-pnt.il Protection
Environmental Research
Laboratory
Athens GA 30613
EPA/600/3-88/020
October 1988
.h and Development
r/EPA
SARAH2, A Near Field
Exposure Assessment
Model for Surface
Water
-------
EPA/600/3-88/020
October 1988
SARAH2, A Near Field Exposure Assessment Model
for Surface Water
by
Scarlett B. Vandergrift and Robert B. Ambrose, Jr.
Assessment Branch
Environmental Research Laboratory
Athens, GA 30613
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GA 30613
:- D, Linrar - 1-
Dearborn S'^r
,- -IL 60604
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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.
11
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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 regulation of land disposal for hazardous wastes. These have
been updated in response to public comment, private peer review, and contin-
uing improvements in environmental science. Additional equations have been
added to address toxicant disposal through wastewater treatment facilities.
The resulting Near Field Exposure Assessment Model, (SARAH2) is not meant to
represent OSW policy on analysis of land disposal facilities. Rather, it is
intended to provide analysts the means to rapidly explore the consequences of
a variety of exposure and effects scenarios resulting from disposal of toxi-
cants. 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
111
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ABSTRACT
The nearfield surface water model (SARAH2) calculates maximum allowable
hazardous waste concentrations based upon predicted exposure to humans or
aquatic life from contaminated surface water. The surface water contami-
nation pathways 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 or lagoon. The human exposure path-
ways considered include ingestion of treated drinking water and consumption
of contaminated fish. Acceptable leachate or treated industrial waste dis-
charge constituent concentrations are estimated by a "back calculation" pro-
cedure starting from chemical safety criteria in surface water, drinking
water, or fish. "Forward calculations" predict the instream concentrations
from leachate or discharge concentrations.
SARAH2 is an interactive, menu-driven computer program with three default
data sets that can be rapidly modified. The analytical solutions for
contaminant behavior in a catchment or stream near the facility allow
rapid, multiple calculations needed for good sensitivity analysis. SARAH2 is
a modular FORTRAN program; modifications and expansions are obtained by the
addition of new modules. The first version is written for a VAX 11/785 mini-
computer. A subsequent version will operate on personal computers.
This report covers a period from January 1987 to May 1, 1988.
IV
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CONTENTS
Disclaimer ii
Foreword iii
Abstract iv
Figures ix
Tables xi
1. Introduction 1
2. Potential Exposure Pathways 5
2.1 Landfill/ground water 7
2.1A Scenario 1A: Exposure to humans through drinking water
contaminated by landfill leachate 9
2.IB Scenario IB: Exposure to humans through consumption
of fish contaminated by landfill leachate 11
2.1C Scenario 1C: Exposure of aquatic life due to landfill
leachate 12
2 .2 Landfill/Steady Storm Runoff 13
2.2A Scenario 2A: Exposure to humans through drinking
water contaminated by a steady landfill runoff
from the 25-year, 24-hour storm event 13
2.2B Scenario 2B: Exposure to humans through
consumption of fish contaminated by steady
landfill runoff from the 25-year, 24-hour storm
event 14
2.2C Scenario 2C: Exposure to aquatic life by steady
landfill runoff from a 25-year, 24-hour storm
event 15
2. 3 Landfill/Catastrophic Storm Runoff 16
2.3A Scenario 3A: Exposure to humans through
drinking water contaminated by catastrophic
landfill runoff loading to the stream 17
2.3B Scenario 3B: Exposure to humans through
consumption of fish contaminated by catastrophic
runoff loading 17
v
-------
CONTENTS (Continued)
2.3C Scenario 3C: Exposure of aquatic life due to
leachate carried through catastrophic runoff
loading to the stream 17
2.4 Industrial Waste/Continuous Discharge 18
2.4A Scenario 4A: Exposure to humans through drinking
water contaminated by a continuous industrial
discharge 18
2.4B Scenario 4B: Exposure to humans through
consumption of fish contaminated by a continuous
industrial discharge 20
2.4C Scenario 4C: Exposure of aquatic life due to a
continuous industrial discharge 21
2.5. Industrial Waste/Pulse Discharge 22
2.5A Scenario 5A: Exposure to humans through drinking
water contaminated by a pulse industrial
discharge 22
2.5B Scenario 5B: Exposure to humans through consumption
of fish contaminated by a pulse industrial
discharge 23
2.5C Scenario 5C: Exposure of aquatic life due to a
pulse industrial discharge 23
2. 6 Lagoon/Ground water 24
2.6A Scenario 6A: Exposure to humans through drinking water
contaminated by lagoon leachate carried by ground
water 25
2.6B Scenario 6B: Exposure to humans through consumption of
fish contaminated by lagoon leachate carried through
ground water 26
2.6C Scenario 6C: Exposure of aquatic life due to lagoon
leachate carried through ground water 27
2.7 Lagoon/Steady Overflow 28
2.7A Scenario 7A: Exposure to humans through drinking water
contaminated by a steady lagoon overflow 28
2.7B Scenario 7B: Exposure to humans through consumption
of fish contaminated by steady lagoon runoff 29
2.7C Scenario 7C: Exposure of aquatic life by steady
lagoon overflow 30
2.8 Lagoon/Pulse Failure 31
2.8A Scenario 8A: Exposure to humans through drinking water
contaminated by lagoon catastrophic failure 31
2.8B Scenario 8B: Exposure to humans through consumption of
fish contaminated by lagoon leachate carried through
catastrophic failure 32
VI
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CONTENTS (Continued)
2.8C Scenario 8C: Exposure of aquatic life due to catastrophic
lagoon failure 33
2.9 Lagoon/Continuous Discharge 34
2.9A Scenario 9A: Exposure to humans through drinking water
contaminated by a continuous discharge from a lagoon.. 35
2.9B Scenario 9B: Exposure to humans through consumption
of fish contaminated by a continuous discharge
from a lagoon 36
2.9C Scenario 9C: Exposure of aquatic life due to a
continuous discharge from a lagoon 37
2.10 Overview of the Analyses 40
3 . Development of Equations 46
3.1 Pathways 46
3.1.1 Ground water pathway 47
-Landfill 47
-Lagoon 48
-Leachate loading and dilution upon entry into
the stream 51
3.1.2 Surface runoff pathway 60
-Landfills 60
-Lagoon 63
-Transport and erosion 65
3.1.3 Direct discharge pathway 80
-Direct loading from a treatment facility 80
-Lagoon 81
-Direct discharge mixing 82
3 . 2 Transport of Contaminants Downstream 85
-Stream transport below continuous ground water loading 85
-Stream transport below pulse overflow loading 87
-Stream transport below pulse discharge loading 88
3. 3 Exposure and Effects 88
-Human exposure to contaminants through drinking water 88
-Human exposure to contaminants through consumption of
fish 89
-Delivery of contaminants through fish to humans 90
-Delivery of contaminants to aquatic organisms 91
4. User' s Manual 93
4.1 Explanation of menus 93
VII
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4. 2 Explanation of function keys 100
4. 3 Example problem 101
4. 4 Scenario variables 107
4. 5 Default variables 107
References 137
Appendix A 139
A.I Advection 139
A. 2 Dispersion 141
A. 3 Chemical transformation 143
Appendix B. Analytical Solution for Two-dimensional Flow due to
Pulse Loading 148
Appendix C. List of Symbols 152
Appendix D. Output Samples 165
Vlll
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FIGURES
Number Page
1.1 Routes of exposure to hazardous chemicals in surface water 2
1.2 Schematic of exposure routes 3
2.1 SARAH2 source and pathway combinations 6
2.1.1 Flow chart for Scenario 1A 10
2.1.2 Flow chart for Scenario IB 11
2.1.3 Flow chart for Scenario 1C 12
2.2.1 Flow chart for Scenario 2A 13
2.2.2 Flow chart for scenario 2B 14
2.2.3 Flow chart for scenario 2C 15
2.3.1 Flow chart for scenario 3A 16
2.3.2 Flow chart for scenario 3B 17
2.2.3 Flow chart for scenario 3C 18
2.4.1 Flow chart for scenario 4A 19
2.4.2 Flow chart for scenario 4B 20
2.4.3 Flow chart for scenario 4C 21
2.5.1 Flow chart for scenario 5A 22
2.5.2 Flow chart for scenario 5B 23
2.5.3 Flow chart for scenario 5C 24
2.6.1 Flow chart for scenario 6A 25
2.6.2 Flow chart for scenario 6B ?6
2.6.3 Flow chart for scenario 6C 27
2.7.1 Flow chart for scenario 7A 29
2.7.2 Flow chart for scenario 7B 30
2.7.3 Flow chart for scenario 7C 31
2.8.1 Flow chart for scenario 8A 32
ix
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FIGURES (Continued)
Number Page
2.8.2 Flow chart for scenario 8B 33
2.8.3 Flow chart for scenario 8C 34
2.9.1 Flow chart for scenario 9A 35
2.9.2 Flow chart for scenario 9B 36
2.9.3 Flow chart for scenario 9C 37
3.1.1 Variation of dilution factor with stream flow for steady
ground water loading 47
3.1.2 Ground water stream interception 57
3.1.3 Ground water loading to the stream showing mass balance and
concentration profiles 58
3.1.4 Ground water/stream interception zone 61
3.1.5 Surface runoff from land disposal units 62
3.1.6 Lagoon overflow 64
3.1.7 Lagoon dam failure 65
3.1.8 Slope effect chart 67
3.1.9 Soil moisture-soil temperature regimes of the Western US 68
3.1.10 Slope effect chart for areas where 3.1.9 are not applicable.... 69
3.1.11 Runoff/stream mixing 76
3.1.12 Precipitation and runoff flows 78
3.1.13 Direct discharge mixing 83
3.2.1 Downstream contaminant transport from the edge of inital mixing
zone 86
3.3 Variation of dilution factor with stream flow for steady
ground water loading 92
A. Tri-axial graphs at-a-station hydraulic geometry exponents 140
B.I Schematic description of two dimensional transport in uniform
flow 148
B.2 Treatment of lateral boundary conditions using image sources... i50
x
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TABLES
Number Page
2.1 List of reduction factors 7
2 .2 Summary of potential exposure scenarios 8
2 . 3 Summary of forward and backward calculations 38
3.1.1 Descriptive statistics for hydraulic (K£W) conductivity 52
3.1.2 Parameter values for permeation equation (at 25°C) 53
3.1.3 Permachor values of some organic liquids in polyethylene and
PVC 54
3.1.4 Water permachor value for dry polymers 55
3.1.5 "C" values for permanent pasture, rangleland, and idle land 70
3.1.6 "C" values for woodland 71
3.1.7 Runoff curve numbers 72
4.4.1 Calculations for scenario 1 108
4.4.2 Input variables for scenario 1 109
4. 4.3 Calculations for scenarios 2, 3 Ill
4. 4.4 Input variables for scenarios 2, 3 113
4. 4. 5 Calculations for scenarios 4, 5 117
4. 4. 6 Input variables for scenarios 4, 5 118
4.4.7 Calculations for scenario 6 121
4.4.8 Input variables for scenario 6 122
4.4.9 Calculations for Scenarios 7, 8 125
4.4.10 Input variables for scenarios 7, 8 127
4.4.11 Calculations for scenario 9 130
4.4.12 Input variables for scenario 9 131
4.5 Default values 134
xi
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SECTION 1
INTRODUCTION
Industrial wastes containing potentially hazardous chemicals 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 chemicals 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 municipal treatment plants or disposal
sites. To help the analyst establish minimum pretreatment levels, the original
surface water assessment model (R.B. Ambrose and S.B. Vandergrift) was developed
to "back calculate" appropriate pretreatment concentrations from chemical
safety criteria for exposure to humans and aquatic life. SARAH2 also allows
"forward calculations" to determine the chemical concentrations in-stream.
SARAH2 allows 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 or surface impoundment.
The first step in a screening analysis is to describe a set of scenar-
ios that might lead to the undesired consequences. As illustrated in Figure
1.1, three contaminant sources considered in SARAH2 are industrial waste-
water effluent, a land disposal site, and a surface impoundment. The path-
ways or loading routes to surface water are: 1. direct discharge, 2.
overland runoff, and 3. leaching to groundwater. Once in surface water,
chemicals are advected, dispersed, and degraded by several mechanisms.
The resulting aqueous concentrations may result in exposure to aquatic life
and to humans through drinking water or consuming fish. Figure 1.2 outlines
the contamination scenarios considered in SARAH2.
The second step is to assign probabilities to each event (for example:
occurance of a release or failure). It is virtually certain that aqueous
chemicals introduced at a wastewater treatment facility will be discharged in
the effluent. On the other hand, the probability that chemical solids intro-
duced to some land disposal sites will escape through runoff or leaching can
be very small. Design and operating requirements for land disposal facilities
are promulgated under Parts 264 and 265 of the Resource Conservation and
Recovery Act (RCRA) . For example, RCRA may require liners, le-ache.te collec-
tion and removal systems, ground water monitors, -Corrective actions, and run-
on and runoff controls. SARAH2 assumes failure of all controls, leading to
surface water contamination from both a ground water and a surface runoff
route (the probability of occurrence of various scenarios is set to 1.0)
SARAH2 helps the analyst investigate the consequences of these scenarios.
-------
WATERSHED
UPSTREAM
FLOW
LAND DISPOSAL
SITE
LEACHATE
/ I \ '-,
RUNOFF '. \ "--..,
^ ^ '-- X M,
WASTE LAGOON
WASTEWATER
TREATMENT
FACILITY
/w\
a a a
o a a
\aaafaf] TiBirili TsBBlBir
DRINKING
WATER
PLANT
IBB BlBB IBB
RESIDENCES
Figure 1.1 Routes of Exposure to Hazardous Chemicals in Surface Water
-------
HAZARDOUS
WASTE
WASTEWATER
TREATMENT
FACILITY
*( SLUDGE
LAND DISPOSAL
FACILITY
E
F
F
L
U
E
N
T
R
U
N
0
F
F
L
E
A
C
H
I
N
G
GROUND
WATER
'
SURFACE WATER
AQUATIC
EXPOSURE
AQUATIC
TOXICITY
FISH
BIOACCUMULATION
Figure 1.2 Schematic of Exposure Routes
3
LAGOON
R
U
N
O
F
F
L
E
A
C
H
I
N
G
GROUND
WATER
DRINKING
WATER
HUMAN
EXPOSURE
E
F
F
L
U
E
N
T
-------
The third step is to investigate the consequences of each scenario
and control failure. Aquatic and human exposure to hazardous chemicals at
excessive concentrations can result in such undesired consequences as chronic
toxicity in aquatic organisms and human health effects. The SARAH2 analysis
begins with criteria set to protect against such adverse impacts. 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 concentrations assuming specified patterns of water and fish
consumption. SARAH2 begins its back calculations with these resulting "safe"
concentrations and assumes that lower concentrations produce no adverse
effects. The forward calculations begin with leachate or industrial stream
concentrations and predict the surface water chemical concentration profile.
SARAH2 consists of nine surface water contamination scenarios: (1) leach-
ing from a landfill and subsequent delivery of contaminated ground water
to streams; (2) steady runoff from a landfill from a design storm event
that is stored for a 24-hour period and released over a short time period
into a receding stream; (3) catastrophic storm runoff from a design
storm event; (4) steady loading of an industrial wastewater effluent, (5)
pulse loading of an industrial wastewater effluent, (6) contaminant loading
from a lagoon leaching to the groundwater (7) contaminant loading through a
steady overflow from a lagoon that has exceeded its free board depth, (8)
contaminant loading by a pulse overland flow after a catastrophic lagoon dam
failure, and (9) contaminant loading by the direct discharge of lagoon waste-
water effluent. For each contamination route, SARAH2 can consider up to
three potential adverse effects: (a) human exposure through consumption of
contaminated drinking water, (b) human exposure through consumption of contam-
inated fish, and (c) toxicity to the aquatic community. Unrealistic combi-
nations of contaminant release and adverse effects are not implemented in
SARAH2, as discussed in later sections.
This manual contains three main sections that can be used independently.
The first, Potential Exposure Pathways, characterizes the potential pathways
leading to hupan and environmental exposure. This section describes each
step and associated comtaminant reduction factor from the source to a specified
distance downstream. Using the defined reduction factors, this section sets
up the final equations that compute the in-stream concentration (by forward
calculations) or the maximum allowable leachate, overflow runoff, or discharge
concentrations (by backward calculations).
The second, Development of Equations, 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 disposal
on human health and the environmental impacts. The overall approach is
based on a "back-calculation" method to identify acceptable wastewater or
leachate concentrations given health-based or enviromental thresholds that
are not to t^ exceeded at specified exposure points (or routes). This section
characterizes potential pathways leading to human and enviromental exposure,
evaluates the likelihood of exposure for each pathway, and sets up back-
calculation procedures for those pathways and exposure routes that are likely.
-------
SECTION 2
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
waste water treatment (including lagoons) or land disposal facilities. The
sources of contamination modeled in SARAH2 are: a land disposal facility,
surface impoundment, and an industrial waste water treatment facility. The
pathways modeled in SARAH2 are ground water transport, surface runoff, and
direct discharge.
As illustrated by Figure 2, not all sources contaminate surface water
by all pathways. The following is the list of exposure scenarios modeled in
SARAH2.
1. Steady ground water loading from a landfill.
2. Steady storm runoff from a landfill.
3. Catastrophic storm runoff from a landfill.
4. Continuous treatment facility discharge loading.
5. Batch treatment facility discharge loading.
6. Steady ground water loading from a lagoon.
7. Steady overflow and runoff from a lagoon.
8. Catastrophic failure and runoff from a lagoon.
9. Steady direct discharge from a lagoon.
A release rate estimation involves the determination of both the
contaminant concentration in the release and the volumetric flux of the
release. Modeling the release rate of toxic constituents can thus be done in
terms of either instantaneous time-varying releases or the annual average
release (i.e., steady state release rate based on an annual average). Rain-
storms come ir discrete intervals separated by dry periods. Using steady
state equations to model rainfall-induced leaching, however, assumes that
l/365th of the annua.i. recharge occurs each day (Versar, Inc., 1987).
The overail approach of this model is to define all possible con-
taminant reductions. Equations are then d-/eloped to define each reduction
factor in later sections.
-------
In this section, each scenario will be analyzed from source to stream to
determine the reduction factors necessary to compute maximum leachate or
overflow concentrations. A summary of all reduction factors are listed in
Table 2.1.
In many scenarios, equations will be repreated from previous scenarios.
Although these sub-sections may seem redundant, they deserve repeating due to
the fact that the source or effect may vary and slightly alter the final
equation. Also, the equations derived in this section are too important to
the overall solution scheme of SARAH2 to be deleted. Therefore, it is
suggested that the user does not read this section in its entirity, but only
the section(s) pertaining to the scenario of interest.
Nine sets of scenarios are considered. The nine sets (1, 2, 3, 4, 5, 6,
7, 8, and 9) are distinguished from one another by the pathway and source
through which contaminants reach and eventually enter 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 2.2.
LANDFILL
'/////////////A
DIRECT
DISCHARGE
Figure 2. SARAH2 source and pathway combinations.
6
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2.1 LANDFILL/GROUNDWATER
Scenario 1 (steady ground water loading from a landfill) assumes (1)
liner failure, (2) that the landfill is hydraulically connected to the
stream, and (3) that l/365th of the annual rainfall recharge occurs each day.
Leachate enters the aquifer directly below the land disposal unit and is
transported by ground water flow until it intersects a surface water body.
TABLE 2.1 List of Reduction Factors
Reduction
Factor Definition
Reduction factor due to wastewater
treatment
Reduction factor due to treatment of
the drinking water
Aquatic exposure factor
p Bioconcentration factor due to the bio-
chemical exchange processes with the fish
_ Reduction factor due to transport in the
ground water
p Reduction factor due to dilution during
runoff processes
s Reduction factor due to ground water and
stream entry point
Reduction factor due to dilution of the
upstream concentration by ground water,
precipitation or effluent
Reduction factor due to longitudinal
mixing and degradation in the stream (one
dimens ional)
Reduction factor due to lateral and longi-
tudinal mixing and degradation in the stream
(two dimensional)
fx y Laterally averaged reduction factor fx y.
(This is equal to (Cx)) -
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TABLE 2.2 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
groundwater seepage
from a landfill
steady surface runoff from a
landfill
pulse surface runoff from a
landfill
steady discharge from an industrial
wastewater treatment facility
batch discharge from an industrial
wastewater treatment facility
human exposure via
drinking water
human exposure via
fish comsumption
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
-------
TABLE 2.2 (CONT.) SUMMARY OF POTENTIAL EXPOSURE SCENARIOS
SCENARIO
SOURCE PATHWAY
EXPOSURE ROUTE
6A
6B
6C
7A
7B
7C
8A
8B
8C
9A
9B
9C
groundwater seepage
from a lagoon
steady overflow and surface
runoff from a lagoon
pulse failure surface runoff from
a lagoon
steady discharge from a lagoon
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
2.1A Scenario 1A: Exposure to Humans through Drinking Water Contaminated by
Landfill Leachate
This scenario consists of four stages between failure of the landfill con-
tainment facility and the exposure of the contaminant to humans via drinking
water (Figure 2.1.1). Through these stages, the concentration is successively
reduced from the leachate concentration, C^, to the concentration in drinking
water, Cpy. The relationship between C^y, C^, and C^ is given by (forward
calculation):
-------
DW
JU
where f
,
fx and
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. fsu is the dilution
factor for the upstream concentration by the ground water flow, Cy is the
upstream chemical concentration and fx y is the average concentration
reduction factor for downstream transformation.
To determine whether a potential health hazard due to surface water
contamination exists, the drinking water concentration can be equated to the
reference dose concentration,
Thus:
"RFD
(2.1.2)
and the maximum allowable leachate concentration must be (backward
calculation):
CRFD '
CU
(2.1.3)
STREAM FLOW
LANDFILL
LINER
FAILURE
TRANSPORT IN
GROUND WATER
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(STEADY SOURCE)
DRINKING
WATER PLANT
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 2.1.1 Flow chart for Scenario 1A
10
-------
2 . IB Scenario IB: Exposure to Humans through Consumption of Fish Contam-
inated by Landfill Leachate
This scenario consists of three stages between the landfill containment
failure and human exposure via consumption of fish residing in the contami
nated surface water (Figure 2.1.2). Through these stages, the input concen-
tration is successively reduced from the leachate concentration, C^, to the
stream concentration, and then increased to the bioconcentrated level in the
fish, Cp. The relation between C^,
calculation) :
and CF is given by (forward
CF =
g
5g
U
where fp 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 reference intake bioaccumulation concentration,
C'RFD. Thus:
RFD
(2.1.5)
and the maximum allowable leachate concentration is given by (backward
calculations):
RFD
cu
(2.1.6)
x,y
STREAM FLOW
LANDFILL
LINER
FAILURE
TRANSPORT IN
GROUND WATER
MIXING AT
ENTRY POINT
UPTAKE BY
FISH
EXPOSURE TO HUMANS
VIA FISH CONSUMPTION
Figure 2,1.2 Flow chart for Scenario IB
11
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2 . 1C Scenario 1C: Exposure of Aquatic Life due to Landfill Leachate
This scenario consists of two stages between the landfill containment
unit failure and aquatic exposure (Figure 2.1.3). Through these stages, the
input concentration is successively reduced from the leachate concentration,
CL, to the average stream concentration, CQ. The relationship between
CL, Cjj, and CQ is given by (forward calculation):
where :
£"EXP "" a
-------
2.2 LANDFILL/STEADY STORM RUNOFF
Scenario 2 (steady storm runoff of a landfill) assumes that 1)
the once in 25 year storm event occurs, 2) the contaminated catchment over-
flows, and 3) runoff occurs continously throughout the storm.
