vvEPA
United States
f nvu<>nme'Hr(i Pio'ection
Agency
Environmental Res«atch
Laboratory
Athens GA 3061 3
EPA/600/3-86'
December 1986
SARAH,
A Surface Water
Assessment Model
for Back Calculating
Reductions in
Abiotic Hazardous
Wastes
-------
EPA/600/3-86/058
December 1986
SARAH, A Surface Water Assessment Model for Back Calculating
Reductions in Abiotic Hazardous Wastes
by
Robert B. Ambrose, Jr., and Scarlett B. Vandergrift
Assessment Branch
Environmental Research Laboratory
Athens, GA 30613
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GA 30613
Protection Agency
..',:."„ iv (r;T;L-16)
00111 otL-aet, Room 1670
c.0604
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DISCLAIMER
The information in this document has been funded wholly or in part by
the United States Environmental Protection Agency. It has been subject to
the Agency's peer and administrative review, and it has been approved for
publication as an EPA document. Mention of trade names or commercial pro-
ducts does not constitute endorsement or recommendation for use by the U.S.
Environmental Protection Agency.
ii
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FOREWORD
As environmental controls become more costly to implement and the penal-
ties of judgment errors become more severe, environmental quality management
requires more efficient management tools based on greater knowledge of the
environmental phenomena to be managed. As part of this Laboratory's research
on the occurrence, movement, transformation, impact, and control of environ-
mental contaminants, the Assessment Branch develops state-of-the-art mathema-
tical models for use in water quality evaluation and management.
The calculational framework and many of the equations incorporated into
this model were originally developed for EPA's Office of Solid Waste (OSW) in
support of the Land Disposal Banning Rule. These have been updated in res-
ponse to public comment, private peer review, and continuing improvements in
environmental science. Additional equations have been added to address toxi-
cant disposal through wastewater treatment facilities. The resulting Surface
water Assessment model for back calculating Reductions in Abiotic Hazardous
wastes (SARAH) is not meant to represent OSW policy on analysis of land dis-
posal facilities. Rather, it is intended to provide analysts the means to
rapidly explore the consequences of a variety of exposure and effects scenar-
ios resulting from disposal of toxicants. Appropriate application of the
model will provide valuable information on which to base pollution management
decisions by various industrial, state, and Federal organizations.
Rosemarie C. Russo, Ph.D.
Director
Environmental Research Laboratory
Athens, Georgia
iii
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ABSTRACT
The nearfield surface model (SARAH) calculates maximum allowable hazard-
ous waste concentrations based upon predicted exposure to humans or aquatic
life from contaminated surface water. The surface water contamination path-
ways analyzed in SARAH include groundwater leachate from a land disposal
facility, storm runoff from a land disposal facility, and discharge through a
waste water treatment facility. The human exposure pathways considered
include ingestion of treated drinking water and consumption of contaminated
fish. Acceptable leachate or industrial waste contaminant concentrations are
predicted by a "back calculation" procedure from chemical safety criteria in
surface water, drinking water, or fish.
SARAH is an interactive, menu-driven computer program with three default
data sets that can be rapidly modified. The analytical solutions for
contaminant behavior in the catchment and stream near the facility allow
rapid, multiple calculations needed for good sensitivity analysis. SARAH is
a modular FORTRAN program that can be modified and expanded with ease. The
first version is written for a VAX 11/785 minicomputer. A subsequent version
will operate on personal computers.
This report covers a period from January 1985 to September 1986, and
work was completed as of September 1986.
iv
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CONTENTS
Di sclaime r i i
Foreword ill
Abstract iv
Figures viii
Tables x
Acknowledgments. xi
1. Introduction 1
2. Theoretical Basis of Model 6
2.1 Potential Exposure Pathways.... 6
2.1.1 Contaminant Loading to the Stream 6
- Contaminant leaching and transport in groundwater 6
- Surface runoff from land disposal units 8
- Direct loading from a treatment facility 9
2.1.2 Initial Dilution in Stream 10
- Groundwater mixing 12
- Runoff mixing 12
- Direct discharge mixing 13
2.1.3 Transport of Contaminants Downstream...... 13
2.1.4 Exposure and Effects.. 15
- Human exposure to contaminants through drinking water.. 15
- Human exposure to contaminants through consumption
of fish 15
- Direct exposure of aquatic organisms 16
2. 2 Exposure Scenarios 17
2.2.1 Scenario 1A: Exposure to humans through drinking
water contaminated by leachate carried through
ground water to the stream 17
2.2.2 Scenario IB: Exposure to humans through consumption of
fish contaminated by leachate carried through
ground water to the stream.... 19
2.2.3 Scenario 1C: Exposure of aquatic life due to
leachate carried through ground water to the
stream 20
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CONTENTS (Continued)
2.2.4 Scenario 2A: Exposure to humans through drinking
water contaminated by leachate carried through
runoff from the 25-year, 24-hour storm event to
the stream. 22
2.2.5 Scenario 2B: Exposure to humans through consumption
of fish contaminated by leachate carried through
runoff from the 25-year, 24-hour storm event to
the stream 23
2.2.6 Scenario 2C: Exposure of aquatic life to leachate
carried through runoff from a 25-year, 24-hour
storm event to the stream 23
2.2.7 Scenario 3A: Exposure to humans through drinking
water contaminated by leachate carried through
catastrophic runoff loading to the stream 23
2.2.8 Scenario 3B: Exposure to humans through consump-
tion of fish contaminated by leachate carried
to the stream 25
2.2.9 Scenario 3C: Exposure of aquatic life to leachate
carried through catastrophic runoff loading to
the stream 25
2.2.10 Scenario 4A: Exposure to humans through drinking
water contaminated by a continuous discharge 25
2.2.11 Scenario 4B: Exposure to humans through consumption
of fish contaminated by a continuous direct
discharge 27
2.2.12 Scenario 4C: Exposure of aquatic life due tc a
continuous discharge ,. 27
2.2.13 Scenario 5A: Exposure to humans through drinking
water contaminated by a pulse discharge. 29
2.2.14 Scenario 5B: Exposure to humans through consumption
of fish contaminated by a pulse discharge 30
2.2.15 Scenario 5C: Exposure of aquatic life due to a
pulse discharge 30
2.2.16 Overview of the Analysis 32
2.3 Development of Equations.. 34
2.3.1 Leachate loading and dilution upon entry Into the
stream. 35
- Ground water loading and initial dilution 35
- Storm runoff loading and initial dilution 38
- Wastewater loading and initial dilution 42
vi
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CONTENTS (Continued)
2.3.2 Transport and transformation in stream 43
- Stream transport below continuous ground
water loading. 44
- Stream transport below pulse runoff loading. 44
- Stream transport below pulse discharge loading 45
2.3.3 Contaminant delivery to drinking water and fish 40
- Delivery of contaminant through drinking water 45
- Delivery of contaminants to aquatic organisms 46
- Delivery of contaminants through fish to humans.... 46
3. User's Manual 48
3.1 Explanation of Menus 48
3.1.1 Selection of scenarios... 48
3.1.2 Operation of model 49
3.2 Scenario Variables 51
3.3 Default Values 51
4. Programmer's Manual 63
4.1 Hardware and Software Requirements 63
4.2 VAX Installation and Implementation 63
4.3 Program Description 64
4.3.1 Input/output units 64
4.3.2 Common block 64
4.3.3 Common block listing... 65
4.3.4 Subroutine descriptions , 66
References 71
APPENDIX A: Advection, Dispersion and Chemical Transformation 72
APPENDIX B: Analytical Solution for Two-Dimensional due to Pulse
Loading 81
APPENDIX C: List of Symbols 85
APPENDIX D: Output Samples 93
vii
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FIGURES
Number
1 Routes of exposure to hazardous chemicals in surface water „ 2
2 Routes of exposure to hazardous chemicals in surface water 3
3 Contaminant tracking and transport in ground water system 7
4 Surface runoff from land disposal units 8
5 Loading of contaminant into the stream: a) Ground water
loading; b) Surface runoff loading; c) Direct discharge....... 11
6 Downstream contaminant transport from the edge of initial
mixing zone. • 14
7 Variation of dilution factor with stream flow for steady
groundwater loading 17
8 Flow chart for scenario 1A 19
9 Flow chart for scenario IB 20
10 Flow chart for scenario 1C 21
11 Flow chart for scenario 2A 22
12 Flow chart for scenario 2B 24
13 Flow chart for scenario 2C ... 24
14 Flow chart for scenario 3A 24
15 Flow chart for scenario 3B 26
16 Flow chart for scenario 3C < 26
17 Flow chart for scenario 4A 26
18 Flow chart for scenario 4B 28
19 Flow chart for scenario 4C 28
viii
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FIGURES (Continued)
Nmrtb
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TABLES
Number Page
1 Summary of potential exposure scenarios 18
2 Calculations for scenario 1 52
3 Input variables for scenario 1 53
4 Calculations for scenarios 2 and 3 55
5 Input variables for scenarios 2 and 3 56
6 Calculations for scenarios 4 and 5..... 58
7 Input variables for scenarios 4 and 5 59
8 Default values 1, 2, and 3 , 61
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ACKNOWLEDGMENTS
The nearfield exposure model described in this manual was developed for
EPA's Office of Solid Waste in support of the Land Disposal Banning Rule,
published in the January 14, 1986, Federal Register. This manual is based
upon the background report "A Methodology for Assessing Surface Water Contam-
ination Due to Land Disposal," and we gratefully acknowledge the contribu-
tions of two of the co-authors—Lee A. Mulkey and Peter S. Huyakorn. The
overall scope and technical approach was significantly influenced by Mr.
Mulkey. Original drafts of the background report were reorganized and en-
hanced technically by Dr. Huyakorn. We also acknowledge the patient efforts
of the OSW project officer Eydie Pines. Ms. Pines coordinated the technical
and policy reviews of the original analysis, prepared summaries for the
Federal Register, and supervised the modification and application of the
methodology.
Ronnie Moon, of Computer Sciences Corporation, created the original
computer program and updated it to keep track of changes in the methodology.
Michael J. Ungs, with Tetra Tech, thoroughly reviewed both code and documen-
tation, and programmed the enhancements suggested by Dr. Huyakorn. Gerhard
Jirka reviewed the documentation and offered a valuable critique. Many
others provided criticism and suggestions in public comment to the proposed
rule in the Federal Register. Annie J. Smith was responsible for the typing
and final preparation of the manuscript. Her efforts continue to earn our
respect and appreciation.
xi
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SECTION 1
INTRODUCTION
Industrial wastes containing potentially hazardous compounds are often
disposed of through wastewater treatment facilities or land disposal sites.
Contamination of surface water and exposure of humans and aquatic life to
hazardous compounds can occur from industrial wastes discharged from waste-
water treatment facilities or leaked from land disposal sites. If expected
exposure levels are too high, industrial wastes must be pretreated to an
acceptable level before introduction to treatment plants or disposal sites.
To help the analyst establish minimum pretreatment levels, the surface water
assessment model (SARAH) was developed to "back calculate" appropriate pre-
treatment concentrations from chemical safety criteria for exposure to humans
and aquatic life. SARAH should allow the user to screen a list of chemicals
and identify those that should be restricted or more fully treated before
discharge from an industrial plant.
The first step in this kind of analysis is to describe a set of scenar-
ios that might lead to the undesired consequences. As illustrated in Figure
1, the three loading routes to surface water considered in SARAH are direct
discharge in municipal and industrial wastewater effluent, overland runoff
from a land disposal site, and leaching to ground water from a land disposal
site. Once in surface water, chemicals are advected, dispersed, and degraded
by several mechanisms, reducing their concentrations. These aqueous concen-
trations may result in exposure to aquatic life and to humans through drink-
ing water or consumption of fish. Figure 2 outlines the contamination sce-
narios considered in SARAH.
The second step is to assign probabilities to each scenario. It is
virtually certain that aqueous chemicals introduced at a wastewater treatment
facility will be discharged in the effluent. On the other hand, the probabi-
lity that chemical solids introduced to some land disposal sites will escape
through runoff or leaching can be very small. Design and operating require-
ments for land disposal facilities promulgated under Parts 264 and 265 of the
Resource Conservation and Recovery Act (RCRA), for example, include liners,
leachate collection and removal systems, ground water monitoring, corrective
actions, and run-on and runoff controls. Nevertheless, this exposure model
assumes failure of all controls, leading to surface water contamination from
both a ground water and a surface runoff route. Thus, SARAH sets the proba-
bility of occurrence of various scenarios to 1.0 and helps the analyst inves-
tigate the consequences.
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.WATERSHED
LAND DISPOSAL
SITE
RUNOFF \ ^GROUNDWATCR
WASTEWATER EFFLUENT
TREATMENT
FACILITY
DRINKING
WATER
PLANT
RESIDENCES
Figure 1. Routes of exposure to hazardous chemicals in surface
water.
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WASTE
TREA
FAC
i
f
1
I
I
1
r
"WATER <
TMENT
ILITY
J
^
r
r
AQUAT
EXPOSU
1
C AQUATIC "\ /
\^ TOXICITY J \
HAZARDOUS
WASTE
— SLUDGE
R
L
N
C
F
F
>
> IAND DIS
SITE
5,
}
1
I
r
. SURFACE <
WATER
1C
RE
1
FISH ^ /
BIOACCUMULATION J \
•w ^S
3OSAL
L
E
A
C
H
I
N
G
GROUND
WATER
i
DRINKING
WATER
i <
^ HUMAN ^
^EXPOSURE ^
Figure 2. Routes of exposure to hazardous chemicals in surface
water.
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The third step is to investigate the consequences of each scenario.
Aquatic and human exposure to hazardous chemicals at high enough concentra-
tions can result in such undesired consequences as chronic toxicity in aqua-
tic organisms and cancer in humans. This analysis begins with criteria set
to protect against such adverse effects. A stream concentration criterion is
designated to protect aquatic life resident in the stream. Dose criteria set
to protect humans must be translated to drinking water and fish concentra-
tions assuming specified patterns of water and fish consumption. SARAH
begins its back calculations with these resulting "safe" concentrations and
assumes that lower concentrations produce no adverse effects.
SARAH includes five scenarios for the contamination of surface water:
(1) leaching and subsequent delivery of contaminated ground water to streams;
(2) steady runoff from a once-in-25-year, 24-hour storm event averaged over a
24-hour period; (3) pulse runoff from a once-in-25-yearj, 24-hour storm event
that is stored for a 24-hour period and released over a short time period
into a receding stream flow; (4) steady loading through a wastewater effluent,
and (5) pulse loading through a wastewater effluent. For each contamination
route, SARAH can consider up to three potential adverse effects: (a) human
exposure through consumption of contaminated drinking water, (b) human expo-
sure through consumption of contaminated fish, and (c) direct toxicity to the
aquatic community. Unrealistic combinations of contaminant release and ad-
verse effects are not implemented in SARAH, as discussed below.
This manual contains three main sections that can be used independently.
