United States
Environmental Protection
Agency
Office of Health and
Environmental Assessment
Washington DC 20460
EPA/60Q/8-88/075
May 1988
vvEPA
Research and Development
Selection Criteria for
Mathematical Models
Used in Exposure
Assessments:
Ground-Water Models
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EPA/600/8-88/075
May 1988
SELECTION CRITERIA FOR MATHEMATICAL
MODELS USED IN EXPOSURE ASSESSMENTS:
GROUND-WATER MODELS
Exposure Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, D.C.
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DISCLAIMER
This document has been reviewed in accordance with U.S. Environmental
Protection Agency policy and approved for publication. Mention of trade names
or commercial products does not constitute endorsement or recommendation for
use.
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CONTENTS
Tables and Figures ..... . ......... . -. . . . : ,; ; ; . . . . . v
Foreword vi
Preface .......... : . . ... . vii
Abstract viii
Authors, Contributors, and Reviewers .. . . . . . . .... . ix
1. EXECUTIVE SUMMARY 1-1
1.1. Introduction 1-1
1.2. Background Information 1-1
1.3. General Guidelines and Principles of Model
Selection Criteria 1-2
1.3,1. Technical Criteria 1-3
1.3.2. Implementation Criteria 1-4
1.3.3. Other Factors Affecting Model Selection 1-5
1.4. Model Selection Decision Process 1-5
1.5. Model Selection Example Problems 1-8
1.6. Appendix A 1-9
2. INTRODUCTION 2-1
3. BACKGROUND INFORMATION 3-1
3.1. Primer on Ground-Water Flow 3-1
3.1.1. Ground Water and the Hydro!ogic Cycle 3-1
3.1.2. Porosity and Hydraulic Conductivity 3-4
3.1.3. Flow in Ground-Water Systems 3-6
3.2. Primer on Contaminant Transport 3-8
3.2.1. Advective Dispersion Equation 3-8
3.2.2. Attenuation and Degradation Mechanisms 3-11
3.2.2.1. Sorption - 3-12
3.2.2.2; Degradation 3-13
3.2.3. Definition of Terms 3-15
4. GENERAL GUIDELINES AND PRINCIPLES
OF MODEL SELECTION CRITERIA 4-1
4.1. Overview: Modeling Process 4-1
4.2. Overview: Model Selection Criteria 4-4
4.2.1. Objectives Criteria 4-4
4.2.2. Technical Criteria ' 4-6
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4.2.2.1. Transport and Transformation Processes 4-6
4.2.2.2. Domain Configuration 4-7
4.2.2.3. Fluid(s) and Media Properties 4-8
4.2.3. Implementation Criteria. ..... ... ....;...,;-. . . . 4-9
4.2.4. Other Factors Affecting Model Selection 4-9
4.3. Model Selection vs Model Application 4-12
4.4. Familiarity with a Model. ... . . . . . . <.c....... . . ... 4-13
4.5. Model Reliability 4-14
5. MODEL SELECTION DECISION PROCESS 5-1
5.1. Technical Criteria used for Model Selection 5-1
5.2. Model Selection from the Reviewers Point of View 5-29
5.3. Model Selection Worksheet 5-30
5.4. Waste Management Models . . 5-40
5.4.1. Risk Assessment Methodology for Regulatory
Sludge Disposal Through Land Application ..... . . . 5-41
5.4.2. Risk Assessment Methodology for Regulating
Landfill Disposal of Sludge 5-41
5.4.3. RCRA Risk/Cost Policy Model (WET Model) 5-42
5.4.4. The Liner Location Risk and Cost Analysis Model .... 5-43
5.4.5. Landfill Ban Model 5-45
6. MODEL SELECTION EXAMPLE PROBLEMS 6-1
6.1. Screening Analysis Example Problem 6-1
6.1.1. Objectives of the Study 6-1
6.1.2. Conceptual Model of the Study Area 6-2
6.1.3. Model Selection Process 6-2
6.2. Detailed Analysis Example Problem 6-4
6.2.1. Statement of the Problem 6-4
6.2.2. Objectives of the Study 6-4
6.2.3. Conceptual Model of the Study.Area 6-5
6.2.4. Model Selection Process 6-7
7. REFERENCES 7-1
APPENDIX A: ANALYTICAL AND NUMERICAL MODEL SUMMARIES A-l
IV
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TABLES
5-1 Analytical Solutions, Names, and References. 5-32
5-2 Analytical Solutions Worksheet 5.34
5-3 Analytical and Numerical Models Worksheet. . . . 5-37
FIGURES
5-1
6-1
Code selection decision tree
Model region for the assessment-level example problem
5-2
6-6
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FOREWORD
When performing exposure assessments using predictive methods, assessors
frequently ask the following questions: "How do I select the best fate model to
use in my assessment," "How can I tell if the model someone else used in their
assessment is appropriate," and "What are the strengths and weaknesses of these
models?" This document is a first step in addressing these questions.
One of the functions of the Exposure Assessment Group is to develop
guidelines for exposure assessments. On September 24, 1986, the U.S.
Environmental Protection Agency published Guidelines for Estimating Exposures.
During the development of the guidelines and subsequent review and comment, four
areas were identified that required further research. One of these areas was
selection criteria for mathematical models. This document, which is the second
selection criteria document in the series, deals with ground-water models. The
first dealt with surface water models. Similar documents will follow dealing
with air models, and int he future, other types of models.
This document is designed to help the exposure assessor evaluate the
appropriateness of models for various situations. The report defines the terms
and discusses the general approaches that modelers take to a problem so that
exposure assessors may more readily evaluate the appropriateness of both new and
existing models. In addition, step-by-step criteria are provided to enable the
assessor to answer the questions posed above.
Michael A. Callahan
Director
Exposure Assessment Group
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PREFACE
The Exposure Assessment Group of the Officeof Health and Environmental
Assessment (OHEA) is preparing several documents addressing selection criteria
for mathematical models used in exposure assessments. These,documents will
serve as technical support documents for thetGuidelines for Estimating
Exposures, one of five risk assessment guidelines published by the U.S.
Environmental Protection Agency in 1936.
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.
.' , - "'.'' ' ' : ;'" ..'.-;- - ' , ' ' > (;, , ,.;.-',
The literature search to support the models discussed in,this report is
current to September 1986.
vii
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ABSTRACT
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 for 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 identified that required further research. One
of these was the area of selection criteria for mathematical models used in
exposure assessments.
The purpose of this document is to present criteria which provide a means
i
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
procedure for selecting the appropriate mathematical model for a particular
application.
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AUTHORS, CONTRIBUTORS, AND REVIEWERS
The Exposure Assessment Group within the U.S. Environmental Protection
Agency's Office of Health and Environmental Assessment was responsible for the
preparation of this document and provided overall direction and coordination
during the production effort. The information in this document has been funded,
wholly or in part, by the U.S. Environmental Protection Agency under Contract
No. 68-01-6939 to Camp Dresser & McKee Inc. The work was performed by ICF
Technology Inc., a subcontractor (Seong Hwang, Project Manager).
AUTHORS
f
Frederick Bond
ICF Northwest
Richland, WA
Seong Hwang
Exposure Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, DC
CONTRIBUTORS:
Paul van der Heijde
International Ground-Water Modeling Center
Indianapolis, IN
Scott Yates
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
Ada, OK
REVIEWERS
P. B. Bedient
Rice University
Houston, TX
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Carey Carpenter
Office of Ground-Water Protection
U.S. Environmental Protection Agency
Washington, DC
Norbert Dee
Office of Ground-Water Protection
U.S. Environmental Protection Agency
Washington, DC
Ron Hoffer
Guidelines Implementation Staff
Office of Ground-Water Protection
U.S. Environmental Protection Agency
Washington, DC i
Joe Hughart
Water Management Division
U.S. Environmental Protection Agency, Region 4
Atlanta, GA
David Kyllonen
U.S. Environmental Protection Agency, Region 9
San Francisco, CA
James Mercer
Geo Trans, Inc.
Herndon, VA ;
Frank Mink
Environmental Criteria and Assessment Office
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Cincinnati, OH
Charles Ris
Carcinogen Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, DC
John Segna
Exposure Assessment Group
Office of Health and Environmental Assessment
U.S. Environmental Protection Agency
Washington, DC
John Years!ey
Environmental Services Division
U.S. Environmental Protection Agency, Region 10
Seattle, WA
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The following individuals, members of the EPA Ground-Water Model Selection
Criteria Work Group, participated in meetings, provided advice on formulating
the criteria, and reviewed drafts of this document. Their efforts were greatly
appreciated.
Stuart Cohen >
Office of Pesticide Programs
Stephen Cordle
Office of Research and Development
Norbert Dee ,
Office of Ground-Water Protection
Annett Mold
Office of Toxic Substances
William Wood
Office of Research and Development
Saleem Zubair
Office of Solid Waste
Malcolm Field
Exposure Assessment Group
Office of Health and Environmental Assessment
U. S. Environmental Protection Agency
Washington, DC
xi
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1. EXECUTIVE SUMMARY
1.1. INTRODUCTION^
This document presents a set of criteria which provide a means of selecting
the most appropriate mathematical model for conducting an exposure assessment
related 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.
1.2. BACKGROUND INFORMATION
Some of the general background information necessary to understand the
selection of a ground-water flow and/or contaminant transport model is discussed
in this section. This chapter is intended for the exposure assessor or the
non-modeler who is not completely familiar with hydrogeologic 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
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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 repor.t.
1.3. GENERAL GUIDELINES AND PRINCIPLES OF MODEL SELECTION CRITERIA
In order to enhance understanding and facilitate implementation of the
mathematical model selection criteria, the following terms are defined:
mathematical model, process equation, analytical solution, analytical models,
numerical models, objectives criteria, technical criteria, and implementation
criteria. The relationship between these terms may be thought of as follows. A
mathematical model consists of .two aspects: a process equation and a solution
technique to solve the process equation. 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 equation numerically with a computer program. In the context of
this document, mathematical 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
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3. Implementation criteria.
The objectives criteria refer to the level of modeling detail required to
meet the objectives of the study. There are many different 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 purpose is to make a preliminary
screening of a site or to make a general comparison between several sites. A
detailed study, on the other hand, is one where the objective is to make an
assessment of the environmental 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 technical selection
criteria discussed below.
1.3.1. 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.
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Transport and transformation process criteria relate to those significant
processes or phenomena known to occur on site that must be modeled in order to
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properly represent 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 appropriate. 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 corresponds to the ability of the
mathematical model to represent the spatial variability of fluid(s) atid media
properties of the geohydrologic site.
Once the level of model has been decided, the technical criteria will
direct the analyst to the specific type of model needed to properly simulate the
transport and transformation aspects of the environmental setting.
1.3.2. Implementation Criteria
The third level of consideration when selecting a mathematical model is
related to the implementation criteria. Implementation criteria are those
criteria dependent on the ease with which a model can be obtained and its
acceptability demonstrated. Whereas the technical criteria identify the models
capable of simulating-the relevant phenomena within the specified environmental
setting, the implementation criteria identify documentation, verification,
validation requirements, and ease of use so that the model selected provides
accurate, meaningful results.
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1.3.3. 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 complexity of system(s) under
study. Schedule and budget constraints refer to the amount of
time and money available for the assessment. If both analytical and numerical
models meet the selection criteria, time and cost may be considered factors for
electing to use an analytical approach.
1.4. MODEL SELECTION DEC.ISION PROCESS
The decisions to be made when selecting a ground-water flow model are
discussed 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 followed by those for contaminant transport.
Are you simulating a water table (i.e., unqonfined) 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
combination of both?
Is it necessary to simulate three-dimensional flow or can the
dimensionality 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 (heterogeneous) of hydraulic conductivity, porosity,
recharge, and/or specific storage?
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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
fluctuate with time (transient condition)?
After all these criteria has 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) contaminant transport
model, or the user can continue 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 selecting 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.
t 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
dimensionality be reduced without losing a significant amount of accuracy?
§ Does the model simulate dispersion?
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t Does the model simulate adsorption (i.e., distribution or partitioning
coefficient) and, if so, does it simulate temporally and/or spatially
variable adsorption? Temporally or spatially variable adsorption is
important where the soil conditions 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 influenced by the density and viscosity of the water, which are
influenced by the temperature of the water and the concentration of the
solute. In some cases (i.e., large heat source or large fluctuations in
solute concentration) it may be important to consider temperature and
contaminant concentration effects on 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 selected above, or select a cpmbined 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
technical 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.
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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
the selection of the actual model or suite or 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 (coded 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 document 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.
1.5. MODEL SELECTION EXAMPLE PROBLEMS
Two site-specific example problems are provided in this section to
demonstrate the procedure for selecting the appropriate mathematical model for a
particular application. The first example is an application where the objective
is to perform a screening study, while the objective of the second example is to
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perform a detailed study. The discussions of the example problems 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.
1.6. 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. The models
are divided into seven categories:
1. analytical flow models;
2. analytical transport models;
3. numerical flow models which can be applied 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 solutions
for pressure, temperature, and concentration (coupled models).
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2. INTRODUCTION
This document presents a set of criteria which provide a means of selecting
the most appropriate mathematical model for conducting an exposure assessment
related 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.
These selection criteria are particularly directed toward exposure
assessments. However, the same or very similar criteria would be applicable to
all aspects of managing ground-water contamination problems/sites. To manage
contamination problems/sites, mathematical models are needed to perform initial
screening studies, assist in the design of disposal schemes, assess the probable
contaminant performance of specific sites, predict contaminant migration, and
aid in the design of monitoring programs and remedial action alternatives.
In the context of this document, the term mathematical model refers to both
analytical and numerical solutions. Analytical solutions refer to both those
which are coded for the computer as well as those which are suitable for hand
calculation. Numerical solutions refer only to those which are coded for
solution on the computer since this is the only practical solution technique.
Throughout most of the report, the term mathematical model is shortened simply
to model.
When performing an exposure assessment, the primary interest is in
predicting the transport of contaminants. However, since ground-water flow is
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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. Related models, such as
unsaturated flow, nonaqueous phase liquid, and geochemical models, are not
discussed in this document. ='.-,.
In order to develop a tractable, useful model, the importance of the
various processes controlling contaminant migration in ground water must be
identified. Only the dominant processes are incorporated in the mathematical
models. The explicit incorporation of every known or observed process is not
practical because the resulting model would require excessive computational time
and would contain too many internal coefficients that must be adjusted in the
t ''
calibration or initial phase of a modeling study. In addition, the effect of
the minor processes, in terms of the predicted concentration levels, is very
small in comparison with the dominant transpprt processes and attenuation
mechanisms.
All of the contaminant transport models discussed in this report are
designed for situations where the contaminant is at trace concentration levels.
Trace concentrations, in this context, are defined as concentrations that have a
negligible impact on the density and viscosity of the fluid and, therefore, have
an insignificant effect on the ground-water movement. The models are not
designed to be used in an emergency response framework, such as an accidental
spill, because in those situations 1) the contaminant is not likely to be at
trace concentrations initially and 2) the time required to set up the model, run
the model, and evaluate results is generally greater than the emergency response
times.
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This document is intended primarily to assist potential model users who are
not experts in water quality modeling. A concerted effort has been made to
define specific terminology and to characterize the important assumptions and
limitations of the existing models. The existing models are generally the best
available technology and are useful tools when applied properly. However, model
accuracy is very sensitive to input parameters and calibration with field data
is essential. In any modeling study the .assumptions and limitations of a
particular model along with the means by,which it is applied should be clearly
understood by the model user as well as by persons making decisions based, in
part, on the modeling results. Although the guidance provided in this document
is primarily directed toward applications-oriented users of mathematical models,
the information presented is also important to managers and other decision
makers who will have the ultimate responsibility of assessing and controlling
contamination problems.
In view of the diversity in typical modeling needs and objectives
associated with exposure assessments and related studies, these selection
criteria are formulated as a general guideline for selecting a relevant or
appropriate mathematical model. They are not intended to serve as an absolute
set of standards for accepting or rejecting models for possible use in exposure
assessments.
These criteria deal only with the selection of existing mathematical models
for predicting ground-water flow and contaminant transport. The criteria do not
deal with the development of numerical algorithms for constructing new models.
Two other reports which address the issue of model selection criteria are
Simmons and Cole, 1985, and U.S. EPA, 1987.
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The organization of this document is as fallows:
Chapter 2 -- Background Information -- General discussion of ground-water
flow and contaminant.transport, description of ..equations .and processes, and
definition of specific terms. . . .
' ' ' M '..:.' ' ,.,',, j.i,: . "'!, ./.- >,.>.:. . - ':' .'I-,.,''. ...... I'!?..
Chapters -- General Guidelines, and Principles of Model .Selection ;i
Criteria -- Overview,of the modeling p,roces,s, overview of model selection
criteria, and important issues .related to .model selection...
Chapter 4 --Model Selection Decisipn Process Step-by-step process to,
identify the appropriate model(s) for a specific application. ,
Chapter 5 -- Model Selection Example Problems, -.-Examples of how to use the
selection criteria. , , .....:,
Appendix A -- Analytical and Numerical Model, Summaries, ; ., , ;
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3. BACKGROUND INFORMATION
Some of the general background information necessary to understand the
selection of a ground-water flow and/or contaminant transport model is discussed
in this section. This chapter is intended for the exposure assessor or the
non-modeler who is not completely familiar with hydrogeologic and modeling
terms. It should be emphasized that the information presented here is a brief
overview. For much more detailed discussions the reader is directed to the
following sources: Freeze and Cherry, 1979; Chow, 1964; Davis and DeWest, 1966;
Javandel et al., 1984; Bachmat et al., 1980, and Mercer and Faust, 1981.
The first section provides a primer on ground-water flow. The second
section provides background information on contaminant transport in ground
water. The last section provides definitions for terms used throughout this
report.
3.1. PRIMER ON GROUND-WATER FLOW
This section is intended to provide a brief summary of the background
information necessary to understand a ground-water problem. 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.
3.1.1. Ground Water and the Hvdroloqic Cycle
The hydrologic cycle can be defined as the endless circulation of water
between ocean, atmosphere, and land. The hydrologic cycle is composed of
precipitation, storage, runoff, and evaporation of the earth's water during the
cycle. The total amount of water is essentially fixed, but its form may change
(i.e., solid, liquid, gas).
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Our interest for the purposes of this report is in the land-based-portion
of the cycle, particularly the portion that infiltrates the land surface and
flows underground. The subsurface distribution of water can be divided into
five categories:
1. Soil Zone -- That area where evaporation and transpiration of water occurs
(partially saturated).
2- Vadose (Unsaturated) Zone Partially-saturated zone consisting of
sediments whose interconnected pore space (porosity) is not completely
filled with water. Water flow in this region can be both horizontal and
vertical as stratification of the sediments will cause significant
conductivity contrasts.
3' The Capillary Fringe A transition zone from the partially-saturated
vadose zone to the fully-saturated phreatic (water table) surface.
4« Phreatic (Saturated) Zone Below the phreatic surface, the porous
material is fully saturated with water (with the exception of entrapped
gas). Water in this zone is under hydrostatic pressure. The porous
material is called the aquifer.
5. Dense Rock The phreatic zone merges at depth into a zone of dense rock
with water in the pore spaces but few or none of these pore spaces are
interconnected and flow of water is severely limited.
That portion of the hydrologic cycle beneath the land surface can be called
the subsurface flow system. Inflow or recharge to the subsurface flow system
arrives as precipitation (in the form of rainfall or snowmelt) or as
infiltration from surface water bodies. Outflow or discharge occurs as
evapotranspiration or evaporation and as flow to surface water bodies.
Artificial recharge and discharge occur as injection or pumping, respectively.
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In this report, the selection of models developed to simulate ground-water
flow and contaminant transport in the saturated zone is discussed in detail.
Therefore, the rest of this background discussion is directed to flow in the
phreatic or saturated zone.
Water that infiltrates the land s.urface generally moves vertically downward
to the water table and the phreatic zone. Water in the phreatic zone generally
moves horizontally from areas of greater to areas of lesser hydrostatic head
(i.e., energy: .see Section 3.1.3). In both zones, unsaturated and saturated,
the prime moving force is gravity.
The occurrence, movement, and storage of ground water are related to and
influenced by the porous media structure, lithology, thickness; hydraulic
conductivity,, hydraulic gradient, and porosity. A formation, or group of
formations, that contains sufficient saturated permeable material to yield
significant quantities of water to wells and springs is defined as an aquifer.
Movement and storage of water in an aquifer are chiefly controlled by the
aquifer hydraulic conductivity, permeability, and porosity. Aquifers can be
subdivided into three main types as follows:
1. Unconfined (Water Table) Aquifer -- An aquifer in which the top of the
saturated zone (water table) is in direct contact with the atmosphere
through the open pores of the earth material above.
2. Confined (Artesian) Aquifer . An aquifer which has an overlying layer
which does not allow direct contact of the aquifer with the atmosphere.
Water in a confined aquifer is under pressure and wells penetrating into
the aquifer will have a water level that reflects the pressure in the
aquifer at the point of .penetration.
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3. Perched Aquifer Beds of clay or silt or other materials of limited areal
extent which present a restriction to flow of downward moving water in the
vadose zone may cause local areas of saturation above the regional water
table. An unsaturated zone is present between the bottom of the perching
bed and the water table.
Aquifers have a higher hydraulic conductivity than adjacent units. The
lithologic units of low hydraulic conductivity relative to the aquifer are
commonly called aquitards. Appreciable quantities of water can move through an
aquitard, in most cases vertically upward and/or downward, from aquifers above
and below. If very little flow occurs, the unit is termed an aquielude.
3.1.2. Porosity and Hydraulic Conductivity
The portion of an aquifer's volume which consists of openings or pores and
not solid material is defined as porosity. Porosity is an index of how much
water can be stored in the saturated material and is usually expressed as a
percentage of the bulk volume of the material. Effective porosity is defined as
the ratio of the transmissive pore volume to the total unit volume, where the
transmissive pore volume is that portion which contributes to the net flow
through the system.
Hydraulic conductivity (K) is a measure of the capacity of a porous rock,
soil, or sediment to transmit water. Aquifers having high hydraulic
conductivity generally consist of clean coarse sands and mixtures of sand and
gravel and fine sands, silts, or clays. Aquifers having low hydraulic
conductivity generally consist of very fine sands, silts, and clays, glacial
till, or stratified clays.
Average values of hydraulic conductivity for different soil classes are as
follows:
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Hydraulic Conductivity
Soil Class (cm/sec)(apd/ft*)
Clay
Sand
Gravel
10-6-KJ-3 10-2-10,
10-3-1.0 10, -10*
1.0 -102 104 -106
If a hydraulic conductivity is independent of position in an aquifer, the
formation is homogeneous. If the conductivity is dependent on position, the
formation is heterogeneous (i.e., K varies from point to point in the medium).
If the conductivity is independent of the direction of measurement at a point in
the aquifer, the formation is isotropic at that point. If conductivity varies
with the direction of measurement at a point in an aquifer, the formation is
anisotropic at that point. A formation can be isotropic and heterogeneous,
which is not at all uncommon. Anisotropy is common when the conductivity varies
in the x (horizontal) and z (vertical) direction. In many aquifers the vertical
conductivity can be estimated as one tenth the horizontal conductivity.
The transmissivity of an aquifer is defined as the rate at which water of
the prevailing kinematic viscosity is transmitted through a unit width under a
unit hydraulic gradient. Though spoken of as a property of the aquifer, it
embodies also the saturated thickness and the properties of the contained
liquid. Transmissivity is also defined as the product of hydraulic conductivity
and aquifer thickness.
The storage coefficient of an aquifer is defined as the volume of water
released from storage in a vertical column of 1.0 square feet when the water
table or other piezometric surface declines 1.0 feet. In an unconfined aquifer,
it is approximately equal to the specific yield, which is defined as the amount
of water that drains from a soil due to the force of gravity.
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3.1.3. Flow In Ground-Water Systems
In 1856 Henry Darcy reported that flow between two points in a soil column
is directly proportional to the difference in potential head (energy) between
the points and inversely proportional to the distance between the points. These
two quantities together (difference in head divided by the distance between the
points) are known as the hydraulic gradient. Darcy's Law can be written as
Q = -KA (h!-h2)/L (3-1)
where Q « flow rate (L3/t)
K = permeability or hydraulic conductivity of the media and fluid
(L/t)
A = cross-sectional area of flow (L2)
hi,h2 = potential head at two points on a line parallel to flow (L)
L » length of flow path from hj to \\2 (L)
hj-h2/L = hydraulic gradient = head drop per unit distance
The negative sign in Equation 3-1 indicates that ground-water flows from
high to low potential. Headj potential, fluid potential, and potential head are
all the same and can be defined as the mechanical energy per unit mass of a
fluid at any given point in space and time with respect to an arbitrary state
and datum (typically mean sea level).
Darcy's Law is valid for steady flow with constant flux. The law is only
valid for laminar flow, not when the flow becomes turbulent which is not common
in ground water. Darcy's Law is a measure of the average or bulk velocity
through a given cross section of a porous medium. The true ground-water
velocity between soil grains is defined as the Darcy velocity divided by the
porosity of the soil.
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The fundamental equation of ground-water flow can be derived from Darcy's
Law
plus a continuity equation
to yield
q - Q/A = -KVH
S aH/at 3 - V. q
s aH/at = .KVH
(3-la)
(3-2)
(3-3)
where V - del operator, or
= a2/ax2 + a2/ay2 + a2/az2
S = storage coefficient
H = hydraulic head
K = hydraulic conductivity
Equation 3-3 can take many forms depending on whether the flow is steady state
or transient and whether the media is homogeneous or heterogeneous and isotropic
or anisotropic. Refer to the references at the beginning of the chapter for the
various forms of the equation. Steady-state flow occurs when the magnitude and
direction of the flow velocity are constant with time at any point in the flow
field. Transient flow (unsteady flow) occurs when the magnitude or direction of
the flow velocity changes with time at any point in the flow field.
Each form of the ground-water flow equation has an infinite number of
solutions. To get a specific solution for a problem, the initial and boundary
conditions must be specified. Initial conditions pertain to transient flow
cases only, and specify the value of the dependent variable (head) initial time
(t - 0). Boundary conditions are where the head or flux conditions at the
boundaries of the problem must be specified as either prescribed head
(Dirichlet) or flux (Neumann). For prescribed head conditions, the head is
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specified at points along the boundary. For prescribed flux conditions, the
flux of water (either in, out, or no flow) is specified at points along the
boundary.
3.2. PRIMER ON CONTAMINANT TRANSPORT
This section is intended to provide a brief summary of the background
information necessary to understand the transport of contaminants in ground
water. The chapter begins with the basic equation for advective-dispersive
transport and discusses the important terms in detail.
3.2.1. Advective Dispersion Equation
Movement of contaminants in the soil can be described by the following
equation (van Genuchten and Alves, 1982)
ac/at = D* ac2/ax2 - V* ac/ax - kc (3-4)
where C - solution concentration (mg/1)
D* = D/R
V* - V/R
R = 1 + (B/N) Kd = retardation factor (dimensionless)
D « dispersion coefficient (cm2/day)
V » average interstitial pore-water velocity (cm/day)
k - degradation rate coefficient (day'*)
B » bulk density (g/cm3)
N » effective porosity (dimensionless)
Kd <* partition coefficient (ml/g)
Equation 3-4 states that the change in contaminant concentration with time at
any distance, (X) is equal to the algebraic sum of the dispersive transport (1st
term to right of equal sign), the convective transport (2nd term), and the
degradation or decay of the compound (3rd term). Van Genuchten and Alves (1982)
3-8
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note that various modified forms of this same basic equation have been
used for a wide range of contaminant transport problems in soil science,
chemical and environmental engineering, and water resources.
Equation 3-4 considers only one-dimensional transport of contaminants.
This equation considers dispersion, advection, equilibrium adsorption (linear
isotherm), and degradation/decay (first-order kinetics).
A wide variety of physical processes occur in ground-water systems which
are important, to varying degrees, in the analysis of contaminant fate and
transport. A more detailed description of these processes is given by Fischer
et al. (1979) and Schnoor (1985). Some of the important hydrologic transport
processes include:
e Advection -- The process by which solutes are transported by the bulk
motion of the flowing ground water. As a result of advection, nonreactive
contaminants are carried at an average rate equal to the average linear
velocity of the water.
9 Molecular Diffusion -- The process whereby ionic or molecular constituents
move under the influence of their kinetic activity in the direction of
their concentration gradient. Diffusion occurs in the absence of any bulk
hydraulic movement of the solution. Diffusion is a dispersion process
which is important only at low velocities.
Hydrodvnamic Dispersion -- The tendency of a contaminant to spread out from
the path that it would be expected to follow according to the advective
hydraulics of the flow system. Dispersion occurs because of mechanical
mixing during fluid advection and because of molecular diffusion due to the
thermal-kinetic energy of the solute particles.
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Mechanical (Hydraulic) Dispersion -- Dispersion that is caused entirely by
the motion of the fluid.
e Longitudinal Dispersion -- Spreading of the contaminant in the direction of
bulk flow.
t Transverse Dispersion --' Spreading of the contaminant in the directions
perpendicular to the bulk flow.
Host contaminant transport models simulate hydrodynamic dispersion only and
disregard the molecular diffusion component because it is so small. Some models
do simulate the molecular diffusion component for cases where the ground-water
velocity is small and the diffusive component can become significant.
Host models available today simulate contaminant transport using a form of
the advective-dispersion equation. Increasing evidence suggests that the
conventional advective-dispersive equation does not always adequately describe
contaminant transport in a natural geohydrologic system as a result of 1) random
variations in ground-water velocity that are induced by media heterogeneities,
and 2) the failure of Pick's diffusion law to properly describe hydrodynamic
dispersion at field scales (Gelhar et al., 1979; Gelhar and Axness, 1983; Smith
and Schwartz, 1980; Hatheron and DeHarsily, 1980; Dagan and Bresler, 1979; and
Dagan, 1982). Field determinations of dispersivity have shown a scale
dependence, that is, the observed dispersivity was dependent on the size of the
experiment rather than being exclusively a media property. A more detailed
discussion of recent findings regarding dispersivity can be found in Gelhar and
Axness (1983), Freyberg (1986), Gelhar et al. (1985), and Pickens and Grisak
(1981).
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3.2.2. Attenuation and Degradation Mechanisms
The primary physical processes included in contaminant transport models are
sorption and degradation. The kinetic formation and rate constants used to
describe these processes are typically based on laboratory measurements. The
results of the laboratory measurements are incorporated in the models as source
or sink terms in the general advection dispersion equation.
The direct transfer of controlled experimental results to natural ground-
water systems is not always straightforward. Uncertainties arise in the
definition of driving forces such as whether the system is aerobic or anaerobic,
the pH of the natural system, and the chemical equilibria of the natural system
(i.e., whether other ions are present which may catalyze or retard various
reactions and the organic content of the soil). One of the biggest problems
with simulating natural ground-water conditions in the laboratory is properly
representing the geologic media (i.e., layering, heterogeneity, hydraulic
conductivity, porosity, etc.). In spite of the uncertainties, these processes
are incorporated in many ground-water models, and some models have been
calibrated to field conditions. Careful calibration has shown that they are
useful for representing the transport of various chemicals.
Most of the available models use some form of first-order reaction kinetics
to represent the different processes that will degrade or transform a specific
chemical. For a simple first-order reaction, ignoring all other mechanisms, the
concentration can be represented as a first-order differential equation
dc/dt - -kc (3-5)
where k is the rate constant (1/T). In the simpler models, the rate constant
does not change, in the more complex models the rate constant(s) may be variable
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and calculated as a function of changing environmental conditions. The
analytical solution to this equation when k is a constant is
C(t) = C0 e'kt
(3-6) ,
where Co is the initial concentration. From this equation an estimate of the
time required for the process to reduce the contaminant concentration below a
fixed "action level" can be determined.
t = Ln Cm/C0 (3-7)
-k
Often the reaction rate of various chemicals subject to different kinetic
processes are characterized in terms of their half life, tj/2- This is a
measure of the time required for some kinetic process to degrade or transform
the specific chemical to one-half of the initial concentration. The half-life
is calculated from Equation 3-7 with the C(t)/C0 set to 1/2.
A brief description of the sorption and degradation processes is included
for potential users unfamiliar with the terminology. Much more detailed
descriptions including assumptions, limitations, kinetic formulations, and
methods for estimating rate constants are given by Bohn et al . (1979), Bolt and
Bruggenwert (1978), Peterson et al. (1986), and Freeze and Cherry (1979).
3.2.2.1. Sorption -- Sorption is a transfer process whereby dissolved chemicals
in the ground water become attached to sedimentary materials and/or organic
matter. The process is commonly described using a partition coefficient. The
definition of the partition coefficient is the ratio of the mass of chemical
sorbed on the solid phase divided by the mass of chemical left in solution at
equilibrium, as shown in Equation 3-4. The important assumptions in using this
1 ' t 0*
formulation are: 1) the chemical is at trace concentrations, hence the sorption
isotherm may be assumed to be linear; and 2) the system is at equilibrium.
3-12
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Some problems associated with field application of this concept include:
1) many chemicals exhibit nonreversible sorption characteristics, hence,
desorption from sediments to the water column may not be correctly represented;
2) sorption characteristics are dependent on particle size (sand, silt, clay)
and particle size is variable in a natural system; 3) sorption characteristics
are dependent on pH and ionic strength which are often variable in a natural
system; and 4) the presence of other compounds in a natural system results in
competition for sorption sites on the soil matrix. Some of the compounds that
may be strongly affected by sorption include heavy metals and many organic
compounds. For organ compounds, partition coefficients are frequently
normalized to the organic carbon content of the soil (Karickhoff, 1980, 1981,
and 1984; and Gschwend and Wu, 1985). As noted previously, the relationship
between dissolved and adsorbed forms of a contaminant is usually represented in
the form of an equilibrium partition coefficient (Kd). The partition
coefficient is defined as the ratio of the mass of the substance adsorbed to the
particulates (per unit mass of particulates) over the dissolved concentration of
the solute. The retardation factor is calculated from the partition
coefficient, bulk density, and the effective porosity, and is a number which
describes how many times slower than water a contaminant travels through a
porous media system.
3.2.2.2. Degradation -- Degradation in ground water systems may result from one
or more of three mechanisms: biological transformations, hydrolysis, or
chemical reactions. Biological transformations are reactions due to the
metabolic activity of aquatic microbes, primarily bacteria. Depending on the
specific chemical, the transformations may be very fast due to the presence of
enzymes and for other compounds the process may be very slow. The rate and
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nature of by-products will also be dependent on the availability of oxygen. In
unsaturated aerated zones, aerobic degradation will predominate, while anaerobic
mechanisms will be controlling in anoxic zones. For chemicals where
the transformation is fast, degradation is often the most important
transformation process in the aquatic environment. Various kinetic formulations
have been proposed including first- and second-order forms. The rate
coefficients are known to be a function of temperature, pH, and available
nutrients. The second-order kinetic formulations describe the degradation rate
as a function of the concentration of the compound and the bacterial population
which is changing as the compound is degraded. A variety of organic compounds
may be subject to degradation. A discussion of various compounds is provided by
Klecka (1985).
Hydrolysis is the reaction of chemicals with water. Typically a compound
is altered in a hydrolysis reaction by the replacement of some chemical group of
the compound with a hydroxyl group. The hydrolysis reactions are commonly
catalyzed by the presence of hydrogen or hydroxide ions and hence the reaction
rate is strongly dependent on the pH of the system. Hydrolysis reactions alter
the structure of the reacting compound and may change its properties. The new
compound is usually less toxic than the original, compound, but this is not
always the case depending on the specific reaction. Neely (1985) lists several
functional groups that are susceptible to hydrolysis reactions including alkyl
ha!ides, amines, carbamates, carboxylic acid esters, epoxides, lactones,
phosphoric acid esters, and sulfonic acid esters. For many functional groups,
and therefore a considerable number of compounds, hydrolysis will not occur.
