&EPA
United States
Environmental Protection
Agency
Robert S Kerr
Environmental Research Laboratory
Ada, OK 74820
EPA/600/2-89/028
December 1988
Research and Development
Modeling:
An Overview and
Status Report
fiUG
l
1 W89
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EPA/600/2-89/028
December 1988
GROUNDWATER MODELING: AN OVERVIEW AND STATUS REPORT
by
Paul K.M. van der Heijde, Aly I. El-Kadi,
and Stan A. Williams
International Ground Water Modeling Center
Holcomb Research Institute
Butler University
Indianapolis, Indiana 46208
CR-812603
Project Officer
Joe R. Williams
Extramural Activities and Assistance Division
R.S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
, 12th Floor
Chicago, IL 60604-3590
U.S. ENVIRONMENTAL PROTECTION AGENCY
R.S. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
ADA, OKLAHOMA 74820
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DISCLAIMER NOTICE
The information in this document has been funded in part by the United
States Environmental Protection Agency under CR-812603 to the Holcomb Research
Institute, Butler University, Indianapolis, Indiana. It has been subjected to
the Agency's peer and administrative review, and it has been approved for
publication as an EPA document. Mention of trade names or commercial products
does not constitute endorsement or recommendation for use.
11
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SUMMARY
This report focuses on groundwater models and their application in the
management of water resource systems. It reviews the kinds of models that
have been developed and their specific and general role in water resource
management.
The report begins with the introduction of system concepts applicable to
subsurface hydrology and presents groundwater modeling terminology, followed
by a discussion of the role of modeling in groundwater management with special
attention to the importance of spatial and temporal scales. The model devel-
opment process is discussed together with related issues such as model
validation. A separate section provides information on model application
procedures and issues. In addition to a review of the model application
process, this chapter contains discussion of model selection and model
calibration and provides information on specific aspects of pollution
modeling. The report also contains an extensive overview of current model
status. Here, the availability of the models, their specific characteristics,
and the information, data, and technical expertise needed for their operation
and use are discussed. Also discussed are quality assurance in groundwater
modeling and management issues and concerns. The report concludes with a
review of current limitations in modeling and offers recommendations for
improvements in models and modeling procedures.
iii
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FOREWORD
EPA is charged by Congress to protect the nation's land, air and water
systems. Under a mandate of national environmental laws focused on air and
water quality, solid waste management and the control of toxic substances,
pesticides, noise and radiation, the Agency strives to formulate and implement
actions which lead to a compatible balance between human activities and the
ability of natural systems to support and nurture life.
The Robert S. Kerr Environmental Research Laboratory is the Agency's
center of expertise for investigation of the soil and subsurface
environment. Personnel at the Laboratory are responsible for management of
research programs to: (a) determine the fate, transport and tranformation
rates of pollutants in the soil, the unsaturated and the saturated zones of
the subsurface environment; (b) define the processes to be used in
characterizing the soil and the subsurface environment as a receptor of
pollutants; (c) develop techniques for predicting the effect of pollutants on
ground water, soil, and indigenous organisms; and (d) define and demonstrate
the applicability and limitations of using natural processes, indigenous to
soil and subsurface environment, for the protection of this resource.
This report contains the result of a study performed to improve the
quality of modeling in groundwater protection. It provides an introduction to
groundwater modeling procedures and quality assurance, presents an overview of
the status of major types of groundwater models, and discusses problems
related to the development and use of groundwater models.
Clinton W. Hall
Director
Robert S. Kerr Environmental
Research Laboratory
iv
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BACKGROUND AND REPORT ORGANIZATION
In the mid-1970s, by request of the Scientific Committee on Problems of
the Environment (SCORE), part of the International Council of Scientific
Unions (ICSU), the Holcomb Research Institute (HRI) at Butler University,
Indianapolis, Indiana, carried out a groundwater modeling assessment. This
international study, funded in large part by the U.S. Environmental Protection
Agency (EPA) through its R.S. Kefr Environmental Research Laboratory in Okla-
homa, resulted in a report published by the American Geophysical Union (AGU)
in its series, water Resources Monographs. In 1985 a second edition of this
monograph (AGU Monograph 5) was published, based on information collected at
HRI through its International Ground Water Modeling Center (IGWMC) from its
inception in 1978 until December 1983. The Center was established at HRI as
an international clearinghouse for groundwater models and a technology trans-
fer center in groundwater modeling. Since 1983 the Center has been linked to
the TNO Institute of Applied Geosciences, Delft, The Netherlands which
operates the European office of the IGWMC. Supported largely by the EPA and
in part by HRI, the Center operates a clearinghouse for groundwater modeling
software, organizes and conducts short courses and seminars, and carries out a
research program to advance the quality of modeling in groundwater management,
in support of the Center's technology transfer functions. The Center's Inter-
national Technical Advisory Committee provides guidance and active support to
its program.
The present report contains the result of research and information pro-
cessing activities performed by the IGWMC under a research and technology
transfer cooperative agreement initiated in 1985. The report serves three
functions: (1) it provides an introduction to groundwater modeling and
related issues for use as instruction material in short courses and for self
study; (2) it provides an overview of the status of major types of groundwater
models; and (3) it presents a discussion of problems related to the develop-
ment and use of groundwater models.
The review of models has been based on information gathered since 1975 by
the Holcomb Research Institute, through research and interviews. To manage
the rapidly growing amount of information, HRI, through its IGWMC, maintains a
series of information databases, currently being transferred from the DEC/VAX
environment to the 80286/80386 MS DOS environment.
The subject of this report is groundwater models and their application in
the management of water resource systems. Attention is focused on the kinds
of models that have been developed and their specific and general role in
management. The availability of the models, their specific characteristics,
and the information, data, and technical expertise needed for their operation
and use are also discussed.
Chapter 1 introduces groundwater as a system accessible to analysis and
simulation and presents the groundwater modeling terminology. In Chapter 2
the role of modeling in groundwater management is discussed with special
attention to the importance of scale. Chapter 3 describes the model devel-
opment process and discusses related issues such as model validation. In
Chapter 4 model application, as it relates to environmental decision making,
is discussed. In addition to a review of the model application process, this
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chapter contains discussion of model selection and model calibration and pro-
vides information on specific aspects of pollution modeling. Chapter 5 over-
views the current model status as an update of AGU Monograph 5 (second edi-
tion). Chapter 6 presents terminology and approaches to quality assurance in
groundwater modeling, while Chapter 7 focuses on management issues and con-
cerns. Finally, in Chapter 8 the authors discuss current limitations in
modeling and offer recommendations for improvements in models and modeling
procedures.
The authors are grateful to Milovan S. Beljin and P. Srinivasan for their
past contributions to the IGWMC model assessment studies; to Richard E. Rice
for his contributions on geochemical equilibrium models; to Deborah L. Cave
for her assistance in collecting model information and reviewing hydrochemical
modeling literature; to Michal Stibitz for his assistance in processing model
information; to Margaret A. Butorac and Karen Ochsenrider for project assis-
tance; to Ginger Williams and Eric Roach for word processing; to James N.
Rogers for manuscript editing; and to Colleen Baker and Barbara Stackhouse for
graphics.