2.2A Scenario 2A: . Exposure to Humans through Drinking Water Contaminated
by a Steady Landfill Runoff from a Design Storm Event- -
This scenario consists of four stages between the landfill containment
failure and exposure of the contaminant to humans via drinking water (Figure
2.2.1). Through these stages, the concentration is successively reduced from
the runoff concentration, C, to the concentration in the drinking water,
The relationship between CDW,
DW.
calculation) :
DW
and CR is given by (forward
R
?DW CU
where fR, fsu, fx, and fDW are reduction factors due to dilution during
runoff, initial mixing at the stream entry area, transport in the stream, and
drinking water treatment, respectively.
Because of the pulse runoff loading condition, the concentration CDW
is time dependent. Thus, it is averaged over a 1-day period. This average
concentration, , can then be equated to the reference dose CRFD.
It follows that:
BASE FLOW +
WATERSHED
RUNOFF
WASTE
CONTAINMENT
FAILURE
STORM
RUNOFF
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(STEADY SOURCE)
DRINKING
WATER PLANT
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 2.2.1 Flow chart for Scenario 2A
13
-------
JRFD
(2.2.2)
and the maximum allowable runoff concentration is given by (backward
calculation):
RFD
U
(2.2.3)
where angular brackets are used to denote the 1-day average of the enclosed
quantity.
2.2.B Scenario 2B: Exposure to Humans through Consumption of Fish
Contaminated by Steady Landfill Runoff from the Design Storm Event--
This scenario consists of four stages between the landfill contain-
ment failure and exposure of contaminant to humans via consumption of fish
(Figure 2.2.2). Through these stages, the input concentration is altered
from the runoff concentration, C^, to the average concentration in the fish,
Cp. The infrequency of design runoff events and the length of time required
for food fish to attain high body burdens (weeks to months) should prevent
significant contaminant doses to humans. Consequently, the backward
or forward calculation formulas are not developed.
BASE FLOW +
WATERSHED
RUNOFF
WASTE
CONTAINMENT
FAILURE
STORM
RUNOFF
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(STEADY SOURCE)
UPTAKE BY
FISH
HUMAN EXPOSURE
VIA FISH
CONSUMPTION
Figure 2.2.2 Flow chart for Scenario 2B
14
-------
2.2.C Scenario 2C: Exposure of Aquatic Life to Steady Landfill Runoff from a
Design Storm Event--
This scenario consists of three stages between the landfill containment
unit failure and aquatic exposure (Figure 2.2.3). Through these stages, the
input concentration is reduced from the runoff concentration, CR, to
the stream concentration GX y. The relationship between CR, Cy and
GX y is given by (forward calculation):
Cx,y =
-------
2.3 LANDFILL/CATASTROPHIC STORM RUNOFF
Scenario 3A (catastrophic storm runoff of a landfill) assumes that
once the design storm event occurs, the contaminated catchment design fails,
and the adjacent surface water is loaded within a one hour time period.
2.3A Scenario 3A: Exposure to Humans through Drinking Water Contaminated
by Catastrophic Landfill Runoff Loading to the Stream--
This scenario consists of four stages between the landfill containment
failure and exposure of the contaminant to humans via drinking water (Figure
2.3.1). Through these stages, the concentration is successively reduced
from Cn to Gnu.
In a similar manner to Scenario 2A, a daily averaged concentration in
drinking water, , is obtained and equated to C^PD- This yields
the following equation for the maximum runoff concentration, C^, (backward
calculation) :
RFD
CU
(2.3.1)
where
and
are reduction factors due to dilution
during runoff, initial mixing of runoff and upstream flow, transport in
the stream, and drinking water treatment, respectively.
BASE FLOW +
WATERSHED
RUNOFF
WASTE
CONTAINMENT
FAILURE
CATASTROPHIC
RUNOFF
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
DRINKING
WATER PLANT
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 2.3.1 Flow chart for Scenario 3A
16
-------
2.3B Scenario 3B: Exposure to Humans through Consumption of Fish
by Catastrophic Runoff Loading- -
This scenario consists of four stages between the landfill containment
failure and exposure of the contaminant to humans via consumption of fish
(Figure 2.3.2). Through these stages, the concentration is successively reduced
from Cp to Cp. For reasons given in Scenario 2B, significant contaminant
doses to humans are ruled out. Back- calculation formulas are not developed.
2.3C 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 landfill containment
unit failure and aquatic exposure (Figure 2.3.3). Through these stages, the
input concentration is reduced from the runoff concentration . C^, to the
stream concentration Cx y. The relationship between CXjV,
'
x y.
is given by ( forward' calculation) :
and
Cx,y =
-------
Cx,y - ccc
(2.3.3)
and the maximum allowable concentration is given by (backward calculation)
ccc
CR -
cu
BASE FLOW +
WATERSHED
RUNOFF
WASTE
CONTAINMENT
FAILURE
CATASTROPHIC
RUNOFF
MIXING AT
ENTRY POINT
(2.3.4)
TRANSPORT
IN STREAM
(PULSE SOURCE)
EXPOSURE TO
AQUATIC ORGANISMS
Figure 2.3.3 Flow chart for Scenario 3C
2.4 INDUSTRIAL WASTE/CONTINOUS DISCHARGE
Scenario 4 (continous industrial discharge loading) assumes a direct
discharge from a treatment facility is occurring at a steady daily load with
a constant concentration.
2.4A Scenario 4A: Exposure to Humans through Drinking Water Contaminated
by a Continuous Industrial Discharge--
This scenario consists of four stages between the industrial waste
stream and exposure of the contaminant to humans via drinking water (Figure
2.4.1). Through these stages, the concentration is successively reduced from
18
-------
STEADY
INDUSTRIAL
WASTE
STREAM
DISCHARGE
THROUGH
TREATMENT
FACILITY
DRINKING
WATER PLANT
UPSTREAM
FLOW
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 2.4.1 Flow chart for Scenario 4A
the industrial waste concentration, Cw, to the concentration in the drinking
water C. The relationship between CDW, %, and GW is given by (forward
JDW
calculation):
DW
x,y
CW
U
(2.4.1)
where fD, fsu, fx v, and fDW are reduction factors due to wastewater
treatment, initial mixing at the stream entry area, transport in the stream,
and drinking water treatment, respectively.
To determine whether a potential health hazard due to surface water
contamination exists, the drinking water concentration can be equated to the
reference dose, C- Thus:
r r
CDW ~ CRFD
(2.4.2)
and the maximum allowable concentration is given by (backward calculation) :
cw =
RFD
CU
(2.4.3)
x,y
19
-------
2.4B Scenario 4B: Exposure to Humans through Consumption of Fish
Contaminated by a Continuous Industrial Dischare- -
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 2.4.2). Through these stages, the input concen-
tration is successively reduced from the industrial waste concentration, Cy,
to the average stream concentration through a specified reach. Then it is
increased to the bioconcentrated level in the fish, Cp. The relationship
between Cy, Cy, and Cp is given by (forward calculation):
CW
CU
(2.4.4)
For back- calculation, the average concentration in the fish,fCp,
equated to a specified reference bioaccumulation concentration,
Thus:
can be
CF = CRFD
(2.4.5)
and the maximum allowable discharge concentration is given by (backward
calculation):
cw =
RFD
(2.4.6)
UPSTREAM
FLOW
STEADY
INDUSTRIAL
WASTE
STREAM
DISCHARGE
THROUGH
TREATMENT
FACILITY
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
UPTAKE BY
FISH
HUMAN EXPOSURE
VIA FISH
CONSUMPTION
Figure 2.4.2 Flow chart for Scenario 4B
20
-------
2.4C Scenario 4C: Exposure of Aquatic Life due to a Continuous Industrial
Discharge--
This scenario consists of three stages between the industrial waste
stream and aquatic exposure (Figure 2.4.3). Through these stages, the input
concentration is successively reduced from the industrial waste concentration,
Cy, to the average stream concentration, Cx y. The relation between Cy, Cy,
and GX is given by (forward calculation):'
x,y
.y CW
x CU
(2.4.7)
For back-calculation, the average concentration in the stream can be
equated to the CCC by:
x,y
(2.4.8)
and the maximum allowable discharge concentration is given by (backward
calculation):
ccc -
cu
STEADY
INDUSTRIAL
WASTE
STREAM
(2.4.9)
DISCHARGE
THROUGH
TREATMENT
FACILITY
1
UPSTREAM
FLOW
!
MIXING AT
ENTRY
POINT
^ TRANSPORT
IN STREAM
EXPOSURE TO
AQUATIC ORGANISMS
Figure 2.4.3 Flow chart for Scenario 4C
21
-------
2.5 INDUSTRIAL WASTE/PULSE DISCHARGE
Scenario 5 (Batch industrial discharge loading) assumes a direct
discharge from a treatment facility within a one hour (or less) time period.
2 . 5A Scenario 5A: Exposure to Humans through Drinking Water Contaminated
by a Pulse Industrial Dischare- -
This scenario consists of four stages between the industrial waste stream
and exposure of the contaminant to humans via drinking water (Figure 2.5.1).
Through these stages, the concentration is successively reduced from Cw to
"DW-
In a similar manner to Scenario 4A, a time-averaged concentration in
drinking water, , is obtained and equated to CRFD to yield the following
equation for the maximum discharge concentration, Cy (backward calculation):
cw =
RFD
(2.5.1)
where
and
are reduction factors due to wastewater
treatment, initial mixing at the stream entry area, transport in the stream,
and drinking water treatment, respectively.
UPSTREAM
FLOW
BATCH
INDUSTRIAL
WASTE
STREAM
DISCHARGE
THROUGH
TREATMENT
FACILITY
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
DRINKING
WATER PLANT
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 2.5.1 Flow chart for Scenario 5A
22
-------
2.5B Scenario 5B: Exposure to Humans through Consumption of Fish
Contaminated by a Pulse Industrial Discharge--
This scenario consists of four stages between the industrial waste
stream and human exposure via consumption of fish residing in the contaminated
surface water (Figure 2.5.2). Through these stages, the input concentration is
successively reduced from the industrial waste concentration, Cy, to the
average stream concentration throughout a specified reach. Then it is
increased to the bioconcentrated level in the fish, Cp. A time-averaged
bioconcentrated level in the fish, , is obtained and equated to a spec-
ified reference bioaccumulation concentration, CRpD- Thus (backward
calculation):
=
RFD
CU
(2.5.2)
2.5C Scenario 5C:
Discharge--
EXDOsure of Aquatic Life due to a Pulse Industrial
This scenario consists of three stages between the industrial waste
stream and aquatic exposure (Figure 2.5.3). Through these stages, the input
concentration is successively reduced from the industrial waste concentration,
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 2.5.2 Flow chart for Scenario 5B
23
-------
UPSTREAM
FLOW
BATCH
INDUSTRIAL
WASTE
STREAM
DISCHARGE
THROUGH
TREATMENT
FACILITY
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
EXPOSURE TO
AQUATIC ORGANISMS
Figure 2.5.3 Flow chart for Scenario 5C
Cy, to the time and stream averaged concentration, . The relationship
between Cy, GU( and is given by (forward calculation):
Cw+
U
For back- calculation, the average concentration in the stream can be
equated to a specified CCC. Thus:
= ccc
(2.5.4)
and the maximum allowable discharge concentration is given by (backward
calculation):
ccc -
cu
(2.5.5)
2.6 LAGOON/GROUND WATER
Scenario 6 (steady ground water loading from a lagoon) 1) assumes the
waste leaves the lagoon by percolating through the clay liner or the native
soil, or 2) it permeates the flexible membrane liner (FML). Since precipi-
tation has a minimal influence on leachate generation, the liquid waste will
percolate to the watertable under the influence of gravity at a rate deter-
24
-------
mined by the permeability of the liner and the head or underlying soil
(Versar Inc., 1987).
1.
Except for the source, scenario 6 is essentially the same as scenario
Therefore, equations will be the same except for the source term.
2.6A Scenario 6A: Exposure to Humans through Drinking Water Contaminated
bv Laeoon Leachate Carried By Ground Water--
This scenario consists of four stages between failure of the lagoon liner
and the exposure of the contaminant to humans via drinking water (Figure
2.6.1). Through these stages, the concentration is successivley reduced from
the leachate concentration, CL, to the concentration in drinking water,
CDW. The relationship between CDW, Cy, and CL is given by (forward
calculation)
U
(2.6.1)
where
and
are reduction factors due to transport
, fSg, fsu, ?x,
in ground water, mixing at the area of leachate entry into the stream,
transport in the stream, and reduction in the drinking water plant,
is the dilution factor for the upstream concentration by the ground water
flow.
STREAM FLOW
LAGOON
LINER
FAILURE
TRANSPORT IN
GROUND WATER
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(STEADY SOURCE)
DRINKING
WATER PLANT
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 2.6.1 Flow chart for Scenario 6A
25
-------
To determine whether a potential health hazard due to surface water
contamination exists, the drinking water concentration can be equated to the
reference dose, C^pn. Thus:
JDW
JRFD
(2.6.2)
and the maximum allowable leachate concentration must be (backward cal-
culation) :
RFD
U
(2.6.3)
2 . 6B Scenario 6B: Exposure to Humans through Consumption of Fish Comtaminated
by Laoon Leachate Carried throuh Ground Water
This scenario consists of three stages between the containment failure
and human exposure via consumption of fish residing in the contaminated
surface water (Figure 2.6.2). Through these stages, the input concentration
is successively reduced from the leachate concentration, C^, to the stream
concentration, and then increased to the bioconcentrated level in the fish,
The relation between C
calculation) :
^,
and Cp is given by (forward
STREAM FLOW
LAGOON
LINER
FAILURE
TRANSPORT IN
GROUND WATER
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
UPTAKE BY
FISH
HUMAN EXPOSURE
CONSUMPTION
Figure 2.6.2 Flow chart for Scenario 6B
26
-------
CF =
U
(2.6.4)
where fp is the bioconcentration factor due to the biochemical exchange
processes within the fish.
For back-calculation, the average concentration in the fish, Cp, can be
equated to a specified reference bioaccumulation concentration, C'
Thus:
CF ~ C'RFD
(2.6.5)
and the maximum allowable leachate concentration is given by (backward
.calculations):
RFD
u
x.y
(2.6.6)
2.6C Scenario 6C: Exposure of Aquatic Life due to Lagoon Leachate
Carried through Ground Water
This scenario consists of two stages between the waste containment unit
failure and aquatic exposure (Figure 2.6.3). Through these stages, the input
concentration is successively reduced from the leachate concentration, C^, to
the average stream concentration, CQ. The relationship between CL, C^, and
CQ is given by (forward calculation):
TRANSPORT
IN STREAM
STREAM FLOW
LAGOON
LINER
FAILURE
TRANSPORT IN
GROUND WATER
MIXING AT
ENTRY POINT
EXPOSURE TO
AQUATIC ORGANISMS
Figure 2.6.3 Flow chart for Scenario 6C
27
-------
C0 = f S"S £"x, $"EXP CL + fsu £"x ^EXP CU (2.6.7)
For back- calculation, the average concentration in the stream can be
equated to the criteria, CCC. Thus:
C0 = CCC (2.6.8)
and the maximum allowable leachate concentration is given by (backward
calculation) :
CCC - fsu f
CL = -- ....... ---- -------- (2.6.9)
fx.y
2.7 LAGOON/STEADY OVERFLOW
Scenario 7 (steady overflow from a lagoon) assumes the depth of the lagoon
has exceeded its free -board- depth due to the addition of rainfall. The loading
event occurs over a time period greater than an hour, but less than one day.
Except for the source, scenario 7 is essentially the same as scanario 2.
Therefore, equations will remain the same except the source term.
2 . 7A Scenario 7A: Exposure to Humans through Drinking Water Contaminated
by Steady Lagoon Overflow.
This scenario consists of four stages between the waste containment
failure and exposure of the contaminant to humans via drinking water (Figure
2.7.1). Through these stages, the concentration is successively reduced from
the overflow concentration, Cjj, to the concentration in the drinking water,
Cpy. The relationship between Cp^, C^, and CR is given by (forward
calculation) :
CDW = + 5"SU fx fDW CU (2.7.1)
where f^, fsU' ^x1 anc* ^DW are reduction factors due to dilution
during overflow and initial mixing at the stream entry area, transport in the
stream, and drinking water treatment, respectively.
Because of the pulse loading condition, the concentration Cpy
is time dependent. Thus, it is averaged over a 1-day period. This average
concentration, , can then be squated to the specified reference dose
CRFD- t-t f°ll°ws that:
" CRFD (2.7.2)
and the maximum allowable overflow concentration is given by (backward
calculation) :
28
-------
BASE FLOW +
WATERSHED
RUNOFF
LAGOON
DEPTH EXCEEDS
FREE BOARD
DEPTH
RUNOFF
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
DRINKING
WATER PLANT
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 2.7.1 Flow chart for Scenario 7A
CRFD '
CU
(2.7.3)
where angular brackets are used to denote the 1-day average of the
enclosed quantity.
2.7B Scenario 7B: Exposure to Humans through Consumption of Fish
Contaminated by Steady Lagoon Overflow
This scenario consists of four stages between the waste containment
failure and exposure of contaminant to humans via consumption of fish
(Figure 2.7.2). Through these stages, the input concentration is altered
from the ovreflow concentration, CR, to the average concentration in the fish,
CF.
The infrequency of this event and the length of time required
for food fish to attain high body burdens (weeks to months) should prevent
significant contaminant doses to humans. Consequently, the backwards or
forward-calculation formulas are not developed.
29
-------
LAGOON DEPTH
EXCEEDS FREE
BOARD DEPTH
RUNOFF
UPTAKE BY
FISH
BASE FLOW +
WATERSHED
RUNOFF
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
HUMAN EXPOSURE
VIA FISH
CONSUMPTION
Figure 2.7.2 Flow chart for Scenario 7B
2.7C Scenario 7C: Exposure of Aquatic Life by Steady Lagoon Overflow Loading
This scenario consists of three stages between the waste containment unit
failure and aquatic exposure (Figure 2.7.3). Through these stages, the input
concentration is reduced from the overflow concentration, CR to the stream
concentration Cv,^..
x. y
The relation between CR Cy and Cx y is given by (forward cal-
culations) :
x,y
CU
(2.7.4)
For back calculation, the average concentration in the stream can be equated
to the CCC by:
x,y
CCC
(2.7.5)
30
-------
and the maximum allowable discharge concentration is given by (backward
calculation):
CCC -
(2.7.6)
BASE FLOW +
WATERSHED
RUNOFF
LAGOON DEPTH
EXCEEDS FREE
BOARD DEPTH
RUNOFF
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
EXPOSURE TO
AQUATIC ORGANISMS
Figure 2.7.3 Flow chart for Scenario 7C
2.8 LAGOON/PULSE FAILURE
Scenario 8 (catastrophic release from a lagoon) assumes a dam or berm
failure due to poor design or a storm. Release occurs over a time period
equal to or less than one hour.
Except for the source, scenario 8 is essentially the same as scenario
3. Therefore, equations will remain the same except for the source term.
2.8A Scenario 8A: Exposure to Humans through Drinking Water Contaminated
by Lagoon through Catastrophic Failure
This scenario consists of four stages between the waste containment
failure and exposure of the contaminant to humans via drinking water (Figure
31
-------
2.8,1). Through these stages, the concentration is successively reduced from
CR to CDW-
In a similar manner to Scenario 7A, a daily averaged concentration in
drinking water, , is obtained and equated to C^pp to yield the
following equation for the maximum release concentration, C^, (backward
calculation):
RFD
CU
CR -
where f^, fgu> fX' 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.
(2.8.1)
BASE FLOW +
WATERSHED
RUNOFF
LAGOON
DAM
FAILURE
CATASTROPHIC
RUNOFF
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
DRINKING
WATER PLANT
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 2.8.1 Flow chart for Scenario 8A
2.8B
Scenario 8B: Exposure to Humans through Consumption of Fish Contaminated
by Lagoon throuh Catastrohic Failure
This scenario consists of four stages between the waste containment
failure and exposure of the contaminant to humans via consumption of fish
(Figure 2.8.2). Through these stages, the lagoon concentration is successively
reduced to Cr-.
32
-------
The infrequency of this event and the length of time required
for food fish to attain high body burdens (weeks to months) should prevent
significant contaminant doses to humans. Consequently, neither the backwards
or forward-calculation formulas are not developed.
BASE FLOW +
WATERSHED
RUNOFF
LAGOON
DAM
FAILURE
CATASTROPHIC
RUNOFF
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
UPTAKE BY
FISH
HUMAN EXPOSURE
VIA FISH
CONSUMPTION
Figure 2.8.2 Flow chart for Scenario 8B
2 . 8C Scenario 8C: Exposure of Aquatic Life due to Catastrophic Lagoon Failure
This scenario consists of three stages between the waste containment unit
failure and aquatic exposure (Figure 2.8.3). Through these stages, the input
concentration is reduced from the release concentration, C^, to the stream
concentration Cv,v.
* j
The relationship between C^, Cy, and CX,Y is given by the time
averaged equation (forward calculation) :
x,y
CR
CU
(2.8.2)
CCC
(2.8.3)
33
-------
and the maximum allowable release concentration is given by (backward
calculation):
CCC -
(2.8.4)
BASE FLOW +
WATERSHED
RUNOFF
LAGOON
DAM
FAILURE
CATASTROPHIC
RUNOFF
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
(PULSE SOURCE)
EXPOSURE TO
AQUATIC ORGANISMS
Figure 2.8.3 Flow chart for Scenario 8C
2.9 LAGOON/CONTINUOUS DISCHARGE
Scenario 9 (steady direct discharge from a lagoon) assumes that the
lagoon contents are directly discharged into the surface water at a constant
concentration, and a constant rate. The discharge occurs over a time period
of one day.
Except for the source, scenario 9 is essentially the same as scenario
4. Therefore, equations will remain the same except for the source term.
2.9A Scenario 9A: Exposure to Humans through Drinking Water Contaminated
by a Continuous Discharge from a Lagoon
This scenario consists of four stages between the industrial waste stream
and exposure of the contaminant to humans via drinking water (Figure 2.9.1).
34
-------
Through these stages, the concentration is successively reduced from the
industrial waste concentration, Cy, to the concentration in the drinking
water C^y. The relationship between C^y, Cjj, and Cy is given by
(forward calculation):
DW
W
CU
(2.9.1)
where f^, fgu, ^x v an<* ^DW are Deduction factors due to waste-
water treatment, inital mixing at the stream entry area, transport in the
stream, and drinking water treatment, respectively.
To determine whether a potential health hazard due to surface water con-
tamination exists, the drinking water concentration can be equated to the
specified reference dose, C. Thus:
CDW " CRFD
(2.9.2)
and the maximum allowable waste concentration is (backward calculation) :
CW
RFD
CU
(2.9.3)
STEADY
LAGOON
WASTE
STREAM
DISCHARGE
THROUGH
TREATMENT
FACILITY
DRINKING
WATER PLANT
UPSTREAM
FLOW
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
HUMAN EXPOSURE
VIA DRINKING WATER
CONSUMPTION
Figure 2.9.1 Flow chart for Scenario 9A
35
-------
2.9B Scenario 9B: Exposure to Humans through Consumption of Fish Contaminated
by a Continuous Discharge- -from a Lagoon
This scenario consists of four stages between the industrial waste stream
and humam exposure via consumption of fish residing in the contaminated surface
water (Figure 2.9.2). Through these stages, the input concentration is suc-
cessively reduced from the industrial waste concentration, Cy, to the average
stream concentration through a specified reach, and then increased to the bio-
concentrated level in the fish, C. The relation between C
is given by (forward calculation) :
w,
and C
cp =
cw
cu
(2.9.4)
For back calculation, the average concentration in the fish, Cp, can be
equated to a specified reference intake bioaccumulation concentration,
C'RFD. Thus:
CF = C'RFD
(2.9.5)
and the maximum allowable discharge concentration is given by (backward
calculation):
CW =
C'RFD - fsu
cu
(2.9.6)
UPSTREAM
FLOW
STEADY
LAGOON
WASTE
STREAM
DISCHARGE
THROUGH
TREATMENT
FACILITY
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
UPTAKE BY
FISH
HUMAN EXPOSURE
VIA FISH
CONSUMPTION
Figure 2.9.2 Flow chart for Scenario 9B
36
-------
2 . 9C Scenario 9C: Exposure of Aquatic Life due to a Continuous Discharge- -
from a Lagoon
This scenario consists of three stages between the industrial waste
stream and aquatic exposure (Figure 2.9.3). Through these stages, the input
concentration is successively reduced from the industrial waste concentration,
cu-
w
is given by (forward calculation):
STEADY
LAGOON
WASTE
STREAM
DISCHARGE
THROUGH
TREATMENT
FACILITY
UPSTREAM
FLOW
MIXING AT
ENTRY POINT
TRANSPORT
IN STREAM
EXPOSURE TO
AQUATIC ORGANISMS
Figure 2.9.3 Flow chart for Scenario 9C
x,y
CW
CU
(2.9.7)
For back-calculation, the average concentration in the stream can be
equated to the CCC by:
(2.9.8)
Cx,y = CCC
and the maximum allowable discharge concentration is given by (backward
calculation):
ccc - fsu ^x f EXP Cu
^D ^x,y 5" EXP
(2.9.9)
A complete summary of all forward and backward calculations is given
in Table 2.3.
