mean la used as the beat estimate of
r (i). The component model equation for the complete isotherm is:
o
r0(i)
with t and r0(i) aa the fitted constants.
Two examples are presented in fig. 1. The top panela illuatrate the iso-
therm data and the conformity to the model eq. (7) using the indicated value
of t . The middle panela compare the calculated resiatant component data
r (i,*j) (aymbola) from eq. (6) together with the eatimates of the presumed
constant resistant component concentration. rQ(i) (horizontal lines). The
bottom panel illustrates, in these cases at least, that the adsorption of the
resistant component follows a linear lunity log-log slope) isotherm
. * C ' <8>
o a
For parathion, the model provides an excellent fit to the data. For
atrazine some deviations are present - the reaiatant component estimates are
not exactly eonatant - but the fit to the experimental data (top panel) is
reasonable and parsimonious since only two parameters are necessary: »x and
. Fig. 2 presents other adsorption-consecutive desorption isotherms and the
reversible-resistant component model isotherms (eq. 7) , fit to ttte data as
described above. These"'examples are chosen to illustrate that the model is
applicable to isotherms from a wide range of organic and inorganic sorbates
and sorbents: soils, lake sediments, and inorganic particles.
The division of sorbed chemical into two components - reversible and
resistant - can be viewed as a convenient operational method that distin-
guishes between the rapidly sorbed, labile component, which also rapidly
deaorba; and a nonlabile slowly deaorbing component. In fact a kinetic des-
cription of the sorption process is more fundamentally correct. The gas purge
experimenta of Karickhoff (56) are a direct examination of these phenomena.
He finda both a labile (rapidly adsorbing and desorbing) component and a non-
labile component with slower desorption rates. The separation we ptopose
essentially isolates the 'labile component partitioning behavior within the
context of available consecutive desorption experimental data.
A substantial portion of the reversible component partition coefficients
analyzed below are computed from reported adsorption and consecutive desorp-
tion data using the average slope method (Table 1) . Unfortunately not all
reported desorption experiments include the actual data. For these cases
estimates of are made in various ways, depending on the reported results.
The estimation equations are based upon the definition of *x , eq. (4), and a
mass balance requirement:
Bra * oca - mrd + cd (9)
-------
P4/?/1 T/-//CW - ACID SULPHA TF
m 0.1 tcg/L
CONSECUTIVE DESORPTION
«x - 30.7 L/KQ
s
CO
ac
o
(0
10-K
10-1
PESISTANT COMPONENT
OESOBPTION
t0ic
o
M
ecacP
10
e
10-1
ATRAZINF-SANDY LOAM
m - 0.4
CONSECUTIVE DESORPTION
rrx 0.194 L/KO
|
I 10«
S
10«
10*
PES1STANT COMPONENT
DESORPTION
i
o
at
o
m
10«
a a a
A
X
io«
to*
RESISTANT COMPONENT
ABSORPTION
10°
1
«0 - 68.7
10
-l
DISSOLVCD (mcj/UJ
RESISTANT COMPONENT
AOSOPPTION
«0 - 0.0525 L/kQ
10° 101
DISSOLVED (mg/U
,. 1. components model fit to consecutive desorption datn for Pu «'> >"
121 and Aerazine (61.
-------
PICLORAM - NORGE LOAM
m - o.i
CONSECUTIVE DESOPPTION
rtx - 0.129 L/kg
I
g 10-1
-I
10
DIURON-LAKE SEDIMENT
m - 0.2 kg/L
CONSECUTIVE DESOPPTION
icx 8.86 L/kg
a
(0
STRONTIUM -90
CALCAREOUS SAND
m 0.1
CONSECUTIVE DESOPPTION
XX - 1.7
3 10-*
I
a
CO
Pig. 2.
DtURON-CaMON TMORILL ONI TE
m - 0.1 kg/L
CONSECUTIVE DESORPT10N
ffx - 4.3 L/kq
*
I
S 10*
10° 101
FLUOMETURON-NORGE LOAM
m - 1
CONSECUTIVE DESORPTION
irx - 0.234
10-
a
-------
RSEo£te^D.i. Foriaula gffip.ovsd
TABLE I. METHODS FOB CALCULATING X
'*' References
Adsorption and Single
Desorption Isotherm data
Single Point Adsorption « . n fc|i _ -Ar
and Desorption i Sorbed data only « lcT-mra» - m»r
Adsorption Isotherm Partition Coeffl- , _
cient Single Point Desorptlons Data *K - j _ a - roo«
as fraction desorbed __
Aqueous concentrations "x " m|c -c^l
Adsorption and Consecutive ~- -n -.11 \<
Desorption Isotherm data ^ . rjl^j - ^}^jn) -
3,13.16".21.41
18.26.28,37,51,54
Single Point Adsorption. Single or
Consecutive Desorption data
; ' , _ .. . 20.23,27.28.30.35
Adsorption and Single a d 38.39,40,43,44
Desorptjon Partition "x i - a + I1a~f«l
Coefficients . _
Ar ' 22.24.32.34
A. 19.25.29,31
Single Point Adsorption and. Desorption t cd " °ca 2B
Single Point Consecutive Desorptionsi Least Square fit of. j_, 45.46.48
Data reported as sorbed fraction r|ij| ro . i . « ,| 2»
remaining at cycle j fJT~ " *> » * m'x I*BI"K rT
Ca| See Notation list for definitions
* Data reconstructed from reported Freundlich constants and mass balance equation (9)
-------
where . is the p-rticl- concentration and - is tha volu-a fr.ction of aqueous
phase not removed before uncontaminated aqueous phase ia added to initiate
daaorption. This equation requires that the chemical remaining in the vessel
both on the particles, mra, and in the remaining aqueous phase, «ca. be
accounted for after desorption aa either on the particles, «rd, or in the
aqueous phase c,. This ia equivalent to assuming that no significant vessel
adsorption or desorption occurs during desorption equilibration. Only experi-
ments for which essentially the same particle concentration was maintained
throughout are considered. Where possible the standard deviation of the esti-
mated ' is also computed. Tha result is over 200 estimates of ', from these
reporteS experiments for a wide variety of sorbates and sorbents. For neutral
hydrophobic chemicals, the estates are listed in Table 2, together with the
octanol-water partition coefficient to be used subsequently.
REVERSIBLE PARTITION COEFFICIENTS ! NEUTRAL ORGANIC CHEMICALS
The adsorption partitioning of neutral organic chemicals to soils and
sediment particles has been shown to be a function of the weight fraction of
sediment organic carbon, foc, and the octanol-water partition coefficient,
K , of the chemical (see Ref . 57 for an excellent review) . The basic rela-
tSnahip ia that the organic carbon normalized adsorption partition coeffi-
cient X - /f ia aediment independent ao long as the swelling clay weight
fraction"^ t'ha /'sediment ia not large and that a relationship exists between
KQC and Kw of the form:
al l°9 Kow
Fig. 3 examines this relationship for both the adsorption, *a/foc' and rever-
sible component, /£. carbon normalized partition coefficients. The data
has been stratified into two groups, low particle concentration experiments
with m f K < 1 and high particle concentration experiments: m focKQW * 1°-
The ratiwaJe for this choic. will become clear subsequently. Fig. 4 examines
the expected linearity between partitioning and fQC. Mote that for m focKQW
< 1, the data support both organic carbon normalization and linearity with
respect to 1C.. However at high particle concentrations, the relationships
break down, indicating that the particle concentration itself influences the
extent of sorption.