Chemical reactions refer to the interaction of contaminants with other
chemicals in the ground water besides the water itself. Many chemical reactions
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are of the oxidation-reduction type (redox). Redox reactions involve the
transfer of electrons from one chemical (the reducing agent) to the other (the
oxidizing agent). In the process, toxicity and solubility properties are often
changed. Possible couples for redox reactions can be determined from oxidation
potential tables.
3.2.3. Definition of Terms
Throughout this report a number of terms or phrases are used which may be
interpreted as having somewhat different meanings by different readers with
various backgrounds, experience, and general inclinations. In an attempt to
avoid any misinterpretations, this section defines the specific meaning intended
for a few key terms.
1. Calibration -- In this document we will use the term calibration to
describe the initial phase of a modeling study where the input coefficients
of a model are adjusted in an attempt to match measured field data (e.g.,
velocity, concentration). The types of coefficients that are commonly
adjusted in a ground-water flow model are recharge and discharge, hydraulic
conductivity or transmissivity, and porosity. The types of coefficients
that are commonly adjusted in a transport model include dispersion
coefficients, degradation rate constants, sorption properties, and possibly
source and sink terms.
2. Validation -- The term validation will be used to describe a separate step
of a modeling study where the calibrated model (i.e., fixed coefficients,
no more adjustments) is applied to a different set of conditions and the
results are compared with a separate set of field data. The validation
phase is an attempt to see if the model can reproduce field data under
conditions different than those used in the calibration phase. This
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distinction between calibration and validation is easy to define and
appropriate from an idealistic point of view. Real applications may find
it impossible to obtain a separate data set or the validation phase may
indicate poor model performance and the validation data set might be used
for additional calibration. Under these circumstances, larger uncertainty
in the model results, and this needs to be incorporated into any
decision-making process.
3. Verification -- The term verification will be used to define the process of
comparing the results of one model against those of another model. For
example, it is common to compare the results of a tested and accepted
analytical solution/model against a more sophisticated numerical model in
order to verify the numerical solution technique.
4. Mathematical Model -- The term mathematical model will be used to describe
the mathematical representation of the physical system. The model may
represent an analytical solution to these equations and in other cases the
model may be an approximate numerical representation of these equations.
In some cases, the models based on analytical solutions are simple enough
that the calculations can be performed using a hand calculator. In other
cases the analytical models are more complex and often are implemented as a
program to be run on a computer. All of the numerical models are
implemented as programs to be run on a computer. Computer models are often
referred to as codes or computer codes. We have used the term model, as
opposed to code, wherever appropriate in this document. Mathematical model
in this definition is equivalent to mathematical systems model involving
multi-processes.
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5. Process Equation -- The mathematical representation of a physical
phenomenon or process for a system. For example, solute transport in a
saturated system may be described by the solution of the advective
dispersion equation. A process equation in this definition is equivalent
to a multi-process equation involving several different phenomena.
6. Analytical Models -- A computer program written to solve a particular
process equation. For example, the AT123D model (Yeh, 1981) is a computer
program written to analytically solve the advective dispersion transport
equation for a variety of simple initial and boundary conditions.
7. Numerical Model -- A computer program written to solve a particular process
equation for which no general solution exists. For example, the CFEST
model (Gupta et a!., 1986) is a computer program, part of which is written
to numerically solve the advective dispersion transport equation for a
variety of simple or complex initial and boundary conditions.
The relationship between the above terms may be thought of as follows. A
mathematical model consists of two aspects: a process equation and a solution
technique to solve the process equation. 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 equation numerically with a computer program. In the context of
this document, mathematical model refers to all three solution techniques
(analytical solution, analytical model, numerical model) 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.
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The term analytical or numerical code typically refers to the computer
program (the set of computer instructions written in a programming language and
acted on by a computer), whereas an analytical or numerical model is the
implementation of the code with a specific data set (either site specific or
generic) to test the simulated representation of the system against observed or
measured behavior. In this document the analytical solutions referenced in
Table 5-1 and the analytical and numerical codes summarized in Appendix A are
all included in the general category of mathematical models.
8. Objectives Criteria -- Criteria related to the level of modeling detail
required to meet the objectives of the study. In the context of model
selection, objectives are classified into two categories: perform a
screening or generic study where simple analytical solutions/models would
most likely be used, or perform a detailed study using numerical models.
9. Technical Criteria -- Criteria related to a code's ability to simulate the
transport and fate phenomena of importance. These criteria are based on
the physical, chemical, and biological characteristics of the site and the
contaminant of interest.
10. Implementation Criteria -- Criteria related to the ease with which a code
can be obtained and its acceptability demonstrated. Relevant factors
include sources of the code, documentation, verification, and validation.
11. Screening and Detailed Assessment -- The types of modeling analysis that
are described in this document may be very broadly categorized as screening
or detailed (site specific) exposure assessment studies. Obviously, these
categories cannot be distinguished by definitive criteria but rather there
is more of a "gray" area between the two. We have chosen to use the term
screening analysis to represent studies where limited calibration and
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validation data are available and the uncertainty associated with the
predicted results Is comparatively large, somewhere In the nature of an
order of magnitude. The term detailed or site-specific analysis is used to
represent studies where a smaller uncertainty in the predicted results is
necessary, on the order of a factor of two to ten. Calibration and
validation data are necessary in order to reduce the uncertainty inherent
in the results and also attempt to quantify the bounds associated with the
uncertainty through the validation phase and sensitivity studies. The
models used for a screening analysis are generally easier to use but make
certain restrictive assumptions. The more complex site-specific assessment
models are more difficult to use and generally do not make as many
restrictive assumptions; the input data requirements, however, may be
substantially greater.
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.)« f
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4. GENERAL GUIDELINES AND PRINCIPLES
OF MODEL SELECTION CRITERIA
This chapter discusses some of the general guidelines and principles
related to model selection criteria. The first section discusses the steps that
should be taken in the overall modeling process. The second section provides a
general discussion of the model selection process and discusses the three
principle criteria used to select a model: objectives criteria, technical
criteria, and implementation criteria. The last three sections discuss some
important issues related to model selection: model selection vs model
application familiarity with a model, and model reliability.
4.1. OVERVIEW: MODELING PROCESS
The selection of models for the analysis of exposure to contaminants
involves factors addressing a number of issues, not all of which are amenable to
expression in specific criteria. Certain judgmental factors are better suited
to statement in the form of general guidelines and principles. Many of these
arise from the nature of the overall modeling process of which model selection
is but a single step. Five general steps may be identified in the modeling
process. Although model selection is meant to be the primary emphasis of this
report, the different steps influence each other and need to be described. The
five general steps are:
1. Problem Characterization -- The analyst clearly identifies the exposure
assessment study objectives and constraints.
2. Site Characterization -- The analyst reviews available data on the site,
develops a conceptual model identifying processes of interest, performs a
screening analysis; if a modeling study is necessary, the analyst then
identifies data needs and fill those needs. The results of the site
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characterization will determine technical specifications for model
selection by identifying the single processes at the site.
3. Model Selection Criteria -- The analyst matches the objective, technical,
and implementation criteria to available models and selects the most
appropriate model(s).
4. Code Installation -- If the model selected is a computer code, the code is
installed on the computer system and tested to document proper installation
and ability to reproduce accepted solutions to standard problems.
5. Model Application -- The verified model uses site characterization data as
input for the exposure assessment simulation.
These five general steps are not the model selection criteria but rather
the overall process by which a problem is identified and a model selected to
perform an exposure assessment study. Model selection criteria is listed as the
third step in this process. The two previous steps, problem characterization
and site characterization, are crucial in the selection of an appropriate
model(s). While the steps can be considered sequential in nature, it is
important to recognize interactions and feedback mechanisms between them. For
instance, knowledge of the model selection criteria is important to assure that
site characterization is adequate and properly formatted. An understanding of
code installation procedures is required for proper scheduling and resource
allocation. Familiarity of candidate models is needed to assure that site
characterization provides necessary input data.
Problem characterization is important because a wide variety of models and
modeling approaches are available. Different modeling techniques are suitable
for different objectives and physical problems. The exposure assessment
objective must define what the goal of the analysis should be and must also be
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defined in a manner consistent with known project constraints such as schedule,
budget, and other resources.
Site characterization is an important step that needs more description
because the conceptualization of the physical system, whether it is a specific
site or a generic problem, will obviously influence any additional steps. If
the objectives of the exposure assessment are to evaluate an existing
contamination problem, then this step should include the availability of field
measurements in the specific study area. Depending on the problem, the field
measurements may include geologic structure data, pump tests, recharge/discharge
data, elevations of surface water bodies, contaminant sampling, and source
characterization. Field measurements may identify the extent of the
contamination problem and whether or not the concentration levels are above some
regulatory or dangerous level. In addition, if these initial studies identify a
contamination problem and a modeling study is to be performed, then the field
measurements will be used in the selection of an appropriate model and for model
calibration.
Model selection criteria (the primary goal of this report) is entirely
dependent on the first two steps. This step is covered in more detail in the
rest of this chapter and in Chapter 4.0.
Code installation only applies when the model chosen in the third step is a
computer code. When a code is first obtained and installed on a specific
computer system, it is essential that the model be tested to verify that it is
working correctly and can reproduce suitable example problems. Various computer
systems and the necessary model software may have a variety of differences, some
distinct and others more subtle. These differences may require modifications to
an acquired code (e.g., double precision arithmetic or changing output formats)
4-3
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on different computer systems. Verification assures that modifications have not
changed model results significantly. This step should be performed by the
person doing the actual model analysis.
Model application relates the use of a model in an attempt to answer the
questions to the use of a model in an attempt to answer the questions defined in
the objectives. Depending on the objectives of the analysis, this step may
consist of several parts including calibration, validation, and application to
evaluate different conditions or scenarios.
4.2. OVERVIEW: MODEL SELECTION CRITERIA
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.
4.2.1. Objectives Criteria
The first level of consideration when selecting a mathematical model is
related to the objectives of the study. Based on the objectives, the analyst
can limit the choice to either simple analytical solutions/models or to more
complex numerical models.
The objectives criteria refer to the level of modeling detail required to
meet the objectives of the study. There are many different objectives of
modeling studies, however, in the context of model selection, all objectives can
be 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 purpose is to make a preliminary
screening of a site or to make a general comparison between several sites. A
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screening assessment can also be generic (i.e., not site specific) where the
objective is to compare several hypothetical cases or designs.
A screening study may be appropriate when sufficient data is not available
to properly characterize the site. Although lack of data is no excuse for not
modeling a site correctly, often there are times when a screening comparison of
cases/sites can be quite helpful in analyzing a problem. A screening study can
help direct the data collection effort at a site. For generic studies, it is
most often not possible to select a detailed data set which is representative of
all the hypothetical sites/cases being simulated. By virtue of the fact that it
is a generic study, the data base is typically quite simple such that it is
representative of several sites/cases.
A detailed study, on the other hand, is used when the objective is to make
a detailed assessment of the environmental impact, performance, or safety of a
specific site. This type of study requires detailed data for a specific site or
for a number of sites, and the results of the study are typically used to make
specific decisions regarding the site or sites. For example, a detailed study
might involve predicting concentration of a particular contaminant at a specific
aquifer location. The results of the study would be used by decision makers to
determine whether remedial action is needed at the site.
Screening and detailed studies usually require the use of screening and
detailed models, respectively. A screening model would typically be ,an
analytical solution or model with minimal data requirements. Usually these
analytical solutions/models are used for special, simplified physical conditions
*
that represent the behavior of particular physical processes when isolated from
other effects. Compared to numerical models, screening models require less
data, are easier to implement, and are less expensive to run.
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Detailed models are typically numerical models which have more extensive
data requirements, are more difficult to implement, and cost more to operate
(take longer to set up, calibrate, and evaluate results and require more
computer time) than analytical models/solutions. Detailed models usually have
more realistic initial and boundary conditions and possibly more time-dependent
inputs and outputs than screening models.
Based on the objectives of the study (screening or detailed), the analyst
or modeler will select either a screening or a detailed model. The specific
model to be used will be selected based on the technical selection criteria
discussed below.
4.2.2. 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. These criteria are based on the physical,
chemical, and biological characteristics of the site and the contaminant of
interest. The characteristics of the site and the processes that need to be
simulated are determined from the hydrogeologic and contaminant data and the
conceptual model of the site.
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.
4.2.2.1. Transport and Transformation Processes -- 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 represent the site. The
transport process is the physical migration process controlled by adsorption,
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attenuation, diffusion, dispersion, volatilization, and density effects related
to temperature and/or concentration. The transformation processes that effect
contaminant migration can be divided into chemical and biological processes.
Chemical processes include complexation, hydrolysis, chemical degradation, and
oxidation-reduction. Biological processes include biodegradation, biological
transformation, metabolism, and respiration. The mathematical model selected
must be able to simulate all the relevant physical processes occurring within
the specified environmental setting.
4.2.2.2. Domain Configuration -- The second category of the technical criteria
relates to the ability of the model to represent the domain configuration of the
geohydrologic system. The relevant parameters related to geometry include:
t Water table or confined flow system
t Porous media or fracture flow
t Steady-state or transient flow
t Single- or multi-phase flow
Constant, flux, or no-flow boundary conditions
Single- or multi-layer system
Constant or variable thickness layers
One-, two-, or three-dimensional system
Source configuration
Constituents
Point, line, or area source
Initial value, constant, or variable source
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
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numerical models are most appropriate. If simplifying the site geometry can be
defended on a geotechnical basis, then the use of a simpler analytical
model/solution may be justified.
Analogously, the natural dimension of the system can be reduced if at least
one dimension can be integrated to a single value. For example, if a
contaminant is distributed evenly in a single aquifer in the vertical direction,
the level of contamination can be expressed as a single value in a
two-dimensional transport model of the horizontal plane (x-y). In effect, the
contaminant mass in the vertical (z) dimension is integrated into a single
representative value.
4.2.2.3. Fluidfs) and Media Properties -- The third category of technical
criteria corresponds to the ability of the mathematical model to represent the
spatial variability of fluid(s) and media properties of the geohydrologic site.
The relevant issue in this category is whether the site can be considered
homogeneous or heterogeneous with regard to hydraulic conductivity, recharge,
porosity, and specific storage. If homogeneous conditions can be assumed, it is
often possible to simulate the site with an analytical solution/model.
Heterogeneous conditions almost always require a numerical model. For example,
an aquifer may consist of several geologic material types all having different
hydraulic conductivities. Proper simulation of the spatially variable hydraulic
conductivity would require the use of a numerical model.
As stated above, the objectives criteria will direct the analyst to select
either a screening or a detailed model. Once the level of model has been
decided, the technical criteria will direct the analyst to the specific type of
model needed to properly simulate the transport and transformation aspects of
the environmental setting.
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4.2.3. Implementation Criteria
The third level of consideration when selecting a mathematical model is
related to the implementation criteria., Implementation criteria are those
criteria dependent on the ease with which a model.can be obtained and its
acceptability demonstrated. Whereas the technical criteria identify models
capable of simulating the relevant phenomena within the specified environmental
setting, the implementation criteria identify documentation, verification,
validation requirements, and ease of use so that the model selected provides
accurate, meaningful results.
Relevant questions to be considered concerning the implementation of a
particular model include: 1) what is the source of the model and how easy is it
to obtain (i.e., is it a proprietary model); 2) are documentation and user's
manuals available for the model and, if so, are they well written and easy to
use; 3) has the model been verified: against analytical solutions and other
models and, if so, are the test cases available so the analyst can test the
model on his computer system; and.5) has the model been validated against field
data?
The technical criteria can be used to narrow the model selection to a few
codes in the same general category. The implementation criteria can then be used
to further narrow the decision to one or several of the technically acceptable
models. >
4.2.4. Other Factors Affecting Model Selection
Other general factors related to model selection which should never
override the technical or implementation criteria include data availability,
schedule, budget, staff and equipment resources, and level of complexity of
system(s) under study. Schedule and budget constraints refer to the amount of
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time and money available for the assessment. If both analytical and numerical
models meet the selection criteria, .time and cost may be considered factors for
electing to use an analytical approach. Analytical solutions/models are easier
to install on a computer system, are more quickly mastered, and are dependent on
more easily-obtainable input data than numerical models. The time factor will
be of increased importance if staff are not familiar with any of the appropriate
models. In this case, schedule considerations may dictate selection of a
different modeling team; one experienced with the appropriate models.
Staff resources are also a major consideration in modeling. Regardless of
the quality of the model selected, the expertise of the analyst has a major
impact on model results. This can also impact model selection when the analyst
is familiar with one or more of the appropriate models. In the simplest case,
if the analyst has direct experience with an acceptable model, then that model
is preferred. Similarly, if the analyst has experience with a specific type of
model (e.g., finite element vs finite difference), one of that type should be
selected. In certain cases, familiarity with a model more complex than required
may dictate use of that model rather than a simpler one since there
will be no loss of resolution and the added staff experience would compensate
for time and cost differences. In no case, however, should familiarity with a
model dictate its selection when it does not satisfy the technical and
implementation criteria. In practice, many models are rightfully applied to
situations which are not fully compatible with the model's design
characteristics. However, justification of the choice should indicate the
correctness of the model's use.
Hardware requirements are similar to staff requirements. The more complex
mathematical models require more powerful computers with larger mass storage
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devices and extra peripheral equipment. If both analytical and numerical models
meet the selection criteria, available hardware may dictate the use of the
simpler analytical models. If a sophisticated model is required and adequate
equipment is not available, alternate means of conducting the modeling must be
found. Equipment constraints cannot be used to select a model other than those
meeting the selection criteria.
As noted in the preceding paragraphs, subjective factors such as
objectives, schedule, budget, and staff and equipment may be used to select one
model from a group of models all found to meet selection criteria. Alternately,
subjective factors may dictate use of a different modeling team to improve the
quality of results obtained from a given model. Under no circumstances,
however, shall subjective factors be used to select a model which otherwise
fails the selection criteria.
In summary, the first step of the model selection process is to define the
objectives of the study. If the objective is to perform a screening-level or
generic type study, a simple analytical solution/model or a simple numerical
model should be selected. If the objective is to perform a detail-level study,
a more complex numerical model should be selected unless the study area is such
that it can be simulated on a technically sound basis with a simpler model.
The decision as to which category of models or type of model can accurately
simulate a site or perform an assessment is based on the
technical criteria. The technical criteria are based on a model's ability to
correctly simulate the transport and transformation processes, domain
configuration, and fluids and media properties of a site. Depending on the
objective of the study, the technical criteria can be used to narrow the
selection of either screening or detailed models.
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Once the appropriate models have been selected on the basis of technical
criteria, the list can be further narrowed by use of the implementation
criteria. The implementation criteria relate to factors such as availability of
models, documentation, verification, and validation.
If a list of models still remain after satisfying the objectives,
technical, and implementation criteria, the final decision should be based on
such subjective factors as schedule, budget, and staff and equipment resources.
Under no circumstances, however, should subjective factors be used to select a
model which otherwise fails the selection criteria.
4.3. MODEL SELECTION VS MODEL APPLICATION
While this document is concerned with the issue of model selection, it is
important to realize that in most cases the biggest differences in model
predictions are a result of how the model is applied, not which model was
selected. For most modeling studies, there are typically a number of models
which satisfy the objectives, technical, and implementation criteria. If all of
these models are applied to the same data set, they will all obtain virtually
the same results. Differences may arise based on how the initial and
boundary conditions and grid (numerical models) are specified in the model, but
in all cases these differences should be insignificant.
The big difference in modeling assessments results from how the model is
applied, not from which model is selected. The difference in how the model is
applied stems from the fact that different modelers interpret the same data set
differently. For example, if you gave ten different modelers the same raw data
set and the same model code, they would probably develop ten different models of
the site based on ten different interpretations of the data. The differences in
the models might be small in many cases, but it is not unreasonable.that large
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differences (i.e., completely different ground-water flow directions or
contaminant concentrations) could occur; especially for large, complex data sets
requiring a detailed modeling approach. If, on the other hand, you gave ten
different modelers the same model input data set (i.e., the inputs are defined
for them, not a raw data set) and ten different models, with which they were
very familiar, they should all arrive at about the same results.
Where the major differences occur in any modeling study is in the
interpretation of the raw data and in the conceptualization of the study area.
Since it is impossible to know everything about a ground-water flow/contaminant
transport system, raw data are always subject to different interpretation. As a
result of this basic fact, it is important to remember that the major
differences in modeling studies will probably result from differences in the
application of the model(s), not from the selection of the specific model to
use.
4.4. FAMILIARITY WITH A MODEL
It is important to emphasize the importance of familiarity with a model,
especially with regard to the more complex models. Detailed models, especially
numerical models, can be quite complex with a large number of input variables,
switches, outputs, and simulation/computer related requirements. Often it
requires months or even years of experience and several studies to fully
comprehend all the aspects of a model. Because of this, it is strongly advised
that an analyst select a model with which he/she is familiar if it possesses all
the selection criteria.
Many people feel that a more complex model should not be selected if a
simpler model can do the job. They argue that the complex model requires too
much data, will take longer to implement, and will cost more to run on the
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computer than the simpler model. This may not be the case at all. Most complex
codes can be run in a less complex mode which requires less data and
implementation time. Even if computer costs are a little higher, the costs are
almost always far offset by the savings in labor costs because the analyst is
familiar with the model and can use it far more efficiently.
When dealing with the more sophisticated numerical models, only analysts
familiar with the selected model should perform the assessment. If experienced
persons are not available within the group, expert help from outside the group
should be obtained. Simpler models can be used by analysts with little or no
specific experience with the model. However, the work should be reviewed by a
more experienced user to ensure that the model was set up and the results were
interpreted correctly.
4.5. MODEL RELIABILITY
Because a natural ground-water system is very complex and heterogeneous, a
model will never form an exact replica of the system. Because every model will
inevitably be a simplification of the actual system, mathematical models should
not be used to make "exact" predictions of ground-water flow or contaminant
concentrations. Ideally, models should only be used to make comparisons between
cases, whether site specific or generic.
When developing a model of a study area, simplifications must be made at
every step in the process. The simplifications are a consequence of limitations
in the acquisition of field data, limitations in developing a conceptual model
of the systems, limitations in properly representing the data and physical
processes in the model, and limitations in predictive mathematical theory for
some physical processes. Because of all the limitations and simplifications, it
is often difficult to place a great deal of confidence in predictive model
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results (I.e., prediction of a contaminant concentration at a well). When
comparing various cases or scenarios with a model, however, all the cases are
subject to the same limitations and simplifications. Therefore, model results
are more reliable in a situation where one case or alternative is compared to
another.
Another method by which model results can be made more useful, is to perform
a sensitivity analysis. A sensitivity analysis is an analysis that quantifies
the change in a specific performance assessment measure (i.e., ground-water
velocity or concentration) resulting from a change in a specific input parameter
or set of parameters to the model. For example, the model could be used to
predict a range of ground-water velocities based on a range of hydraulic
conductivities and gradients thought to be representative of the aquifer. A
sensitivity analysis is a means of dealing with the inherent uncertainty which
exists in the measurement of many hydrogeologic and contaminant transport
parameters.
Although the many limitations and simplifications make it difficult to
place a lot of confidence in model predictions, the use of models to make such
predictions can often be justified in that, in most cases, a model is the only
means or the best means available to make the prediction. For sites with
complex hydrogeologic conditions, the use of a model is often the only means of
integrating all the data into a meaningful package. In all cases, no matter how
simple the site or how extensive the input data, model output or predictions
always need careful evaluation because they are generally only as accurate as
the model input data and the knowledge of the system upon which the model is
based. Model results, whether "exact" predictions, a comparative analysis or a
sensitivity run should always be considered as a guide to the probable system
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response. Despite their limitations, when properly applied, models are often
the best tools available for assistance in making decisions on ground-water flow
and contaminant transport problems.
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5. MODEL SELECTION DECISION PROCESS
. -- ,:.. i
This chapter discusses the technical criteria used to select the
appropriate mathematical model for a specific application. The first section
provides a detailed discussion of the technical criteria and the errors
associated with selecting one option over another. The second section briefly
discusses the model selection process from the point of view of a reviewer from
a regulatory agency. The last section groups the available models into
categories and provides the framework for selecting the appropriate model or
category of models based on the response to the technical criteria.
5.1. TECHNICAL CRITERIA USED FOR MODEL SELECTION
The technical criteria used to select the appropriate performance
assessment mathematical model(s) for ground-water applications are outlined in
Figure 5-1.
The first task in any contaminant transport analysis is to simulate the
ground-water flow. The ground-water flow can be simulated separately from the
contaminant transport, or both can be simulated with one model. However, each
approach requires sequential simulations; first the ground-water flow followed
by the contaminant transport. For this reason, Figure 5-1 is divided into two
sections. The first section addresses the technical decisions that need to be
made to select the appropriate ground-water flow model (or flow portion of a
combined ground-water flow and contaminant transport model), while the second
section addresses the technical decisions that need to be made to select the
appropriate contaminant transport model.
The decisions that need to be made when selecting a ground-water
flow/contaminant transport model are discussed in detail below. Guidance is
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Ground-Water Flow
Hater Table or Confined Aquifer? I
Porous Media or Fracture Flow?
I 1. 2, or 3 Dimensional? I
| Single Phase or Multi-Phase
Homogeneous or Heterogeneous?
Hydraulic Conductivity. Recharge. Porositv. Specific Storage
I Single Laver or Multi-Layer? I
I Constant or Variable Thickness Layers? I
I Steady-State or Transient 1
Select the Appropriate Analytical or
Numerical Ground-Water Flow Code
or
Continue with the Decision Tree and Select a Combined
Ground-Water Flow and Contaminant Transport Model
Figure 5-1. Code selection decision tree.
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I Contaminant Transport
Point. Line, or Area! Source?")
I Initial Value or Constant Source?
I 1, 2. or 3 Dimensional? I
Dispersion?
Adsorption?
« Temporal Variability
Spatial \
ariability
Degradation?
1st Order/2nd Order
Radioactive Decay
Density Effects?
t Thermal and/or Concentration
Select the Appropriate Analytical or
Numerical Contaminant Transport Code
Figure 5-1. (continued)
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provided for making each decision and some discussion is provided regarding the
errors associated with making an incorrect choice (i.e., selecting a model that
does not contain the desired feature); for example, the use of a porous media
model to simulate fracture flow.
In all cases, the impact of an incorrect decision or the use of an
L " '=-..- ' -
incorrect feature of a model is difficult to quantify. For many cases, the
errors are difficult to quantify because they are site specific; they depend on
the actual site data. For example, the error associated with using a
homogeneous hydraulic conductivity distribution where a heterogeneous
distribution should have been used can only be quantified on a site-by-site
basis. In other cases, the errors are difficult to quantify even for a
site-specific application because the necessary parameters are unknown or cannot
be measured. An example where it is difficult to quantify the associated error
would be using a model that uses a uniform value of recharge over a study area
versus one that uses a recharge distribution because recharge is difficult to
measure in the field. '
Many of the decisions that need to be made when selecting an appropriate
model can be made on the basis of past experience. Although this document
provides insight regarding decisions based on experience, there is really only
one way to gain the knowledge that comes from experience and that is to get
involved in modeling studies and in the selection of the appropriate models for
those studies.
Several questions need to be answered when selecting an appropriate ground-
water flow model. Such questions deal primarily with the flow media, but some
questions address such aspects as steady-state or transient flow and whether the
fluid is single or multi-phase. The following paragraphs list the questions
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needing to be answered when selecting an appropriate flow model with a brief
explanation of each.
1. Are you simulating a water table (i.e., unconfined) or a confined aquifer,
or a combination of both (i.e., conditions change spatially)?
t
The analyst needs to select a model which can simulate the type of aquifer
conditions which exist at the site, either water table, confined, or a
spatial combination of both. Most ground-water flow models simulate
confined aquifer conditions, whereas not all models can simulate water
table conditions or a combination of both. The reason for this is that the
solution for the water table case is more complicated and requires more
time to solve. As a result, it is not uncommon that a confined model will
be used to solve a problem with water table or mixed water table and
confined conditions.
The problem associated with using a confined model for unconfined aquifer
conditions is that the aquifer thickness is not allowed to vary. As a
result, the transmissivity (defined as the aquifer thickness times the
hydraulic conductivity) remains constant when it should be adjusting with
the fluctuations in the water table. The error associated with using a
confined model for unconfined aquifer conditions is small as long as the
fluctuations in the water table are small compared to the total thickness
of the aquifer. Small fluctuations are usually defined as where the water
table elevation changes by less than 10% of the total aquifer thickness.
This criterion is valid under most circumstances. Typically, the criterion
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is violated when there are large stresses on the system such as pumping or
recharge, or when the aquifer is very thin (in general, less than 25-ft
thick).
2. Is the ground-water flow through porous media, fractures, or a combination
of both?
The analyst needs to select a model which can simulate the types of media
which exist at the site, either porous media, fractured media, or a
combination of both. Most ground-water flow models simulate porous media.
Although few models are designed to simulate fracture flow, most numerical
models can handle soils with different porosity (i.e., dual porosity). As
a result, to date most fracture flow systems are approximated by porous
media models. The validity of this assumption is dependent on two factors:
1) how highly fractured are the media, and 2) what is the scale (size) of
the fracture system. In this approximation, it is generally assumed that a
highly fractured system can be thought of as a rock that is so highly
fractured that it resembles a continuum porous medium. A quantitative
definition of a highly fractured system does not exist. However, for this
approximation, highly fractured could possibly be considered as fractured
rock with an effective porosity resembling the effective porosity of a
porous media which is typically on the order of 10 to 25%.
The ability to simulate a fractured system with a porous media model is
also scale dependent. The larger the scale of a fractured system, the more
the flow pattern through fractures represents flow in porous media. As the
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scale gets smaller and smaller, It eventually gets down to simulating the
flow in a single fracture which cannot be simulated with a porous media
model.
In some instances, a finite-element model can be used to simulate flow in
faults, where a fault is defined as a large fracture. The fault can have a
higher or lower permeability than the surrounding rock depending on the
nature of the rubble in the fault zone. In this case, the fault is
simulated as a series of long, narrow elements in the model and the
hydrologic properties (hydraulic conductivity, porosity, etc.) of those
elements are set accordingly.
3. Is it necessary to simulate three-dimensional flow or can the
dimensionality be reduced without losing a significant amount of accuracy?
The analyst needs to select a model which can simulate the dimensionality
needed to properly represent the site, either one-, two-, or
three-dimensional.
In general, models should be selected in three dimensions unless it can be
shown that the degree of media homogeneity and spatial symmetry of the
aquifer are such that they justify the selection of a lower dimensional
model. If, for example, the problem consists of a single aquifer with
uniform hydraulic properties and concentrations in the vertical (z)
dimension, then a two-dimensional x-y simulation is justified. If the
hydraulic properties and concentrations are also uniform in one of the two
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horizontal dimensions (x or y in addition to z), then one is justified in
making a one-dimensional simulation.
Lower dimensional simulations are not always made because they are
justified based on the homogeneity or spatial symmetry of the data. In
many instances, a lower dimensional simulation is made because the data are
not available to perform a three- or two-dimensional simulation, or even to
know if the higher dimensional simulation is required. The use of a
three-dimensional model without adequately detailed site characterization
data can easily lead to incorrect results.
Even though a lower dimensional simulation is performed where a higher
level model was warranted, the results can still be quite useful in
assessing a particular problem. The lower dimensional model can be used as
a screening-level model to make numerous, low-cost runs which, in many
cases, can provide valuable insight into a problem.
It is important to remember that performing a complete three-dimensional
analysis does not eliminate uncertainty in the results. It is virtually
impossible to completely characterize a ground-water flow/contaminant
transport system, and no matter how well the system is characterized, the
model, whether one-, two-, or three-dimensional, is always a simplified
representation of the real system. Three-dimensional model results, as
well as one- and two-dimensional model results, need to be analyzed very
carefully to determine if they make sense.
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The dimensions of the ground-water flow model can be dictated by the needs
of the contaminant transport model. For example, if the flow is occurring
in a single homogeneous aquifer of constant thickness, a two-dimensional
x-y model should be selected. However, if the contaminant plume is not
uniformly distributed over the thickness of the aquifer or if a remedial
action requires pumping from a screened interval less than the total
aquifer thickness, then a three-dimensional transport model is required.
If a three-dimensional transport model is required, then the flow should
be simulated in three dimensions. It is possible to simulate the ground-
water flow with a one-dimensional model and then simulate the contaminant
transport with a three-dimensional model, but in this case the transport
simulation will not truly be a three-dimensional simulation since the flow
vector is in only one direction.
4. Are you simulating a single-phase (i.e., water) or a multi-phase (i..e.,
water and an insoluble contaminant) flow system?
The analyst needs to select a model which can simulate the type of flow
system which exists at the site, either single-phase or a multi-phase
system.
Very few mathematical models are available today which can be practically
applied to a multi-phase ground-water flow problem. Much of the original
research in this area was performed in the petroleum industry for the
analysis of three-phase flow of oil, gas, and water. The petroleum
industry work has been adopted in the ground-water industry to study
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multi-phase flow between water and contaminants, but the ground-water
efforts are in the infant stages.
Host contaminant transport analyses assume the contaminant is soluble in
water. This single-phase approach is accurate enough for almost all
practical purposes. For the case where the contaminant is immiscible in
water, the single-phase approach does not apply. If a single-phase model
with proper boundary conditions such as an area source of continuous
release is applied to a multi-phase problem, it can provide some insight
into the extent of plume migration for a relatively large source of the
immiscible contaminant phase which would float on the aquifer's surface or
sink to the bottom of the aquifer. Significant inaccuracies are likely to
arise if the contaminant travels with ground water along the flow line.
5. Can the system be simulated with uniform (homogeneous) or spatially
variable (heterogeneous) values of hydraulic conductivity, porosity,
recharge, and/or specific storage?
Homogeneous in this sense refers to spatially uniform values in the x
direction or the x-y plane. Some mathematical models, particularly
analytical solutions or simple numerical codes, only simulate a single
value of a hydraulic property spatially. For example, the hydraulic
conductivity or recharge may have to be uniform over the entire model
region. In a heterogeneous model, on the other hand, many of the
parameters (particularly the hydraulic conductivity and the recharge) can
be specified on a node-by-node (finite difference) or an element-by-element
(finite element) basis. Thus, it is possible to represent a spatial
distribution of certain parameters over the study area.
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Quantifying the errors associated with using a single average value versus
using the actual distribution is difficult and very site specific. In a
general sense, many of the criteria discussed above apply here. With
regard to hydraulic conductivity, if all the spatial values are within a
factor of 10, using a single average value is probably justified. If the
spatial values of recharge, porosity, and storage do not vary by more than
about 25%, using a single average value is probably justified. In most
modeling studies, the recharge, porosity, and storage are not well enough
known to define a spatial distribution. For site-specific, detailed
studies, if spatially-variable values are required but are not available,
additional data should be obtained. However, model results using
spatially-averaged values can still be valid and quite helpful for
comparing alternatives, for conducting screening-level studies, for
identifying data deficiencies, and/or for gaining some general insight into
the nature of a problem.
As stated above, the error associated with using an average value versus a
spatial distribution is very site specific. For example, the average
ground-water velocity over a model region could be the same if the region
is simulated ,with one average value of hydraulic conductivity or if a
spatial distribution is used with a range of high and low values. In
another similar case, the low values of hydraulic conductivity could be
distributed such that they control the flow, and the velocities for the two
cases could be very different.
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6. How many hydrogeologic layers are to be simulated?
The analyst needs to select a model which can simulate either single or
multiple hydrogeologic layers/aquifers depending on the conditions which
exist at the site.
Some mathematical models, particularly analytical solutions, can only
simulate a single aquifer. The single-aquifer approach is valid for cases
. ' ' " - - ,= ' ' » J ' L ' . ' ' ' S ,
where the major portion of the ground-water flow and contaminant transport
, : ' *" ' !" "'' 5 ' .>>' ' ' ' '' "*
occurs in a single layer of a multi-layered system, or where the hydraulic
properties of all the layers of a multi-layered system are very similar.