37
-------
TABLE 2.3 SUMMARY OF FORWARD AND BACKWARD CALCULATIONS
EFFECT A (Drinkin Water)
Scenario
Backwards
Forward
and 6
RFD
CU cx,y = CL
+ cu
2 and 7
RFD
CU Cx,y = y rDW>
x,y = Cw
+ CU
RFD
CU y
CL fg fsg rx>y fp
U
2 and 7
3 and 8
Not modeled
Not modeled
38
-------
TABLE 2.3 SUMMARY OF FORWARD AND BACKWARD CALCULATIONS (Continued)
EFFECT B (Cont.)
Scenario Backward Forward
4 and 9 C'RFD - rSU ?x ?F CU cx,y - Cw C
cw = .................... + CU
(or CL) fD fx> fp
cw
C'RFD ' fsu fx fF cu cx,y = cw fo fx,
(or CL) rD fsg rx>
EFFECT C (Aquatic Exposure)
Scenario Backward Forward
atld 6 CCC - ?SU fx ^EXP CU cx,y = CL
CL = ........ =^^- ........ + CU
fg fsg ?x,y
2 and 7 CCC - fgu fx f^p Cy Cx>y - y - y rEXP>
CR = .................... + CU
ccc - fsu fx fgxp Cy cXiy, =
-------
2.10 Overview of the Analyses--
Scenario 1A: Exposure to humans through drinking water due to landfill
leaching
o Release from landfill facility to ground water
o Transport in ground water to surface water body
o Mixing with the stream
o Transport in stream to drinking water intake
o Treatment of drinking water
Scenario IB: Exposure to humans through fish consumption due to landfill
leaching
o Release from landfill facility to ground water
o Transport in ground water to surface water body
o Mixing with the stream
o Uptake by fish through gills, gut, and skin
Scenario 1C: Exposure to aquatic organisms due to landfill leaching
o Release from landfill facility to ground water
o Transport in ground water to surface water body
o Mixing with the stream
Scenario 2A: Exposure to humans through drinking water due to steady runoff
from a landfill
o Surface runoff from landfill facility
o Overland transport assuming no reduction in mass
o Mixing with the stream
o Transport in stream to drinking water intake
o Treatment of drinking water
Scenario 2B: Exposure to humans through fish consumption due to steady
runoff from a landfill facility
Not modeled.
40
-------
Scenario 2C: Exposure to aquatic organisms due to steady runoff from a
landfill facility
Not modeled.
Scenario 3A: Exposure to humans through drinking water due to pulse runoff
from a landfill facility
o Surface runoff loading from landfill facility
o Overland transport assuming no reduction in mass
o Mixing with the stream
o Transport in the stream to drinking water intake
o Treatment of drinking water
Scenario 3B: Exposure to humans through fish consumption due to pulse
runoff from a landfill facility
Not modeled.
Scenario 3C: Exposure to aquatic organisms due to pulse runoff from a
landfill facility
Not modeled.
Scenario 4A: Exposure to humans through drinking water due to a steady
industrial waste discharge
o Discharge to treatment facility
o Dilution and degradation in treatment facility
o Mixing with the stream
o Transport in stream to drinking water intake
o Treatment of drinking water
Scenario 4B: Exposure to humans through fish consumption due to a steady
industrial waste discharge
o Discharge to treatment facility
o Dilution and degradation in treatment facility
o Mixing with stream
o Uptake by fish through gills, gut, and skin
41
-------
Scenario 4C: Exposure to aquatic organisms due to a steady industrial waste
discharge
o Discharge to treatment facility
o Dilution and degradation in treatment facility
o Mixing with the stream
Scenario 5A: Exposure to humans through drinking water due to a pulse
industrial waste discharge
o Discharge to treatment facility
o Dilution and degradation in treatment facility
o Mixing with the stream
o Transport in stream to drinking water intake
o Treatment of drinking water
Scenario 5B: Exposure to humans through fish consumption due to a pulse
industrial waste discharge
o Discharge to treatment facility
o Dilution and degradation in treatment facility
o Mixing with stream
o Uptake by fish through gills, gut, and skin
Scenario 5C: Exposure to aquatic organisms due to a pulse industrial
waste discharge
o Discharge to treatment facility
o Dilution and degradation in treatment facility
o Mixing with the stream
Scenario 6A: Exposure to humans through drinking water due to lagoon
leaching
o Release from lagoon waste facility to ground water
o Transport in ground water to surface water body
o Mixing with the stream
o Transport in stream to drinking water intake
42
-------
o Treatment of drinking water
Scenario 6B: Exposure to humans through fish consumption due to lagoon
leaching
o Release from lagoon waste facility to ground water
o Transport in ground water to surface water body
o Mixing with the stream
o Uptake by fish through gills, gut, and skin
Scenario 6C: Exposure to aquatic organisms due to lagoon leaching
o Release from landfill facility to ground water
o Transport in ground water to surface water body
o Mixing with the stream
Scenario 7A: Exposure to humans through drinking water due to steady runoff
from an overflowing lagoon
o Overflow from lagoon waste facility
o Overland transport assuming no reduction in mass
o Mixing with the stream
o Transport in stream to drinking water intake
o Treatment of drinking water
Scenario 7B: Exposure to humans through fish consumption due to steady
runoff from an overflowing lagoon
o Overflow from lagoon waste facility
o Overland transport assuming no reduction in mass
o Mixing with the stream
o Uptake by fish thorugh gills, gut, and skin
Scenario 7C: Exposure to aquatic organisms due to steady runoff from an
overflowing lagoon
o Overflow from lagoon waste facility
o Overland transport assuming no reduction in mass
43
-------
o Mixing with stream
Scenario 8A: Exposure to humans through drinking water due to catastrophic
lagoon dam failure
o Surface runoff loading from failed lagoon facility
o Overland transport assuming no reduction in mass
o Mixing with the stream
o Transport in the stream to drinking water intake
o Treatment of drinking water
Scenario 8B: Exposure to humans through fish consumption due to catastrophic
lagoon dam failure
o Pulse surface runoff loading from failed waste lagoon
o Overland transport assuming no reduction in mass
o Mixing with the stream
o Uptake by fish through gills, gut, and skin
Scenario 8C: Exposure to aquatic organisms due to catastrophic lagoon
dam failure
o Pulse surface runoff event from failed waste lagoon
o Overland transport assuming no reduction in mass
o Mixing with stream
Scenario 9A: Exposure to humans through drinking water due to a steady
industrial waste lagoon discharge
o Discharge to lagoon
o Dilution and degradation in lagoon
o Mixing with the stream
o Transport in stream to drinking water intake
o Treatment of drinking water
Scenario 9B: Exposure to humans through fish consumption due to a steady
lagoon discharge
44
-------
o Discharge to lagoon
o Dilution and degradation in treatment facility
o Mixing with stream
o Uptake by fish through gills, gut, and skin
Scenario 9C: Exposure to aquatic organisms due to a steady lagoon discharge
o Discharge to lagoon facility
o Dilution and degradation in lagoon facility
o Mixing with the stream
45
-------
SECTION 3
DEVELOPMENT OF EQUATIONS
The fundamental principle underlying this model is conservation of
mass. The equations solved by SARAH2 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, then the equations describing reduction factors are
developed corresponding to the various contaminant pathways.
This section is organized into the three sub-sections: pathways,
stream transport and effects. The equations describing the mass
transport, dilution, and transformation processes are developed for each
pathway and each stage. Next, equations will be developed for the mass
transport, dilution and transformation processes in the stream. Finally,
equations describing the effects will be developed.
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,
surface runoff, or direct discharge. Contaminants in stream are subject to
advection, lateral mixing, longitudinal mixing, physical reactions, chemical,
reactions 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 dishcharge. These sequential path-
ways are explored in the following sections.
3.1 PATHWAYS
The pathways can be divided into three stages or zones, that may vary
according to the source: (1) the leaching or transport zone, (2) the stream
interception zone and (3) the instream mixing zone. Therefore, each pathway
will be sub-divided into these three stages and equations describing the mass
transport, dilution, and transformation processes will be developed for each
appropriate source (landfill, industrial treatment plant, and lagoon).
46
-------
3.1.1 Ground Water Pathway
Contaminant leaching and transport in ground water system--The release
and transport of hazardous constituents from a landfill or lagoon through the
ground water pathway of the model assumes that the disposal unit, is
hydraulically connected to a stream (Figure 3.1.1). When liners or leachate
collectors at the base of the land disposal unit or lagoon 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 combined influences of
1) advection and hydrodynamic dispersion as well as 2) sorption and
biochemical degradation for nonconservative species. The contaminants
discharge into the surface water through the zone where the aquifer and
the stream intercept.
Landfill
The mass flux at the ground water interception zone or surface
water entry area, me, and the mass flux of leachate, m may be
related by (refer to Figure 3.1.1):
mg-
(3.1.1)
where the mass flux units are expressed in grams per second, and
is a ground water attenuation factor accounting for the effects of
hydrolysis in the aquifer. The average concentration at the ground
water interception zone and in the leachate may be obtained by dividing
the mass fluxes by the flow rates:
DISPOSAL UNIT
LINER
GROUND WATER
FLOW
Figure 3.1.1 Variation of Dilution Factor with Stream Flow for Steady
Groundwater Loading
47
-------
Cg-mg/Qg (3.1.2)
where flow units are expressed in cubic meters per second, concentration
units are expressed in milligrams per liter, and subscripts g and wg
refer to ground water/stream inteception zone, and waste site/ground
water origination zone, respectively. Combining the above equations, the
average concentration at the ground water interception zone and the leachate
concentration may be related by:
Cg " fg ' Cwg (3.1.4)
where f£ is the ground water reduction (due to hydrolysis and
dilution) factor:
fg-fHg ' Qwg/Qg (3.1.5)
QWg is the average volumetric rate of percolation through the land
disposal site, in cubic meters per second, and may be estimated by:
P . (l-fRw) . Aw
Qwg - " (3.1.6)
100 . 86400 . (365.25)
where P is the average annual precipitation rate, in cm/year, (
is the fraction of precipitation that leached 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 ^ will be equal to the actual surface area of the
disposal facility.
Lagoon
The only difference between the lagoon and the landfill source is
the rate of permeation or percolation. Therefore, all equations are the
same subsequent to the leaching zone. The leachate mass flux equation
is:
mg - %
where the m^ is the leachate mass flux rate. The average concentration
at the ground water interception zone and in the leachate can be obtained
by dividing the mass fluxes by the flow rates:
48
-------
= mg/Qg (3.1.8)
Cwl
where subscripts g and wl refer to ground water/stream inteception zone,
and lagoon/ groundwater origination zone, respectively. Combining the
above equations, the average concentration at the ground water
interception zone and the leachate concentration may be related by:
Cg-fg . Cwl (3.1.10)
where $ -, is the ground water reduction factor:
o
(3.1.11)
is the average volumetric rate of percolation through the
surface impoundment, in cubic meters per second, which depends on
whether the lagoon is lined or unlined. Precipitation has a minimal
influence on leachate generation, as liquid waste will percolate to the
watertable under the influence of gravity. The rate-determining step
is the permeability of the liner or underlying soil (if there is no
liner). Under the assumptions that a clay liner is fully saturated
and that the underlying soil remains unsaturated and accepts all water
which flows through the liner, the steady-state value of the volumetric
flux (seepage) rate, Qw^, can be estimated by (Marin 1988):
. 54x10"5 mil (Du) + Hla\
- - (3.1.12)
r2.54 x 10° mil\ (Du)
m
where:
o
Qw^ - volume loading rate (m /sec)
Kg - Darcy's coefficient, for unlined lagoons use native soil
hydraulic conductivity, Table 3.1.1 (cm/hr)
A^a - area of lagoon (m )
H^a = depth of liquid in lagoon (m)
DI^ liner thickness (mils)
Equation 3.1.12 models the release rate from a lagoon whether the
flow through the vadose zone is saturated or unsaturated. For unlined
active lagoons, the flow is typically saturated all the way to the
watertable. For clay-lined lagoons, the flow is saturated through the
liner and unsaturated between the liner and the watertable (assuming no
breaches in the liner). Equation 3.1.12 is appropriate when analyzing
lagoon releases, but should not be used for spills or other conditions
where the chemicals on the surface do not pond for a long time. In
49
-------
these conditions, the assumption of saturated flow (through the liner or
soil) may be violated.
Equation 3.1.12 applies to liquids that are mostly water. For
lagoons that contain organic fluids, however, the equations may need to
be corrected. For liquids having a density or viscosity that differs from
water, KS is corrected for this different viscosity and density by
calculating the term KC, using:
Kc =Kgw . DC/DW . UW/UC (3.1.13)
where :
Kc = corrected KS term = hydraulic conductivity of contaminant,
(cm/hr) .
Kg^ = hydraulic conductivity of groundwater, Table 3.1.1 (cm/hr).
D - density of liquids: c - contaminant, w = water, (kg/m ) .
U = dynamic viscosity of liquids: c - contaminant, w water.
(kg/m. sec.)
and then substituting KC for Kg in Equation 3.1.12.
The release rate from an intact lined landfill or lagoon can be
calculated for a small group of contaminants. Failed liners can be
modeled as a function of the extent of the failure using the modeling
equations for clay or natural soil -lined facilities. Although a
flexible membrane (FML) liner appears to allow no migration through the
barrier, it may indeed be penetrated by organic compounds and
contaminated water, although the rate of permeation is understandably
small. The rate at which a contaminant permeates through a polymeric
material has been shown to be dependent upon various properties of the
permeant, such as size, shape, polarity, and other factors (Steingiser
et al. 1978).
Salame and others proposed the use of a permeability equation to
predict the rate of permeation of liquids and gases through various
polymers (Salame 1961, 1973, 1985; Steingiser et al. 1978)
Ps - Ap e- (3.1.14)
where
g - mil
PS permeation rate , ............. ---
100 in2 day cmHg
Ap - constant solely dependent on the type of polymers used,
g - mil
100 in2 day cmHg
S - constant solely dependent on the type of polymers used,
(cc/cal).
- the polymer "permachor" calculated for each polymer permeant
pair, (cal/cc).
50
-------
Salame lists values for these parameters obtained from his extensive
experimental work. These values are shown in Tables 3.1.2, 3.1.3, and
3.1.4.
For permeation of water through FMLs, polymers are categorized into
five groups based on the values of the solubility parameter as shown in
Table 3.1.1. This grouping was achieved after examining experimental
data for about 70 different polymers (Salame 1985). The solubility
parameter provides an indication of polymer interaction with water, with
more interaction occurring at higher values of the solubility parameter.
Examples of hydrogen bonding for polymer group 5 include hydroxyl (OH)
and amid (NHCO) radicals as found in nylon and polyvinyl alcohol. The
polymer with hydrogen bonding (but with the value of "delta" less than
11) does not belong to group 5. Permachor values for some selected
organic liquids and for water are shown in Tables 3.1.3 and 3.1.4, res-
pectively. The water "permachor" values for various polymers given in
Table 3.1.4 apply under dry conditions. For water permeation under wet
conditions, permachor values may be reduced by about 20 percent.
The term Pg can be used to calculate the release rate in cubic
meters per second. Pg is multiplied by the area of the liner, and then
divided by its thickness and the contaminant density. This assumes a
normal water vapor pressure of 1 cm Hg at ambient temperature. The
general equation is:
Qwl -
-------
The concentration can be obtained by dividing the mass fluxes by the
stream flow:
fsg Cg
(3.1.18)
where CQ is the laterally averaged concentration at the downstream edge
of the mixing zone, and fSg and fsu are dilution factors for
ground water and upstream concentrations, respectively:
TABLE 3.1.1 Descriptive Statistics for Hydraulic (K_,) Conductivity
(cm/hr) (Carsel, 1988)
Conductivity (K^)
Soil Type
Clay+
Clay Loam
Loam
Loamy Sand
Silt
Silt Loam
Silty Clay
Silty Clay Loam
Sand
Sandy Clay
Sandy Clay Loam
Sandy Loam
X
0.20
0.26
1.04
14.59
0.25
0.45
0.02
0.07
29.70
0.12
1.31
4.42
s
0.42
0.79
1.82
11.36
0.33
1.23
0.11
0.19
15.60
0.28
2.74
5.63
CV
210.3
267.2
174.6
77.9
129.9
275.1
453.3
288.7
52.4
234.1
208.6
127.0
n
114
345
735
315
88
1093
126
592
246
46
214
1183
*n - Sample size, x = Mean, s
of variation (percent)
Standard deviation CV - Coefficient
"^Agricultural soil, less than 60 percent clay
52
-------
sg
(3.1.19)
(3.1.20)
where Qy is the upstream flow rate and Q is the ground water flow
from the catchment intercepted by the stream:
(3.1.21)
and Qg is the downstrean flow rate, or the sum of Q and Qy.
Contaminants reaching a stream via ground water will assured to
enter the water body continuously, i.e. at a steady state, and uniformly
along the sides and bottom of the stream. This assumes that the ground
water flow field is not influenced by the adjacent surface water (Figure
3.1.2). Therefore, for the ground water pathway, the average edge-of-
stream concentration can be calculated from the leachate concentration
via a ground water equation that considers advection, retardation, and
chemical hydrolysis and ignores dispersion.
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 attenuation factor, which is used in equation 3.1.1, 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.
TABLE 3.1.2 Parameter values for Permeation Equation (at 25°C)
Liquid Organics ina Water in polymer category
Parameter PE PVC 12345
s -
100 inZdaycmHg
1x10'
1x10
11.5 10.2 5.4xl02 25
(c)
S (cc/cal)
0.506 0.23 0.16 0.135 0.115 0.035 0.099
(cal/cc)
Table 3.1.3
Table 3.1.4
a Source: Salame no date; Salame 1967.
b See Table 2-8 regarding polymer category. Source: Salame 1985.
c A=0.33(0.056 x 5*), where fi is the solubility parameter,
(cal/cc)
53
-------
TABLE 3.1.3 Permachor Values of Some Organic Liquids in Polyethylene
and PVCa
Liquid
Acetic acid
Benzaldehyde
Benzene
2-Butoxy ethanol
Butyl acetate
Butyl alchol
Butyl ether
Butyraldehyde
Cap ry lie acid
Carbon tetrachloride
p-Chlorotoluene
Cyclohexane
Dibutylphthalate
Diethylamine
Ethanol
Heptane
Mexane
Methyl ethyl ketone
Methanol
Nitroethane
1- Pentyl prophonate
1 - Propylamine
Trichloroethylene
In nonpolar polvmer
*
13.0
15.0
5.4
24.4
13.0
18.0
10.4
13.5
19.0
5.8
7.6
7.0
31.4
10.0
16.0
7.0
6.0
12.5
15.0
15.4
15.0
11.0
5.4
54
In polar polvmer
*
44.0
4.0
7.0
75.0
5.0
50.0
46.0
0.0
50.0
22.0
7.5
45.0
17.0
5.7
48.0
44.0
43.0
1.0
47.0
7.0
7.0
6.7
3.0
-------
TABLE 3.1.3 Permachor Values of Some Organic Liquids in Polyethylene and
PVCa (Continued)
Liquid In nonpolar polymer In polar polymer
o-Xylene 9.4 11.0
p-Xylene 7.4 9.0
aPolyethlene and PVC are nonpolar and polar polymers, respectively
Sources: Salame, no date; Salame and Steingiser 1977.
TABLE 3.1.4 Water Permachor Value for Dry Polymers
Permachor
Polymer value
Polyvinyl alcohol 160
Polyacrylonitrile 109
Cellulose 97
Polyvinylidene chloride 87
Polycaprolactam (dry) 80
Polyacrylonitrile styrene 76
(70/30) (Lopac)
Polyacrylonitrile styrene/butadiene 75
(70/23/7) (Cycopac 930)
Polychlorotrifluoroethylene 71
Polyethylene terephthalate 68
Polyvinyldene flouride (Nynar) 67
Polyacrylonitrile styrene/-a/butadiene 65
(56.27/4/13) (Cycopac 920)
55
-------
TABLE 3.1.4 Water Permachor Value for Dry Polymers (Continued)
Permachor
Polymer value
Polyvinyl chloride 62
Polyoxymethylene (Delrin) 57
Polymethyl methacrylate 55
Polyvinyl acetate (dry) 45
Polystyrene/acrylontrile (74/26) 45
Polyethylene (HD) 40
Polysulfone 34
Polypropylene 33
Polycabonate (Lexan^) 33
Polystryrene 28
Polyethylene (LD) 26
Polyisobutylene 17
Polyethylene/vinyl acetate (85/15) 15
Polybutadrene 8
Polymethyl penetene (IPX) 8
Polydimethyl siloxane (dry) -4
Sources: Salame 1967; Salame no date; Salame and Steingiser 1977.
As contaminated water from the aquifer system enters the stream
along the side and bottom, it mixes with surface water supplied by
the upland watershed (Figure 3.1.3). Lateral mixing spreads the
contaminants until lateral concentration gradients disappear. The
laterally averaged concentration, GX, 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.
56
-------
DISPOSAL UNIT
Figure 3.1.2 Ground water Stream Interception
The equations previously developed relate contaminant concentrations
in the leachate with concentrations in ground water, and these with concen-
trations in stream. Combining equations 3.1.18 and 3.1.21 gives:
C "
CU
(3.1.22)
where:
leachate concentration (mg/1)
leachate flow rate (m^/sec)
ground water attenuation factor accounting for the effects
of hydrolysis in the aquifer (unitless)
fraction of ground water flow from the contaminated catchment
that is intercepted by the stream (unitless)
upstream concentration (mg/1)
57
-------
LAND DISPOSAL
I Q wg\
» p
0 wg
Q,
Q
B
>-
1
1
1
1
1
I/
"I
1
!c
I
I
'X
/
/
/
/
j
I
1
1
CX'CS|
4 fc1
'j
I/
/
Y /
/I
[ /I
j
I
1
k
3
r
x = o
AVERAGE
CONCENTRATION
x = o
DISTANCE, X
Figure 3.1.3 Ground water loading to the stream showing mass
balance and concentration profiles
58
-------
o
QU - upstream flow (m /sec)
Qs - total stream flow below the interception point (m /sec)
These items are discussed below.
fHP--This attenuation factor is the fraction of the
contaminant mass not transformed by hydrolysis during ground water
transport to the stream. Assuming a homogenous aquifer, this factor can
be calculated by:
('Kg rg> (3.1.23)
where KE is the total effective decay constant in ground water, in
years , and r£ 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, KR is equal to the overall hydrolysis rate
constant given by equation A27 and A29 in Appendix A. The travel time
of contaminants in ground water is given by:
Xg
r = ...?.... (3.1.24)
where X_ is the distance from the site to the stream, in meters, V_ is
the ground water seepage velocity, in meters per year, and fpE is the
fraction of the compound that is dissolved in the aquifer, given by
equation A20 in Appendix A.
attenuation factor is the fraction of the ground water
,, flow from the contaminated catchment that is intercepted by the stream.