The first, Theoretical Basis of Model, documents the equations and assump-
tions underlying the model components. This section describes the procedures
developed for evaluating the influence of wastewater discharge or land dis-
posal on both health-based and environmental impacts. The overall approach
is based on a "back-calculation" to identify acceptable wastewater or leachate
concentrations given health-based or environmental thresholds that are not to
be exceeded at specified exposure points (or routes). This section charac-
terizes potential pathways leading to human and environmental exposure,
evaluates the likelihood of exposure for each pathway, and sets up backcalcu-
lation procedures for those pathways and exposure routes that are likely.
The next section, User's Manual, explains the model menus, documents
the generation of input data, describes the scenario variables, and lists the
default values. The final section, Programmer's Manual, documents the hard-
ware and software requirements necessary to support SARAH. Specifications
for the installation and implementation of SARAH are given and a description
of the computer program, which includes an overview of input/output units,
the COMMON block and subroutines, is provided.
In developing the equations, four main symbols are used:
•
m = chemical mass flux, in grams per second
Q = volumetric flow rate, in cubic meters per second
C = chemical concentration, in milligrams per liter (equivalently,
grams per cubic meter)
-------
£ = multiplication factor, representing attenuation or enhancement
of mass flux or concentration, unitless
Subscripts are used to distinguish the various fluxes, flows, concentrations,
and multiplication factors. Among the most common are:
L = leachate from solid waste disposal facility
W = industrial waste stream
g = groundwater in catchment contaminated by solid waste disposal
facility
D = wastewater effluent discharged to stream
R = surface runoff
U = upstream
0 = instream at downstream edge of initial mixing
y = lateral distance across stream
x = longitudinal distance downstream
DW = drinking water
F = fish uptake
EXP = aquatic exposure
ADI = acceptable daily intake of water by humans
ADI' = acceptable daily consumption of fish by humans
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SECTION 2
THEORETICAL BASIS OF MODEL
The fundamental principle underlying this model is mass conservation.
The equations solved by SARAH describe mass fluxes of chemicals in leachate,
effluent, runoff, and stream. Often, however, stream standards and waste
requirements are specified in terms of concentrations. For each step, mass
flux equations are developed and then presented as a series of concentration
reductions (or enhancements) between the waste release and the point of
exposure. The reduction factors are later considered in detail.
In this section, the potential pathways leading to contamination of sur-
face water and exposure to aquatic organisms and humans are explored. Next,
a set of exposure scenarios resulting from the pathways is considered.
Finally, the actual equations describing the mass transport, dilution, and
transformation processes are developed.
2.1 POTENTIAL EXPOSURE PATHWAYS
Pathways leading to contamination of surface water and exposure to
aquatic organisms and humans begin with the disposal of industrial wastes in
wastewater treatment or land disposal facilities. Wastewater effluent or
land disposal leachate can enter a stream through ground water transport, sur-
face runoff, or direct discharge. Contaminants in stream are subject to
advection, lateral and longitudinal mixing, and physical, chemical, and
biological reactions. Aquatic organisms are exposed directly to instream
concentrations. Human exposure occurs through consumption of contaminated
fish or drinking water that has been processed through water treatment plants
located downstream of the discharge. These sequential pathways are explored
in the following sections.
2.1.1 Contaminant Loading to the Stream—
Contaminant leaching and transport in ground water system—The release
and transport of hazardous constituents from a landfill through the ground
water pathway of the model assumes that the land disposal unit is hydrau-
lically connected to a stream (Figure 3). When liners or leachate collectors
at the base of the land disposal unit fail, leachate enters the aquifer
directly below the land disposal unit. Precipitation of metals is assumed to
occur at this point, placing upper limits on their dissolved concentrations.
Dissolved chemicals are then transported through the aquifer under the com-
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LAND yLINER
DISPOSAL UNIT
QROUNO WATER
FLOW —
//yssss/s/s//s//ssss//s///ss777///rsss/s/s//ss/ss////s/s//sssssss
Figure 3. Contaminant tracking and transport in ground water system.
bined influences of advection and hydrodynamic dispersion as well as sorption
and biochemical degradation for nonconservative species. The contaminants
discharge into the surface water throughout the zone where the aquifer and
the stream intercept.
The mass flux at the ground water interception zone or surface water
entry area, nig, and the mass flux of leachate, m^, may be related by:
mn
mL
(1)
where the mass flux units are expressed in grams per second, and CH is a
ground water attenuation factor accounting for the effects of hydrolysis in
the aquifer. The average concentrations at the ground water interception
zone and in the leachate can be obtained by dividing the mass fluxes by the
flow rates:
Cg = mg/Qg
CL = mL/QL
(2)
(3)
where flow units are expressed in cubic meters per second, concentration
units are expressed in milligrams per liter, and subscripts g and L refer to
ground water and leachate, respectively. Combining the above equations, the
average concentration at the ground water interception zone and the leachate
concentration may be related by:
Cg -
. C
(4)
where £ is the ground water reduction factor:
QL/Q
(5)
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Methods for calculating these parameters are developed in later sections.
Surface runoff from land disposal units—All RCRA Subtitle C land dis-
posal units (landfills, land treatment facilities, waste piles, and surface
impoundments) must be designed such that, at a minimum, runoff from a once-
in-25-years, 24-hour storm event is contained (40 CFR Parts 264 and 265).
Precipitation events of greater magnitude than the 25-year, 24-hour storm
event are assumed to occur at a sufficiently low probability that the protec-
tive design can be considered to provide an acceptable level of performance.
Other land disposal systems (RCRA Subtitle D) may be designed to contain
lesser storm events. "Failure" of a land disposal system, illustrated in
Figure 4, refers to its inability to contain a design storm event. Direct
surface runoff of leachate plus solids from surface impoundments is assumed
to occur from the "failed" containment unit over a time period tg.
//''/ //'////
////y//y/
STORM DETENTION
FACILITY
\\\ = \\\
\\\ -\\\
Figure 4. Surface runoff from land disposal units.
The concentration in the runoff leaving the containment facility is
assumed to be equal to the leachate concentration, CL. This assumption is
somewhat conservative: for the case involving surface impoundments, the
runoff concentration may be slightly reduced due to dilution from precipita-
tion water that fills the freeboard depth; for the case of landfills and
waste piles, not all the precipitation will have contact with the waste and
hence will be at a lower concentration.
-------
Two types of surface runoff are considered. The first assumes contain-
ment failure that allows leachate from storm runoff to enter a stream
steadily throughout the duration of the 24-hour storm. The second assumes
sudden containment failure that allows leachate generated during an entire
storm event to enter the stream as a pulse at the end of the storm. The time
over which the steady loading occurs is assumed to be equal to 24-hours (the
duration of the storm). The duration of the pulse loading is assumed to be
between 1()3 and 10^ seconds (approximately 15 minutes to 3 hours).
Because runoff leaving the containment facility is assumed to be at the
leachate concentration CL, the runoff mass flux mR is equal to:
™R = CL • QR <6)
where OR is the runoff flow rate, in cubic meters per second. The mass flux
in runoff entering the stream is assumed equal to that running off the
facility, because the short travel times should not allow transformation
reactions to occur significantly. Concentrations in the runoff leaving the
land disposal facility and entering the stream can be obtained by dividing
the mass fluxes by the respective flow rates:
CR = mR/QR (7)
CSR = mR/QSR (8)
where QgR is the runoff flow to the stream from the catchment containing the
land disposal facility, in cubic meters per second. Combining the above
equations, the average concentration in runoff entering the stream and the
leachate concentration may be related by:
CSR = CR . CL (9)
where £R is the runoff dilution factor:
Methods for estimating these parameters are developed in later sections. A
conservative analysis could assume that the leachate runoff is not mixed with
and diluted by runoff from upland areas of the catchment containing the land
disposal facility. The runoff mass loading is not affected by this assump-
tion, and stream concentrations below the initial mixing zone should not be
very sensitive to this assumption.
Direct loading from a treatment facility — All treatment facilities
discharging into a stream must comply with EPA rules and regulations. Waste
load allocations are based upon the detrimental effects to humans or aquatic
species and must specify the maximum loading rate and concentration of direct
discharge into a stream, m^ and CQ. In this analysis, maximum loading rates
and concentrations in both the industrial waste stream and in the wastewater
effluent may be estimated from maximum allowable stream concentrations by the
back calculation procedure.
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Two types of contaminant discharge are considered. The first is a
constant loading over a long period of time. The second type of
contaminant discharge is a pulse loading over a short period of time, tp.
The waste-water flow rates, and contaminant concentrations for both types of
discharge are assumed to be constant during the time of discharge.
•
The mass flux in the industrial waste stream, my, and the mass flux in
the treated wastewater effluent, raj), may be related by:
• •
mD = ^W • ™W ( 11)
where £y is the treatment plant attenuation factor (1-fractional removal)
accounting for the effects of sorption and settling, volatilization, and
bacterial degradation. No general equation is developed in this model for
calculating £^. If no measured (or independently estimated) value is
specified by the user, ty defaults to 1 and mass is conserved through the
treatment plant. The concentrations in industrial waste and the wastewater
effluent can be obtained by dividing the mass fluxes by the flow rates:
C^ — my/Q[j (12)
CD = mD/QD (13)
Combining the above equations, the concentrations in the wastewater effluent
and in the industrial waste may be related by:
CD = ^n • % (^)
where CD ^s the wastewater treatment plant reduction factor accounting for
both dilution and mass reduction due to treatment efficiency ey:
Qw
£D = ^w • QW/QD = (i ~ e^) — (15)
QD
All of these parameters are specified by the user, as discussed in later
sections.
2.1.2 Initial Dilution in Stream—
As the contaminated ground water, surface runoff, or treatment facility
effluent enters a stream (Figure 5), it mixes with upstream water with
pollutants at concentration C(j. Loading of contaminants to the stream re-
sulting from ground water interception, surface runoff, and direct discharge
is examined separately in the model. Ground water interception with the
stream is assumed to occur continuously along the sides and bottom of the
stream. Contaminant loading in surface runoff is assumed to occur intermit-
tently at the stream bank over a short time t^. Direct discharge is regarded
as either continuous or intermittent at the stream bank, occuring over time
period tp.
10
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LAND DISPOSAL UNIT
(a)
UNO DISPOSAL UNIT
LAND SURFACE
INITIAL MIXING
ZONE
(b)
WASTEWATER
TREATMENT
FACILITY
(c)
Figure 5. Loading of contaminant into stream—(a) ground water loading,
(b) surface runoff loading, (c) direct discharge.
11
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An initial mixing zone in the stream is developed over the contaminant
discharge area. For upland watersheds where the the stream is shallow,
complete, vertical mixing of the contaminant occurs within this mixing zone.
Lateral mixing may be incomplete, however, as indicated In Figure 5b,c. In
the cases of runoff loading and direct discharge, where lateral mixing is
likely to he incomplete, there is a finite plume width over which a Gaussian
concentration distribution CQ y is assumed. The maximum contaminant concen-
tration and the standard deviation of the Gaussian distribution are denoted
by CR (runoff), CQ (discharge), a^ (runoff), and OQ (discharge), respec-
tively. The standard deviation, a, is a measure of the plume width at the
edge of the mixing zone.
Ground water mixing — The contaminant mass flux loaded into the stream
from ground water, rasg> and the mass flux at the ground water interception
zone, nig, can be related by:
. .
mSg = ?i • mg (16)
where ^ is the fraction of groundwater from the catchment that actually
contributes to stream flow. The total mass flux at the downstream edge of
the mixing zone is the sum of the upstream mass flux, m^j, and the mass flux
loaded into the stream, mgg:
• • •
mo = msg + mu d7)
The concentrations can be obtained by dividing the mass fluxes by the stream
flow:
• Cg + CSU • Cu (18)
where CQ is the laterally-averaged concentration at the downstream edge of
the mixing zone, and £§„ and Cgu are dilution factors for ground water
and upstream concentrations, respectively:
<2°)
where QJJ is the upstream flow rate and Qgg is the ground water flow from the
catchment intercepted by the stream:
QSg = Ci - Qg <21>
and Qg is the downstream flow rate, or the sum of Qgg arid Qy.
Runoff mixing — The contaminant mass flux loaded into the stream from
surface runoff, mgR» ^s assumed equal to the runoff mass flux at the edge of
the stream, mg. The total mass flux at the downstream edge of the mixing
zone is the sum of the upstream mass flux, assumed equally distributed across
the stream, and the runoff mass flux, distributed along the near bank:
mO = mSR + mU (22)
12
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The concentration distribution across the mixing zone can be obtained by
dividing the mass fluxes by the stream flow:
C0,y = ^SR.y • CSR + ?SU • CU
where ?gy is a dilution factor for upstream concentrations:
and £g£ „ is a dilution factor for runoff concentrations describing a
lateral, Gaussian distribution across the stream. This dilution factor,
developed in later sections, declines from 1 at y = 0 to 0 for large values
of y. Qg is the downstream flow rate, or the sum of Q§R and Qy.
Direct discharge mixing — The contaminant mass flux loaded into the stream
from wastewater effluent, mgj), is assumed equal to the effluent mass flux, mp.
The total mass flux at the downstream edge of the mixing zone is the sum of
the upstream mass flux, assumed equally distributed across the stream, and
the effluent mass flux, distributed along the near bank:
• • *
mg = mgo + my (25)
The concentration distribution across the mixing zone can be obtained by
dividing the mass fluxes by the stream flow:
C0,y = ?SD,y • CD + ?SU • CU
where £gy is a dilution factor for upstream concentrations:
and ?gj) y is a dilution factor describing a lateral, Gaussian distribution
for effluent concentrations. This dilution factor, developed in later
sections, declines from 1 at y = 0 to 0 for large values of y. Qg is the
downstream flow rate, or the sum of QQ and Qy.
2.1.3 Transport of Contaminants Downstream —
Following initial dilution in the stream, the contaminant is trans-
ported downstream from the edge of the initial mixing zone. In the cases of
runoff loading and direct discharge, the initial boundary condition assumes a
Gaussian distribution CQ y. In the case of ground water loading, the initial
boundary condition is the laterally averaged CQ. At a specified downstream
measurement point, x, (Figure 6) the contaminant concentration, Cx, is ex-
pressed as:
^x = ^x • ^0 f°r ground water loading (28)
cx,y = ^x y • ^0,y f°r surface runoff and effluent discharge (29)
13
-------
PLUME BOUNDARY
U
TZ;
t
GROUND
WATER
LOADING
H—
\
MEASUREMENT
POINT
(a) Continuous Groundwater Loading
~"7K
Y
•f
B
c « 0,
DISCHARGE
LOADING
h-
H
MEASUREMENT
POINT
(b) Pulse Runoff Loading
Figure 6. Downstream contaminant transport from the
edge of initial mixing zone.
14
-------
where £x and Cx y are concentration reduction factors accounting for the
combined influence of advection, longitudinal and lateral dispersion, degra-
dation and sorption occurring during downstream transport. Note that in the
case of ground water loading, lateral mixing is probably almost complete at x
= 0, because of a fairly extensive contaminant discharge area as compared
to the cases of runoff loading.