If the hydraulic properties of the various layers are significantly
different and contaminants are being transported in more than one layer,
then a multi-layered model should definitely be applied.
'. ' - . . , - i ' "' '.-'',-' ^'- "i T ' '..' ' '' ' !
Significant differences between geologic layers are difficult to define.
For hydraulic conductivities, a significant difference might be anything
greater than a factor of 10. Hydraulic gradients and porosity should at a
minimum be within a factor of 25%, and flow directions should be
essentially the same (both horizontally and vertically). For contaminant
transport considerations, the layers should have similar compositions so
their sorption properties can accurately be simulated with one value.
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7. Do the hydrogeologlc layers vary in thickness spatially?
The analyst needs to select a model which can simulate constant or variable
thickness hydrogeologic layers depending on the conditions which exist at
the site.
Some mathematical models, particularly analytical solutions, can only
simulate constant or uniform thickness within a layer or layers. If the
thickness of a layer(s) does not change significantly spatially, the
uniform assumption is valid. If the thickness changes by more than about
10% of the average thickness, a model should be used that can simulate
spatially-variable thickness.
The principle problem associated with not simulating variable thickness is
that the transmissivity distribution in the model will be incorrect
(transmissivity = hydraulic conductivity x aquifer thickness). Using the
wrong transmissivity distribution could have a significant impact on the
model results depending on the specifics of the problem being simulated.
One of the few ways to determine the magnitude of the impact is to run a
sensitivity analysis with site-specific data. In general, changing
thicknesses are analogous to changing diameters in pipe flow. Velocities
will increase or decrease accordingly, thus affecting travel-time
predictions.
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8. Is the hydrologlc system in a steady-state condition or do water levels
fluctuate with time (transient condition)?
The analyst needs to select a model which can simulate the type of
hydrologic condition which exists at the site, either steady state or
transient.
Steady-state flow is defined as the condition when the magnitude and
direction of the flow velocity (as defined by the hydraulic conductivity
and hydraulic gradient) are constant with time at any point in the flow
field. Transient flow (unsteady flow) is when the magnitude or direction
of the flow velocity changes with time at any point in a flow field (Freeze
and Cherry, 1979, p.49). The application of a steady-state model or
approach .is technically valid only in the somewhat unrealistic case where
the water table maintains the same position for some extended period of
time (throughout the entire simulation period). In most actual cases,
variations in recharge and discharge introduce transient effects on the
flow system. Therefore, technically speaking, a transient model or
approach should always be applied. However, when applying models, the
general rule that is followed is that if the fluctuations in the water
table are small in comparison with the total vertical thickness of the
aquifer (or hydrologic flow system), and if the relative configuration of
the water table remains the same throughout the cycle of the fluctuations
(i.e., the high and low points remain highest and lowest, respectively),
then the transient system can be simulated as a steady-state system with
the water table fixed at its mean position. As was the case for confined
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versus unconflned flow, small fluctuations 1n the water table are generally
defined as less than about 10% of the total thickness of the aquifer (or
flow system).
Transient simulations require much more data and are more difficult to
implement than steady-state simulations. Typically, the additional data
(time series of water-level measurements, recharge, discharge, etc.) are
not available and one is forced to make a steady-state approximation. In
many instances the steady-state approach can yield valuable insight and
information provided that the assumptions used are conservative and that
the limitations of the approach are fully understood.
An approach that can be used to approximate a fully transient simulation
but that requires less data and is easier to implement is a series of
steady-state solutions. In this approach a new potential or head
distribution is solved for whenever a significant stress is imposed on the
system. A significant stress can be a pumping well(s) being turned on for
a pump-and-treat remedial action, or a cyclic recharge event where it is
known, for example, that the majority of the recharge occurs in the winter
months.
The errors associated with using a steady-state approximation of a
transient system are difficult to quantify because they depend on each
specific case. For example, if a water table exhibits very consistent and
small fluctuations over a yearly cycle due to a consistent pumping and
recharge pattern (i.e., pumping occurs between April and September for
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irrigation and natural recharge 1s large 1n the winter and small in the
summer), a steady-state approximation may be valid. If on the other hand,
the pumping schedule is sporadic and it significantly alters hydraulic
gradients and directions of flow, and the recharge is variable from season
to season and year to year, a transient simulation should be performed.
After these questions (criteria) have been addressed, in most cases the
analyst will find that there are several ground-water flow models which meet the
desired criteria. At this point the analyst can either select a ground-water
flow model and then continue the selection process to choose a compatible (but
separate) contaminant transport model, or the user can continue the process to
select a combined flow and transport model. It is quite common to find a fairly
sophisticated flow model linked with a simpler transport model since the
transport model parameters are generally less well known.
The decisions to be made when selecting a contaminant transport model are
discussed in more detail below. Some guidance is provided to help in making the
decision and some discussion is provided regarding the errors associated with
incorrectly using the model or feature(s) of the model.
The errors associated with incorrectly selecting a transport model or
feature of a model are difficult to quantify. Some guidance is given below, but
in many cases these errors are site specific and, therefore, cannot be
quantified in general terms. Following are the questions to be answered when
selecting a contaminant transport model.
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1. 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?
The analyst needs to select a model which can simulate the type(s) of
source(s) that exists at the site, either point, line, or area source.
A point source is characterized by contaminants entering the ground water
at a single location such as a pipe outflow or injection well. A line
source is characterized by contaminants entering the ground water along a
line as in the case of leachate emanating from the bottom of a trench. An
area! source or nonpoint source is characterized by contaminants entering
the ground water over an area as in the case of leachate emanating from a
waste lagoon or an agricultural field. A volume source releases
contaminants in a form of volume in ground water.
A point source can be simulated with either a one-, two-, or
three-dimensional mathematical model whereas a line or area! source should
be simulated with a higher dimensional model. Most two- or
three-dimensional models can simulate point, line, and area! sources.
Three-dimensional models are appropriate for simulating a volume source.
All one-dime;nsional models, particularly analytical solutions, simulate
point sources. Line or area sources can be simulated with one-dimensional
models by assuming that the contaminant concentration is uniform except in
the dimension simulated. Because the analyst typically lacks the necessary
data to perform conceptually correct transport simulations, it is quite
common to use a one-dimensional transport model with averaged values of
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concentration and velocity to simulate line or areal sources. This
approach is discussed in more detail below in the section on
dimensionality.
Typically, when using a one-dimensional transport model to represent a line
or areal source, the plume width is underestimated and its concentration is
overestimated. This effect diminishes as the contaminant migrates farther
and farther from the source. Also, typically when performing
one-dimensional transport simulations, the analyst uses the peak measured
concentration in the interest of being conservative. The analyst must keep
in mind these conservative aspects of the approach when analyzing the
results.
2. Does the source consist of an initial slug of contaminant or is it constant
over time?
The analyst needs to select a model which can simulate the type(s) of
source release that occurs at the site, either pulse, constant or a
combination of both.
Contaminants can enter the ground water either as an instantaneous pulse or
as a continuous release over time. A continuous release may be either
constant or variable. Variable releases may be due to source decay,
variable precipitation on the source, or intermittent source application
(e.g., dumping). Many of the simpler mathematical models can only simulate
slug or constant input releases. Some of the one-dimensional models and
5-18
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most of the higher dimensional models can simulate all the various means by
which contaminants can enter the ground water.
In many transport modeling studies, a one-dimensional model which cannot
properly represent the distribution of the source in time will be used at
the screening-level stage to make a conservative prediction of the
concentration. The errors associated with simplifying the contaminant
input pulse are site specific and, therefore, difficult to quantify. In
general, use of a continuous input model will over-predict concentrations
if the peak value is set as the input. If an average value is set, the
model will under-predict discrete peaks. The effects of using an average
flux will diminish with distance from the source.
3. Is it necessary to simulate three-dimensional transport or can the
dimensionality be reduced without losing a significant amount of accuracy?
The analyst needs to select a model which can simulate the dimensionality
needed to properly represent the site, either one-, two-, or
three-dimensional.
All transport models should be selected in three dimensions unless it can
be shown that the contaminant migration or remediation scheme can be
accurately represented in a lower dimension. Cases where a contaminant
source is distributed both areally (x-y) and vertically (z) would, in most
instances, require a fully three-dimensional model. Similarly, remedial
action simulations employing pumping wells screened at specified depths
and/or cutoff walls not fully penetrating an aquifer would most likely
5-19
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require a three-dimensional model. Cases in which the aquifer is uniformly
contaminated in the vertical direction and where geologic layering is not
important can be simulated in two dimensions, generally,either in x-y or
x-z. Very simple cases consisting of a large plane source, a simple
contaminant distribution, and a uniform velocity distribution can be
simulated with a one-dimensional model.
Because the analyst typically lacks the necessary data to develop a two- or
three-dimensional transport model, it is quite common to simulate
transport in one dimension,. Only in recent years have documented and
verified three-dimensional models become available,and responsible parties
have been willing to spend the time and money required to develop and run
site-specific models. The lack of necessary data is no excuse for running
a lower dimensional model if it is not suited for the specific application,
although this is the approach which apparently is often taken. A
one-dimensional model, however, can still provide valuable results for a
screening study where conservative predictions or alternatives are
compared. .
The limitations of the one-dimensional approach are:
it cannot simulate multiple sources;
§ it can only simulate a large plane source or an average concentration
distribution over a large x-y, x-z, or y-z plane for an areal source;
and
5-20
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o it cannot simulate transverse dispersion (perpendicular to the flow
path).
Although errors associated with these limitations are difficult to
quantify, their general effect is the prediction of very conservative
(higher) concentrations. A conservative prediction can be useful for
screening studies, but often the results are so conservative that they have
little use.
The dimensionality of the transport model should be equal to or less than
the dimensionality of the groundrwater flow model. Although it is possible
to simulate the ground-water flow with a one-dimensional model and then
simulate contaminant transport with a three-dimensional model, the
transport simulation would not truly be a three-dimensional simulation
since the flow vector is in only one direction.
It is important to remember that performing a complete three-dimensional
analysis does not by any means eliminate uncertainty in the results. It is
virtually impossible to completely characterize a ground-water
flow/contaminant transport system, and no matter how well the system is
characterized, the model, whether one-, two-, or three-dimensional, is
always a simplified representation of the real system. Three-dimensional
model results, as well as one- and two-dimensional model results, need to
be analyzed very carefully to make sure they are reasonable.
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4. Does the model simulate dispersion?
Dispersion is the spreading of a solute in porous medium caused by
mechanical mixing of water through the media. Dispersion cannot be
expressed in terms of the mean ground-water velocity alone. Local
variations in flow velocity direction and magnitude caused by the natural
heterogeneity in media properties causes dispersion. The spreading process
is usually associated with unknown and uncharacterized geologic variation
of hydraulic properties. The dominant property causing the spreading is
usually the hydraulic conductivity variation in space(Simmons and Cole,
1985).
Host all contaminant transport models simulate some form of dispersion.
There is much concern, however, as to whether dispersion can be adequately
described in a model because it is related to spatial scale and variations
in hydraulic properties which are difficult to simulate in a model. There
seems to be a clear consensus among ground-water transport researchers that
the conventional convective-dispersive equation may be an inadequate and
inappropriate description of field-scale dispersion (Pickens and Grisak
1981a and b; Jury 1982; Smith and Schwartz 1980; Gelhar et al. 1979;
Matheron and DeMarsily 1980; Dagan and Bresler 1979; Simmons 1982a and b).
Some recognized inadequacies of the conventional approach are prediction of
non-physical upstream migration, failure to predict increased dispersion
caused by larger scales of heterogeneity, inappropriate dependence on
diffusion-like boundary conditions, and incorrect representation of
non-Fickian, asymmetric solute distributions (Simmons and Cole, 1985). For
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5.
the purposes of this report, it will be assumed that the currently
available models are adequate.
It is difficult to quantify the errors associated with simulating
dispersion because they are site specific. Turning off dispersion in a
model only considers the movement of contaminants by the advection process
and hence yields a "worst case" prediction of peak contaminant
concentration. However, this causes the leading edge of the plume to take
longer to arrive at a point downgradient. The larger the value of
dispersion, the greater the spread of the plume and the lower the peak
concentration. Since dispersion coefficients are very difficult to measure
in the field, the best way to choose a value is in the model calibration
process, often requires a large amount of data for field calibration.
Does the model simulate adsorption (i.e., distribution or partitioning
coefficient) and, if so, does it simulate temporally and/or spatially
variable adsorption? Temporally or spatially variable adsorption is
important when the soil conditions and/or concentrations change with time
and space.
There are a number of chemical and biological processes that affect the
rate and manner in which contaminants travel in the ground water
(adsorption, ion exchange, degradation,, biotransformation, etc.). Since
adsorption and degradation (decay) are the only processes that are
typically simulated in contaminant transport models, they are the only
processes discussed in this report. Adsorption is discussed in this
section and degradation in the next section.
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Adsorption is usually represented by a distribution or partitioning
coefficient which relates contaminant concentration in solution to
contaminant concentration associated with (adsorbed to) the soil.
Distribution coefficients are used in transport models to approximate
contaminant retardation in the subsurface. Contaminant retardation relates
ground-water velocity to contaminant velocity.
In screening studies, transport models not simulating adsorption are often
used to make conservative estimates of contaminant concentrations. These
conservative estimates can be useful as long as the predicted
concentrations are not so high that they completely misrepresent the
problem. A general rule for determining when to simulate adsorption might
be that if the contaminant is only mildly retarded, say less than a factor
of 5 times slower than the ground water, then the conservative approach of
not simulating adsorption may be informative in a screening effort. If the
contaminant has a retardation factor larger than 5, a model should
be selected that simulates retardation. In any detailed modeling study
adsorption should always be simulated for all retarded contaminants. The
partitioning coefficients for all contaminants are dependent on the
equilibrium solution concentration. However, in dilute solutions, the
partitioning coefficient is constant for all practical purposes (linear
isotherm). Stated in a different way, a contaminant's absorption
properties remain the same at low concentrations (linear), whereas at
higher concentrations adsorption decreases as the contaminant concentration
in the ground water increases (nonlinear). This nonlinear property can
become very important when predicting the migration of the center of mass
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versus the leading edge of a contaminant plume, or when predicting required
pumping time for a pump-and-treat remedial action. At high concentrations,
the linear assumption will over-predict adsorption and travel times and
under-predict ground-water contaminant concentrations. For hydrophobic
contaminants, the threshold below which linearity can be assumed is about
one half the solubility (Neely and Blau, 1985). For hydrophilic
substances, the threshold must be determined on a case-by-case basis
because of interactions between the water and the contaminant.
Very few currently available transport models can simulate the nonlinear
adsorption case, so adsorption is nearly always simulated as a linear
isotherm. For very low concentrations, this approximation can produce mass
balance errors which typically overestimate the contaminant mass in the
solution phase and underestimate the mass in the solid phase. Therefore,
the approximation with the linear isotherm is more conservative
(i.e., it would predict a higher concentration at a monitoring well at an
earlier time than it should actually arrive).
Certainly, it would be more accurate to use a nonlinear isotherm model for
all cases in which it applies. The currently accepted practice in
transport modeling, however, is to lump all chemical and biological
processes into one term, the adsorption or retardation term, and simulate
it as a linear isotherm. Geochemical models are employing a more
state-of-the-art approach with regard to simulating chemical and biological
processes. Until the science is better understood, however, the accepted
practice will be to lump them all into one term.
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6. Does the model simulate first or second-order decay and/or radionuclide
decay?
Degradation or radlonucllde decay are factors which can significantly
affect predicted concentrations and total mass of contaminants In a ground-
water system. As with adsorption, conservative estimates of concentrations
can be made by neglecting degradation 1n a screening level or "worst-case"
analysis. For a detailed analysis, however, a degradation model should be
used.
Host transport models simulate first-order decay. Only a few models can
simulate higher-order decay. No transport models are currently available
which can simulate the transformation of one chemical constituent into a
breakdown product and then simulate the transport of the transformed
constituent(s). One approach that can be used to simulate the transport of
a parent species and all its transformation products is to simulate the
transport of a parent as if there is no degradation and then
apportion the resulting concentration on the basis of an assumed
transformation efficiency (often 10%) and the ratio of molecular weight.
This only works well if the adsorption coefficients are similar between the
parent and by-product contaminants. It also assumes that the by-product
i'.
does not further transform.
Several transport models, both analytical and numerical, can simulate
radioactive decay. Many of the models can account for the generation and
transport of daughter products in both straight and branched decay chains.
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7. Does the model simulate density effects due to changes in temperature and
concentration? A truly coupled model is one in which the ground-water flow
is influenced by the density and viscosity of the water, which, in turn,
are influenced by the temperature of the water and the concentration of the
solute. In some cases (i.e., involving a large heat source or large
fluctuations in solute concentration) it may be important to consider
temperature and contaminant concentration effects on ground-water flow.
A basic assumption of most ground-water flow and contaminant transport
models is that gradients of fluid density, viscosity, temperature, and
concentration do not affect the velocity distribution. In most cases these
gradients are small and this is a safe assumption. In some cases, however,
these gradients can become large and can significantly affect flow
patterns. In these cases a coupled model solving for pressure,
temperature, and/or solute concentration as functions of fluid density and
viscosity should be used.
An example of such a case is the effect of heat generated by the burial of
high-level radioactive waste on the ground-water flow in the vicinity of
the repository. The heat from the repository will have a buoyant effect on
the surrounding water causing it to rise. The extent of the rise and the
magnitude of the impact can be predicted with coupled models.
Under most naturally-occurring situations, the assumption that flow is not
affected by temperature, density, and concentration gradients is valid. In
cases where extremely deep systems are being simulated, however, the
naturally-occurring geothermal gradients may influence ground-water flow
patterns and should therefore be simulated. The only other cases where one
5-27
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typically needs to be concerned with thermal flow patterns are
anthropogenic phenomenon such as geologic repositories or injection of
heated or cooled fluids.
Similarly, under most naturally occurring circumstances, density and
concentration gradients are small enough they can be neglected. The
classic example of a naturally-occurring density problem that should be
simulated with a coupled model is that of saltwater intrusion. Most
man-made contamination problems result in low enough ground-water
concentrations that they do not affect the ground-water flow. In a few
instances, concentrations become large enough that the density of the water
is affected and a coupled model is required for an accurate prediction of
the flow and transport. An important example is leachate from landfills.
Concentrated leachate plumes often move deep into the aquifer before they
migrate laterally. If the effect of concentration is neglected, the
analysis may under-predict concentration at deeply screened wells.
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 selected above, or select a combined ground-water
flow/contaminant transport model.
Regardless of the approach selected, whether separate or combined flow and
transport models, it is likely that there will be several models which meet the
technical criteria. The selection of the final model(s) should be based on the
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implementation criteria; i.e., the model meets the criteria that it 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, the modeling schedule, available budget, and staff
and equipment resources.
5.2. MODEL SELECTION FROM THE REVIEWERS POINT OF VIEW
The selection criteria are described primarily from the point of view of an
analyst performing an exposure assessment study. The basic process begins with
defining project objectives, assessing a physical situation, and then selecting
a model to represent the important processes relevant to the objectives and
physical conditions. Another use of the selection criteria is from the point of
view of a regulatory agency that is reviewing an exposure assessment study.
Under these circumstances the reviewer needs to evaluate the choice of the model
used in performing the study. The selection criteria must be fundamentally the
same for both applications, however, some differences exist in how the criteria
is used or evaluated. This section is included to describe those differences.
The proper selection of a model is one step in performing an exposure assessment
study. All models are sensitive to the choice of input parameters. The choice
of these parameters will be, in most cases, at least as important as the choice
of a particular model and must be considered in the review process.
The first step for the person reviewing the exposure assessment study is to
identify the characteristics and capabilities of the specific model. This
information can best be obtained from a model user's manual.
5-29
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The single most important step in choosing a model is to define project
objectives. Similarly, the most important step for the reviewer is to have a
clear understanding of the study objectives. The objectives of the analysis
should clearly state whether it is performed as a generic analysis or if a more
detailed site-specific analysis with appropriate data for calibration and
validation is intended. In cases where the objectives are not clearly defined,
then the only option is to interpret how the results and conclusions of the
study are presented (e.g., associated uncertainty, potential impacts, and
importance of decisions based on the results). This is difficult and will
obviously be subjective in some cases. After this initial step, the rest of the
selection criteria are essentially the same for both the selection of a model
and review of a model selection by another person.
It is important that the reviewer examine the presentation of results and
conclusions to see that they are consistent with the study objectives, model
choice, and model application. Any decisions based on model results must
incorporate the uncertainty inherent in the predictions. For a generic
analysis, the level of uncertainty will be about an order of magnitude at best.
For more detailed analysis, the validation phase of a modeling study may provide
some guidance in defining the uncertainty associated with the model predictions.
5.3. MODEL SELECTION WORKSHEET
Section 5.1 discussed the technical criteria used to select a mathematical
model for a specific application. This section provides a model selection
worksheet which facilitates the selection of an actual model or suite of models
based on the response to the technical criteria.
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The model selection worksheets are shown in Tables 5-1, 5-2, and 5-3.
Tables 5-1 and 5-2 are the analytical solutions worksheets and Table 5-3 is the
analytical and numerical model (coded for the computer) worksheets.
Table 5-1 lists a total of 63 analytical solutions by name and reference,
tells which calculator or personnel computer they have been programmed for (if
any), and lists any pertinent comments. The first seven solutions are for
ground-water mounding problems and the remainder are for contaminant transport
problems.
Table 5-2 lists the analytical solutions (by number) in the same order they
are listed in Table 5-1. The technical selection criteria (listed across the
top) are in the same order as they are discussed in Section 5.1 (Figure 5-1).
Table 5-3 presents a list of some of the currently available, documented,
mathematical models. The models are divided into seven categories:
1. Analytical flow models
2. Analytical transport models
3. Numerical flow models which can be applied 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
7. Numerical contaminant and transport models which couple the solutions for
pressure, temperature, and concentration (coupled models).
Within these major categories, the models are listed in alphabetical order. The
technical criteria or specifications for the models (listed across the top) are
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TABLE 5-1. ANALYTICAL SOLUTIONS, NAMES, AND REFERENCES
1>
H
11
4)
1)
()
71
1)
»
10)
11)
11)
11)
14)
15)
10
17)
U)
H)
20)
ID
»)
23)
24)
Analytical Solution names
Analysts »f Creun*at>r Mounting leneatli
Tallin* Pen*
Circular Recharge Area
Ctralir lulu Htcaarje Mound
Hwnd Decay
Circular Recharge Are*
HanxHng
River's Solution
junction ind Dispersion Regional Flew
MAP Flue
H.UC
rtosve
H.0t CROSS-SECTION
RAIDCM UAU
RAW* WALK
U03M9
Htn
Advectlon and Dispersion fro* a Stream
Advectton and Dispersion from a Single
ruling Veil
Advec$1ve Mass Transport Thels Particle Hover
Streamlines and Travel Times for Regional
Flew Affect* by Sources and Sinks
Advectlve Transport Model
S-PaUu
Ground Vater Dispersion
Plume Management Model
Computer Type
TI-SJ
TI-S9
HP-41
TRS-80, Osborne,
Kaypro. IBM
Apple. Victor,
Kaypro II. Vector
Apple
(3)
Apple. Victor,
Kaypro II, Vector
Osborne, Super-
brain. Kaypro, IBH
Osborne
Apple, 'Victor,
Kaypro II, Vector
(6)
(7)
Osborne
Osborne
TltS-80. (3)
TRS-80, (3)
Tl-59
HP-41
HP-41
HP-41
TI-SB/59
TI-59
Comment!
Predicts Hydraulic Head
Predicts Hydraulic Head
Predicts Hydraulic Head
Predicts Hydraulic Head
Preclcts Hydraulic Head
Predicts Hydraulic Head
Predicts Hydraulic Head and
Discharge
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Particle Location Nlth Time
Particle Location ulth Time
Predicts Mass Loading
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Deference
Sandberg et !., INI
Prlckttt an* Vorhees,
Walton, 1983
Ulrlck (1)
Bear, 1972
Wilton. 1983
(2)
Holden, Sunada, and
Varner, 1984
Ballon, 1983
(2)
(2) (4)
(5)
(2)
(2)
(3)
(5)
(5)
Walton. 1983
Walton, 1983
Sandberg et al . , 1981
Prtckett and Vorhees,
Olsthoorn, 1984 (4)
Ulrlck, 1983 (1)
Oberlander and Nelson
Kelly. 1982
Sandberg et al., 1981
Prlckett and Vorhees,
INI
.1981
, 1984
1981
25) Calculator Code for Evaluation Landfill TI-59
Leaehate Plumes *
tfl) Dissipation of a Concentrated Slug of TI-59
Contaminant
27) Advectlon and Dispersion from a Single Solute KP-41
Injection Veil
a) COAST Analytical Solution for One-
Otmenslonal Contaminant Transport
21) TOAST Analytical Solution for Twq-
Dlmenslonal Contaminant Transport
X) LT1KD Semi-Analytical Solution to Radial
Dispersion In Porous Media '
31) KSSq Semi-Analytical Contaminant
Transport
32) RT Mapping Concentration Distribution In
an Aquifer Based on a Time Series Data
Collection Concept
33) Material Release on the Surface with One-
Dimensional Vertical Dovnward Transport
34) Tho-Dlmenslonal Horizontal Flow ulth a Slug
Source
3S1 Tn-Otmonslonal Horizontal Flo* ulth a
Continuous Source
36) Instantaneous Source, Infinite Aquifer Depth
37) Instantaneous Source, Finite Aquifer Depth
38) Instantaneous Source. Finite Aquifer Depth
Average Concentration
39) Continuous Source Release Unsteady State
40) Continuous Source Release Steady State
41) Instantaneous Horizontal Release, Finite
Source Length, Infinite Aquifer Depth
42) Instantaneous Horizontal Release, Infinite
Source Length, Infinite Aquifer Depth
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
Predicts Contaminant Concentration
. Pettyjohn et al., 1982
T.A. Prlckett and Associates (8)
Van der Hetjde, 1984 (4)
Oavandel et al., 1984
Javandel et al., 1984
Oavandel et al., 19S4
Javandel et al., 1984
Javandel et al., 1984
vanGenuchten and Alves, 1982 (9)
Wilson and Killer, 1978 (9)
Wilson and Miller, 1978 (9)
Point Source Solution
Point Source Solution
Point Source Solution
Point Source Solution
Point Source Solution
Line Source Solution
Hwang, '1986
(twang, 1986
Hwang. 1986
Hwang, 1986
Hwang, 1986
Hwang, 1986
Line Source Solution
Hwang, 1986
5-32
-------
TABLE 5-1. (continued)
Analytical Solution
Ty»e
tofertnct
43)
44)
45)
44)
47)
48)
4t)
50)
SI)
52)
S3)
54)
55)
56)
57)
56)
59)
CO)
61)
62)
C3)
Instantaneous Horizontal Release. Finite
Source Length, Finite Aquifer Depth
Instantaneous Horizontal Release, Finite
Source Length, Aquifer OepthrAveraged
Concentration
Continuous Horizontal Release, Finite Source1
Length, Infinite Aquifer Depth
Instantaneous Vertical Release, Infinite
Aquifer Depth
Continuous Vertical Release, Average
Concentration Unsteady State
Continuous Vertical Release, Average
Concentration Steady State
Instantaneous Horizontal Source
Instantaneous Vertical Source
Continuous Horizontal Plane Source
Unsteady State
Continuous Horizontal Plane Source --
Steady State
Continuous Vertical Plane Source
unsteady State
Horizontal Plane Source at a Constant
Boundary Concentration
Vertical Plane Source at a Constant
Boundary Concentration Steady State
Constant Release Rate Downward
Constant Concentration Boundary Reservoir
Voluae Source
Constant Boundary Concentration In a
Radially-Flowing Aquifer
One-Dlnenslonal Mass Transport IBM 360/91
Tw-D1aens1onal Mass Transport I6H 360/91
Three-Dlaenslonal Mass Transport: Patch IBM 360/91
Source; Finite Dimensions
Thrte-D1«ens1onal Mass Transport: B1var1ate IBH 360/91
Line Source Solution
Line Source Solution
Line Source Solution
Line Source Solution
Line Source Solution
Line Source Solution
Area! (Plane) Source Solution
.Areal {Plane} Source Solution
Areal (Plane) Source Solution
Areal (Plane) Source Solution
Areal (Plane) Source Solution
Areal (Plane) Source Solution
Areal (Plane) Source Solution
Infinite Horizontal Plane Source
Infinite Vertical Plane Source
Concentration and Flow Boundary
Conditions
Strip Boundary Condition
Finite and Infinite Width
Two-Dlwnslonal Vertical Source
Hwang, 1986
Hwang, 1966
Hwang, 19S6
Hwang, 1986
Hwang, 1986
Hwang, 19B6
Hwang, 1986
Hwang, 1986
Hwang, 1986
Hwang, 1986
Hwang, 1986
Hwang, 1986
Hwang, 1986
Hwang, 1986
Hwang, 1986
Hwang, 1986
Hwang, 1986
Cleary and Ungs, 1978
II
II
II
Gaussian Source
U) rrograns available froe Janes S. Ulrlck and Associates. 2100 Los Angeles Avenue. Berkeley. CA 94707.
(2) Programs available fron the National Center for Ground Water Research, Oklahoma State University, Stillwater, OK.
(31 Calculator/Computer Type: Osborne, Kaypro, Superbraln, IBM, Radio Shack PC-1 and'PC-2, and Sharp PC 1250 and 1500 programs available.
(4) Prograes available from the International Ground Hater Modeling Center, Holconb Research Institute, Butler University. '4600 Sunset Avenue
Ind1anapol1s, IN 46208*
(5) Programs available from Dr. Michael L. Voorhees of Harzyn Engineering. Inc., Madison. HI.
(6) Calculator/CoBputer Type: Apple, Kaypro II, Victor, Vector, TRS-80, Sharp-PClSOO.
(7) Calculator/Computer Type: Superbraln, Osborne. Sharp-PClSOO.
(8) Programs available fron Thomas A. Prlckett and Associates, Inc., 8 Montclalr Road, Urbana, IL 61801.
(9) See National Council of the Paper Industry for Air and Stream iBprovenents, Inc., Technical Bulletin Ho. 472, October, 1985.
- Point Source
Line Source
- Areal Source
- Radial Flow
x-D1mens1on
y-D1aens1on
2-D1 tension
- Volune
Dispersion In the x Direction
- Dispersion 1n the y Direction
Dispersion 1n the z Direction
5-33
-------
TABLE 5-2. ANALYTICAL SOLUTIONS WORKSHEET
t.
^ t.
a. .«>
o- *»-
1 1
« -0
*~ £
Analytical t. £
Solutions Ho. £ =
(see Table 1) S 3
GrounoVater
1
2
3
4
5
6
7
Con taut nant
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30-
31
32
Mounding
X
X
X
X
X
X
X
Transport
X
X
X
X
X
X X
X X
X
X X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
10
5
£
to
1
£
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
x
X
X
X
X
X
X
X
X
[Fracture Flow
Flow Dinenslon
R
R
R
X-Y
R
R
R
X-Y
X-Y
X-Y
X-Y
X-Z
X-Y
X-Y
X-Y
X-Y
X
R
X-Y
X-Y
X-Y
X-Y
X-Y
X-Y
X-Y
X-Y
R
X
X-Y
R
X-Y
R
o>
IS
£
OI
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
U
i
1
1 Mul « -Phase
Konogeneous Hy
Parameters
X
' X
X
X
X
X
X
X
X
X
X
X
x
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
1
%
Heterogeneous
Parameters
Single-Layer
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
M
M
s
&. 2=
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«? 4-*
i 1
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
i
Variable Thick
[Steady State
[Transient
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X.
X
X
X
1
01
c
1*8
Clrc
C1rc
Clrc
Rect
Circ
Clrc
Rect
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
LS
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P
2
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+*
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X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
0}
Constant Souro
X
X
X
X
X
Dispersion
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Adsorption
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
!
1
cs?
Degradation 1,
Radioactive
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
5-34
-------
TABLE 5-2. (continued)
Analytical
Solutions No.
(see Table 1)
33
34
35
Transport
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
1
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p
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L
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L
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A
A
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X X X X
X X
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X X
X X
X X
X X
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X X
X X
X X
D7 X
Dz X
Dx X
X X
X X
xxx
xxx
xxx
xxx
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
5-35
-------
TABLE 5-2. (continued)
LEGEND
Dimension
X ~ X dimension
Y -- Y dimension
Z Z dimension
Dispersion
Dx -- Dispersion in x direction
Dy Dispersion in y direction
Dz -- Dispersion in z direction
R -- Radial Flow
Source Type
A Area! source
L Line source
P -- Point source
Vol Volume
5-36
-------
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5-39
-------
Identified in the same order as the technical selection criteria discussed in
Section 5.1 (Figure 5-1). The last column in the worksheet includes comments
pertaining to the solution technique (analytical model, finite difference, or
finite element numerical model) and any other pertinent information. A summary
of each of the models listed in Table 5-3 is contained in Appendix A. More
detailed information, user's manuals, and copies of many of these models can be
obtained from the International Ground Water Modeling Center (IGWMC) model data
base. IGWMC is located in Indianapolis, Indiana.
In many instances, selection of a model that has more capabilities than
necessary but with which the analyst is familiar may be more cost effective than
applying a smaller, unfamiliar model with minimum capabilities due to the
acquisition, testing, and learning process that would be required.
5.4. WASTE MANAGEMENT MODELS
A few models have been developed by/for the EPA and others which consist of
a methodology for tracing contaminant movement through the various environmental
media. For the purposes of this report, these models will be called waste
management models. Waste management models typically track the movement of
hazardous waste from the source (point of disposal) through one or more of the
three primary environmental pathways; air, surface water, and/or ground water.
Since this document is concerned with ground-water models, we will only discuss
those waste management models which simulate the ground-water pathway.
Waste management models typically consist of a number of submodels to
simulate the many components of transport from a contaminant source to the point
of exposure. These submodels usually consist of 1) source term generation,
which can include leakage through a liner(s); 2) contaminant transport through
the unsaturated zone; 3) contaminant transport through the saturated zone; and
5-40
-------
4) uptake by humans at the point of exposure. When simulating contaminant
transport, the submodel generally simulates phenomena such as dispersion,
degradation, and adsorption.
It is not the objective of this document to cover waste management models
in any detail. Rather, a few such models are described briefly to make the
reader aware of them. If a waste management model uses a ground-water transport
model that was discussed earlier, this is brought to the attention of the
reader.
5.4.1. Risk Assessment Methodology for Regulatory Sludge Disposal Through Land
Application
ICF Technology, Inc., has recently developed a risk-based approach to
setting sludge criteria for land application disposal for the EPA. The
methodology can also be applied on a site-specific basis to evaluate permit
applications. ICF developed the modules addressing ground water, vapor, and
surface runoff pathways. In each case, analytical models were assembled to
track the movement of contaminants from source to site of exposure. Predicted
levels can be compared to health-based criteria, or health-based criteria can be
input to select limiting sludge contaminant concentration criteria. A series of
representative scenarios are being evaluated with the methodology to identify
criteria thresholds and areas where best management practices should be
prescribed.
5.4.2. Risk Assessment Methodology for Regulating Landfill Disposal of Sludge
ICF Technology, Inc., has been responsible for the development of the
risk-based methodology for EPA upon which sludge landfill disposal regulations
and criteria are being based. The methodology can be* applied on a
national/regional level or on a site-specific basis. For the ground-water
5-41
-------
pathway, it predicts leachate quantity and quality and subsequent impacts on
ground water by modeling contaminant movement through the unsaturated zone and
in the aquifer. Degradation, adsorption, and geochemistry are all accounted
for. A simple vapor-release and atmospheric-dispersion approach is taken for
the vapor pathway. Runoff and particulate suspension are addressed through best
management practices.
The landfill disposal methodology uses the CHAIN model and the AT123D model
to simulate contaminant transport through the unsaturated and saturated zones,
respectively. Both of these models are discussed in the previous section and in
the appendix.