This may vary 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 f^ is set to 1.
Qs--This is the average stream flow at the downstream edge of the
contaminated plume, in cubic meters per second, and may be estimated by:
P .
-------
If the average stream flow per unit area, qs,is known, then Qs can be
approximated by:
Qs - qs - As (3.1.26)
where qs is in units of cubic meters per second per square meter.
Qy-This is the average stream flow at the upstream edge of the
contaminated plume, in cubic meters per second. It may be estimated by:
As - Ac
Qu = QS ...... - °r Qu = qg (Ag - Ac) (3.1.27)
As
where Ac is the surface area of the contaminated catchment, diluting
the leachate. If AC is unknown, it may be conservatively estimated as
the surface area leaching through the land disposal unit, A^ plus the
minimum surface area between the facility and the stream.
_ (3.1.28)
Ac - AW + xg A,
Substituting equations 3.1.23, 3.1.6, and 3.1.25 into 3.1.22 and,
assuming no upstream contamination, gives the stream concentration
resulting from leachate only:
Aw U-fRw) fi
C0 = exp(-K r ) . -- . ------ . ~ . C (3.1.29)
As (l-fRs) fi g
Because clay liners should exhibit lower hydraulic conductivity than
natural watersheds, the ratio (l-fRw)/(l-fRs) should be less than
1.0. The ratio f^/ ^ 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:
C0 = exp(-Kg rg) . ^ ...... . Cwg (3.1.30)
fi As
3.1.2 SURFACE RUNOFF PATHWAY
Contaminant Concentration and Runoff Transport
Landfills --All RCRA Subtitle C land disposal 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 protective
60
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STREAM
V » msg y
Figure 3.1.4 Ground water/Stream Interception Zone
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 3.1.5, refers to its inability to contain a 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 t^.
The concentration in the runoff leaving the containment facility is
assumed to be equal to the leachate concentration, C^. This assumption
is somewhat conservative: for the case involving surface impoundments,
the runoff concentration may be slightly reduced due to dilution from
precipitation 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 loads are considered. The first assumes
containment failure that allows leachate from storm runoff to steadily
enter a stream 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 10 and 10 seconds
(approximately 15 minutes to 3 hours).
Because runoff leaving the containment facility is assumed to be at
the leachate concentration, Cw^ the runoff mass flux, m^ is equal to:
61
-------
""wR " CwR
(3.1.31)
where QwR 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 significantly occur. 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:
CwR "
(3.1.32)
(3.1.33)
where QR 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:
"ill///I Hi III
SURFACE RUNOFF
STORM DETENTION
FACILITY
OVERFLOW
WR
Figure 3.1.5 Surface Runoff from Land Disposal Units
62
-------
CR= CR CwR (3.1.34)
where $"R is the runoff dilution factor:
(3.1.35)
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 assumption, and stream concentrations below the initial
mixing zone should not be very sensitive to this assumption.
QR--The leachate flow running off the facility, (in cubic meters
per second) may be evaluated from:
P25 ' fR ' ^
QR_ _f?_._.*_._.T (3.1.36)
100 tR
where :
?25 - is the precipitation for the 25-year recurrence, 24-hour
duration storm (cm)
TR is the time over which contaminant runoff occurs (sec)
fR - is the fraction of the precipitation that runs off the waste
site (unitless)
AW - is the surface area providing water that leaches through the
disposal facility (m )
For scenario 2, steady runoff is assumed to occur throughout the storm,
and TR is 86400 seconds (one day). For scenario 3, runoff is assumed to
occur over a short period of time following the storm, and tR is 10
to 10 seconds.
Lagoon
There are two instances in which surface runoff loading from a
lagoon may occur and subsequently contaminate adj acent surface water.
Referring to Figure 3.1.6, in the first situation the original depth
plus the storm precipitation exceed the free board depth and the lagoon
is overloaded. Therefore, the new depth can be calculated by the following
equation:
Dnew-»old+ P25/100 (3.1.37)
where:
Dnew ~ new dePth (m)
DQ]^ - old depth before storm (m)
?25 - amount of rainfall (cm)
The volume of runoff to be expected can be calculated by:
63
-------
T
Figure 3.1.6 Lagoon Runoff
d>
new
la
(3.1.38)
where :
3
Vwi - overflow runoff volume (nr )
FBD = free board depth (m)
Ai_ = lagoon surface area (m )
The total time runoff occurs, TR, can be calculated from the following
ratio :
R
(3.1.39)
which gives :
25
storm
(3.1.41)
64
-------
where :
Do the distance from the free board depth to the top of the
broken dam (m)
and the new depth is still the old depth plus the rainfall. The time of
runoff is assumed to be one hour or less .
In both cases, the final runoff flow rate can be calculated by:
Qwi - VWI/TR 0.1.42)
where Qw^ is in cubic meters per second.
The transport and transformation for contaminants in runoff will
remain the same for the lagoon or landfill. Therefore, transport and
stream interception will not be analyzed for both cases.
Figure 3.1.7 Lagoon Dam Failure
Runoff Transport and Erosion
The concentration of the runoff at the waste site, Cwr, and at the
stream interception zone, CR, can be related by:
CwR " $"R ' CR
(3.1.43)
where:
fR - reduction factor for runoff
therefore:
CR-CR/CWR (3.1.45)
and CR and CwR can be calculated using the following equations.
65
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As contaminant is transported across land, a certain amount of
sediment is eroded and added to the stream in addition to the
contaminant. Estimates of the amount of hydrophobic compounds loaded
and removed in landfill waste site runoff can be calculated using the
Modified Universal Soil Loss Equation, (MUSLE) and sorption partition
coefficients derived from the compounds octanol-water partition coeffi-
cient. The modified universal soil loss equaton (Williams 1975), as
presented in Mills et al. (1982) is:
SY - (1.18 x 104) (VR * Qp)°-56 ' K LS ' CF P (3.1.46)
where:
SY = sediment yield (ke/event)
^R = vol111116 °f runoff fm )
Qp = peak flow rate (ur/sec) ^
K = soil erodibility factor (commonly expressed in tons per
acre per dimensionless rainfall erodibility unit) K can
be obtained from the local Soil Conservation Service office
LS = slope length, and slope steepness factor (unitless)
CF - cover facter (unitless) (1.0 for bare soils)
P = erosion control factor (unitless)
Soil erodibility factors are indicators of the erosion potential of
given soil types. As such, they are highly site-specific. K values for
sites under study can be obtained from the local Soil Conservation
Service office. The slope length factor, L, and the slope steepness
factor, S, are generally entered into the MUSLE as a combined factor,
LS, which is obtained from Figures 3.1.8 through 3.1.10. The cover
management factor, CF, is determined by the amount and type of vegetative
cover present at the site. Its value is "1" (one) for bare soils.
Consult Table 3.1.5 and 3.1.6 to obtain C values for sites with
vegetative covers. The factor, P, refers to any erosion control
practices used on-site. Because these generally describe the type of
agricultural plowing or planting practices, and because it is unlikely
that any erosion control would be practiced at an abandoned hazardous
waste site, use a worst-case (conservative) P value of 1 (one) for
uncontrolled sites.
The sediment yield and consequently the volume of runoff and the
peak flow rate must be calculated separately for the three areas in
question: (1) the watershed, (2) the waste site, and (3) the contaminated
catchments that affect the amount of sorbed chemical. The volume of
runoff can be calculated by:
VR - (0.01) (A) (DR) (3.1.46a)
where:
A - area of waste site, contaminated
catchment (minus waste site), or watershed
(minus contaminated catchment, (m )
DR - depth of runoff (cm)
66
-------
Slope Length, Meters
to
o
4-1
O
u.
_o
a
n
D)
o
a
o
20 30 40 60 80 100 150 200 300 400 600 800
40.0
20.0
10.0
6.0
4.0
2.0
1.0
0.6
0.4
0.2
0.1
I T
i r
r
(Slope %) __. eo
so
45
40
35
30
25
20
18
16
14
12
10
_. 2
1
0.5
I
70 100 200 400 600 1000 2000
Slope Length, Feet
Figure 3.1.8 Slope Effect Chart Applicable to Areas A-l in Washington,
Oregon, and Idaho, and All of A-3: See Figure 3-5
(USDA 1974 as Presented in Mills et al. 1982).
NOTE: Dashed lines are extension of LS formulae beyond values tested in
studies.
67
-------
The peak runoff rate, Qp, can be calculated by:
(2.8 x 1CT6) (A) (P25) (DR)
QP -
(Tstorm>
where:
storm
3w
amount of rainfall (cm)
= duration of storm (sec)
= water retention factor (cm)
(3.1.47)
0 100 200
Miles
Figure 3.1.9 Soil Moisture - Soil Temperature Regimes of Western
United States (USDA 1974)
68
-------
3.5 6.0 10
Slope Length, Meters
20 40 60 100 200 400 600
20.0
U
ra
1L
Q.
n
L.
O)
o
a
o
0.2 h
0.1 ^
10
20
40 60 100
200
400 600 1000 2000
Slope Length, Feet
Figure 3.1.10 Slope Effect Chart for Areas Where Figure 3-5 Is Not
Applicable (USDA 1974).
NOTE: The dashed lines represent estimates for slope dimensions
beyond the range of lengths and steepnesses for which data
are available.
69
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TABLE 3.1.5 "C" Values for Permanent Pasture, Rangeland, and Idle Land
Vegetal canopy
Type and height
of raised canopy
Canopy
cover0
Typea
Cover that
Percent
0 20
contacts the
groundwater
40 60
surface
80
95-100
No appreciable canopy
25
Canopy of tall weeds
or short bush
(0.5 m fall height) 50
75
Appreciable brush 25
or brushes
(2 m fall height) 50
75
Trees but no 25
appreciable
low brush 50
(4 m fall height)
75
G
W
G
W
G
W
G
W
G
W
G
W
G
W
G
W
G
W
0.45
0.45
0.36
0.36
0.26
0.26
0.17
0.17
0.40
0.40
0.34
0.34
0.28
0.28
0.42
0.42
0.39
0.39
0.36
0.36
0.20
0.24
0.17
0.20
0.13
0.16
0.10
0.12
0.22
0.16
0.19
0.14
0.23
0.18
0.21
0.17
0.20
0.10 0.042 0.013 0.003
0.15 0.090 0.043 0.011
0.09
0.13
0.07
0.11
0.06
0.09
0.038
0.082
0.035
0.075
0.031
0.067
0.012 0.003
0.041 0.011
0.012 0.003
0.039 0.011
0.011 0.003
0.038 0.011
0.018 0.09 0.040 0.013 0.003
0.145 0.085
0.085 0.038
0.13
0.08
0.17 0.12
0.081
0.036
0.077
0.042 0.011
0.012 0.003
0.041 0.011
0.012 0.003
0.040 0.011
0.19 0.10 0.041 0.013 0.003
0.14
0.09
0.14
0.09
0.13
0.087
0.040
0.085
0.039
0.083
0.042 0.011
0.013 0.003
0.042 0.011
0.012 0.003
0.041 0.011
Source: Wischmeier 1972.
aAll values shown assume: (1) random distribtion of mulch or vegetation and
(2) mulch of appreciable depth where it exists
Averge fall height of waterdrops from canopy to soil surface: m meters
GPortion of total-area surface that would be hidden from view by canopy in
a vertical projection (a bird's-eye view).
G: Cover at surface is grass, grasslike plants, decaying compacted duff,
or litter at least 5 cm (2 in) deep.
W: Cover at surface is mostly broadleaf herbaceous plants (as weeds) with
little lateral-root network near the surface and/or undecayed residue.
70
-------
The depth of runoff, D^, can be calculated by:
(P25 - 0.2 Sw)2
DR = -
(p25 + °-8 ' Sw>
where:
Sw - the water retention factor (cm). Sw, the water
retention factor can be calculated by:
(3.1.48)
Sw - (1000/CN) - 25.4
(3.1.49)
where :
the SCS runoff curve number, Table 3.1.7, (unitless)
TABLE 3.1.6 "C" Values for Woodland
Standard condition
Well stocked
Medium stocked
Poorly stocked
Tree Canopy
percent of
area3
100-75
70-40
35-20
Forest
litter
percent of
area
100-90
85-75
70-40
Unde r growth0
Managed
Unmanaged
Managed
Unmanaged
Managed
Unmanaged
"C" factor
0.001
0.003-0.011
0.002-0.004
0.01-0.04
0.003-0.009
0.02-0.096
Source: Wischmeir 1972.
aWhen tree canopy is less than 20 percent, the area will be considered as grass
land or corpland for estimating soil loss.
Forest litter is assumed to be at least 2 in deep over the percent ground
surface area covered.
°Undergrowth is defined as shrubs, weeds, grasses, vines, etc., on the surface
area not protected by forest litter. Usually found under canopy openings.
Managed - grazing and fires are controlled.
Unmanaged- stands that are overgrazed or subjected to repeated burning.
eFor unmanaged woodland with litter cover of less than 75 percent, C values
should be derived by taking 0.7 of the appropriate values in Table 3-4. The
factor of 0.7 adjusts for much higher soil organic matter on permanent woodland.
71
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TABLE 3.1.7 Runoff Curve Numbers
Soil group Description
Site type
Overall Road/right of way Meadow Woods
sitea
Lowest runoff 59
potential: Includes
deep sands with
very little silt
and clay, also deep,
rapidly permeable
loess (infiltration
rate =8-12 mm/h).
Moderately low runoff 74
potential: Mostly sandy
soils loess less deep or
less aggregated than A,
but the group as a whole
has above-average infil-
tration after thorough
wetting (infiltration
rate = 4-8 mm/h).
Moderately high runoff 82
potential: Comprises
shallow soils and soils
containing considerable
clay and colloids, through
less than those of group D.
The group has below-average
infiltration after pre-satura-
tion (infiltration rate
1-4 mm/h).
Highest runoff potential: 86
Includes mostly clays of
high swelling percent, but
the group also includes some
shallow soils with nearly
impermeable subhorizons near
the surface (infiltration
rate =0-1 mm/h).
74
30
45
84
58
66
90
71
77
92
78
83
Source: Adapted from Schwab et al. 1966.
aValues taken from farmstead category, which is composite including building,
farmyard, road, etc.
72
-------
To predict the degree of soil/water partitioning expected for given
compounds for a storm event use the following equations. First, the
amounts of dissolved and adsorbed substances are determined, using equations
adapted from Haith (1980):
The total runoff concentration at the stream entry point, CR, is
the sum of sorbed and dissolved concentrations:
CR = CLD + CLS (3.1.50)
The sorbed (Cj^g) and dissolved chemical (Cjjj) concentrations at the
stream entry point can be calculated by:
(OR) (CRS) +
-------
"VRC = volume runoff from waste site contaminated catchment (m )
Vg = sorbed substance loss per event (kg)
Mp = dissolved substance loss per event (kg)
VRs = volume of runoff from watershed (nr)
Mg = sorbed substance loss per event (kg)
The total loading to the receiving waterbody is calculated as follows
(adapted from Haith 1980):
SY
Ms = [ ] Ss (3.1.55)
100 .
and
(DRw) (Ds)
MD = (3.1.56)
P25
where:
Mg = sorbed substance loss per event (kg)
SY = sediment yield (metric tons)
pbw = soil bulk density (kg/1)
Sg = sorbed substance quantity (kg, Ib)
MD = dissolved substance loss per event (kg)
DRw - total storm runoff depth, from waste site (cm)
?25 = total storm rainfall (cm)
DS = dissolved substance quantity (kg)
The mass of sorbed and dissolved chemical can be calculated by:
Cw Aw (3.1.57)
Ss = 1 x 10'5
(1+ 6w/(KpW
where:
Ss sorbed chemical mass (kg)
9W volumetric water content of porous medium
(difference between wilting point and field capacity)
(1/1)
/>bw - bulk density of porous medium (kg/1)
KpW = partition coefficient (I/kg)
GW = total substance concentraton in waste site
(mg/m3)
AW = area of waste site (m ) (Actually a volume; assumption is
contamination in upper 1 cm is available for release.)
74
-------
and
0.001
Ds = ---- (3.1.58)
(1 + KpW ' p^w)
where: DS = mass of dissolved chemical (kg)
The bulk density is calculated from the volumetric water content by
the relationship:
/>bw - 2.65 (1 - 9W) (3.1.59)
The partition coefficient, K^w, can be calculated by:
KpW - (0.63 ' KOWW) FOCW (3.1.60)
where:
KOWW = octanol-water partition coefficient of the waste constituent
d/kg)
FOCW - organic carbon fraction of porous medium of the waste
site (kg/1)
This model assumes that only the contaminant in the top 1 cm of soil is
available for release via runoff.
The soil sorption partition coefficient for a given chemical can be
determined from known values of certain other physical/chemical
parameters, primarily the chemical's octanol-water partition
coefficient, solubility in water, or bioconcentration factor. Lyman
et al. (1982) present regression equations that allow the analyst to
determine sorption coefficients for specified groups of chemicals (e.g.,
herbicides, polynuclear aromatics). If parameter values required by the
appropriate equations are not available in chemical reference
literature, they can be estimated according to procedures described in
Lyman et al. (1982). Initially, the octanol-water partition coefficient
can be estimated based on the substance's molecular structure. If
necessary, this value can be used, in turn, to estimate either
solubility in water or bioconcentration factor.
Runoff Mixing
An initial mixing zone in the stream is developed over the
contaminant discharge area. For upland watersheds where the stream is
shallow, complete vertical mixing of the contaminant occurs within this
mixing zone. As indicated in Figure 3.1.11, however, lateral mixing
may be incomplete. In cases of runoff loading and direct discharge,
where lateral mixing is likely to be incomplete, there is a finite plume
75
-------
LAND DISPOSAL UNIT
LAND SURFACE
INITIAL MIXING
ZONE
Figure 3.1.11 Runoff /Stream Mixing
width over which a Gaussian concentration distribution CQ y is
assumed. The maximum contaminant concentration and the standard
deviation of the Gaussian distributon are denoted by C^ (runoff) , Cp
(discharge) a^ (runoff), and aD (discharge). The standard deviation,
a, is a measure of the plume width at the edge of mixing zone.
The contaminant mass flux loaded into the stream from surface
runoff, m^, is assumed equal to the runoff mass flux at the edge of the
stream, m^. 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:
m0 = mR
m +
(3.1.61)
The concentration distributon across the mixing zone can be obtained by
dividing the mass fluxes by the stream flow:
0,y
' C
R
U
(3.1.62)
where fgy is a dilution factor for upstream concentrations:
(3.1.63)
and Cv ,, is a dilution factor for runoff concentration describing a
j y
lateral, Gaussian distribution across the stream. This dilution factor
76
-------
declines from 1 at y - 0 to 0 for large values of y. Qs is the
downstream flow rate, or the sum of Q^ and Qy.
Contaminants reaching a stream via runoff are assumed to enter the
stream as a steady load throughout release duration t^ (Figure 3.1.12).
For scenario 2 and 7, the time over which the contaminant loading
occurs is assumed to be the 1-day duration of the storm. For scenario 3
and 8, contaminant loading is assumed to occur for a short duration
following the storm. During the loading event, an initial mixing zone is
developed over the runoff discharge area. Within this mixing zone,
dilution of the loading concentration occurs but is somewhat limited by
the magnitude of the release flow compared with the stream flow. At
the edge of the inital 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 leachate running off the facility with
concentrations in runoff at the stream bank, and these with
concentrations in stream. Combining equations 3.1.34, 3.1.35, 3.1.62,
and 3.1.63 gives:
QwR %
C0,y - fx.y ' --- ' CwR + " ' CU (3.1.64)
QR Qs
where:
- the runoff concentration (mg/1)
- the runoff flow running off the facility (nr/sec)
- the runoff flow from the contaminated catchment (m /sec)
QU - the upstream flow, Cy the upstream concentration (nr/sec)
Qs - the total down stream flow (m /sec)
fx = a dilution factor for runoff concentrations describing
a lateral, Gaussian distribution across the stream (unitless)
These terms are discussed below.
fX)y--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 runoff concentration, which is diluted laterally according to
the Gaussian distribution:
fx.y = exp(-y2/2a2) (3.1.65)
where y is the lateral distance across the stream and a is the
standard deviation 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 runoff:
mR - mo (3.1.66)
77
-------
PRECIPITATION
cm/day
RUNOFF FLOW
m 3/sec
ELAPSED TIME, sec
(a)
PRECIPITATION
cm/day
RUNOFF FLOW
m Vsec
ELAPSED TIME, sec
(b)
Figure 3.1.12 Precipitation and runoff flows: (a) runoff due to
24-hour precipitation, (b) catastropic pulse runoff
at the end of the 24-hour storm.
78
-------
The runoff mass flux is its flow multiplied by its concentration:
mR = QR ' CR (3.1.67)
The instream mass flux can be obtained by integrating the lateral
concentration distribution width:
B
U . d . J (CR . exp-y2/2 a2)dy (3.1.68)
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 3.1.68 and equating it to 3.1.67 gives:
QR . CR = 7 jr/2 U . d . a . CR . erf(B/a2) (3.1.69)
where erf is the error function, which is equal to 1.0 for B» a. Noting
that stream flow Qg is the product of the mean depth, velocity, and
width (Qg - UdB) , equation 3.1.69 can be solved for a:
B QR QR
a = ..... --- - 0.798 B --- (3.1.70)
J */2 Qs Qs
QR--The runoff flow from the contaminated catchment, in cubic
meters per second, may be estimated by:
P25 fRc (W P25 fRw ^
QR - ................... -- + .............. (3.1.71)
100 . ts 100 . tR
where:
P25 - precipitation for the design storm event (cm)
fRc - average fraction of precipitation that runs off of the
contaminated catchment (unitless)
fRw - fraction of precipitation that runs off waste site (unitless)
Ac - area of contaminated catchment (m )
A^ - area of waste site (m )
ts - total time of design storm event (sec)
tR - total time runoff occurs (sec)
where tg is the duration of the storm, or 86400 sec, and AC is the
land area of the contaminated catchment, in square meters, which
includes the surface area of the facility A^, plus the surface area
between the facility and the stream. Note that for steady runoff
throughout the storm, tR - tg and equation 3.1.70 reduces to:
P25 fRc Ac
-------
For the case of no dilution in overland flow, AC = AW and equation
3.1.72 reduces to:
P25 fRw ^
QR= " ---- = QWR (3.1.73)
100 . ts
Qjj--The stream flow at the upstream edge of the contaminated
runoff, in cubic meters per second, may be estimated by:
P25 fRS f*R (AS-AW)
QU = Q0 + - (3.1.74)
100 . tg
where f^g is the average fraction of the precipitation that runs off
the upper watershed, f ^ is a stream flow recession paramter (0-1) for
scenario 3 runoff events that follow a storm (input value describing
whether the stream flow is at full storm conditions f ^ = 1; or at
before storm conditions, f ^ = 0.), and Q0 is the base flow of the upper
watershed, in cubic meters per second.
Qs--The total stream flow at the downstream edge of the mixing
zone is the sum of the upstream flow and the runoff flow:
Q - + Q (3.1.75)
3.1.3 DIRECT DISCHARGE PATHWAY
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,
rap and Cjj. 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.