Paul K.M. van der Heijde
Indianapolis, Indiana
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CONTENTS
Page
Summary i i i
Foreword iv
Background and Report Organization v
List of Figures x
Li st of Tabl es x i i i
1. INTRODUCTION 1
The Groundwater System 1
Groundwater Qua!ity 7
Sources of Groundwater Pollution 8
Groundwater Modeling: Definitions 10
2. GROUNDWATER MODELING AND MANAGEMENT 12
Groundwater Resource Development .12
Groundwater Quality 13
Site-Specific Modeling 14
Generic Modeling 14
Scales Relevant to Groundwater Management 15
Spat ial Seal es 20
Temporal Scales 21
3. MODEL DEVELOPMENT 23
The Model Development Process 23
Model Validation 27
Definitions and Methods 27
Val idation Criteri a 31
Validation Scenarios 32
Val i dati on Databases 32
4. MODEL APPLICATION 34
The Model Application Process 34
Code Selection 37
The Code Selection Process 37
Code Selection Criteria 39
Availability 39
User Support 40
Usability 40
Portabi 1 i ty 41
Mod if lability 41
Reliability 41
Extent of Model Use 41
Multiple Scales in Modeling Groundwater Systems 41
vi
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Page
Model Grid Design 45
Grid Shape and Size 45
Design Criteria 46
Grid Design and Numerical Accuracy 48
Model Cal ibration 49
The Role of Software; Stages of Data Processing 49
Modeling Sources of Groundwater Pollution 54
Modeling Waste Disposal Facilities, Protection Areas,
Monitoring Networks and Remedial Actions 57
5. MODEL OVERVIEW 64
Types of Models 64
Model Mathematics 67
Flow Models 70
Mathematical Formulation for Saturated Flow 72
Mathematical Formulation for Unsaturated Flow 72
Multiphase Flow 75
Solute Transport Models 84
Advective-Dispersion Equation 86
Convection 87
Dispersion 87
Adsorption 91
Transformation/Degradation 93
Biodegradation 94
Volatilization 95
Plant Processes 95
Heat Transport Models 96
The Heat Transport Equation 97
Hydrochemical Models 99
Gibbs Free Energy and Equilibrium Constants 100
Electrolytes and Activity Coefficients 101
Oxidation-Reduction Reactions 103
Limitations of Hydrochemical Models 104
Modeling Non-Dilute Solutions 105
Stochastic Models 106
Flow and Transport in Fractured Rock 107
Fracture Systems 107
Flow in Fractures 108
Transport in Fractured Media 114
Flow and Transport Models for Fractured Rock 121
6. QA IN MODELING 130
The Role of Quality Assurance 130
Definitions 131
The QA Plan 131
QA in Code Development and Maintenance 132
QA in Code Application 133
QA Assessment 135
QA Organization Structure 136
vi ii
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Page
7. MANAGEMENT ISSUES IN GROUNDWATER MODELING 138
Management Concerns 138
Technology Transfer and Training 140
Training in Groundwater Modeling 141
Information Exchange on Groundwater Modeling 142
Properietary Codes versus Public Domain Codes and
Other Acceptance Criteria 143
Banning the Use of Proprietary Codes 143
Continuing the Use of Proprietary Codes 144
8. CURRENT LIMITATIONS OF MODELING; RECOMMENDATIONS FOR IMPROVEMENTS
The Role of Data 147
Management Issues in Modeling 149
Research Needed 149
Closure 151
9. REFERENCES 152
APPENDIXES 173
Al Saturated Flow Models: Summary Listing 175
A2 Saturated Flow Models: Usability and Reliability 189
81 Variably Saturated Flow Models: Summary Listing 195
82 Variably Saturated Flow Models: Usability and Reliability 199
Cl Solute Transport Models: Summary Listing 201
C2 Solute Transport Models: Usability and Reliability 213
Dl Heat Transport Models: Summary Listing 217
02 Heat Transport Models: Usability and Reliability 224
El Hydrochemical Models: Summary Listing 226
E2 Hydrochemical Models: Usability and Reliability 229
Fl Fractured Rock Models: Summary Listing 230
F2 Fractured Rock Models: Usability and Reliability 235
Gl Multiphase Flow Models: Summary Listing 237
G2 Multiphase Flow Models: Usability and Reliability 241
H Cross-Reference Table for Appendixes A-G 243
ix
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LIST OF FIGURES
Number Page
1 Elements of the hydrologic cycle and their interactions 2
2 Schematic diagram of a regional groundwater system
(after Toth 1963) 5
3 Schematic overview of groundwater resident times in large
regional systems (after van der Heijde 1988) 6
4 Scales and relative sizes of various hydrological systems
(after van der Heijde 1988) 18
5 Model development process and feedback 24
6 Model development concepts 25
7 Assessing model validity 29
8 Model application process 35
9a Typical dimensionalities used to represent surface,
usaturated, and saturated zones in local-scale
groundwater models (after van der Heijde 1988) 43
9b Typical dimensionalities used to represent surface
unsaturated zones in regional groundwater models
(from van der Heijde 1988) 44
10 History matching/calibration using trial and error and
automatic procedures (after Mercer and Faust 1981) 50
11 Decision-support data stream in modeling 51
12 Data preparation and code execution 53
13 Definition of the source boundary condition under a
leaking landfill (numbers 1....4 refer to case 1 4) 55
a. Various ways to represent source.
b. Horizontal spreading resulting from various source
assumptions.
c. Detailed view of 3D spreading for various ways to
represent source boundary.
14 Generalized model development by finite-difference and
finite-element methods (after Mercer and Faust 1981) 69
15 Formulation of the groundwater flow equation 71
16 Schematic relationships between water content and pressure
head for various draining and wetting cycles (from El-Kadi
and Beljin 1987) 74
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Number Page
17 Schematic diagram of a chemical spill of a volume less
than the retention capacity of the partially saturated
soil profile (from Schville 1984) 76
18 Schematic diagram of a lighter-than-water chemical spill
of a volume greater than the retention capacity of the
soil (from Schville 1984) 77
19 Schematic diagram of a heavier-than-water chemical spill
of a volume greater than the retention capacity of the
soil (from Schville 1984) 79
20 Funicular zones for three immiscible fluids 81
21 Schematized vertical infiltration and horizontal spreading
of the bulk of a low-density hydrocarbon atop the water
table (after Dracos 1978) 82
22 Oil bulk zone and spreading of dissolved components in
groundwater from a field experiment by Bartz and Kass
(after Dracos 1978) 83
23 Formulation of the solute transport equation 85
24 Dispersion of a tracer slug in a uniform flow field at
various times; the dispersion coefficients in case B are
about 500 times greater than in case A (A, A2f A3 are
traveled distances of center of mass of plume) 88
25 Dual porosity and scale where continuum approach applies
(after Huyakorn 1987, pers. comm.) 109
26 Generation of a fracture network (after Long and Billaux 1986)....110
27 Relationship between directional fracture properties and
orientation of observation or modeling grid (after Long
and Billaux 1986) Ill
28 Two-dimensional fracture pattern and its influence on
average flow direction versus actual flow direction
(after Davis and Dewiest 1966) 112
29 Laminar flow in a fracture element bounded by two parallel
planes (after Huyakorn and Pinder 1983; Huyakorn et al. 1987) 115
30 Geometry and schematization of a single fracture (after
Elsworth et al. 1985) 116
31 Diffusion from fracture into porous matrix for continuous
source (after Huyakorn et al. 1987) 118
XI
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Number Page
32 Diffusion from active fracture into dead-end pores and
fractures 119
33 Diffusion into and out of porous matrix for a slug source 120
34 Treatment of system with intersecting discrete fractures,
using TRAFRAP.WT (after Huyakorn et al. 1987) 122
35 Idealized model of a fractured porous medium (from
Pruess 1983) 123
36 Basic computational mesh for a fractured porous medium
(from Pruess 1983) 124
37 MINC concept for an arbitrary two-dimensional fracture
distribution (from Pruess 1983) 125
38 Network approach in modeling interconnected fracture
systems (from Endo et al. 1984) 126
39 Simulation of transport in a fracture continuum (from
Schwartz and Smith 1988) 128
40 Combined trajectories of particles simulating random
movement in a fractured system (from Schwartz and Smith 1988) 129
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LIST OF TABLES
Page
Table 1. Summary of mechanisms tending to produce fluctuations in
groundwater levels (Freeze and Cherry 1979) 16
Table 2. Scales in groundwater modeling (van der Heijde 1988) 19
Table 3. Sources of groundwater pollution and model representations
(from van der Heijde 1986) 58
Table 4. Modeling designed-system alterations and corrective action
(after Boutwell et al. 1985) 60
xm
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1. INTRODUCTION
Groundwater modeling is a methodology for the analysis of mechanisms and
controls of groundwater systems and for the evaluation of policies, actions,
and designs that may affect such systems.