The observation that particle concentration affects the adsorption parti-
tion coefficient has been suggested previously by O'Connor and Connolly (55)
who noted that certain chemicals strongly exhibited the effect whereas other
chemicals were less affected. Significant particle concentration effects have
been observed for hexachlorobiphenyl (HCBP) sorption (39). In particular it
has been observed that «x is inversely related to via % - V"1 and that the
values of » observed for various particle types, to within a factor of four
-------
REVEHSIBLE COMPONENT
RELATIONSHIP OF Koc TO Kow
ADSORPTION
I >
Q !
£*»
tlMM
I'M
»!
- K «>.
H *
a a «
log* KOW
r
8§
^
S*
<=\
«-..;/ 0A ^ { Of
i.../ ^ | |
2 3 4 > 6
OV«KOW
m '
oc
m f
oc
8s
. K !«><>
f\
Q !»
x^
*
i«*lMM«
!» ^"
'^ Q Q.
*»Ml«r ||f« *
2 a 4 s a
log. KQM
Fig. J- Organic carbon normalized adsorption C-a/ioc» and reversible compo-
nent ( It \ partition coefficient versus octanol-water partition
coefficient. Top: m f K « : bottom: m fQcl(ow * >°-
-------
ORGANIC CARBON NORMALIZATION
REVERSIBLE COMPONENT
ADSORPTION
m Inn Krtyu< 1
oc "ow
-I
«-»
F
*.,
-I
I..
S -:
-4
4
-a
-a
1
-4
-a
-1
m I
OC *OW
* >
p"
a-a
o
A
O
o
v «..<
f> MO.-MCB
U IwtotM
P »...
O ,..L
8 ::::::
o
a
o
S»Ml*r lit* <«
» tn o a
II !»«. tX
a ^..
-4
I
-I
- I
-4
Fia. 4.
Octanol-Matur normaltieil adsorption I* /K } and reversible compo-
rsuj
> 10.
nent l|x/KQul partition coefficient versus organic carbon fraction.
Top: m f K
1 oc ow
1; butturn: m f K
oc ow
-------
TAB I
ADSORPTION (>a) AND REVERSIBLE (i^)
COMPONENT PARTITION COEFriCIENTS AND STANDARD ERRORS (SE)
Ret
(ja/ki
AUtca'rb
2.00-1
2.00-1
2.00-1
2.00-1
2.00-1
Carbofuran
.16
16
16
16
16
16
16
16
Honu
54
20
4.00-2
4.00-1
4.00-1
4.00-1
4.00-1
4.00-1
4.00-1
4.00-1
2.00-2
5.00-2
Llnuron
20
1.00-2
Fluonetron
32
9
33
33
9
Carl
48
Olui
11
13
24
24
24
24
24
24
24
74
1.25-3
1.00
1.00
1.00
1.00
_
2.50-2
1.00-
1.00-
2.00-
2.00-
2.00-
2.00-
2.00-
2.00-
2.00-
2.00-
f 1
Ac *
<*> "/"> -
__«»_«_»» f
"" " «« 1^4
5.10-1
1.07
2.64
3.80
1.84*1
»»
4.61*1
1.13
1.50
1.64
1.83
2.07
4.17
1.10*1
4.47*1
2.15*1
.46-1
.84-1
.85-1
.78-1
.01
.92*1
.32-
.48-
.97-
.73-
.37-
.64
OR,.
SE
,
s
(L/kg)
toil..
SE
»g,. Kow - 1.13 |78|
.26-
.06-
.31-
.42-
.03-
og,«
.70-
.37-
.13-
.43-
.47-
.57-
.20-
.43 4.93-
.57*1
.63*1
U)g,.
-
. __
LOg, .
2.15*1 1.14*2
__«_»»«..._
« « __
5.40*1 3.94*2
2.90-1 1.36-1
7.54-1 8. 82-1
7.50-1 8.81-1
9.86-1 3.74-1
1.45
4.06-1 1.59
1.22 5.87
4.00-2 7.20-1
8.00-2 2.18
1.90-1 7.70-1
2.20-1 9.11-1
2.60-1 5.80-1
3.00-1 1.03
4.00-1 1.75
4.60-1 2.09
Log,.
6.53-2
3.68-2
2.82-1
4.65-1
2.10
1.22-
1.75-
8.87-
1.26-
9.78-
Kow - 1.63 (78
1.86*1
1.76-1
2.61-1
4.40-1
2.19-1
3.86-1
1.21
2.20
Kow 2.
5.46*1
1.30*1
Kow - 2.
9.08*1
Kow 2.
3.82*2
1.24-1 1.41-1
5.71-2 5.26-1
5.26-1
1.18-2 2.84-1
Log,.
Log,.
Kow - 2.
6.74
Kow - 2.
2.51-2 1.40
1.29-1 2.01
3.15-1
2.24
4.10-1
4.00-1
4.20-1
5.15-1
1.58
1.91
4.93-
2.29-
3.40-
5.20-
3.47-
7.80-
4.04-
8.47-
12 |67|
1.68-1
19 |68|
-
20 |7||
3.00-2
1.96-1
2.49-1
2/28-1
2.94-1
31 |78|
81 |67|
2.2I-.
2.85-2
-
Ret (kg/I)
Dluron (continued)
i*
(L/kg) SE
17
17
17
17
17
17
17
17
2.00-
2.00-
2.00-
2.00-
2.00-
2.00-
2.00-
2.00-1
9.10-1
1.80
1.90
2.30
3.60
6.20
9.30
1.90*1
9.36
7.17
6.04
1.83*1
1.91*1
4.50*1
5.66*1
1.02*2
Hethyl Parithlon
28
1.21-2
1.40
5.00*1
N«propaalde
14
r4
14
14
14
Dial
48
Cam
30
30
48
5
5
19
19
1.00
1.00
1.00
1.00
1.00
A
Idrln-
2.50-2
_ *.»
-nCn
1.00-3
1.00-3
2.50-2
1.00-1
1.00-1
1.00
1.00
3.48-1
6.96-1
9.28-1
1.04
1.22
1.45
.
1.33
1.34
1.45
4.36-1
1.67
4.30-1
3.17
Parathlon
48
18
17
17
17
17
17
17
2
4.
2.50-2
3.11-2
5.00-2
5.UO-2
5.00-2
5.00-2
5.00-2
5.00-2
1.00-1
I. 00- I
1.45
5.10-1
7.00-1
1.13
1.23
2.16
2.64
2.81
4.16-1
3.20
1.92
3.68
U07*l
8.84
2.45*1
_
4.60-2
8.81-2
4.62-2
1.15-1
9.80-2
1.56-1
8.34-2
6.1B-2
7.82
3.89
s.oa
7.86
8.83
1.38*1
1.04*1
2.01*1
7.46-2
9.27-2
6.79-2
8.31-2
6.26-2
1.55-1
1.71-1
1.77-1
-Log,, Kow - 2.94 |78|
-
1.51*1
-Log,, Kow -3.10 |70|
7.08-
7.02-
7.96-
1.58-
1.20-
8. 85-1
1.68
2.20
1.58
2.65
1.59-1
8.37-2
I. 01-1
1.64-1
2.64-1
-Log,. Kow - 3.69 |67|
4.83*1
--log,, Kow - 3.
