United States
Environmental Protection
Agency
Office of Health and
Environmental Assessment
Washington DC 20460
Research and Development
EPA/600/S8-88/075 Sept. 1988
AEPA Project Summary
Selection Criteria for
Mathematical Models Used in
Exposure Assessments:
Ground-Water Models
Prior to the issuance of the Guidelines
for Estimating Exposures in 1986, The
U.S. Environmental Protection Agency
(EPA) published proposed guidelines In
the Federal Register tor public review and
comment. The purpose of the guidelines
is to provide a general approach and
framework for carrying out human and
nonhuman exposure assessments for
specific pollutants. As a result of the
review process, four areas were Iden-
tified that required further research. One
of these was the area of selection criteria
for mathematical models used in expo-
sure assessments.
The purpose of this document is to
present criteria which provide a means
for selecting the most appropriate
mathematical model(s) for conducting
an exposure assessment related to
ground-water contamination.
General guidelines and principles for
model selection criteria are presented
followed by a step-by-step approach to
identifying the appropriate model(s) for
use in a specific application. Several of
the currently-available models are
grouped into categories and a framework
is provided for selecting the appropriate
model(s) based on the response to the
technical criteria. Brief summaries of all
the currently available models discussed
in this report are contained in the
appendix.
Two site-specific example problems
are provided to demonstrate the pro-
cedure for selecting the appropriate
mathematical model for a particular
application.
This Project Summary was developed
by EPA's Office of Health and En-
vironmental Assessment, Washington,
DC, to announce key findings of the
research project that Is fully documented
in a separate report of the same title (See
Project Report ordering information at
back).
Introduction
This document presents a set of criteria
which provide a means of selecting the
most appropriate mathematical model for
conducting an exposure assessment re-
lated to ground-water contamination. These
criteria were developed in recognition of the
growing use of exposure assessments
across the U.S. Environmental Protection
Agency's regulatory programs. Use of the
criteria will expedite the regulatory process
by eliminating the use of unacceptable or
inappropriate models. Their use will also
improve the quality of data used in the
decision-making processes and promote
consistency in exposure assessments.
When performing a predictive exposure
assessment, a major task is to predict the
transport of contaminants. Since ground-
water flow is an integral part of contaminant
transport, it is equally important, if not more
so, to accurately predict the ground-water
flow. Therefore, both ground-water flow and
contaminant transport mathematical
models, and criteria for selecting these
models, are discussed in this document.
Background Information
Some of the general background infor-
mation necessary to understand the selec-
tion of a ground-water flow and/or contami-
nant transport model is discussed in this
section. This chapter is intended for the ex-
posure assessor or the non-modeler who
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is not completely familiar with hydrogeolo-
gic and modeling terms.
The first section provides a primer on
ground-water flow. The intent of this section
is to provide a brief summary of the
background information necessary to
understand ground-water problems. The
chapter discusses the general terms used
to describe and define ground-water flow
and presents the basic equation for flow in
a ground-water system.
The second section provides background
information on contaminant transport in
ground-water. The chapter presents the
basic equation for advective-dispersive
transport and discusses the important
terms in detail.
The last section provides definitions for
terms used throughout the report.
General Guidelines and Prin-
ciples of Model Selection Criteria
In order to enhance understanding and
facilitate implementation of the mathema-
tical model selection criteria, the following
terms are defined: mathematical model,
process equation, analytical solution,
analytical models, numerical models, ob-
jectives criteria, technical criteria, and im-
plementaiton criteria. The relationship be-
tween these terms may be thought of as
follows. A mathematical model consists of
two aspects: a process equation and a solu-
tion technique to solve the process equa-
tion. An analytical solution solves a very
simple process equation analytically by
hand calculations. An analytical model
solves a more complex, but still relatively
simple, process equation analytically with
a computer program. A numerical model
solves a simple or complex process equa-
tion numerically with a computer program.
In the context of this document, mathema-
tical model refers to all three solution
techniques of a process equation. The
more detailed the specific application, the
more complex the process equation. The
complexity of the process equation dictates
the solution technique required.
There are three factors which dictate the
level of complexity of the mathematical
model chosen in the selection process:
1. objectives criteria;
2. technical criteria; and
3. implementation criteria.
The objectives criteria refer to the level
of modeling detail required to meet the ob-
jectives of the study. There are many dif-
ferent objectives of modeling studies,
however, in the context of model selection,
all objectives are classified in two broad
categories: 1) to perform a screening study
or 2) to perform a detailed study.