Models are useful tools for understanding the mechanisms of groundwater
systems and the processes that influence their composition. Modeling serves
as a means to ensure orderly interpretation of the data describing a ground-
water system, and to ensure that this interpretation is a consistent represen-
tation of the system. It can also provide a quantitative indicator for re-
source evaluation where financial resources for additional field data collec-
tion are limited. Finally, models can be used in what is often called the
predictive mode by analyzing the response a system is expected to show when
existing stresses vary and new ones are introduced: they can assist in
screening alternative policies, in optimizing engineering designs, and in
assessing operative actions in order to determine their impacts on the ground-
water system and ultimately on the risks of these actions to human health and
the environment.
In managing water resources to meet long-term human and environmental
needs, groundwater models have become important tools.
The field of groundwater modeling is expanding and evolving as a result
of:
Widespread detection of contaminated groundwater systems
Enhanced scientific capability in modeling groundwater contamination in
terms of the physical, biological, and chemical processes involved
Rapid advancement of computer software and hardware, and the marked
reduction in the cost associated with this technology.
The rapid growth in the use of groundwater models has led to unforeseen prob-
lems in project management. Some of the projects in which these sophisticated
tools have been used have even led to adversary legal procedures in which the
model application or even the model's theoretical framework and coding have
been contested. Often, the key issue is the validity of model-based predic-
tions. Other issues of concern include code availability and reliability,
model selection and acceptance criteria, project review and procurement, data
requirements, information exchange, and training.
THE GROUNDWATER SYSTEM
Groundwater is a subsurface element of the hydrosphere, which is gener-
ally understood to encompass all the waters beneath, on, and above the earth's
surface. Many solar-powered processes occur in the hydrosphere, resulting in
a continuous movement of water. This dynamic system is referred to as the
hydrologic cycle. Its major elements are atmospheric water, surface water,
water in the subsoil (shallow and deep vadose zone), groundwater, streams,
lakes and ocean basins, and the water in the lithosphere (Figure 1).
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transpiration
precip-
itation
evaporation
Infil-
tration
surface
runoff
precipitation
.Surface Water /
// Bodies //
/(rivers, lakes)/
seepage
Soil
/
(root zone)
percolation
Deep Vadose,
'/Zon
///,
recharge
capillary
rise
Interflow
seepage
(wetlands)
discharge
(base flow)
stream
flow
evaporation
discharge
recharge
saltwater
Intrusion
/ / / / ' / / / / / / S/S/S/'S/////'///// /////////
R O U N DXW ATER ZONE/AQUIFERS Y//////,
,SS/S,///Ss,, s X yxx/-XXXXXXXXX//XX/X/////y
LITHOSPHERE
Fig. 1. Elements of the hydrologic cycle and their interactions.
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Movement of water occurs both within each element of the hydrologic cycle
and as exchanges between the elements, and results in the dynamic character of
this relatively closed system. The exchange processes between the surface
subsystem and the atmosphere include evaporation, precipitation (rainfall and
snowfall), and plant transpiration. Infiltration, seepage, groundwater
recharge from streams, and subsurface discharge into lakes and streams (both
interflow and baseflow) are inter-element processes between the earth's sur-
face and subsurface. Surface runoff forms the link between the earth's sur-
face and the network of streams. In addition, interactions take place between
the subsurface hydrosphere and elements of the earth's biological environment
(e.g., consumptive use of water by plants).
A groundwater system is an aggregate of rock in which water enters and
moves, and which is bounded by rock that does not allow any water movement,
and by zones of interaction with the earth's surface and with surface water
systems (Oomenico 1972). In such a system the water may transport solutes and
biota; interactions of both water and dissolved constituents with the solid
phase (rock) often occur.
Water enters the groundwater system in recharge zones and leaves the sys-
tem in discharge areas. In a humid climate, the major source of aquifer
recharge is the infiltration of water and its subsequent percolation through
the soil into the groundwater subsystem. This type of recharge occurs in all
in-stream areas except along streams and their adjoining floodplains, which
are generally discharge areas. In arid parts of the world, recharge is often
restricted to mountain ranges, to alluvial fans bordering these mountain
ranges, and along the channels of major streams underlain by thick and
permeable alluvial deposits.
In addition to these natural recharge processes, artificial or man-made
recharge can be significant. This type of recharge includes injection wells,
induced infiltration from surface water bodies, and irrigation.
Outflows from groundwater systems are normally the result of a combina-
tion of inflows from various recharge sources. Groundwater loss appears as
interflow to streams (rapid near-surface runoff); as groundwater discharge
into streams (resulting in stream baseflow); as springs and small seeps in
hillsides and valley bottoms; as wetlands such as lakes and marshes fed by
groundwater; as capillary rise near the water table into a zone from which
evaporation and transpiration can occur; and as transpiration by phreatophytes
(plants whose roots can live in the saturated zone or can survive fluctuations
of the water table) (Toth 1971, Freeze and Cherry 1979). Other outflows are
artificial or human-induced, as agricultural drainage (tile-drains, furrows,
ditches) and wells for water supply or dewatering (e.g., excavations and
mining).
The unsaturated zone has a significant smoothing influence on the tem-
poral characteristics of the recharge of groundwater systems. Highly variable
(hourly) precipitation and diurnal evapotranspiration effects are dampened and
seasonal and long-term variations in flow rates become more prominent further
from the soil surface. In this dampening the higher-frequency fluctuations
are filtered, a process that continues in the groundwater zone. Its ultimate
effect can be observed in stream base flow, which is characterized by seasonal
and long-term components.
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A groundwater system may consist of a single flow system between its
recharge and discharge areas. This is generally the case when local relief is
negligible and only a gentle regional slope is present. If the relief of the
surface becomes more pronounced, local groundwater flow systems can develop.
If the depth-to-length ratio of the system in the direction of principal
surface gradients is small, a series of local flow systems adjacent to each
other is the result. However, if the aquifer depth-to-width ratio increases,
a combination of flow systems may develop, resulting in a hierarchically
structured groundwater system with local, intermediate, and regional compo-
nents (Figure 2) (Toth 1963). If the groundwater system consists of multiple
aquifers, this hierarchical structure is even more evident (van der Heijde
1988) (Figure 3). The notion that such a hierarchical structure exists has
improved the effectiveness of modeling groundwater systems significantly
(e.g., Freeze and Witherspoon 1966).
The largest hydrogeologic unit is a groundwater basin. It is a system
containing the entire network of flow paths taken by all the water recharging
the basin (Freeze and Witherspoon 1966). A groundwater basin consists of a
single aquifer or several connected and inter-related aquifers. The water
divide between two adjacent groundwater basins is not necessarily the same as
that between the surface water drainage basins overlying them. Watersheds can
lose part of their water to neighboring watersheds through subsurface inter-
basin transfers. In a valley between mountain ranges, the drainage basin of
the surface stream coincides closely with the groundwater basin. In limestone
areas and large alluvial basins, the drainage and groundwater basins may have
entirely different configurations.