5.4.3. RCRA Risk/Cost Policy Model (WET Model)
The RCRA risk/cost policy model establishes a system that allows users to
investigate how trade-offs of costs and risks can be made among wastes,
environments, and technologies (W-E-Ts) in order to arrive at feasible
regulatory alternatives. The model was developed for EPA by ICF, Inc.
There are many components in the system. Eighty-three hazardous waste
streams are ranked on the basis of the inherent hazard of the constituents they
typically contain. The system assesses these waste streams in terms of the
likelihood and severity of human exposure to their hazardous constituents and
models their behavior in three media -- air, surface water, and ground water.
The system also incorporates the mechanisms by which the constituents are
affected by the environment, such as hydrolysis, biodegradation, and adsorption.
A second integral part of the system is the definition of environments in
which the hazardous components are released. Thirteen environments including a
special category for deep ocean waters are defined on the basis of population,
density, hydrology, and hydrogeology. The system adjusts the exposure scores of
5-42
-------
the waste streams' hazardous constituents to account for their varying effects
in the three media in each of the environments.
The third component of the system consists of the technologies commonly
used to transport, treat, and dispose of the hazardous waste streams. This
includes 3 types of transportation, 21 treatment technologies, and 9 disposal
technologies. The system determines costs and release rates for each of these
technologies based on the model's existing data base. It also incorporates
estimates of capacities of the technologies, the amount of waste to be disposed
of, and the proximity of the wastes to the available hazardous waste management
facilities.
EPA's purpose in developing the RCRA risk/cost policy model is to assist
policy makers in identifying cost-effective options that minimize risks to
health and the environment. The framework of the system is intended as a
screen -- to identify situations that are of special concern because of the
risks they pose and to determine where additional controls may not be warranted
in light of the high costs involved. The framework uses a data base that is too
imprecise and general to be the sole basis for regulations. The results of the
model will be used in more detailed regulatory impact analysis to determine
whether some type of regulatory action is warranted.
Contaminant transport is not simulated in the WET model. Rather, a ground-
water exposure/risk score is tallied based on key flow and transport parameters
such as hydraulic conductivity, depth to ground water, adsorption, and
hydrolysis.
5.4.4. The Liner Location Risk and Cost Analysis Model
The liner location risk and cost analysis model, developed for EPA by ICF,
Inc., links a risk and a cost model. The risk model simulates the chronic risk
5-43
-------
to human health from land disposal facilities (landfills and surface
Impoundments) with different,design technology, location, and waste stream
combinations. It integrates a series of submodels and algorithms that trace
constituent releases from landfills and surface impoundments to their movement
through the air and ground, then to resulting human exposures, and finally to
the resultant human risk. To do so, model components predict:
Releases to ground water and subsurface transport. A failure and release
submodel estimates facility failure and the quantity of leachate released;
an unsaturated zone algorithm calculates the time required for the leachate
to reach an underlying aquifer; and a saturated zone submodel calculates
the time and concentrations of constituents reaching a downgradient well.
* Releases to air and atmospheric transport. A volatilization algorithm
calculates the quantity of constituents that volatilize over time; an
atmospheric transport algorithm calculates the concentrations of these
constituents at the exposure points.
Human exposure. An exposure algorithm calculates the exposure from
drinking water and from breathing constituents in air.
Health risks. A hazard estimation submodel calculates expected cancer and
noncancer risks from the exposures.
The model calculates risk over a 400-year time horizon. In doing so, it
embodies many assumptions: facilities operate for 20 years with a 30-year
post-closure period; contamination goes undetected and uncorrected; multiple
contaminants do not interact; and few constituents degrade over time, with
degradation beginning only after facility failure. The model also assumes that
aquifers are homogeneous and isotropic.
5-44
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The companion cost model estimates the costs of land disposal facilities
with differing technologies and sizes. The results of the risk model combined
with the cost data from the cost model provided EPA with the capability to
perform cost/risk and cost-effectiveness analysis.
The liner location model uses the TRANS model (Random-Walk Particle
Transport Model) to model contaminant transport in the saturated zone. The
TRANS model is discussed in the previous section and in the appendix.
5.4.5. Landfill Ban Model
The landfill ban model is a quantitative modeling procedure used by EPA to
evaluate potential impacts on ground water and establish screening levels for
this medium. The ground-water screening procedure involves a back calculation
from a point of potential exposure at a specified distance directly downgradient
from a point of release from a land disposal unit using a fate and transport
model. The ground water back calculation procedure involves the application of
three model components: 1) the HELP model which addresses performance of
engineer controls; 2) the fate and transport model (EPASMOD) which models the
behavior of constituents in the ground-water environment; and 3) the MINTEQ
model which models the behavior of metals in the ground-water environment.
The HELP model was developed by EPA specifically to facilitate estimation
of the amount of runoff, drainage, and leachate that may be expected to result
from a hazardous waste landfill. The model predicts the water balance by
performing a mass balance between flow into various components of a landfill and
water leaving these components. The model uses climatology, soil, and
design data to produce daily estimates of water movement across, into, through,
and out of landfills.
5-45
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The EPASHOD model predicts the fate and transport of constituents in the
ground water. EPSMOD is a three-dimensional, steady-state, advective dispersive
model which utilizes analytical solution procedures to predict transport through
homogeneous and isotropic porous media. The model accounts for advection;
hydrodynamic dispersion in the longitudinal, lateral, and vertical dimensions;
absorption; and chemical degradation.
Estimates of metal species distributions are determined using the
geochemical model MINTEQ. MINTEQ is an equilibrium model that uses the
equilibrium constant approach in solving the chemical equilibrium problem.
The contaminant transport model EPASMOD is not included in the appendix of
this report because it is still in the development stages and at this time is
not well documented.
5-46
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6. MODEL SELECTION EXAMPLE PROBLEMS
Two site-specific example problems are provided below to demonstrate the
procedure for selecting the appropriate mathematical model for a particular
application. The first example is an application 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 problems are presented
in the order that should be followed when conducting a ground-water flow and
contaminant transport modeling study, with model selection being one element of
the process.
6.1. SCREENING ANALYSIS EXAMPLE PROBLEM
Over 300 landfills are licensed to operate within a particular state. The
state is interested in determining whether significant ground-water
contamination is occurring at the sites. As a first step, the state is
interested in using models to define the scope of the problem to determine if
detailed investigations of several of the sites are required. At this stage,
the state is not interested in detailed, site-specific assessments.
6.1.1. Ob.iectives of the Study
The objectives of the study are to develop a generic model of the ground-
water flow and contaminant transport system beneath a landfill and to perform a
sensitivity analysis to determine the likelihood that a significant
contamination problem might exist. The data used in the sensitivity analysis
are generic values representative of the actual landfills. The sensitivity
analysis consists of several model simulations using both average and
conservative values for the model parameters.
6-1
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The study is primarily concerned with a contaminant transport analysis of
five contaminants commonly found in landfill leachates. The contaminant data
have been obtained from existing data for representative sites.
6.1.2. Conceptual Model of the Study Area
Of the 300 sites in the state, 30 are chosen as a representative sample.
The existing data for the 30 sites are .used to develop a generic conceptual
model of a typical landfill site.
For this example, we will assume the conceptual model has been developed
and is very simple. It consists of a contaminant source (either point, line, or
area!) at the water table beneath the landfill; a single layer, homogeneous,
porous-media aquifer; and a discharge location at a specified distance
downgradient. The source strengths, ground-water velocities (hydraulic
conductivity and gradient), distance to the discharge, and other pertinent model
inputs have been determined from the existing data for the initial simulation.
We will also assume the five contaminants of interest and their transport
properties have been identified from the existing data. Dispersion, adsorption,
and degradation are important processes that need to be simulated in the
initial model run and adjusted in the sensitivity analysis.
6.1.3. Model Selection Process
Having developed the conceptual model, the analyst should now follow the
technical criteria to determine which model or suite of models will be
appropriate for this application. Because the objective of this study is to
perform a generic or screening analysis, a screening model should be selected.
Using a screening model allows for making several sensitivity runs relatively
quickly and at low cost. Typically, such a screening model is an analytical
solution, an analytical model, or a simple numerical model.
6-2
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For this study, there is no point in using a detailed model since the data
are not site-specific and the objective is not to predict site-specific exposure
i
levels but rather to compare cases in a sensitivity analysis.
Since the objective is to study the transport of 5 contaminants, a
contaminant transport model should be selected. The ground-water flow is not
simulated in the transport model, but rather it is specified by the available
data (in terms of ground-water velocity, or hydraulic conductivity and hydraulic
gradient which can be used to solve for velocity). Even though ground-water
flow is not simulated, the flow parameters can still be adjusted in the
sensitivity analysis.
The first part of the technical selection criteria (Figure 5-1) relates to
ground-water flow. Based on the conceptualization, the flow portion of the
transport model should have the capability to simulate the following conditions:
water table aquifer, porous media, steady state; single phase, single layer of
constant thickness, and homogeneous hydraulic properties. In a contaminant
transport model, all of these properties are usually represented as a uniform
velocity down a one-dimensional flow path.
The second part of the technical selection criteria relates to contaminant
transport. Based on the conceptualization, the transport model should have the
capability to simulate the following conditions: area! source (point or line
source would be sufficient), constant source term, dispersion, adsorption, and
degradation. The transport can be simulated in either one, two, or three
dimensions. A one-dimensional simulation is most practical since the flow is
one-dimensional. However, a three-dimensional transport simulation could take
6-3
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full advantage of the contaminant concentration reduction resulting from
dispersion in three directions. Density effects are not important in this
application.
At this point, the analyst should go to the model selection worksheet and
select a transport model which has all the capabilities discussed above. Some
logical choices of models are AT123D, CHAIN, or MMT. Most numerical models are
too sophisticated for this application. The final selection of a single model
should be based on the implementation criteria (code has been verified and
documented) and on the analyst's familiarity with and access to the model.
6.2. DETAILED ANALYSIS EXAMPLE PROBLEM
6.2.1. Statement of the Problem
Benzene was disposed of in surface lagoons at an industrial site from 1960
to 1980. The. disposal operation was shut down when benzene was found in
residential wells downgradient (south) of the site. A network of monitoring
wells sampled in 1985 show that the benzene had migrated up to a mile
downgradient, was found near the surface just south of the site, was found at
depth further south of the site, and concentrations ranged between 0 and 2,000
ppb.
6.2.2. Objectives of the Study
The objectives of the study were to select a ground-water flow and
contaminant transport model of the site and use the model to:
1. determine the likelihood that the shallow and deep plumes are connected,
and if so, identify the reason(s) for the plume to migrate to a deeper
depth;
6-4
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2. predict the future extent of the plume and determine if the water supply
wells for a city south of the site will become contaminated; and
3. if benzene levels in the city wells could become too high, design a
pump-and-treat system to cleanup/contain the plume.
6.2.3. Conceptual Model of the Study Area
The site is located in a narrow alluvial valley about 1 mile north of a
small town (Figure 6-1). The waste lagoons are situated just above the water
table of the regional alluvial aquifer. The aquifer consists of uniform sands
and gravels over its entire depth, and its saturated thickness ranges from 0 ft
along the edges at the bedrock outcrops to 100 ft in the center of the valley.
The bottom of the aquifer is defined by bedrock. South of the lagoons in the
area where the benzene plume appears to migrate to a lower depth, a creek cuts
across the valley from east to west. Five pump tests over the study region
yielded values of hydraulic conductivity that ranged between 110 ft/day and 340
ft/day. Recharge in the area is estimated as 10 in./yr and is uniformly
distributed over the study area. Water levels in the valley fluctuate very
little throughout the year. The only significant pumping in the area is the
pumping of the city wells. The creek is located in a low-permeability zone
where it cuts across the valley. A single pump test in the material yielded a
hydraulic conductivity of 25 ft/day and geologic logs show that the zone is
about 50-ft deep and 500-ft wide. The creek is not hydraulically connected to
the aquifer.
The principal contaminant of concern is benzene. Monitoring data show the
plume has migrated about 1 mile south of the site, is shallow (between 0 and 30
ft below the water table) just south of the site and north of the creek, and is
deep (between 50 and 80 ft below the water table) south of the creek. The plume
6-5
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Scale: 3 1/2 in. = 5,000 ft
Bedrock
Outcrop
Direction of
Ground-Water Flow
Low
Permeability
Zone
Bedrock
Outcrop
Figure 6-1. Model region for the assessment-level example problem.
6-6
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has a peak concentration of about 2,000 ppb just south of the lagoons and a peak
of about 100 ppb south of the creek. The width of the plume appears to be
between 1,000 and 1,500 ft.
6.2.4. Model Selection Process
The model selection process first focuses on the capabilities of the
ground-water flow model and then on the capabilities of the contaminant
transport model. In some instances it may be possible to simulate the flow with
one model and the transport with another. This is often done when using
analytical solutions or simple numerical models. In more complicated,
higher-dimensional problems, a single combined model is typically used.
When selecting a model based on the various criteria, the analyst can
always step up to the next level but should never step back. For example, if a
problem only requires a model that can simulate a single layer, the analyst can
always use a model that is capable of simulating multiple layers and only
simulate one.
The conceptualization of this example problem indicates that a water table
model should be used. However, the water table only experiences minor
fluctuations so a confined model could be used. Also, because the water table
remains fairly constant, a steady-state model would be acceptable.
The flow is single phase (since benzene .is soluble in water) through a
porous medium. The flow occurs within a single aquifer with varying thickness.
Based on the above, a porous media model that has the capability to simulate
single phase flow and a single aquifer with variable thickness should be chosen.
For this problem, a three-dimensional flow model is required as a result of
the partially-penetrating, low-permeability zone in the vicinity of the creek.
Since the aquifer appears to be fairly homogeneous, it can be simulated with a .
6-7
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single value of hydraulic conductivity and porosity. However, since the low
permeability zone exists along the creek, a model that allows for an areal
distribution of hydraulic conductivities should be selected. Also, the model
needs to allow for a vertical variation in hydraulic conductivity since the low
permeability zone is only partially penetrating.
At this point the analyst can either choose a three-dimensional ground-
water flow model that satisfies all the requirements (or exceeds the
requirements) and select a separate transport model later, or he/she can
continue with the decision process to select a coupled ground-water flow and
contaminant transport model. Probably the best approach is to determine the
transport model requirements before selecting any models.
Benzene entered the ground water over a period of 20 yrs (1960-1980) by
leaching through the bottom of surface lagoons as it was being disposed of.
Although disposal stopped in 1980, residual levels of benzene in the soils
beneath the lagoons continued to leach into the ground water at reduced rates.
The length of time required to leach all the benzene from the soil was estimated
based on residual levels, solubility, and recharge rate. A complete sample of
all monitoring wells was completed in 1985 to provide data with which to
calibrate the model.
In order to calibrate the model, the analyst would simulate 20 yrs of
leaching at full strength followed by 5 yrs of leaching at a reduced rate and
compare the 1985 model-predicted benzene concentrations to the observed values.
In order to properly simulate the release of benzene over the calibration
period, the analyst needs to select a model that can simulate variable leaching
rates.
6-8
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To predict future concentrations, the analyst can either run the calibrated
model into the future or he can run an initial value problem where the measured
concentration distribution is input to the model in 1985 and the model is run
into the future. For this type of a simulation, the analyst needs to select a
model that can simulate an initial value problem.
The conceptual model indicates that the plume appears to migrate to a lower
depth in the vicinity of the creek. In order to simulate this migration, the
contaminant transport would need to be simulated in either two dimensions in the
x-z plane or in three dimensions. A two-dimensional x-z model may be capable of
assessing whether the plumes are connected and predicting the future extent of
the plume. However, it would not be capable of aiding in the design of a
pump-and-treat remedial action. A fully three-dimensional model would be
required to determine well placement in the x-y plane, number of wells to pump,
pumping rates, and well penetration depths.
Since benzene in this situation does not significantly degrade, a model
that simulates degradation is not required.
Since there are no significant thermal or concentration gradients in the
study area, density effects can be neglected. Therefore, a fully-coupled model
would not be required.
At this point the analyst is ready to select a flow-and-transport model.
Since the problem is fairly complex, requiring three dimensions for both flow
and transport, a single combined flow-and-transport model would be the logical
choice. The analyst would go to the model selection worksheet and select a flow
and transport model which has all the capabilities discussed above. Some
logical choices of models would be SE60L, TRUST, GROVE/GALERKIN, PINDER, CFEST,
or SWIP2. The final selection of a single model would be based on the
6-9
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Implementation criteria (has the model been verified and documented?) and on the
analyst's familiarity with and access to the model.
6-10
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7. REFERENCES
Bachmat, Y.; Bredehoeft, J.; Andrews, B.; Holtz, D.; Sebastian S. (1980)
Groundwater management: the use of numerical models. Water Resources
Monograph American 5, Washington, DC: Geophysical Union.
Bear, J. (1972) Dynamics of Fluids in Porous Media. New York, NY: American
Elsevier.
Bonn, H.; McNeal, B.; O'Connor, G. (1979) Soil chemistry. New York, NY:
John Wiley and Sons, Inc.
Bolt, G.; Bruggenwert, M. (1978) Soil chemistry. A. Basic elements. New
York, NY: Elsevier Scientific Publishing Company.
Chow, Ven Te. (1964) Handbook of applied hydrology. New York, NY:
McGraw-Hill Book Company, Inc.
Cleary, R.W.; Ungs, M.J. (1978) Analytical models for ground-water
pollution and hydrology. Report 78-WR-15, Water Resources Program,
Princeton University, NJ.
Dagan, G.; Bresler, E. (1979) Solute dispersion in unsaturated heterogeneous
soil at field scale. 1. Theory. Soil Sci. Soc. Am. J. 43:461-467.
Dagan, G. (1982) Stochastic modeling of groundwater flow by unconditional and
conditional probabilities: 2. The solute transport. Water Resour. Res.
18(4):835-848.
Davis, S.N.; DeWest, R.J.M. (1966) Hydrogeology. New York, NY: John
Wiley and Sons, Inc.
Freeze, R.A.; Cherry, J.A. (1979) Groundwater. Englewood Cliffs, NJ:
Prentice-Hall, Inc.
Freyberg, D.L. (1986) A natural gradient experiment on solute transport in a
sand aquifer: II. spatial moments and the advection and dispersion of
non-reactive tracers. Water Resour. Res.
Gelhar, L.W.; Gutjarh, A.L.; Naff R.J. (1979) Stochastic analysis of
macrodispersion in a stratified aquifer. Water Resour. Res. 15:1387-1397.
Gelhar, L.W.; Axness, C.L. (1983) Three-dimensional stochastic analysis of
macrodispersion in aquifers. Water Resour. Res. 19(1):161-180.
Gelhar, L.W.; Mantoglou, A.; Welty, C.; Rehfeldt, K.R. (1985) A review of
field-scale physical solute transport processes in saturated and
unsaturated porous media. EPRI EA-4190, Electric Power Research
Institute, Palo Alto, CA.
7-1
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Gschwend, P.M.; Wu, S-C. (1985) On the constancy of sediment-water partition
coefficients of hydrophobic organic pollutants. Environ. Sci. Techno!.
19:90.
Gupta, S.K. (1982) A multi-dimensional finite element code for the analysis
of coupled fluid, energy and solute transport. PNL-4260, Pacific
Northwest Laboratory, Rich!and, WA.
Hwang, S.T. (1986) Mathematical model selection criteria for performing
exposure assessments: groundwater contaminants from hazardous waste
facilities. U.S. Environmental Protection Agency, Exposure
Assessment Group (RD-689), Washington, DC. Unpublished Draft.
Javandel, I.; Doughty, C.; Tsang, C.F. (1984) Groundwater transport:
handbook of mathematical models. Water Resources Monograph 10,
Washington, DC: American Geophysical Union.
Jury, W.A. (1982) Simulation of solute transport using a transfer function
model. Water Resour. Res. 18(2):363-368.
Karickhoff, S.W. (1980) Sorption kinetics of hydrophobic pollutants in
natural sediments. In: Baker, R. A., ed. Contaminants and sediments,
Ann Arbor MI: Ann Arbor Science Publishers Inc., pp. 193-205.
Karickhoff, S.W. (1981) Semi-empirical estimation of sorption of hydrophobic
pollutants on natural sediments and soils., Chemosphere 10:833-846.
Karickhoff, S.W. (1984) Organic pollutant sorption in aquifer systems. J.
Hydraulic Eng. 10(6):707-735.
Kelly, W.E. (1982) Field reports -- ground-water dispersion calculations
with a programmable calculator. Ground Water 20(6).
Matheron, G.; DeMarsily, G. (1980) Is transport in porous media always f
diffusive? Water Resour, Res. 16:901-917.
Mercer, J.W.; Faust, C.R. (1981) Ground-water modeling. Ground Water
18(2-6).
Molden, D.; Sunada, O.K.; Warner, J.W. (1984) Microcomputer model of "
artificial recharge using Glover's solution. Ground Water 22(1).
Neely, W.B.; Blau, G.E. (1985) Environmental exposure from chemicals; Vol.
I. Boca Raton, FL: CRC Press, Inc.
Oberlander, P.L.; Nelson, R.W. (1984) An idealized ground-water flow and
chemical transport model (S-PATHS). Ground Water 22:(4).
Peterson, S.; Hostetler, C.; Deutsch, W.; Cowan, C. (1986) MINTEQ user's
manual. PNL-6106, Pacific Northwest Laboratory, .Rich!and, WA,
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Pettyjohn, W.A.; Kent, D.C.; Prickett, T.A.; Le Grand, H.E.; Witz, F.E.
(1982) Methods for the prediction of leachate plume migration and
mixing. Draft, U.S. Environmental Protection Agency, Municipal
Environmental Research Laboratory, Cincinnati, OH.
Pickens, J.F.; Grisak, 6.E. (1981a) Scale-dependent dispersion in a
stratified granular aquifer. Water Resour. Res. 17:1191-1211.
Pickens,
-------
Yeh, G.T. (1981) AT123D: Analytical transient one-, two-, and
three-dimensional simulation of waste transport in the aquifer system.
ORNL-5602, Oak Ridge National Laboratory, Oak Ridge, TN.
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APPENDIX A
ANALYTICAL AND NUMERICAL MODEL SUMMARIES
-------
CONTENTS
ANALYTICAL FLOW. ...... .... A-l
PATHS . A-2
ANALYTICAL TRANSPORT .... A-5
AT123D . A-6
CHAIN A-8
GETOUT A-10
GWHTM1 and GWMTM2 A-12
NUTRAN A-14
NWFT/DVM ....... A-17
NUMERICAL FLOW (SATURATED/UNSATURATED) A-19
FEMWATER1 A-20
FREEZE A-23
UNSAT1 A-24
UNSAT2 A-25
NUMERICAL FLOW (SATURATED) A-28
BEWTA A-29
COOLEY ; A-30
FE3DGW A-33
FLUMP A-38
FRESURF 1 & 2 A-39
TERZAGI A-40
USGS2D A-41
USGS3D -- Modular A-45
USGS3D -- Trescott A-46
VTT ; A-49
V3 A-52
NUMERICAL SOLUTE TRANSPORT (SATURATED/UNSATURATED) A-55
FEMWASTE1 A-56
PERCOL A-60
SATURN A-61
SEGOL A-64
SUMATRA-I A-65
SUTRA A-66
TRANUSAT A-68
TRUST -....: A-70
NUMERICAL SOLUTE TRANSPORT (SATURATED) A-77
CHAINT A-78
DUGUID-REEVES A-81
GROVE/GALERKIN A-82
A-ii
-------
CONTENTS (continued)
ISOQUAD, ISOQUAD2. .
KONBRED, USGS2D-MOC.
DPCT
MMT
PINDER
ROBERTSON1
ROBERTSON2
SWENT. ........
TRANS ,
TRANSAT2 ,
NUMERICAL COUPLED CODES (SOLUTE AND HEAT TRANSPORT)
CFEST. .
GWTHERM.
OGRE . .
SHALT. .
SWIFT. .
SWIP2. .
A-83
A-84
A-87
A-89
A-91
A-92
A-93
A-94
A-99
A-103
A-105
A-106
A-108
A-109
A-110
A-113
A-117
A-iii
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-------
ANALYTICAL FLOW
A-l
-------
CODE NAME: PATHS , ..,-,.
PHYSICAL PROCESSES: Analytical flow solution with pathline and travel time
post processors.
DIMENSIONALITY: Two-dimensional.
SOLUTION TECHNIQUE: Analytic.
DESCRIPTION: PATHS provides an approximate contaminant transport evaluation
by a direct solution of the pathline equations. The steady cases are evaluated
by holding the uniform gradient, the head in the pond, and the well strengths
constant. Under such steady-state conditions, only one set of flow paths,
advancing fronts, and travel times must be calculated. In the transient cases,
each new set of fluid particles leaving the pond or wells encounters changing
velocity effects. Therefore, a range of typical departure times is selected and
the flow paths, front configurations, and travel times are calculated
successively for each selected set of fluid particles leaving the contaminant
source. The approximate equilibrium coefficient approach is used to give the
ion exchange delay effects for a single constituent. There are, however, no
dispersion effects considered in the preliminary model. The model can consider
as many as 35 wells at optional locations. Wells are represented asnumerically
solved by the code to give the paths of the fluid particles and their advance
with time toward the outflow boundary.
The LOCQUAR component completes the unit outflow rates (i.e., the water outflow
volume per unit time per unit distance, along the outflow boundary). The unit
outflow rate is a function of location as well as time.
The main assumptions of the code are: .
two-dimensional (horizontal plane) infinite aquifer of constant thickness;
confined flow; , ,
homogeneous, isotropic material with constant properties;
t uniform flow direction may include transient gradient (flow) strength;
t round, fully penetrating wells and caverns}
t dissipation of the well and cavern heads occurs over a specified radial
distance;
t diffusion and dispersion processes are neglected; and
contaminant adsorption is based on linear equilibrium isotherms.
CODE INPUT: An interactive computer program actually coaches the user
through preparation of the input file for PATHS. A worksheet is ,given as
Table 1 in Nelson and Schur and its use is recommended because it will help
ensure the use of consistent units. The interactive program can also be
followed without the aid of a worksheet.
A-2
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In general the PATHS code requires the following data:
stratum thickness;
physical properties of wells including location, radius, and flow rate;
t radial distance to remote boundary;
x-coordinate termination of path lines;
0 source radius;
steady-state or dynamic head at source;
hydraulic conductivity;
a effective porosity;
uniform gradient;
starting'times and locations of pathlines;
instructions for plots to be generated; and
linear distribution coefficient.
CODE OUTPUT: A variety of outputs are generated by the three components of
the code. There are:
1) PATHS -- Input data file for GROUND.
2) GROUND -- Hard copy lists and plots of
the fluid or contaminant flow paths;
the rate of advance and shape of the contaminant fronts moving
through the system; and
the location and time of contaminant arrival at the outflow boundary.
3) LOCQUAR -- The water outflow volume per unit time along the outflow
boundary.
COMPILATION REQUIREMENTS: The code is written entirely in FORTRAN-77.
Current versions, originally developed on a Univac 1100/44 system, have been
converted to a Digital Equipment Corporation VAX 11/780 systems. Some minor
changes were made because the two systems differ in their file operations.
The code can capture information on 55 time planes for up to 50 pathlines and
35 wells. The wells are at arbitrary'locations and are represented as
completely penetrating, vertical line sources with steady or time-dependent
flow rates.
PATHS is constructed in a modular fashion and appear to be easily modified.
Versions exist on two hardware configurations. The software allows someone
A-3
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with limited computer background to run the code. The interrogative building
of the input data file coupled with the batch processing of the solution is a
user-friendly and computationally efficient method.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: As an analytical solution, the validation is simply
required to test for errors in formulation of the solution or in the computer
coding. The results of PATHS have been compared to the results from both VTT
and FE3DGW.
The PATHS model was designed to provide a balance between the refinement of the
model and the limited data usually available for initial evaluation of
subsurface contamination problems. It allows the user to make "first cut"
evaluations inexpensively and quickly. Specific applications include:
Initial model for movement from deep underground caverns for the Advanced
Technology Development Section, Research and Engineering Department,
Atlantic Richfield Hanford Company.
t Initial model of accidental release from a fuels reprocessing facility in
South Carolina.
§ Initial evaluation of accidental failure of earthen sewage holding ponds,
Kennewick, Washington.
t Initial evaluation of seepage from a copper tailings reservoir.
Model used in "Groundwater Engineering Short Course," sponsored by
Agricultural Research Service, Chickasha, Oklahoma.
Example evaluation for State of Idaho Department of Water Administration.
Evaluation of a numerical generation scheme for pathlines for Atlantic
Richfield Hanford Company in cooperation with the Pacific Northwest
Laboratory for the U.S. Energy Research and Development Administration.
a Evaluation of potential hazard from subsurface reactor accidental releases
for Sandia National Laboratories, Albuquerque, New Mexico.
DOCUMENTATION/REFERENCES:
Nelson, R.W.; Schur, O.S. (1980) PATHS -- groundwater hydraulic assessment
of effectiveness of geologic isolation systems. PNL-3162, Pacific
Northwest Laboratory, Richland, WA.
SOURCE: PATHS was written by R. W. Nelson and J. A. Schur and was a direct
result of research conducted by Pacific Northwest Laboratory. The research was
supported by the Waste Isolation Safety Assessment Program (WISAP).
A-4
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ANALYTICAL TRANSPORT
A-5
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CODE NAME: AT123D (Analytical Transient 1-, 2-, or 3-Dimensional)
PHYSICAL PROCESSES: Provides analytic or Green's Function solutions to the .:
solute transport equation in 1, 2, or 3 dimensions with a constant uniform
water velocity.
DIMENSIONALITY: One-, two-, or three-dimensional.
SOLUTION TECHNIQUE: Analytic.
DESCRIPTION: The code is limited to a single component, constant, uniform
parallel velocity field, rectangularly shaped sources and regions of interest,
with releases at a constant rate. , The source may be a point, line segment,
rectangle, or rectangular prism. The release may be instantaneous, continue
for a finite time period (band release), or be a step function. Equilibrium
adsorption and radioactive decay are included; but decay chains are not
treated. Aquifers may have finite or infinite depth and width. The program
output is the radionuclide concentration in the groundwater. AT123D requires
that the water flow be known and be approximated by a uniform parallel flow.
The principal simplifying assumptions are as follows:
t validity of the solute transport equation;
all boundaries are of the no-flow type;
a constant, uniform parallel flow velocity;
the source is a rectangular prism, and the rate and duration of release
are the same everywhere within the source;
infinite solubility; and
release of contaminant at a constant rate over some duration.
CODE INPUT: The principal inputs are as follows:
t location and dimensions of the source;
aquifer dimensions;
porosity;
hydraulic conductivity;
hydraulic gradient;
dispersivity;
distribution coefficient; and
duration of release.
A-6
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CODE OUTPUT: The output of the code is a series of tables showing
concentration at selected points and selected times.
COMPILATION REQUIREMENTS: AT123D is written in FORTRAN IV, and should be
adaptable to most computers. Current problem limits are as follows:
t 15 x-locations for output;
10 y-locations for output;
10 z-locations for output;
1,200 time steps; and
1,000 eigenvalues for series evaluation.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: The code has been checked against hand calculations and
laboratory experiments. The code is in the public domain.
DOCUMENTATION/REFERENCES:
Yeh, G.T. (1981) AT123D: analytical transient one-, two-, and three-
dimensional simulation of waste transport in the aquifer system.
ORNL-5602, Oak Ridge National Laboratory, Oak Ridge, TN.
SOURCE: AT123D was written by G. T. Yeh at Oak Ridge National Laboratory.
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CODE NAME: CHAIN
PHYSICAL PROCESSES: Convective-dispersive solute transport, saturated or
unsaturated steady flow, sequential first order radioactive decay, linear
sorption.
DIMENSIONALITY: One dimensional.
SOLUTION TECHNIQUE: Analytical based upon LaPlace transforms.
DESCRIPTION: CHAIN presents analytical solutions to solute transport
involving sequential first-order decay in saturated or unsaturated soil
systems. Solutions of the simultaneous movement of up to four member chains
are provided for the one-dimensional convective-dispersion
equation. A degrading source term may be modeled by invoking the solution to
the Bateman equations. The main assumptions of the code are:
t steady groundwater flow;
constant pore velocity and dispersivity over path length;
linear geochemical sorption model;
linear decay with up to four members;
initial value or flux source condition; and
degrading source term.
CODE INPUT:
§ path lengths;
pore velocity;
water content;
t dispersivity;
decay constants;
retardation coefficients; and
time for which solute concentration are calculated.
CODE OUTPUT: Solute concentrations at various times and positions along path
for up to four members of chain.
COMPILATION REQUIREMENTS: CHAIN is written in FORTRAN and may be easily
installed on essentially all computer systems.
EXPERIENCE REQUIREMENTS: Moderate.
TIME REQUIREMENTS: Days.
A-8
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CODE VERIFICATION: Numerous numerical verification problems are provided in
the user's manual which has been published in the open literature. Field
validation has been performed for the convective-dispersion equation in
numerous tracer experiments in the saturated and unsaturated zones.
DOCUMENTATION/REFERENCES:
found in
A full user's manual and documentation may be
VanGenuchten, M.Th. (1985) Convective-dispersive transport of solutes
involved in sequential first-order decay reactions. Con. of Geosciences
2:129-147.
SOURCE: M. Th. VanGenuchten
U.S. Salinity Laboratory
4500 Glenwood Drive
Riverside, CA 92501
A-9
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CODE NAME: GETOUT . ;
PHYSICAL PROCESSES: Predicts the transport of radionuclide chains along a
one-dimensional path.
DIMENSIONALITY: One dimensional.
SOLUTION TECHNIQUE: Analytical.
DESCRIPTION: The model interfaces directly with the water-dose models, ARRG
and FOOD, and together they are used to predict the dose consequences to people
from radionuclide releases.
The model analyzes the transport of radionuclides by flowing groundwater
following a leach incident at an underground nuclear waste disposal site. This
model assumes that at some arbitrary time after the waste is deposited; the
contents of the site are dissolved at a specific constant rate by groundwater.
The groundwater flows at constant velocity through a homogeneous
one-dimensional column of the geologic medium and discharges
to a surface water body. The dissolved radionuclides are assumed to be in
sorption equilibrium at all points in the geologic medium. Radioactive decay
(including chain decay of the actinides) is modeled both at the disposal site
and during migration through the geologic medium. Trace concentrations of the
dissolved nuclides are assumed and, as a result, the adsorption equilibrium
constants are independent of concentrations. A constant axial dispersion
coefficient is also assumed. This model is applicable to particulate and
fractured media, provided the necessary input data are obtained properly and it
can be applied to heterogeneous media if a weighted averaging technique is
properly applied to the relevant input parameters.
CODE INPUT: Inputs for GETOUT include:
time leaching beings;
duration of leaching;
§ path length;
pore velocity of water; and
t dispersion coefficient.
CODE OUTPUT: The output of the code is the rate of discharge of each
nuclide. Digital and graphic output is printed and results are written to a
file that can be read by the biosphere code FOOD. Peak discharge rates are
reported for key nuclides.
COMPILATION REQUIREMENTS: GETOUT is written in FORTRAN IV and implemented on
a UNIVAC-1100/44 EXEC-8 system. It has been converted to CDC equipment.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
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CODE VERIFICATION: Verification work by E. L. J. Rosinger at Whiteshell
(ref. 4) uncovered problems in early unpublished versions of the code and
confirmed the accuracy of the published version by comparison with analytic
solutions. The code is in the public domain.
DOCUMENTATION/REFERENCES:
DeMier, W.V.; Cloninger, M.O.; Burkholder, H.C.; Liddell, P.O. (1979)
GETOUT -- a computer program for predicting radionuclide decay chain
transport through geologic media. PNL-2970, Pacific Northwest
Laboratories.