A screening study is one where the pur-
pose is to make a preliminary screening of
a site or to make a general comparison be-
tween several sites. A detailed study, on the
other hand, is one where the objective is
to make an assessment of the environmen-
tal impact, performance, or safety of a
specific site.
Based on the objectives of the study
(screening or detailed levels), the analyst
or modeler will select either a screening or
detailed model. The specific model to be
used will be selected based on the tech-
nical selection criteria discussed below.
Technical Criteria
The second level of consideration when
selecting a mathematical model is the
technical criteria. Technical criteria are
those criteria related to the mathematical
model's ability to simulate the site-specific
contaminant transport and fate phenomena
of importance.
With regard to model selection, the
technical criteria can be divided into three
categories:
1. transport and transformation processes;
2. domain configuration; and
3. fluid(s) and media properties.
Transport and transformation process
criteria relate to those significant processes
or phenomena known to occur on site that
must be modeled in order to properly repre-
sent the site. Domain configuration relates
to the ability of the model to accurately
represent the geohydrologic system. When
high levels of resolution are required to
predict contaminant concentrations for
comparison to health or design standards,
it is generally necessary to simulate site-
specific geometry and dimensionality for
which numerical models are most ap-
propriate. If simplifying the site geometry
can be defended on a geologic and
hydrologic basis, then the use of a simpler
analytical model solution may be justified.
The third category of technical criteria cor-
responds to the ability of the mathematical
model to represent the spatial variability of
fluid(s) and media properties of the geohy-
drologic site.
Once the level of model has been decid-
ed, the technical criteria will direct the
analyst to the specific type of model need-
ed to properly simulate the transport and
transformation aspects of the environmen-
tal setting.
Implementation Criteria
The third level of consideration when
selecting a mathematical model is related
to the implementation criteria. Implemen-
tation criteria are those criteria dependent
on the ease with which a model can be ob-
tained and its acceptability demonstrated. (
Whereas the technical criteria identify the
models capable of simulating the relevant
phenomena within the specified environ-
mental setting, the implementation criteria
identify documentation, verification, valida-
tion requirements, and ease of use so that
the model selected provides accurate,
meaningful results.
Other Factors Affecting Model
Selection
Other general factors related to model
selection which are secondary to the
technical or implementation criteria include
data availability, schedule, budget, staff and
equipment resource, and level of complex-
ity of system(s) under study. Schedule and
budget constraints refer to the amount of
time and money available for the assess-
ment. If both analytical and numerical
models meet the selection criteria, time and
cost may be considered factors for electing
to use an analytical approach.
Model Selection Decision
Process
The decisions to be made when selec-
ting a ground-water flow model are discuss-
ed in detail in this section. Some guidance
is provided for making the decision and
some discussion is provided regarding the
errors associated with using the incorrect
model or feature(s) of a model. The criteria
for ground-water flow are presented follow-
ed by those for contaminant transport.
•Are you simulating a water table (i.e.,
unconfined) or a confined aquifer, or a
combination of both (i.e., conditions
change spatially)?
•Does the ground water flow through
porous media, fractures, or a combina-
tion of both?
• Is it necessary to simulate three-
dimensional flow or can the dimen-
sionality be reduced without losing a
significant amount of accuracy?
•Are you simulating a single-phase (i.e.,
water) or a multi-phase (i.e., water and
oil) flow system?
•Can the system be simulated with a
uniform value (homogeneous) or
spatially variable values (heterogene-
ous) of hydraulic conductivity, porosity,
recharge, and/or specific storage?
•Is there a single or are there multiple
hydrogeologic layers to be simulated?
•Is (are) the hydrogeologic layer(s) of
constant or variable thickness spatially?
•Is the hydrologic system in a steady-
state condition or do water levels fluc-
tuate with time (transient condition)?
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After all these criteria have been
satisfied, in most cases there will be several
ground-water flow models which would be
appropriate. At this point the analyst can
either select a ground-water flow model and
then continue with the selection process to
select a compatible (but separate) contami-
nant transport model, or the user can con-
tinue the process to select a combined flow
and transport model. It is quite common to
develop a fairly sophisticated flow model to
predict ground-water travel paths and
velocities and link it with a simpler transport
model.
The decisions to be made when selec-
ting a contaminant transport model are
discussed in detail in this section. Some
guidance is provided to help in making the
decision and some discussion is provided
regarding the errors associated with using
the incorrect model or feature(s) of the
model.