A groundwater system has two basic hydraulic functions: it is a reservoir
for water storage, and it serves as a conduit by facilitating the transmission
of water from recharge to discharge areas. A groundwater system can be con-
sidered as a reservoir that integrates various inputs and dampens and delays
the propagation of responses to those inputs (van der Heijde 1988). The water
movement is dictated by hydraulic gradients and system-dependent hydraulic
conductivity. In turn, these gradients are influenced by boundary conditions
on the groundwater system. These conditions could include anthropogenic
stresses on the system (e.g., pumping), climatic effects, surface topography,
and other possible geomorphic features of the physical system such as streams,
reservoirs, etc.
The rate of groundwater movement can be expressed in terms of time re-
quired for groundwater to move from a recharge area to a discharge zone. This
time ranges from a few days in zones adjacent to discharge areas in small
local systems, to thousands of years for water that moves through deeper parts
of the groundwater system (Figure 3).
Groundwater systems are characterized by complex relationships among
patterns for system recharge, discharge, and groundwater storage. Obviously,
system discharge patterns are influenced by the origin and pathways of the
groundwater. For several reasons, the relationships are difficult to define
directly from observed input and response data. These include the dampening
effect of storage on inflow, the lag or delay between the time water enters
and exits the system, the variable rate and sometimes diffuse nature of
recharge and discharge, and the heterogeneous nature of the geologic system.
Therefore, deterministic, mathematical models, based on a mechanistic descrip-
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GROUNDWATER BASIN
REGIONAL
DISCHARGE
AREA
LOCAL
RECHARGE
AREA
REGIONAL
RECHARGE
AREA
LOCAL
DISCHARGE
AREA
GROUNDWATER
DIVIDE
Local
Raw
System
Regional Flow System
Fig. 2. Schematic diagram of a regional groundwater system (after Toth 1963)
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I»MJ*J
Water Table
Aquifer .
Recharge
I I I
^>
'°<
7// '//// /v // // /\// // / /Ixxx'//7 77~7
X^-VVxUpper Confining Bed//y/V/XX
xVCX^XXxx xfxxx ^xi/xx/xxt' ////////?.
' ' ... '.*'";''".. .'*' :-.' ' '".. _^j-»^~jr^rvTr^g;^
Upper Confined; .' '.'.'' .'.'...'''.'-.'...'.''". . " .8 '.''.' ' JS- ' :^\'-.': '.'''
': Mi'ddie Confined ': y-:\\:\'.''-': ''.';' \-l: :'': :'\-'- ''.'':".'.'-.."? .'.'^';'1 - ''' '':. '"'';V;\v ^v.'/;'v--^-v';':'^
.' ; '' Aquifer '.' .' '''-''." ''": '.''.'.' ' \ ': .'' . '-.'':.'.-/Decades .. '''.'.,'.>'.',:.': :.':'.'.,:.''.':.:
ower Confining Bed
Lower Confined | | | | | (
I I Aquifer I I I I I hCenluries-r I I =i
I I I I I \==\
KXXXX'tXXXXXTXXXXX
Bedrock
Fig. 3. Schematic overview of groundwater resident times in large regional
systems (after van der Heijde 1988).
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tion of the physical and chemical processes that describe the groundwater
system, are widely used in groundwater hydrology (van der Heijde 1988).
GROUNDWATER QUALITY
In the last few decades, groundwater contamination from organic and inor-
ganic chemicals, radionuclides, and microorganisms from domestic, industrial,
and agricultural activities has become a significant environmental problem
(EPA 1977, Jackson 1980, Pye et al. 1983, NRC 1984). This increased concern
with the quality of groundwater has been catalyzed by the widespread detection
of contamination of groundwater systems, more public awareness of the health
and environmental risks associated with groundwater contamination, and the
increase of industrial waste and the problem of hazardous waste disposal (OTA
1984).
The quality of groundwater is typically described by its chemical compo-
sition. This quality is the result of natural processes and human interven-
tion, either by introducing chemical or biological components directly into
the groundwater system, or indirectly by modifying the effects of natural
processes on the system (e.g., salt water intrusion).
Natural groundwater can be defined as groundwater whose composition is
determined only by natural, non-human-induced processes. The composition of
natural groundwater is the result of its hydrogeological and geochemical his-
tory. In its role as part of the hydrologic cycle, groundwater is recharged
by water from the atmosphere and from bodies of surface water. It is now or
once was part of a dynamic system of movement through and interaction with the
geologic environment.
Atmospheric precipitation, because of its chemical composition and physi-
cal characteristics, is a major influence on the quality of groundwater. It
is a source of such chemicals as oxygen, nitrogen, and carbon dioxide and is
slightly acid (pH * 6.5; Hem 1970). This acidity can increase significantly
(e.g., pH 2-4) when man-made pollutants such as oxides of sulfur and nitrogen
are introduced into the atmosphere.
Precipitation can have a diluting effect on groundwater, as when the con-
centration of dissolved chemicals in the precipitation is lower than that of
the groundwater. In addition, the precipitation temperature can alter the
temperature of the soil and thus change reaction and transformation rates of
groundwater processes in the soil.
Another important natural process is evaporation, which can influence the
amount of water available for infiltration to deeper formations, thus reducing
the diluting effect of precipitation on groundwater. Evaporation can have a
concentrating effect on salts in soil; only the water evaporates and the
solutes are left behind.
Infiltrated water is a potential leaching agent of soils and rock. In
arid regions, leaching is a major cause of saline pollution of groundwater,
resulting in a high value for total dissolved solids and high chloride content
of the groundwater. Other common natural leachate products are sulfates,
nitrates, fluorides, and iron (Hem 1970). Under the influence of the carbon
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dioxide introduced into the soil and hence into groundwater, calcium and mag-
nesium carbonate are formed, resulting in an increase in water hardness. In
some areas leaching of uranium ore under natural conditions causes a signifi-
cant increase in the natural radioactivity of soil.
Sources of Groundwater Pollution
Although human intervention in the environment began many centuries ago,
its significant effects on groundwater are of recent origin, and in general
are restricted to regions of significantly altered land use, as by urbani-
zation, mining, or agriculture.
Pollution of groundwater may result from direct introduction of chemical
or biological components, and indirectly from induced alterations in water
quality through modification of external or related system conditions. Such
intervention may be the result of planned or illegal domestic, commercial,
industrial, or agricultural waste disposal; upconing of saline water by pump-
ing a freshwater aquifer over a saltwater aquifer; discharge of polluted water
in streams that recharge aquifers; mine drainage; acidification of soils by
acidic precipitation resulting from industrial and vehicular releases of con-
taminants; runoff from road deicing salts; infiltration of polluted surface
water; and by salt water intrusion from oceans or from saline aquifers. The
intervention may also be accidental, as with spills and leakage of storage
tanks and pipelines.
A major cause of widespread groundwater pollution is the introduction of
solid and liquid wastes into the subsurface or near-surface soil. Liquid
waste and the leachate from solid waste directly affect groundwater quality.
The resulting deterioration in water quality may be so serious that the source
is a hazard to human health or the environment.
Various types of solid wastes occur: domestic waste, solid commercial
waste, solid compounds of industrial waste, sludge from waste treatment
plants, sludge from water supply treatment plants or air-pollution control
facilities, and mine tailings. As determined by the type of waste, various
leachate compositions may develop. For example, the leachate of household
waste contains high concentrations of sulfate, chloride, and ammonia. Commer-
cial solid waste produces oils, phenols, and organic solvents. A more com-
plete description of the composition of various waste leachates is presented
by Jackson (1980) and Pye et al. (1983).