2.1.4 Exposure and Effects —
Human exposure to contaminants through drinking water — Humans are ex-
posed to dissolved chemicals through the consumption of water obtained from a
treatment plant that is located in the zone of contamination downstream from
the initial mixing zone. The plant takes in water from the stream, with a
contaminant concentration, Cx y. The water is assumed to be treated by a
primary settling process allowing suspended solids and adsorbed chemicals to
settle out. As a result of this treatment, the contaminant concentration is
reduced from Cx v to Cpy. The relationship of Cpy and Cx v is expressed as:
CDW = £DW • cx,y
where CDW ^s the factor accounting for the reduction in contaminant concen-
tration achieved through the treatment process, i.e. , the pollutant removal
efficiency.
Human exposure to contaminants through consumption of fish — Another
route resulting in human exposure to chemicals in leachate and discharge is
the consumption of contaminated fish. To be conservative, it is assumed that
these fish reside continuously within the most polluted reach of the stream
where concentrations are not reduced by dilution or chemical transformation.
The allowable daily intake adopted here is based on an average 70-year con-
sumption of contaminated fish.
For the case of runoff loading, the infrequency of runoff events (2 or 3
occurrences in 70 years) and the length of time required for food fish to
attain high body burdens (weeks to months) should prevent significant contami-
nant doses to humans. For the case of ground water and direct discharge load-
ing, the continuous nature of discharge and ground water seepage into stream
may cause fish to attain high body burdens and result in significant contami-
nant doses to humans over a life time. Delivery of contaminants through
consumption of fish, then, is a long— term average, steady— state process. The
model allows for the fact that a fish population can be quite mobile over the
length and width of a contaminated stream. Furthermore, a single fish may be
exposed to a wide range of concentrations during its life time_. The typical
fish will be exposed to the average concentration denoted by CQ in the case
of ground water loading (given by equation 18) and by Cx y in the case of
direct discharge.
Chemicals enter a fish through biochemical exchanges across its gill and
gut membranes and through its skin. When these exchange processes have
reached equilibrium, the average concentration in the whole body of the fish
becomes Cp, which is related to the exposure concentration by:
15
-------
co (3D
" (32)
where £p is a bioaccumulation factor depending on both the nature of the
chemical and the species of fish.
Conceptually, one more step is required in calculating average chemical
dose through fish consumption. Most fish are cleaned, with much of the fat
removed before consumption. Because organic chemicals are concentrated in
fat, another reduction factor could be used to derive fillet concentrations
from whole fish concentrations. To be conservative, however, it is assumed
that there is no reduction in chemical concentration due to the preparation
of fish for consumption.
Direct exposure of aquatic organisms — If contaminant concentrations are
high enough, aquatic organisms may suffer chronic toxic effects. Water qual-
ity criteria have been established by EPA to protect against these effects.
These criteria specify acceptable concentrations, durations of averaging
periods, and frequency of allowed excursions. To prevent a potential hazard
to aquatic life, the average contaminant concentration in the surface water
is directly equated to the Criterion Continuous Concentration (CCC) Water
Quality Criteria. The duration of the averaging period is set at 4 days, and
the frequency of allowed excursions is no more than once in 3 years. To be
conservative, it is assumed that the fish reside continuously within the most
polluted reach of the stream where concentrations are not reduced by degrada-
tion.
For the case of runoff loading, the infrequency of runoff events (2 or 3
occurrences in 70 years) and their duration (approximately 1 day) should pre-
vent chronic toxic effects in aquatic organisms. For the case of ground water
loading and direct discharge, the continuous nature of seepage into streams
may result in chronic toxic effects. Because ground water loading is expected
to be relatively steady, highest stream concentrations should occur when the
stream reaches low, base flow conditions, providing the least dilution water.
For these conditions, both loading and dilution are driven by ground water
flow. The dilution factor should be steady for a wide range of base flows,
as illustrated by Figure 7. The model allows for the fact that a fish popu-
lation can be mobile over the width of a contaminated stream during a 4 day
period. Thus, the typical fish in the_most contaminated stream reach will be
exposed to the averaged concentration
CEXP = SEXP • co
or
CEXP = ^EXP • cx,y
where CgxP ^s an aquatic exposure factor, here equal to 1 and for ground
water and discharge loading, respectively.
16
-------
Stream
Concentration
C3
Dilution
Factor
BASE FLOW
STORM FLOW
tog Q,
Figure 7. Variation of dilution factor with stream flow for
steady ground water loading.
2.2 EXPOSURE SCENARIOS
Five sets of scenarios are considered. The five sets (1, 2, 3, 4, and
5) are distinguished from one another by the pathway through which contam-
inants reach and eventually enter into the stream. Each set consists of
three potential exposure routes (A, B, and C) that threaten humans or
aquatic organisms. These are summarized in Table 1.
2.2.1 Scenario 1A; Exposure to Humans through Drinking Water Contaminated
by Leachate Carried through Ground Water to the Stream—
This scenario consists of four stages between failure of the waste con-
tainment facility and the exposure of the contaminant to humans via drinking
water (Figure 8). Through these stages, the concentration is successively
reduced from the leachate concentration, CL , to the concentration in drinking
water, CD^J. The relationship between CD^, CU» anc* CL is given bY:
•-DW
CL
u
(35)
where ?„, Cgg» ^SU ^x» anc* ^DW are reduction factors due to transport in
ground water, mixing at the area of leachate entry into the stream, transport
in the stream, and treatment in the drinking water plant.
To determine whether a potential health hazard due to surface water
contamination exists, the drinking water concentration can be equated to the
specified acceptable daily intake concentration, C^pj. Thus:
17
-------
TABLE 1. SUMMARY OF POTENTIAL EXPOSURE SCENARIOS
SCENARIO
SOURCE PATHWAY
EXPOSURE ROUTE
1A
IB
1C
2A
2B
2C
3A
3B
3C
4A
4B
4C
5A
5B
5C
ground water seepage
steady surface runoff from a
design storm event
pulse surface runoff from a
design storm event
steady discharge from a wastewater
treatment facility
batch discharge from a wastewater
treatment facility
human exposure via
drinking water
human exposure via
fish consumption
direct exposure of
aquatic organisms
human exposure via
drinking water
human exposure via
fish consumption
direct exposure of
aquatic organisms
human exposure via
drinking water
human exposure via
fish consumption
direct exposure of
aquatic organisms
human exposure via
drinking water
human exposure via
fish consumption
direct exposure of
aquatic organisms
human exposure via
drinking water
human exposure via
fish consumption
direct exposure of
aquatic organisms
18
-------
STREAM FLOW
WASTE
CONTAINER
FAILURE
TRANSPORT IN
GROUND WATER
-X
MIXING AT
ENTRY POINT
X-
TRANSPORT
IN STREAM
(STEADY SOURCE)
DRINKING WATER
PLANT
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 8. Flow chart for scenario 1A.
CDW ~ CADI
and the maximum allowable leachate concentration must be:
CADI ~ ^SU ?x ?DW CU
(36)
(37)
2.2.2 Scenario IB; Exposure to Humans through Consumption of Fish Contam-
inated by Leachate Carried through Ground Water to the Stream—
This scenario consists of three stages between the containment failure
and human exposure via consumption of fish residing in the contaminated
surface water (Figure 9). Through these stages, the input concentration is
successively reduced from the leachate concentration, CL, to the stream
concentration, and then increased to the bioconcentrated level in the fish,
Cp. The relation between CL, Cy, and Cp is given by:
CL
cu
(38)
19
-------
WASTE
CONTAINER
FAILURE
TRANSPORT IN
GROUND WATER
STREAM FLOW
MIXING AT
ENTRY POINT
UPTAKE BY
FISH
EXPOSURE TO HUMANS
Figure 9. Flow chart for scenario IB.
where Cp is the bioconcentration factor due to the biochemical exchange
processes with the fish.
For back—calculation, the average concentration in the fish, Cp, can be
equated to a specified acceptable daily intake bioaccumulation concentration,
C'ADI- Thus:
CF - G^JJJ (39)
and the maximum allowable leachate concentration is given by:
"ADI
"SU
(40)
2.2.3 Scenario 1C; Exposure of Aquatic Life due to Leachate Carried through
Ground Water to the Stream-—
This scenario consists of two stages between the waste containment unit
failure and aquatic exposure (Figure 10). Through these stages, the input
20
-------
concentration is successively reduced from the leachate concentration, CL , to
_the average stream concentration, CQ. The relationship between CL, GU, and
CQ is given by:
C0 ~
CL
U
(41)
WASTE
CONTAINER
FAILURE
TRANSPORT IN
GROUND WATER
STREAM FLOW
MIXING AT
ENTRY POINT
(EXPOSURE TO
AQUATIC ORGANISMS
Figure 10. Flow chart for scenario 1C.
For back-calculation, the average concentration in the stream can be
equated to a specified Criterion Continuous Concentration Water Quality
Criteria, CCC. Thus:
CQ = CCC
and the maximum allowable leachate concentration is given by:
CCC -
CL =
(42)
(43)
21
-------
2.2.4 Scenario 2A: Exposure to Humans through Drinking Water Contaminated
by Leachate Carried through Runoff from the 25-Year, 24-Hour Storm
Event—
This scenario consists of four stages between the waste containment
failure and exposure of the contaminant to humans via drinking water (Figure
11). Through these stages, the concentration is successively reduced from
the leachate concentration, CL, to the concentration in the drinking water,
The relationship between CDW, Cy, and CL is given by:
CDW =
CL
U
(44)
where ?R, ?s» ^x> anc* ?DW are reduction factors due to dilution during runoff,
initial mixing at the stream entry area, transport in the stream, and drinking
water treatment, respectively.
BASE FLOW +
WATERSHED
RUNOFF
WASTE
CONTAINER
FAILURE
STORM
RUNOFF
X
MIXING AT
ENTRY POINT
X.
TRANSPORT
IN STREAM
(PULSE SOURCE)
DRINKING WATER
PLANT
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 11. Flow chart for scenario 2A.
22
-------
Because of the pulse runoff loading condition, the concentration Cpy
is time dependent. Thus, it is averaged over a 1-day period. This average
concentration, , can then be equated to the specified acceptable daily
intake concentration, C^jjj. It follows that:
= CADI
and the maximum allowable leachate concentration is given by:
CADI
where angular brackets are used to denote the 1-day average of the enclosed
quantity.
2.2.5 Scenario 2B; Exposure to Humans through Consumption of Fish
Contaminated by Leachate Carried through Runoff from the 25-Year,
24-Hour Storm Event—
This scenario consists of four stages between the waste containment
failure and exposure of contaminant to humans via consumption of fish (Figure
12). Through these stages, the input concentration is altered from the
leachate concentration, CL, to the average concentration in the fish, Cp.
The infrequency of runoff events (2 or 3 occurrences in 70 years) and the
length of time required for food fish to attain high body burdens (weeks to
months) should prevent significant contaminant doses to humans from this
scenario. Consequently, back-calculation formulas are not developed.
2.2.6 Scenario 2C; Exposure of Aquatic Life to Leachate Carried by
Runoff from a 25-Year, 24-Hour Storm Event—
This scenario consists of three stages between the waste containment
unit failure and aquatic exposure (Figure 13). Through these stages, the
input concentration is reduced from the leachate concentration, CL, to
the stream concentration Cx „. The infrequency of runoff events (2 or 3
occurrences in 70 years) and their duration (approximately 1 day) should
prevent chronic toxic effects in aquatic organisms. Consequently, back-
calculation formulas are not developed.
2.2.7 Scenario 3A; Exposure to Humans through Drinking Water Contaminated
by Leachate Carried through Catastrophic Runoff Loading to the Stream—
This scenario consists of four stages between the waste containment
failure and exposure of the contaminant to humans via drinking water (Figure
14). Through these stages, the concentration is successively reduced from CL
t O
23
-------
Figure 12. Flow chart for scenario 2B.
Figure 13. Flow chart for scenario 2C.
Figure 14. Flow chart for scenario 3A.
24
-------
In a similar manner to Scenario 2A, a daily averaged concentration in
drinking water, , is obtained and equated to C^ni to yield the following
equation for the maximum leachate concentration, C^.
ADI - SU x DW U
where £R, 5g, ?x, and ?Q^ are reduction factors due to, respectively,
dilution during runoff, initial mixing at the stream entry area, transport in
the stream, and drinking water treatment.
2.2.8 Scenario 3B: Exposure to Humans through Consumption of Fish
Contaminated by Leachate Carried through Catastrophic Runoff Loading
to the Stream—
This scenario consists of four stages between the waste containment
failure and exposure of the contaminant to humans via consumption of fish
(Figure 15). Through these stages, the concentration is successively reduced
from CL to Cp. For reasons given in Scenario 2B, significant contaminant
doses to humans from this scenario are ruled out. Back-calculation formulas
are not developed.
2.2.9 Scenario 3C; Exposure of Aquatic Life due to Leachate Carried through
Catastrophic Runoff Loading to the Stream—
This scenario consists of three stages between the waste containment
unit failure and aquatic exposure (Figure 16). Through these stages, the
input concentration is reduced from the leachate concentration, 0^, to the
stream concentration Cx y. The infrequency of runoff events (2 or 3 occur-
rences in 70 years) and their duration (approximately 1 day) should prevent
chronic toxic effects in aquatic organisms. Consequently, back-calculation
formulas are not developed.
2.2.10 Scenario 4A; Exposure to Humans through Drinking Water Contaminated
by a Continuous Discharge —
This scenario consists of four stages between the industrial waste
stream and exposure of the contaminant to humans via drinking water (Figure
17). Through these stages, the concentration is successively reduced from
the industrial waste concentration, C^, to the concentration in the drinking
water Cpy. The relationship between Cpy, Cjj, and Cy is given by:
CDW = SD SSD £x,y ?DW cw + ?su ?x ?DW cu
where CQ, £sD» ^SU» ^x y» an<* ^DW are reduction factors due to wastewater
treatment, initial mixing at the stream entry area, transport in the stream,
and drinking water treatment, respectively.
25
-------
Figure 15. Flow chart for scenario 3B.
Figure 16. Flow chart for scenario 3C.
Figure 17. Flow chart for scenario 4A.