•Does the contaminant enter the ground-
water flow system at a point or is it
distributed along a line or over an area
or a volume?
•Does the source consist of an initial slug
of contaminant or is it constant over
time?
•Is it necessary to simulate three-
dimensional transport or can the dimen-
sionality be reduced without losing a
significant amount of accuracy?
•Does the model simulate dispersion?
•Does the model simulate adsorption
(i.e., distribution or partitioning coeffi-
cient) and, if so, does it simulate tem-
porally and/or spatially variable adsorp-
tion? Temporally or spatially variable ad-
sorption is important where the soil con-
ditions and/or concentrations change
with time and space.
•Does the model simulate first or
second-order decay and/or radionuclide
decay?
•Does the model simulate density effects
related to changes in temperature and
concentration? A truly coupled model is
one where the ground-water flow is in-
fluenced by the density and viscosity of
the water, which are influenced by the
temperature of the water and the con-
centration of the solute. In some cases
(i.e., large heat source or large fluctua-
tions in solute concentration) it may be
important to consider temperature and
contaminant concentration effects or
ground-water flow.
After sequencing through the decision
tree, there will, in most cases, be several
models which meet the desired criteria.
Since several models could meet the
desired criteria, it is difficult to list a single
model as a standard model. At this point
the analyst can either select a transport
model which is compatible with the flow
model selection above, or select a combin-
ed ground-water flow/contaminant transport
model.
Regardless of the approach selected,
separate or combined flow and transport
model, it is likely that there will be several
models which meet the techical criteria.
The selection of the final model(s) should
be based on the implementation criteria,
i.e., the model has been through a rigorous
quality assurance program so that it is
thoroughly verified and the model is well
documented with user's manuals and test
cases.
If several models pass the quality
assurance and documentation criteria, the
final selection of a model should be based
on familiarity with and availability of the
model, schedule, budget, and staff and
equipment resources.
A model selection worksheet is included
in this section which facilitates a selection
of the actual model or suite of models to
be used based on the response to the
technical criteria. Separate worksheets are
provided for both analytical solutions and
for analytical and numerical models (cod-
ed for the computer). A summary of each
of the models contained in the worksheets
is contained in Appendix A.
A discussion of waste management
models has been included in this section.
Waste management models are defined as
models which trace contaminant movement
through the three primary environmental
pathways: air, surface water, and/or ground
water. It is not the objective of this docu-
ment to cover waste management models
in any detail. Rather, a few such models are
described briefly to make the reader aware
of them. The models discussed are:
1. risk assessment methodology for
regulatory sludge disposal through land
application;
2. risk assessment methodology for
regulating landfill disposal of sludge;
3. RCRA risk/cost policy model (WET
model);
4. the liner location risk and cost analysis
model; and
5. landfill ban model.
Model Selection Eample
Problems
Two site-specific example problems are pro-
vided in this section to demonstrate the pro-
cedure for selecting the appropriate
mathematical model for a particular ap-
plication. The first example is an applica-
tion where the objective is to perform a
screening study, while the objective of the
second example is to perform a detailed
study. The discussions of the example pro-
blems are presented in the order that
should be followed when conducting a
ground-water flow and contaminant
transport model study, with model selecting
being one element of the process.
Appendix A
The appendix of the document contains a
summary page for each of the analytical
and numerical mathematical models
discussed in Table 5-3 of the full report. The
models are divided into seven categories:
1. analytical flow models;
2. analytical transport models;
3. numerical flow models which can be ap-
plied to both saturated and unsaturated
systems;
4. numerical flow models which can only be
applied to saturated systems;
5. numerical contaminant transport models
which can be applied to both saturated and
unsaturated systems;
6. numerical contaminant transport models
which can only be applied to saturated
systems; and
7. numerical contaminant and heat
transport models which couple the solu-
tions for pressure, temperature, and con-
centration (coupled models).
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Frederick Bond is with ICF Northwest, Rich/and, WA, and the EPA author Seong
Hwang (also the EPA Project Officer, see below) is with the Office of Health
and Environmental Assessment, Washington, DC 20460.
The complete report, entitled "Selection Criteria for Mathematical Models Used
in Exposure Assessments: Ground-Water Models," (Order No. PB 88-248
752/AS; Cost: $25.95, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield. VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington. DC 20460
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300
EPA/600/S8-88/075
PS
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