Solid waste is often disposed of through dumps, landfills, sanitary land-
fills, or secured landfills. Uncontrolled dumps and weakly controlled land-
fills are the major causes of groundwater pollution. The leachate formed from
these sources consists primarily of dissolved minerals, heavy metals, and
organic chemicals.
Another major source of groundwater pollution is liquid waste. Various
disposal methods are in use, such as wastewater impoundments, deep subsurface
injection, land spreading of the liquid waste, and discharge into surface
water bodies. The waste water may be diluted before it is discarded.
A major type of liquid waste is municipal wastewater, which consists of
domestic, industrial, and stormwater components. Although municipal waste-
-------
water is often treated before it is discharged into the environment, many
sanitary sewer systems leak untreated wastewater into the ground. This is
particularly true when sewer pipes are above the water table and water
pressure is not available to prevent leakage of the sewage. If the sewer
system is also used for stormwater removal, heavy storms can cause overflow of
the storage lagoons in the system, thus contributing to groundwater pollution
by direct infiltration into the soil. Finally, land disposal of treated muni-
cipal wastewater may cause problems. Various disposal methods are used, such
as agricultural irrigation, rapid infiltration ponds, overland runoff, dis-
charge into dry streambeds and ditches, and land spraying.
Industrial wastewater is often disposed of directly by the industry that
produces it. Treated wastewater may be discharged to a surface water body.
Untreated wastewater is often stored in impoundments such as pits, ponds,
lagoons, or pools, either temporarily until treatment is available, or
indefinitely. Leakage of wastewater into the ground occurs frequently with
this type of waste storage. The leakage may be caused by a poorly designed or
constructed facility, such as one without liners or with leaking liners, or by
accidental overflow of basins resulting in infiltration into the underlying
soil. Some impoundments are designed to overflow and discharge regularly into
bays, oceans, lakes, or streams. Liquid waste in nondischarging impoundments
may be lost through evapotranspiration or seepage into the soil. The liquid
residuals of oil and gas extraction and animal feedlot wastes are often stored
in such impoundments.
Another method of liquid waste disposal is through deep well injection.
This method, which is frequently used to dispose of brine and other residuals
from oil and gas drilling and well-bore maintenance, is also used for various
industrial wastes. Major problems with this method are leakage through the
well bore because of construction faults, or breakthrough and seepage through
the confining layers separating an aquifer targeted for disposal from an aqui-
fer utilized for water supply. Such breakthrough and seepage may result from
insufficient thickness of the confining layer or from hydraulic fracturing.
In certain areas, hydraulic short circuiting through abandoned oil and gas
wells occurs. Problems arising from with deep well injection often are caused
by the high pressures necessary to force the waste into the aquifer. Direct
injection into an already-exploited aquifer may occur, or the increased
pressures caused by the injection may cause displacements of saline waters
toward water supply wells. In some cases the injected waste migrates to a
freshwater part of the aquifer and causes deterioration of its quality.
Widespread use of individual sewage disposal systems is another major
wastewater source discharging directly into groundwater. Three methods of on-
site domestic waste disposal are practiced: septic tanks with a subsurface
disposal system, cesspools, and pit privies. All three are located in the
near-surface soil. Properly sited, constructed, and maintained septic tanks
are generally no problem. However, many septic tanks are not well-constructed
or are poorly maintained and overloaded (Pye et al. 1983).
Accidental spills and leakage form another category of liquid waste
pollution sources. These can occur in a wide variety of situations, as in
Industrial processes, storage activities, and during transport. In general,
the effects of these pollution sources are local, although their ultimate
effects on groundwater quality may be wide-ranging.
-------
The major causes of pollution from agricultural activities are the wide-
spread use of pesticides, herbicides, and fertilizers, and the production of
manure, especially in feedlots. Application of fertilizers to crops often
leads to nonpoint pollution from runoff organics and nitrate. Irrigation
return flow can contribute significantly to this problem.
A special type of pollution is caused by radioactive waste disposal.
Frequently, this waste contains solid, liquid, or gaseous chemicals of both
radiological and chemical toxicity. From a management point of view, two
types of radioactive waste are distinguished: high and low level. In general,
these are disposed of in a controlled manner. However, transport spills and
accidental operational discharges to the environment may occur. Identifi-
cation of the source, its chemical characteristics and its temporal behavior
are important issues in studying groundwater pollution problems. Knowing
source location and behavior is prerequisite to most groundwater modeling
efforts. It influences model selection and modeling strategy and ultimately
the accuracy of model-based predictions.
A more detailed discussion of modeling groundwater quality is presented
in Chapter 4.
GROUNDWATER MODELING: DEFINITIONS
Although a consensus may exist as to what groundwater modeling entails,
the definition of a "model" per se is somewhat nebulous. As a generalized
definition, a model is a non-unique simplified description of an existing
physical system. In order to create such a simplified version of the system,
various assumptions are made with respect to physical system characteristics,
technical issues involved, and relevant managerial constraints. Groundwater
models are generally intended to provide practical, descriptive, and predic-
tive problem-solving tools.
Although physical groundwater models can be useful for studying certain
problems, the present focus is on mathematical models in which the causal
relationships among various components of the system and the system and its
environment are quantified and expressed in terms of mathematics and uncer-
tainty of information. This definition is still rather broad and is not
limited to where the physical, chemical and biological processes themselves
are well defined. Thus, mathematical models might range from rather simple,
empirical expressions to complex multi-equation formulations.
In hydrogeology, the term "groundwater model" has also become synonymous
with conceptual models, mathematical models, analytic or numerical models,
computer models, and simulation models. (A detailed discussion of these
latter terms is given in Chapter 5.) For the present discussion of computer-
based modeling, we refer to a groundwater model as the mathematical descrip-
tion of the processes active in a groundwater system, coded in a programming
language, together with a quantification of the groundwater system it simu-
lates in the form of boundary conditions and parameters. The generic computer
code that is used in this problem-specific system simulation is often referred
to as a computer model. The most complex of these simulation models are
usually based on numerical solution techniques which allow simulation of
heterogeneous systems controlled by a variety of coupled processes that des-
10
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cribe the hydrology, chemical transport, geochemistry, and biochemistry of the
heterogeneous near-surface and deep underground. This use of the term ground-
water model includes fluid flow and solute transport models for both the satu-
rated and unsaturated zones and reflects the highly multidisciplinary nature
of contemporary hydrogeology. Although other types of models have been devel-
oped for simulating soil processes and processes in the deeper subsurface
(e.g., air and vapor transport in soils, soil mechanics, fracture propagation,
stress-strain behavior of rock, and steam flow and related heat transport in
multiphase geothermal reservoirs, the discussion in this report is restricted
to models that relate directly to soil and groundwater.
11
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2. GROUNDWATER MODELING AND MANAGEMENT
Groundwater management is concerned with the efficient utilization of
groundwater resources in response to current and future demands, while pro-
tecting the integrity of the resources to sustain general environmental needs.
Groundwater modeling has become an important methodology in support of the
planning and decision-making processes involved in groundwater management.
Groundwater modeling provides an analytical framework for understanding
groundwater flow systems and the processes and controls that influence their
quality, particularly those processes influenced by human intervention in the
hydrogeologic system. Models can provide water resource managers with neces-
sary support for planning and screening of alternative policies, making
management decisions, and reviewing technical designs for groundwater remedia-
tion based on a risk analysis of benefits and costs. Such support is particu-
larly advantageous when applied to development of groundwater supply, ground-
water protection, and aquifer restoration.