26
-------
To determine whether a potential health hazard due to surface water
contamination exists, the drinking water concentration can be equated to the
specified acceptable daily intake concentration, C^DI* Thus:
CDW = CADI
and the maximum allowable concentration must be:
CADI ~ ?SU ?x ?DW CU
(50)
2.2.11 Scenario 4B; Exposure to Humans through Consumption of Fish
Contaminated by a Continuous Direct Discharge —
This scenario consists of four stages between the industrial waste
stream and human exposure via consumption of fish residing in the contami-
nated surface water (Figure 18). Through these stages, the input concentra-
tion is successively reduced from the industrial waste concentration, Cy, to
the average stream concentration through a specified reach, and then increased
to the bioconcentrated level in the fish, Cp. The relation between Cy, Cy,
and Cp is given by:
CF = SD SSD £x,y ^F cw + ^su ^x SF cu
For back-calculation, the average concentration in the fish, Cp, can be
equated to a specified acceptable daily intake bioaccumulation concentration,
CADI. Thus:
(52)
and the maximum allowable discharge concentration is given by:
r' — r r r C
LADI GSU Sc ^F U
Cy = (53)
2.2.12 Scenario 4C; Exposure of Aquatic Life due to a Continuous Discharge—
This scenario consists of three stages between the industrial waste
stream and aquatic exposure (Figure 19). Through these stages, the input
concentration is successively reduced froin the industrial waste concentration,
Cy, _tp the average stream concentration, Cx y. The relation between Cy, Cy,
and Cx y is given by:
Cx,y = £D £SD ?x,y CW + ^SU ^x CU (54)
For back-calculation, the average concentration in the stream can be
equated to the CCC by:
27
-------
STEADY
INDUSTRIAL
WASTE
STREAM
DISCHARGE
THROUGH
TREATMENT
FACILITY
HUMAN EXPOSURE
VIA FISH
CONSUMPTION
Figure 18. Flow chart for scenario 4B.
STEADY
INDUSTRIAL
WASTE
STREAM
EXPOSURE TO
AQUATIC ORGANISMS
Figure 19. Flow chart for scenario 4C.
28
-------
(55)
and the maximum allowable discharge concentration is given by:
CCC -
CW =
(56)
2.2.13 Scenario 5A; Exposure to Humans through Drinking Water Contaminated
by a Pulse Discharge—
This scenario consists of four stages between the industrial waste stream
and exposure of the contaminant to humans via drinking water (Figure 20).
BATCH
INDUSTRIAL
WASTE
\ STREAM /
DISCHARGE
THROUGH
TREATMENT
FACILITY
DRINKING WATER
PLANT
UPSTREAM
FLOW
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 20. Flow chart for scenario 5A.
29
-------
Through these stages, the concentration is successively reduced from Cy to
CDW* *n a similar manner to Scenario 4A, a time-averaged concentration in
drinking water, , is obtained and equated to CADI to yield the following
equation for the maximum discharge concentration, C^:
CADI -<^su ?x ?DW> cu
CW = ----------------------- (57)
where £D, ?Su, £x,y» anc* ^DW are reduction factors due to initial mixing at
the stream entry area, transport in the stream, and drinking water treatment,
respectively.
2.2.14 Scenario 5B; Exposure to Humans through Consumption of Fish
Contaminated by a Pulse Discharge —
This scenario consists of four stages between the industrial waste
stream human exposure via consumption of fish residing in the contaminated
surface water (Figure 21). Through these stages, the Input concentration is
successively reduced from the industrial waste concentration, Cy, to the
average stream concentration throughout a specified reach, and then increased
to the bioconcentrated level in the fish, Cp. A time-averaged bioconcentrated
level in the fish, , is obtained and equaled to a specified acceptable
daily intake bioaccumulation concentration, CADI. Thus::
t
CADI ~ ?SU ?x ?F CU , ^
= ------------------- (58)
2.2.15 Scenario 5C; Exposure of Aquatic Life due to a Pulse Discharge —
This scenario consists of three stages between the industrial waste
stream and aquatic exposure (Figure 22). Through these stages, the input
concentration is successively reduced from the industrial waste concentration,
Cy, to the time and s_tream averaged concentration, . The relationship
between Cy, %, and is given by:
= y> + csu ^x cu
For back-calculation, the average concentration in the stream can be
equated to a specified CCC. Thus:
= CCC (60)
and the maximum allowable discharge concentration is given by:
CCC -
30
-------
UPSTREAM
FLOW
BATCH
INDUSTRIAL
WASTE
STREAM
DISCHARGE
THROUGH
TREATMENT
FACILITY
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
UPTAKE BY
FISH
HUMAN EXPOSURE
VIA FISH
CONSUMPTION
Figure 21. Flow chart for scenario 5B.
UPSTREAM
FLOW
BATCH
INDUSTRIAL
WASTE
STREAM
v,
s
DISCHARGE
THROUGH
TREATMENT
FACILITY
>
\
/
MIXING AT
ENTRY POINT
TR
1 (PUL
TRANSPORT IN
STREAM
(PULSE SOURCE)
EXPOSURE TO
AQUATIC ORGANISMS
Figure 22. Flow chart for scenario 5C.
31
-------
2.2.16 Overview of the Analyses—
Scenario 1A: Exposure to humans through drinking water due to ground water
interception with the stream
• Release from waste facility containment to ground water
• Transport in ground water to surface water body
• Mixing with the stream
• Transport in stream to drinking water intake
• Treatment of drinking water
Scenario IB: Exposure to humans through fish consumption due to ground water
interception with the stream
• Release from waste facility containment to ground water
• Transport in ground water to surface water body
• Mixing with the stream
• Uptake by fish through gills, gut, and skin
Scenario 1C: Exposure to aquatic organisms due to ground water interception
with the stream
• Release from waste facility containment to ground water
• Transport in ground water to surface water body
• Mixing with the stream
Scenario 2A: Exposure to humans through drinking water due to steady runoff
from a design storm event
• Surface runoff from waste containment facility
• Overland transport assuming no reduction in mass
• Mixing with the stream
• Transport in stream to drinking water intake
• Treatment of drinking water
Scenario 2B: Exposure to humans through fish consumption due to steady
runoff from a design storm event
Not modeled.
32
-------
Scenario 2C: Exposure to aquatic organisms due to steady runoff from a
design storm event
Not modeled.
Scenario 3A: Exposure to humans through drinking water due to pulse runoff
from a design storm event
• Surface runoff loading from waste containment facility
• Overland transport assuming no reduction in mass
• Mixing with the stream
• Transport in the stream to drinking water intake
• Treatment of drinking water
Scenario 3B: Exposure to humans through fish consumption due to pulse
runoff from a design storm event
Not modeled.
Scenario 3C: Exposure to aquatic organisms due to pulse runoff from a
design storm event
Not modeled.
Scenario 4A: Exposure to humans through drinking water due to a steady
waste discharge
• Discharge to treatment facility
• Dilution and degradation in treatment facility
• Mixing with the stream
• Transport in stream to drinking water intake
• Treatment of drinking water
Scenario 4B: Exposure to humans through fish consumption due to a steady
waste discharge
• Discharge to treatment facility
• Dilution and degradation in treatment facility
• Mixing with stream
• Uptake by fish through gills, gut, and skin
33
-------
Scenario 4C: Exposure to aquatic organisms due to a steady state discharge
• Discharge to treatment facility
• Dilution and degradation in treatment facility
• Mixing with the stream
Scenario 5A: Exposure^ to humans through drinking water due to a batch waste
discharge
• Discharge to treatment facility
• Dilution and degradation in treatment facility
• Mixing with the stream
• Transport in stream to drinking water intake
• Treatment of drinking water
Scenario 5B: Exposure to humans through fish consumption due to a batch
waste discharge
• Discharge to treatment facility
• Dilution and degradation in treatment facility
• Mixing with stream
• Uptake by fish through gills, gut, and skin
Scenario 5C: Exposure to aquatic organisms due to a batch waste discharge
• Discharge to treatment facility
• Dilution and degradation in treatment facility
• Mixing with the stream
2.3 DEVELOPMENT OF EQUATIONS
In this section, equations for determining the reduction factors corre-
sponding to various contaminant pathways are presented. Where appropriate,
the key equations are derived. Major symbols used are listed in Appendix C.
The scenarios for leachate loading and initial dilution are considered first.
Next, equations for stream transport and transformation are developed.
Finally, contaminant delivery to drinking water and fish is considered.
34
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2.3.1 Leachate Loading and Dilution upon Entry into the Stream—
Loading of contaminants into the stream can be supplied from ground
water flow through an aquifer intercepting the stream, from surface runoff
and overland flow, or from direct discharge from a wastewater treatment
facility. For the ground water and continuous discharge loading, the steady-
state loading assumption will be used. The surface runoff and batch discharge
loading assumes intermittent pulse loading.
Ground water loading and initial dilution—Contaminants reaching a
stream via ground water will essentially enter the water body continuously,
if hydraulic impacts of such interception are ignored. This assumes that
the ground water flow field is not influenced by the adjacent surface water.
Therefore, for the ground water pathway, the average edge-of-stream concen-
tration can be calculated from the leachate concentration via a ground water
equation that considers advection, retardation, and chemical hydrolysis.
For this analysis, it is not necessary to calculate a full three-
dimensional concentration distribution for the ground water. In fact, only
the average ground water concentration across the plume is needed to the
point of its interception with the stream. The average ground water attenua-
tion factor, which is used in equation 1, can be calculated using a one-
dimensional mass balance. This mass balance is equivalent to using a three-
dimensional ground water equation, then averaging over the width and depth of
the plume.
As the contaminated water from the aquifer system enters the stream
along the side and bottom, it mixes with fresh surface water supplied by the
upland watershed as illustrated in Figure 23. Lateral mixing spreads the
contaminants until lateral concentration gradients disappear. The laterally-
averaged concentration, C^, increases with increasing distance reaching a
maximum near the downstream edge of the contaminated ground water plume,
where x = 0. At the section where x = 0, Cx corresponds to CQ and can be
calculated by a simple mass balance.
The equations developed in Sections 2.1.1 and 2.1.2 relate contaminant
concentrations in the leachate with concentrations in groundwater, and these
with concentrations in stream. Combining equations 4, 5, 18-21 gives:
QL Qu
c0 = SH • Si. . — . CL + — . cu (62)
Qs Qs
where CL and QL are the leachate concentration and flow rate, ?jj is a ground
water attenuation factor accounting for the effects of hydrolysis in the
aquifer, £-[ is the fraction of the ground water flow from the contaminated
catchment that is intercepted by the stream, Qg is the total ground water
flow from the contaminated catchment, Cy and Qy are the upstream concentration
and flow, and Qs is the total stream flow below the contaminated catchment.
These terms are discussed below.
35
-------
LAND DISPOSAL
.E2T
xxxxx 'xxxxxxxxx,
I QQ
1 Cg
B
X/VXXXXX/TXXX
x=o
CX
AVE.
CONG.,
CX
DISTANCE, X
Figure 23. Ground water loading to the stream showing mass balance
and concentration profiles.
36
-------
£H — This attenuation factor is the fraction of the contaminant mass not
transformed by hydrolysis during ground water transport to the stream.
Assuming a homogeneous aquifer, this factor can be calculated by:
CH = exp (-Kg . Tg) (63)
where K is the total effective decay constant in ground water, in years ,
and Tg is the time taken by the contaminant to travel from the land disposal
site to the stream entry point, in years. For those chemicals that hydrolyze,
Kg is equal to the overall hydrolysis rate constant given by equations A23
and A25 in Appendix A. The travel time of contaminants in ground water is
given by:
Xg
T = ---- - --- (64)
Vg . fDg
where Xg is the distance from the site to the stream, in meters, Vg is the
ground water seepage velocity, in meters per year, and fj)g is the fraction of
the compound that is dissolved in the aquifer, given by equation A16 in
Appendix A.
?£ — This attenuation factor is the fraction of the ground water flow
from the contaminated catchment that is intercepted by the stream. This
can be quite variable, depending on location in the watershed and time of
year. If this factor is unknown for a given site, a conservative analysis
is suggested in which ?i is set to 1.
QL — This flow is the average volumetric rate of percolation through
the land disposal site, in cubic meters per second, and may be estimated
by:
P . (l-fR) . A,,
QL = --------------- . ------- (65)
100 . 86400 . (365.25)
where P is the average annual precipitation rate, in cm/year, (l-fR) is
the fraction of precipitation that leaches through the waste site to
ground water, and AW is the surface area providing water that leaches
through the disposal facility, in square meters. If the sides of the
disposal facility remain properly lined, and failure occurs through the
bottom only, then Aw will be equal to the actual surface area of the
disposal facility.
Qg — This is the average stream flow at the downstream edge of the
contaminated plume, in cubic meters per second, and may be estimated by:
? . U-TR) . ?£ . As
QS = ---------------------- (66)
100 . 86400 . (365.25)
37
-------
where P is the average annual precipitation rate, in cm/year, (l-f^) is
the average fraction of precipitation that leaches through the upper
watershed to ground water, £^ is the average fraction of ground water
flow contributing to stream flow in the upper watershed, and As is the sur-
face area of the upper watershed (hydraulically including the contaminated
catchment and above). If the average stream flow per unit area is known,
then QS can be approximated by:
QS = Qs • As (67>
where qg is in units of cubic meters per second per square meter.
QU — This is the average stream flow at the upstream edge of the contami
nated plume, in cubic meters per second. It may be estimated by:
As - A
QS • ------- (68)
AS
where Ag is the surface area of the contaminated catchment, diluting the
leachate. If Ag is unknown, it may be conservatively estimated as the
surface area leaching through the land disposal unit Aw plus the minimum
surface area between the facility and the stream.
Ag = Aw + Xg ./A (69)
Substituting equations 63, 65, and 66 into 62 and assuming no upstream
contamination gives the stream concentration resulting from leachate only:
AW (!
C0 = exp(-Kg Tg) . — . --- ~- . — . CL (71)
AS (l
Because clay liners should exhibit lower hydraulic conductivity than natural^
watersheds, the ratio (l-f^)/(l-fj^) should be less than 1.0. The ratio ?i/?i
could be less than or greater than 1.0, depending on the location of the land
disposal site. A conservative analysis could be run assuming equal hydraulic
conductivities and the fraction of the contaminated plume intercepted = 1:
_ AW
C0 = exp(-Kg Tg) . Z ------ . CL (72)
q . AS
Storm runoff loading and initial dilution — Contaminants reaching a
stream via storm runoff are assumed to enter the stream as a steady load
throughout runoff duration t^ (Figure 24). For scenario 2, the time over
which the contaminant loading occurs is assumed to be the 1-day duration of
the storm. For scenario 3, contaminant loading is assumed to occur for a
short duration following the storm. During the runoff event, an initial
mixing zone is developed over the runoff discharge area. Within this mixing
38
-------
PRECIPITATION
cm/day
RUNOFF FLOW
m3/sec
ELAPSED TIME, sec
(a)
PRECIPITATION
cm/day
RUNOFF FLOW
m3/sec
ELAPSED TIME, sec
(b)
Figure 24. Precipitation and runoff flows: (a) runoff due to
24-hour precipitation, (b) catastrophic pulse
runoff at the end of the 24-hour storm.
39
-------
zone, dilution of the runoff concentration occurs but is somewhat limited by
the magnitude of the runoff flow compared with the stream flow. At the edge
of the initial mixing zone (x = 0), it is assumed that the transverse concen-
tration distribution is a Gaussian distribution.
The equations developed in Sections 2.1.1 and 2.1.2 relate contaminant
concentrations in the leachate running off the facility with concentrations
in runoff at the stream bank, and these with concentrations in stream. Com-
bining equations 9, 10, 23, and 24 gives:
QR Qu
C0,y - ?SR,y • . CL + — . Cy (73)
QSR Qs
where CL is the leachate concentration, QR is the leachate flow running off
the facility, QSR is the runoff flow from the contaminated catchment, Qy is
the upstream flow, Cy the upstream concentration, Qg is the total down stream
flow, and £gR y is a dilution factor for runoff concentrations describing a
lateral, Gaussian distribution across the stream. These terms are discussed
below.