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, nip, may be related by:
80
-------
"VD (3.1.76)
where fwD 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 f^. If no measured (or
independently estimated) value is specified by the user, fyjj
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:
(3.1.77)
CD - mD/% (3.1.78)
Combining the above equations, the concentrations in the wastewater
effluent and in the industrial waste may be related by:
CD - fD CwD (3.1.79)
where fp is the wastewater treatment plant reduction factor accounting
for both dilution and mass reduction due to treatment efficiency e^:
QwD
CD- fwo QWD/QD- d - ewo> (3.1.80)
QD
Lagoon
The only type of discharge considered for the lagoon scenario is a
constant loading over a long period of time. The mass flux entering the
lagoon, my^,, an
-------
Combining the above equations, the concentrations in the wastewater
effluent and in the industrial waste may be related by:
CD = fi Cwl (3.1.84)
where f^ is the wastewater treatment plant reduction factor
accounting for both dilution and mass reduction due to treatment
efficiency ey^:
fl - fwl ' Owl/SB (3.1.85)
- C1 - ewl> Owl
(3.1.86)
Direct discharge mixing- -The contaminant mass flux loaded into the
stream from wastewater effluent, rngp, is assumed equal to the effluent
mass flux, mD (Figure 3.1.13). 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 near the bank:
niQ = mgj) + my (3.1.87)
The concentration distribution across the mixing zone can be obtained by
dividing the mass fluxes by the stream flow:
C0,y - fx.y ' CD + fsu CU (3.1.88)
where fsu is a dilution factor for upstream concentrations:
fSU = QU/QS (3.1.89)
and fx y is a dilution describing a lateral, Gaussian
distribution for effluent concentrations. This dilution factor,
developed in the runoff section, declines from 1 at y - 0 to 0 for large
values of y. Qg is the downstream flow rate, or the sum of QD and Qy.
Contaminants reaching a stream via wastewater discharge or lagoon
releases are assumed to enter the stream as steady load of duration tp.
For scenarios 4 and 7 , 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
concentration occurs but is somewhat limited by the magnitude of the
discharge flow compared with the stream flow. At the edge of the
82
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WASTEWATER
TREATMENT
FACILITY
INITIAL MIXING
ZONE
Figure 3.1.13 Direct Discharge Mixing
initial mixing zone (x - 0), it is assumed that the transverse
concentration distribution is a Gaussian distribution.
The equations relate contaminant concentrations in the industrial
waste stream with concentrations in the wastewater effluent, and these
with concentrations in stream. Combining equations 3.1.79, 3.1.80,
3.1.88 and 3.1.89 gives:
J0,y
x,y
QwD
QD
Qu
wD
CU
(3.1.90)
where:
Cwp - the industrial waste concentration (mg/1)
QwD - the industrial waste flow, Q (m /sec)
QJJ - the wastewater effluent flow (m /sec)
fwD - is the treatment plant mass attenuation factor (unitless)
QU - the upstream flow (m /sec)
Cy - the upstream concentration, Qs is the total downstream
flow (vr/sec)
£x y - a dilution factor for effluent concentrations describing a
lateral, Gaussian distribution across the stream (unitless)
Qs - stream flow downstream source (m /sec)
These terms are discussed below.
83
-------
fx y--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 mixing zone is at the effluent concentration, which is
diluted laterally according to the Gaussian distribution:
fX|y - exp(-y2/2a2) (3.1.91)
where y is the lateral distance across the stream and a is the standard
deviation of the distribution. This parameter can be derived by following
equation 3.1.66-3.1.70, substituting mD for mSR and QD for QSR to give:
B QD QD
a = . 0.798 . B . -- (3.1.92)
yn/2 QS QS
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
fy. If no measured or independently estimated value is specified by
the user, fyp defaults to 1 and mass is conserved through the
treatment plant.
Qwp--The flow rate for the industrial waste stream, in cubic
meters per second, must be specified by the user. If total loading
and concentration CwD are known, then Qyp can be calculated by:
"wO
QwD - -------- (3.1.93)
CwD CD
where m^ is expressed in grams, CWQ is expressed in mg/L (or grams
per cubic meter), and tp is expressed in seconds.
Qp--The flow rate of the wastewater treatment effluent, in cubic
meters per second, must be specified by the user.
Qjj--The stream flow, in cubic meters per second, can be specified
by the user. If known, an average flow condition can be calculated:
% - qs - As (3.1.94)
where qs is the average stream flow per unit drainage area, in cubic
meters per second per square meter, and Ag is the surface area of the
watershed above the discharge , in square meters .
Qs--The stream flow at the point of mixing is the sum of the
upstream flow and the effluent flow:
Q = Q + Q (3.1.95)
84
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3.2 Transport of Contaminants Downstream
Following initial dilution in the stream, the contaminant is
transported 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 of CQ v. In the case of
ground water loading, the initial boundary condition is the laterally
averaged CQ. At a specified downstream measurement point, x, (Figure
3.2.1) the contaminant concentration, Cx, is expressed as:
cx = ^x C0 f°r Sroun y u > y
where fx and fx y are concentration reduction factors accounting
for the combined influence of advection, longitudinal and lateral
dispersion, degradation 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.
Following initial dilution in the stream, contaminants at peak
concentration, CQ, are routed downstream under the combined influence
of advection, longitiudinal and lateral dispersion, degradation and
sorption. The concentration at downstream distance x from the edge of
the inital mixing zone is GX and is related to CQ via equations 3.2.1
and 3.2.2, in which fx is the attenution factor for transport in
surface water. The expressions for fx 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 3.2.1). At a given measurement
point located at distance x from the edge of the mixing zone (see Figure
3.2.la), 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-r (3.2.3)
r - x/U (3.2.4)
where:
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
85
-------
U
PLUME BOUNDARY
////////////. b:
\
GROUND
WATER
LOADING
MEASUREMENT
POINT
(a) Continuous Ground Water Loading
Y ,.-'''
i
\ \ ^^
[ J
/.v.v. /!!
/.v.v.v. .'.'.
Aviv."" ."!!"
L ^ X
X
* X
^ /
x '
/
c = 0, i>\R/
t
t f
niiMOrr on ^ v ^
nuiNUnf vJri 1^ j\ w
DISCHARGE
LOADING
f.'' i
X
X
L
,-''' B
X
*
>» "
W XX
\
\
\
MEASUREMENT
POINT
(b) Pulse Runoff Loading
Figure 3.2.1 Downstream Contaminant Transport from the Edge of
Initial Mixing Zone
86
-------
area where the effect of degradation is insignificant (x = 0).
Therefore in this case fx is 1, and Cx becomes CQ.
Stream transport below pulse runoff loading--Pulse runoff loading
produces a lateral concentration profile that is a Gaussian
distribution characterized (at x 0) by a minimum CR and a standard
deviation of a over the contaminant loading period tR (see Figure
3.2.1b). Downstream transport will be accompanied by lateral mixing
until the contaminants are evenly dispersed across the stream. The
concentrations at a given measurement point located at distance point,
x, will increase from zero to a relatively steady value between times
(x/U) and x/U + tR). 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:
- [C* (x.y.t) + S C* (x.y.t)
'y f i-1 fi
00
-C* (x,y,t-tR - S C* (x,y,t-tR>] (3.2.5)
f i-1 fi
where:
ax exp (U/2EX)
C* (x.y.t) - ------ . I (3.2.6)
f (2jrEx)1/2
x2 y2 U2r
exp ( - Kr) dr
t 4EX T 4EV T + 2a2 4E,.
I - / - y- * (3.2.7)
0 T 3/2 (2
-------
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 tp. 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 + tD). 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 3.2.5 - 3.2.8 (with tp substituted for t^ in equation
3.2.5).
3.3 EXPOSURE AND EFFECTS
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 CDW, the aquatic
exposure concentration Cg^p, and the fish body concentration Cp must
be calculated from Cv.
A.
Human exposure to contaminants through drinking water- -Humans are
exposed 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, GX 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 form Cx y to
Cpy. The relationship of C^y and Cx y is expressed as:
CDW ~ 5"DW Cx,y (3.3.1)
where fpy is the factor accounting for the reduction in contaminant
concentration achieved through the treatment process, i.e., the
pollutant removal efficiency.
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 GX is treated by allowing suspended solids and adsorbed
chemicals to settle out. This leads to a reduction of concentration from
Cx to CDy. The relationship between CDW and GX is given by
equation 3.1.77 with fDW being the dilution factor corresponding to the
fraction of the compound that is dissolved, fD. The expression for fp
is developed in Appendix A. This may be written as:
88
-------
1 + 0.41 Kow . foc . S . lO
where:
= octanol-water partition coefficient ('oct/-'-water)
fQC - organic carbon fraction of sediment (unitless)
S sediment concentration (mg/1)
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 consumption of contaminated fish.
For the case of runoff loading, the infrequency of runoff events (2
or 3 occurences 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. For the case of ground water
direct discharge and lagoon loading the continuous .nature of discharge
and ground water seepage into streams may cause fish to attain high body
burdens which result in significant contaminant doses to humans over a
lifetime. Delivery of contaminants through consumption of fish 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 lifetime. The _
typical fish will be exposed to the average concentration denoted by CQ
in the case of ground water loading (given by equation 3.1.27) and GX 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:
Cp = fp CQ (for ground water loading) (3.3.3)
Cp - ? p . Cx y (for direct discharge) (3.3.4)
where fp 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
89
-------
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.
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 compound 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 equilibirium
level is contolled 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:
CB = KFC fD Cx <3-3-5>
where Cg is the dissolved concentration in the blood, mg/L, fp is the
fraction of chemical dissolved, Kp^ is the food chain bioaccumulation
factor, expected to range from 2 to 3 and Cx is the stream concentration.
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:
cl = Kl CB (3.3.6)
and
Cnl =Knl CB <3-3-7>
where :
C-^ lipid (or fat) biomass concentration (mg/kg)
K^ = lipid phase partition coefficient (I/kg)
Cn^ non- lipid (blood-muscle) biomass concentration (mg/kg)
- non-lipid partition coefficient (I/kg)
The average whole fish concentration Cp (mg/kg) is the weighted sum of
the tissue concentrations :
CF - fl cl + d-fl) Cnl (3.3.8)
where f^ - fraction of biomass that is lipid. Substituting equation 3.3.8
and 3.3.6 into 3.3.7 gives :
90
-------
CF = KFC . KF fD Cx (3.3.9)
where Kp is the entire fish partition coefficient, or bioconcentration
factor given by:
KF - K]_ fx + K^ (l-f^ (3.3.10)
Equation 3.3.9 reduces to equation 3.3.4 provided that the parameter
fp is defined as:
Tp = KFC . KF . fD (3.3.11)
Note that unlike the dilution factors, fp is not dimensionless. The
unit for fp is I/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 . fx (3.3.12)
For less hydrophobic compounds, K^ may contribute significantly to
Kp. 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 - Kow . (fx + 0.01) (3.3.13)
For highly polar compounds and metals, the bioconcentration factor
Kp can not be estimated from the octanol-water partition coefficient
and lipid fraction. In this case, observed field or experimental values
of Kp must be used directly.
Delivery of contaminants to aquatic organisms--Aquatic organisms
are exposed to contaminants at a distance x downstream from the point of
discharge. 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 effect is generally referenced to the total concentration
of a compound. Therefore, CgXP ^s set to ^ anc* ^EXP ^s ecluated
to Cx.
If contaminant concentrations are high enough, aquatic organisms
may suffer chronic or acute toxic effects. Water quality 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
91
-------
4 nonconsecutive 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 degradation.
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 prevent 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
concentratons 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 3.3. The model allows for the fact that a fish population
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
or
EXP
EXP
Jx,y
(3.3.14)
(3.3.15)
where fjjXP ^s an aquatic exposure factor, equal to 1 for
ground water and discharge loading, respectively.
Stream
Concentration
Dilution
Factor
BASE FLOW
STORM FLOW
log Q,
Figure 3.3 Variation of dilution factor with stream flow
for steady ground water loading.
92
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SECTION 4
USER'S MANUAL
SARAH2 is a full-screen interactive model. The computer program,
through a series of menus and questions, can build and save a user-
specific data file from a pre-existing default data set. This section
describes all interactive screens, explains the function keys, presents
an example run, describes all variables, and lists all default values.
4.1 EXPLANATION OF MENUS
SARAH2 interactively allows the user to select the chemical release
pathway and exposure effect scenario. Subsequent menus include:
the listing or nonlisting of intermediate calculations, forward or backward
calculations, a lined or unlined lagoon (in case of a lagoon scenario),
inclusion of erosion calculations (in the case of landfill runoff or
lagoon overflow), exiting the program, editing the data set, or executing
the program. The following is a description of all menus illustrated in
Figure 4.
The first menu allows the user to specify one of nine possible loading
scenarios:
MENU: Potential Contaminant Sources
1. Steady groundwater loading from landfill
2. Steady storm runoff from landfill
3. Catastrophic storm runoff from landfill
4. Continuous industrial discharge loading
5. Batch industrial discharge loading
6. Lagoon loading through groundwater
7. Lagoon loading through steady runoff
8. Lagoon loading through catastrophic dam failure
9. Lagoon loading by steady direct discharge
The second menu allows the user to specify one of three possible
exposure scenarios:
93
-------
Model Parameterization
Select Scenario
Scenario 1
Scenario 2
Scenario 9
X
( \
\ /
Scenario Menus
Lagoon
Erosion
\
;
Select Effect
Drinking Water
Fish
Aquatic Org.
,? j
User Soeci
t \
\ )
Select Data Set
Default Values
User Specified:
Your Files
Foreign Files
/
ied N
Intermediate Output
f \
\ )
No
Yes
^ X
f
*w
Your Files Foreign Files
Selection Scrn. 1
I
Selection Scrn. N
File Name
Forward
CL Value
\
/
Backward
Model Execution
N
)
Display Solution
Solution Scrn. 1
Solution Scrn. 2
I
Solution Scrn. 3
Figure 4. Menus available in SARAH2.
94
-------
MENU: Potential Effect of Release
1. Human exposure through drinking water
2. Human exposure through fish consumption
3. Toxicity to aquatic organisms
If the user selects scenario 6, he/she needs to specify whether
the lagoon is lined or unlined:
MENU: Is the lagoon lined or unlined?
1. Unlined
2. Lined
If the runoff or overflow pathway (scenarios 2, 3, 7, or 8) is selected,
whether to include erosion calculations needs to be specified:
MENU: Erosion Equations Included?
1. No erosion
2. Erosion
The following combination of loading and exposure scenarios can not
be specified due to the unsubstantial amount of time to create an
exposure problem.
Steady Landfull Runoff/Fish Consumption
Catastrophic Landfill Runoff/Fish Consumption
Steady Lagoon Overflow/Fish Consumption
Catastrophic Lagoon Failure/Fish
Consumption
Source
2
3
7
8
Effect
2
2
2
2
95
-------
The user specifies his data set in the third menu:
MENU: Select Data Set
1. Default Values
2. User Specified: Your Files
3. User Specified: Foreign Files
The default data set is a pre-existing data set describing a small,
flat watershed containing a large land disposal facility and a slow,
shallow stream. To create his own, the user should choose the default
data set and alter or edit the numbers to represent his scenario. If
the user has already created and saved his data set, he may select
#2, a user specified file. If a user specified file is chosen, the next
screen lists all available files:
MENU: User Specified
1. Data Set #1
2. Data Set #2
3. Data Set #3
The "foreign files" refers to an external file that has not
previously been a part of the model. If the user selects a foreign file
he must give the name in the following menu.
MENU: User Specified
Enter file name for user-specified
foreign data file.
The fourth menu allows the user to view all intermediate calculations:
MENU: Do you wish to see the model's intermediate output?
1. No
2. Yes
96
-------
The fifth menu is the main operational menu
MENU: SARAH2 model EDIT/RUN/RETURN/HELP/QUIT
1. Edit Input Values
2. Run SARAH2
3. Return to Scenario Menu
4. Save Current Dataset Values
5. Exit to System
If the user selects to "edit input values," the model allows two
methods of editing:
MENU: Edit Ground water Input Values by Category
1. Edit All Scenario Input Values by Category
2. Edit All Scenario Input Values
The quickest editing procedure would be by category, which allows
the choice of the following categories.
MENU: Edit Groundwater Input Values by Category
1. Edit Watershed and Landfill Values
2. Edit Precipitation and Wind Values
3. Edit Stream Environment Values
4. Edit Chemical Values
5. Edit Loading/Exposure Values
6. Edit Groundwater Values
For example, if the user should need to alter the size of the
watershed, he should select the "watershed and landfill" category.
Entering a "1" results in the following screen.
97
-------
MENU: Groundwater Input Values
Watershed and Landfill
AS: Surface area of the upper watershed
AW: Surface area that provides water
AC: Surface area of contaminated catchment
> 0.1000E+08 m**2
> 1000000. m**2
> 0 m**2
DIST: Distance from land disposal site to stream > 150.
FRS: Avg frac of precip runs off upper watershed > 0.2
FRW: The frac of precip runs off waste site > 0.4
FRC: Avg frac of precip runs off contam. catchment> 0
meters
unitless
unitless
unitless
After the new value has been entered, the model returns to the
editing menu:
MENU: SARAH2 model EDIT VARIABLE MENU
1. Edit All Scenario Input Values by Category
2. Edit All Scenario Input Values
To return to the fifth menu (or the main "operational menu"), the
user should press the F5 function key (end).
If the user elects to edit all scenario input values, the program
will step the user through all subject categories. To exit a category
use the "enter" key (F3). To exit the editing process use the "end" key
(F5) which will return the user to the main operational menu:
MENU: SARAH2 Model EDIT/RUN/RETURN/HELP/QUIT
1. Edit Input Values
2. Run SARAH2 Model
3. Return to Scenario Menu
4. Save Current Dataset Values
5. Exit System
The user may return to menu 1 (scenario menu) by entering choice 3,
or exit the program by entering choice 5. If the user has altered the
data set, he should select number 4, "save current data set values," at
98
-------
this point. If he chooses to save his new data set, the next screen will
ask him to name the data set:
MENU: User Specified Save File Name and Description
Enter file name for user supplied data file
Enter any user comments on the data file:
The file name entered will appear on the list of optional files and
the comment lines, which should be a brief description of the scenario,
should appear any time the user requests help on that data file.
When the user elects to run the program, the next screen will ask
for the direction of calculations direction:
MENU: Backward and Forward Calculations
1. Backward Calculations
2. Forward Calculations
If the user selects "backwards," then he must know the stream standards
and want to determine the maximum leachate concentration. On the other
hand, if he chooses "forward" calculations, the program needs C^ (the
leachate concentration) and calculates the stream concentration profile.
Therefore, if C^ is zero the screen will request a nonzero number:
MENU: Leachate Concentration
To do forward calculations the Leachate
Concentration must be nonzero.
CL: Maximum allowable leachate concentration > 1.0 mg/L
The default value is one, but the user may enter any reasonable
concentration representative of his scenario.
At this point, the model will continue and calculate leachate or
instream concentrations. The next few screens will be the intermediate
output or the final results. To progress through the screens, the user
should press the space bar.
99
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4.2 EXPLANATION OF FUNCTION KEYS
There are six function keys:
Fl
F2
F3
F4
F5
F6
- Help
- CMOS
- Next
- Back
- End
- Exit
Fl allows the user to obtain vital information pertaining to the
highlighted field contained in the current screen. Help information is
available for every input variable (definition, mode, format, units, and
range), every output variable (definition, mode, format, units and
range), every scenario (description of source and pathway), and data set
(user supplied information). Help can be accessed anytime during the
model run.
F2 lists the function keys and their functions:
List of function key commands
Fl Display help information about the highlighted menu item
F2 Display a list of function key command descriptions
F3 Complete current operation and return control to calling program
F4 Suspend current operation and return to previous program
F5 Abort program execution and return control to previous program
F6 exit from the current job and return control to previous program
To exit this screen press F2 again.
F3 is basically an "enter" key. Any editing must be saved by this
key. F3 also proceeds to the next logical screen.
F4 returns the user to the previous screen. This is useful if the
user realizes a mistake was made on any one of the previous screens.
F5 is best used to end an editing session. This key returns the
user to the operational menu. The user must use caution in that this key
does not save any entered values. The user should use the following
sequence when editing: enter the input variable value, press F3 to save,
and then press F5 to exit editing mode.
F6 allows the user to exit the program. Exiting is allowed any time
during the program execution. The user must use this key cautiously if
data set storage is desired.
100
-------
4.3 EXAMPLE PROBLEM
This section describes in detail the execution, results, and conclusion
of an example problem. The overall approach is to demonstrate the difference
in forward and backward calculations:
1) Given the maximum leachate concentration (from a landfill) in the
groundwater, forward-calculate the instream concentration.
2) Using this calculated instream concentration as the drinking water
standard (C^p) , back-calculate the maximum leachate concentration.
In this situation, the maximum leachate concentration should be equal
to the concentration given in part 1 (CL) .
4.3.1. Problem
Description
Source:
Pathway:
Effect:
Problem 1:
Problem 2:
Purpose:
Landfill
Groundwater
Drinking Water
Calculate in-stream
concentration (Cx,y) given that the
leachate concentration, CL, is equal to 1 mg/L.
Calculate maximum leachate concentration (CL) given that the
drinking water standard, Cp^, is equal to Cx,y.
To check forward against backward calculations.
4.3.2. Forward
Execution
To determine the in-stream concentration, Cx y, perform the following
steps:
Menu 1
MENU: Potential Contaminant Sources
1. Steady Groundwater Loading from Landfill
2. Steady Storm Runoff from Landfill
3. Catastrophic Storm Runoff from Landfill
4. Continuous Industrial Discharge Loading
5. Batch Industrial Discharge Loading
6. Lagoon loading through groundwater
7. Lagoon loading through steady runoff
8. Lagoon loading through catastrophic dam failure
9. Lagoon loading by steady direct discharge
Select 1 (Steady ground water loading from landfill). Press F3.
101
-------
Menu 2
MENU: Potential Effect of Release
1. Human Exposure Through Drinking Water
2. Human Exposure Through Fish Consumption
3. Toxicity to Aquatic Organisms
Select 1 (Human exposure through drinking water). Press F3.
Menu 3
MENU: Select Data Set
1. Default Values
2. User Specified: your files
3. User Specified: foreign files
Select 1 (Default Values). Press F3.
Menu 4
MENU: Do you wish to see the model's intermediate output?
1. No
2. Yes
Select 1 (No). Press F3.
Menu 5
MENU: SARAH2 model EDIT/RUN/RETURN/HELP/QUIT
1. Edit Input Values
2. Run SARAH2 Model
3. Return to Scenario Menu
4. Help for SARAH2 variables
5. Exit to System
Select 2 (Run SARAH2 Model). Press F3.
102
-------
Menu 6
MENU: Backward or Forward Calculations
1. Backward Calculations
2. Forward Calculations
Select 2 (Forward Calculations). Press F3.
Menu 7
MENU: Leachate Concentration
To do forward calculations the Leachate
Concentration must be nonzero.
CL: Maximum allowable concentration > 1.0 mg/L
Enter 1.0 (CL concentration). Press F3.
4.3.3. Results
At this point, the model computes the in-stream concentrations and the
results are contained in the next three screens.
Screen 1
CU = 0.00000 mg/L
Forward calculations for chemical concentrations across
stream, mg/L
Distance across stream is (0 - 15.68098) meters
Press Space bar to continue
103
-------
Screen 2
X
20.00
20.00
20.00
20.00
20.00
0.000
0.038
0.038
0.038
0.038
0.038
3.920
0.038
0.038
0.038
0.038
0.038
Press
7.840
0.038
0.038
0.038
0.038
0.038
space bar to
11.761
0.038
0.038
0.038
0.038
0.038
continue
15.681
0.038
0.038
0.038
0.038
0.038
Screen 3
For a Leachate Concentration of 0.10000E+02 the
Predicted Drinking Water Concentration is mg/L
0.38018E-01
Press space bar to continue
4.3.4 Backward
Execution
The data set must be altered to compute the maximum leachate
concentration (backward calculations) from stream standards (CjyD - 0.038
mg/L)
Menu 1:
MENU: SARAH2 model EDIT/RUN/RETURN/HELP/QUIT
1. Edit Input Values
2. Run SARAH2 Model
3. Return to Scenario Menu
4. Help for SARAH2 variables
5. Exit to System
Select 1 (Edit Input Values). Press F3,
104
-------
Menu 2:
MENU: SARAH2 model EDIT VARIABLE MENU
1. Edit All Scenario Input Values by Category
2. Edit All Scenario Input Values
Select 1 (Edit by category). Press F3.