Burkholder, H.C.; Cloninger, M.O.; Baker, D.A.; Jansen, 6. (1976) Incentives
for partitioning high-level waste. Nuclear Technology 31:150, also as
BNWL-1927, Pacific NorthwestLaboratories Report BNWL-1927.
Lester,'D.-.H.; Jansen, G.; Burkholder, H.C. (1975) Migrationofradionucli.de
chains through an; adsorbing medium. AIChE Symposium Series 152,
Adsorption and Ion Exchange 71.
Burkholder, H.C.; Rosinger, E.L.J. (1980) Nuclear Technology 49.
Elert, M.; Grundfelt, B.; Stenquist, C. KBS Teknisk Rapport 79-18.
SOURCE: GETOUT'was originally written by D. H. Lester, H. C. Burkholder, and
M. 0. Cloninger at,Pacific Northwest Laboratory. The current FORTRAN IV
version was developed by H. C. Burkholder, M. 0. Cloninger, W. V. DeMier, and
P. J. Liddell. '.:..
-------
CODE NAME: GWMTM1 and GWMTM2 (Groundwater Mass Transport Model 1 Dimensional
and 2 Dimensional)
PHYSICAL PROCESSES: Determines contaminant concentrations in the vicinity of
a decaying source under steady-state flow conditions.
DIMENSIONALITY: One or two dimensional depending upon code used.
SOLUTION TECHNIQUE: Analytical.
DESCRIPTION: The codes are deterministic, one- or two-dimensional analytical
solutions of the transient convective-dispersive mass transport equation
modified for first-order decay, with an exponentially decaying, Gaussian
boundary condition. The one-dimensional model is designed to solve for
vertical infiltration of wastewater through saturated or unsaturated soil media
under constant vertical seepage velocity. Presumably it could be used to model
one-dimensional horizontal transport also under steady-state flow conditions.
The two-dimensional code is designed for estimating the two-dimensional (area!
or vertical cross section) concentration pattern downgradient from sanitary
landfills, wastewater lagoons, or other groundwater pollution sources.
CODE INPUT: GWMTM1: Dispersion coefficient, kinetic decay constant,
constant seepage velocity, and surface constant (if surface concentration is
not constant), user specified space, and time positions.
GWMTM2: Fewer than ten cards for parametric information plus space and time
positions for desired concentration calculations.
CODE OUTPUT:
and time.
Concentrations are printed at user-specified locations in space
COMPILATION REQUIREMENTS: The model is written in standard FORTRAN IV and
has been run on an S/360/91; it should run on any standard digital computer.
The program requires a region size of approximately 100K on the S/360/91. One
can learn to run the model in less than a half hour and only four FORTRAN
statements need to be punched (space and time positions are specified as data
cards). Setup time is insignificant and FORTRAN programming knowledge is
unnecessary. It has also been run on minicomputers using less than 100K of
core.
EXPERIENCE REQUIREMENTS: Minimal.
TIME REQUIREMENTS: Days.
CODE VERIFICATION: The two-dimensional version has been "used to check the
numerical accuracy of several solution schemes of two-dimensional, numerical
models of groundwater quality. It has been distributed widely through short
courses dealing with groundwater pollution and has been used principally to
simulate leachate plumes from landfills and check the accuracy of
two-dimensional, numerical models."
A-12
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DOCUMENTATION/REFERENCES:
Professor Robert W. deary
r P. 0. Box 2010
Princeton, NJ 08540 ..- , , ; ,
Cleary, R.W. (1977) Final 208 report to the Naussau-Suffolk Regional Planning
Board, Hauppauge, New York.
SOURCE: Bob Cleary, Princeton, NJ.
A-13
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CODE NAME: NUTRAN
PHYSICAL PROCESSES: NUTRAN calculates the consequences (in terms of releases
of radioactivity or doses to humans) of groundwater releases of radioactivity
from a repository. NUTRAN evaluates the combined effect of systems of natural
and engineered barriers; some barriers are modeled in detail and others are
simply characterized by a number summarizing their performance (e.g., for a
canister, lifetime).
DIMENSIONALITY: One, two, or three dimensional.
SOLUTION TECHNIQUE: Analytical.
DESCRIPTION: The principal phenomena treated by NUTRAN are:
t the resaturation of the repository cavity with water;
t leaching of the waste matrix;
dissolution of the radioactive elements in the waste;
diffusion through clay cylinders around waste canisters;
transport of waste by groundwater through the repository, surrounding
strata, and adjacent aquifers (calculated using a network of
one-dimensional flow paths, with a two-dimensional method used for
aquifers containing wells);
withdrawal of contaminated groundwater through wells;
a transport of waste in surface waters and associated ecosystems; and
human exposure and dose mechanisms.
NUTRAN performs most of the functions involved in analyzing long-term effects
of a waste repository. NUTRAN 'contains only an extremely simple model for
groundwater flow. In many cases the results of a flow code such as VTT must be
used to prepare the inputs to NUTRAN. Among these cases are those in which'
two- or three-dimensional effects are important or thermal convection or large
density gradients are present.
The code is based on representing the flow field as a network of
one-dimensional path segments. Arbitrary numbers and configurations of path
segments can be accommodated. Simple models of several of the engineered
barriers in the repository and waste package are also included.
The principal assumptions of the code are:
t the one-dimensional solute transport equation is valid within each path
segment;
sorption may be represented as equilibrium adsorption;
once a canister has any holes in it, it disappears entirely as a barrier
to waste dissolution;
A-14
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when a clay buffer cylinder is present, wastes diffuse through it in
approximately a steady state; and
water in waste storage rooms is well mixed,
CODE INPUT: NUTRAN permits the user to divide nuclides into classes with
identical sorption behavior. It also permits "states" with different water
flow to occur over time. The principal inputs to WASTE are as follows:
retardation factor of each class of nuclides in each leg in each state;
cross-sectional area of each Teg in each state;
longitudinal dispersivity of each leg;
t hydraulic conductivity of each leg in each state;
heads at leg junctions in each state;
length of each leg;
effective porosity of each leg in each state; '
repository dimensions and backfill characteristics;
age of wastes at repository commissioning;
canister lifetime;
rates or times of transitions among states;
9 solubilities of any nuclides (optional);
locations and pumping rates of wells; and
transverse dispersivity of aquifer from which wells draw.
The inputs to PLOT, other than disk files written by ORIGEN, BIODOSE, and
WASTE, usually consist only of control variables.
CODE OUTPUT: The primary output of NUTRAN is the rate at which radioactivity
is released or the dose to individuals or populations. Both totals due to all
nuclides and the contributions of any number of individual nuclides selected by
the user are available. Doses or release rates are given as functions of time
with peak values identified; release rates and population doses may also be
integrated over all time. Both digital and graphic output may be obtained.
A variety of intermediate quantities used in the calculations may also be
output.
COMPILATION REQUIREMENTS: The code is written in PL/I and has been run on a
number of IBM machines. The user must supply IMSL (International Mathematical
Statistical Language) routines and, if graphical output is desired, the DISSPLA
plotting package is used. The test cases in the User's Guide require 2 to 3
minutes CPU time on an IBM 370/3031. BIODOSE requires one megabyte of core;
A-15
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WASTE and PLOT require 512 K. A small amount of disk storage is required for
communication among the programs.
TASC has not released the program to the public.
EXPERIENCE REQUIREMENTS: Extensive. '
TIME REQUIREMENTS: Months. '
' ' - " - - '"''',', 'J
CODE VERIFICATION: NUTRAN has been compared to GETOUT and BIOPATH for a
one-dimensional problem (ref. 1), and to a number of analytic solutions.
DOCUMENTATION/REFERENCES: ' ' . .
Ross, B.; Koplik, C.M.; Giuffre, M.S.;, Hodgin, S.P. (1981) A computer model
of long-term hazards =frorh waste repositories. Radioactive Waste
Management 1:325-338. . ' ;,
Ross, B., Koplik, C.M.; Giuffre, M.S.; Hodgin, S.P.; Duffy, J.J. (1979)
NUTRAN: a computer model of long-term hazards from waste repositories.
The Analytic Science Corporation Report UCRL-15150.
Ross, B,; Koplik, C.M. (1979) A new numerical method for solving the solute
transport equation. Water Resour. Res. 15:949-55.
Giuffre, M.S.; Ross, B. .(1979) The effect of retardation factors on
radionuclide migration. In G. J. McCarthy, ed., Scientific Basis for
Nuclear Waste Management 1:439-442, Plenum, NY, and Longon.
Ross, B ; Koplik, C.M. (1978) A statistical approach to modeling transport of
pollutants in ground water. Mathematical Geology 10:657-672.
Berman, I.E.; Ensminger, D.A.; Giuffre, M.S.; Koplik, C.M.; pston, S.G.;
Pollak, G.D.; Ross, B.I. (1978) Analysis of some nuclear waste
management options. The Analytic Sciences Corporation Report UCRL-13917.
Ross, B.; Koplik, C.M.; Giuffre, M.S.; Hodgin, S.P.; Duffy, J.J.; Nalbandian,
J.Y. (1980) User's guide to NUTRAN: .a computer analysis system for
long-term repository safety. Atomic Energy of Canada^ Ltd., Technical
Report AECL-TR-121.
SOURCE: The code was developed by B. Ross, C. M. Koplik, M. S. Giuffre, J.
J. Duffy, S. P. Hodgih; and others at the Analytic Sciences Corporation.
A-16
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CODE NAME: NWFT/DVM (Network Flow and Transport/ Distributed Velocity
Method)
PHYSICAL PROCESSES: Predicts fluid flow and transport of radionuclide
chains. The rate at which nuclides enter groundwater can be limited by both
leach rates and equilibrium solubility. Water velocities can reflect density
forces caused by nonuniformities in salt concentrations.
DIMENSIONALITY: One dimensional.
SOLUTION TECHNIQUE: Numerical convolution of analytical solution for a
discretized flow network; utilizes the "distributed velocity method."
DESCRIPTION: NWFT/DVM uses a network of one-dimensional flow paths. A
steady-state water velocity is calculated in each path, with pressures and
brine densities considered. Radionuclides enter groundwater at a rate
determined by the combined effects of kinetic leaching and equilibrium
solubility. Transport of radionuclides can be handled by either an analytic
solution (similar to GETOUT and NUTRAN) within each path segment (or "leg") or
by the Distributed Velocity Method (DVM) which is unique to this code.
Daughter nuclides whose velocity differs from their parents' must be treated by
DVM.
NWFT/DVM is a far-field code. It is designed to analyze repositories in well
stratified sedimentary.rocks. NWFT/DVM is finite-difference ,or finite-element
code. .
The principal assumptions of the code are:
fluid flow proceeds only along a specified network of 15 path segments;
t Darcy's Law is valid;
the one-dimensional solute transport equation is valid within each path
... segment;
I ,- - ! : '.-.., ' - '-'.-. . ' " ' . . '
t thermal convection can be neglected;
all water .flowing through the repository contacts the waste;
brine concentration and pressures do not change over time; and
t sorption can be represented as equilibrium adsorption.
CODE INPUT: Inputs for NWFT/DVM include:
conductivity in each leg;
t cross-sectional area of each leg;
elevation of each node;
porosity of each leg;
rock density in each leg (optional);
A-17
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brine concentration in each leg;
t mass of each nuclide;
t half life of each nuclide;
t initial inventory of each nuclide;
distribution coefficient of each nuclide in each leg;
leach time;
dispersion constant (same value everywhere);
t solubility of each nuclide;
time leaching beginnings; and
cutoff time.
CODE OUTPUT: The principal output is the discharge rate of each nuclide in
Ci/day as a function of time. The total integrated discharge and the peak
discharge rate are also given. A variety of intermediate quantities can be
output as well.
COMPILATION REQUIREMENTS: The code is written in FORTRAN. The code uses one
IMSL (International Mathematical Statistical Library) routine to solve a system
of linear equations. This routine or a substitute must be supplied by the
user.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Results from NWFT/DVM have been compared with results of
GETOUT for a range of one-path-segment problems. Also, it has been compared to
SWIFT for a problem with a six-member decay chain. The code is in the public
domain.
DOCUMENTATION/REFERENCES:
Campbell, J.E.; Longsine, D.E.; Cranwell, R.M. (1981) Risk methodology for
geologic disposal of radioactive waste: the NWFT/DVM computer code user's
manual. Sandia National Laboratories Report NUREG/CR-2081.
NWFT/DVM lecture notes. Draft, Sandia National Laboratories.
Campbell, J.E.; Longsine, D.E.; Reeves, M. (to be published) The distributed
velocity method of solving the convective-dispersion equation.
SOURCE: The NWFT/DVM model was developed at Sandia National Laboratories.
The original NWFT model was developed at Sandia and INTERA Environmental
Consultants by Campbell, Kaestner, Langkopf, and Canty. NWFT/DVM incorporates
the DVM, developed by Campbell and Longsine of Sandia and Reeves of INTERA.
A-18
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NUMERICAL FLOW (SATURATED/UNSATURATED)
A.19
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CODE NAME: FEMWATER1
PHYSICAL PROCESSES: Predicts groundwater flow through saturated or
unsaturated porous media.
DIMENSIONALITY: Two dimensional (x-y, x-z cartesian).
SOLUTION TECHNIQUE: Numerical, finite element, quadrilateral element.
DESCRIPTION: FEMWATER1 is a revision of the Yeh and Ward subsurface flow
model. It is a flow-only code that creates a data file specifically for the
operation of the FEMWASTE1 pollutant transport model. FEMWATER1 applies to
flow in porous media which is:
t transient or steady state;
two dimensional (horizontal or vertical cross section); and
saturated-unsaturated.
The model is based on the conservation of mass and momentum and includes soil
and water compressibility effects. Water is exchanged between the surface and
subsurface media by:
t seepage or ponding;
infiltrating runoff from rainfall;
artificial recharge and withdrawal; and
ponds, lakes, and streams.
FEMWATER1 uses quadrilateral bilinear and triangular finite elements to
represent the two-dimensional porous media domain. The Galerkin method ;of
weighted residuals is used to solve the continuity equation and Richards'
equation. Finite difference discretization of the time derivatives can be
specified in one of three ways:
1) backward difference;
2) central difference; or ;
3) mid-difference.
The mid-difference time stepping scheme was added to the previously available
options of central and backward differencing schemes. The method of
mid-differencing assumes linear variation of the unknown variable over the time
interval such that the computer matrices are evaluated at the midpoint of the
time interval. " ,
With the three time stepping and two mass Tumping options, six numerical :
solution procedures are available in FEMWATER1. Other than the general
recommendations above, no discussion of the stability or accuracy
characteristics of the various solutions is presented. .:5
A-20
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Soil properties and hydraulic conductivities in FEMWATER1 are functions of
pressure head alone. Because pressure head is the dependent variable, the
equation set to be solved is nonlinear, requiring iterative solution
techniques. The Newton-Raphson iteration with the option of over- and
under-relaxation is used. For large problems, a line successive
over-relaxation technique is available.
Unlike most flow models that calculate the velocity field by taking derivatives
of the solved pressure field, FEMWATER1 formulates Darcy's Law with the finite
element solution method. This approach has the advantage of continuous
velocity distributions at the model boundaries.
Mass balance computations are built into FEMWATER1 to monitor numerical error
generation.
The main assumptions of the code are:
Darcy's Law is valid and hydraulic-head gradients are the only significant
driving mechanisms for fluid flow; and
the nonlinear soil properties and the hydraulic conductivity are functions
of the pressure head only.
CODE INPUT: Inputs to FEMWATER1 include:
grid geometry;
initial heads;
prescribed head and flux boundary conditions;
t hydraulic-conductivity tensor;
t modified storage coefficient; and
a material nonlinearities.
CODE OUTPUT: The output from FEMWATER1 consists of the pressure distribution
and velocity field at each time step.
COMPILATION REQUIREMENTS: FEMWATER1 is written in FORTRAN and was originally
installed on an IBM 360 machine. The code is generally compatible with most
all mainframe or virtual memory machines.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Two sample problems to which solutions had previously
been obtained by other validated numerical models, namely 1) the seepage pond
problem and 2) the Freeze transient problem, were solved. In addition, results
by all six alternative numerical schemes discussed below in the section on
numerical approximations were compared in both examples. No field validation
has been performed.
A-21
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DOCUMENTATION/REFERENCES:
Yeh, G.T.; Ward, D.S. (1979) FEMWATER: a finite-element model of water flow
through saturated-unsatureted porous media. Oak Ridge National Laboratory
Report ORNL-5567.
Reeves, M.; Duguid, J. 0. (1976) Water movement through saturated-
unsaturated porous media: a finite-element Galerkin model. Oak Ridge
National Laboratory Report ORNL-4927.
SOURCE: FEMWATER1 was developed at Oak Ridge National Laboratory by G. T.
Yeh and D. S. Ward. It is an extension of work done by Reeves and Duguid.
code is in the public domain.
The
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CODE MAME: FREEZE
PHYSICAL PROCESSES: Predicts water flow in a groundwater basin under
transient saturated-unsaturated conditions.
DIMENSIONALITY: Three dimensional.
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: A three-dimensional finite-difference model has been developed
for saturated-unsaturated transient flow in small, nonhomogeneous, anisotropic
geologic basins. The uniqueness of the model lies in its inclusion of the
unsaturated zone in a basin-wide model that can also handle both confined and
unconfined saturated aquifers under both natural and developed conditions. The
integrated equation of flow is solved by the line successive overrelaxation
technique. The model allows any generalized region shape and any configuration
of time-variant boundary conditions. When applied to natural flow systems, the
model provides quantitative hydrographs of surface infiltration, groundwater
recharge, water table depth, and stream base flow.
Results of simulations for hypothetical basins provide insight into the
mechanisms involved in the development of perched water tables. The
unsaturated basin response is identified as the controlling factor in
determining the nature of the base flow hydrograph. Application of the model
to developed basins allows one to simulate not only the manner in which
groundwater withdrawals are transmitted through the aquifer, but also the
changes in the rates of groundwater recharge and discharge induced by the
withdrawals. For any proposed pumping pattern, it is possible to predict the
maximum basin yield that can be sustained by a flow system in equilibrium with
the recharge-discharge characteristics of the basin.
CODE INPUT: Inputs consist of standard unsaturated or saturated zone
hydrologic parameters.
CODE OUTPUT: Output consists of a pressure or head distribution.
COMPILATION REQUIREMENTS: FREEZE is written in FORTRAN and is operational on
an IBM system.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Freeze, R.A. (1971) Three-dimensional transient saturated-unsaturated flow in
a ground water basin. Water Resour. Res. 7(2):347-366.
SOURCE: This code was developed by R. A. Freeze of the University of British
Columbia. The code is in the public domain.
A-23
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CODE NAME: UNSAT1
PHYSICAL PROCESSES: Provides a simulation capability for flow in a
one-dimensional unsaturated or saturated soil column.
DIMENSIONALITY: One dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: The UNSAT1 model provides numerical solutions to the
one-dimensional flow problem of an unsaturated-saturated medium. It employs a
Galerkin finite-element analysis of this one-dimensional physical domain. The
hermite cubic polynomial is used as the basis for the finite-element
approximation to the continuum.
CODE INPUT: Inputs consist of standard unsaturated or saturated zone
hydro!ogic parameters..
CODE OUTPUT: Output consists of a pressure or head distribution.
COMPILATION REQUIREMENTS: UNSAT1 is written in FORTRAN IV.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
van Genuchten, M.Th. Numerical solutions of the one-dimensional
saturated-unsaturated flow equation. 78-WR-09, Princeton University,
Princeton, NJ.
SOURCE: This code was written by M. Th. van Genuchten of the U.S. Salinity
Laboratory. The code is in the public domain.
A-24
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CODE NAME: UNSAT2
PHYSICAL PROCESSES:
porous media.
Simulates nonsteady seepage in saturated or unsaturated
DIMENSIONALITY:
cylindrical).
Two dimensional (x-y or x-z cartesian), Ax-isymmetric (r-z
SOLUTION TECHNIQUE:;NUmericaK finite element, triangular: elements,
DESCRIPTION: The program can be used to investigate problems involving two
spatial dimensions in the horizontal or vertical plane. Three-dimensional
problems can be handled provided that the flow pattern retains an axial
symmetry about the vertical coordinate. Jhe flow region may have any complex
shape and it may consist of different soil materials arranged in arbitrary
patterns. Each soil material may exhibit an arbitrary degree of local
anisotropy with the principal hydrauljc conductivities oriented.at any desired
angle with respect to the coordinates. ...--^
A wide range of time-dependent boundary conditions can be treated: prescribed
pressure head; prescribed flux normal to the boundary;, seepage faces arid .
evaporation and infiltration boundaries where the maximum rate of flux is
prescribed by atmospheric or other external conditions while the.actual rate is
initially unknown. In addition, the program can handle water uptake by plants
assuming that the maximum rate of transpiration is determined by atmospheric ,
conditions while the actual rate of uptake depends on atmospheric as well as
soil and plant conditions. Internal volumetric sinks or sources of prescribed
strength can be included in the flow system at any stage of the computation: A
special provision has been made for the.analysis of axisymmetric flow to a well
of finite radius partially penetrating an unconfined aquifer,system ind
discharging at a prescribed time-dependent rate. The well may be partially
cased and its capacity for storing water is taken into account. Several layers
can be tapped by the well at the same time.
The domain simulated by UNSAT2 is discretized using three-noded triangular
elements. The time domain is discretized by finite-difference techniques.
The main assumptions of the code are:
Darcy's Law is valid and hydraulic-head gradients are the only significant
driving mechanism for fluid flow;
the rate of uptake by roots is proportional to the pressure head gradient
across the soil-root interface;
there is no hysteresis in the water retention or relative permeability
curves; and
the relative permeability and capillary pressures are functions of
moisture content.
CODE INPUT: Inputs to UNSAT2 include:
t grid geometry;
A-25
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initial heads (total head or pressure head);
boundary conditions;
» rates of infiltration, evaporation, and transpiration;
root effectiveness function;
hydraulic conductivity tensor; . ..- i '
relative permeability function;
capillary pressure function; and
storage coefficient.
CODE OUTPUT: The printed output of the program consists of a listing of all "
input information, a complete description of the finite-element network,: the
boundary codes of all nodes, and the properties of each material. During each
time step the program prints a listing of total head values, pressure head
values, moisture content values, and discharge into or out of the system (not
flow through the system) at all nodes. The rate of convergence of the
iterative procedure is printed during each time step together with additional
information pertaining to the particular problem at hand.
COMPILATION REQUIREMENTS: UNSAT2 is written in FORTRAN IV and was originally
installed on an IBM 370/165 machine. The code is generally compatible with
most all mainframe or virtual memory machines.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Due to the lack of analytic solutions to problems of flow
in the unsaturated zone at the time UNSAT2 was developed, verification could
only be performed by comparing the results to results obtained from other,
previously validated, numerical models. The effect of vertical flow in the
presence of evapotranspiration was simulated using both a finite-difference
code and the finite-element code, UNSAT2. The results were compared.
Two field problems were simulated by UNSAT2 as reported in Ref. 1. These are:
1) a field experiment performed by Feddes (ref. 2) at the groundwater level
experimental field Geestmerambacht in the Netherlands, and 2) a field
experiment taken from the subirrigation experimental field "De Groeve" in the
Netherlands (ref. 3).
DOCUMENTATION/REFERENCES:
Neuman, S.P.; Feddes, R.A.; Bresler, E. (1974) Finite element simulation of
flow in saturated-unsaturated soils considering water uptake by plants.
Technion, Hydrodynamics, and Hydraulic Eng. Laboratory Report, July.
Feddes, R.A. (1971) Water, heat, and crop growth. Thesis Comm. Agric. Univ.
Wageningen 71-12, pp. 184.
A-26
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Feddes, R.A.; van Steenbergen, M.G. (1973) Sub-irrigation field 'De
Groeve'." Mpta 735, Inst. for Land and Water Management Res., Wageningen,
pp. 184.
Feddes, R.A.; Bresler, E.; Neuman, S.P. (1974) Field test of an improved
numerical model for water uptake by root systems. Unpublished manuscript.
Hanks, R.J.; Klute, A.; Bresler, E. (1969) A numeric method for estimating
infiltration, redistribution, drainage, and evaporation of water from
soil. Water Resour. Res. 5(5):1064-1069.
Neuman, S.P. (1972b) Finite element computer programs for flow in
saturated-unsaturated porous media. Second Annual Report, Project No.
A10-SWC-77, Hydraulic Engineering Laboratory, Technion, Haifa, Israel,
pp. 87.
Neuman, S.P. (1973) Saturated seepage by finite elements. Prpc. ASCE, J.
Hydraul. Division, 99(HY12):2233-2250.
SOURCE: UNSAT2 was developed at Technion, Israel Institute of Technology, by
S. P. Neuman, R. A. Feddes, and E. Bresler. The code is in the public domain.
A-27
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NUMERICAL FLOW (SATURATED),
A-28
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CODE NAME: BEWTA
PHYSICAL PROCESSES: Predicts the Boussinseq equation for a two-dimensional
water table aquifer.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE: Numerical, finite-difference.
DESCRIPTION: The aquifer is given by a two-dimensional discrete
representation in the horizontal plane. Its boundary is irregular and mixed,
and it is superimposed by a meandering stream. Aquifer parameters are assigned
to each nodal point and an be slightly anisptropic and nonhomogeneous.
Transient groundwater flow through a water table aquifer is described by the
Boussinesq equation, which assumes that the Pupuit-Forchheimer assumptions are
valid. The principal conductivity components are colinear with the coordinate
system X and Y. The water is released from storage mainly by gravity drainage
with an instantaneous decline in head. The stream bed is semi-confined, and
the leakage obeys Darcy's Law. The flow from the unsaturated zone and the
change in fluid density over time are negligible. Replenishment of the aquifer
system occurs through gravity drainage and stream bed leakage.
The model simulates transient groundwater flow through a two-dimensional water
table aquifer using the alternative direction implicit method. The Boussinesq
equation is approximated by a two-dimensional finite-difference equation of
linearized form, employing the noniterative alternat'in9 direction implicit
method. The equation is written for two half-time steps, and is done for each
node along either a row or a column, The resulting simultanepus equations are
solved by the Thomas algorithm. The calculations are carried on successions!ly
row by row for the first half-time step and column by column for the second
half-time step (where results are approximations to the transient solution of
the problem under discussion).
CODE INPUT: Standard saturated zone hydrologic parameters.
CODE OUTPUT: Head distribution at each time step.
COMPILATION REQUIREMENTS: BEWTA is written in FORTRAN.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES: Not available,
SOURCE: BEWTA was developed by Chang L- Lin of the Nova Scotia Department of
the Environment.
A-29
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CODE NAME: COOLEY
PHYSICAL PROCESSES: Predicts the transient or steady-state hydraulic head
distribution and velocity flow field in a confined, semi confined, or unconfined
aquifer.
DIMENSIONALITY: Two-dimensional (x-y or x-z cartesian, r-z radial).
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: The code is applicable to confined, semi confined, or unconfined
flow problems which obey the generalized Boussinesq equation. Flow may be
steady or nonsteady. The aquifer may be given an area! (plan view) or radial
description or may be cross sectional. Aquifer parameters may be distributed
or zoned and the system may be anisotropic with the principal components
aligned with the global coordinate axes. In the
area! description, if used, leakage from confining beds (or river bottoms,
etc.) is vertical and storage in the confining beds is neglected. The
Dupuit-Forchheimer assumptions and delayed (or no delayed) yield constant are
used for the water table case in plan view. The basic discretization method is
the subdomain finite-element method with the time discretized by a weighted
average technique.
COOLEY is best suited for a single layer aquifer system. A layered aquifer
system, however, may be analyzed within using the radial coordinate system.
The code represents a two-dimensional area, whether area!, plane cross
sectional, or axisymmetric cross sectional, as a series of zones. The zone
shapes may be triangular or quadrilateral and of nearly any convex shape except
that the boundaries must pass through, and not between, all nodes.
There are three basic versions of the program, the differences among them being
the methods used to solve the matrix equation. The choice depends on the site.
COOLEY is most applicable to porous media. Fractured media can also be modeled
if the fractures are sufficiently numerous that they can be approximated by a
porous medium.
The principal numerical approximations in COOLEY are the following:
Discretization of space by the finite-element method of using the
"subdomain collocation" version of the weighted residual method (ref. 3,
p.40).
Discretization of time by the explicit Euler forward difference, the
semi-implicit Crank-Nicholson central difference, or the fully implicit
backward difference scheme.
The main assumptions of the code are:
Darcy's Law is valid and hydraulic-head gradients are the only significant
driving mechanisms for fluid flow.
The porosity and, hydraulic conductivity of the aquifer are constant with
time.
A-30
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t Gradients of fluid density, viscosity, and temperature do not affect the
velocity distribution.
Assumptions analogous to the Dupuit-Forchheimer assumptions are used for
unconfined aquifers.
The transmissivity tensor has principal axes parallel to the coordinate
axes.
CODE INPUT: Inputs to COOLEY include:
t grid geometry;
prescribed head and flux boundary conditions;
transmissivity in both x and y (or r and z) directions;
0 storage coefficient or specific yield for area! problems and specific
storage for cross-sectional or radial-flow problems;
hydraulic conductance for an adjacent aquitard for area! flow problems;
known recharge or discharge rates; and
initial hydraulic-head distribution.
CODE OUTPUT: The output from COOLEY consists of the pressure distribution
and velocity field at each time step.
COMPILATION REQUIREMENTS: The basic programs are dimensioned such that the
maximum mesh size is 50 by 50 (2500) nodes, and the maximum number of time
steps is 100. In addition, the maximum number of iterations for program LSOR
is 100. With these dimensions, LSOR and ADIPIT occupy about 25,000 words and
SIP occupies about 32,500 words of core on a CDC 6400 computer. However, the
dimensions can easily be modified to accommodate other problem sizes and
smaller or larger computers. No special library functions or subroutines are
used, and the only peripheral equipment needed is a card reader. The final
versions of the program were tested on a CDC 64000 computer. COOLEY is
programmed in FORTRAN IV.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: The code was verified for four problems to which
analytical solutions were available.
Field validation runs simulated the influence of seasonal pumping of irrigation
wells on groundwater levels in Ash Meadows, California, and Nevada.
DOCUMENTATION/REFERENCES:
Cooley, R.L. (1974) Finite element solutions for the equations of groundwater
flow. Nevada University.
A-31
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Bear, J. (1972) Dynamics of fluids in porous media. New York,.NY: .American
Elsevier. -...'.. v ,-.-1
Zlenkiewicz, O.C. (1971) the finite element method of engineering1science!
London: McGraw-Hill. ' ' ;;
SOURCE: COOLEY was developed at the Center for Water Resources Research,
Desert Research Institute, University of Nevada, by R. L. Cooley. The code is
in the public domain.
A-32
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CODE NAME: FE3DGW
PHYSICAL PROCESSES: Saturated groundwater flow in a homogeneous or
heterogeneous geological system. The code provides water flow paths and travel
times.
DIMENSIONALITY: Three-dimens'iorial, radial flow (r-z)l "'.[.,'':'._ / './",.
SOLUTION TECHNIQUE: Numerical, finite element quadrilateral elements.
DESCRIPTION: FE3DGW is a set of codes designed to be executed in uncoupled
stages. This allows the user to verify the accuracy of the input data before a
full simulation is made, while storing information on disk for access by the
main program. A plotting package is included in the data preprocessing stage
to display node and element locations and vertical logs of the hydrogeologic
strata. Contour plots of potential surfaces and strata interfaces are produced
in three-dimensional projections to help identify obvious errors. Once the
model parameters have been stored successfully on disk, they need not be
processed again unless the problem configuration is changed. This is because
boundary conditions are entered in a separate stage of the data storage
process.
The equation set is linear with spatially varying conductivities. Convergence
will be perfect if the integration of the element volumes is exact. A Gaussian
quadrature scheme using two, three, or five integration points is used for the
numerical integration. A necessary condition for convergence is that the basis
functions used in the Galerkin technique must be defined such that constant
values of any of the first derivatives are available throughout the element
when suitable nodal values of potential are assigned. Backward differencing of
the time derivatives is used with the initial time step, and central
differencing is used subsequently.
The semiconfining layers, which are represented by the finite elements, are
simultaneously solved for changes in pressure by a fully three-dimensional
treatment of the nodal equations. EQSOLV is the matrix inversion algorithm
used in FE3DGW to solve the large, sparse, nonbanded system of equations. In
this algorithm, row pivoting is about the minimum nonzero element; whereas, the
pivot column is about the largest absolute element in the pivot row.
The main assumptions of the code are:
Darcy's Law is valid and hydraulic-head gradients are the only significant
driving mechanism for fluid flow.
The porosity and hydraulic conductivity are constant with time.
Gradients of fluid density, viscosity, and temperature do not affect the
velocity distribution.
The storage term is a function of the compressibility of the fluid and
porous medium only.
The medium is fully saturated.
A-33
-------
Hydraulic conductivity principal axes are aligned parallel to the
coordinate axes.
CODE INPUT: Input requirements include specification of geologic
stratigraphy, liquid and media properties, positioning and rates of manmade
aquifer stresses, boundary conditions at the areal extent of the aquifer, and
initial conditions for dynamic simulations. Specifically, these requirements
include:
t Geologic stratigraphy
Number of distinct geologic layers
Total aquifer thickness
Elevation of geologic media interfaces
x,y coordinates of elevation data
a Liquid properties
Viscosity
Density ;
Temperature profile
Media properties
Intrinsic permeability or hydraulic conductivity
Porosity
Storativity
a Manmade stresses
x,y coordinates of wells
Screened elevation
Rate of withdrawal or injection
t Boundary conditions
Water levels of hydro!ogically significant water bodies (e.g.,
streams, lakes, oceans)
Nodal fluxes due to pumping
Vertical infiltration
Lateral recharge defined by data or modeling conducted on a larger
scale ,,
Lateral no-flow boundaries defined by groundwater divides or
impermeable media
t Initial conditions for dynamic simulations
Water table elevations in unconfined zones
Spatial distribution of pressure in confined zones.
Two- and three-dimensional plotting routines are included in the FE3DGW
technology for the purpose of visualizing any obvious errors in the input
data. Inconsistency in the entered data is also monitored by built-in
consistency checks and diagnostics.
CODE OUTPUT: Results are in the form of:
§ Flow field;
a Flow paths; and
A-34
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0 Travel times.
Various levels of output detail are available:
Geometric description;
Number of nodes;
0 Types of nodes;
Dimensions;
t Surface node coordinates;
0 Input data echo; and
0 Output of all nodes and elements at selected time levels.
Written output can be directed to the line printer or disk. Plotted output is
in the form of contour maps, grid displays, and three-dimensional,
dependent-variable surfaces.
COMPILATION REQUIREMENTS: FE3DGW is written in FORTRAN IV and is currently
being run on a VAX 11/780. The code is generally compatible with most all
mainframe or virtual memory machines.
Current program limits are:
0 768 surface nodes;
0 2560 system nodes;
0 20 layers per well log;
0 99 materials;
0 768 potential boundary conditions;
0 128 stream nodes;
0 20 nonzero element nodes;
0 2048 unknown nodes;
0 128 nonzero,element bandwidth;
0 768 surface elements;
0 2000 system elements; and
0 70 time steps
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
A-35
-------
CODE VERIFICATION: Verification analysis of the three-dimensional model was
accomplished using two-dimensional or quasi-three-dimensional analytical
solutions. These include radial confineo" and leaky aquifer solutions given by
Theis (ref. 2) and Hantush (ref. 4), respectively, and also the two-dimensional
analytic solution PATHS (ref. 5). , , ......,.
FE3DGW has been applied extensively to the grbundwater. system beneath Lpng
Island, New York (ref. 6). The Long Island groundwater basin is one of the
most intensively monitored systems in the U.S.
The model has also been applied to the groundwater system at Sutter Basin,
California, where it has been inferred (ref. 7) that fresh water which is
recharging at Sutter Buttes rises through the Sutter Basin fault, creating a
salt-water mound.