CSR „—Runoff entering a stream adds to the stream flow along the bank.
It is assumed that stream flow at the bank in the mixing zone is at the run-
off concentration, which is diluted laterally according to the Gaussian
distribution:
CSR,y = exP(-y2/2 °2> (74)
where y is the lateral distance across the stream and ° is the standard devia-
tion of the distribution, which can be derived from mass balance principles
as follows. For the case of no upstream concentrations, the mass flux in the
stream at the edge of the mixing zone is equal to the mass flux entering the
stream as runoff:
• •
mSR = "0
The runoff mass flux is its flow times its concentration:
•
mSR = QSR • CSR
The instream mass flux can be obtained by integrating the lateral concentra-
tion distribution over width:
B
mo = U . d . / CSR . exp(-y2/2 O2)dy (77)
0
where U is average stream velocity, in meters per second, d is average stream
depth, in meters, and B is stream width in meters. Integrating equation 77
and equating it to 76 gives:
40
-------
QSR . CSR = /ir/2 . U . d . o . CgR . erf(B/o 2) (78)
where erf is the error function, which is equal to 1.0 for B» o. Noting
that stream flow Qg is the product of the mean depth, velocity, and width (Qg
= UdB), equation 78 can be solved for a:
B QSR QSR
0 = ---- . . --- = 0.798 . B . --- (79)
/?72" Qs Qs
QR — The leachate flow running off the facility, in cubic meters per
second, may be evaluated from:
P25 • fR • Aw
QR = ------------- (80)
100 . tR
where ?25 is the precipitation for the 25-year recurrence, 24-hour duration
storm, in cm, tR is the time over which contaminant runoff occurs, in sec, fR
is the fraction of the precipitation that runs off the waste site, and Aw is
the surface area providing water that leaches through the disposal facility,
in square meters. For scenario 2, steady runoff is assumed to occur through-
out the storm, and tR is 86400 seconds. For scenario 3, runoff is assumed to
occur over a short period of time following the storm, and tR is 10 - 10
seconds.
QgR — The runoff flow from the contaminated catchment, in cubic meters
per second, may be estimated by:
P25 • fR • (Ag-Aw) P25 • fR • Aw
QSR = ------------------ + ------------- (81)
100 . ts 100 . tR
where ts is the duration of the storm, or 86400 sec, and Ag is the land area
of the contaminated catchment, in square meters, which includes the surface
area of the facility Aw plus the surface area between the facility and the
stream. Note that for steady runoff throughout the storm, tR = ts and equa-
tion 81 reduces to:
P25 • fR • Ag
QSR - ------------- (82)
100 . ts
For the case of no dilution in overland flow, Ag = Aw and equation 81 reduces
to:
P25 • fR • AW
QSR = ------------- - QR (83)
100 . ts
41
-------
QU—The stream flow at the upstream edge of the contaminated runoff, in
cubic meters per second, may be estimated by
B P25 * fR * fR ' AU
u s 100 . ts
where fR is the average fraction of the precipitation that runs off the
upper watershed, fR is a stream flow recession parameter (0—1) for scenario
3 runoff events that follow a storm, AIT is the surface area of the watershed
73
hydraulically above the contaminated catchment, in square meters, and Q~ is
the base flow of the upper watershed, in cubic meters per second.
Qg—The total stream flow at the downstream edge of the mixing zone is
the sum of the upstream flow and the runoff flow:
P25 fR . AU fR . (Ag-A^ fR . Aw
Qs = Q| + . [ + + ] (85)
100 ts ts tR
Wastewater loading and initial dilution-Contaminants reaching a stream
via wastewater discharge are assumed to enter the stream as a steady load of
duration tjj. For scenario 4, the time over which the contaminant loading
occurs is assumed to be indefinite. For scenario 5, contaminant loading is
assumed to occur for a short duration on a regular basis.
During wastewater discharge, an initial mixing zone is developed over
the discharge area. Within this mixing zone, dilution of the discharge con-
centration occurs but is somewhat limited by the magnitude of the discharge
flow compared with the stream flow. At the edge of the initial mixing zone
(x = 0), it is assumed that the transverse concentration distribution is a
Gaussian distribution.
The equations developed in Sections 2.1.1 and 2.1.2 relate contaminant
concentrations in the industrial waste stream with concentrations in the
wastewater effluent, and these with concentrations in stream. Combining
equations 14, 15, 26, and 27 gives:
Qw Qu
C0,y ~ ?SD,y • ?W • — • CW + — • CU (86)
% Qs
where Cy is the industrial waste concentration, Qy is the industrial waste
flow, Op is the wastewater effluent flow, £^ is the treatment plant mass
attenuation factor, QJJ is the upstream flow, Cy is the upstream concentra-
tion, Qg is the total downstream flow, and Cgjj v is a dilution factor for
effluent concentrations describing a lateral, Gaussian distribution across
the stream. These terms are discussed below.
Sgj) „—Wastewater effluent entering a stream adds to the stream flow at
a point near the bank. It is assumed that stream flow at the bank in the
42
-------
mixing zone is at the effluent concentration, which is diluted laterally
according to the Gaussian distribution:
CSD,y = exp(-y2/2a2) (87)
where y is lateral distance across the stream and 0 is the standard deviation
of the distribution. This parameter can be derived following equations 75-
79, substituting rap for mSR and QD for QgR to give:
B QD QD
a = --- . — = 0.798 . B . — (88)
/TT /2 Qs Qs
Cy — The treatment plant mass attenuation factor accounts for the effects
of sorption and settling, volatilization, and bacterial degradation. No
general equation is developed here for calculating Cy. If no measured or
independently estimated value is specified by the user, ?y defaults to 1 and
mass is conserved through the treatment plant.
Qy — The flow rate for the industrial waste stream, in cubic meters per
second, must be specified by the user. If total loading ny and concentration
Cy are known, then Qy can be calculated by:
mw
QW = ------- (89)
Cw . tD
where ny is expressed in grams, Cy is expressed in mg/L (or grams per cubic
meter), and tj) is expressed in seconds.
QQ — The flow rate of the wastewater treatment effluent, in cubic meters
per second, must be specified by the user.
The upstream flow, in cubic meters per second, can be specified by
the user. If unknown, an average flow condition can be calculated:
QU = qs . As (90)
where q§ is the average stream flow per unit area, in cubic meters per second
per square meter, and Ag is the surface area of the watershed above the dis-
charge, in square meters.
Qg — The stream flow at the point of mixing is the sum of the upstream
flow and the effluent flow:
Qs = Qu + QD (9D
2.3.2 Transport and Transformation in Stream —
Following initial dilution in the stream, contaminants at peak concen-
tration, CQ, are routed downstream under the combined influence of advection,
43
-------
longitudinal and lateral dispersion, degradation and sorption. The concen-
tration at downstream distance x from the edge of the initial mixing zone is
Cx and is related to CQ via equations 28 and 29, in which Cx is the attenu-
tion factor for transport in surface water. The expressions for Cx can be
obtained from analytical solutions of the transient two-dimensional transport
equation. Two cases corresponding to continuous loading and pulse loading of
contaminants are considered.
Stream transport below continuous ground water loading—The laterally
averaged concentration at the downstream edge of the ground water plume (x =
0) is CQ (see Figure 24). At a given measurement point located at distance x
from the edge of the mixing zone (Figure 6a), the concentration will quickly
reach a steady-state value under base flow conditions. The steady-state,
laterally averaged solution for concentrations at the measurement point is
given by:
Cx = e-K'T (92)
where: T = X/U (93)
K = decay rate constant, sec-1
U = mean downstream velocity, m/sec
For calculating bioconcentration in scenario IB or chronic toxicity in
scenario 1C, we assume that the fish reside continuously in the upstream
area where the effect of degradation i^s insignificant (x = 0). Therefore
in this case Cx is 1, and Cx becomes CQ.
Stream transport below pulse runoff loading—Pulse runoff loading pro-
duces a lateral concentration profile that is a Gaussian distribution charac-
terized (at x = 0) by a maximum CR and a standard deviation of o over the
contaminant loading period t^ (see Figure 6b). Downstream transport will be
accompanied by lateral mixing until the contaminants are evenly dispersed
across the stream. The concentrations at a given measurement point, x, will
increase from zero to a relatively steady value between times (x/U) and (x/U
+ tft). At subsequent times, the concentrations will decrease gradually and
become zero as the contaminant slug passes through the measurement point.
The general analytical solution for transient, two-dimensional transport from
a Gaussian pulse source is presented in Appendix B. This solution may be
written as:
X'y
[C*(x,y,t) + I
-C* (x,y,t-tR) - I C*f± (x,y,t-tR)j (94)
where:
44
-------
ox exp (U/2EX)
C*f(x,y,t) = -___ . I (95)
(2nE )!/2
.A.
X2
y2 U2T
t 4E T 4E T +
_ r "
- J
- KT) dT
^ 4Ev
_
, /9
0 T (20+4E T)1/2
Cfi = Cf (x' 2Bi + 6 cos (l7r)' t) (97)
E = longitudinal dispersion coefficient, m /sec
X
o
E = lateral dispersion coefficient, m /sec
The infinite series in equation 94 is evaluated in a computer subroutine
using finite sums of N terms, where N corresponds to the number of image
sources described in Appendix B. Good convergence is obtained with N <10.
The integral I is evaluated numerically using Gaussian quadrature.
Stream transport below pulse discharge loading — Pulse discharge loading
produces a lateral concentration profile that is a Gaussian distribution
characterized (at x = 0) by a maximum CQ and a standard deviation of a over
the contaminant loading period tj>. Downstream transport will be accompanied
by lateral mixing until the contaminants are evenly dispersed across the
stream. The concentrations at a given measurement point, x, will increase
from zero to a relatively steady value between times (x/U) and (x/U + tp).
At subsequent times, the concentrations will decrease gradually and become
zero as the contaminant slug passes through the measurement point. The
general analytical solution for transient, two-dimensional transport from a
Gaussian pulse source is presented in Appendix B. This solution is given by
equations 94-97 (with tj> substituted for t^ in equation 94).
2.3.3 Contaminant Delivery to Drinking Water and Fish —
At a distance x downstream, contaminants at concentration Cx may be
taken into a drinking water plant or exposed to aquatic organisms, including
fish. The drinking water concentration Cpy, the aquatic exposure concentra-
tion Cgxp> and the fish body concentration Cp must be calculated from Cx.
Delivery of contaminant through drinking water — Drinking water plants
take in raw water at a distance x downstream from the point of discharge. As
a minimum requirement, it is assumed that in any drinking water plant, the
raw water having contaminant concentration Cx is treated by allowing suspended
solids and adsorbed chemical to settle out. This leads to a reduction of
concentration from Cx to CDW. The relationship between CQ^ and Cx is given by
equation 13 with £j)^ being the dilution factor corresponding to the fraction
45
-------
of the compound that is dissolved, fp. The expression for fp is developed in
Appendix A. This may be written as:
- fp -
1 + °'41 Kow • foc ' S • 10"6
where:
KOW = octanol-water partition coefficient, ^
foc = organic carbon fraction of sediment
S = sediment concentration, mg/1
Delivery of contaminants to aquatic organisms—Aquatic organisms are
exposed to contaminants at a distance x downstream from the point of dis-
charge. Only dissolved species of a compound cross fish membranes and cause
internal exposure. There is some evidence, however, that suspended solids
with sorbed species can enhance the rate of uptake and thus internal exposure
of a compound. The CCC set to protect against chronic toxic effects is
generally referenced to the total concentration of a compound. Therefore,
is set to 1 and Cgxp is equated to Cx.
Delivery of contaminants through fish to humans—Dissolved neutral
organic compounds in the water can be taken up by fish through exchange
across the gill and gut membranes and through the skin. Contaminated food
can be ingested, resulting in further exchange of compounds across the gut
membrane. Concentration levels in the fish will rise until the activity of
the compound in the blood equals the activity of the compound in the water.
This condition represents chemical equilibrium. Further uptake of the com-
pound resulting in higher blood concentrations will lead to net exchange out
of the fish through the gill, gut, kidney, and skin. Consequently, any
chemical buildup above the equilibrium level is controlled by the relative
rates of ingestion, metabolism, and exchange. There is some evidence that
active transport across the gut can cause the equilibrium concentration to
be exceeded:
Cg — Kpc ^D ^x (99)
where Cg is the dissolved concentration in the blood, mg/L, fp is the
fraction of chemical dissolved, and Kpf; is the food chain bioaccumulation
factor, expected to range from 2-3.
If the fish is exposed to steady aqueous concentrations over a long
period of time, the distribution of the compound within the various fish
tissues will equilibrate, so that:
Ci - K4 . CB (100)
and
46
-------
Cn£ = K^ . CB (101)
where:
G£ = lipid (or fat) biomass concentration, mg/kg
K£ = llpid phase partition coefficient, L/kg
Cn# = non-lipid (blood, muscle) biomass concentration, mg/kg
Kn£ = non-lipid partition coefficient, L/kg
The average whole fish concentration CF (mg/kg) is the weighted sum of the
tissue concentrations:
CF = f£ . cz + (i-fA) cnX, (102)
where f£ = fraction of biomass that is lipid. Substituting equation 99 and
100 into 101 gives:
CF = KFC KF fD GX (103)
where KF is the entire fish partition coefficient, or bioconcentration
factor given by:
KF = K£ fa + Kn£ (1-ffc) (104)
Equation 103 reduces to equation 32 provided that the parameter £F is
defined as:
?F = KFC . KF . fD (100)
Note that, unlike the dilution factors, CF is not dimensionless. The unit
for £F is L/kg. For strongly hydrophobic compounds, lipid storage dominates
KF. The lipid phase partition coefficient can be replaced by the octonal-
water partition coefficient, so that, approximately:
KF = Kow . fa (106)
For less hydrophobic compounds, Kn£ may contribute significantly to KF.
Non-lipid tissue is composed primarily of water, along with protein and
carbohydrates. Assuming that partitioning to non-lipids is always less than
or equal to 1% of the partitioning to lipids, a conservative estimate of KF
is approximately (R.R. Lassiter, USEPA, personal communication):
KF = KQW . (f£ + 0.01) (107)
For highly polar compounds and metals, the bioconcentration factor KF
can not be estimated from the octanol-water partition coefficient and lipid
fraction. In this case, observed field or experimental values of KF must be
used directly.
47
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SECTION 3
USER'S MANUAL
SARAH is an interactive model. The computer program, through a series
of menus and questions, will automatically build a data set or default to
predefined values at the user's discretion.
3.1 EXPLANATION OF MENUS
SARAH interactively allows the user a choice of chemical release and
exposure scenarios. For each scenario, the user can default to predefined
input values or enter site-specific input values. Many calculations can be
performed for each scenario by systematically varying selected input values.