Menu 3:
MENU: Edit Groundwater Input Values by Category
1. Edit Watershed and Landfill Values
2. Edit Precipitation and Wind Values
3. Edit Stream Environment Values
4. Edit Chemical Values
5. Edit Loading/Exposure Values
6. Edit Groundwater Values
Select 5 (Edit loading/exposure values). Press F3.
Menu 4:
MENU:
X:
Y:
CRFD:
CPRFD :
CCC:
CL:
FL:
KFC:
KF:
Groundwater Input Values
Loading/Exposure
Dist of interest downstream of source
Horizontal distance
Specified acceptable daily intake cone
Specif acceptable daily bioaccumulation
Water quality std for aquatic organism
Max allowable leachate concentration
> 100.
> 15.68098
> 0.038
> 1.
> 1.
> 10.
Fraction of biomass that is lipid in fish> 0.3
Food chain bioaccumulation factor
Entire fish partition coefficient
> 3.
> 0
M
M
mg/L
mg/L
mg/L
mg/L
Unitless
3 mg/L
L/Kg
Change CRFD = 1 mg/L to CRFD = 0.038 mg/L. Press F3.
105
-------
Menu 5:
MENU: SARAH2 model EDIT VARIABLE MENU
1. Edit All Scenario Input Values by Category
2. Edit All Scenario Input Values
Press F5 to exit editing process.
Menu 6:
MENU: SARAH2 model EDIT/RUN/RETURN/HELP/QUIT
1. Edit Input Values
2. Run SARAH2 Model
3. Return to Scenario Menu
4. Help for SARAH2 variables
5. Exit to System
Select 2 (Run SARAH2 Model). Press F3.
Menu 7:
MENU: Backward or Forward Calculations
1. Backward Calculations
2. Forward Calculations
Select 1 (Backward Calculations). Press F3.
4.3.5 Results
For a Drinking Water Concentration of
0.3800E-01 the Allowable Leachate
Concentration is 0.99953E+01 mg/L
Press space bar to continue
4.3.6 Conclusion
The forward calculations calculate an instream concentration of 0.038 mg/L
when the leachate concentration was 1 mg/L. By running in the backwards mode,
106
-------
the model calculated an allowable leachate concentration approximately equal to
1 mg/L when the stream standard was set equal to the answer given in the forward
model (CRFD - 0.038).
4.4 SCENARIO VARIABLES
Numerous equations have been presented. Together they describe leachate
loading, dilution, instream transport and transformation, and exposure to
humans through drinking water and fish consumption. The many variables are
categorized by scenarios. Then they are grouped into those scenarios
describing:
1) watershed hydrology
2) stream and ground water environments
3) compound properties
4) loading/exposure scenarios
5) wind
6) dispersion
7) lagoon
8) runoff
The number of potential input variables may appear to make the practical
application of these analyses difficult. Fortunately, many of these inputs
can be estimated from other more readily available variables. Furthermore,
many terms in the equations can be ignored for 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 1) conservative ana-
lyses with a minimum set of data, 2) more complete analyses with a recommended
set of data, and 3) "full equation" analyses with an optional data set.
The steps for calculating an allowable leachate concentration for Scena-
rio 1 are summarized in Table 4.4.1. Input variables are given in Table 4.4.2.
The calculations and input data for Scenarios 2 and 3 are summarized in Tables
4.4.3 and 4.4.4. Calculations and input data for Scenario 4 and 5 are
summarized in Tables 4.4.5 and 4.4.6., etc.
4.5 DEFAULT VALUES
SARAH2 contains a default data file. A user may use this data set
as is, or build a totally new data set. This data set represents a
small, flat watershed containing a large land disposal facility and a slow,
shallow stream for each variable are listed in Table 4.5.
107
-------
TABLE 4.4.1 CALCULATIONS FOR SCENARIO 1
Step
Calculate
Explanation (and Equations)
rg(TAUG)
Kg(KHG)
Travel time of contaminant from land disposal
facility to stream, years (A17, A16, 3.1.18)
First-order rate coefficient for hydrolysis in
ground water, years" (A23, A25).
Mass attenuation factor in ground water (3.1.17).
10
11
12
fgK(ZSG) Concentration dilution factor in ground water and
stream (3.1.6, 3.1.19, 3.1.20).
fsu(ZSU) Concentration dilution factor for upstream contami-
nants (3.1.22, 3.1.21, QU/QS).
f(TAU) Travel time of contaminant downstream, seconds
(A4, 3.2.4).
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).
fx(ZX) Concentration reduction factor for downstream
transformations (3.2.3).
fjjy(ZDW) Drinking water treatment reduction factor (A15,
3.3.2).
fF(ZF) Fish bioaccumulation factor (3.1.13, A15, 3.3.6).
fp(ZG) Concentration dilution factor due to transport in
ground water (=fH fj_ QL/QS) (3.1.17, 3.1.6,
3.1.19).
CL(CL) Acceptable leachate concentration, mg/L
(Drinking Water: fsu, 3.2.3, 3.3.2, fg, 67; 3.1.20,
Aquatic Organisms: fgu> ^E> 3.1.20
Fish Accumulation: fsu, 3.3.6, f_, 3.1.20).
108
-------
TABLE 4.4.2 INPUT VARIABLES FOR SCENARIO 1
Input Value
Variable Units Range
Watershed and Landfill
Aw m2 104
o /
Ac m^ 104
As m2 107
Dist m 10
f Rs - - ° !
fRc " 0-1
f p« - - 0.1
- 106
- 106
- 109
- 103
- 0.5
- 0.5
- 0.5
Computer
Code
Variable
AW
AC
AS
DIST
FRS
FRC
FRW
Recommendation
Conservative
Optional
Conservative
Recommended
Recommended
Recommended
Recommended
Precipitation
cm/year
10-200
Ground water
ocg
Tg
PBAR
Recommended
--
°c
1/1
°c
m/sec
--
0.001-0
5 -
.10
8
10 - 20
0.3 -
10 -
1 -
0.1 -
0.1 -
0.5
20
105
1.0
1.0
FOGG
PHG
TG
THETAG
TREF
VG
ZI
ZIBAR
Recommended
Recommended
Re c ommende d
Recommended
Re c ommende d
Recommended
Recommended
Recommended
109
-------
TABLE 4.4,2 INPUT VARIABLES FOR SCENARIO 1 (Continued)
Input
Variable
Stream Env.
CU
do
foc
n
Qo
qs
Slope
S
Ts
U0
pH
Wind
Wz
Z
Chemical
H
kHA
kHB
kHN
Kow
MW
Units
mg/1
m
--
sec/nr-/3
0
m/sec
o o
m /sec/m
m/m
mg/1
°C
m/sec
m/sec
m
atm - m
mole
I/mole/sec
I/mole/sec
sec"
1/1
--
Computer
Value Code
Range Variable
--
0.1 - 3
0.01 - 0.10
0.02 - 0.08
ID'2 - 10
10-9 - 10-8
10 - 50
ID'4 - ID'2
5 - 30
0.1 - 2
5 - 8
0 - 10
0 - 10
10'7 - 10'1
0 - 10'1
0 - 10'1
0 - 10"^
10 - 107
10 - 103
110
CU
DO
FOC
NN
QQS
QS
SLOPE
SS
TSTREAM
UO
PH
WZ
Z
HENRY
KHA
KHB
KHN
KOW
MW
Recommendation
Optional
Recommended
Recommended
Optional
Optional
Optional
Recommended
Optional
Recommended
Recommended
Optional
Optional
Optional
Optional
Recommended
Recommended
Recommended
Conservative
Optional
-------
TABLE 4.4.2 INPUT VARIABLES FOR SCENARIO 1 (Continued)
Input
Variable
K
Exposure
CRFD
CRFD
KFC
fl
X
ccc
CL
Value
Units Range
I/mole/sec 0 - 10 '1
mg/1
mg/1
mg/1 1 - 3
0.01 - 0.25
m 0 - 5000
mg/1
mg/1
Computer
Code
Variable
KK
CPRFD
CRFD
KFC
FL
X
CCC
CL
Recommendation
Optional
Conservative
Conservative
Recommended
Conservative
Optional
Conservative
Optional
TABLE 4.4.3 CALCULATIONS FOR SCENARIOS 2. 3
Step
Calculate
Explanation (and Equations)
With Erosion
1 SY
Without Erosion
1 CR(ZRU)
CX)y(ZXY)
CSU(ZSU)
Sediment yield (3.1.49, 3.1.48, 3.1.47, 3.1.46a,
3.1.46)
Concentration dilution factor in surface runoff
(3.1.35, 3.1.70, 3.1.34).
Concentration dilution factor across stream at
point of mixing (A3, 3.1.73, 3.1.74, A4, A5, A7,
3.1.69, 3.1.64).
Concentration dilution factor for upstream
contaminants (3.1.88).
Ill
-------
TABLE 4.4.3 CALCULATIONS FOR SCENARIOS 2. 3 (Continued)
Step
Calculate
Explanation (and Equations)
4 r(TAU)
5 K(KK)
rx>y(ZXY)
CL(CL)
With Erosion
Travel time of contaminant downstream, seconds
(A4, 3.2.4).
First order rate coefficient for hydrolysis and
volatilization in stream, seconds" (A15, A22,
A24, A30, A29, A34, (A32, A33, or A35), A31, A27,
A28, A26, A19).
Concentration reduction factor for downstream
transformation (A8, A9, AlO, 3.2.7, 3.2.6, 3.2.8,
3.2.5).
Drinking water treatment reduction factor (A15,
3.3.2).
Acceptable leachate concentration, mg/L (3.1.88,
3.1.34, 3.1.64, 3.3.2, 3.2.5, 2.2.3).
Sediment concentration at stream entry point,
sorbed and dissolved (3.1.57, 3.1.58, 3.1.54,
3.1.60, 3.1.55, 3.1.56, 3.1.53, 3.1.54, 3.1.51,
3.1.52, 3.1.60)
112
-------
TABLE 4.4.4 INPUT VARIABLES FOR SCENARIOS 2, 3
Input
Variable Units
Watershed and Landfill
Aw m
Ac m
AS m
%c
fRs
fRw
f*
R
Di ct. m
Value
Range
IO4 -
IO4 -
IO7 -
0.1 -
0.1 -
0.1 -
0 -
10 -
IO6
IO6
IO9
0.5
0.5
0.5
1
IO3
Computer
Code
Variable
AW
AC
AS
FRC
FRS
FRW
FRSTAR
DIST
Recommendation
Conservative
Optional
Conservative
Recommended
Recommended
Re c ommende d
Re c ommende d
Recommended
Precipitation
cm/year
'25
"storm
cm
sec
10 - 200
10 - 15
103 - 106
Stream Environment
u
Qo
PBAR
P25
TSTORM
mg/1
m
m /sec
i3/sec/m2
ig/1
0.1 -
10-2 .
io-9 -
io-4 -
3
10
io-8
ID'2
cu
DO
QQO
QS
SS
Recommended
Recommended
Recommended
Optional
Conservative
Optional
Conservative
Recommended
113
-------
TABLE 4.4.4 INPUT VARIABLES FOR SCENARIOS 2, 3 (Continued)
Input
Variable
n
Ts
b
TR
£
foc
Slope
U0
PH
Qs .
Dispersion
Ex
Ey
Wind
W
wz
Z
Chemical
Kow
kHA
kHN
kHB
MW
Value
Units Range
sec/m1/3 0.02
°C 5
0.02
°C 5
0.2
0.01
m/m 10 "4
m/sec
5
0 O
nr/sec 10 "^
0
nr/sec 1
m2/sec 10"2
m/sec 0
m 0
1/1 10
I/mole/sec 0
sec"1 0
I/mole/sec 0
10
- 0.08
- 20
- 0.5
- 20
- 0.7
- 0.10
- io-2
--
- 8
- 20
- 10
- io-1
- 10
- 10
- IO7
- io-1
- lO"5
- io-1
- IO3
Computer
Code
Variables
NN
TSTREAM
BEXP
TREF
FEXP
FOC
SLOPE
UO
PH
QQS
EX
EY
WZ
Z
KOW
KHA
KHN
KHB
MW
Recommendation
Recommended
Recommended
Recommended
Recommended
Recommended
Recommended
Recommended
Optional
Optional
Optional
Optional
Optional
Optional
Optional
Conservative
Optional
Optional
Optional
Optional
114
-------
TABLE 4.4.4 INPUT VARIABLES FOR SCENARIOS 2, 3 (Continued)
Input .. Value
Variable Units Range
H atm - m3 10'7 - 10"1
mole
K I/mole/sec 0 - 10 '1
Exposure
CRFD "S/1
CRFD mS/l
KFC mg/1 1 - 3
fx -- 0.01-0.25
X m 0 - 5000
y m 0 - B
CCC mg/1
CR mg/1
Groundwater
Ft -- o.i - i.o
Dispersion
Ex m2/sec 1-10
Ey m2 10'2 - 10'1
Runoff
Cpy -- 0.01 - 1.0
K,, tons/acre 0.1 - 0.5
Lsw -- 0.1-40.0
CVITJ -- 30 - 100
Computer
Code
Variables
HENRY
KK
CPRFD
CRFD
KFC
FL
X
Y
CCC
CR
ZIBAR
ELONG
ELAT
CFW
KW
LSW
CNW
Recommendation
Optional
Optional
Conservative
Conservative
Recommended
Conservative
Conservative
Recommended
Conservative
Optional
Re c ommende d
Optional
Optional
Recommended
Recommended
Recommended
Recommended
115
-------
TABLE 4.4.4 INPUT VARIABLES FOR SCENARIOS 2, 3 (Concluded)
Input
Variable
pw
CFS
KS
Lss
CNS
ps
CFC
KC
Lsc
CNC
Pc
6w
KOWW
Fnru
Value
Units Range
--
0.01
tons/acres 0.1
0.1
30
1
0.01
tons/acres 0 . 1
0.1
30
--
1/1 0.3
1/1 10
0.01
1.0
- 1.0
- 0.5
- 40.0
- 100
.0
- 1.0
- 0.5
-40.0
- 100
1.0
- 0.5
- 107
-0.10
Computer
Code
Variables
PW
CFS
KS
LSS
CNS
PS
CFC
KC
LSC
CNC
PC
THETAW
KOWW
FOCW
Recommendation
Conservative
Recommended
Recommended
Recommended
Recommended
Conservative
Recommended
Recommended
Recommended
Recommended
Conservative
Recommended
Recommended
Recommended
116
-------
TABLE 4.4.5 CALCULATIONS FOR SCENARIOS 4. 5
Step Calculate Explanation (and Equations)
fD(ZWD)
Concentration reduction factor in wastewater treat-
ment (3.1.92, 3.1.79).
fx(ZX)
Concentration dilution factor across stream at point
of mixing (3.1.93, 3.1.94, A4, A5, A7, 3.1.91,
3.1.64).
fsu(ZSU)
Concentration reduction factor for upstream
contaminants (3.1.88).
T(TAU)
Travel time of contaminant downstream, seconds
(A4, 3.2.4).
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).
rx,y(ZXY)
Concentration reduction factor for downstream
transformation (A8, A9, A10, 3.2.7, 3.2.6, 3.2.8,
3.2.5).
fDW(ZDW)
Drinking water treatment reduction factor (A15,
3.3.2).
?F(ZF)
Cy(CW)
Fish bioaccumulation factor (3.3.13, A15, 3.3.6),
Acceptable industrial waste concentration, mg/L
(2.4.3, 2.5.1, 2.9.6, or 2.9.9).
117
-------
TABLE 4.4.6 INPUT VARIABLES FOR SCENARIOS 4, 5
Input
Variable Units
Value
Range
Computer
Code
Variable
Recommendation
Watershed and Landfill
o
Ag nT
FRS
Precipitation
P cm/year
Stream Environment
o o
qs m /sec/m
Q0 m3/sec
GU mg/1
t^ sec
d0 m
Slope m/m
n sec/mVS
b
f
foc
S mg/1
UO mg/1
pH
Ts °c
Wind
Wz m/sec
Z m
107 - 109
0.1 - 0.5
10 - 200
10'9 - 10'8
10'2 - 10
--
103 - 106
0.1 - 3
1C'4 - lO'2
0.02 - 0.08
0.02 - ,0.5
0.2 - 0.7
0.01 - 0.10
io-4 - io-2
--
5 - 8
5 - 30
0 - 10
0 - 10
AS
FRS
PBAR
QS
QQO
CU
TR
DO
SLOPE
NN
BEXP
FEXP
FOC
SS
UO
PH
TSTREAM
WZ
Z
Conservative
Recommended
Re c ommende d
Conservative
Optional
Optional
Optional
Conservative
Recommended
Recommended
Recommended
Re c ommende d
Conservative
Conservative
Optional
Optional
Optional
Optional
Optional
118
-------
TABLE 4.4.6 INPUT VARIABLES FOR SCENARIOS 4, 5 (Continued)
Input
Variable
Dispersion
Ex
Ey
Chemical
Kow
kHA
kHN
kHB
MW
H atm
mo
K
Loading and
Exposure
TR
CRFD
CRFD
KFC
Value
Units Range
m2/sec 1 - 10
m2/sec 10'2 - 10'1
1/1 10 - 107
I/mole/sec 0 - 10 "-1
sec'1 0 - 10'1
1/mole/sec 0 - 10 '1
10 - 103
- m3 10'7 - 10'1
le
I/mole/sec 0 - 10" 1
sec 15 - 25
mg/1
mg/1
mg/1 1 - 3
Computer
Code
Variable
ELONG
ELAT
KOW
KHA
KHN
KHB
MW
HENRY
KK
TR
CPRFD
CRFD
KFC
Recommendation
Optional
Optional
Conservative
Optional
Optional
Optional
Optional
Optional
Optional
Optional
Conservative
Conservative
Recommended
119
-------
TABLE 4.4.6 INPUT VARIABLES FOR SCENARIOS 4, 5 (Concluded)
Input
Variable
fl
X
Y
CCC
QWD
ci
KFC
TD
mass
fwD
QD
Value
Units Range
0.01 - 0.25
m 0 - 5000
m 0 - B
mg/1
o
m /sec
mg/1
mg/1 0 - 4
sec 60 - 86400
g
0-1
3
m /sec
Computer
Code
Variable
FL
X
Y
CCC
QWD
CL
KFC
TD
WMASS
fW
QD
Recommendation
Conservative
Conservative
Recommended
Conservative
Recommended
Recommended
Optional
Recommended
Conservative
Conservative
Conservative
120
-------
TABLE 4.4.7 CALCULATIONS FOR SCENARIO 6
Step
Calculate
Explanation (and Equations)
Lined Lagoon
1 Ps (PS)
2 Qwl (QWL)
Unlined Lagoon
1 Kc (KG)
5
6
10
11
12
13
14
Qwl (QWL)
Tg(TAUG)
Kg(KHG)
fSg(ZSG)
CSU(ZSU)
f(TAU)
K(KK)
rx(zx>
fp(ZF)
CF(ZG)
CL(CL)
Permeation rate (3.1.14).
Contaminant loading rate (3.1.15).
Corrected hydraulic conductivity term (3.1.13).
Contaminant loading rate (3.1.12).
Travel time of contaminant from land disposal
facility to stream, years (A17, A16, 3.1.18)
First-order rate coefficient for hydrolysis in
ground water, years"-*- (A23, A25).
Mass attenuation factor in ground water (3.1.17).
Concentration dilution factor in ground water and
stream (3.1.6, 3.1.19, 3.1.20).
Concentration dilution factor for upstream contami-
nants (3.1.22, 3.1.21, QU/QS).
Travel time of contaminant downstream, seconds
(A4, 3.2.4).
First order rate coefficient for hydrolysis and
volatilization in stream, seconds"1 (A15, A22, A24,
A30, A29, A34, (A32, A33, or A35), A27, A28, A26,
A19).
Concentration reduction factor for downstream
transformations (3.2.3).
Drinking water treatment reduction factor (A15, 3.3.2)
Fish bioaccumulation factor (3.1.13, A15, 3.3.6).
Concentration dilution factor due to transport in
ground water (-fu £, Qi/Qc) (3.1.17, 3.1.6,
3.1.19).
Acceptable leachate concentration, mg/L
(Drinking Water: fsu, 3.2.3, 3.3.2, rg, 67; 3.1.20,
Aquatic Organisms: fgyi fe> 3.1.20
Fish Accumulation: fsu, 3.3.6, fg, 3.1.20).
121
-------
TABLE 4.4.8 INPUT VARIABLES FOR SCENARIO 6
Input Value
Variable Units Range
Watershed and Landfill
Aw m2 104
Ac m2 104
As m2 107
Dist m 10
fRs " O-1
fRc " O-1
fDTT " 0.1
- 106
- 106
- 109
- 103
- 0.5
- 0.5
- 0.5
Computer
Code
Variable
AW
AC
AS
DIST
FRS
FRC
FRW
Re c ommenda t i on
Conservative
Optional
Conservative
Recommended
Recommended
Recommended
Recommended
Precipitation
cm/year
10-200
PBAR
Recommended
Ground water
f
ocg
pHg
T
-------
TABLE 4.4.8 INPUT VARIABLES FOR SCENARIO 6 (Continued)
Input
Variable
Stream Env.
CU
d0
foc
n
Qo
qs
Slope
S
T
U0
PH
Wind
Wz
Z
Chemical
H
kHA
kHB
kHN
Kow
MW
Units
mg/1
m
--
sec/m1/3
m/sec
0 O
m /sec/m
m/m
mg/1
°C
m/sec
--
m/sec
m
o
atm - m
mole
I/mole/sec
I/mole/sec
sec"
1/1
--
Value
Range
-
0.1 -
0.01 -
0.02 -
10-2 .
io-9 -
10 -
io-4 -
5 -
0.1 -
5 -
0 -
0 -
1C"7 -
0 -
0 -
0 -
10 -
10 -
123
Computer
Code
Variable
-
3
0.10
0.08
10
10'8
50
ID'2
30
2
8
10
10
lO'1
io-1
lO'1
IO-5
IO7
IO3
CU
DO
FOC
NN
QQS
QS
SLOPE
SS
TSTREAM
UO
PH
WZ
Z
HENRY
KHA
KHB
KHN
KOW
MW
Recommendation
Optional
Recommended
Recommended
Optional
Optional
Optional
Recommended
Optional
Re c ommende d
Recommended
Optional
Optional
Optional
Optional
Recommended
Recommended
Recommended
Conservative
Optional
-------
TABLE 4.4.8 INPUT VARIABLES FOR SCENARIO 6 (Continued)
Input
Variable
K
Exposure
CRFD
CRFD
KFC
fl
X
ccc
CL
Lined Lagoon
Ap g
100 in
SH
*
ALI
VP
DLI
Dc
Unlined Lago
Dc
Dw
Uw
Uc
Value
Units Range
I/mole/sec 0 - 10 -1
mg/1
mg/1
mg/1 1 - 3
0.01 - 0.25
m 0 - 5000
mg/1
mg/1
- mil
. _ . in . i nnn
2 ' day ' CmHg
cc/cal 0.1 - 0.6
cal/cc 1.0 - 160
m2 1000 - 8000
cmHg .1-5
mils 1 - 5
kg/m3 700 - 14,000
on
kg/m3 700 - 14,000
kg/m3 990 - 1000
kg/m 'sec 0.1 - 0.7
kg/m -sec 0.1 - 4.0
Computer
Code
Variable
KK
CPRFD
CRFD
KFC
FL
X
CCC
CL
AP
t\L
SH
PHI
ALI
VP
DLI
DC
DC
DW
UW
UC
Recommendation
Optional
Conservative
Conservative
Re c ommende d
Conservative
Optional
Conservative
Optional
Recommended
Recommended
Recommended
Recommended
Recommended
Recommended
Recommended
Recommended
Recommended
Recommended
124
-------
TABLE 4.4.8 INPUT VARIABLES FOR SCENARIO 6 (Concluded)
Input
Variable
KGW
ALA
Units
cm/hr
m2
Value
Range
0.01 - 30.0
1000 - 8000
Computer
Code
Variable
KGW
ALA
Recommendation
Recommended
Recommended
TABLE 4.4.9 CALCULATIONS FOR SCENARIOS 7, 8
Step
1
2
3
Calculate
DNEW
TR
Vwl
Explanation (and Equations)
The new lagoon depth after the storm or
after the dam failure (3.1. 37).