3.35*2
2.08*2
_
1.21*1
4.37*1
2.37
2.58*1
2.42-1
1.18-1
6.85-2
9.10-3
1.62*2
8.77*1
3.26*1
2.47
1.98*1
1.17-1
1.40
Log,, Kow »3.
2.17*1
6.15*1
5.71*1
4.16*1
1.17*2
7.13*1
7.43
11.00*2
1.57-2
1.27-2
1.48*1
1.94*1
2.69*1
4.31*1
4.37*1
3.83*1
6.34*1
6.06*1
4.18
3.07H
72 |69|
3.30-1
1.35-1
1.96-1
6.46-1
-
76 |78|
1.10-
2.84-
2.67-
9.89-
2.05-
1.49-
2.91-
2.29-
3.00-
-------
TABLE 2
(continued)
(fc«/D (X) (L/kg)
Parachion (continued)
Kepone (continued)
1.00-
1.00-
2.00-
2.00-
2.00-
2.00-
2.00-
II/MI _
t_-nai
1.00-1
I.OO-I
pha-HCII
I.OO-I
I.OO-I
lasloon
B-. 2.50-2
ho race -
2.00-1
2.00-1
2.00-1
2.00-1
2.00-1
rbufoa
2.00-1
2.00-1
2.00-1
2.00-1
2.00-1
:hlorpyr!foa
.8 2.50-2
14 2.00-2
18 2.50-2
il 1.00-5
,1 7.00-5
; i i .00-4
il 1.00-4
11 4.90-4
.1 5.00-4
13 5.00-4
4.77
1.41+1
5.10-1
1.07
2.64
3.80
1.84*1
4.36-1
1.67
4.16-1
1.67
1.88*2
4.62*2
5.16
1.10*1
3.75*1
5.23*1
4.23*2
^M
8.2.
5.46*1
-».--»
*" ~«" ~~f~
7.04
3.42*1
.82-2 5.62+1 1.97-1
.57-2 8.17+1 1.02-1
.01-1 1.67 6.46-2
.64-2 7.66 5.57-2
.22-2 1.10*1 1.48-1
.29-1 1.94*1 7.42-2
.88-2 1.51*1 1.41-1
-08it Kow - 1.80 (69 |
.45-2 4.90 2.25-1
.14-2 2.25*1 1.96-1
og,« Kow - 1.81 |69|
.28-2 2.78 1.77-1
.90-3 1.08+1 4.41-1
Log,, Kow - 1.81 (78|
1.45
5.10-1
1.07
2.64
3.80
1.84*1
5.10-1
1.07
2.64
3.80
1.84*1
1.45
2.34
1.45
5.44
5.44
2.91*1
2.91*1
2.91*1
5.44
5.44
7.95
Log,. Kow -3.81 |78|
2.11 3.17-2 1.68 1.58-
4.89 4.96-2 3.63 1.17-
8.89 4.39-2 5.08 1.51-
1.49*1 7.15-2 8.01 2.60-
7.13*1
3.17
1.06*1
8.48
2.22*1
5.61*1
!
2.82+1
1.75+4
4.17*1
5.bO*J.
5.52*1
4.49*1
10.00*2
7.10+2
1.09-2 1.26+1 3.51-
Log,. Kow - 4.48 (78
3.01-2 2.52 1.88-
1.42-1 6.60 5.15-
1.88-2 2.81 4.10-
2.46-2 5.99 4.84-
2.34-2 4.01 8.59-2
Log,. Kow - 4.96 |78|
7.89*1
Log,. Kow - 5.18 |44|
2.80-2 8.16*2 1.86-1
Log,. Kou - 5.14 |68|
1.09*2
Log,. Kou - 5.50 |41|
I.S6t4
4.06+1
4.J2»1
4.2itl
2.12+1
a.m2
6.67*2
41 5.00-4 2.91*1
41 6.50-4 5.44
41 5.00-1 5.44
11 1.00-1 8.40-1
48 2.50-2 1.45
Pa rae t hr 1 n-
25 2.61-2 2.49*1
La pc ophos
12 1.25-3 5.40*1
48 2.50-2 1.45
Beni( a) Anthracene
28 9.70-5 4.00*1
B-n_(_)Pyrene
28 3.20-5 3.80
28 9.60-5 4.00*1
Arochlor 1254
27 7.50-2 6.00-1
27 7.50-2 3.00
pp Buy1 ---«
21 1.00-4 6.00-1
21 1.00-4 1.10
21 1.00-4 2.50
21 1.00-4 2.70
21 1.00-4 5.70*1
21 1.00-4 5.70*1
H 1 rax
28 6.00-6 4.00*1
jm _.
40 1.00-5 4.40
40 2.50-5 4.40
18 5.50- 4.42
18 2.20- 4.42
19 I. 10- 4.40
19 1.10- 4.42
19 1.10- 5.05
J9 1.10- 5.19
19 1.10- 5.57
19 1.10- 5.74
19 1.10- 8.70
19 2.20- I. 74-1
1.99*1 2.04+1
1.14*1 1.27*1
9.70*2 8.51*2
to,,, KoM . 5.57 |67 1
9.98*3 3.51*2 .
2.03*2
Log,, Kow - 5.70 (80 1
3.89*2 .4.24*1 1.75-1
-----l.nff Knu » 5 flfl I7AI
» * itOij | Q ffJhUlV "" ^ «* I * V I
4.47*3 |7.27*2 2.04-1
3.31*2
______ _l na Vnu S 91 I7&I
» -- LOg,, KOW J.»l |«*|
1.16+5 8.10-2 8.00*4 5.91-1
Log,. Kow - 6.00 |79l
1.82*4 9.70-2 1.82*4 9.70-2
3.11*4 8.20-2 3.11*4 8.20-2
log,. Kow 6.03 |73|
5.70*2 3.00-1 5.97 3.00-1
2.55+1 3.00-1 1.48 3.00-1
_ -..--t.ncr KAU » 6 19 1671
1.20*4 3.60-2 10.00*3 1.01-
1.80*4 4.80-2 1.13*4 1.63-
4.50*4 1.90-2 3.75*4 3.15-
4.80*4 3.60-2 3.41*4 3.02-
3.00*5 1.65-1 6.38*3 3.08-
2.45*5 8.60-2 1.28*4 2.71-
Log|i Kow - 6.89 |74
3.98*5 1.00-1 3.98*5 1.00-
._________! o~ ir«.. _ & an ID
5.55*4 4.24+4 1.60-
3.17+4 2.76*4 2.24-
1.71*4 1.10-1 1.19*4 1.00-
1.21*4 6.00-2 1.08*1 2.10-
7.01*1 7.30-2 4.51*2 2.12-
7.05+1 5.00-2 5.02*2 4.10-
1.12*4 1.00-2 1.07*1 1.98-
I.O7*4 9.00-2 5.94*> 2.61-
9.61+1 5.20-2 6.18+2 1.79-
1.21*4 7.80-2 5.71+2 1.61-
1.48*4 6.50-2 8.12*2 1.81-
1.60*1 1.15-1 2.48*1 1.15-
-------
ana
(0.3-1.2), are independent of sediment particle properties such as tQC
particle identity (clay, silica etc). The experimental range of particle con-
centration was in 10-22,000 rag/L.
This puzzling finding prompted the present analysis of available adsorp-
tion-desorption data for other chemicals in order to assess the generality of
the finding.