Successful utilization of modeling is possible only if the methodology is
properly integrated with' data collection, data processing, and other techni-
ques and approaches for evaluation of hydrogeologic system characteristics.
Furthermore, frequent communication between managers and technical experts is
essential to assure that management issues are adequately formulated and that
the technical analysis using models is well targeted.
GROUNDWATER RESOURCE DEVELOPMENT
According to Freeze and Back (1983), the earliest application of numeri-
cal simulation to a subsurface flow problem was documented in Shaw and South-
well (1941). In those days all calculations were performed by hand. Stallman
(1956) is considered the first to have shown the feasibility of applying
numerical methods in groundwater hydrology. In the 1960s, the rapid devel-
opment of computer technology made it possible to simulate groundwater systems
efficiently through the use of software instead of physical scale models or
electric analogs. Since that time, modeling has become an increasingly popu-
lar and useful tool in groundwater management (Prickett 1975).
Since the major means to exploit groundwater resources is through
pumping, management is concerned with determining location, spacing, and
sizing of wells or well fields, and the rates and time schedules of pumpage.
Extracting groundwater through pumping might reduce the natural discharge of
groundwater in streams and thus reduce base flow. In addition, if the pumping
is excessive enough to lower the water levels significantly, exploitation of
the resource may lead to land subsidence or, in karstic areas, to collapse of
the ground surface.
With the development of computer technology and modeling methodology,
more powerful tools became available for investigations into such groundwater
management issues as the optimum design of well fields, the quantitative
analysis of regional groundwater supplies, and the prediction of water level
declines due to groundwater withdrawals. The first groundwater computer
models were constructed to facilitate the development of well fields in local
12
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and regional aquifer systems while limiting the environmental impacts of such
developments.
From the beginning, the U.S. Geological Survey (USGS) has contributed
significantly to groundwater modeling. In the late 1960s the USGS initiated
the development of digital models to replace analog models (Pinder and Brede-
hoeft 1968). Since then, the USGS has developed a comprehensive suite of
generic simulation and parameter estimation models, many of which are widely
used in the United States and abroad. An overview of the early USGS contribu-
tions to groundwater modeling was presented by Appel and Bredehoeft (1976).
Recently, Appel and Reilly (1988) compiled a listing of all pertinent USGS
modeling codes.
GROUNDWATER QUALITY
The predictive capabilities of groundwater quality models are used to
evaluate the potential impact of design alternatives for waste disposal
facilities, proposed alterations in the groundwater flow system either through
changing its boundaries, parameter values, or stresses (e.g., development of
well fields, excavations for construction sites or open-pit mining, and
dewatering operations), and the development of aquifer protection zones.
Where precise aquifer and contaminant characteristics have been reason-
ably well established, groundwater models may provide a viable, if not the
only, method to predict contaminant transport and fate, locate areas of poten-
tial environmental risk, identify pollution sources, and assess possible reme-
dial actions. Some examples in which mathematical models have assisted in the
management of groundwater protection programs are (van der Heijde and Park
1986):
Determining or evaluating the need for regulation of specific waste
disposal, agricultural, and industrial practices
Analyzing policy impacts, as in evaluating the consequences of setting
regulatory standards and rules
Assessing exposure, hazard, damage, and health risks
Evaluating reliability, technical feasibility and effectiveness, cost,
operation and maintenance, and other aspects of waste disposal facility
designs and of alternative remedial actions
Providing guidance in siting new facilities and in permit issuance and
petitioning
Developing aquifer or well head protection zones
Assessing liabilities such as post-closure liability for waste disposal
sites.
Models generally applied to groundwater pollution problems can be divided
in two broad categories: (1) flow models describing hydraulic behavior of
single or multiple fluids or fluid phases in porous soils, or porous or frac-
13
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tured rock, and (2) contaminant transport and fate models for analysis of
movement, transformation, and degradation of chemicals present in the subsur-
face. In the context of groundwater protection programs a distinction is
often made between site-specific and generic modeling.
The success of a given model depends on the accuracy and efficiency with
which the natural processes controlling the behavior of groundwater, and the
chemical and biological species it transports, are simulated. The accuracy
and efficiency of the simulation, in turn, depend heavily on the applicability
of the assumptions and "simplifications adopted in the model, the availability
and accuracy of process information and site characterization data, and on
subjective judgments made by the modeler and management.
It should be noted that the dimensionality required for solving the
pollution problem adequately must be matched by the dimensionality of the
model. One- and two-dimensional characterizations of the subsurface are no
longer widely accepted for such analysis, as is illustrated by the rapid
increase in applications of quasi- and fully three-dimensional models. Actual
flow and transport in the three-dimensional environment can differ markedly
from predictions obtained from one- and two-dimensional models based on ideal-
izations of the three-dimensional world, even if the aquifer properties do not
change significantly with depth.
Site-Specific Modeling
Whether for permit issuance, investigation of potential problems, or
remediation of proven contamination, site-specific modeling is required as a
necessary instrument for compliance under a number of major environmental
statutes. The National Environmental Policy Act of 1970 (NEPA) stipulates a
need to show the impact of major site-specific construction activities in
Environmental Impact Statements; although not required by the regulations,
potential impacts are often projected successfully by mathematical models.
Some of the most challenging site-specific problems involve hazardous
waste sites falling under the purviews of RCRA (Resource Conservation and
Recovery Act of 1976) and CERCLA (Comprehensive Environmental Response,
Compensation, and Liability Act of 1980Superfund), both administered by the
U.S. Environmental Protection Agency. Associated with most of these sites is
an intricate array of chemical wastes and the presence of or potential for
groundwater contamination. Furthermore, the hydrogeologic settings of such
sites are usually complex. Under such conditions, groundwater models are
useful instruments for analyzing compliance with RCRA and CERCLA legislation.
Generic Modeling
Where the results of environmental analysis must be applied to many
sites, data availability is limited or other constraints are present. In such
cases, site-specific modeling is not feasible. As a result, many decisions
are made by applying models to generic management issues and hydrogeologic
conditions. Models used for this type of analysis are more often analytical
than numerical in their mathematical solutions, in contrast to models used for
detailed analysis of site-specific conditions. Because of their limited data
requirements, analytical models can be applied efficiently to a large number
of simple datasets or to statistical analyses representing a wide variety of
14
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field conditions. The cost of such exercises would often be prohibitive when
using numerical models. However, the limitations imposed by analytical models
on the simulation of a complex groundwater system require restraint in the use
of computed results. Therefore, in choosing representative scenarios and
model input, a so-called "conservative" approach is frequently taken, thus
lowering the risk for subsequent management decisions.
Typical examples of generic modeling reflect the statutory responsibili-
ties of such agencies as the U.S. EPA (van der Heijde and Park 1986), includ-
ing the estimation of potential environmental exposures and their integration
with dose-response models to yield health-based risk assessments. These
assessments are necessary, for example, in issuing compound-specific rulings
on products subject to preregistration requirements under the Toxic Substances
Control Act of 1976 (TSCA) and the Federal Insecticide, Fungicide, and Roden-
ticide Act. of (FIFRA). More generalized policy formulations also benefit from
generic modeling; examples include policy decisions about land disposal
"banning," setting Alternate Concentration Limits (ACLs), preparing Technical
Enforcement Guidance Documents (i.e., for monitoring network designs), and
"delisting" of particular types of waste under RCRA.