3.1.1 Selection of Scenarios
The user must first define a complete problem to analyze, including the
loading and the exposure scenarios. The first menu allows the user to speci-
fy one of five possible loading scenarios, or to exit the program:
(1) Steady ground water loading
(2) Storm runoff loading
(3) Catastrophic pulse loading
(4) Continuous discharge loading
(5) Batch discharge loading
(6) Exit
The second menu allows the user to specify one of three possible exposure
scenarios:
(1) Human exposure through drinking water
(2) Human exposure through fish consumption
(3) Toxicity to aquatic organisms
48
-------
If Loading Scenario 2 or 3 was previously selected, then the specifica-
tion of Exposure Scenario 2 or 3 results in a return to the Loading Menu,
because human exposure through fish and direct aquatic exposure by runoff
loading are not implemented.
3.1.2 Operation of Model
Following specification of the problem, the user is supplied the follow-
ing Operation Menu:
(1) Use default input values
(2) Display default input values
(3) Enter sets of input values
(4) Display current input values
(5) Enter selected input values
(6) Run program
(7) Return to main menu
Before the user may run the program, a data set must be specified using
choices: 1, 3, or 5. To use the default values, select choice 1 and specify
one of three options in the Default Input Menu:
(1) Use default input values #1
(2) Use default input values #2
(3) Use default input values #3
The values and description of each default selection (1, 2, or 3) are
listed in Section 3.3.
After default input values are selected, the model will return to the
Operation Menu.
If choice 3 is selected, the user may enter sets of input values grouped
by subject matter. Selections can be made from the Subject Matter Menu:
49
-------
Enter all input values
(1) Hydrologlcal
A _
If subject 1 Is selected, the model will request the user to define the
new value of A
If variable 3 is selected, the model will request a value for S. After
the user defines S, the model will return to the Selected Input Menu and
50
-------
allow the user to select another variable. The user may return to the
Operation Menu at any time by entering a zero.
At this point, the user may select to run the program by entering (6),
Output variables and intermediate variable values will be printed on the
screen. The user can return to the Operation Menu following each "Run"
command by entering (7).
3.2 SCENARIO VARIABLES
Numerous equations have been presented that together describe leachate
loading, dilution, instream transport and transformation, and exposure to
humans through drinking water and fish consumption. The many variables are
categorized by scenario, then grouped into those describing the watershed
hydrology, the stream and ground water environments, the compound properties,
and the loading/exposure scenario.
The number of potential input variables may appear to make practical
application of this analysis difficult. Fortunately, many of these inputs
can be estimated from other more readily available variables. Furthermore,
many terras in the equations can be ignored for a more conservative analyses.
The input variables for each scenario are listed in the following tables.
These tables are designed to give the user the choice of a conservative anal-
yses with a minimum set of data, more complete analyses with a recommended
set of data, and "full equation" analyses with an optional set of data.
The steps for calculating an allowable leachate concentration for Scena-
rio 1 are summarized in Table 2. Input variables are given in Table 3. The
calculations and input data for Scenarios 2 and 3 are summarized in Tables 4
and 5. Calculations and input data for Scenario 4 and 5 are summarized in
Tables 6 and 7.
3.3 DEFAULT VALUES
SARAH contains three default data sets. A user may use any one of the
three as is, alter variables in any of the three, or build a totally new data
set.
The first data set represents a small, flat watershed containing a large
land disposal facility and a slow, shallow stream. The second set represents
a small, moderately steep watershed containing a medium-sized land disposal
facility and a faster, deeper stream. The third set reflects a large, steep
watershed containing a large land disposal facility and a fast, shallow
stream. All three contain a small wastewater treatment facility that receives
a steady industrial waste stream. The input values for each variable are
listed in Table 8.
51
-------
TABLE 2. CALCULATIONS FOR SCENARIO 1
Step
Calculate
Explanation (and Equations)
Tg(TAUG)
Kg(KHG)
Travel time of contaminant from land disposal
facility to stream, years (A17, A16, 64).
First-order rate coefficient for hydrolysis in
ground water, years"1 (A23, A25).
Mass attenuation factor in ground water (63).
8
9
10
11
12
CSg(RSG)
?SU(RSU)
C(TAU)
K(KK)
CX(RX)
CDW(RDW)
?p(RG)
Concentration dilution factor in gi-ound water and
stream (65, 66, 67).
Concentration dilution factor for upstream contami-
nants (69, 68, Qu/Qs).
Travel time of contaminant downstream, seconds
(A4, 93).
First order rate coefficient for hydrolysis and
volatilization in stream, seconds'"! (A15, A22, A24,
A30, A29, A34, (A32, A33, or A35), A27, A28, A26,
A19).
Concentration reduction factor for downstream
transformations (92).
Drinking water treatment reduction factor (A15, 98).
Fish bioaccumulation factor (107, A15, 100).
Concentration dilution factor due to transport in
ground water (=?H ^1 QL/Qs) (63, 65, 66).
Acceptable leachate concentration, mg/L (Drinking
Water: ?su» 92, 98, Cg, 67; Aquatic Organisms:
Cg, 67; Fish Accumulation: ^SU» 100> ^g> 67).
52
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TABLE 3. INPUT VARIABLES FOR SCENARIO 1
Input
Variable
Hydrological
AW
Ag
As
"p
fR
fR
Ci
?i
Cj Q
\J O
Ground water
Xg
Vg
0g
focg
Tg
pHg
Value
Range
104 - 106
104 - 106
107 - 109
10 - 200
0.1 - 0.5
0.1 - 0.5
0.1 - 1.0
0.1 - 1.0
10~9- 10~8
10~2- 10
10 - 103
1 - 105
0.3 - 0.5
0.001-0.10
10 - 20
5-8
Conservative Recommended
X
X
X
X
X
X
X
X
X
X
X
X
X
Optional
X
X
X
53
-------
TABLE 3. INPUT VARIABLES FOR SCENARIO 1 (Continued)
Input
Variable
Stream Env.
cu
u
do
s
n
^oc
S
T
W(WZ, z)
PH
Compound
Kow
kHA
kHN
kHB
TR
MW
H
Value
Range Conservative
—
0.1 - 2
0.1 - 3
10-4 _ io-2
0.02 - 0.08
0.01 - 0.10
10 - 50
5-30
0-10
5-8
10 - 107 X
0 - 10"1
0 - 10~5
0 - 10"1
15 - 25
10 - 103
10-7 _ io-l
Recommended Optional
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
54
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TABLE 3. INPUT VARIABLES FOR SCENARIO 1 (Continued)
Input
Variable
Exposure
»
CADI
CADI
KFX
ft
X
ccc
Step
1
2
3
4
5
Value
Range Conservative Recommended Optional
X
X
1-3 X
0.01 - 0.25 X
0 - 5000 X
X
TABLE 4. CALCULATIONS FOR SCENARIOS 2, 3
Calculate Explanation (and Equations)
CR(RRU) Concentration dilution factor in surface runoff
(80, 81, 10).
CgR)y(RSRY) Concentration dilution factor across stream at
point of mixing (A3, 84, 85, A4, A5, A7 , 79, 74).
Cgu(RSU) Concentration dilution factor for upstream
contaminants (27).
T(TAU) Travel time of contaminant downstream, seconds
(A4, 93).
K(KK) First order rate coefficient for hydrolysis and
7
8
Cx,y(RXY)
CL(CL)
volatilization in stream, seconds"1 (A15, A22,
A24, A30, A29, A34, (A32, A33, or A35), A31, A27,
A28, A26, A19).
Concentration reduction factor for downstream
transformation (A8, A9, A10, 96, 95, 97, 94).
Drinking water treatment reduction factor (A15, 98),
Acceptable leachate concentration, mg/L (27, 10,
74. 98. 94. 46).
55
-------
TABLE 5. INPUT VARIABLES FOR SCENARIO 2 AND 3
Input
Variable
Hydrological
AW
Ag
Au
P25
fR
fR
f*
rR
IB
Q|
t
tR
St ream Env.
GU
do
s
n
b
f
^ oc
S
Value
Range
10* -
IO4 -
IO7 -
10 -
0.1 -
0.1 -
0 - 1
io-9 -
ID"2 -
103 -
IO3 -
—
0.1 -
10-4 _
IO6
IO6
IO9
15
0.5
0.5
IO""8
10
IO6
IO6
3
10-2
0.02 - 0.08
0.02 -
0.2 -
0.01 -
10-4 _
0.5
0.7
0.10
10-2
Conservative Recommended Optional
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
56
-------
TABLE 5. INPUT VARIABLES FOR SCENARIO 2 AND 3 (Continued)
Input
Variable
T
W
PH
Ex
Ey
Compound
Kow
kHA
kHN
kHB
TR
MW
H
Exposure
t
CADI
CADI
KFC
f£
X
y
ccc
Value
Range
5 - 30
0-10
5-8
1 - 10
lO-2 - 10-1
10 - 107
0 - 10"1
0 - 10~5
0 - 10-1
15 - 25
10 - 103
1(T7 - 10-1
—
—
1 - 3
0.01 - 0.25
0 - 5000
0 - B
._—
Conservative Recommended Optional
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
57
-------
TABLE 6. CALCULATIONS FOR SCENARIOS 4, 5
Step Calculate Explanation (and Equations)
Concentration reduction factor in wastewater treat-
ment (89 (i.e. , 89, 15)).
y(RSRY) Concentration dilution factor across stream at point
of mixing (90, 91, A4, A5, A7, 88, 74).
Concentration reduction factor for upstream
contaminants (27).
r(TAU)
Travel time of contaminant downstream, seconds
(A4, 93).
K(KK)
First order rate coefficient for hydrolysis and
volatilization in stream, seconds'"! (A15, A22, A24,
A30, A29, A34, (A32, A33, or A35), A27, A28, A26,
A19).
£x y(RXY) Concentration reduction factor for downstream
transformation (A8, A9, A10, 96, 95, 97, 94).
CDW(RDW)
CF(RF)
cw(cw)
Drinking water treatment reduction factor (A15, 98),
Fish bioaccumulation factor (107, A15, 100).
Acceptable industrial waste concentration, mg/L
(50, 57, 53, 41, 56, or 61).
58
-------
TABLE 7. INPUT VARIABLES FOR SCENARIO 4 AND 5
Input
Variable
Hydrological
Aw
Ag
As
P25
J- ID
£ O
4
qs
Q|
t
CR
Value
Range
10* -
IO4 -
IO7 -
10 -
0.1 -
0.1 -
0 - 1
io-9 -
ID'2 -
IO3 -
IO3 -
IO6
IO6
IO9
15
0.5
0.5
10~8
10
IO6
IO6
Conservative Recommended Optional
X
X
X
X
X
X
X
X
X
X
X
Stream Environment
cu
*0
s
n
b
f
foe
S
—
0.1 -
10-4 _
0.02 -
0.02 -
0.2 -
0.01 -
10-4 _
3
10-2
0.08
0.5
0.7
0.10
10-2
X
X
X
X
X
X
X
X
59
-------
TABLE 7. INPUT VARIABLES FOR SCENARIO 4 AND 5 (Continued)
Input
Variable
T
W
PH
EX
Ey
Compound
K
ow
kHA
kHN
kHB
TR
MW
H
Loading and
Exposure
t
CADI
CADI
KFC
f£
X
y
ccc
Value
Range Conservative
5-30
0-10
5-8
1 - 10
10~2 - lO"1
10 - 107 X
0 - 10-1
0 - 10"1
0 - lO"1
15 - 25
10 - 103
10-7 - io-l
X
X
1 - 3
0.01 - 0.25 X
0 - 5000 X
0 - B
X
Recommended Optional
X
X
X
X
X
X
X
X
X
X
X
X
X
60
-------
TABLE 7. INPUT VARIABLES FOR SCENARIO 4 AND 5 (Continued)
Input
Variable
Value
Range
Conservative
Recommended
Optional
0-1
103-106
X
QD
0.004-12
TABLE 8. DEFAULT VALUES FOR DATA SETS #1, #2, AND #3
AS
AW
P25
RS
RW
BEXP
FEXP
Q
S
DO
DD
NN
FR
FL
TS
TL
Hydrology
#1
1.0D7
1.0D6
12.5DO
0.4DO
0.5DO
0.23DO
0.42DO
0.5D-8
9.0D-5
0.3DO
l.ODO
0.04DO
l.OODO
0.3DO
8.64D4
7.2D3
and Hydrogeometry
#2
1.0D7
1.0D5
15. ODO
0.4DO
0.4DO
0.40DO
0.20DO
l.OD-8
1 . OD-3
l.ODO
l.ODO
0.02DO
0.6000
0.2DO
8.64D4
3.6D3
#3
1.0D8
1.0D6
10. ODO
0.4DO
0.3DO
0.55DO
0.30DO
l.OD-9
5. OD-3
0.2DO
l.ODO
0.06DO
l.OODO
0.1DO
8.64D4
1.8D3
Ground water
VWG
THETAG
TG
FOGG
TRG
XG
PHG
10. ODO
0.5DO
20. ODO
0.01DO
25. ODO
150. ODO
5. ODO
150. ODO 900. ODO
0.4DO
15. ODO
0.005DO
25. ODO
150. ODO
6.6DO
0.3DO
10. ODO
0.001DO
25. ODO
150. ODO
8. ODO
61
-------
TABLE 8. DEFAULT VALUES FOR DATA SETS #1, #2, AND #3 (Continued)
Hydrology and Hydrogeometry
#1 #2 #3
Environmental
T
SS
PH
FOC
WW
Z
K
KHA
KHB
KHN
HH
MW
KOW
20.0DO
10. ODD
7.0DO
0.05DO
2.0DO
10.0DO
O.ODO
O.ODO
O.ODO
O.ODO
l.OD-7
1.0D3
1.0D3
25.0DO
50.0DO
7.5DO
0.1DO
4. ODD
10.0DO
Chemical
O.ODO
O.ODO
O.ODO
O.ODO
l.OD-7
1.0D3
1.0D4
15.0DO
100. ODO
6.5DO
0.01DO
l.ODO
10. ODO
O.ODO
O.ODO
O.ODO
O.ODO
l.OD-7
1.0D3
1.0D5
Loading/Exposure
X
Y
CADI
CPADI
RW
TD
QWI
QD
1.0D3
O.ODO
l.ODO
l.ODO
l.ODO
8.6D4
4.0D-3
4.0D-3
1.0D3
O.ODO
l.ODO
l.ODO
l.ODO
8.6D4
4.0D-3
1 . OD-3
1.0D3
O.ODO
l.ODO
l.ODO
l.ODO
8.6D4
l.OD-1
2.0D-1
Note: D5 = 105
62
-------
SECTION 4
PROGRAMMER'S MANUAL
This section contains information to familiarize the user with the
programming aspects and operational characteristics of the model. The hard-
ware and software section contains information on program compilation and a
description of the files on the distribution tape with a listing of required
disk space. The installation and Implementation section lists commands for
mounting the tape and running the model. The program description section
describes the input/output device, the common block and each subroutine.