. INTERACTION MODEL
One immediate problem is that the relationship »x - Vm cannot Persist
indefinitely as » * 0 since one is left with the absurd prediction that, in
the limit, a single particle can reversibly sorb the same- quantity of chemical
as can collectively be sorbed by many particles.
we have recently suggested a model for reversible component sorption (58)
which relies upon the hypothesis that, in addition to the usual adsorption and
desorption reactions:
c- <»»
c * m
Cllb)
where c is dissolved - chemical , m is the particle concentration, and c-m is
sorbed chemical concentration, there exists an additional desorption reaction
for the reversible component:
k
p-d
c«m + m c + 2m (12)
which occurs as particles interact, possibly via close encounters or colli-
sions. At steady state these reactions imply that:
, _ ^^ . _^ = r=- (13)
X
where » - k A /It d, the classical reversible partition coefficient, and *x
. k /kC ,, the r'a'tio of adsorption to particle interaction induced desorp-
tiondrate7 Mote that at low particle concentrations 'x - »xc which predicts
that at sufficiently low particle concentration, there should be no effect on
the extent of reversible sorption. but that at large particle concentrations,
* * v /m so that m» * »,. This suggests that the reason »x/fQC is systemat-
ical^" less than K0* for certain chemicals (fig. 3) is that additional par-
tiele induced desorption is lowering »x.
This model provides a framework within which to analyze the «x data
presented in Table 2. Following conventional adsorption theory we expect that
the classical partition coefficient *xc to be linear with respect to particle
-------
organic carbon, and log linear with respect to KW. Thusi
xc oc oc
where
lo9lOKoc ao * allo9lOKow (14b)
The result from eq. (13) is that »x is a function of m, fQC, and KQ^ via:
f KX
, oc oc (1.5)
The superscript x is used to emphasize that K*^. applies to reversible compo-
nent partitioning. The idea is that »x * »xc at low particle concentrations
and In this limit the classical reversible partition coefficient, »xc/ is
given by the usual organic carbon, octanol-water relationships: »xc * eoc**c
with Kx given by eq. (14b). However at larger particle concentrations, m fQc
Kx » v , only the particle concentration is important so that » * v /m. In
OC X . xn
this region particle induced desorption is overwhelming spontaneous desorption
and only the particle concentration, m, and the ratio «x » ka
-------
in
M
s
mvcnsiau coMPoneNT PARTITION
COMPAMSON TO PAPTICLB INTWACTIOM MQOKL
ORCAMC CMCMKALS
r.ai.4o' ^jK^.o.oooaa+o.aaa lo, K^
s
4
3
a
i
o
«r
-t . o i a 3
CALCULATED lo«n IT,
a
3
a
m
« .
Fiq. S. . Comparison of eq. 114-15) to data: observed versus calculated
(top) and in nprmalized form (bottom).
-------
-3-1-10133*
-3 -2 -1 0 1 2 3 «
10123*
2
1
0
-1
3
1
0
-3
If-
§<&»x
. Q rm
X MM
O NP»
IWJ
11*1
-a -2
e i J
Fl«. ». »ow»llM* plots of individual ch.-ic.l d*e-.
-------
-3-1-10123*
B.3«< <04|g KOWS3.99
-3-2-10123*
-3 -a -1 01 234
.3-2-1 01 234
2
1
0
-1
I «
*fe,
/ '
. o
.3-2-101994
fitj. 7. NerHlisad pleta o< Individual ch««lc»l data.
-------
TABLE 3. NONLINEAR LEAST SQUASES PIT OP
-------
LOG10
10
5
3
2
O
0.5
0.3
0.2
0.1
»l«ro«
KIMM
' DDT
,
i
t
LOG10Kow
Fig. 8. Parameters obtained from individual fits of eq. (14) to chemical
data versus oetanol-water partition coefficient.
-------
EFFECTS OF CHEMICAL AND PARTICLE PROPERTIES AND CONCENTRATION
The proposed reversible component partitioning model has two distinct
regions in which particle concentration either does or does not have an effect
on V For mfocKjc « vx, »x . f^K*^ which is a linear function^ of fQC and
Kxc. The upper panels of Figs. 3 and-4 present the data for mfoc.Koc < 1. ^The
expected relationships: *x/foc Ver9us Kow with the line corresponding to KQC -
X , and « /K* versus fQC with the line corresponding to the expected linear
relationship are shown. There are no apparent systematic deviations.
Conversely for »*ocxjc » »x only particle concentrations determine the
magnitude of «x. Fig. 9 presents the data for mf0<.xjc > 10. Again no syste-
matic deviations are apparent. It is interesting to note that even for chemi-
cals with fairly low KOW'S the particle concentration can dominate »x if it
and f are large enough. In addition chemicals with large KQW"s can exhibit
extremely low reversible partitioning at high particle concentrations (e.g.
HCBP, DDT, and Aroclor 1254).
Me illustrate these effects on reversible partitioning using actual
adsorption-desorption data in fig. 10 which are plots of adsorption and single
or consecutive desorption isotherms. Only one of the isotherms (there are
typically 4 or 5, e.g. fig. 1-2) are plotted for each sorbent for clarity.
For Diuron (logloXQW. - 2.81) we expect xjc - 635 and for m - 0.2 kg/L the
breakpoint in fQe above which fQC should not influence »x is f - vx/(mKSc)
(Table 31 i.e. f -5.5%. Note that the slope of the consecutive desorption
isotherms, «x, is increasing from fQC - 1.9 to 2.3% but that it slows its
increase at fQC - 6.2% and is essentially constant as fQC increases to 9.3%.
For Terbufos at the same particle concentration, since KQW is more than an
order of magnitude larger than for Diuron, the breakpoint in fQC is corres-
pondingly less: fQC - 0.24% (Table 3). And, in fact, as shown in fig. 10 the
slopes for f -0.51-18.4% are all essentially equal as predicted.
Conversely for large X^ chemicals, varying the particle concentration
for the same particle type strongly affects the slope. For both Xepone and
HCBP at-f » 5%, the particle concentration breakpoint m gx/l*ocKoc'is m "
84 mg/L and m « 5 mg/L respectively (Table 3) and as m increases beyond these
values indeed the slope of the desorption isotherms decrease.
The predicted relationships: both the absence of «x increases as fQC
increases at constant m (Terbufos), as well as the particle concentration
effect (Kepone and HCBP) can be directly seen in these examples. Thus they
are not artifacts of the data reduction techniques used to generate «x but are
real features of reversible component partitioning.
-------
6
3 -2 -1
Diuron
Hopropomde
<> Ganna-HCH
Parathion
Bcto-HCH
Alptut-HCH
Anth
Q Benr
-------
EFFECT Of PARTICLE ORGANIC CARBON
DURON (17)
TERBUFOS (3)
200
160
iiao
u so
40
ADSORPTION
foBSORPTION
04 12 10
AOUIIOUS CONC (mg/U
10
i
U 4
2
I a
ADSORPTION
4- OUORPTION
0.0 . 0.3 0.4 0.8 0.8
AQUEOUS CONC (m«/U
i.O
PARTKU CONCENTRATION
lo«lw Kw»
REPONI (431
S SJO I
NCBP (401
3.4*
4.4%
aoo
soo
?
X
?400
U
U300
w
a
oioa
M
too
. ADSORPTION
4>OMORPriON
v
300
290
JOO
tse
Tf
10 20 30
AQUEOUS CONC (uo/k)
40
2 4 a 10
AOUIOUS CONC. (n«/O
Tig. 10. Consecutive desorption data for varying f (top) and parci(cle con-
centration (bottom).