However, generic modeling approaches are being increasingly contested
through public comment on draft regulations or in courtroom legal proce-
dures. An example is the recent court decision that EPA's VHS model (Vertical
Horizontal Spread model, EPA 1985) cannot be used to grant or deny a delisting
petition under the RCRA permitting program (Ground water Monitor, February 17,
1988, p. 26). Another example is the shelving of the EPA Screening Level
Model (SLM) designed for use in the development of banning decisions regarding
land disposal under RCRA, as a result of changes in interpretation of EPA's
mandate in this area (EPA 1986a).
SCALES RELEVANT TO GROUNDWATER MANAGEMENT
A major aspect of the application of models is defining the spatial and
temporal scales to be used in the model. Different scales might apply to
various subsystems simulated by the model. The selection of scales is depen-
dent on the management of objectives, the nature of the system(s) modeled, and
the chosen numerical method, among other considerations.
A wide range of both spatial and temporal scales is involved in the study
of groundwater problems. Spatial scales range from less than a nanometer, for
studying such phenomena as the interactions between water molecules and dis-
solved chemicals (Cusham 1985), to hundreds of kilometers, for the assessment
and management of regional groundwater systems (Toth 1963). For temporal
scales, two major categories can be distinguished: steady-state or average
state, and a time-varying or transient state. Periodic fluctuations on a
diurnal or seasonal scale are frequent in hydrogeology. Other processes
display certain trends or occur rather randomly in nature (Table 1). Many
processes exhibit a strong temporal effect immediately after their initiation
but become stable after a while, moving to a steady state. Other processes
fluctuate on a scale that is often much smaller than necessary to include in
the analysis of such systems. An averaging approach is then taken, resulting
in steady-state analysis. The steady state is also assumed when the analysis
period is so short that temporal effects are not noticeable.
15
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Table 1. Summary of mechanisms tending to produce fluctuations in
groundwater levels (Freeze and Cherry 1979)
CU > E <1)
C T3 0) >- i J- CJ
r- 0> r TJ r to O) O»C
>4- C -l-> C O I C O 3 « C T- U-
CO-
Groundwater recharge
(infiltration to water table) x x x x x
Air entrapment during ground-
water recharge x x x x
Evapotranspiration and
phreatophytic consumption x x x x
Bank storage effects
near streams x x x x
Tidal effects near oceans x x x x x
Atmospheric pressure effects x x x x x
External loading of confined
aquifers x x x
Earthquakes x x x
Groundwater pumpage x x x x
Deep well injection x x x
Artificial recharge:
leakage from ponds,
lagoons, landfills x x x
Agricultural irrigation
and drainage x x x x x
Geotechnical drainage of
open pit mines, slopes,
tunnels, excavation sites x x x
16
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Dimensions in the time domain range from millenia in paleohydrological
simulations and risk analysis for long-term isolation of radioactive waste
through year by year, to seasonal, monthly, weekly, daily, and hourly scales
for field systems, to modeling of real-time systems on a basis of minutes and
even seconds in some laboratory experiments.
Scales in groundwater hydrology can be viewed from two perspectives.
First is the physical scale on which the hydrological processes take place
(Figure 4, Table 2). These processes provide the physical setting in which
human interaction can be studied, as they occur in unintentional or managed
alterations in the natural system (van der Heijde 1988). The scale on which
hydrological processes are analyzed often differs between the various subsys-
tems of the hydrological cycle, dependent on the system's physical charac-
teristics and on the study objectives. Furthermore, analyses of the principal
features of the subsystems often requires a hierarchical discretization that
differs between the subsystems. Among other cases, this is the case between
the atmospheric and subsurface processes in watershed response to
precipitation patterns, and between soils and aquifers for analysis of flow
and pollutant transport. Another perspective is that of resource management,
where socioeconomic and political conditions are paired with the hydrological
and engineering aspects of a groundwater system.
In general, human-induced influences on groundwater systems affect local
and intermediate scales, while large, regional-scale phenomena are of natural
origin. Some human-induced changes are also on a regional scale, such as the
amalgamated effect on water levels and return flow of groundwater withdrawal
for irrigation; nonpoint pollution caused by use of fertilizers, herbicides,
and pesticides in agriculture; acidification of groundwater as a result of
acidic precipitation; and the changes in quality resulting from urbanization.
From a management point of view a system can be hierarchical, divided
into administrative elements such as townships, counties, states, and river
basins. If modeling is intended to provide optimal courses of action in the
management of the water resources, an approach based on administrative ele-
ments can be successful. However, such an approach does not follow natural
boundaries and elements and therefore, often, does not accurately consider the
effect of physical processes and stresses occurring outside the administrative
area.
In many management situations, selection of the scale of analysis is
influenced by the restrictions in data availability. In part, such restric-
tions are imposed by the lack of techniques for obtaining higher-resolution
data. For example, in groundwater modeling the recharge term of the subsur-
face water balance is directly related, through precipitation and evaporation,
to atmospheric processes and conditions. These exchange variables between
atmosphere and soil surface are obtained either through direct measurement
(rainfall) or indirectly through calculation (evaporation), using various
atmospheric variables. Such data were formerly available only for a limited
number of sampling stations. Consequently, such stations are considered to
represent a rather large area, thus limiting severely the accuracy with which
the recharge can be determined. In recent years remote sensing has developed
as a promising means for obtaining area! values for a number of significant
parameters (e.g., soil moisture and snow cover).
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ATMOSPHERE
EARTH
SURFACE
SOIL
GROUNDWATER
A / /\ /' / /
Y / / v y /
I 7 / /, 7i /
SURFACE
(WATERSHEDS)
4. Scales and relative sizes of various hydrological systems (after van
der Heijde 1988).
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Table 2. Scales in groundwater modeling (van der Heijde 1988).
Site
Local
Intermediate
Regional
area
examples
geology
flow
solute
transport
<100m
tracer test,
pumping test
homogeneous
single aquifer
or part of aquifers;
homogeneous,
possibly anisotropic
homogeneous
100-1000m
point source,
pollution,
small well fields
single horizontal
unit; some vertical
layering
single aquifer
or part of aquifers;
homogeneous,
possibly anisotropic
homogeneous in
horizontal direction,
1ayered
1000-10000m
small aquifers,
large point-
source pollution
a few horizontal
units and significant
vertical layering
single or multiple
aquifer(s);
heterogeneous in
horizontal direction,
anisotropic,
possibly some
vertical layering
heterogeneous,
1ayered
>10,000m
basins
large aquifers,
nonpoint pollution
heterogeneous
in both horizontal
and vertical
directions
multiple aquifers;
heterogeneous,
anisotropic,
vertically layered
heterogeneous,
1ayered
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Spatial Scales
Water supply problems are generally related to availability of sufficient
water to cover water needs, and to drawdown of groundwater levels and reduc-
tion of pressures and storage as a result of the exploitation of the resource
(van der Heijde 1988). Industrial and municipal water supply requires well-
fields with the wells relatively closely spaced (50-200 m) in order to obtain
an efficient connection with the distribution network. Their area of influ-
ence can range from less than 1 km2 to more than 100 km2. Private, single-
household wells have a small area of influence (often less than 100 m in
radius), but individual irrigation wells may have a significant influence on a
system (up to a few thousand meters). In some areas the combined drawdown of
a large number of private wells can cause serious aquifer depletion. This is
especially true with agricultural water use. The total effect of large-scale
irrigation from groundwater may lower the water levels in entire aquifer sys-
tems, e.g., the long-term depletion of the Central Valley aquifers in Cali-
fornia, and of the Ogallala aquifer in the High Plain region. This problem
occurs most often in areas with low to moderate recharge from precipitation.