The model has been used on several other occasions to better understand the
groundwater flow portion of a contaminant transport application (ref. 8, 9, and
Ivy
DOCUMENTATION/REFERENCES:
Gupta, S.K.; Cole, C.R.; Bond, F.W. (1979) Finite element three dimensional
ground water (FE3DGW) flow model formulation, program listings and user's
manual. Pacific Northwest Laboratory Report PNL-2939.
Theis, C.V. (1935) The relation between the lowering of the piezometric
surface and the rate and duration of discharge of a well using groundwater
storage. Trans. Amer. Geophys. Union 2:519-524.
Jacob, C.E. (1950) In: Rouse, H., ed. Engineering Hydraulics.
New York, NY: John Wiley and Sons, pp. 321-386.
Hantush, M.S. (1960) Modification of theory of leaky aquifers. J. Geophys
Res. 65:3713-3725.
Nelson, R.W.; Schur, J.A. (1980) PATHS groundwater hydrogeological model
Pacific Northwest Laboratory Report PNL-3162.
Gupta, S.K.; Pinder, G.F. (1978) Three-dimensional finite element model for
multilayered ground-water reservoir of Long-Island, New York. Department
of Civil Engineering, Princeton University, Princeton, NJ.
Gupta, S.K.; Tanji, K.K. (1976) A three-dimensional Galerkin finite element
solution of flow through multiaquifers in Sutter Basin, California. Water
Resour. Res. 12(2):155-162.
Bond, F.W.; Eddy, C.M. (1985) Remedial action modeling assessment, Western
Processing Site, Kent, Washington. Prepared for the U.S. Environmental
Protection Agency, Region X, Seattle, WA.
Schalla, R.; McKown, G.L.; Meuser, J.M.; Parkhurst, R.G.; Smith, C.M.; Bond,
F.W.; English, C.J. (1984) Source identification contaminant transport
simulation and remedial action analysis, Anniston Army Depot, Anniston,
Alabama. Prepared for Commander, Anniston Army Depot, Anniston, AL.
A-36
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Cole, C.R.; Bond, F.W.; Brown, S.M.; Dawson, G.W. (1983) Demonstration/
application of groundwater modeling technology for evaluation of remedial
action alternatives. Prepared for the U.S. Environmental Protection
Agency, Municipal Environmental Research Laboratory, Cincinnati, OH.
SOURCE: FE3DGW was written by S. K. Gupta, C. R. Cole, and F. W. Bond as a
result of research conducted by Pacific Northwest Laboratory and supported by
the Waste Isolation Safety Assessment Program (WISAP). FE3DGW is a derivative
of DAVIS/FE which was also written by S. K. Gupta.
A-37
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CODE NAME: FLUMP
PHYSICAL PROCESSES: Predicts two-dimensional groundwater flow.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE: Numerical, finite element, and a mixed explicit-implicit
point iterative solution.
DESCRIPTION: The FLUMP model evolved from the TRUST model, although it has
been modified considerably by S. P. Neuman. It is considerably easier to use
on groundwater flow problems than is TRUST, although it is restricted to
two-dimensional flow in either vertical or horizontal
planes. FLUMP uses a finite-element numerical scheme which has been shown to
represent only a small change from the original approach used in TRUST.
CODE INPUT: Standard saturated zone hydro!ogic parameters.
CODE OUTPUT: Head distribution at each time step.
COMPILATION REQUIREMENTS: FLUMP is written in FORTRAN and is operational on
a CDC system. : ,
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Fogg, G.E.; Simpson, E.S.; Neuman, S.P. (1979) Aquifer modeling by numerical
methods applied to an Arizona groundwater basin. PB 298962, National
Technical Information Service, Springfield, VA, 140 pp.
Narasimhan. T.N.; Neuman, S.P.; Edwards, A.L. (1977) Mixed explicit-implicit
iterative finite element scheme for diffusion-type problems. 2. Solution
strategy and examples. Int. J. Numer. Methods Eng. 11:235-244.
Neuman, S.P.; Narasimhan, T.N. (1977.) Mixed-explicit-implicit iterative
finite element scheme for diffusion-type problems. 1. Theory. Int. J
Numer. Methods Eng. 11:309-323.
Neuman, S.P.; Narasimhan, T.N.; Witherspoon, P.A. (1977) Application of mixed
explicit finite element method to nonlinear diffusion type problems. In:
Pinder, G.F.; Gray, W.E., eds. Proceedings of the First International
Conference on Finite Elements in Water Resources, Princeton, NJ, Pentech,
pp. 1.153-1.185.
SOURCE: This code was developed by S. P. Neuman of the University of
Arizona, Department of Hydrology. The code is in the public domain.
A-38
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CODE NAME: FRESURF 1 & 2
PHYSICAL PROCESSES: Predicts two-dimensional and axisymmetric flow.
DIMENSIONALITY: Two dimensional and axisymmetric.
SOLUTION TECHNIQUE: Finite element.
DESCRIPTION: In this two-dimensional model, the specifics of the
free-surface boundary as described by Neuman are incorporated into the
finite-element solution scheme used. The free boundary is handled by the
finite-element network, expanding or contracting to accommodate the movement of
the free surface with time. The total derivative or the potential, with
respect to time, is combined with specific free-boundary conditions that are
substituted into the generalized variational principle for the saturated flow
problem to give the expression for the free surface. This expression is a set
of nonlinear ordinary differential equations. A Crank-Nicholson time-centered
scheme is used to solve the nonsteady flow with the free surface. The regular
finite-element approach, based on the variational principle, provides the
potential distribution below the free surface.
The above features for handling the free surface and potential distribution are
used in the model to solve both two-dimensional and axisymmetric flow
problems. The program also solves for the seepage face, if one occurs, through
a two-step iterative procedure. It would appear that considerable additional
development would be required to extend the procedure to a three-dimensional
situation. Since it is two dimensional, the predictions are restricted to only
vertical sections when the free-surface feature is used.
CODE INPUT: Standard saturated zone hydro!ogic parameters.
CODE OUTPUT: Head distribution at each time step.
COMPILATION REQUIREMENTS: FRESURF 1 and 2 are written in FORTRAN and
operational on a CDC system.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Neuman, S.P.; Witherspoon, P.A. (1971) Analysis of nonsteady flow with a free
surface using the finite element method. Water Resources Research,
7(3):611-623.
SOURCE: FRESURF 1 and 2 were written by S. P. Neuman of the University of
Arizona, Department of Hydrology. The code,is in the public domain.
A-39
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CODE NAME: TERZAGI
PHYSICAL PROCESSES: TERZAGI solves for three-dimensional fluid flow with
one-dimensional consolidation in saturated systems.
DIMENSIONALITY: Three dimensional.
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: This model numerically simulates the movement of water in
saturated deformable porous media. The theoretical model considers a general
three-dimensional field of flow in conjunction with a one-dimensional vertical
deformation field. The governing partial differential equation expresses the
conservation of fluid mass in an elemental volume that has a constant volume of
Ull j'r JS^nUmu^ua1. solution is based on the integrated finite difference
method (IFDM), which is very convenient for handling multi-dimensional
heterogeneous systems composed of isotropic materials.
Tm1c?reSe.n$DnS?!puter P^grm is based on modifications of earlier versions of
TRUST and TRUMP.
CODE INPUT: Standard saturated zone hydro!ogic parameter plus consolidation
parameters.
CODE OUTPUT: Head distribution, consolidation information.
COMPILATION REQUIREMENTS: TERZAGI was written in FORTRAN IV and implemented
on a CDC system.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES: ..',-,
Narasimhan, T.N.; Witherspoon, P.A. (1976) An integrated finite difference
method for analyzing fluid flow in porous media. Water Resources Research
i & (1). .
SOURCE: The code was developed by^T. N. Narasimhan of the University of
California. This code is in the public domain.
A-40
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CODE NAME: USGS2D
PHYSICAL PROCESSES: Saturated groundwater flow in a confined, unconfined, or
combined confined and unconfined aquifer.
DIMENSIONALITY: Two dimensional (x-y or x-z cartesian).
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: USGS2D is a finite-difference saturated flow code. ,It is
restricted to two-dimensional (areal) flow, but has many options. USGS2D
provides the user with a variety of options for 1) groundwater flow conditions;
2) source terms; 3) numerical solution techniques; and 4) input-output. The
options for groundwater flow conditions include:
confined conditions;
unconfined conditions; and ,
t combined confined and unconfined conditions.
Variations of source terms include:
transient leakage from confining beds;
steady leakage from confining beds; . '...._
recharge;
« pumping wells; and
evapotranspiration.
The program is fairly general. The flow field is represented as a
two-dimensional grid. The size of the grid blocks is variable to allow the
desired level of spatial detail. Variable time steps are also allowed.
The major variable is hydraulic head, although drawdowns may be computed from
the initial head condition.
The model was designed primarily for areal simulations but can be used for some
cross-sectional problems. Generally this is done using the artesian option.
An example of a cross-sectional simulation is provided in the documentation.
A minor problem is that the code is programmed such that two extra columns and
two extra rows are required to border the gridded area. This results in some
additional work when preparing input data. It is also difficult to convert the
code to run on non-IBM machines.
USGS2D is designed for most types of geological media where two-dimensional
flow in a porous medium can be assumed. The main assumptions of the code are:
Darcy's Law is valid and hydraulic-head gradients are the only significant
driving mechanism for fluid flow.
A-41
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t Vertically averaged properties may be used.
t Gradients of fluid density, viscosity, and temperature do not affect the
velocity distribution.
Transmissivity principal components are aligned along coordinate axes.
Linear evapotranspiration.
Maximum evapotranspiration rate may not vary spatially. '. ;
The porosity and hydraulic conductivity are constant with time.
CODE INPUT: USGS2D may read single or multiple data sets. The contents of a
data set are described in Table A-l.
CODE OUTPUT: USGS2D prints the following: 1) all input; 2) tinie-step
information; 3) mass-balance information; 4) matrix-iteration information; and
5) computed hydraulic head or drawdown. ;
COMPILATION REQUIREMENTS: USGS2D was programmed in FORTRAN IV for use on an
IBM machine. It has been successfully adapted for use on CDC and UNIVAC
machines as well. Model results can be presented on the line printer (rows
should be numbered in the short dimension) and pen plotters with a program that
utilizes the graphical display software available from the U.S. Geological
Survey Computer Center Division. In addition, included in the model are
options for reading input data from a disk and writing intermediate results on
a disk.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: USGS2D has been compared to analytical solutions
including those for leaky aquifers. It has also been used to simulate several
hypothetical problems where detailed mass balance calculations were made. ;
This code has been the work horse of the U.S. Geological Survey for more than
ten years. It has been applied to numerous sites throughout North America.
Most of these applications have dealt with water supply problems associated
with relatively shallow aquifers. Some of the field problems include the
Washington, D.C., area (ref. 3), west-central Minnesota (ref. 4), and Nova
Scotia (ref. 5).
DOCUMENTATION/REFERENCES:
Documentation (refs. 1 and 2) for USGS2D is available in two government
publications.
Trescott, P.C.; Pinder, G.F.; Larson, S.P. (1976) Finite-difference model
aquifer simulation in two dimensions with results of numerical
experiments. U.S. Geological Survey, Techniques of Water-Resources
Investigations, Book 7, Chapter Cl.
for
A-42
-------
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A-43
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Larson, S.P. (1979) Direct solution for the two-dimensional ground-water flow
model. U.S. Geological Survey, Open-File Report 78-202.
Papadopulos, S.S.; Bennett, R.R.; Mack, F.K.; Trescott, P.C. (1984) Water
from the coastal plain aquifers in the Washington, D.C., metropolitan
area. U.S. Geological Survey Circular 697.
Larson, S.P.; McBride, M.S.; Wolf, R.J. (1975) Digital models of a glacial
outwash aquifer in the Pearl-Sallie Lakes Area. U.S. Geological Survey
Water-Resources Investigations 40-75.
Pinder, G.F.; Bredehoeft, J.D. (1968) Application of the digital computer for
aquifer evaluation. Water Resour. Res. 4:(5):1069-1093.
SOURCE: USGS2D was developed at the U.S. Geological Survey and is,described
in Techniques of Water-Resources Investigations, Book 7, Chapter Cl, by P C
Trescott, G. F. Pinder, and S. P. Larson. The code is in the public domain
In addition, the USGS offers some support for certain users and applications
A-44
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CODE NAME: USGS3D --Modular
PHYSICAL PROCESSES: Predicts groundwater flow in confined/unconfined
aquifers. ,
DIMENSIONALITY: Three-dimensional.
SOLUTION TECHNIQUE: Numerical, finite-difference.
DESCRIPTION: Groundwater flow within the aquifer is simulated using a
block-centered finite-difference approach. Layers can be simulated as
confined, unconfined, or a combination of confined,and unconfined. Flow from
external stresses, such as flow to wells, area! recharge, evapotranspiration,
flow to drains, and flow through riverbeds, can also be simulated. The
finite-difference equations can be solved using either the Strongly Implicit
Procedure or Slice-Successive Overtaxation.
The modular structure consists of a main program and a series of highly
independent subroutines called "modules." The modules are grouped into
"packages," each package addresses a specific feature of the hydrologic system.
CODE INPUT: Standard saturated zone hydrologic parameters.
CODE OUTPUT: Head distribution at each time step.
COMPILATION REQUIREMENTS: The program is written in FORTRAN '66 and will run
without modification on most computers which have a FORTRAN '66 compiler. It
will also run, without modification* with most extended FORTRAN '77 compilers
and with minor modifications on standard FORTRAN '77 compilers.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
McDonald, M.6.; Harbaugh, A.W. (1984) A modular three-dimensional
finite-difference groundwater flow model. U.S. Geological Survey
Open-File Report 83-875.
SOURCE: The code was written by Michael McDonald and Arlen Harbaugh of the
U.S. Geological Survey. This code is in the public domain.
A-45
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CODE NAME: USGS3D -- Trescott
PHYSICAL PROCESSES: Fully three-dimensional or quasi-three-dimensional
saturated groundwater flow in confined, unconfined, or combined confined and
unconfined aquifers.
DIMENSIONALITY: Fully three-dimensional, quasi-three-dimensional.
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: USGS3D simulates three-dimensional flow in a porous medium
which may be heterogeneous and anisotropic and have irregular boundaries. The
uppermost hydrologic unit may have a free surface. The stresses considered are
wells and recharge from precipitation.
One or more layers of nodes can be used to simulate each hydrogeologic unit.
It it is reasonable to assume that storage is negligible in a confining bed and
that horizontal components of flow can be neglected, the effects of vertical
leakage through a confining bed can be incorporated into the vertical component
of the anisotropic hydraulic conductivity of adjacent aquifers.
A major advantage of this code is that it can be used in a fully
three-dimensional mode or it can be reduced to a quasi-three-dimensional model
1n terms of the equations being solved and computer memory requirements. This
is accomplished by using a sequence of two-dimensional (areal) groundwater flow
models to represent aquifers. These models are coupled by terms representing
flow through intervening confining beds to form a quasi-three-dimensional
model. This latter model converges to a solution much faster than the fully
three-dimensional model because all equations are solved simultaneously. It
should be noted, however, that the leakage in this quasi-three-dimensional
model is steady, that is, it ignores storage. For long-term simulations which
approach steady state, this type of leakage is adequate.
The flow field can be represented as a three-dimensional grid or a sequence of
two-dimensional grids. The program is fairly general in that the size of the
grid blocks is variable to allow the desired level of spatial detail. Variable
time steps are also allowed.
The major variable is hydraulic head, although drawdowns may be computed from
the initial head condition. The main assumptions of the code are:
Darcy's Law is valid and hydraulic-head gradients are the only significant
driving mechanism for fluid flow. '
* The porosity and hydraulic conductivity are constant with time.
t Gradients of fluid density, viscosity, and temperature do not affect the
velocity distribution.
Hydraulic conductivity principal components are aligned with Cartesian
coordinate system.
t Steady leakage from confining bed? can be incorporated into anisotropic
hydraulic conductivity of adjacent aquifers.,
1 A-46 "
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CODE INPUT: The data required to run USGS3D includes finite-difference data,
such as spacing and physical data. The physical data includes:
initial heads;
boundary conditions;
storage coefficient distribution;
transmissivity distribution; and
recharge rate.
If the upper unit is unconfined, then hydraulic cdnductivity and the elevation
of the bottom of the water table layer is read in place of transmissivity.
CODE OUTPUT: USGS3D prints the following: 1) all input; 2) time-step
information; 3) mass-balance information; 4) matrix-iteration information; and
5) computed hydraulic head or drawdown.
COMPILATION REQUIREMENTS: USGS3D was programmed in FORTRAN IV for use on an
IBM machine, using some machine-dependent features.
Rows should be numbered in the short dimension, for plotting maps on the line
printer or for plotting data with an X-Y drum plotter. The core requirements
and computation time are proportional to the number* of nodes representing the
porous medium.
To reduce the number of cards that must be read with each run, the program
includes options to place the arrays on disk and,'on subsequent runs, read the
data from disk rather than from cards.
The documented program was designed to take advantage of certain features of an
IBM machine. Because of this, there are difficulties in converting the code to
a non-IBM machine.
EXPERIENCE REQUIREMENTS: Extensive. <
TIME REQUIREMENTS; Months. .
CODE VERIFICATION: The code has .been applied to several field problems and
code results have been compared with analytical solutions. USGS3D does have a
detailed mass balance to ensure that the solution'has converged.
This code has been applied to several field problems, including flow problems
associated with mining, hazardous waste, and radioactive waste (Columbia
Plateau). As an example of a field application of this code to a mining
problem, see ref. 3.
DOCUMENTATION/REFERENCES:
Trescott, P.C. (1975) Documentation of finite-difference model for simulation
of three-dimensional ground-water flow. U.S.' Geological Survey Open-File
Report 75-438.
A-47
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Trescott, P.C.; Larson, S.P. (1976) Documentation of finite-difference model
for simulation of three-dimensional ground-water flow. U.S. Geological
Survey Open-File Report 76-591, supplement to Open-File Report 75-438.
Weeks, J.B.; Leavesley, G.H.; Wleder, F.A.; Saulneir, G.J., Jr. (1984)
Simulated effects of oil-shale development on the hydrology of Piceance
Basin, Colorado. U.S. Geological Survey Professional Paper 908.
SOURCE: USGS3D was developed at the U.S. Geological Survey and is described
1nu?,se!)ies of reP°rts by p- c- Trescott and S. P. Larson. The code is in the
public domain. In addition, the USGS offers some support for certain users and
applications.
A-48
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CODE NAME: VTT
PHYSICAL PROCESSES: Predicts the transient or steady-state hydraulic head
distribution and provides water flow paths and travel times.
DIMENSIONALITY: Two dimensional (x-y cartesian).
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: The model is capable of calculating water flow in a
multilayered aquifer system. The system may be confined, unconfined, or
semiconfined. The main simplifying assumption transforms a three-dimensional
system to a layered two-dimensional system with interaquifer transfer via a
potential-driven leakage term. The mathematical model which utilizes this set
of simplifying assumptions is the multi-aquifer formulation of the Boussinesq
equations. VTT uses a horizontal, two-dimensional, finite-difference approach
for saturated flow in each aquifer. The code may analyze flow in such a system
for a variety of initial and boundary conditions for steady or non-steady flow.
The velocity field in the porous medium is part of the output of VTT. The
analysis of the flow field is the first stage in predicting the transport of
contaminants in a porous medium. The output of the flow field could
subsequently be used to develop inputs for such transport codes as MMT or
FEMWASTE.
For numerical formulations, a horizontal x-y coordinate grid system is adopted
with uniform nodal spacing. Standard finite-difference approximations and a
fully implicit representation of the time derivative are used.
When considering confined flow, the compressibility effects of the fluid and
matrix are incorporated, but they are neglected when considering unconfined
flow. This assumption is quite valid as long as the specific yield is not of
the same magnitude as the specific storage.
The main assumptions of the code are:
t Darcy's Law is valid and hydraulic-head gradients are the only significant
driving mechanism for fluid flow.
The porosity and hydraulic conductivity are constant with time.
Gradients of fluid density, viscosity, and temperature do not affect the
velocity distribution.
Hydraulic conductivity and effective porosity can be represented by the
vertically averaged values and are isotropic throughout the region but may
be inhomogeneous.
The free-surface slope and the aquifer bottom slope are both slight (<5o).
Vertical velocities are small and can be neglected.
Flow in the capillary finge is neglected.
Seepage surfaces cannot be handled and are neglected.
A-49
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CODE INPUT: Inputs to VTT include:
t total stress or recharge at each node;
t aquifer top elevation;
aquifer bottom elevation;
initial aquifer potential;
aquifer storage coefficient;
interaquifer transfer (leakage) coefficient; and
t aquifer hydraulic conductivity (or transmissivity) at each node.
CODE OUTPUT: The output for VTT is the new spatial variation of potential
throughout the aquifers. From this potential distribution in conjunction with
other input data, the following information can be calculated:
t groundwater velocities;
groundwater flow paths;
t travel times; and
§ new recharge/discharge relationships along streams and rivers.
Types of model output that can be produced include:
Contour maps of:
equal potential
equal drawdown
equal transmissivity
t Three-dimensional projection plots of:
potential
drawdown
transmissivity
§ Cross-sectional plots showing aquifer top, aquifer bottom, and aquifer
potential.
Flow path plots with associated listings of travel times.
t Numerical listings of the input data or calculated potentials.
Difference maps showing the node-by-node predictions of potential changes.
COMPILATION REQUIREMENTS: VTT is written in FORTRAN IV-PLUS. The code can
be run on a POP 11/70 or VAX machines. The code was converted to a CDC machine
by Intera, Inc.
EXPERIENCE REQUIREMENTS: Extensive.
A-50
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TIME REQUIREMENTS: Months.
CODE VERIFICATION: VTT has been compared with solutions from a more general
three-dimensional model, FE3DGW, and a model which uses an analytical solution,
PATHS.
DOCUMENTATION/REFERENCES:
Reisenauer, A.E. (1979) Variable thickness transient groundwater flow model
(VTT), formulation, user's manual and program listings. Pacific Northwest
Laboratory Report PNL-3160-1, PNL-3160-2, and PNL-3160-3.
Gupta, S.K.; Cole, C.R.; Bond, F.W. (1979) Finite element three dimensional
groundwater (FE3DGW) flow model, formulation, program listings and user's
manual. Pacific Northwest Laboratory Report PNL-2939.
Kellogg, O.C. (1954) Foundations of potential theory. Dover, NY.
SOURCE: VTT Was developed at Battelle, Pacific Northwest Laboratory. The
work was supported by the Department of Energy. The code is in the public
domain.
A-51
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CODE NAME: V3
PHYSICAL PROCESSES: Predicts groundwater flow in heterogeneous anisptropic
aquifers under a variety of flow conditions.
DIMENSIONALITY: Two-dimensional (x-y cartesian).
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: This series of computer programs simulates one- or
two-dimensional nonsteady-state flow problems in heterogeneous anisotropic
aquifers under water table, nonleaky, and leaky artesian conditions.
Multiple-aquifer problems with leakage between aquifers can also be treated.
These programs cover time-varying pumpage from wells, natural or artificial
recharge rates, the relationships of water exchange between surface waters and
the groundwater reservoir, the process of groundwater evapotranspiration, the
mechanism of possible conversion of storage coefficients from artesian to water
table conditions, and the multiple-aquifer problem. .
The program is fairly general. One- or two-dimensional grids, or sequences of
two-dimensional grids, may be used. The size of the grid blocks are variable
to allow the desired level of spatial detail. Variable time steps are also
allowed. The code considers several different flow conditions such as
hydraulic conductivity, storage properties, leakage properties, and recharge
properties. ,
V3 is programmed in modular fashion that allows relatively convenient
modification. In general, the modules .contain logical work tasks. The
modules, however, are not contained in subroutines; everything is contained in
the main program.
The main assumptions of the code are: , ,
Darcy's Law is valid and hydraulic-head gradients are the. only significant,
driving mechanism for fluid flow.
The porosity and hydraulic conductivity are constant with^time.
Gradients of fluid density, viscosity, and temperature do not affect the
velocity distribution. , > :
Vertically averaged properties can be used. * ; ;
Transmissivity principal components are aligned with cartesian coordinate
system. . , , ,
Leakage is steady state.
'.I.'"' .. >'-'. ''''.'I
§ Linear evapotranspiration.
CODE INPUT: Input for the basic aquifer simulation program includes:
parameter and default value cards;
§ array data;
A-52
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transmissivity;
storage coefficient;
0 initial hydraulic heads; and
0 pumpages.
With modifications to the program, additional data are read as follows:
Option
Additional Data
Variable Pumping Rates
Leaky Artesian Conditions
Induced Infiltration
Evapotranspiration
Storage Coefficient
Conversion
Water Table Conditions
Time and pumping rate of each period
Vertical hydraulic conductivity and thickness of
confining bed; head difference across confining bed
Same as leaky artesian conditions plus areas of the
stream bed
Land surface elevation; elevations of the water
table below which ET ceases; maximum ET rate
Elevation of aquifer top; water table storage
coefficient
Water table storage coefficient; elevation of
aquifer bottom
CODE OUTPUT: The primary outputs of V3 are hydraulic head or drawdowns.
There are options for displaying these in a readable fashion, such as
time-water level graphs.
COMPILATION REQUIREMENTS: The computer programs were written in FORTRAN IV
for use on an IBM 360 system model 75 with a G-level compiler. However, the
programs will operate, with modifications, on other computers. Also, these
computer programs are written so that they will operate with any consistent set
of units.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: V3 is one of the most widely used groundwater flow
codes. It has been compared to several analytical solutions, including those
by Theis, Hantush, and Jacob.
DOCUMENTATION/REFERENCES:
Prickett, T.A.; Lonnquist, C.G. (1971) Selected Digital Computer Techniques
for groundwater resource evaluation. Illinois State Water Survey,
Bulletin 55.
A-53
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McDonald, M.G.; Fleck, W.B. (1978) Model analysis of the impact on '
groundwater conditions of the Muskegon County waste-water disposal system,
Michigan. U.S. Geological Survey Open-File Report 78-99.
SOURCE: V3 was developed at Illinois State Water Survey. The code is in the
public domain.
A-54
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NUMERICAL SOLUTE TRANSPORT
(SATURATED/UNSATURATED)
A-55
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CODE NAME: FEMWASTE1 (Finite-Element Model of Waste Transport)
PHYSICAL PROCESSES: Predicts waste transport through saturated-unsaturated
porous media under dynamic groundwater conditions.
DIMENSIONALITY: Two-dimensional (x-y, x-z cartesian).
SOLUTION TECHNIQUE: Numerical, finite-element.
DESCRIPTION: FEMWASTE1 is an upgraded version of the FEMWASTE code developed
by Yeh and Ward for subsurface transport. It is a transport-only code that
requires fully specified hydrodynamics as part of the input data set.
FEMWATER1, a flow model using an identical numerical representation of the
problem domain, creates a geometric and hydrodynamic data file expressly for
FEMWASTE1.
FEMWASTE1 is capable of transient, two-dimensional simulations of pollutant
transport in saturated and unsaturated porous media. The model includes the
following transport processes:
advection;
hydrodynamic dispersion;
sorption;
first-order decay; and;
source/sink.
FEMWASTE1 uses quadrilateral bilinear elements for spatial discretization of
the porous media. Solution is by the finite element weighted residual method.
Two finite element weighting techniques are available: Galerkin and upwind.
The option of "lumping" the finite element mass matrix into a type of finite
difference unit mass matrix by scaling is also available. In some situations
the lumping technique has been more accurate. Included in the FEMWASTE1
formulation is the option of three time-stepping techniques:
1) central difference;
2) backward difference; and
3) mid-difference.
Regardless of the technique selected, Gaussian elimination is used to invert
the resulting matrices.
With the options of weighting, lumping, and time stepping, 12 different
computational approaches are possible with FEMWASTE1.
FEMWASTE1 is designed to be applied uncoupled from the flow field
calculations. This design implicitly assumes that transport processes do not
affect the fluid transport; The model is applied to a single chemical species
without considering .the effects of other chemicals that may be present in the
, A-56
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porous media. The only irreversible reaction in FEMWASTE1 is in the
first-order decay process where degradation is assumed to be directly
proportional to the total pollutant concentration (including dissolved and
adsorbed phases). FEMWASTE1 does not explicitly account for biological uptake
or other degradation mechanisms, although these effects can be included
approximately by adjusting the decay constant. Transformation and loss
mechanisms can be represented by the source/sink term local to each element.
Chemical sorption is assumed to be a reversible fast-exchange reaction that
attains local equilibrium within a single time interval according to a linear
isotherm. The distribution coefficient, Kd, is moisture independent in
FEMWASTE1. This assumption restricts the model application to cases where all
soil grains are effective in the adsorption process. The calculated
retardation factor, however, is an inversely dependent function of the moisture
content.
CODE INPUT: FEMWASTE1 requires standard material and aquifer properties:
t adsorption distribution coefficient;
t bulk density;
longitudinal dispersivity;
transverse dispersivity;
decay constant;
porosity; and
modified coefficient of compressibility.
Aquifer characteristics can be entered on a regional basis or can be specific
to a given element.
Three types of boundary conditions are possible with FEMWASTE1:
1) Dirichlet, specifications of time-varying concentrations at a particular
element;
2) Neuman, specification of time-varying waste fluxes at a particular
element; and
3) Cauchy, waste-flux boundary conditions that are specific to inflow
boundaries.
Initial conditions are concentrations of pollutant in the porous media.
An error checker is present in FEMWASTE1 to ensure that the input data are
correct. When errors are detected, execution is stopped.
CODE OUTPUT: Output from FEMWASTE1 consists of formatted line-printer
listings of concentrations at specified locations and times. An auxiliary
storage device file is created for post processing on local hardware.
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COMPILATION REQUIREMENTS:
on the program are:
FEMWASTE1 is written in FORTRAN. Current limits
595 nodes;
528 elements;
500 time steps;
29 water boundary conditions;
199 boundary elements;
t 200 boundary nodes;
99 rainfall seepage element sides; and
a 100 rainfall seepage element sides.
FEMWASTE1 is designed to be applied in a batch mode. The model is constructed
in a modular fashion with one main program and 15 subroutines. Efficient
storage of the banded matrix arrays are used in FEMWASTE1. Annotation of the
source listing is good with short descriptions and identified computations.
Conversion to the VAX 11/780 is straightforward.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS Months.
CODE VERIFICATION: A sample problem of transport from a seepage pond
reported by Duguid and Reeves was used to compare the simulation by the
original computer codes with that by the new waste-transport code coupled with
the revised water-flow code. The code is in the public domain.
DOCUMENTATION/REFERENCES:
Bear, J. (1972) Dynamics of fluids in porous media.
Elsevier.
New York, NY: American
Duguid, J.O.; Reeves, M. (1976) Material transport in porous media: a finite
element Galerkin model. ORNL-4928, Oak Ridge National Laboratory, Oak
Ridge, TN.
Reeves, M.; Duguid, J.O. (1975) Water movement through saturated- unsaturated
porous media: a finite-element Galerkin model. ORNL-4927, Oak Ridge
National Laboratory, Oak Ridge, TN.
Yeh, G.T. (1982) Training course no. 2: the implementation of FEMWASTE
(ORNL-5601) computer program. ORNL/TM-8328, NUREG/CR-2706, U.S. Nuclear
Regulatory Commission, Washington, DC.
Yeh, G.T.; Ward, D.S. (1981) FEMWASTE: a finite-element model of waste
transport through saturated-unsaturated porous media. ORNL-5601, Oak
Ridge, National Laboratory, Oak Ridge, TN.
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Yeh, 6.T.; Ward, D.S. (1980) FEMWATER: a finite-element model of water flow
through saturated-unsaturated porous media. ORNL-5567, Oak Ridge National
Laboratory, Oak Ridge, TN.
SOURCE: FEMWASTE was developed at Oak Ridge National Laboratory and is
described in Report No. ORNL-5601 by G. T. Yeh and D. S. Ward. It is an
extension of work done by Duguid and Reeves.
A-59
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CODE NAME: PERCOL
PHYSICAL PROCESSES: Predicts the movement of a solute through a soil column.
DIMENSIONALITY: Unknown.
SOLUTION TECHNIQUE: Numerical, Newton-Raphson method.
DESCRIPTION: PERCOL has been developed to simulate the movement of
radionuclides through porous media as a function of measurable chemical
parameters of the media. System parameters include soil type, radionuclide
type, waste composition, flow rate, column length, and soil saturation.
CODE INPUT: Standard transport parameters.
CODE OUTPUT: Predictions of concentrations.
COMPILATION REQUIREMENTS: PERCOL is written in FORTRAN and implemented on an
IBM 360 machine.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS Months.
CODE VERIFICATION: Laboratory column studies have been conducted to verify
the model.
DOCUMENTATION/REFERENCES:
Owen, P.T. An inventory of environmental impact models relating to energy
technologies. ORNL/EIS-147, Oak Ridge National Laboratory, Oak Ridge, TN.
Routson, R.C.; Seme, R.J. (1972) One-dimensional model of the movement of
tracer radioactive solute through soil columns: the PERCOL model.
BNWL-1718, Battelle, Pacific Northwest Laboratories, Richland, WA.
SOURCE: PERCOL was written by R. C. Routson of Argonne National Laboratory
and R. 0. Serne of Battelle, Pacific Northwest Laboratories. The code is in the
public domain.
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CODE NAME: SATURN
PHYSICAL PROCESSES: Predicts saturated-unsaturated flow and radioactive
radionuclide transport.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: SATURN is a two-dimensional finite.-element model developed to
simulate fluid flow and solute transport processes in variably saturated porous
media. The model solves the flow and transport equations separately.
Transport mechanisms considered include advection, hydrodynamic dispersion,
adsorption, and first-order decay.
The flow equation is discretized using the Galerkin finite-element method.
Nonlinearity is treated using either Picard or Newton-Raphson iterations. The
transport equation is discretized using an upstream-weighted finite-element
method designed to alleviate the problem of numerical oscillations. Simple
rectangular and triangular elements are used. The combination of such elements
enables flow regions of complex geometry to be modeled accurately. A highly
efficient "influence coefficient" technique is used to generate element
matrices. This technique avoids numerical integration and leads to a reduction
in CPU time required for element matrix generation. For rectangular elements,
the saving of CPU time
prescribed values of nodal fluid flux;
longitudinal dispersivity;
transverse dispersivity;
molecular diffusion coefficients;
0 decay coefficient;
retardation coefficient;
initial inventory of solute;
0 leach duration;
prescribed values of concentration; and
t prescribed values of solute flux.
CODE OUTPUT: The primary line printer output from the flow model of SATURN
includes nodal values (at various time levels) of pressure head and element
centroidal values of Darcy velocity components and saturation at various time
levels. SATURN allows the user to select the fluid mass balance calculation
option. This budget contains information about the net flow rate of fluid due
to boundary fluxes, sources, and sinks; the rate of fluid accumulation in the
entire flow domain; the mass balance error; and the cumulative fluid storage up
to the current time.
A-61
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The primary line printer output of the transport model of SATURN includes nodal
values (at various time levels) of solute concentration. SATURN also allows
the user to select the solute mass balance calculation option. If the solute
mass balance budget is activated, information about the total dispersive and
advective fluxes; the net rate of material accumulation taking into account
storage, adsorption, and decay; the mass balance error; the cumulative mass of
solute still remaining in the porous medium at the current time; and the
cumulative mass decay up to the current time value will be printed at the end
of each time step.
COMPILATION REQUIREMENTS: SATURN is written in FORTRAN with versions
existing on the following computer systems:
PRIME;
DEC VAX 11/780; and
t CDC 7600.
The code is written in double precision (eight-byte decimal words). The code
treats the transport processes as an uncoupled phenomenon from the flow
processes; thus, two successive applications of SATURN are necessary to
simulate flow and transport.