-------
REVERSIBLE PARTITIONING - ORGANIC ACIDS. BASES AND INORGANIC SORBENTS
The particle interaction model can only be directly tested if,, for each
chemical of interest, the data span a large enough range in mfQC so that »xc
and v can both be estimated. Alternately an independent method of estimating
. can be utilized such as that employed in the previous section for neutral
organic chemicals and organic carbon containing particles where »xc fQCKoc
and Kx is estimated from KQW. For ionizable organic chemicals or for sorp-
tion onto inorganic particles 'no analogous methods are available. Thus no
direct test is possible.
However the model (eq. IS) does make one prediction that is not. dependent
upon the magnitude of »xc:
-
M«V w Y
l * mT5-
m xc
namely that " should be less than vx/m regardless of the magnitude of «xc.
Hence plots of " versus m should either exhibit values below «x/m correspon-
ding to insignificant particle interaction induced desorption, or along the
line - v /m corresponding to desorption being dominated by the particle
xx « .
interaction desorption mechanism.
Fig. 11 presents the observations for neutral organic chemicals and
inorganic sorbents (nearly all clays). With rare exceptions the points are
either below or on the line corresponding to ^ a l. Fig. 12 presents similar
results for organic acids and bases and the few available inorganic chemical
data. Without an independent or at least generally applicable method of esti-
mating « , no further test is possible. However the substantial number of
observed *«C that are near vx/m suggests that the particle concentration effect
on reversible partitioning is not limited to just neutral organic chemicals
and organic carbon containing particles, but is a ubiquitous feature of rever-
sible component partitioning.
A large set of metal sorption data: Mi, Co as sorbates with montmorillo-
nite and quarts: as sorbents that has the requisite range in particle concen-
tration are also in conformity with the same reversible component partitioning
model (58) employed above, eq. (15), thus supporting this view.
ALTERNATE POSSIBILITIES - A THIRD PHASE
The most popular explanation ((50-62,81) for the particle concentration
effect is that,, in addition to the aqueous and particle phases, there exists a
sorbing (third) phase which is not removed from the supernate by the particle
-------
REVERSIBLE PARTITION COEFTCENT
NEUTRAL ORGANIC CHEMICALS-INORGANIC SORBENTS
Q «*««*hr«It"« tO
+ Homron C293
C3O
X Olwoii C133
a nti«*i»M«
64MM-MCM C3M
A DOT C313
X ' DOT C233
C4«3
fl«. II. Coav«rl.on of d.t. to eh. pr.dlction
inorganic »otb«nta.
., .,/ for socptvon to
-------
REVERSIBLE PARTITION COEFFICIENT
INORGANIC CHEMICALS
t"
*
-t
C193
+ Sr-9« CIU
£ riuandt C123
X Annoni* C2J3
-I
X
O
O
V
X
O
O
7
ORGANIC AGIOS AND BASES
a
Oie«i»ba C323
2.4 0 C2I3
2.« 0 CS4J
Tpicycltzait C2I3
PU1o»«n £73
Ptdortn C-MJ
ler.fi C333
C3S1
1.4.3 T C«93
2,4.: T C383
C133
.IT. <
-4 .3 -2 -1
ORGANIC ACIDS AND BASES
CI33
C293
C2S3
C323
CC3
C29I
C«'.3
C4«J
CJ33
C493
C4«J
C943
T. < -?r
1
. 12. Conp«rison of d«e« to th« prtdietien th«c | < «|/» for serption of
inari|«nie eA«mteals (topi and orqanie jeidi. Jnd bases '(middle and
-------
separation technique (usually centrifugation) employed to operationally mea-
sure the "dissolved" concentration. This third phase is identified as being
either dissolved organic matter or colloidal particles. To apply this hypo-
thesis to reversible component partitioning we assume that the "dissolved"
concentrations at adsorption and desorption steady state, cfl and cd» are the
sum of the truly dissolved concentrations, c^ and cd, and that sorbed (or
complexed) to the nonseparateH third phase, m^r^ and m£rd, where m^ and m^ are
the nonseparated third phase aqueous concentrations (kg/I) and r^ and r£ are
the sorbed chemical concentrations (mg/kg-third phase)' at adsorption (a) and
desorption (d) steady states. Thus
ed ed * ndrd
and *x (eq. 4) becomes:
»
x * "Va' " tcd * mdrd'
or
r_ - ^
"
c(l * «£«J) - cdu
(20)
where «' and »i are the adsorption and single desorption partition coeffi-
3 O
cients for the nonseparated phase. To convert this expression to that found
to be descriptive of the data, eq. (151, a number of assumptions are required:
(1) that the concentration of nonseparated third phase at adsorption and
desocption steady states (for each consecutive deaorption step) are equal: m^
mi m1 and (2) that the partitioning to this phase is reversible: "^ "^
« in which case eq. (20) becomes:
f , . . ' " '« _ 121)
x (el - cij U * m'»')
** t
Defining:
r - r,
(22)
as the "true" partition coefficient the result is:
t
V
x 1 * mf«
xe .. (23)
In order to convert this equation to eq. (IS), -which describes the data, mul-
tiply m't' by "1IXC/»1IXC " l so
-------
rxe (24)
*xc m«^_
from which v in eq. (IS) is:
*
m n*xc (25)
The empirical finding that vx - 1 requires that
'-",.
For neutral organic chemical and organic "carbon containing particles:
. . f K* and if we assume (3) that the same normalization applies to the
BSseparaCte°dC phase: .' - f^, then eq. (26) requires that
m'f1 . mf (27)
that is, that the quantity of organic carbon associated with the nonseparated
phase (m'f ) is approximately equal to that contained .in the separated
particles °m fo<.) . Alternately if specific surface area, ,
-------
If, on the other hand, the third phase is assumed to be dissolved organic
carbon that desorbs from the particles, then the requirement (eq. 27) that ,
.T t-«f forces the conclusion that there is as much dissolved organic
carbon in the aqueous phase as there is particulate organic carbon in the par-
ticulate phase, per unit aqueous phase volume, at both adsorption and at each
desorption. In facfm'f',. - »*oc requires that desorable particle organic
carbon has a partition coefficient of - 1 L/kg-organic carbon which is ex-
tremely small. Even liquid octanol which has an aqueous solubility of ^ 10 M
and therefore a partition coefficient of - 103 L/«ole-octanol - 10.4 L/kg-
organic carbon which is ten-fold larger than that required for desorable
with such a low partition coefficient isthat substan-
tial organic carbon would be removed at each desorption cycle. Hence at
adsorption equilibrium, one-half of the original particulate organic carbon
nass must desorb and be in solution. Since this is discarded before desorp-
tion is initiated, it is difficult to see how «; - »d. Rather m' - ma/2
where j is the desorption cycle index. It would further suggest that simply
washing particles in water should remove substantial quantities of particle-
bound organic- carbon. Finally it is difficult to see how dissolved organic
carbon coulrf be implicated with Inorganic sorbents.