4.1 HARDWARE AND SOFTWARE REQUIREMENTS
SARAH was compiled under the PDF IAS FORTRAN 77 and the VAX VMS FORTRAN.
The files contained on the distribution tape (for a VAX system) are:
SARAH.CMN, SARAH.COM, SARAH.FOR, and SARAH.EXE. The following is a descrip-
tion of each file and the disk space required by each.
Number of Blocks
File Description (512 byte records)
SARAH.CMN Include file with common 3
blocks
SARAH.COM Command file for compiling 1
and linking source code
SARAH.FOR FORTRAN source code 178
SARAH.EXE Executable image 96
4.2 VAX INSTALLATION AND IMPLEMENTATION
The following steps and commands are required to install SARAH on a
VAX system:
63
-------
Description Command
Mounting tape MOU/NOASSIST/OVERRIDE=OWNER-ID MSA0:
SARAH
Setting directory default SET DEF DBA0:[xxx. yyy]
Copying contents COPY MSA0:*.*;*DBA0:[xxx.yyy]
Verifying files were copied DIR
Dismounting the tape DISMOUNT MSA0:
Compiling code (if necessary) @ SARAH.COM
The VAX command file (SARAH.COM) deletes the previous executable file,
compiles the source code SARAH.FOR to create the object file SARAH.OBJ,
links the object file to the executable file (SARAH.EXE) which is used to
run the model, cleans out account, and renames all versions to 1. The
following is a listing of SARAH.COM:
$ SET VERIFY
$! SARAH.COM
$ ON WARNING THEN CONTINUE
$ DEL SARAH.EXE;*
$ FORTRAN SARAH
$ LINK SARAH
$ PURGE SARAH.*
$ DEL SARAH.OBJ;*
$ REN SARAH.*;* SARAH.*;!
$ EXIT
4.3 PROGRAM DESCRIPTION
4.3.1 Input/Output Units
Because SARAH is an interactive program, all variables and results are
defined and printed onto the terminal screen (IUNIT5). To run the model
type: RUN SARAH.
4.3.2 Common Block
SARAH uses a common block (SARAH.CMN) to transfer data between subrou-
tines. This common block consists of real, integer (both are double pre-
cision), or character specifications for variables. The common block is
divided into 12 subsections according to subject matter,, The following is a
listing and a short definition of each subsection.
64
-------
Subsection Definition
OTHERR Real variables
OTHERC Character variables
OTHERI Integer variables
CALCV Variables used in calculations
HYDR Hydrology and hydrogeometry variables
STREAM Environmental variables
CHEM Chemical variables
LOADEX Loading/exposure variables
CLEARS Variables used to clear terminal screen
10 Input/output variables
CONST Constant variables
GWATER Groundwater variables
Further definitions for each variable may be found in Appendix A.
4.3.3 Common Block Listing
C SARAH.CMN
C
IMPLICIT REAL*8(A-H,0-Z)
INTEGER*2 IMAGE,IUNITS,Ml,m2,M3,M4,M5,M7,N,CC,M51,M61,M71,
X IERR,M8,M1A
CHARACTER ANS,CLR1(10),CLR2(10),HOLDIT,MENU,SLAB(3)*40,
X TERM
REAL*8 K20,KH,KK,K02,KV,K,KHA,KHB,KHN,KOW,MW,NN,DATA(30),
X KF,FD,DDP,CPADI,FL,NU,KHG,KHGO
C
COMMON/OTHERR/ DATA
C
COMMON/OTHERC/ ANS,CLR1,CLR2,HOLDIT,MENU,SLAB
C
COMMON/OTHERI/ IMAGE,Ml,M2,M3,M4,M5,M7,N,CC,M51,M61,M71,
X IERR,M8,M1A
C
C
COMMON/CALCV/ A.ALPHA,ARC1,ARG2,Bl,B2,BETA,
X DELTA,DPRIME,E,E1,EQ1,EQ2,EQ3,EQ4,
65
-------
X F,H,
X OMEGA,R,RDATA,RL,
X TERM1,TERM2,TR,
X USV,W,WAT,WZ,XPRIME,YY,FL,DDP,KF
C
COMMON/HYDR/ AS,AW,BBO,BB,D,DO,QQO,QQ,P25,Q,RS,RW,S,
X BEXP,FEXP,UO,U,NN,FR
C
COMMON/STREAM/ B,DD,DF,EX,EY,FOC,PH,POH,SS,T,TK,WW,W10,QW
C
COMMON/CHEM/ HH,K,KHA,KHB,KHN,KOW,MW,K20,K02,KV,KH,FS,FD,KK
C
COMMON/LOADEX/ CADI,CL,TAU,TSD,TL,X,Y,Z,CPADI,SIGMA
C
COMMON/CLEARS/ TERM
C
COMMON/IO/ IUNIT5
C
COMMON/CONST/ RGAS.G
C
COMMON/GWATER/ VWG,THETAG,RHOBG,TG,TRG,FOCG,XG,PHG,POHG,
X FDG,FSG,KHGO,KGH,RTG,VSOLG,TAUG,RG
4.3.4 Subroutine Descriptions
Figure 25 is a flow chart of SARAH illustrating the functional relation-
ships among the subroutines. (Note: SARAH has no overlay structure.) The
following is a brief explantion of each subroutine function.
Description Function
SARAH.FOR Calls first menu program DWM1.FOR.
(main program)
CLSCR.FOR Subroutine used to clear terminal screen.
DWMl.FOR Subroutine to display menu of potential
contaminant sources.
DWM2.FOR Subroutine to display menu of default
values use, display default values, enter
input values, display input values, enter
selected input values, run program, or
return to main menu.
DWM3.FOR Subroutine to display menu for default
value sets #1, #2, or #3 menu.
DWM4.FOR Subroutine to display choice of display-
ing selected default values.
66
-------
OO
r
o •
M
'
—
!~~
cs
00
• §
o
00
• s|
Q
[
I
\
,_
i
Q
o
o
o
o
-8
Q
f %
»-
UJ
Q
IO
£
Q
CM
£
I— _-
1 !
g
'K
LH
KJ u.
§—s
CE
<-
S^
Q
T—
~ ? '
Q
CNJ
rl"
— *
K
(A)
_l
O
Hi
i Q J ~
1 T- 1 O
; to i
! Q
\
1 in
j 2
i §
! O
1
>
r-fS g
IS ^
m
J
OJ
c
•H
-P
en
K
Q
o
1C
H in
Q ^C
B Li
W
C
O
•H
3
Cn
•H
67
-------
DWM5.FOR
DWM51. FOR
DWM6.FOR
DWM61.FOR
DWM7.FOR
DWM71.FOR
DWM8.FOR
DWM81.FOR
DWM82.FOR
DWS1.FOR
DWS2.FOR
DWS3.FOR
DWS4.FOR
Subroutine used for entry of all input
values when potential contaminant source
is not steady ground water loading.
Subroutine used for entry of all input
values when potential contaminant source
is steady ground water loading.
Subroutine used to display all input values
when potential contaminant source is not
steady ground water loading.
Subroutine used to display all input values
when potential contaminant source is steady
ground water loading.
Subroutine used for entry of selected
input values when potential contaminant
source is not steady ground water loading.
Subroutine used for entry of selected
input values when potential contaminant
source is steady ground water loading.
Subroutine that calls the set of calcula-
tion programs when potential contaminant
source is not steady ground water loading.
Subroutine that calls the set of calcula-
tion programs when potential contaminant
source is steady ground water loading and
potential effect of release is human
exposure through fish consumption.
Subroutine that calls the set of calcula-
tion programs when potential contaminant
is steady ground water loading and poten-
tial effect of release is toxicity to
aquatic organisms.
Subroutine used by Scenario 2/3 for
advection calculations.
Subroutine used by Scenariio 2/3 for
stream transport calculations.
Subroutine used by Scenario 2/3 for
dispersion calculations.
Subroutine used by Scenario 2/3 for
chemical transformation calculations.
68
-------
DWS5.FOR
DWS6.FOR
DWS10.FOR
DWS11.FOR
DWS12.FOR
CERF.FOR
DF1.FOR
DF2.FOR
DF3.FOR
DISF1.FOR
DISF2.FOR
DISF2.FOR
REOX.FOR
ENTRY.FOR
VALUE.FOR
Subroutine used by Scenario 2/3 for
rectangular distribution calculations.
Subroutine with analytical solution to the
transient two-dimensional ground water
pollution model.
Subroutine used by Scenario 1 for
calculations.
Subroutine used by Scenario IB for
calculations.
Subroutine used by Scenario 1C for
calculations.
Subroutine used to compute an error func-
tion with a complex argument.
Subroutine with 1st set of 3 sets of
default values assigned to variables.
Subroutine that defines values to the
first set of 3 sets of default variables.
Subroutine that defines values to the
second set of 3 sets of default.
Subroutine that defines values to the
third set of 3 sets of default variables.
Subroutine used to display values assigned
to variables by DF1.FOR.
Subroutine used to display values assigned
to variables by DF2.FOR.
Subroutine used to display values assigned
to variables by DF3.FOR.
Subroutine called by DWS4.FOR to perform
calculations.
Subroutine used to convert a character
string input into a numerical value for
calculation and perform error checking of
input for valid entries.
A function used in character to numerical
value conversion.
69
-------
ERF.FOR A function program used to evaluate the
error function.
EXERFC.FOR A subroutine to compute the complementary
error function of y times an exponential
with argument x.
70
-------
REFERENCES
1. Ambrose, R.A., Mulkey, L.A. , and Huyakorn, P.S. 1985. A Methodology
for Assessing Surface Water Contamination due to Land Disposal. EPA
draft report.
2. Burns, L.A., Cline, D.M., and Lassiter, R.R. 1982. Exposure Analysis
Modeling System (EXAMS): User Manual and System Documentation. U.S.
Environmental Protection Agency, Athens, GA. EPA-600/3-82-023.
3. Covar, A.P. 1976. Selecting the Proper Reaeration Coefficient for Use
in Water Quality Models. Presented at the U.S. EPA Conference on
Environmental Simulation and Modeling, Cincinnati, OH, April 19-22, 1976.
4. Fischer, H.B., List, E.J. , Koh, R.C.Y., Imberger, J., and Brooks, N.H.
1979. Mixing in Inland and Coastal Waters. Academic Press, New York.
5. Israelsen, O.W. and Hansen, V.E. 1962. Irrigation Principles and
Practices. John Wiley and Sons, Inc., New York. 447 pp.
6. Karickhoff, S.W. 1981. Semi-Empirical Estimation of Sorption of
Hydrophobic Pollutants on Natural Sediments and Soils. Chemosphere.
10(8):833-846.
7. Karickhoff, S.W., Brown, D.S., and Scott, T.A. 1979. Sorption of
Hydrophobic Pollutants on Natural Sediments. Water Res. 13:241-248.
8. Leopold, L.B. and Haddock, T. 1953. The Hydraulic Geometry of Stream
Channels and Some Physiographic Implications. U.S. Geological Survey,
Washington, DC. Professional Paper No. 252.
9. Liss, P.S. 1973. Processes of Gas Exchange Across an Air-Water Inter-
face. Deep-Sea Res. 20:221-238.
10. Park, C.C. 1977. World-Wide Variations in Hydraulic Geometry Exponents
of Stream Channels: An Analysis and Some Observations. Journal of
Hydrology, 33 (1977):133-146.
11. Whitman, R.G. 1923. A Preliminary Experimental Confirmation of the
Two-Film Theory of Gas Absorption. Chem. Metallurg. Eng. 29:146-148.
71
-------
APPENDIX A
ADVECTION, DISPERSION AND CHEMICAL TRANSFORMATION IN STREAM
In this appendix procedures and formulas for estimating physical parame-
ters of advection, dispersion and chemical transformation in surface water
are presented.
A.I. ADVECTION
A compound introduced to a water body will be advected downstream with
the bulk water at mean velocity U such that
U = Q/ (B.d) (Al)
where Q = stream flow, m^/sec
For a given flow in a specific stream reach, width, depth, and velocity are
related empirically by the following equations (Leopold and Maddock, 1953).
B = aQ> (A2a)
d = cQf (A2b)
U = kQm (A2c)
where the sum of the exponents (b+f+m) and the product of the constants
(a.c.k) must equal 1.0. Although theoretical considerations predict that
b = 0.23, f = 0.42, and m = 0.35, considerable variations have been obser-
ved among sites. Figure A.I presents the exponents observed at 139 sites,
as analyzed by Park (1977).
The upstream base flow for subwatersheds can be calculated from the re-
lationship where:
Qi = AU ' «s (A3>
o
where q = average flow per unit area m /sec
S ^
Velocity at baseflow, Uo can be calculated by Manning's equation: (A4)
72
-------
(a) NATURAL
CHANNELS
10x0
(b) PRO-GLACIAL
(d) SEMI-ARID
(f) FLUME
STUDIES
10 08 06 04 02 0
Theoretical
ALeopold and Langbeln (1962)
10A0
(c) HUMID
TEMPERATE
Afirltaln
• U.S.A.
(e) TROPICAL
• Perennial
AEphemeral
(g) TIDAL
ESTUARIES
10
• Malaysia
A Puerto Rico
Figure A. Tri-axial graphs of at-a-station hydraulic geometry
profiles.
73
-------
». • V/3 •
where: do = depth baseflow, m
s = channel slope, m/m
n = Manning's roughness coefficient, sec/ml/3
The width at baseflow B , can be calculated from U , d , and the baseflow Q?
using equation Al rearranged:
O o O O
The upstream flow during a storm includes both baseflow and runoff, as
given by operation A6:
QU = QS + AU P25 V100 ' ts (A6)
Given the baseflow values BQ, dQ, UQ, and Q| and the stormflow value Q, the
widths, depths, and velocities for stormflow conditions can be calculated as:
B = BQ (Qu/Qg)b (A7a)
d = dQ (Qu/oJ)f (A7b)
U = Un (QII/Q§)1~b~f (A7c)
\j U O
When the theoretical values for b and f hold, U increases with Q to the 1/3
power. A ten-fold increase in flow, then, results in a doubling of velocity.
Streamflows and the associated hydraulic variables, then, can be syn-
thesized from distributions of watershed areas As, areal flows q, channel
slopes, s, channel roughness factors n, precipitation totals P25> runoff
coefficients fR, and the hydraulic geometry exponents b and f.
A.2. DISPERSION
A compound advected through a water body will be mixed vertically,
laterally, and longitudinally from areas of high concentration to areas of
low concentration. The rate of mixing is proportional to the concentration
gradient and either a turbulent mixing coefficient or a dispersion coeffi-
cient. A turbulent mixing coefficient in rivers is proportional to the
length scaled and the intensity of turbulence, which is represented by the
shear velocity:
U* = / g.d.s (A8)
where: U* = shear velocity, m/sec
74
-------
s = channel slope, m/m
d = mean depth, m
g = acceleration of gravity, m/sec2
Because vertical mixing in streams occurs very quickly, we assume com-
pletion during the initial dilution stage. Lateral mixing is most impor-
tant in the near field. It is smallest for uniform straight channels, and
increases with curves and irregularities. Fischer et al. (1979) suggest
calculating the lateral diffusion coefficient as:
Ey = 0.6 . d . U* , _+ 50% (A9)
The proportionality factor can vary evenly between 0.4 and 0.8.