Current problem limits:
500 nodal points;
450 elements;
20 materials;
99 Dirichlet boundary conditions;
99 flux boundary conditions;
40 semi-bandwidth for global matrix;
§ 10 time-dependent Dirichlet boundary nodes;
t 10 time-dependent flux boundary nodes;
20 entry pairs for relative permeability versus saturation; and
20 entry pairs for pressure head versus saturation.
Due to the manner in which these limits are prescribed in the code, changes in
dimension can require the modification of common blocks, in almost every
subroutine.
EXPERIENCE REQUIREMENTS: Extensive.
i (i
TIME REQUIREMENTS Months.
A-62
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CODE VERIFICATION: The code has been verified against several test problems
and against UNSAT2. . :
DOCUMENTATION/REFERENCES:
Huyakorn, P.S.; Thomas, S.D.; Mercer, J.W.; Lester, B.H.. (1983) SATURN: a
finite element model for simulating saturated-unsaturated flow and
radioactive radionuclide transport. Prepared by Geotrans for the Electric
Power Research Institute, Palo Alto, ,CA.
SOURCE: SATURN is a proprietary code. It was developed by P. S. Huyakorn,
S. D. Thomas, J. W. Mercer, and B. H. Lester, all of Geotrans, Incorporated.
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CODE NAME: SEGOL
PHYSICAL PROCESSES: Predicts contaminant transport and flow for combined
saturated and partially-saturated flow systems.
DIMENSIONALITY: Three dimensional.
SOLUTION TECHNIQUE: Numerical, finite element,
DESCRIPTION: The transport equations are solved using a Galerkin
finite-element approach. The model solves for three-dimensional combined
partially-saturated and saturated flow. Since solution for both saturated and
partially-saturated flow is possible, the free surface is very nicely handled.
At the same time, a more realistic representation of flow from ponds or lakes
is provided by the model, rather than requiring the assumptions involved when
only saturated models are used. The SEGOL model uses finite elements for the
numerical reduction with isoparametric elements. It is an operational model
and has been tested, but has not yet been extensively used with field
problems. A severe test case indicated that a spatial discretization of a few
centimeters may be necessary for some problems.
CODE INPUT: Standard transport parameters.
CODE OUTPUT: Predictions of head and concentration.
COMPILATION REQUIREMENTS: SEGOL is written in FORTRAN.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS Months.
CODE VERIFICATION: SEGOL has been verified by comparison to field data.
DOCUMENTATION/REFERENCES:
Segol, G.A. (1976) Three-dimensional Galerkin finite element model for the
analysis of contaminant transport in variably saturated porous
media -- user's guide. Department of Earth Sciences, University of
Waterloo, Waterloo, Ontario, Canada, June.
Segol, G.A. (1977) A three-dimensional Galerkin-finite element model for the
analysis of contaminant transport in saturated-unsaturated porous media.
In: Gray, W.G.; Pinder, G.F., eds., Finite elements in water resources,
(Proceedings of the First International Conference, July, 1976).
SOURCE: SEGOL was developed by G. A. Segol of Bechtel Corporation. The code
is in the public domain.
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CODE NAME: SUMATRA-I
PHYSICAL PROCESSES: Predicts the simultaneous flow of water and solutes
transport in a vertical soil profile under transient saturated-unsaturated
conditions.
DIMENSIONALITY: One dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: SUMATRA-I is based on a Hermitian (cubic) finite-element
solution of the governing transport equations. The model includes such
processes as linear equilibrium adsorption and zero- and first-order decay.
Flow in the saturated-unsaturated medium,is posed and solved with a pressure
head dependent variable The convection dispersion equation is amended to
include retardation by adsorption and decay mechanis.ms. These continuum models
are driven by complete physical properties and boundary condition information
including: transient data for soil surface, boundary conditions, hydraulic
functions relating moisture content and,hydraulic conductivity, and physical or
chemical parameters (e.g., density, dispersivity, adsorption, and decay
parameters).
CODE INPUT: Standard groundwater flow and contaminant transport parameters.
CODE OUTPUT: Predictions of head and concentration.
COMPILATION REQUIREMENTS: Predictions of head and concentration.
EXPERIENCE REQUIREMENTS: SUMATRA-I is written in FORTRAN IV. It consists of
the main program and nine subprograms.
TIME REQUIREMENTS Extensive.
CODE VERIFICATION: Months.
DOCUMENTATION/REFERENCES:
van Genuchten, M.Th. (1978a) Mass transport in saturated-unsaturated media:
one-dimensional solutions. Research Report 78-WR-ll, Water Resources
Program, Department of Civil Engineering, Princeton University, Princeton,
NO.
van Genuchten, M.Th. (1978b) Numerical solutions of the one-dimensional
saturated-unsaturated flow equation. Research Report 78-WR-9, Water
Resources Program, Department of Civil Engineering, Princeton University,
Princeton, NJ.
SOURCE: SUMATRA-I was written by van Genuchten of the U.S. Salinity
Laboratory. The code is in the public domain.
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CODE NAME: SUTRA (Saturated-Unsaturated Transport)
PHYSICAL PROCESSES: Predicts fluid movement and the transport of either
energy or dissolved substances in a subsurface environment.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE:
finite-element.
Numerical, finite-element, and integrated
DESCRIPTION: SUTRA flow simulation may be employed for areal and
cross-sectional modeling of saturated groundwater flow systems, and for
cross-sectional modeling of unsaturated zone flow. Solute transport simulation
using SUTRA maybe employed to model natural or man-induced chemical species
transport including processes of solute sorption, production, and decay, and
may be applied to analyze groundwater contaminant transport problems and
aquifer restoration designs. In addition, solute transport simulation with
SUTRA may be used for modeling of variable density leachate movement and for
cross-sectional modeling of salt-water intrusion in aquifers at near-well or
regional scales, with either dispersed or relatively sharp transition zones
between fresh water and salt water. SUTRA energy transport simulation may be
employed to model thermal regimes in aquifers, subsurface heat conduction,
aquifer thermal energy storage systems, geothermal reservoirs, thermal
pollution of aquifers, and natural hydrogeological convection systems.
Mesh construction is quite flexible for arbitrary geometries employing
quadrilateral finite elements in Cartesian or radial-cylindrical coordinate
systems. The mesh may be coarsened employing "pinch nodes" in areas where
transport is unimportant. Permeabilities may be anisotropic and may vary both
in direction and magnitude throughout the system as may most other aquifer and
fluid properties. Boundary conditions, sources, and sinks may be
time-dependent. A number of input data checks are made in order to verify the
input data set. An option is available for storing the intermediate results
and restarting simulation at the intermediate time. An option to plot results
produces output which may be contoured directly on the printer paper. Options
are also available to print fluid velocities in the system and to make temporal
observations at points in the system.
CODE INPUT: Standard groundwater flow and contaminant transport parameters.
CODE OUTPUT: SUTRA provides, as the primary calculated result, fluid
pressures and either solute concentrations or temperatures, as they vary with
time, everywhere in the simulated subsurface system.
COMPILATION REQUIREMENTS: SUTRA was written in FORTRAN 77.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS Months.
CODE VERIFICATION: Unknown.
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DOCUMENTATION/REFERENCES:
Voss, C.I. A finite-element simulation model for saturated-unsaturated,
fluid-density-dependent groundwater flow with energy transport or
chemically-reactive single species solute transport, USGS Water Resources
Investigations Report 84-4369.
SOURCE: The code was developed by C. I. Voss of the USGS Water Resources
Department. The code is in the public domain.
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CODE KAHE: TRANUSAT
PHYSICAL PROCESSES: Predicts the transient migration of water and
contamination in unsaturated and saturated geologic media.
DIMENSIONALITY: One and two dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: The fundamental equations solved are the pressure head
formulation of unsaturated water flow, Darcy's equation, and contaminant mass
conservation. The principal assumptions are as follows:
t fluid flow is described by Darcy's equation;
t functional relationships exist for pressure head versus moisture content
and hydraulic conductivity versus moisture content;
t solute transport may include advection, dispersion, diffusion, adsorption,
and first-order reactions; and
system properties may vary spatially.
CODE INPUT: Standard groundwater flow and contaminant transport parameters.
CODE OUTPUT: Predictions of head and concentration.
COMPILATION REQUIREMENTS: This one- and two-dimensional cartesian model
includes the following boundary conditions:
specified pressure head;
specified fluid flux;
specified concentration;
zero concentration gradient;
cauchy boundary condition; and
t boundary conditions may vary temporally.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Pickens, J.F.; Gillham, R.W.; Cameron, D.R. (1979) Finite-element analysis of
the transport of water and solutes in tile-drained soils. Journal of
Hydrology 40:243-264.
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Pickens, J.F.; Gillham, R.W. (1980) Finite element analysis of solute
transport under hysteretic unsaturated flow conditions." Water Resour.
Res. 16(6):1071-1078.
SOURCE: TRANUSAT is a Geologic Testing Consultants, Ltd., proprietary code
developed at GTC.
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t
§
CODE NAME: TRUST
PHYSICAL PROCESSES: Predicts transient fluid movement in a
multi-dimensional, partially saturated or saturated, deformable porous media.
DIMENSIONALITY: Multi-dimensional.
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: TRUST is based on a volumetric expression of the continuity
equation applied to a flow region of finite volume. The method of integral
finite differences is used to represent the problem. Essentially, the model
domain is a conglomeration of arbitrarily shaped volumes linked by connectors
representing the porous media between volume nodal points. Changes in pressure
at each node are computed for each time step by a finite-difference algorithm
that uses both explicit (point-by-point) and implicit (simultaneous) solution
schemes. Darcy velocities are calculated through finite-difference gradients
of computed pressure heads.
It features the processes of:
pore desaturation;
hysteresis in permeability and saturation behavior;
fluid compressibility; and
one-dimensional (vertical) deformation of the soil skeleton due to water
withdrawal.
The discretization of the continuity equation features a variable weighting
scheme that allows the solution to range between central and backward
differencing. The weighting factor is computed by TRUST at every time step
based on the rate of pressure change. Slowly changing phenomena are weighted
toward central differencing while rapid changes are weighted toward backward
differencing. Regardless of the weighting scheme, the discretized equation
contains both explicit and implicit parts. The explicit portion of the
equation is used to solve for the pressure change over the entire domain. At
locations where the explicit stability constraint for time step size is
violated, the implicit part of the equation is applied and added to the
existing explicit solution. Thus, the final matrix of equation coefficients
created by the mixed explicit-implicit algorithm can be partitioned into those
submatrices that require simultaneous solution.
The volumetric equation of mass conservation balances external fluxes and
internal fluid generation with changes in mass storage. Nonlinearity in the
formulation arises in the pressure-dependent permeability and fluid density in
the external flux calculation, and pressure-dependent processes of fluid
compressibility. Nonlinearity also arises from soil skeleton deformation and
pore desaturation in the mass storage calculation. TRUST circumvents an
iterative solution by using a point-slope prediction of pressure at the new
time level to calculate the dependent parameters. Pressure is then solved with
the nonlinear equation set.
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TRUST uses an iterative over-relaxation matrix solver to compute the pressure
changes at the new time level. For smaller matrices, iterative solvers are
more efficient than direct solution techniques. However, convergence in highly
nonlinear problems can be poor.
Selecting an appropriate time step is crucial to the success of the
quasi-linearization approximation used in TRUST. For this reason, time step
size is computed internally, based on the following criteria:
the maximum pressure change is maintained at an average of a specified
value;
time- and pressure-dependent functions are not allowed to change more than
an average of 1%; and
convergence of the matrix solution must be satisfied in under 80
iterations.
Results of time steps that exceed any of these limits are discarded and the
time step is halved.
Mass balance error in TRUST is monitored for each node and for the entire
system being modeled. Model errors are discussed in the following categories:
inaccurate specifications or interpolation;
time truncation;
pressure truncation;
convergence; and
t machine roundoff.
Assumptions and simplifications for TRUST are:
t parameters can be functions of time, space, or pressure;
hysteresis is modeled approximately by the use of scanning curves;
fluid density, volume, void ratio, and saturation are functions of
pressure only;
flow region deforms with time;
deformation of the media structure is one dimensional according to
Terzaghi's theory of consolidation;
for shallow reservoirs, deformation is expressed at the ground surface as
subsidence;
deep reservoirs with overburden are not resolved accurately by the
consolidation computation;
soil structure has a constant volume of incompressible solids;
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during the time interval, the elevation of the matrix is unchanged;
t time effects of consolidation are ignored;
media properties are isotropic; and
t the model is best suited to soils of moderate to high saturation.
CODE INPUT: System properties required by TRUST are standard soil data
usually included in a field sampling program:
initial drying or wetting state;
elevation to land surface from zero datum;
average specific gravity of flow region material;
fracture length or characteristic length;
flow rate from well per unit aquifer thickness;
permeability, analytical, or tabulated function of pressure;
specific storage, analytical, or tabulated function of pressure;
saturation, tabulation function of pressure;
reference void ratio;
reference effective stress;
t void ratio as a function of effective stress;
deformability of matrix;
t swelling index;
compression index; and
slope of the void ratio versus log permeability relationship.
Fluid properties required by TRUST can be found in handbooks:
viscosity;
compressibility coefficient;
density at atmospheric pressure; and
t gravitational constant.
Initial concentrations for TRUST are spatially distributed pressure heads and
fluid generation rates. An application of the steady-state option of the model
will generate a physically meaningful initial condition. Boundary conditions
fall into three categories:
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1) flux;
2) pressure head; and '
3) flux or pressure head, when controlling conditions are unknown.,
These boundary conditions can be constant, time-dependent, or sinusoidal. Flux
boundary conditions occur at nodes with very small fluid mass capacity where a
fixed or variable fluid generation rate is specified. These "artificial nodes
are then connected to the actual surface nodes of the problem. For fluid flux
from the problem domain, external connectors with constant or tabulated
functions of pressure or time are used to transfer fluid. Seepage faces are
possible in TRUST with the assumptions of atmospheric pressure and one-way
efflux.
The time-dependent boundary conditions can be input on a regional basis and can
be incremented by a constant change. Regional input of parameter data is also
available. Changes in the problem geometry can be done by using the
model-scale factor to regionally reduce or measure the length scales of the
original problem.
During execution, TRUST performs a check of the input data for consistency.
Upon detection of an error, diagnostic statements are printed, which enable the
user to trace and correct the mistake. The user's manual presents guidelines
for the input of data tables and possible actions to correct inaccurate
results.
CODE OUTPUT: TRUST has the following output results:
t input data echo
a input error summary
t results of the first, second, and last time steps are always printed
system results
net fluid flow into system
average pressure change
average fluid flow rates
fluid mass capacity
moisture content
fluid generation rate , ,
fluid generation amount
levels of output to select from
fluid pressure
elevation
pressure change during time step
estimated time derivatives of pressure
fluid generation ,
total fluid content
change in fluid content ,
net fluid transported into node by internal and external
information
A-7 3
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t boundary information
pressure
net fluid flow into system from boundary node
average fluid flow rate
flow into node
flow rate across connection
nodal
type
volume
density
fluid capacity
permeability
conductance from node, N
time constant
void ratio
saturation
preconsolidation stress
§ connection
area
overall conductance
net fluid flow
average rate of fluid flow
flow into node
flow rate across a connection
fluid transfer coefficient (for external connection)
diagnostics
flags node changing to a special node
nonconvergence
repeat of a time step due to criteria violation
The user has control over the frequency and level of detail for the output.
COMPILATION REQUIREMENTS: TRUST is written in FORTRAN with versions existing
on the following computer systems:
t UNIVAC
t CDC 6400/6000/7000
DEC VAX 11/780.
Single- and double-precision versions exist on the VAX. The double-precision
version has an accuracy of eight byte words, which is standard on the UNIVAC
and CDC machines. In addition, the VAX versions return run-time information to
the terminal from which they are run.
Current problem limits are:
10 materials;
§ 1 fluid property;
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300 nodes;
600 internal connections;
t 20 external connections;
20 boundary nodes;
100 fluid generation tables;
t 300 initial conditions; and
100 table lengths.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS Months.
CODE VERIFICATION: TRUST has been verified against analytical solutions of
flow problems, in particular:
Theis solution for radial flow to a well; and
Carslaw and Jaeger solution for a continuous point source in an isotropic
three-dimensional medium.
Validation of the consolidation mechanism of the code has been performed in the
following problem areas:
saturated flow;
unsaturated flow;
saturated-unsaturated flow; and
liquefaction.
Most of the validation tests are based on results observed with laboratory
models, and encompass one-, two-, and three-dimensional problems on both
rectangular and radial coordinate systems.
DOCUMENTATION/REFERENCES:
McKeon, T.J.; Tyler, S.W.; Mayer, D.W.; Reisenauer, A.E. (1983) TRUST-II
utility package: partially saturated soil characterization, grid
generation, and advective transport analysis. NUREG/CR-3443, U.S. Nuclear
Regulatory Commission, Washington, DC.
Narasimhan, T.N. (1975) A unified numerical model for saturated- unsaturated
groundwater flow. LBL-8862, Lawrence Berkeley Laboratory, Berkeley, CA.
Narasimhan. T.N.; Witherspoon, P.A. (1977) Numerical model for
saturated-unsaturated flow in deformable porous media, 1. theory. Water
Resour. Res. 13(3):657-664.
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Narasimhan, T.N.; Witherspoon, P.A.; Edwards, A.L. (1978) Numerical model for
saturated-unsaturated flow in deformable porous media, 2. The algorithm
Water Resour. Res. 14(2):255-261.
Narasimhan, T.N.; Witherspoon, P.A. (1978) Numerical model for saturated-
unsaturated flow in deformable porous media, 3. Applications. Water
Resour. Res. 14(6):1017-1034.
Reisenauer, A.E.; Key, K.T.; Narasimhan, T.N.; Nelson, R.W. (1982) TRUST: a
computer program for variably saturated flow in multidimensional
deformable media. PNL-3975, Pacific Northwest Laboratory, Rich!and, WA.
SOURCE: TRUST was developed by T. N. Narasimhan at the Lawrence Berkeley
Laboratory. The code is in the public domain.
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NUMERICAL SOLUTE TRANSPORT (SATURATED)
A-77
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CODE NAME: CHAIN!
PHYSICAL PROCESSES: Simulates the transport of radionuclides in a fractured
porous medium.
DIMENSIONALITY: Two dimensional (x,y cartesian).
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: The CHAINT model simulates multicomponent nuclide transport in
a fractured-porous medium. The processes modeled include advection,
dispersion/diffusion, sorption, chain decay coupling, and mass release. The
computational method is based on a finite-element solution of the system of
equations. Continuum portions of the medium are modeled as a single porosity
system using two-dimensional isoparametric elements.'Discrete fractures are
modeled using isoparametric line elements embedded along the sides of the
two-dimensional elements. Principal input to the code is the groundwater flow
calculation obtained with the MAGNUM2D code (or a comparable nonisothermal flow
model).
The principal assumptions of the code are:
The diffusive flux Jri is assumed to be Fickian.
Radionuclide transport occurs only in the fractures.
Sorption may be represented by equilibrium adsorption.
In addition, the assumptions incorporated in MAGNUM2D must also be incorporated
in CHAINT, these being:
The fractured-porous medium is nondeformable.
The fluid is slightly compressible.
t Flow is laminar (Darcian).
Macroscale (REV) hydraulic gradients are independent of fracture
orientation or geometry.
The fluid system is single phase.
The medium is fully saturated. ,
Moisture is stored in both primary, apd secondary pores.
Flow in fractures is governed by a nonisothermal version of Darcy's Law.
Flow between primary and secondary pores depends on the difference between
primary and secondary heads.. ,
Heat flux is governed by the convection-diffusion equation.
A-78
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Conservation of mass applies separately in the primary and secondary
storage systems, but conservation of energy applies in the system as a
whole.
CODE INPUT: As previously mentioned, principal input to the code is the
groundwater flow calculation obtained with the MAGNUM2D code (or a comparable
nonisothermal flow model). Other necessary inputs include:
t mesh geometry;
half lives of the radionuclide contaminants;
retardation factor of each contaminant;
velocity field;
t mass dispersion tensor;
nuclide splitting;
decay constants;
secondary porosity;
mass source term; ;
t fluid density; .,,
t initial parent concentrations; and
initial daughter product concentrations
i, . / < ,
CODE OUTPUT: Output for CHAIN! consists of the concentration of each
radionuclide in the fractures at each time stepJ
COMPILATION REQUIREMENTS: Unknown.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: The code CHAINT was tested against an analytical solution
based on the uranium decay series. The code is in the public domain.
DOCUMENTATION/REFERENCES:
King, I.P.; Mclaughlin, D.B.; Norton, W.R.; Baca, R.G.; Arnett, R.'C. (1981)
Parametric and sensitivity analysis of waste isolation in a basalt
medium. Rockwell Hanford Operations Report RHO-BWI-C-94.
Baca, R.G.; Arnett, R.C.; King, I.P. (1981) Numerical modeling of flow and
transport in a fractured-porous rock system. Rockwell Hanford Operations
Report RHO-BWI-SA-113.
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Neretnieks, I. (1980) Diffusion in the rock matrix: an important factor of
radionuclide retardation? J. Geophys. Res. 84(B8):4379-4397.
SOURCE: CHAIN! was developed by*Resource Management Associates, Lafayette,
California, for Rockwell Hahfbrd Operations/
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CODE NAME: DUGUID-REEVES
PHYSICAL PROCESSES: Predicts contaminant transport for use on the flow model
results produced by the REEVES-DUGUID flow model.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: The model considers advection, dispersion, and exchange of one
chemical constituent which may involve radioactive decay under partially
saturated flow conditions. The single chemical component exchange reaction is
handled through an equilibrium exchange coefficient modified by the moisture
content when partially-saturated conditions exist. The spatial integration is
accomplished through the Galerkin finite-element approach using linear basis
functions. The time integration uses a modified Crank-Nicholson
finite-difference form.
A special, rather standard numbering scheme for element nodes is used to reduce
the matrix bandwidth that must be stored and operated upon for solution.
Special treatment of various boundary condition is also used to maintain the
desired matrix form. The actual solution is standard Gaussian elimination by
decomposition into the product of upper and lower triangular matrices. The
lower triangular matrix is used to modify the right-hand side for
back-substitution into the upper triangular matrix to obtain the solution.
CODE INPUT: Input for DUGUID-REEVES is the saturated/unsaturated flow model
results from REEVES-DUGUID.
CODE OUTPUT: Predicts contaminant concentrations.
COMPILATION REQUIREMENTS: DUGUID-REEVES is written in FORTRAN and is
operational on IBM systems.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Duguid, J.O.; Reeves, M. (1976) Material transport through porous media: a
finite element Galerkin model. ORNL-4928, Oak Ridge National Laboratory,
Oak Ridge, TN, March.
Reeves, M.; Duguid, J.O. (1975) Water movement through saturated-unsaturated
porous media: a finite-element Galerkin model. ORNL-4927, Oak Ridge
National Laboratory, Oak Ridge, TN.
SOURCE: The code was developed by J. 0. Duguid of Battelle Memorial
Institute and M. Reeves of Oak Ridge National Laboratory. The code is in the
public domain.
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CODE NAME: GROVE/GALERKIN
PHYSICAL PROCESSES: This model employs Galerkin finite-element methods to
solve mass transport equations. The model successfully simulates solute
transport for an unreactive conservative solute chloride, a solute with a
first-order irreversible rate reaction, radioactive decay, and a solute with
equilibrium controlled ion exchange.
DIMENSIONALITY: Three dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: The partial differential equation that describes the transport
and reaction of chemical solutes in porous media was solved using the Galerkin
finite-element technique. These finite elements were superimposed over finite
difference cells used to solve the flow equation. Both convective and flow due
to hydraulic dispersion were considered. Linear and Hermite cubic
approximations (basis functions) provided satisfactory results; however, the
linear functions were found to be computationally more efficient for
two-dimensional problems. Successive overrelaxation (SOR) and iteration
techniques using Tchebyschef polynomials were used to solve the space matrices
generated using the linear and Hermite cubic functions, respectively.
Comparisons of the finite-element methods to the finite-difference models arid
to analytical results indicate that a high degree of accuracy may be obtained
using the method outlined The technique was applied to a field problem
involving an aquifer contaminated with chloride, tritium, and 90Sr.
CODE INPUT: Unknown.
CODE OUTPUT: Unknown.
COMPILATION REQUIREMENTS: GROVE/GALERKIN is written in FORTRAN and is
operational on an IBM 360 system.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Grove, D.B. The use of Galerkin finite-element methods to solve mass-transport
equations. Water Resources Investigation 77-49, U.S. Geological Survey,
Water Resources Division, Denver, CO.
SOURCE: This code is written by D. B. Grove of the U.S. Geological Survey,
Water Resources Division. The code is in the public domain.
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CODE NAME: 1SOQUAD, ISOQUAD2
PHYSICAL PROCESSES: Predicts contaminant transport.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: This model uses a Galerkin approximation with various basis
functions, with a finite-element integration scheme to solve the conservative
transport equation. The time integration is performed through a backward
difference time scheme.
CODE INPUT: Unknown.
CODE OUTPUT: Unknown.
COMPILATION REQUIREMENTS: ISOQUAD and ISOQUAD2 are written in FORTRAN and
implemented on an IBM 360/91 machine.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Pinder, 6.F. (1973) A Galerkin-finite-element simulation of groundwater
contamination of Long Island, New York. Water Resour. Res.
9(6):1657-1669.
SOURCE: The codes were written by George Pinder of Princeton University and
Emil Frind of the University of Waterloo. The code is in the public domain.
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CODE NAME: KONBRED, USGS2D-MOC
PHYSICAL PROCESSES: KONBRED simulates groundwater flow and solute transport
in one or two dimensions. Radioactive decay is not included in the program as
originally published. A modified version has been prepared which incorporates
decay of single species but omits formation of radioactive daughter products.
DIMENSIONALITY: One or two dimensional.
SOLUTION TECHNIQUE: Groundwater flow -- numerical, finite difference.
Transport -- random walk.
DESCRIPTION: KONBRED solves the groundwater flow equation by a
finite-difference method. It then computes solute transport in the calculated
flow field by the method of characteristics. Both steady-state and transient
flows can be calculated, and the aquifer may be heterogeneous and anisotropic.
Forces resulting from differences in temperature or concentrations of dissolved
solids are not considered.
Advective transport is computed by tracking particles, and a finite-difference
method is used after each step to treat dispersion, fluid sources and sinks,
and velocity divergence. The code can accommodate injection and withdrawal
wells, diffuse leakage, and a variety of boundary and initial conditions. The
modified version includes radioactive decay (but not formation of radioactive
daughters) and equilibrium sorption. The code represents a two-dimensional
area as a rectangular network of equally-spaced nodes. As presently written,
there can be no more than 20 rows and 20 columns of nodes. The principle
assumptions of the code include:
§ Darcy's Law is valid and hydraulic-head gradients are the only significant
driving mechanism for fluid flow.
The porosity and hydraulic conductivity of the aquifer are constant with
time, and porosity is uniform in space, ,
Gradients of fluid density, viscosity, and temperature do not affect the
velocity distribution.
t The two-dimensional solute transport equation is valid.
Sorption may be represented as equilibrium adsorption.
Vertical variations in head and concentration are negligible.
The aquifer is homogeneous and isotropic with respect to the coefficients
of longitudinal and transverse dispersivity.
CODE INPUT: The principal inputs to the original versions are as, follows:
t transmissivity tensor;
aquifer thickness at each node;
diffuse recharge and discharge at each node;
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initial head at each node;
initial solute concentration at each node;
storage coefficient;
location of no-flow boundaries;
t effective porosity;
longitudinal dispersivity;
lateral dispersivity;
locations of wells;
pumping rate of each well;
solute concentrations at each injection well; and
pumping period.
The revised version requires additional inputs describing sorption and
radioactive decay.
CODE OUTPUT: The principal output are the heads and concentrations. These
can be printed out either after each time step at up to 5 "observation wells"
or at all nodes after each 50 time steps.
COMPILATION REQUIREMENTS: The original program is written in FORTRAN IV and
is compatible with many computers. It has been run successfully on Honeywell,
IBM, DEC, Univac, and CDC computers. The revised program is written in FORTRAN
77 and, apparently, has run on IBM and CDC computers.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: KONBRED has been tested by comparison with several
analytical solutions. Results from these comparisons are included in the
documentation (ref. 1) and include both one-dimensional steady-state flow and
plane radial steady-state flow.
This code (or earlier versions of it) has been applied to a wide variety of
field problems. These include 1) chloride movement at the Rocky Mountain
Arsenal (ref. 2); 2) chloride buildup in a stream-aquifer system (ref. 3); and
3) radionuclide transport at INEL (ref. 4).
DOCUMENTATION/REFERENCES:
Konikow, L.F.; Bredehoeft, J.D. (1978) Computer model of two-dimensional
solute transport and dispersion in groundwater. Techniques of
Water-Resources Investigations of the United States Geological Survey,
Book 7, Chapter C2.
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Konikow, L.F. (1977) Modeling chloride movement in the alluvial aquifer at
the Rocky Mountain Arsenal, Colorado. U.S. Geological Survey Water-Supply
Paper 2044.
Konikow, L.F.; Bredehoeft, J.D. (1974) Modeling flow and chemical quality
changes in an irrigated stream-aquifer system. Water Resour. Res.
10(3):546-562.
Robertson, J.B. (1974) Digital modeling of radioactive and chemical waste
transport in the Snake River plain aquifer at the National Reactor Testing
Station, Idaho. U.S. Geological Survey Open-File Report IDO-22054.
Tracy, J.V. (1982) User's guide and documentation for adsorption and decay
modifications to the U.S.G.S. solute transport model. U.S. Nuclear
Regulatory Commission Report NUREG/CR-2502.
SOURCE: The model was developed by L. F. Konikow and J. D. Bredehoeft of the
U.S. Geological Survey. The modifications were made by J. V. Tracy of ERTEC.
The code is in the public domain.
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CODE NAME: DPCT (Deterministic-Probabilistic Contaminant Transport)
PHYSICAL PROCESSES: Predicts groundwater flow and contaminant transport
accounting for advection, dispersion, radioactive decay, and equilibrium
sorption for a single contaminant.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE: Flow distribution -- numerical, finite element. Solute
transport -- particle-tracking method.
DESCRIPTION: The code treats a two-dimensional vertical cross-section.
Almost any water table and geologic configuration is permissible, and there are
a variety of allowable boundary conditions. Water flow is steady state.
The cross section is divided into a rectangular array of cells. The head
distribution is found by the finite-element method. Solute transport is then
treated by tracking the motion of individual particles.
DPCT will calculate the long-term effects of a repository for specified
scenarios, if used in conjunction with a biosphere transport code (e.g.,
PABLM). The code solves an inherently deterministic problem -- solute
transport with known velocity and dispersion -- in a probabilistic manner. It
does not treat any probabilistic problems.
The principal assumptions of the code are:
A treatment in a two-dimensional cross section is acceptable.
The solute transport equation is valid.
Sorption may be represented as equilibrium adsorption with the
distribution coefficient given by Equation 8.25.
Principal axes of the transmissivity tensor are parallel to coordinate
axes everywhere.
Groundwater flows are steady state.
CODE INPUT: Inputs for DPCT include:
hydraulic conductivity (horizontal and vertical) at each node;
t porosity at each node;
longitudinal dispersivity at each node;
t ion exchange capacity at each node;
t location of water table;
boundary conditions; and
contaminant input rates and locations.
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CODE OUTPUT: The principal outputs are maps of velocity or head and of
contaminant concentration at any times selected by the user. A wide variety of
other optional outputs are available.
COMPILATION REQUIREMENTS: The program is written in FORTRAN IV and has .been
run on an Amdahl 470V/7 computer. The code is in the public domain.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION:
(1980) A deterministic-probabilistic model for
, U.S. Nuclear Regulatory Commission Report
DOCUMENTATION/REFERENCES:
Schwartz, F.W.; Crowe, A.
contaminant transport
NUREG/CR-1609, August
CGS, Inc. (1980) Scenario development and evaluation related to the risk
assessment of high level radioactive waste repositories. U.S. Nuclear
Regulatory Commission Report NUREG/CR-1608, August.
Schwartz, F.W. (1978) Application of probabilistic-deterministic modeling to
problems of mass transport in groundwater system. Third International
Hydrology Symposium, Ft. Collins, pp. 281-296.
Detailed derivations are given in:
Ahlstrom, S.W.; Foote, H.P.; Arnett, R.C.; Cole, C.R.; Seme, R.J. (1977)
Multicomponent mass transport model: theory and numerical implementation
(discrete-parcel-random walk version). Battelle, Pacific Northwest
Laboratory Report PNL-2127.
SOURCE: DPCT was developed by Franklin Schwartz and A. Crowe of CGS, Inc.
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CODE NAME: MMT (Multicomponent Mass Transport)
PHYSICAL PROCESSES: Predicts the transport profile of dissolved contaminants
in groundwater.
DIMENSIONALITY: One dimensional.
SOLUTION TECHNIQUE: Discrete-parcel random-walk method.
DESCRIPTION: In the formulation of a mathematical model for simulating
transport processes in the environment, the system of interest can be viewed as
a continuum of matter and energy or as a large set of small discrete parcels of
mass and energy. The latter approach is used to formulate the discrete-parcel
random-walk transport model. Each parcel has associated with it a set of
spatial coordinates, as well as a set of discrete quantities of mass and
energy. A parcel's movement is assumed to be independent of any other parcel
in the system. A Lagrangian scheme is used to compute the parcel advection,
and a Markov random-walk concept is used to simulate the parcel diffusion and
dispersion. The random-walk technique is not subject to numerical dispersion,
and it can be applied to three-dimensional cases with only a linear increase in
computation time. A wide variety of complex source-sink terms can be included
in the model with relative ease. Examples of the model's application include
the areas of oil spill drift forecasting, coastal power plant effluent
analysis, and solute transport in groundwater systems.
The principal assumptions of the code are:
The effect of changing atmospheric pressure is negligible
Flow patterns are independent of the chemical composition or temperature
of the groundwater solution.
Hydrodynamic dispersion processes can be included with molecular
diffusion.
Relative mass flux can be adequately described by Pick's First Law.
0 Darcy's Law holds for description of saturated groundwater flow.
Total mass density of the mixture is constant.
The number or type of particles does not significantly alter the flow
properties of the host medium.
The one-dimensional solute transport equation is valid.
Sorption may be represented by equilibrium adsorption.
CODE INPUT: Inputs for MMT include:
retardation coefficient;
t dispersion;
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t half lives for all nuclides;
path length;
t groundwater velocity;
flow tube size;
initial inventory;
time after repository closure when the breach occurs;
leach information to control entry of waste into groundwater system; and
a mapping illustrating the parent-daughter relationships.
CODE OUTPUT: The principal outputs of MMT are the release rates of the
contaminants. Both printed and graphic output are available and the output can
be communicated to codes which calculate doses to humans.
COMPILATION REQUIREMENTS: MMT is written in FLECS, a higher-order language
which compiles into FORTRAN, and is operational on a VAX machine. The code is
in the public domain.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: MMT was compared to analytic results from GETOUT for a
variety of problems.
DOCUMENTATION/REFERENCES:
Ahlstrom, S.W.; Foote, H.P.; Arnett, R.C.; Cole, C.R.; Seme, R.J. (1977)
Multicomponent mass transport model: theory and numerical implementation
(discrete-parcel-random-walk version). Pacific Northwest Laboratory
Report BNWL-2127, May.
Washburn, J.F.; Kaszeta, F.E.; Simmons, C.S.; Cole, C.R. (1980)
Multicomponent mass transport model: a model for simulating migration of
radionuclides in groundwater. Pacific Northwest Laboratory Report
PNL-3179, July.
SOURCE: MMT was developed at Battelle, Pacific Northwest Laboratories.
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CODE NAME: PINDER
PHYSICAL PROCESSES: Predicts the movement of groundwater contaminants.
DIMENSIONALITY: Three dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: The Galerkin method of approximation in conjunction with the
finite-element method of analysis is used to simulate the movement of
groundwater contaminants. In solving groundwater flow and mass transport
equations, this approach allows a functional representation of the dispersion
tensor, transmissivity tensor, and fluid velocity, as well as an accurate
representation of boundaries of irregular geometry.