Perhaps the most convincing experiments which appear to preclude nonsep-
arable third phase as an explanation are resuspension experiments (58,63) :n
which, instead of desorption into new uncontaminated aqueous phase, the par-
ticles are resuspended into a reduced volume of the aqueous phase remamir.c
after adsorption and centrifugation. For this experimental design the concen-
tration of the nonseparated third phase in the supernatant must be the same at
both adsorption and resuspension equilibration. Only the concentration of the
separated particles is increased by resuspension into a reduced aqueous phase
volume. For these experiments the partition coefficienc is observed to
decrease as particle concentration increases from the adsorption to the resus-
pension equilibrations. If a desorbing third phase (dissolved organic carbon)
is involved then the problem of explaining the decreased partitioning is just
transferred to explaining why there is increased desorption of the third phase
into the original supernatant when only particle concentration is increased at
the resuspension equilibration.
Dilution experiments (59,63) dispense with centrifugation of the experi-
mental vessel completely and decrease particle concentration by adding either
uncontaminated aqueous phase (63) or equivalently contaminated aqueous phase
from a parallel vessel (58). These experiments yield increasing partition
coefficient with decreasing particle concentration.
Thus nonseparable third phase .models require that the nonseparable phase
has properties that are both ubiquitous, very specialized and, for desorbing
organic carbon, not chemically, realistic. Further they appear to be precluded
by resuspension and dilution experiments designed expressly to strongly disr
criminate against such models.
-------
n^nnti Kinetics and Particle Aggregation
In examination of desorption kinetics using an air stripping
remove dissolved chemical from the sorbent suspension (56, precludes the need
f" consecutive particle separations by centrifugation that characterizes he
desorption data analyzed above. The results of a series of these experiments,
by Karickhoff and Morris (64,, indicates that there exists a labile
ncnt that desorbs rapidly « 1 h*> «* a .nonlabile or resistant componen
desorption rate they correlate to the equilibrium partition coefficient
R . f K This result and square root of time dependence of deSorption of
tne non°fab°ne fraction strongly suggest intraoarticle diffusion as the kinetic
mechanism controlling nonlabile component desorption.
"or the labile component, Karickhoff and Morris (64, found that the
labile fraction of total sorbed chemical. Xff decreased as n*p increased.
where m is the particle concentration. Their data analysis suggested:
Xl ' 2.5
(29)
If we i-d.nti.fy ^ - rx/ra, consistent with the component model, eq. (1-2) then
__., :< .a, .«.«*.ion aauilibrium ». K_ t^Jt>--t then:
X . /« and if at sorption equilibrium «a Kp
m A O
(30)
Using eq. (IS) for «x and assuming KQC - Kjc yields:
* «focKoc/vx
(31)
which is the same functional form as that suggested by Karickhoff and Morris,
eq (29,. The results of a fit of their data to eq. (14,, is shown below.
Least Square Fit
Chemical
Trifluralin
Pyrene
Pentachlorobenzene
Kexachlorobenzene
lo*10Kow
3
4
4
5
-*i
.94
.64
.97
.50
:_
(0
(0
(0
(0
2S
.18)
.22)
.37,
.39,
^^^^^^^^^
3
4
4
5
.06
.88
.94
.23
M
,
,
,
,
5
5
5
5
.34
.18
.19
.50
^m^^^~^**
[67J
[77]
[76]
(681
,[68]
,168]
,[68]
,[751
Parameter (Standard error of estimate)
«(log.~ *-) 0.302
'10 V
Karickhoff and Morris (64,
-------
^ 22) is found as well as the expected log
T.M J ^ ^ ^ ^ ^ larger %
P related in aome way to the
i, unclear at present - l» f"^1" . but the refflarlcable result Ls that
completely different experiment. design ^ ^ ^ ^
the same functional for.. eq. (311 . iinent we take this to be fur-
.
A significantly larger % -
linearity between KQC and K .
«». of
b.
p«tlcl. ecne.ntr»tlon "«*
-iero.«pie.llY
. ......
Mtheu,h this ~y
-«tlel. ,u.pen»lons »t
(lBd nc
Ur,.r
th.
of
th.
. Jolely ln
o<.Koe-
==
the patticU concentration.
that ,l.ld. this f««-
r.ther 6h.n
.<, th. orc.ni= carbon
It is difficult to imagine a
tional dependence.
Discussion particle interaction' model which is
t
,.sc it may "=' *« constant but ratn.r
L ,=.cu,at. th.t =oth th. adacrptxon
de,orption rat. are ohy.io.UY »th.r
interaction induced
d.t.ined by. for
«hll. «- «*"-
ienc. level
be q»i»
on. pl.c. of evidence th« .«PP=«, the
th«. in th.
to . cOn,«nt and th.
^
-in,.,
p.rticl« are stationary and. ,. the
-------
actions that enhance deaorption if particle concentrations "are large enough
and, as a consequence, particle interactions are frequent enough for this
reaction to be significant.
Finally we observe that partition coefficients (actually distribution
coefficients) inferred from field measurements of dissolved and particulate
chemical- concentrations also display an inverse relationship to particle con-
centration (39,66) so that the effect is an important factor in determining
the partitioning of chemicals between particulate and dissolved phases in
natural waters.
The most significant shortcoming of the model presented above is the lack
of a mechanistic explanation for the particle interaction induced desorption
reaction, eq. (12). One would surely like to know what, exactly, is the
physics and chemistry of this reaction. Or, more critically, if the reaction
itself is the correct explanation for what appears to be the correct result,
eq. (15). The success of eq. (IS) in correlating large amounts of adsorption-
desorption data is undeniable, fig. 5-7, but its derivation via the reaction
scheme, eq. (11-12) must be regarded as speculative.
From a practical point of view, the correlative power of the model for
neutral organic -chemicals and organic carbon containing particles is quite
useful since a knowledge of the chemical's KQW, the particle's fQC and its
concentration, «. suffices to determine fx, the reversible component partition
coefficient. For inorganic sorbents and ionizable or inorganic chemicals an
upper bound to the expected partition coefficient, tx < vx/m, is available.
From a theoretical point of view, the most surprising and intuitively
disturbing result is the observation that vx is of order one (± one half an
order of magnitude) for all chemicals and particle types examined. This gen-
erality suggests either that there exists a universal feature of reversible
sorption which has heretofore been unsuspected or that the entire analysis
Itself is flaw«sd in some subtle way. The author prefers to believe that the
former is the case and that its explanation is via a particle interaction
induced desorption reaction.
Acknowledgements
The participation of our research associates and assistants at Manhattan
College: Joanne Guerriero. Michael Labiak, Salil Kharkar in the laborous task
of assembling and reducing the data employed in this paper is gratefully
acknowledged. Alan Felsot kindly provided the data from his useful experi-
ments, as did John Connolly and Samuel Karickhoff. Conversations with the
members of our research groupi Donald O'Connor, Robert Thomann, John Connolly,
John Jeris, John Mahony, and Richard "infield were, as always, helpful and
stimulating. Other colleagues have also endured discourses on this subject,
and their patience and insights are appreciated. The continuing support of.
the EPA Large Lakes Research Station, CR807853 and CR810799 and particularly
Nelson Thomas (EPA-Duluth) and William Richardson (EPA-Grosse He) is greatly
appreciated.