Longitudinal turbulent mixing is generally much smaller than shear flow
dispersion, which is caused by velocity gradients. Fischer and coworkers,
suggest calculating the logitudinal dispersion coefficient with the approxi-
mate relationship:
Ex = 0.011 U2 . B2 / d . U* (A10)
Here, again, the proportionality factor can vary + 50%.
A. 3. CHEMICAL TRANSFORMATION
A compound transported through a water body can undergo several physical
and chemical transformations. Fast reactions are treated by assuming local
equilibrium conditions. Sorption is considered to be in equilibrium with
desorption:
A
S' + Cw = Cs (All)
where: S1 = sediment concentration, kg/1
Cw = dissolved aqueous concentration, mg/1
A
Cs = sorbed concentration, mg/1
A
The local equilibrium concentrations Cw and Cs are governed by the equili-
brium distribution coefficient Kp (a/kg):
A
Cs (A12)
Kp =
75
-------
Karickhoff et al. , 1979, have shown that for sorption of hydrophobic organic
compounds:
Kp = Koc • foc
-------
The reaction rate R^ (mg/£-sec) for process "i" is:
Ri = ki • Yi • fD • c (A19)
where: k^ = second order rate constant for process "i"
Y£ = yield coefficient for process "i"
C = total concentration of compound, mg/£.
Given a local value for [E]., a pseudo-first order rate constant K. (sec )
can be calculated:
Ki = ki • [EJi • Yi • fD
For a compound undergoing several competing reactions, the overall pseudo-
first order rate constant K(sec~l) is
K - I % (A21)
i
This general second order reaction method can be used to predict reac-
tion rates for photolysis, hydrolysis, oxidation, and bacterial degradation.
For short reaches of rivers with travel times of hours, these reactions are
not not likely to significantly reduce instream concentrations. For tran-
sient loads during storms, darkness should further reduce photolysis and,
indirectly, oxidation. Bacterial communities are unlikely to acclimatize in
hours to the transient loads. Of these transformation reactions, then, only
hydrolysis will be considered for those few compounds with large rate con-
stants. The nominal hydrolysis rate constant is calculated from the acid-
catalyzed, neutral, and base-catalyzed pathways (Burns et al. , 1982):
KHo = (kHA[H1 (ct'fs+fD) + kHN + kHB[OH~] .(fD»/3600. (A22)
where: ky^ = second-order acid-catalysis hydrolysis rate constant,
i /mole-hour
[H+] = hydrogen ion concentration = 10"?^ mole/£
pH = stream pH
a = acid-catalysis hydrolysis rate enhancement fractor for
sorbed compound = 10
k™ = neutral hydrolysis rate constant, sec~^
kjiB = second-order base-catalysis hydrolysis rate constant,
A/mole-sec
[OH~] = hydronium ion concentration = 10~pOH, mole/ H
77
-------
pOH = stream pOH = 14 - pH.
For ground water, the nominal hydrolysis rate constant (in years'l) is
calculated from an equivalent expression:
Kgo = (kHA[H+]g(a'fsg+fDg) + kHN + kHB[OH-]g.fDg).(24).(365.25) (A23)
where: [H ] = hydrogen ion concentration = 10~P &, mole/A
o
pHg = ground water pH
[Otf~] = hydronium ion concentration = 10~P 8, mole/£
O
pOHg = ground water pOH = 14~PHg
The nominal hydrolysis rate constants KHO and KgO apply to a reference
temperature, TR (usually 25 °C). These can be corrected to ambient surface
or ground water temperatures (T or Tg) with the following Arrhenius expres-
sions.
1 1
KR = KHo . exp[104 . ( )] (A24)
TR+273 T+273
1 1
K = K . exp[104 . ( )] (A25)
8 8 TR+273 Tg+273
A final transformation pathway to consider is volatilization. The vo-
latilization rate constant KV (sec ) can be calculated from the Whitman, or
two-resistance model (Whitman, 1923; Burns et al., 1982):
1 1
Kv = - . . fD (A26)
d RL + RG
where: d = mean stream depth, m
RL = liquid phase resistance, sec/m
RG = gas phase resistance, sec/m.
The second term in equation A26 represents the conductivity of the com-
pound through a liquid and a gas boundary layer at the water surface. The
liquid phase resistance to the compound is assumed to be proportional to the
transfer rate of oxygen, which is limited by the liquid phase only:
1
R = (A27)
32/MW
78
-------
where: K~ = reaeration rate constant, sec
MW = molecular weight of the compound
32 = molecular weight of oxygen.
The gas phase resistance to the compound is assumed to be proportional to
the transfer rate of water vapor, which is limited by the gas phase only:
1
(A28)
H . WAT . / 18/MW
RT'
where: WAT = water vapor exchange constant, m/sec
18 = molecular weight of water
H = Henry's law constant, atm-m^/mole
R = ideal gas constant = 8.206 x 1CT5 m^-atm/mol °K
T1 = water temperature ( °K) = 273 + T.
The reaeration and water vapor exchange constants will vary with stream
reach and time of year. They can be calculated using one of several empiri-
cal formulations. The water vapor exchange constant will be calculated using
wind speed and a regression proposed by Liss (1973):
WAT = 5.16 x 10-5 + 3,156 x 1Q-3 . w (A29)
where: W = wind speed at 10 cm above surface, m/sec.
Wind speed measured above 10 cm can be adjusted to the 10 cm height assuming
a logarithmic velocity profile and a roughness height of 1 mm (Israelsen and
Hanson, 1962):
W = Wz . log (0.1/0.001)/log (z/0.001) (A30)
where: Wz = wind speed at height z (m/s)
Z = wind measurement height (m)
The reaeration rate constant will be calculated by the Covar method using
stream velocity U and depth d, then corrected for temperature (Covar, 1976).
K02 = K20 '
where: K = reaeration rate at 20°C
For shallow streams where depth is less than 0.61 m, the Covar method uses
the Owens formula:
79
-------
K2Q = 6.194.10"5 . U0'67 . d"1'85 (A32)
For deeper, slower streams (d>0.61, U>0.518), the formula selected depends
upon the transition depth:
Kon = 4.555 .10 . U * . d (A33)
£ U
For deeper, faster streams (d>0.61, U>0.518), the formula selected depends
upon the transition depth:
dT = 4.1404 . u2'9135 (A34)
When d>dx>0.61, the O'Connor-Dobbins formula is used. When dx>d>0.61, the
Churchill formula is used:
K2Q = 5.825 . 10~5 . u0'969 . d~U673 (A35)
In summary, three transformation processes are considered in this analy-
sis: sorption, hydrolysis, and volatilization. Sorption of hydrophobic or-
ganic compounds is calculated by equation Al5 using data for KQW, fow, and s.
Hydrolysis is calculated by equations A22 and A24 using data for pH, kg^,
kjjfj, and k^B* Volatilization is calculated by equations A26 through A30
using data for U, d, W, T, MW, and H. When insufficient data are available,
conservative analyses can be completed ignoring any of these processes.
80
-------
APPENDIX B
ANALYTICAL SOLUTION FOR TWO-DIMENSIONAL DUE TO PULSE LOADING
The stream transport model described in the main body of this report is
based on our analytical solution for two-dimensional transport from a distri-
buted vertical plane source in uniform flow (Figure B.I). The case involving
pulse release of contaminant is considered. The analytical solution for this
case is developed in this appendix.
Figure B.I Schematic description of two-dimensional transport
in uniform flow in a stream of finite width, B.
81
-------
Consider the region with the Gaussian distributed source shown in Figure
B.I. The advective—dispersive equation for transport of a nonconservative
contaminant in uniform stream flow can be written as:
9c 92c 32c 9c
U Ex Ey + Kc + — = 0 (Bl)
9x 8x2 8y2 at
where Ex and Ey are dispersion coefficients in the logitudinal, x, and trans-
verse, y, directions, respectively; U is the main flow velocity in the x-
direction; c is the solute concentration; K is the first-order decay constant;
and t is the elapsed time.
The initial and boundary conditions associated with equation Bl may be
expressed as:
c (x,y,0) = 0 (B2)
c (°°,y,t) = 0 (B3)
8c
-- (x,0,t) = 0 (B4)
ay
3c
— (x,B,t) = 0 (B5)
9y
c (0,y,t) = Cg exp (-y2/2o2), t <_ tR (B6)
c (0,y,t) =0 , t > tR
where Cs and a are the.peak concentration and standard deviation of the
Gaussian source assumed to be located at x = 0.
The analytical solution for the above case can be derived in two steps.
The first step involves an application of the image source theory to the
fundamental solution of the corresponding case in which the stream is of
infinite width and the contaminant is continuously released from the source.
Let C-: denote the fundamental solutions. The expression for Cf has been
derived in the report dealing with groundwater screening procedures. It may
be written as:
ox exp (UX/2EX)
C* (x,y,t) = [ --- . I]C (B7)
(2TTEJ1/2
82
-------
where
x2 y2 U2T
exp (- KT) dT
t 4Exi 4E T + 2o2 4Ex
0 T3/2 (2o2+4E T)12
Image sources must be applied and their effects must be added to the fundamen-
tal solution to satisfy the zero normal gradient lateral boundary conditions.
(Figure B.2 the actual source plus the first four image sources.) In general,
an infinite number of image sources is required to reproduce the lateral
boundary effect exactly. The resulting solution becomes:
CO
C* (c,y,t) = C [C* (x,y,t) +1 C* (x,y,t)] (B9)
S * i=l "
where
ct. = C*f (x, 2Bi + y cos (iir), t) (BIO)
r i r
The second step in the derivation involves an application of Duhamel's theorem
of superposition in the time domain to satisfy the pulse source boundary
condition (B6). Figure B.3 illustrates how the pulse load condition is
obtained by superposing two continuous loads staggered over time interval t^.
The combined response is the required analytical solution and is given
by:
CO
_,*, . Y*, v
x,y,t s i=i
(Bll)
CO
,*
- Cf (x,y,t-tR) + I Cfl (x,y,t-tR)]
83
-------
IUACC S hrd
SOURCE
IMAGE 2
IMAGE 4
Figure B.2 Treatment of lateral boundary conditions
using image sources.
84
-------
APPENDIX C: LIST OF SYMBOLS
Text
Ag
AS
Screen
Input
A
-------
Screen Source Screen
Text Input Code Output Definition
average stream concentration, mg/X,
Cp average bioaccumulation concen-
tration of dissolved contaminant
in fish, mg/kg
Cf fundamental solution for stream
concentration, mg/£
Cg average concentration across con-
taminated area of interception
between ground water system and
stream, mg/£
Cj C
-------
Text
Cr
Screen Source
Input Code
Screen
Output
Definition
D
d
D'
DF
fDg
fl
oc
ocg
d<0
f
-------
Text
g
H
[H+]
kHA
kHB
kHN
KF
K
g
Kfc
K
oc
K
ow
K,
Sc reen
Input
H
k
-------
Text
Iflr
TTltD
•
MW
n
pH
pHg
pOH
pOHg
~P
p25
q
Q
QD
Qg
QL
QR
QS
QB
Screen Source
Input Code
MW MW
N N
pH PH
PHG PHG
POH
POHG
P<25 P25
q Q
QQ
Q
-------
Screen Source Screen
Text Input Code Output Definition
Qw Q
-------
Text
U
U0
u*
vg
w
WAT
X
Screen Source
Input Code
U
uo
usv
VWG VWG
W W10
WAT
X
Screen
Output
U
UO
usv
W10
WAT
X
Definition
stream velocity during storm, m/sec
stream velocity at base flow, m/sec
stream shear velocity, m/sec
ground water seepage velocity, m/year
wind speed at 10 cm above surface,
m/sec
water vapor exchange constant, m/sec
downstream (longitudinal) distance
XG
XG
Yl
ALPHA
BETA
RD
RG
from discharge, m
distance from land disposal site to
stream, m
yield coefficient for process "i"
Y lateral distance from discharge, m
ALPHA acid-catalysis hydrolysis rate
enhancement factor for sorbed
compound
BETA kinetic reduction exponent = k . x/U
aquatic exposure factor
R
-------
Text
Cw
Screen
Input
Source
Code
RW
SIGMA
THETAG
TAUG
THETAG
Screen
Output
R
-------
APPENDIX D
SAMPLE OUTPUTS
Sample Output:
D.I Scenario IB (Ground Water/Fish Consumption), Default Values #1
SARAH Model Scenario 1C
Scenario 1 Steady Ground Water Loading Run Program
KHG(/YR) = O.OOOOOE + 00
TAUG = 0.17797E + 03
RG = 0.10000E + 01
D' - 0.10000E + 00
C
-------
Sample Output:
D.3 Scenario 2A (Steady Storm/Drinking Water), Default Values #1, Gaussian
Solution
Drinking Water Model
Scenario 2A Storm Runoff Loading Run Program
QQO =
QQ
DO
D
BBO
BB
UO
U
QW
DF
DD
B
SIGMA =
USV
EY
EX
FD
POH
ALPHA =
FS
KH
W10
WAT
TK
RG
RL
KV
KK
0.50000E -
0.59817E +
0.30000E +
0.22378E +
0.15687E +
0.47147E +
0.10624E +
0.56696E +
0.72338E +
0.12093E +
0.10000E +
0.57016E +
0.45492E +
0.44449E -
0.59681E -
0.79016E -
0.99980E +
0.70000E +
0.10000E +
0.20496E -
O.OOOOOE +
0.10000E +
0.32076E -
0.29300E +
0.55871E +
0.24382E +
0.79932E -
0.79932E -
01
01
00
01
01
01
00
00
00
00
01
00
00
01
01
00
00
01
02
03
00
01
02
03
09
06
09
09
94
-------
Sample Output:
D.4 Scenario 3A (Catastrophic Runoff Loading/Drinking Water), Default
Values #1, Gaussian Solution
Drinking Water Model
Scenario 3A Catastrophic Pulse Loading Run Program
QQO =
QQ
DO
D
BBO
BB
UO
U
QW
DF
DD
B
SIGMA =
USV
EY
EX
FD
POH
ALPHA =
FS
KH
W10 =
WAT
TK
RG
RL
KV
KK
0.50000E -
0.11856E +
0.30000E +
0.29826E +
0.15687E +
0.55181E +
0.10624E +
0.72033E +
0.86806E +
0.73219E +
0.10000E +
0.40403E +
0.32237E +
0.51316E -
0.91835E -
0. 11355E -
0.99980E +
0.70000E +
0.10000E +
0.20496E -
O.OOOOOE +
0.10000E +
0.32076E -
0.29300E +
0.55871E +
0.24973E +
0.59970E -
0.59970E -
01
02
00
01
01
01
00
00
01
00
01
01
01
01
01
01
00
01
02
03
00
01
02
03
09
06
09
09
. GOVERNMENT PRINTING OFFICE: 19 87 .71*8- 12V 40707
95
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