Total time of runoff (3.1.40).
Volume of runoff (3.1.38 for no dam failure,
With Erosion
5 SY
Without Erosion
5 fR(ZR)
fx>y(ZXY)
fsu(ZSU)
and 3.1.41 for dam failure.
Runoff flow rate (3.1.42).
Sediment yield (3.1.49, 3.1.48, 3.1.47,
3.1.46a, 3.1.46).
Concentration dilution factor in surface runoff
(3.1.35, 3.1.70, 3.1.34).
Concentration dilution factor across stream at
point of mixing (A3, 3.1.73, 3.1.74, A4, A5, A7,
3.1.69, 3.1.64).
Concentration dilution factor for upstream
contaminants (3.1.88).
125
-------
TABLE 4.4.9 CALCULATIONS FOR SCENARIOS 7, 8 (Concluded)
Step
Calculate
Explanation (and Equations)
11
12
r(TAU)
K(KK)
10 fx>y(ZXY)
fDW(ZDW)
CL(CL)
With Erosion
13
Travel time of contaminant downstream, seconds
(A4, 3.2.4).
First order rate coefficient for hydrolysis and
volatilization in stream, seconds" (A15, A22,
A24, A30, A29, A34, (A32, A33, or A35), A31, A27,
A28. A26, A19).
Concentration reduction factor for downstream
transformation (A8, A9, A10, 3.2.7, 3.2.6,
3.2.8, 3.2.5).
Drinking water treatment reduction factor (A15,
3.3.2).
Acceptable leachate concentration, mg/L (3.1.88,
3.1.34, 3.1.64, 3.3.2, 3.2.5, 2.2.3).
Sediment concentration at stream entry point,
sorbed and dissolved (3.1.57, 3.1.58, 3.1.54,
3.1.60, 3.1.55, 3.1.55, 3.1.56, 3.1.53, 3.1.54,
3.1.51, 3.1.52, 3.1.50).
126
-------
TABLE 4.4.10 INPUT VARIABLES FOR SCENARIOS 7, 8
Input
Variable Units
Watershed and Landfill
Aw m
Ac m
Ag m
fRc
fRs
fRw
f*
fR
Dist m
Precipitation
P cm/year
?25 cm
t SGC
Stream Environment
GU mg/1
d0 m
QQ m /sec
O 0
qs m /sec/nr
S mg/1
n sec/m1/3
T T
is ^
b
Value
Range
104 - 106
104 - 106
107 - 109
0.1 - 0.5
0.1 - 0.5
0.1 - 0.5
0 - 1
10 - 10'3
10 - 200
10 - 15
103 - 106
--
0.1 - 3
102 - 10
10'9 - 10'8
1C'4 - ID'2
0.02 - 0.08
5 - 20
0.02 - 0.5
Computer
Code
Variable
AW
AC
AS
FRC
FRS
FRW
FRSTAR
DIST
PBAR
P25
TSTORM
CU
DO
QQO
QS
SS
NN
TSTREAM
BEXP
Recommendation
Conservative
Optional
Conservative
Recommended
Recommended
Re c ommende d
Recommended
Recommended
Recommended
Recommended
Recommended
Optional
Conservative
Optional
Conservative
Recommended
Recommended
Recommended
Recommended
127
-------
TABLE 4.4.10 INPUT VARIABLES FOR SCENARIOS 7, 8 (Continued)
Input
Variable
TR
f
foe
slope
U0
pH
Dispersion
Ex
Ey
Wind
*Z
Z
Chemical
Kow
kHA
kHN
kHB
MW
H
K
Exposure
CRFD
Value
Units Range
°C 5-20
0.2 - 0.7
0.01-0.10
m/m 10"4 - 10'2
m/sec
5-8
m2/sec 1 - 10
m2/sec 10"2 - 10"1
m/sec 0 - 10
m 0-10
1/1 10 - 107
I/mole/sec 0 - 10" 1
sec"1 0 - 10"5
I/mole/sec 0 - 10 "1
10 - 103
atm - m3 10"7 - 10"1
mole
I/mole/sec 0 - 10" -1-
mg/1
Computer
Code
Variables
TREF
FEXP
FOG
SLOPE
UO
PH
EX
EY
WZ
Z
KOW
KHA
KHN
KHB
MW
HENRY
KK
CPRFD
Recommendation
Recommended
Recommended
Recommended
Recommended
Optional
Optional
Optional
Optional
Optional
Optional
Conservative
Optional
Optional
Optional
Optional
Optional
Optional
Conservative
128
-------
TABLE 4.4.10 INPUT VARIABLES FOR SCENARIOS 7, 8 (Concluded)
Input
Variable Units
CRFD mS/l
KFC mg/1
fl
X m
y m
CCC mg/1
CR mg/1
Groundwater
fl
Dispersion
0
EJJ m /sec
Ey m2
Runoff
CFW
^ tons/acre
LSW
CNW
Lagoon
DB m
FBD m
DOLD m
ALA m
ew 1/1
Koww 1/1
Value
Range
--
1 - 3
0.01 - 0.25
0 - 5000
0 - B
--
--
0.1 - 1.0
1 - 10
10'2 - 10'1
0.01 - 1.0
0.1 - 0.5
0.1 - 40.0
30 - 100
0 - 5
0.5 - 10.0
0.5 - 5.0
1000 - 8000
0.3 - 0.5
10 - 107
Computer
Code
Variables Recommendation
CRFD Conservative
KFC Recommended
FL Conservative
X Conservative
Y Recommended
CCC Conservative
CR Optional
ZIBAR Recommended
ELONG Optional
ELAT Optional
CFW Recommended
KW Recommended
LSW Recommended
CNW Recommended
DB Recommended
FBD Recommended
DOLD Recommended
ALA Recommended
THETAW Recommended
KOWW Recommended
129
-------
TABLE 4.4.11 CALCULATIONS FOR SCENARIO 9
Step
Calculate
Explanation (and Equations)
Concentration reduction factor in wastewater treat-
ment (3.1.92, 3.1.79).
(ZSRY) Concentration dilution factor across stream at point
of mixing (3.1.93, 3.1.94, A4, A5, A7, 3.1.91,
3.1.64).
fsu(ZSU)
Concentration reduction factor for upstream
contaminants (3.1.88).
r(TAU)
Travel time of contaminant downstream, seconds
(A4, 3.2.4).
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).
Concentration reduction factor for downstream
transformation (A8, A9, AlO, 3.2.7, 3.2.6, 3.2.8,
3.2.5).
fDW(ZDW)
Drinking water treatment reduction factor (A15,
3.3.2).
fF(ZF)
CW(CW)
Fish bioaccumulation factor (3.3.13, A15, 3.3.6),
1/kg.
Acceptable industrial waste concentration, mg/L
(2.4.3, 2.5.1, 2.9.6, or 2.9.9).
130
-------
TABLE 4.4.12 INPUT VARIABLES FOR SCENARIO 9
Input
Variable
Watershed
As
FPC
Value
Units Range
and Landfill
m2 107 - 109
0.1 - 0.5
Computer
Code
Variable
AS
FRS
Recommendation
Conservative
Recommended
Precipitation
P cm/year 10 - 200
Stream Environment
FBAR
Recommended
-------
TABLE 4.4.12 INPUT VARIABLES FOR SCENARIO 9 (Continued)
Input
Variable
Value
Units Range
Computer
Code
Variable
Recommendation
Dispersion
Ex
Ey
Chemical
Kow
kHA
kHN
kHB
MW
H
K
Loading
Exposure
TR
t
CRFD
GRFD
KFC
fl
X
Y
CCC
QWD
m2/sec 1 - 10
m2/sec 10'2 - 10'1
1/1 10 - 107
I/mole/sec 0 - 10 "1
sec"1 0 - 10'1
I/mole/sec 0 - 10 "*
10 - 103
atm - m3 10'7 - 10"1
mole
I/mole/sec 0 - 10 "1
and
sec 15 - 25
mg/1
mg/1
mg/1 1 - 3
0.01 - 0.25
m 0 - 5000
m 0 - B
mg/1
o
m /sec
ELONG
ELAT
KOW
KHA
KHN
KHB
MW
HENRY
KK
TR
CPRFD
CRFD
KFC
FL
X
Y
CCC
QWD
Optional
Optional
Conservative
Optional
Optional
Optional
Optional
Optional
Optional
Optional
Conservative
Conservative
Recommended
Conservative
Conservative
Recommended
Conservative
Recommended
132
-------
TABLE 4.4.12 INPUT VARIABLES FOR SCENARIO 9 (Concluded)
Input
Variable
Cl
RFC
TD
w
mass
^wD
QD
Units
mg/1
mg/1
sec
g
--
o
m /sec
Value
Range
--
0 - 4
60 - 86400
.
0 - 1
Computer
Code
Variable
CL
KFC
TD
WMASS
fW
QD
Recommendation
Recommended
Optional
Recommended
Conservative
Conservative
Conservative
133
-------
TABLE 4.5. DEFAULT VALUES
#1
AS
AW
AC
EIST
FRS
FRSTAR
FRSTAR
FRW
FRW
FRW
FRC
P25
PBAR
TSTORM
BEXP
FEXP
QS
SLOPE
EO
NN
QQO
UO
TSTREAM
SS
PH
FOG
CU
TREF
Watershed and Landfill
1.0E9
1.0E6
O.OEO
150. OEO
0.20EO
(SCEN.EQ. 3) l.OEO
(SCEN.EQ. 2) l.OEO
0.4EO
(SCEN.EQ. 2) l.OEO
(SCEN.EQ. 3) 0.60EO
O.OEO
Precipitation
30. OEO
10. OEO
86400. OEO
Stream Environment
0.23EO
0.42EO
0.5E-8
Stream Environment (cont.)
9.0E-5
0.1EO
0 . 04EO
O.OEO
O.OEO
20. OEO
10. OEO
7. OEO
0.05EO
O.OEO
25. OEO
*Note E5 = 10-
134
-------
TABLE 4.5. DEFAULT VALUES (Cont.)
Z
WZ
Wind
10.OEO
1.4EO
Chemical
KK
KHA
KHB
KHN
HENRY
MW
KOW
X
Y
CRFD
CPRFD
CCC
CL
FL
KFC
TR
TR
TE
TE
WMASS
ZW
QWE
QE
VG
THETAG
osure
(SCEN.EQ.
(SCEN.EQ.
O.OEO
O.OEO
O.OEO
O.OEO
l.OE-7
1.0E3
1.0E3
1.0E3
O.OEO
l.OEO
l.OEO
l.OEO
O.OEO
0.3EO
3. OEO
2) 8.64E4
3) 7.20E3
Loading/Exposure
(SCEN.EQ. 4) 8.64E4
(SCEN.EQ. 5) 7200.OEO
O.OEO
l.OEO
4.0E-3
4.0E-3
Ground water
10.OEO
0.5EO
135
-------
TABLE 4.5. DEFAULT VALUES (Cont.)
TG
FOGG
TREF
ZIBAR
ZI
PHG
ELAT
ELONG
EC
EW
KGW
UW
UC
ALA
AP
SH
PHI
TR
FEE
EOLE
EB
QWL
QE
LMASS
CWL
ZL
20.0EO
0.01EO
25.0EO
0.5EO
l.OEO
5.0EO
Dispersion
O.OEO
O.OEO
Lagoon
1500. OEO
998. 2EO
0.2EO
1.002EO
0.5EO
1.0E2
1.0E4
0.23EO
44 . OEO
O.OEO
4. OEO
4. OEO
O.OEO
4.0E-3
O.OEO
O.OEO
O.OEO
O.OEO
136
-------
REFERENCES
1. Ambrose, R.A., Mulkey, LNA. , and Huyakorn, P.S. 1985. A methodology
for assessing surface water contamination due to land disposal. EPA
draft report.
2. Ambrose, R.A., Vandergrift, S.B. 1986. SARAH, A surface water
assessment model for back calculating reductions in abiotic
hazardous wastes. U.S. Environmental Protection Agency,
Athens, GA. EPA-600-3-86-058.
3. 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.
4. Carsel, R.F. and R.S. Parrish. 1988. Developing joint probability
distributions of soil-water retention characteristics. Water Resources
Research (in press).
5. 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.
6. 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.
7. Haith DA. 1980. A mathematical model for estimating pesticide losses in
runoff. Journal of Environmental Quality. 9(3):428-433.
8. Israelsen, O.W. and Hansen, V.E. 1962. Irrigation principles and
practices. John Wiley and Sons, Inc., New York. 447 pp.
9. Karickhoff, S.W. 1981. Semi-empirical estimation of sorption of
hydrophobic pollutants on natural sediments and soils. Chemosphere.
10(8):833-846.
10. Karickhoff, S.W., Brown, D.S., and Scott, T.A. 1979. Sorption of
hydrophobic pollutants on natural sediments. Water Res. 13:241-248.
11. Leopold, L.B. and Maddock, T. 1953. The hydraulic geometry of stream
channels and some physiographic implications. U.S. Geological Survey,
Washington, DC. Professional Paper No. 252.
12. Liss, P.S. 1973. Processes of gas exchange across an air-water inter-
face. Deep-Sea Res. 20:221-23B.
137
-------
13. Lyman, W.J., Reehl W.F., Rosenblatt DH. 1982. Handbook of chemical
property estimation methods. New York. McGraw-Hill.
14. Marin, Carlos. 1988. Personal communication.
15. Mills, W.B., Dean, J.D., Porcella, D.B., et al. 1982. Water quality
assessment: a screening procedure for toxic and conventional pollutants:
parts 1, 2, and 3. U.S. Environmental Protection Agency, Athens, GA.
EPA/600/6-85/002 a, b, c.
16. 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.
17. Salame, M. (no date) Permeability-structure relationships of high
polymers. Obtained by private communication. Monsanto Co., Bloomfield,
CT.
18. Salame, M. 1961. The prediction of liquid permeation in polyethylene and
related polymers. SPE Trans. 1(4):153.
19. Salame, M. 1973. Transport properties of nitrile polymers. J. Polymer
Sci. 41:1-15.
20. Salame, M. 1985. Private communication. Monsanto Co., Bloomfield, CT.
21. Schwab, G.O., Frevert, R.K., Edminster, T.W., Barnes, K.K. 1966.
Soil and water conservation engineering. 2nd edn. John Wiley and Sons,
New York, NY.
22. Steingiser, S., Nemphos, S.P., Salame, M. 1978. Barrier polymers.
In: Kirk-Othmer encyclopedia of chemical technology, 3rd ed. John Wiley
and Sons, New York, NY.
23. Versar, Inco 1983. Theoretical evaluation of sites located in the zone
of saturation. Draft final report. Versar, Inc., Chicago IL. U.S.
Environmental Protection Agency. Contract No. 68-01-6438.
24. Versar, Inc. 1987. Superfund Exposure Assessment Manual. U.S. EPA
draft report. OSWER Directive 9285.5-1. pp 2-33 - 2-42; 2-46- 2-55.
25. Whitman, R.G. 1923. A preliminary experimental confirmation of the
two-film theory of gas absorption. Chem. Metallurg. Eng. 29:146-148.
26. Williams, J.R. 1975. Sediment-yield prediction with the universal
equation using runoff energy factor. In: present and prospective
technology for predicting sediment yields and sources. U.S. Department
of Agriculture, Washington, DC. ARS-S-40.
27. Wischmeier W.H. 1972. Estimating the cover and management factor on
undisturbed areas. U.S. Department of Agriculture, Oxford, MS:
Proceedings of the USDA Sediment Yield Workshop.
138
-------
APPENDIX A
ADVECTION, DISPERSION AND CHEMICAL TRANSFORMATION IN STREAM
This appendix describes procedures and formulas for estimating the
physical parameters of advection, dispersion and chemical transformation in
surface water.
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 - aQb (A2)
d - cQf (A3)
U = kQm (A4)
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:
Q^ - As . qs (A5)
where q average flow per unit area m /sec
s
.....
m
o
As = area of the watershed (m )
139
-------
(a) NATURAL
CHANNELS
10 08 06 04 02 0
Theoretical
Leopold and Langbeln (1962)
(b) PRO-GLACIAL 10 o
(c) HUMID 10 o
TEMPERATE
Britain
U.S.A.
White River
A A *A
Appalachian Plateau
' " -₯ X
/\ /\
0 / \/ \ / River Glonma \ 10
10
m
(d) SEMI-ARID
10 o (e) TROPICAL
Perennial
Ephemeral
10
Malaysia
* Puerto Rico
(f) FLUME
STUDIES
10 o
(g) TIDAL
ESTUARIES
10
Figure A. Tri-axial Graphs of At-a-Station Hydraulic Geometry
Exponesnts
140
-------
Velocity at baseflow, UQ can be calculated by Manning's equation:
U0 = d02/3 . sl/2/n (A6)
where: dQ - depth baseflow (m)
s = channel slope (m/m)
n - Manning's roughness coefficient (sec/m ' )
The width at baseflow BQ, can be calculated from UQ, dQ, and the baseflow
using equation Al rearranged:
B - Q/
o oo o
The upstream flow during a storm includes both baseflow and runoff, as
given by equation A6 :
QU - QQ + Ay P25 fR/(100 . ts) (A8)
Given the baseflow values BQ, dQ , UQ, and QQ and the stormflow value Q, the
widths, depths, and velocities for stormflow conditions can be calculated as:
B = B0 (Qu/Qo>b
d = d0 (Qu/Q0)f
u = u0 (%/Qo)1"^
When the theoretical values for b and f hold, U increases with Q to the 1/3
power. A ten- fold increase in flow, results in a doubling of velocity.
Streamflows and the associated hydraulic variables, can be syn-
thesized from: 1) distributions of watershed areas, AS 2) areal flows, q
3) channel slopes, slope 4) channel roughness factors n, precipitation
totals ?25i 5) runoff coefficients, f^ 6) 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):
Usv = J g.d.s (A12)
141
-------
where: Ugv = shear velocity (m/sec)
s = channel slope (m/m)
d = mean depth (m)
e\
g = acceleration of gravity (m/sec )
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 ' Usv, + 50% (A13)
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 . Usv (A14)
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:
SS + Cw - Cs (A15)
where: SS = sediment concentration (kg/1)
GW = dissolved aqueous concentration (mg/1)
Cs = sorbed concentration (mg/1)
The local equilibrium concentrations Cw and Cs are governed by the equili-
brium distribution coefficient 1C (I/kg):
C^ (A16)
o
S' Cw
142
-------
Karickhof f et al . , 1979 , have shown that for sorption of hydrophobia organic
compounds :
Kp - Koc . foc (A17)
where: KQC - organic carbon partition coefficient (I/kg)
f = organic carbon fraction of sediment (unitless)
Karickhof f et al. (1979) further correlated KQC with KQW for organic sedi-
ments. Subsequent work by Karickhof f (1981) suggested the proportionality
factor for mixed sediments of 0.4:
KOC - °-41 Kow
Combining equations A16 - A18 and rearranging terms gives an expression
for the fraction of the compound that is dissolved:
1 (A19)
fD - ...............................
1 + 0.41 . Kow . foc . SS . ID'6
The sorbed chemical fraction fs is equal to 1- fp.
The fraction of the compound that is dissolved in ground water can
be calculated from an equivalent expression:
............. § ................
0g + 0.41 . Kow . focg .
3 3
where: 9_ - volumetric water content of porous medium, 1/1
o
foc - organic carbon fraction of porous medium (unitless)
- bulk density of porous medium (kR/l)
and pbg - 2.65 . (l-9g) (A21)
The sorbed chemical fraction fg_ is equal to 1- fng.
Slower chemical transformation reactions can be treated generally by
using mixed second order kinetics (Burns et al., 1982):
Cw + [E]j_ -» P (A22)
where: [E]^ - environmental property for process "i"
P - transformation product (mg/1)
143
-------
The reaction rate R£ (mg/l-sec) for process "i" is:
Ri - ki Yi fD c
where: k^ = second order rate constant for process "i"
Y^ = yield coefficient for process "i"
C = total concentration of compound (mg/1)
Given a local value for [E]^, a pseudo-first order rate constant K^ (see"*)
can be calculated:
^ = kt . (E]± . Yi . fD (A24)
For a compound undergoing several competing reactions, the overall pseudo-
first order rate constant K(sec ) is:
K = S K£ (A25)
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 likely to significantly reduce instream concentrations. For transient
loads during storms, darkness should further reduce photolysis and, indirectly,
oxidation. Bacterial communities are unlikely to acclimate in hours to the
transient loads. Of these transformation reactions, then, only hydrolysis
will be considered for those few compounds with large rate constants. The
nominal hydrolysis rate constant is calculated from the acid-catalyzed,
neutral, and base-catalyzed pathways (Burns et al., 1982):
KHo =
-------
For ground water, the nominal hydrolysis rate constant (in years ) is
calculated from an equivalent expression:
Kgo ' (k^^l^a.fsg+fDg) +kHN + kHB[OH-]g.fDg).(24).(365.25
where: [H+]_ - hydrogen ion concentration 10~P 8 (mole/1)
O
pHg - ground water pH
[OH']- - hydronium ion concentration - 10"POHS (mole/1)
o
pOHg = ground water pOH - 14"PHS
The nominal hydrolysis rate constants K«o and KEO apply to a. reference
temperature, TR (usually 25 'C). These can be corrected to ambient surface
or ground water temperatures (T or Te) with the following Arrhenius expres-
sions.
1 1
KH - KHo exp[104 . ( )] (A28)
TR+273 T+273
. 1 1
K - K . exp[104 . ( )] (A29)
TR+273 Tg+273
A final transformation pathway to consider is volatilization. The vo-
latilization rate constant Vi^ (sec ) can be calculated from the Whitman, or
two-resistance model (Whitman, 1923; Burns et al., 1982):
1 1
KV - - fD (A30)
d RL + RG
where: d mean stream depth (m)
RL = liquid phase resistance (sec/m)
RG = 8as Pnase resistance (sec/m)
The second term in equation A30 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
RL - (A31)
KQ2.d. J 32/MW
145
-------
where: KQ2 = 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) :
(A32)
_H_ . WAT . J 18/MW
RT'
where: WAT = water vapor exchange constant (m/sec)
18 = molecular weight of water
o
H = Henry's law constant (atm-m /mole)
R = ideal gas constant «= 8.206 x 10"5 m3-atm/mol 'K
T' = 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 1CT5 + 3.156 x 10'3 . W (A33)
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) (A34)
where: Wz = wind speed at height z (m/sec)
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).
KQ2 = K20 . 1.0241-20 (A35)
where: K2Q - reaeration rate at 20 'C
146
-------
For shallow streams where depth is less than 0.61 m, the Covar method uses
the Owens formula:
K20 - 6.194.10'5 . U0-67 . d'1'85 (A36)
For deeper, slower streams (d>0.61, IK0.518), the formula selected depends
upon the transition depth:
K20 - 4.555 . 10'5 . U0-5 . d'1'5 (A37)
For deeper, faster streams (d>0.61, U>0.518), the formula selected depends
upon the transition depth:
dr - 4.1404 . u2-9135 (A38)
When d>dT>0.61, the O'Connor-Dobbins formula is used. When dT>d>0.61, the
Churchill formula is used:
K2Q - 5.825 . 10'5 . u0-969 . d'1'673 (A39)
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 A19 using data for KQW, fQW, and s.