-------
NOTATION
rli.jl - sorbed concentration (mg/kg); i^ isotherm, J** desorption cycle
c(i,-|) - aqueous concentration (mg/L), ith isotherm, Jth desorption cycle
adsorption (single desorption) sorbed concentration log/kg)
reversible (resistant) component sorbed concentration (mg/kg)
adsorption (single desorption) aqueous concentration (mg/L)
c(i,j)
Vrd>
*x"o>
£ I £ 1 w aM0w*» |» ««^« » »- j
t*U ) - adsorption (single desorption) partition coefficient (L/kg)
/ - reversible component partition coefficient tL/kg), eq. 4
x . k /lc dimensionless reaction rate constant ratio, eq. (13)
X . k V classical reversible component partition coefficient IL/kg)
*xc ads s~d
adsorption reaction rate constant
spontaneous desorption reaction rate constant
- particle interaction induced desorption rate constant
fP~d - particle organic carbon weight fraction (kg/kg)
particle concentration (kg/L)
i« "third" phase concentration (kg/L)
. -third" phase organic carbon weight fraction (kg/kg)
°C particle specific surface area (m /kg)
- "third" phase specific surface area Ira /kg)
c . mr * c initial total chemical concentration (mg/L)
rT - initial sorbed chemical concentration (rag/kg)
Aj . r . r., desorbed chemical concentration (mg/kg)
4 » Ar/r . fraction chemical desorbed
- volume fraction of aqueous phase not removed before desorption
r - resistant component sorbed chemical concentration (mg/kg)
K° . ,a/foe, organic carbon normalized adsorption partition coefficient
(L/kg-organic carbon)
Kx . . /f . organic carbon normalized classical reversible component
°C partition coefficient (L/kg-organic carbon)
m
0
I
K - octanol-water partition coefficient (L/L)
ow
-------
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'» saa 2d sH .-s.: P.
S61, 1972.
1122-1125, 1981
Civil Engineers, p.
^^^SiJ-i^
Contam. Toxicol. 24, 20-26, 1980
^.ii.
cali in Frelhwiter Systems, Part II: Laboratory Studies
EPA-600/7-78-074, Nay 1978.
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31. Picer,
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32. Carringer, R.D., J.B. Weber, and T.J. Monaco, "Absorption-Desorption of
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Compounds, Minerals, and Ions in Volcanic-ash-derived Soils: I. Adsorp-
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de la pyrazone par quelques colloides organiques et ninreaux, Weed
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36. Bowman, B.T. and W.W. Sans, "Influence of Methods of Pesticide Applica-
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ponents of Hexachlorobiphenyl Adsorption-Desorption: Isotherms. Environ.
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ponents-of PCS Adsorption and Desorption: Adsorbent Concentration Effects.
J. Great Lakes Res. 8(2):336-349.
0 .
4.0. Di Toro. 0. H., L.M. Horzempa and M.C. Casey. 1982. Adsorption and
Oesorption of Hexachlorobiphenyl. A. Experimental Results and Discus-
sions B. Analysis of Exchangeable and Nonexchangeable Components.
EPA-600/53-83-088.
41. Farmer, W.J., Aochi, Y. 1974. Picloram Sorption by Soils.. Soil Sci.
Soc. Amer.. Proc. 38, p. 418-423.
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1
March-April 1977.
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1517-1523.
ef
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p. T5TI
" Sffi.'i-i£- WJR;
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al., Ann
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64 Karickhoff. S.W. and K.R« Morris. 1984. Sorption Dynamics of Hydro-
phobic Pollutant in Sediment Suspensions. US EPA Env. Res. Lab.,
Athens, Ga.
6S. Di Toro. D.M., J.S. Jeris. 0. Ciarcia. 1985. Diffusion and pf"itionin«
of Hexachlorobiphenyl in Sediments. To appear, Environ. Sci. Technol.
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5-^2 in Physical Behavior of PCB's in the Great Lakes, ed. 0. Mackay et
al., Ann Arbor Science, p. 181.
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67.
600/3-82-060, p. 23-25.
S2«.is. irt-srajSis1^^^ &SRS n.rr
833.
70. Min,.Urin. «.. I. fcnjta. "ijj»3£«g1£ijj "f'SS^'WlitJ
Mechanism of Nonionic Chemicals Adsorption eo aoixa. «*.*«»>« t
12(1).
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pounds in Octanol-Mater Systems, Environ. Sci. Technol., 16, p. 4
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p. 1227-1229.
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Sci. Technol. 16, p. 274-278.
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.o M.M** B 3 Harrison. P.L. 1984. The Octanol-Water Partition Coeffi
79> SiiSif 8en«H(" J?«nl; Measurement, Calculation, and Environmental
Implications, Bull. Environ. Contain. To*. 32(3), p.
" BS: Viii^S^ -'SS=Wi!:;BS
Permethrin by Chironomus Tentans Larvae in Sediment and
Tox. Chem. 4, p. 51.
Technol. 19(1) , p. 90.
(Received in Germany 2O June 1985; accented 16 Auoust 1985)
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APPENDIX D
BIOCONCENTRATION AND DEPURATION BY AQUATIC ORGANISMS
D. 1 INTRODUCTION-
The presence of hazardous substances in Che aquatic food chain is a
problem of rapidly developing dimensions and magnitude. New produce
production and the ever present potential for insect and pest infestations
with attendant effects on man and animal result in continuing demand for
product development. Considerable effort has been devoted in recent years
to the development of predictive schemes that would permit an a priori
judgment of the effects of a chemical on the environment.
An important .distinction is to be1 made between Che fate of the
substance and its effects as shown on Figure D-l. The substance raay be
accumulated at various locations in the ecosystem and at various
concentrations may produce effects that limit growth or reproduction. Such
effects in turn feed back to the fate of the substance in terms of altering
the basic biomass distribution. The explicit inclusion of the effects of a
toxicant ia not included in this review and emphasis is on Che fate of the
substance.
Figure D-2 shows the general framework and indicates the interaction of
laboratory and field data with the modeling framework. As with all water
quality problems, specification of the inputs of the toxic substance is
1R.V. Thomann, Mathematical Modeling of Water Quality - Toxic Substances,
31st Institute in Water Pollution Control, Manhattan College, Bronx, New
York, June 1986.
-------
BIOMASS
(PHYTOPLANKTON,
ZOOPLANKTON,
FISH, ETC.)
INPUT
LAKE, BAY, ESTUARY,
RIVER (FLOW, GEOMETRY)
CONCENTRATION IN
FOOD CHAIN
(WEB)
DISTRIBUTION AND FATE
OF HAZARDOUS SUBSTANCE
EFFECT OF CONCENTRATION
ON AQUATIC ECOSYSTEM
EFFECT ON MAN AND
MAN'S ACTIVITIES
EFFECT AND CONSEQUENCE
'OF HAZARDOUS SUBSTANCE
FIGURED-8 INTERACTION OF FATE
r\ -1 c /i i! n nc i Q i fc
-------
LABORATORY AND CONTROLLED
FIELD EXPERIMENTS
HAZARDOUS^
SUBSTANCE f^WATER BODY
SUB-SYSTEM
COMPARTMENT MODELS
ADSORPTION,
SETTLING
KINETIC BEHAVIOR
(UPTAKE,CLEARANCE,
TROPHIC TRANSFER)
CONCENTRATION IN
FOOD CHAIN
(WEB)
FIGURE D-2 PRINCIPAL COMPONENTS OF MODEL FRAMEWORK
FOR FATE OF HAZARDOUS SUBSTANCE
-------
essential. The Inputs Include all sources such as municipal and industrial
discharges, urban and agricultural runoff and atmospheric inputs. In the
vater column, Che principal physical and chemical phenomena to be included
are:
- adsorption and desorptlon between dissolved and particulate forms,
chemical interactions,
deposition and resuspension of particulate forms,
diffusion of dissolved forms from bed sediment, and
volatilization, photo-oxidation, biodegradation.