CODE INPUT: Unknown.
CODE OUTPUT: Unknown.
COMPILATION REQUIREMENTS: PINDER is written in FORTRAN and implemented on an
IBM 360 or 390 machine.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: A field application of the method to chromium
contamination on Long Island, New York, shows that accurate simulations can be
obtained.
DOCUMENTATION/REFERENCES:
Pinder, G.F. (1973) A Galerkin-finite element simulation of groundwater
contamination on Long Island, New York. Water Resour. Res.
9(6):1657-1669.
SOURCE: PINDER was developed by G. F. Pinder at Princeton University. The
code is in the public domain.
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CODE NAME: ROBERTSON1
PHYSICAL PROCESSES: Predicts the'movement of radionuclides by groundwater
and soil transport.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE: Analytical and numerical, finite difference.
DESCRIPTION: Aqueous chemical and low-level radioactive effluents have been
disposed to seepage ponds since 1952 at the Idaho National Engineering
Laboratory. The solutions percolate toward the Snake River Plain aquifer
(9,135 m below) through interlayered basalts and unconsolidated sediments and
an extensive zone of groundwater perched on a sedimentary layer about 40 m
beneath the ponds. A three-segment numerical model was developed to simulate
the system, including effects of convectional hydrodynamic dispersion,
radioactive decay, and adsorption. The first segment uses an analytical
solution to simulate transport from the ponds to the 25-m thick perched water
lens, assuming steady vertical flow through a 15-m long saturated homogeneous
column. The second segment simulates two-dimensional horizontal transport in
the perched water body using finite-difference methods, assuming complete
vertical mixing with vertical leakage from the bottom. The third segment
simulates simulates vertical solute transport from the perched water body
toward the aquifer by assuming unsatu'rated, but steady water flow in a series
of contiguous, nonhomogeneous independent vertical columns. The transport
equation is solved by a "hop-scotch" finite-difference scheme for each column.
Simulated hydraulics and solute migration patterns for all segments agree
adequately with the available fteld data. The model can be used to project
subsurface distributions of waste solutes under a variety of assumed conditions
for the future.
CODE INPUT: Standard hydrologic and transport parameters.
CODE OUTPUT: Predicts head and concentration.
COMPILATION REQUIREMENTS: ROBERTSONl is written in FORTRAN and implemented
on a CDC machine.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: The code has been verified by the Idaho site application.
DOCUMENTATION/REFERENCES:
Robertson, J.B. (1974) Digital modeling of radioactive and chemical waste
transport in the Snake River plain aquifer at the National Reactor Testing
Station, Idaho. U.S. Geological Survey Open-File Report, AEC No.
IDO-22054, 41 pp.
SOURCE: ROBERTSONl was developed by J. B. Robertson of the U.S. Geological
Survey, National Center. The code is in the public domain.
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CODE NAME: ROBERTSON2
PHYSICAL PROCESSES: Predicts groundwater transport of radioisotopes.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE: Numerical, finite-difference, and
method-of-characteristics solution technique.
DESCRIPTION: ROBERTSON2 was developed to predict radioisotope migration at
the National Reactor Testing Station. The influences on migration include
space and time variations in groundwater flow, hydraulic dispersion,
radioactive decay, ion exchange, and other chemical reactions. These processes
are included in problems of movement of radioactive wastes in groundwater;
design and analysis of tracer tests in groundwater systems; and analysis of
natural isotope distributions in groundwater. The model is composed of two
coupled phases: the first simulates the hydraulics, and the second simulates
solute transport. The hydraulic phase solves the transient, two-dimensional,
partial-differential equation of groundwater flow for a bounded,
two-dimensional, one-layer aquifer, using finite-difference techniques
(iterative, alternating direction, implicit scheme). This method is described
by Bredehoeft and Pinder. Groundwater velocity vectors are computed by this
equation, for every grid point at any finite time step. The velocities are
transferred to the solute transport phase of the model that solves the
transient particle differential equation of t.he transport, using the method of
characteristics. The method characterizes the dissolved nuclides by
characteristic imaginary particle. Considered terms of the solute transport
phase are: hydraulic dispersion, convective.transport, aquifer compression
factors, sources and sinks, radioactive decay, and sorption.
CODE INPUT: Input for the model includes transmissivity, storage
coefficient, boundaries, hydraulic dispersion coefficients (transverse and
longitudinal), initial concentration distributions, ion exchange, distribution
coefficient, radioactive decay constant, and source-sink .inputs.
CODE OUTPUT: Predicts head and concentration.
COMPILATION REQUIREMENTS: ROBERTSON2 is written in FORTRAN and implemented
on a CDC machine.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Bredehoeft, J.D.; Pinder, G.F. (1973) Mass transport in flowing
groundwater. Water Resour. Res. 9(1):194-210.
SOURCE: ROBERTSON2 was developed by J. B. Robertson of the U.S. Geological
Survey, National Center. The code is in the public domain.
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CODE NAME: SWENT
PHYSICAL PROCESSES: Predicts fluid, energy, and solute radionuclide
transport.
DIMENSIONALITY: One dimensional, two dimensional, axisymmetric (r-z), and
three dimensional. ,
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: SWENT is based on the coupled, transport solution of the fluid,
energy, and solute transport equations. Fluid density and viscosity in this
code are treated as functions of pressure, temperature, and solute
concentration; thus, the transport equation set being solved is nonlinear.
SWENT can be applied in one-dimensional, two-dimensional (x-y, x-z),
axisymmetric (r-z), and three-dimensional (x-y-z) heterogeneous geologic
systems. The code also features a comprehensive radionuclide transport model
that includes a radionuclide data base and the ability to account for the
generation and transport of daughter products in straight or branched decay
chains. The user has the option to solve for any or all of the dependent
variables. Basic processes addressed by SWENT include:
confined flow of a two-component, single-phase fluid;
pressure-dependent aquifer porosity;
vertical recharge;
detailed well-bore modeling based on well characteristics;
§ convective and conductive heat transport;
solute advection;
hydrodynamic dispersion;
t first-order decay reactions;
equilibrium isothermal sorption; and
salt dissolution.
SWENT has an aquifer reservoir model that is coupled to a well-bore model. The
well-bore model offers a more detailed account of the well-bore physics than is
possible with the finite difference mesh of the general problem. Results from
the modeling of the well are then applied as boundary conditions to the aquifer
reservoir. The radionuclide modeling is not coupled to the flow, energy, and
solute computations; consequently, this part of the simulation is performed
independently after the pressure field has been established.
SWENT has an option that allows the effect of the surrounding aquifer to be
incorporated into the aquifer boundary conditions without actually modeling the
regional problem. Aquifer influence functions allow subregional modeling by
posing boundary conditions that respond as if a larger aquifer were being
modeled. Generally, these influence functions are necessary when the
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simulation time is long enough for calculated changes to occur at peripheral
grid blocks.
The well-bore model uses a direct simultaneous solution of the energy equation
to calculate the pressure and temperature changes over the well-bore depth. On
the other hand, the reservoir model is based on a semi-implicit
finite-difference scheme of the flow, energy, and solute equations. The
dependent variables in this formulation, pressure, temperature, and
concentration appear in the space derivatives at the new time level.
An iterative procedure is used for the problem solution. Changes in the
pressure, temperature, and concentration are computed by applying each equation
sequentially with updated values for all dependent variables.
Transmissibilities and dispersion, on the contrary, are always treated at the
old iterate level. The iterative procedure ceases when the fractional density
change falls below an internal tolerance.
Solution of the simultaneous equation is performed by a direct, reduced-band
Gaussian elimination technique or an iterative, two-line, successive,
overrelaxation method. Each method has an optimal range of applicability which
is presented in the model documentation.
The principal assumptions of the SWENT code are:
only a single-phase fluid exists;
porous medium is saturated with fluid;
flow is laminar and governed by Darcy's Law;
kinetic energy is negligible in the energy balance;
fluid viscosity is an exponential function of temperature, or a power law
function of concentration;
salt dissolution is a first-order reaction;
linear equilibrium, sorption;
hydrodynamic dispersion is a linear function of velocity; and
effects of hydrodynamic dispersion and molecular diffusivity are additive.
CODE INPUT: The input requirements of SWENT are as follows:
t fluid compressibility;
rock compressibility;
fluid thermal expansion factor;
heat capacity of rock;
resident and injection fluid densities;
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resident and injection fluid viscosities;
t thermal conductivity of porous medium;
§ hydrodynamic dispersivities;
§ molecular diffusivity;
§ porosity;
§ hydraulic conductivity;
t well data
depth
diameter
roughness
heat transfer coefficient
pressure conditions; and
adsorption distribution coefficient.
The specified boundary conditions of SWENT are as follows:
constant pressure, temperature, concentration (Dirichlet);
t radiation boundary condition (Cauchy);
t steady-state or transient aquifer influence functions;
heat loss to overburden and underburden;
well specification of pressure, temperature; and concentration;
radioactive sources; and
recharge.
SWENT has many features that reduce the tedium of data entry: 1) grid-block
characteristics can be entered on a regional basis; 2) boundary conditions are
entered only when an update occurs; 3) any system of units can be used with the
proper entry of conversion factors; 4) variable timestepping can be performed
by a user-defined function; and 5) inclusion of a radionuclide data library
There is an input data checker in SWENT that alerts the user to up to 69 error
conditions.
CODE OUTPUT: SWENT produces a very readable line printer output of computed
results. The detail and frequency of the output is at the option of the user
Specifically, the available output include:
t
input data echo;
Darcy velocities;
flow, heat, diffusive transmissibilities; viscosity, enthalpy,
dispersivities; thermal conductivities in all grid blocks;
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fluid, energy, component, and nuclide balance;
maximum pressure, temperature, concentration changes, and the
corresponding grid blocks;
well performance summary (pressure, concentration, temperature) at well
head and bottom hole, and water, heat, and inert component production
rates and their integrated values over time;
t aquifer influx rates for water, heat, and inert components;
nuclide discharge rates at biosphere grid blocks;
integrated nuclide discharge rates to different regions;
pressure, temperature, component concentrations, and nuclide
concentrations at all grid blocks;
two-dimensional area! contour maps for pressure, temperature, brine,
concentration, and nuclide concentration; and
plots of pressure, temperature, and brine concentration for observed and
calculated values at wells.
* -
COMPILATION REQUIREMENTS: SWENT is written in FORTRAN with versions existing
on the following computer systems: >
CDC 7600; and ,
9 DEC VAX 11/780.
The code was designed to be executed on a CDC 7600 and includes external
references to CDC-specific functions Conversion to the VAX 11/780 was hampered
by these references. The VAX version of the code has dispensed with the
dynamic allocation of core storage available on CDC hardware and replaced other
CDC routines with function subroutines coded into the software. To equal the
level of accuracy and range of the CDC 7600, real variables in the code were
double-precisioned from four- to eight-byte decimal words with an extended
range option.
Current limits to the code are:
20 wells; '
7 overburden layers;
e 7 underburden layers;
t 50 aquifer influence functions; and
t 10 entries in the viscosity and temperature tables.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months. '
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CODE VERIFICATION: SWENT has been verified against analytical solutions of
fluid flow, heat flow, inert component transport, and radionuclide transport.
Good agreement between model results and analytical solutions was found in each
of the 11 cases cited. Three field applications of SWENT are included in the
code documentation. The predicted SWENT results are in reasonable agreement
with field observations.
DOCUMENTATION/REFERENCES:
INTERA Environmental Consultants, Inc. (1983) SWENT: a three- dimensional
finite-difference code for the simulation of fluids, energy, and solute
radionuclide transport. ONWI-457, Prepared for Battelle Memorial
Institute, Office of Nuclear Waste Isolation, Columbus, OH.
SOURCE: SWENT was developed by S. B. Pahwa, R. B. Lantz, and B. S. Ramaro of
INTERA Environmental Consultants, Inc.
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CODE NAME: TRANS
PHYSICAL PROCESSES: Predicts groundwater pollution problems.
DIMENSIONALITY: Two dimensional.
SOLUTION TECHNIQUE: Random walk.
DESCRIPTION- TRANS provides a generalized computer code that can simulate a
large class of problems involving convection and dispersion of chemica
contaminants associated with fertilizer applications hazardous waste leachate
from landfilled and other sources, and injection of chemical waste into the
subsurface using disposal wells. TRANS does not address density-induced
convection. Concentration distribution in the aquifer represents a
vertically-averaged value over the saturated thickness of the aquifer.
TRANS is capable of considering:
. Saturated groundwater flow in a single confined or unconfined aquifer
where wate? flow is typically horizontal. (The code addresses temporal
variations in two-dimensional (x-y) flow for a variety of boundary
conditions and arbitrary x-y geometry.)
Advection of a chemical contaminant in a saturated groundwater system
released from a variety of typical sources.
Hydrodynamic dispersion (both lateral and transverse) and diffusion of a
chemical contaminant in a saturated groundwater system.
Retardation of a chemical contaminant when it can be characterized by a
constant Kd and the assumptions of instantaneous and reversible adsorption
are adequate.
Radioactive decay of a chemical contaminant.
TRANS addresses only a single aquifer. Spatial and temporal distribution of
head in the aquifer can be calculated by four methods:
1) analytic (HSOLV2) solution for a uniform 1-ft/d flow in the x direction;
2) analytic (HSOLV4) solution to the Theis formula centered at node (15, 15);
3) numerical finite difference solution (HSOLVE) to the two-dimensional (x-y)
vertically-averaged groundwater flow equation* (this solution is for
transient or steady-state flow); and
41 user-supplied subroutine for reading or calculating head on the
finite-difference grid used in the TRANS transport model.
The transport model portion of TRANS uses a direct simulation technique The
SJcenSatlon of a chemical constituent in a groundwater Astern is assumed to
be represented by a finite number of discrete particles. Each of these
particles is moved according to the advective velocity and dispersed according
?o random-walk theory. The mass assigned to each partic e represents a
fraction of the total mass of chemical constituents involved. In the limit, as
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the number of particle approaches the molecular level, an exact solution to the
actual situation is obtained. This kind of transport model is inherently mass
conservative. Convergence can be checked by increasing the,number of
particles. There are restrictions, as with any numerical method, which limit
the size of time step that can be taken for both a time-dependent and
spatially-dependent problem. Time steps for particles are limited such that
advective plus dispersive movement is no greater than the spacing between
velocity (head) nodes.
The principal assumptions regarding flow are:
§ Darcian flow is assumed;
flow in the aquifer is horizontal and controlled only by hydraulic head
gradients;
leakage between the simulated aquifer, rivers, lakes, other aquifers, and
springs is a linear function of head difference with the slope of this
relationship determined from the leakage parameter, K/m, where K is the
permeability of the aquitard (or stream bed) and m is the thickness; and
storage in the stream, lake, or river beds and aquitards is ignored.
The principal assumptions regarding contaminant transport are:
the advection-diffusion equation for solute transport is assumed valid;
dispersion in porous media is random process; and
retention of a contaminant (or retardation of a concentration front) may
be represented by an instantaneous and reversible sorption process.
CODE INPUT: Input requirements for the code are those typically available
from standard field or laboratory measurements. For the flow portion of the
model they include:
a variable finite-difference grid description;
time step and number of time steps to be run;
t area! distributions of
permeability
source aquifer potential for leaky artesian simulations
aquifer bottom elevations;
aquifer top elevations;
head (initial conditions)
aquitard thickness and permeability for leaky artesian aquifers
simulations
artesian and water table storage coefficients;
pumping and recharge well locations and temporal rates;
t stream (river or lake) node locations, surface-water elevations, stream or
lake bed thickness and permeability; fraction of node area available for
transfer;
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constant head node locations and elevation for held head;
a location of springs, elevation at which spring flow begins, and slope of
the spring flow versus groundwater head for the spring production line;
and
a locations of nodes where evapotranspiration from the water table is to be
considered and the slope of the rate versus head line and the water-table
elevation at which evapotranspiration effects are to be ignored.
For the transport model, additional input requirements include:
a longitudinal dispersivity;
a lateral dispersivity;
a effective porosity;
a retardation factor or Kd;
a bulk mass density of porous medium;
a location and concentration of sources, description of source geometry, and
selection of method for release of particles; and
a sink locations and groupings of sink locations for summarizing outflow
versus time results.
The model contains no checking of input for consistency and automatic
termination for faulty or inconsistent inputs.
CODE OUTPUT: Results are printed in a 132-character format with a concise
and readable output layout. The code echoes input parameters and produces line
printer plots of head, numbers of particles, and concentrations. The code also
reports the concentration of water entering sink nodes and groups of sink nodes
versus time. The code produces no contour maps or output fields that can be
passed on to other computer system programs for plotting and produces no mass
balance summaries for water flow or transport.
COMPILATION REQUIREMENTS: The TRANS code is written in FORTRAN and run on a
CDC CYBER-175 machine. The code has also been brought up on a Digital
Equipment Corporation VAX 11/780.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: The code has been compared to analytic and
hand-calculated examples.
DOCUMENTATION/REFERENCES:
McDonald, M.G.; Fleck, W.B. (1978) Model analysis of the impact on
groundwater conditions of the Muskegon County waste-water disposal system,
Michigan. U.S. Geological Survey Open-File Report 78-79.
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Prickett, T.A.; Lonnquist, C.G. (1971) Selected Digital Computer techniques
for groundwater resource evaluation. Illinois State Water Survey Bulletin
55.
Prickett, T.A.; Namik, T.G.; Lonnquist, C.S. (1981) A random-walk solute
transport model for selected groundwater quality evaluations. Illinois
State Water Survey Bulletin 65.
SOURCE: The program was written by Thomas A. Prickett of Thomas A. Prickett
and Associates, and Thomas 6. Naymik and Carl 6. Lonnquist of Illinois Water
Survey.
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CODE NAME: TRANSAT2
PHYSICAL PROCESSES: Predicts groundwater flow and contaminant transport in
saturated geologic media.
DIMENSIONALITY: Multi-dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: The fundamental equations solved are those of fluid mass
conservation, Darcy's equation, and contaminant mass conservation. The
principal assumptions are as follows:
fluid flow may be described by Darcy's equation;
t steady-state groundwater flow exists;
solute transport includes advection, dispersion, diffusion, adsorption,
and first-order reactions (i.e., radioactive decay); and
system properties may vary spatially.
TRANSAT2 utilizes the Galerkin finite-element technique with linear triangular
elements. The solution technique is a Gaussian elimination method. This
multi-dimensional code includes the following boundary conditions:
specified hydraulic head;
t specified fluid flux;
zero concentration gradient;
cauchy boundary condition; and
temporally varying solute boundary conditions.
CODE INPUT: Standard groundwater flow and contaminant transport.
CODE OUTPUT: Predicts head and concentration.
COMPILATION REQUIREMENTS: Unknown.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Pickens, J.F.; Lennox, W.C. (1976) Numerical simulation of waste movement in
steady ground-water flow systems. Water Resour. Res. 12(2):171-180.
A-103
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Lee, D.R.; Cherry, J.A.; Pickens, J.F. (1980) Groundwater transport of a salt
tracer through a sandy lake bed. Limnology and Oceanography 25(1):45-61.
Grisak, G.E.; Pickens, J.F. (1980) Solute transport through fractured
media -- I. the effect of matrix diffusion. Water Resour. Res.
26(4):719-730.
SOURCE: TRANSAT2 is a GTC proprietary code developed at Geologic Testing
Consultants in Ottawa, Ontario, Canada.
-------
NUMERICAL COUPLED CODES
(SOLUTE AND HEAT TRANSPORT)
A-105
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CODE NAME: CFEST -- Coupled Fluid, Energy and Solute Transport
PHYSICAL PROCESSES: Fluid, energy, and solute transport in a confined,
saturated aquifer.
DIMENSIONALITY: Up to three dimensional.
SOLUTION TECHNIQUE: Finite element.
DESCRIPTION: CFEST was developed for the analysis of a confined aquifer's
response to thermal energy storage. This model employs a standard Galerkin
finite-element method in the solution of the coupled equations of mass energy
and solute-mass conservation. A sequential solution algorithm bearing
resemblance to the SWIP model is used to solve the flow of water, the transport
of energy, and finally the transport of solute. The finite-element
approximation to the continuum is made with a bilinear, two-dimensional,
quadrilateral element that is simply expanded to the trilinear, eight-node
brick when three-dimensional analysis is warranted. CFEST can be used to
analyze two-dimensional vertical or horizontal planes, two-dimensional
axisymmetric cross sections, and fully three-dimensional aquifer situations
Verifications against analytical and semianalytical solutions have been made
and are given in documentation on the model. CFEST has been applied to the
analysis of solid waste landfills for the U.S. Environmental Protection Agency.
CFEST simulates confined, saturated aquifer systems. Unconfined, saturated
aquifers can be simulated by assuming the top elevation of the aquifer is at
the water table and assigning piezometric heads based on the water table
elevation.
CODE INPUT: Finite-element grid describing soil profile geometry (two or
three dimensional), soil hydraulic characteristics, recharge, solute
characteristics (Kds), and time step size.
CODE OUTPUT: Output consists of line-print listings (output data files) and
plots (output plot files) of potentials, temperatures, and solute
concentrations at user-specified nodes (grid points).
COMPILATION REQUIREMENTS: CFEST is available in FORTRAN and is currently
being used on DEC VAX 11/780 and MICRO-VAXs.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: CFEST has been verified against analytical and
semianalytical solutions. Results of the verification are included in the
model documentation.
DOCUMENTATION/REFERENCES:
Gupta, S.K.; Kincaid, C.T.; Meyer, P.R.; Newbill, C.A.; Cole, C.R. (1982) "A
multidimensional finite element code for the analysis of coupled fluid,
energy, and solute transport (CFEST). PNL-4260, Pacific Northwest
Laboratory, Richland, WA.
A-106
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SOURCE:
S. K. Gupta
Office of Nuclear
Batten e Memorial
505 King Avenue
Columbus, OH 43201
Waste Isolation
Institute
C. T. Kincaid or C. R. Cole
Battelle, Pacific Northwest Laboratory
Battelle Boulevard
Richland, WA 99352
A-107
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CODE NAME: GWTHERM
PHYSICAL PROCESSES: Predicts fluid flow and transport in a heated porous
medium. r
DIMENSIONALITY: Two dimensional .
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: GWTHERM is a two.-dimensional model based on the equations for
nomsothermal single-phase flow and solute transport in porous media. It allows
for amsotropy of hydraulic conductivities and inhomogeneous density and
temperature-dependent fluid properties, and it uses the alternating-direction
implicit technique with an integrated finite difference scheme to provide an
?S?S?DM ^"nli?,,!?^16.50]^10] Procedure- Recent development has coupled
GWTHERM to DAMSWEL to include dependence of permeability on effective stress
changes. In this sense the connection between these models is sequential
code^keaSTEALTH/HARTUd' ^ U represents a "Polity available only in a
CODE INPUT: Unknown.
CODE OUTPUT: Unknown.
?E(*UIREMENTS:
system.
is written in FORTRAN and implemented on a
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Runchal, A.jTreger, D.; Segal, G. (1979) Program EP21 GWTHERM:
Sr/TMmP«Si?nal/luid flow' heat and mass transport in porous media.
ATG/TN-LA-34, Advanced Technology Group, Los Angeles, CA, April.
SOURCE: GWTHERM was developed by A. Runchal of Dames & Moore's Advanced
Technology Group. The code is in the public domain.
A-108
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CODE NAME: OGRE
PHYSICAL PROCESSES: Predicts groundwater flow and nuclide transport in a
heated porous medium.
DIMENSIONALITY: One or two dimensional.
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: OGRE can be used for the time simulation of fluid flow and mass
transport through porous media, Using an implicit (backward Euler)
finite-difference scheme. Specifically, OGRE has been used to simulate the
time-dependent flow of groundwater into or out of underground openings and the
mass transport of radionuclides under the influence of a pressure gradient.
Parameters may be either time and space dependent or fixed in either time or
space. Initial and boundary conditions may also vary with time and space.
Zoning of the grid must be constant in both directions, but zoning is dynamic
and set at execution time.
CODE INPUT: Unknown.
CODE OUTPUT: Unknown.
COMPILATION REQUIREMENTS: OGRE is written in FORTRAN and implemented on a
CDC 7600 machine.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
DOCUMENTATION/REFERENCES:
Korver, J.A. (1970) UCRL-50820, Lawrence Livermore Laboratory, Liyermore, CA,
February.
SOURCE: OGRE was written by J. A. Korver of the Lawrence Livermore
Laboratory. The code is in the public domain.
A-109
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CODE NAME: SHALT (Solute, Heat, and Liquid Transport)
PHYSICAL PROCESSES: Predicts liquid flow, heat transport, and solute
transport in a regional groundwater flow system.
DIMENSIONALITY: Two dimensional (x-y or x-z cartesian).
SOLUTION TECHNIQUE: Numerical, finite element.
DESCRIPTION: SHALT performs the two-dimensional simulation of fluid flow,
solute transport, and heat transport in a porous medium. The spatial domain is
discretized using three-noded triangular elements and the time domain by a
fully implicit backward difference scheme'. The aquifer parameters may be
distributed or zoned and the system may be anisotropic. The viscosity of the
liquid phase and the diffusion coefficient of the solute are functions of
temperature. The density of the liquid phase is represented as a function of
temperature and total solute concentration. The equations describing the fluid
flow, energy transport, and solute transport are fully coupled with the
dependent parameters upgraded after each time step. Fractured media may be
modeled by treating the fractured rock as a continuum.
SHALT may be considered both a near-field and far-field code as
temperature-dependent parameters have been implemented in this code. It would
be considered more as a far-field code, however, as deformation and the
stress/strain relationships are not considered in this model.
The main assumptions of the code are:
Darcy's Law is valid;
the compressibility and heat capacity of the liquid phase are constant;
k, , o, and QP can vary spatially but do not vary with time and are not
dependent on the concentration or the temperature;
the thermal dispersion tensor for the liquid phase includes the effects of
mechanical dispersion and thermal conduction and is a function of
velocity;
t the exchange of heat and solute is instantaneous between the liquid and
solid phases at the same point; and
* the hydrodynamic dispersion tensor for the liquid phases includes the
effects of mechanical dispersion and thermal conduction and is a function
of velocity.
CODE INPUT: Inputs to SHALT include:
mesh geometry;
initial heads;
initial concentrations and initial temperatures;
fluid density;
A-110
t
-------
porosity;
compressibility of the fluid and porous medium;
the permeability tensor;
t viscosity;
solute density;
heat capacity of both the solid and liquid phases;
the thermal conductivity tensor;
the thermal dispersivity tensor;
0 the hydrodynamic dispersivity tensor;
the first-order reaction constant;
distribution coefficient; and !
the bulk density.
CODE OUTPUT: The output of SHALT consists of the pressure, concentration,
and temperature distribution at each time step.'
COMPILATION REQUIREMENTS: SHALT is written in FORTRAN IV.
EXPERIENCE REQUIREMENTS: Extensive. '
TIME REQUIREMENTS: Months.
> ,
CODE VERIFICATION: The liquid flow portion of the model was tested by
calculating steady-state pressure and hydraulic head distributions for various
flux inputs. Values of system parameters were chosen to be constant. The
calculated hydraulic head gradient for steady-state conditions was correct.
The heat transport portion of the model was tested by comparison with results
of the analytical solution of Bredehoeft and Papadopulos (ref. 2) for
one-dimensional steady-state transport.
The solute transport portion of the model was tested by comparison with results
of the analytical solution by Ogata and Banks (ref. 3) for one-dimensional
advection-dispersion with a step input in concentration.
SHALT was used successfully to model results of pressure testing in fractured
rock at Chalk River (ref. 4).
DOCUMENTATION/REFERENCES:
Pickens, J.F.; Grisak, G.E. (1979) Finite element analysis of liquid flow,
heat transport, and solute transport in a ground-water flow system:
governing equations and model formulation. Atomic Energy of Canada, Ltd.,
Report TR-81, September.
A-I'll
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Bredehoeft, J.D.; Papadopulos, S.S. (1965) Rates of vertical groundwater
movement estimated from the earth's thermal profile. Water Resour. Res
l(2):325-328.
Ogata, A.; Banks, R.B. (1961) A solution of the differential equation of
longitudinal dispersion in porous media. U.S. Geological Survey
Professional Paper 411-A.
Davison, C.C. (1981) Physical hydrogeologic measurements in fractured
crystalline rock: summary of 1979 research program at WNRE and CRNL
Atomic Energy of Canada, Ltd., Technical Record 161.
SOURCE: SHALT was developed by J. F.' Pickens and G. E. Grisak of the Inland
Waters Directorate, Environment Canada for Atomic Energy of Canada, Ltd. The
code is in the public domain.
A-112
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CODE NAME: SWIFT (Sandia Waste Isolation Flow and Transport)
PHYSICAL PROCESSES: Predicts flow, solute, and heat migration from the
repository through the groundwater system. ,
DIMENSIONALITY: The pressure, temperature, and concentration field is
represented by a series of three-dimensional rectangular cartesian grid
points. In addition, a two-dimensional (r,z) grid system is also
provided.
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: The code simulates the flow and transport of energy, solute,
and radionuclides in a geologic media. SWIFT is a three-dimensional,
finite-difference, groundwater flow and nuclide transport code. The model
takes into account saturated flow in an isothermal or heated porous medium as
well as sorption and desorption mechanisms. In addition, the code takes into
explicit account nuclide decay and the creation of daughter products. For the
nuclide decays, the code considers conservation of dissolved contaminants,
energy, and total liquid mass. The fluid density can be a function of
pressure, temperature, and concentration. Viscosity can also be a function of
temperature and concentration. Aquifer properties can vary spatially.
Hydrodynamic dispersion is described as a function of velocity. Boundary
conditions allow natural water movement in the aquifer, heat losses to the
adjacent formation and location of injection, production, and observation
points anywhere in the system.
SWIFT solves four coupled differential equations, together with a number of
submodels describing the nonlinearities, in a sequential manner. Options
include:
steady-state or transient flow;
solute transport;
eat transport;
well bore;
t heterogeneous and/or anisotropic media;
confined and/or water table conditions; and
recharge and/or wells.
SWIFT is a descendant of the code SWIP (Survey Waste .Injection Program, ref. 3)
developed for the U.S. Geological Survey. SWIP was originally put together, in
part, from oil industry codes.
The main assumptions of the code are:
Flow follows Darcy's Law. -
A-113
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t
CODE
t
t
t
§
Fluid density can be a function of pressure, temperature, and
concentration of the inert component. Fluid viscosity can be a function
of temperature and concentration.
Injection wastes are miscible with the in-place fluids.
Aquifer properties vary with position (i.e., porosity, permeability,
thickness, and elevation can be specified for each grid block in the
model).
Hydrodynamic dispersion 1s described as a function of fluid velocity.
Radioactive constituents are present in trace quantities only, that is
fluid properties are independent of the concentrations of these
contaminants.
The energy equation can be described as "enthalpy in - enthalpy out =
change in internal energy of the system." This is rigorous except for
kinetic and potential energy which have been neglected.
Boundary conditions allow natural water movement in the aquifer, heat
losses to the adjacent formations, and the location of injection,
production, and observation points anywhere within the system.
INPUT: Inputs for SWIFT include:
half-life of each nuclide;
distribution coefficient of each nuclide on each rock type;
fluid compressibility;
porous medium compressibility;
coefficient of thermal expansion of fluid;
fluid heat capacity;
rock heat capacity;
thermal conductivity of rock-fluid mixture in each direction for each rock
type;
longitudinal and transverse dispersivities for each rock type;
molecular diffusivity in porous medium;
rock density;
fluid density;
pressure and temperature of injected or produced fluids in each well;
thermal diffusivity of rock surrounding well bores;
A-114
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t fluid viscosity as a function of temperature and brine concentration;
0 hydraulic conductivity of each rock type in each direction;
t porosity of each rock type;
heat capacity of each rock type;
boundary conditions;
initial velocities and concentrations;
salt dissolution rate in each rock type;
size, placement, and contents of waste canisters;
solubility limits;
production rate of each well;
t location, angle, and depth of each well;
diameter and pipe roughness of each well; and
a leaching time of wastes.
CODE OUTPUT: Output for SWIFT consists of the pressure, temperature, solute
concentration, and the concentration of each radioactive isotope. These are
given at every grid point after each time step as required.
COMPILATION REQUIREMENTS: SWIFT is written in FORTRAN IV for use on a CDC
6600 machine. With minor modifications, it can be used on other machines.
This modification primarily involves the real-time dimensioning feature of
SWIFT.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: To evaluate the effect of numerical truncation errors
arising due to isotope decay terms and to develop a set of criteria to delete
components in numerical simulations without losing any accuracy in the results,
SWIFT was compared against the results from ORIGEN (ref. 2). The ORIGEN model
is a matrix exponential solution of the Bateman equations for radioactive
decay. The comparison was considered excellent. Other parts of SWIFT that
solve for flow and transport have been tested against both analytical and
laboratory results.
DOCUMENTATION/REFERENCES:
Dillon, R.T.; Lantz, R.B.; Pahwa, S.B. (1978) Risk methodology for geologic
disposal of radioactive waste: the Sandia waste isolation flow and
transport (SWIFT) model. Sandia National Laboratories Report SAND
78-1267.
A-115
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Bell, M.J. (1973) ORIGEN -- the ORNL Isotope generation and depletion code.
Oak Ridge National Laboratory Report ORNL-4628.
Reeves, H.; Cranwell, R.M. (1981) User's manual for the Sandia waste-
in2;^lSn«flow and transP°rt model- Sandia National Laboratories Report
NUREG/CR-2324, November. K
Papadopulos, S.S.; Larson, S.P. (1978) Aquifer storage of heated water: part
II -- numerical simulation of field results. Ground Water 16:242-48.
SOURCE: SWIFT was developed by R. T. Dillon at Sandia Laboratories and by R
B. Lantz and S. B. Pahwa at Intera, Incorporated.
A-116
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CODE NAME: SWIP2
.-,
PHYSICAL PROCESSES: Predicts the effects of liquid waste disposal in deep
saline aquifers.
DIMENSIONALITY: Three dimensional (cartesian or radial} --
SOLUTION TECHNIQUE: Numerical, finite difference.
DESCRIPTION: SWIP2 is a transient, three-dimensional subsurface waste
disposal model to provide methodology to design and test waste disposal
systems. The model is a finite-difference solution to the pressure, energy,
and mass-transport equations. Equation parameters such as viscosity and
density are allowed to be functions of the equations' dependent variables.
Multiple user options allow the choice of x, y, and z cartesian or r and z
radial coordinates, various finite-difference methods, iterative and direct
matrix solution techniques,,restartroptions, |and various provisions for output
display. Well-bore heat and pressure-loss calculation capabilities are also
available. /
The 1979 update of the SWIP model involved additions and modifications to
include free water surface, vertical recharge, equilibrium controlled linear
adsorption, and a first-order irreversible rate reaction. These modifications
make this model more adaptable to general hydro!ogic problems and those
involving waste disposal with simple chemical reactions.
CODE INPUT: Unknown.
CODE OUTPUT: Unknown.
COMPILATION REQUIREMENTS: SWIP2 is written in FORTRAN and implemented on a
CDC machine.
EXPERIENCE REQUIREMENTS: Extensive.
TIME REQUIREMENTS: Months.
CODE VERIFICATION: Unknown.
/
DOCUMENTATION/REFERENCES:
INTERA Environmental Consultants, Inc. \1976) A model for calculating effects
r of liquid waste disposal/in deep saline aquifer, part I -- development,
part II -- documentation'. Houston, TX, June.
INTERA Environmental Consultants, Inc. (1979) Revision of the documentation
for a model for calculating effects of liquid waste disposal in deep
saline aquifers. U.S. Geological Survey, Water Resources Investigations
79-96.
SOURCE: SWIP2 was developed by INTERA Environmental Consultants,
Incorporated. This code is in the public domain.
A-117
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