Hydrolysis is calculated by equations A26 and A28 using data for pH, kj^,
^HN1 aru^ ^HB- Volatilization is calculated by equations A22 through A34
using data for U, d, W, T, MW, and H. When insufficient data are available,
ignoring any of these processes is acceptable in order to complete conservative
analyses.
147
-------
APPENDIX B
ANALYTICAL SOLUTION FOR TWO-DIMENSIONAL FLOW 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.
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:
C= Cc e
* t
/
Figure B.I.
Schematic Description of Two-Dimensional Transport
in Uniform Flow
148
-------
3c 32c 32c 3c
U -- - £x --- - Ey --- + Kc + 0 (Bl)
ax ax2 ay2 at
where: EX longitudinal dispersion coefficients
Ey - tranverse dispersion coefficients
IT - the main flow velocity in the x-direction
C = the solute concentration
K the first-order decay constant
1 the elapsed time
The initial and boundary conditions associated with equation Bl may be
expressed as:
c (x.y.O) = 0 (B2)
c («,y,t) - 0 (B3)
3c
-- (x.O.t) - 0 (B4)
3y
ac
-- (x.B.t) = 0 (B5)
ay
c (O.y.t) - Cs exp (-y2/2a2), t < tR (B6)
c (O.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 this case the stream is
of infinite width and the contaminant is continuously released from the source.
Let Cf denote the fundamental solutions. The expression for Cf has been
derived in the report dealing with ground water screening procedures. It may
be written as:
ax exp (UX/2EX)
C| (x.y.t) = [ ------ . I]CS (B7)
149
-------
IMAGE 3
-4B-Y
IMAGE 1
x
-2B-Y
x
x
SOURCE
B
1
IMAGE 2
IMAGE 4
X
Figure B2 Treatment of Lateral Boundary Conditions Using
Image Sources
150
-------
where
x2 y2 U2T
exp ( KT) dr
t 4Evr 4EV T + 2a2 4E..
I - J X y- X (B8)
0 T3/2 (2a2+4EyT)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 are required to precisely reproduce the
lateral boundary effect. The resulting solution becomes:
co
C* (c.y.t) - Cg [Cj (x.y.t) + S C^ (x.y.t)]
-------
APPENDIX C: LIST OF SYMBOLS
Variable
Ac
(AC)
(ALA)
(ALI)
a
(ALPHA)
As
(AS)
(AW)
B
(BB)
b
(BEXP)
B0
(BBO)
CCC
(CCC)
Definition Units Type
The surface area of the m Input or
contaminated catchment, calculated
diluting the leachate
o
The lagoon surface area m Input
Surface area of lagoon m Input
liner
Found in
Subroutines
GRND2A, GRND2B
STM1, USEDF1,
USEDF2, USEDF3
UNLINED
LINED
Acid-catalysis hydrolysis
rate enchancement factor
for the sorbed compound
Unitless Constant = 0
Constant solely dependent G-Mil Input
on the type of liner (100 in
day cmHg)
Surface area of the upper Unitless Input
watershed (hydraulically
including the contaminated
catchment and above)
Surface water that provides m Input
water which leaches through
the disposal facility
Stream width below contami- M Calculated
nated source
Width exponent for stream
hydraulic geometry
Stream width before storm
Specified Criterion
Continous Concentration
Water Standard for aquatic
organisms
Unitless Input
GRND1, GRND3,
STM4, DISCH4
LINED
GRND2A, GRND2B,
STM1, STM4,
USEDF1, USEDF2,
USEDF3
GRND2A, GRND2B,
STM1, CERF,
USEDF1, USEDF2,
USEDF3
STM1, STM2,
STM3, DISCH1,
DISCH2, DISCH3,
GAUSS
STM1, DISCH1,
LARF1, LADD1
m
Calculated STM1, DISCH1
mg/1
Input
AQUTIC, CERF,
USEDF1, USEDF2,
USEDF3
152
-------
Variable
(CL)
Definition
Units
(CFW)
(CFS)
(CFC)
Cnc
(CNC)
Cns
(CNS)
(CNW)
0 RFD
(C'RFD)
(CRFD)
Cu
(CU)
(CWL)
DO
(DO)
UB
(DB)
(DC)
Maximum allowable leachate mg/1
concentrat ion
Cover factor for waste
site
Cover factor for water-
shed
Cover factor for con-
taminated catchment
The SCS runoff curve
number for the con-
taminated catchement
(Table 3.1.7)
The SCS runoff curve
number for the water-
shed (Table 3.1.7)
The SCS runoff curve
number for the waste
site (Table 3.1.7)
Reference dose pertaining
to fish consumption
Reference dose pertaining
to drinking
Chemical concentration
upstream
Concentration in lagoon
discharge stream
Depth of baseflow
Distance from the lagoon
free board depth to the
top of the broken dam
Density of contaminant
Unitless
Unitless
mg/1
mg/1
mg/1
mg/1
m
m
kg/nr
Type
Calculated
Unitless Input
Input
Input
Unitless Input
Unitless Input
Unitless Input
Found in
Subroutines
DISCH1, DWATER,
FISH, AQUTIC,
GAUSS, USEDF1,
USEDF2, USEDF3
RUNOFF
RUNOFF
RUNOFF
RUNOFF
RUNOFF
RUNOFF
Calculated FISH, USEDF1,
USEDF2, USEDF3
Input
s
Input
DWATER, USEDF1,
USEDF2, USEDF3
USEDF1, USEDF2,
USEDF3
Input or LADDl
Calculated
Input
Input
Input
GRND2B, STM1,
DISCH1, USEDF1,
USEDF2, USEDF3
LARF1
UNLINED
153
-------
Variable
Definition
Units
Type
Found in
Subroutines
D Mean stream depth below
(DEPTH) contaminated source
after storm
m
Calculated GRND2B, GRND3,
STM1, STM3, STM4,
DISCH1, DISCH2,
DISCH3
Df
(DF)
Dilution factor
Unitless
Constant
1
STM2, DISCH2
D Distance from land
(DIST) disposal site to
stream
m
Input
USEDF1, USEDF2,
USEDF3
ULI
(DLI)
Lagoon liner thickness
mils
Input
LINED
DNEW Tne new depth of a m
(DNEW) lagoon after the addition
of percipitation
Calculated LARF1
(DOLD)
Original depth of lagoon m
before storm or dam break
Input
LARF1
DT
(DT)
Transition stream depth
m
Calculated GRND3
Dw
(DW)
Density of water
kg/nr
Input
UNLINED
Ex
(ELONG)
Longitudinal dispersion
coefficient
o
m /sec
Input or
Calculated
STM3, DISCH3,
GAUSS, CERF
Lateral dispersion
coefficient
o
m /sec
Input or
Calculated
STM3, DISCH3
Ex
(EX)
Longitudinal dispersion
coefficient
o
m /sec
Calculated
STM3, DISCH3,
GAUSS, CERF
Ex
(EY)
Lateral dispersion
coefficient
o
m /sec
Calculated STM3, DISCH3
rBD
(FED)
Lagoon free board depth
m
Input
LARF1
(FD)
Fraction of dissolved
compound in stream
Unitless Calculated
GRND3, STM4,
DISCH4, EFFECT
* DG
(FDG)
Fraction of dissolved
compound in ground water
Unitless Calculated GRND1
154
-------
Variable
(FL)
roc
(FOC)
rocw
(FOCW)
Definition
Fraction of biomass that
is lipid in fish
Organic carbon fraction
of suspended sediment
Organic carbon fraction
of suspended sediment in
the waste
Units
Unitless
Type
Found in
Subroutines
Calculated USEDF1, USEDF2,
USEDF3
Unitless Input
Unitless Input
GRND3, STM4,
DISCH4, USEDF1,
USEDF2, USEDF3
RUNOFF
*OCG
(FOGG)
*RC
(FRC)
(FRS)
F*
R
(FRSTAR)
(FS)
rSG
(FSG)
g
(GRAV)
H
(HENRY)
Fraction of organic carbon Unitless
of porous medium through
which ground water flows
Input
Unitless Input
Average fraction of
precipitation that runs
off the contaminated catch-
ment area (defaults to fj^s
if not input)
Average fraction of the Unitless
precipitation that runs off
upper watershed
Stream flow recession
parameter (0-1) for
scenario #3 runoff events
that follow a storm
Fraction of precipi-
tation that runs off of
wastesite
Sorbed chemical fraction
Sorbed chemical fraction
in ground water
Acceleration due to
gravity
Henry's law constant,
chemical specific
Input
Unitless Input
Unitless Input
GRND1, USEDF1,
USEDF2, USEDF3
GRND2A, STM1,
DISCH1, USEDF1,
USEDF2, USEDF3
GRND2A, STM1,
DISCH1, USEDF1,
USEDF2, USEDF3
STM1, USEDF1,
USEDF2, USEDF3
STM1, USEDF1,
USEDF2, USEDF3
Unitless Calculated GRND3, STM4,
DISCH4
Unitless Calculated GRNDl
m/sec^ Constant = STM3, DISCH3
9.81
Atm-m3/ Input GRND3, STM4,
Mole DISCH4, USEDF1,
USEDF2, USEDF3
HC
(HC)
Corrected hydraulic
conductivity for con-
taminants with viscosity
different than water
m/sec
Calculated UNLINE
155
-------
Variable
HG
(HG)
K20
(K20)
Kc
(KG)
Definition Units
Hydrogen ion concentration mole/1
Reaeration rate at
20 Degrees C
Soil erodibility factor
for contaminated catch-
ment
sec
-1
Type
Calculated
Found in
Subroutines
GRND1
Calculated GRND3, STM4,
DISCH4
ton/acre Input
RUNOFF
Kp Entire fish partition
(KF) coefficient, or bio-
concentration factor
lAg
Calculated EFFECT
KFC
(KFC)
KG
(KG)
Food chain bio- Constant
accumulation factor 3 mg/1
Hydrolysis rate constant I/years
at ground water tempera-
ture TG
= Input
USEDF1, USEDF2,
USEDF3
Calculated GRND1
KGO
(KGO)
(KGW)
Nominal hydrolysis rate
constant at a reference
temperature (Usually 25 C)
I/year
Hydraulic conductivity of
ground water in natural soils cm/hr
Calculated GRND1
Input
UNLINE
(KH)
KHO
(KHO)
KHA
(KHA)
Hydrolysis rate constant at yr
ambient surface temperature
Nominal hydrolysis rate sec
constant
-1
-1
Calculated
Calculated
Second-order acid-catalysis l/(mole- Input
hydrolysis rate constant hr)
GRND3
GRND3
GRND1, GRND3,
STM4, DISCH4,
USEDF1, USEDF2,
USEDF3
^HB Second-order base-catalysis I/mole-
(KHB) hydrolysis rate constant hr
Input
^HN Neutral hydrolysis rate hr
(KHN) constant
-1
Input
GRND1, GRND3,
STM4, DISCH4,
USEDF1, USEDF2,
USEDF3
GRND1, GRND3,
STM4, DISCH4,
USEDF1, USEDF2,
156
-------
USEDF3
Variable
K
(KK)
K02
(K02)
Ks
(KS)
(KOW)
(KOWW)
Definition
Overall pseudo-first
order rate constant
Reaeration rate constant
Soil erodiblity factor
for watershed
Octanol water partition
coefficient for stream
Octanol water partition
coefficient for waste-
site
Units
-1
sec
sec
-1
loct/
Iwater
loct/
Iwater
Type
Found in
Subroutines
Calculated GRND3, STM4,
DISCH4
Calculated GRND3, STM4,
DISCH4
ton/acre Input
Input
Input
RUNOFF
GRND1, GRND3,
STM4, DISCH4,
EFFECT, USEDF1,
USEDF2, USEDF3
RUNOFF
^ Soil erodibility factor
for wastesite
Ky Volatilization rate
(KV) constant
LMASS Total mass loading
(LMASS) from a lagoon directly
discharging into a stream
ton/acre
.-1
sec
Input
RUNOFF
Calculated GRND3, STM4,
DISCH4
Input
LADD1
Lsc
(LSC)
Lss
(LSS)
Slope length and slope
steepness factor for
contaminated catchment
Slope length and slope
steepness factor for
watershed
Unitless
Unitless
RUNOFF
RUNOFF
Lgw Slope length and slope
(LSW) steepeness factor for
watershed
Unitless
RUNOFF
(MAX) Maximum number of iterations
allowed before the series is
assumed to have failed to
converge
Unitless Constant
GAUSS
157
-------
Variable Definition Units
MW Molecular weight of the Unitless
(MW) compound
n Manning's roughness sec/
(NN) coefficient m1/-*
OH Hydronium ion mole/1
(OH) concentration
Type
Found in
Subroutines
Calculated GRND3, STM4,
DISCH4, USEDF1,
USEDF2, USEDF3
Input
GRND2B, STM1,
DISCH1, USEDF1,
USEDF2, USEDF3
Calculated GRND3
OHG Hydronium ion
(OHG) concentration in
ground water
?25 Precipitation for
(P25) the 25-year re-
occurance, 24 hour
deviation storm
mole/1
cm
Calculated GRND1
Input
STM1, USEDF1,
USEDF2, USEDF3
P Average annual
(PBAR) precipitation rate
cm/yr
Input
GRND2A, STM1,
DISCH1, USEDF1,
USEDF2, USEDF3
Pc
(PC)
Erosion control
practice factor for
contaminated catch-
ment
Unitless Input
RUNOFF
pH
(PH)
(PHG)
Stream hydrogen ion
concentration
Ground water pH
g-Atoms/ Input
1
USEDF1, USEDF2,
USEDF3
g-Atoms/ Calculated GRND1, USEDF1,
1 USEDF2, USEDF3
The polymer "permachor1
(PHI) calculated for each
polymer-permeant pair
(lagoon)
pOH Hydroxyl ion concen-
(POH) tration
pOHg Ground water hydroxyl
(POHG) ion concentration
Cal/CC
Input
LINED
g*Atoms/ Calculated GRND3, STM4,
1 DISCH4
g*Atoms/ Calculated GRND1
1
158
-------
Variable
Ps
(PS)
Definition
Erosion control
factor for water-
shed
Units
Unitless
Type
Input
Found in
Subroutines
RUNOFF
Pw
(PW)
Erosion control
factor for wastesite
Unitless Input
RUNOFF
QD
(QD)
Qg
Qwl
(QWL)
(QQO)
Qs
(QQS)
OR
(QR)
(QS)
Qu
(QU)
Flow rate of waste-
water treamtent
effluent at stream
interception
Contaminated ground
water discharge flow
rate at stream inter-
ception site
Average volumetric
rate of percolation
through the land
disposal site
Flow rate leaving the
contaminated lagoon
m /sec
o
m /sec
o
m /sec
nr/sec
o
Stream baseflow before m /Sec
storm
o
The stream flow m /sec
downstream of source
Contaminated runoff nr/Sec
flow rate at stream
interception site
o
The average stream flow m /sec/
at the downstream edge m
of the contaminated
plume
The average stream flow m^/sec
at the upstream edge of
the contaminated plume
Input DISCH1, DISCH2,
USEDF1, USEDF2,
USEDF3
Calculated GRND2A
Calculated GRND2A
Calculated
or Input
Input
Input or
Calculated
LINED, UNLINE
LAGW2, LARF1,
LADD1, USEDF,
USEDF2, USEDF3
STM1, DISCH1,
USEDF1, USEDF2,
USEDF3
GRND2A, GRND2B,
STM1, STM2,
DISCH1, DISCH2
Calculated STM1, STM2
Calculated GRND2A, STM1,
or Input DISCH1, USEDF1,
USEDF2, USEDF3
Calculated GRND2B, STM1,
DISCH1, USEDF1,
USEDF2, USEDF3
159
-------
Variable
QwD
(QWD)
R
(KG)
R
(RGAS)
(RL)
(SH)
(SIGMA)
S
(SLOPE)
S
(SS)
r
(TAU)
(TD)
(TG)
Definition
Flow rate for indus-
trial waste stream
Gas phase resistance
to the compound
Ideal gas constant
Bulk density of
porous medium
Liquid phase re-
sistance
Constant dependent
upon the type of poly-
mer liner
Standard deviation of
Gaussian source
Channel slope
Stream sediment
concentration
Travel time of
pollutants in stream
The time taken by the
contaminant to travel
from the land disposal
site to the stream
entry point
Total time of dis-
charge into stream
(Scenario 4 and 5)
Ground water tempera-
ture
m
nits
3
m -Atm/
Mol H
kg/1
m
m/m
mg/1
sec
Yr
sec
Type
Calculated
sec/m Calculated
Constant =
8.206 *
ID'5
Calculated
sec/m Calculated
Cal/CC Input
Calculated
Input
Input
Input
Calculated
Degrees
C
Input
Input
Found in
Subroutines
DISCH1, DISCH2,
USEDF1, USEDF2,
USEDF3
GRND3, STM4,
DISH4
GAUSS, EXERF
GRND1
GRND3, STM4,
DISCH4
LINED
STM2, DISCH2,
GAUSS
GRND2B, STM1,
STM3, DISCH1,
DISCH3, USEDF1,
USEDF2, USEDF3
USEDF1, USEDF2,
USEDF3
GRND3
GRND1
DISCH1, GAUSS,
USEDF1, USEDF2,
USEDF3
GRND1, USEDF1,
USEDF2, USEDF3
160
-------
Variable
(T§ETAG)
ew
(THETAW)
(TK)
Tl
(TL)
T
(TR)
T
(TREF)
Definition
Volumetric water
content of porus medium
Volumetric water content
of waste site (top 1 cm)
Water temperature
Total time of waste
loading (TD or TR)
Total time of runoff
loading to the stream
(Scenario 2 and 3)
Reference temperature
(Usually 25 C)
Units
I3/!3
I3/!3
Degrees
sec
sec
Degrees
C
Type
Input
Input
Calculated
Input as
TD or TR
Input
Input
Found in
Subroutines
GRND1, USEDF1,
USEDF2, USEDF3
RUNOFF
STM4, DISCH4
GAUSS
STM1, GAUSS,
USEDF1, USEDF2,
USEDF3
GRND2, GRND3,
STM4, DISCH4,
(TSD)
(TSTREAM)
U
(U)
UO
(UO)
(UC)
usv
(USV)
Uw
(UW)
'G)
Time since discharge
Water temperature
Mean downstream
velocity
Stream velocity at
base flow (Calculated
by Manning's equation)
Dynamic viscosity
of contaminant
Shear velocity
Dynamic viscosity
of water
Ground water seepage
velocity
sec
Input
Degrees Input
C
m/sec Calculated
m/sec Calculated
kg/m'sec Input
kg/nrsec Input
m/yr Input
USEDF1, USEDF2,
USEDF3
GAUSS
GRND3, STM4,
DISCH4, USEDF1,
USEDF2, USEDF3
GRND2B, GRND3,
STM1, DISCH1
GRND2B, STM1,
DISCH1
UNLINE
M/sec Calculated STM3, DISCH3
UNLINE
USEDF1, USEDF2,
USEDF3
161
-------
Variable
(VP)
Vwl
(VWL)
WAT
(WAT)
WM
(WMASS)
Wz
(WZ)
z
(Z)
(Zl)
(Z2)
(Z3)
(Z4)
(Z5)
(ZD)
Definition Units
Vapor pressure of cmHg
contaminant
o
Volume of runoff m
from the waste lagoon
Water vapor exchange m/sec
constant
Total mass loading g
from an industrial
site
Wind speed at height Z m/sec
(ZDW)
Wind measurement
height
See ZD
See ZT
See ZXY
See ZSU
See ZDW or ZF or
ZEXP
Reduction factor
for direct discharge
(dilution plus reaction)
The dilution factor
corresponding to the
fraction of the com-
pound that is dis-
solved
m
See
ZD
See
ZT
See
ZXY
See
ZSU
See
ZDW or
ZF or
ZEXP
Type
Input
Calculated
Calculated
Input
Input
Input
See ZD
See ZT
See ZXY
See ZSU
See ZDW or
ZF or ZEXP
Unitless Calculated
Unitless Calculated
Found in
Subroutines
LINED
LINED
GRND3, STM4,
DISCH4
GRND3, DISCH1,
USEDF1, USEDF2,
USEDF3
GRND3, STM4,
DISCH4, USEDF1,
USEDF2, USEDF3
GRND3, USEDF1,
USEDF2, USEDF3
DWATER, FISH,
AQUTIC
DWATER, FISH,
AQUTIC
DWATER, FISH,
AQUTIC
DWATER, FISH,
AQUTIC
DWATER, FISH
AQUTIC
DISCHARGE,
STORM, DISCHARGE,
EFFECT
162
-------
Variable Definition
CEXP Aquatic exposure
(ZEXP) factor
fp Bioaccumulation
(ZF) factor in fish due
to the biochemical
exchange process with
the fish
Units Type
Unitless Calculated
Calculated
Found in
Subroutines
STORM, DISCHARGE,
EFFECT
STORM, DISCHARGE,
EFFECT
(ZHG)
(ZI)
(ZIBAR)
Reduction factor due to Unitless
transport in ground water
Calculated
Attenuation factor for
the fraction of con-
taminant of mass not
transformed by hydrolysis
during ground water trans-
port to the stream
Unitless Calculated
Attenuation factor for
interception of stream
and ground water
Average fraction of
ground water flow con-
tributing to stream
flow in the upper
watershed
Unitless Calculated
Unitless Input
GRND2A
GRND1, GRND2A
GRND2A, USEDF1,
USEDF2, USEDF3
GRNDA2, STM1,
USEDF1, USEDF2,
USEDF3
(ZL)
?R
(ZR)
f se
(ZSG)
fsu
(ZSU)
Reduction factor for
lagoon direct discharge
(dilution plus reaction)
Unitless Input
Runoff dilution factor Unitless Calculated
Reduction factor due
to mixing at area
leachate entry into
stream
Reduction factor due
to transport in stream
Unitless Calculated
Unitless Calculated
LADD1
STORM, STM1
GRND2A
GRND2B, STORM,
STM1, DISCHARGE,
DISCH1
163
-------
Variable
(ZW)
Definition
Units
Type
The treatment plant
mass attenuation factor
accounting for the
effects of sorption and
settling, volitization and
bacterial degradation
Unitless Input
Found in
Subroutines
DISCH1, USEDF1,
USEDF2, USEDF3
(ZX)
>xy
(ZXY)
(18)
(32)
The steady-state
laterally averaged
solution for con-
centrations at the
measurement point
Concentration re-
duction factor for
downstream trans-
formation
Molecular weight of
water
Molecular weight of
oxygen
Unitless Calculated STM3, DISCH3
Unitless Calculated
STORM, DISCHARGE,
DISCH1
164
-------
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 - 01
- 0.59817E + 01
= 0.30000E + 00
= 0.22378E + 01
- 0.15687E + 01
= 0.47147E + 01
- 0.10624E + 00
= 0.56696E + 00
= 0.72338E + 00
= 0.12093E + 00
= 0.10000E + 01
- 0.57016E + 00
- 0.45492E + 00
= 0.44449E - 01
- 0.59681E - 01
= 0.79016E - 00
- 0.99980E + 00
= 0.70000E + 01
= 0.10000E + 02
- 0.20496E - 03
- O.OOOOOE + 00
= 0.10000E + 01
- 0.32076E - 02
= 0.29300E + 03
= 0.55871E + 09
= 0.24382E + 06
= 0.79932E - 09
= 0.79932E - 09
U. S. GOVERNMENT PRINTING OFFICE: 1988 6t8-163--870'(8
166
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