These phenomena describe the concentration of the substance in the
water column. Various sectors of the ecosystem may then accumulate the
substance from one or both of two principal routes:
direct uptake, I.e., absorption and/or adsorption from the
-available" form In the water ("available" may include dissolved
form and toxicant adsorbed on microparticulate organic or
inorganic particles), and
ingestion of the substance through predation of contaminated prey.
It should be noted that the first route, i.e., direct uptake of the
substance from the water, separates models of the fate of toxicants from
models of other water quality variables. For example, in analysis of
nutrient enrichment problems, it is assumed that upper levels of the food
chain receive nutrients only from predation and not directly from the
water.
The toxicant may then be excreted from the food chain by physiological
processes, released upon death, egested as uneaten or undigested food or
metabolized as part of the chemical processing by the organism.
As shown on Figure D-2, data from laboratory and controlled field
experiments can be used with sub-system compartment models to obtain
estimates of kinetic behavior including values of uptake, clearance or
-------
transfer between trophic levels. These sub-system models are generally
composed 'of single or at most four to five discrete compartments, i.e.,
discrete units of the aquatic ecosystem such as phytoplankton, zooplankton
and fish. Analysis using compartments of the ecosystem permits the
determination of bioconcentration factors, i.e., the ratio of the substance
in the organism to that in the water. Accordingly, it is well to begin
analysis of the fate of a toxicant by -a simple mass balance of a single
ecological compartment (say, fish; exposed to a controlled environment in a
laboratory aquarium.
0.2 BIOCONCENTRATION AND DEPURATION
The uptake of a chemical directly from water through transfer across
the gills as in fish or through surface sorption and subsequent cellular
incorporation as in phytoplankton is an important route for transfer of
toxicants. This uptake is often measured by laboratory experiments where
cest organisms are placed in aquaria with known (and. fixed) water
concentrations of Che chemical. The accumulation of the chemical over time
is then measured and the resulting equilibrium concentration in che
organism divided by' the water concentration is termed che bioconcencration
factor (BCF). A simple representation of this mechanism is given by a mass
balance equation around a given organism. Thus,
dt
where >»' la the whole burden of the chemical (ug), ku is the uptake
sorption and/or transfer rate (l/d-g(w)). w is the weight of the organsm
(g(w)), c is the available water concentration (ug/1), K is the desorption
and excretion rate (d'1) and t is time. This equation indicates chat if
the mass input (wg/d) of toxicant given by Kw is greater than by the mass
lost due to depuration (ug/d) given by KM', then the chemical will
accumulate in the organism. At an equal mass of uptake and depuration, che
chemical win have reached an equilibrium level. It is assumed in the mass
balance thai: the rate of uptake of the chemical is directly proportional to
-------
the concentration of the chemical in the water. For most chemicals at
normally'encountered concentrations in water this is a good assumption.
For example, the studies of PCS by Vreeland (1974) for oysters and Hansen
et al. (1974) for pinfish, show that the resultant PCB concentration in the
test animal was linear to the exposure water concentration.
The whole body burden v1 is given by:
(D-2)
V* VW
where v is the concentration of the chemical (ug/g(w)). Substition of
Equation (D-3) into Equation (D-l) gives:
- Kvw
Expanding the derivative and grouping terms yields:
£ - ^ - (g/v * «v
K c- ,*£/- - w. (D-4)
Letting
where :
G(d~l) -.the net growth rate of the organism, and
V - K * C
then
$ - kuc - K'v <°-7>
It is seen that the loss term on the concentration includes the loss (or
gain) due to the changing weight of the organsm during the test and aay
therefore be termed an apparent depuration. The solution to Equation (D-7)
is:
-------
v . V (1 . cxp(.K.t)) + VQ exp<-K')t CD-6)
n
where v is the initial concentration of the chemical in the test organism.
Note that this expression indicates that the rate of accumulation is a
function of K', the sum of the depuration rate and the net growth rate.
At equilibrium or steady-state,
kuc (D-9)
* 'IT"
In order to standardize this equilibrium concentration, the BCF is
defined as the ratio of the steady-state concentration to the water
concentration at zero growth rate of the organism.
form
The ratio NW, the BCF, is shown here in unit's ug/g * ug/1. In a
representative of a' pseudo dimensionless ratio, the BCF is -in typical units
of wg/kg(w) * ug/1, i.e., ppb/ppb and then
1000
The BCF under actual field conditions, i.e., the accumulation of the
chemical from the water only (excluding food intake) would be less than the
Ntf given by Equation (D-10) when growth is positive and would, be greater
than Equation (D-10) when growth is negative (i.e., a net weight loss).
D.2.1 Bioeoneentration Equations
For organic chemicals, various equations have been suggested that
relate the* BCF to the octanol water partition coefficient, KQW, on the
grounds that the lipophylic nature of the organic chemicals will result in
partitioning exclusively to the lipid compartments of the organism. Thus,
-------
Veith et al. (19790 as a result of uptake experiments with fathead minnows
(and green sunfish and rainbow trout) suggested the following:
log M - 0.85 log K
ow
- 0.70 <°-l2)
However, if one assumes a partitioning into the lipid pool, the slope
of Hf versus KQW should be unity. That is:
» -K - (D"13)
NwA Kow K
where N' is the lipid based BCF (ug/kg(lipid) * wg/D and ^ is a lipid
w&
based uptake rate.
Makay ( 1982) reviewed data on BCF versus KQW and concluded chat a good
approximation indeed was that the slope was one if it is assumed that ac
the higher KQtf values the tests for BCF may not have been conducted long
enough to rea°ch equilibrium. (Growth rate at the higher level of KQW could
also reduce the BCF.) For preliminarV estimates of .the BCF for organic
chemicals we may assume then that the lipid based BCF is equal to the Xotf.
Again, it should be noted that the Nwt is defined for zero growth of che
organism. This is explored further below.
0.3 CHEMICAL DEPURATION
in depuration experiments, the organism is transferred to a tank with
zero toxicant concentration and the time history of the loss of the
chemical is measured. Equation (D-8) then becomes for c-0:
v-voexp<-K')t
or in terms of whole body burden:
»-«' exp<-K)t
-------
Again, the weight change of .Che organism must be properly taken into
account. 'Equation (D-14) can be used to estimate Kf and from the net
growth rate, the depuration rate K can be obtained. Or, Equation (D-15)
can be used directly where the whole body burden is plotted and the
depuration rate obtained from such data.
Two examples of uptake and loss due to excretion are shown on Figure
D-3. For the PCB case (Figure D-3a), the BCF (for pinfish), NW is 17 ug/gm
f ug/1 (Nf - 17,000) (assuming C-0). If the excretion rate Is estimated
from the uptake it is found to be 0.045/day or approximately four tines the
depuration rate of 0.012/day. Growth of the pinfish and storage in various
body compartments may account for the difference. For malathion in carp,
N .006 (M1 - 6), an indication of the lower tendency for malathion to be
accumulated. Depuration is rapid at an excretion rate of 1.23/day or
approximately two orders of magnitude faster than the PCB. The excretion
rate calculated from the. uptake experiment is approximately 0.6/day or
approximately half that calculated from the depuration experiment. Results
of the type shown on Figure D-3a and D-3b provide estimates of the key rate
parameters and equilibrium conditions for a variety of organisms and
substances.
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|