Groundwater pumpage aimed at lowering water levels may assume large-scale
proportions, as with dewatering for mining operations. An example is the
open-pit mining of lignite in the northern part of the Rhenish lignite mining
district of West Germany, where drawdowns of more than 100 m occur to keep the
pit dry. The influence of this dewatering is felt more than 20 km off-site,
and the affected area is still expanding as a result of continuing dewatering
(Boehm 1983).
Operation of groundwater systems and conjunctive management of coupled
groundwater-surface water systems have their special scale requirements,
ranging from the scale of a major watershed or river basin (for policy deci-
sions) to that of sections of the aquifer or stretches of the river (for local
planning and engineering purposes).
So-called human-induced point-source groundwater contamination, as from
spills, leaching from landfills or lagoons, and underground tank failures,
often occurs on a much more local scale (100-1000 m). However, if nothing is
done about such groundwater deterioration, the affected area can become quite
extensive (1000-10,000 m).
Some basins are affected by a large group of individual point sources
such as septic tanks or landfills and dumps. The aggregated effect of these
is comparable with that of nonpoint pollution. In such cases, individual
mitigation has no effect and regulatory action for the entire basin is
required.
Related to the discussion of spatial scales in groundwater systems is the
phenomenon of hydrogeologic heterogeneity or nonuniformity. Various types of
heterogeneity exist: layered, discontinuous, and trending hetrogeneity (Freeze
and Cherry 1979). Layered heterogeneity occurs in sedimentary deposits, while
discontinous heterogeneity, also found in sedimentary deposits, is caused by
faults or large-scale stratigraphic features. The last class, trending heter-
ogeneity, exists within similar geologic formations in response to sedimenta-
tion processes. These classes of heterogeneity may be treated deterministi-
cally. Uncertainty exists, however, due to the lack of information about the
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system or to the variable nature of certain properties or processes. As dis-
cussed by Dettinger and Wilson (1981), uncertainty results from the absence of
enough or accurate information about the system but may be reduced through
measurements. Intrinsic uncertainty (i.e., due to variability) is caused by
small-scale fluctuations superimposed on deterministic, large-scale varia-
tions. The small-scale fluctuations contain smaller fluctuations, and so
forth. Intrinsic uncertainty is a physical variability, and in contrast to
information uncertainty, cannot be reduced by measurements. However, the
accuracy of characterizing the physical variability increases by increasing
the number of observations. Through the use of widespread measurements,
descriptions of the intrinsic variability in a field system can help reduce
information uncertainty.
Temporal Scales
For water management purposes, temporal scales are important. Incidental
local situations, such as construction site dewatering and chemical spills,
have mainly short-term effects for weeks or months. Seasonal effects are
related to agricultural uses and the use of aquifers as thermal energy sources
or storage. Mid- to long-term scales (1-20 years) apply to many wellfield
operations, dewatering of mining sites, and local pollution problems. Long-
term effects (20-100 years) are of special interest in regional water resource
development, hazardous waste displacement, and regional nonpoint pollution.
Historical periods (100 years to millions of years) are of interest for paleo-
hydrogeological studies and for isolation of highly toxic, nondegradable
chemicals and long-living radionuclides.
A typical example of temporal scales as applied in groundwater models is
the study of the South Platte River in Colorado (Morel-Seytoux and Restrepo
1985). This model currently simulates about a 160 km stretch of river and
hydraulically connected aquifer. The model is used for two types of analysis:
(1) daily operation of the conjunctive use river-aquifer system, aimed at
allocation of irrigation water according to availability and water rights, and
(2) evaluation of policies and legislation. In the operational mode a daily
simulation time-step is used for the surface water system and a weekly simu-
lation is used for the groundwater away from the river. To account for the
more rapid responses of the groundwater near the river, a correction is made
to the results of the weekly simulations for the parts of the aquifer along
the river. For the use of the model in the development of policies and in
evaluating new legislation, as in the formulation of new water distribution
rules, the scale is much larger because long-term effects are of interest. In
the South Platte River study, a weekly timestep is used for surface water, a
monthly timestep for groundwater.
In planning remedial action, temporal scales are directly dependent on
the extent of the polluted area, the geology, the important hydrological and
biochemical processes, and the remedial action itself. For example, remedial
actions designed for control of erosion and runoff, such as grading and sur-
face water diversion, could require transient simulation with short timesteps
for the rainfall and runoff processes that fluctuate rapidly (daily scale).
In the saturated zone the flow is more regular and changes occur within a time
frame of months or even years. Dynamically linked submodels, each with its
own time scale, are then required for efficient simulation. To evaluate the
threat of pollution to humans and the environment, or to analyze the effects
21
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of remedial action, simulation periods of 20-100 yrs are common. Much longer-
term effects may have to be included, as in the case of long-living radionu-
clides and chemically inert toxic organics.
An example of temporal scale is radioactive waste storage in unsaturated
systems, where effects must be evaluated for time periods up to 10,000 yrs
(EPA 1982). Because of the strongly nonlinear character of the flow and
transport equations for the unsaturated zone, the timesteps cannot be too
large (Reisenauer et al. 1982, Tripathi and Yeh 1985). Tripathi and Yeh
(1985) used variable time steps up to 20,000 yrs to simulate an unsaturated
system for such an extended time.
22
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3. MODEL DEVELOPMENT
In groundwater modeling a distinction is often made between two major
categories of activities: model development and model use in management.
Model development consists of researching the quantitative description of the
groundwater system, a software development component, and model testing.
Model development is closely related to the scientific process of increasing
knowledge: observing nature, posing hypotheses for the observed information,
verifying the proposed relationships, and thus establishing a credible theo-
retical framework and improving our understanding of nature. Model develop-
ment is often driven by the short-term and less frequently by the long-term
needs of natural resources management. The resulting, often-generic computer
codes are used in model application as part of a larger set of activities
which included data collection and interpretation, technical design, economi-
cal evaluation, and so forth. The present chapter discusses the model devel-
opment processes (Figure 5) and related issues, while Chapter 4 discusses the
model application process.
THE MODEL DEVELOPMENT PROCESS
The development and use of models encompasses a broad spectrum of techni-
cal expertise. At one end is management; at the other end is scientific
research. Between are two principal categories: model builders engaged in
the development of models, and technical experts concerned with their opera-
tional use (Bachmat et al. 1978). The four categories are not rigidly sepa-
rated. However, considering the categories as distinct helps elucidate the
general framework of model development and use and of modeling-related
problems.
The roots of model building lie in research. The fundamental understand-
ing of a groundwater system is the product of research synthesized by theory.
The object of such research is a prototype natural system containing selected
elements of the real world multi-element groundwater resources systems. The
selection is driven by management needs and the researcher's interest, and is
influenced by the initial, often cursory conceptualization based on sampling
of the real-world system (Figure 6). The conceptual model of the groundwater
system thus derived forms the basis for determining the causal relationships
among various components of the system and its environment. These relation-
ships are defined in mathematical terms, resulting in a mathematical model.
If the solution of the mathematical equations is complex, as with some closed-
form analytical solutions (see Chapter 5), or when many repetitious calcula-
tions are necessary, as with numerical solutions, the use of computers is
essential. This requires the coding of the solution to the mathematical
problem in a programming language, resulting in a computer code. The
conceptual formulations, mathematical descriptions, and the computer coding
together constitute the prototype model (Figure 6).
In model development, the next step is code testing. This important
phase is aimed at removing programming errors, testing embedded algorithms,
and evaluating the operational characteristics (e.g., input/output facilities,
user friendliness, efficiency; see code selection section of Chapter 4) of the
code through its execution on carefully selected example datasets (Adrion
23
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QA
System Definition
Mathematical
Formulation
Mathematical
Solution
Code Design
Criteria
JC
o
A
.O
o
«
0
U.
Computer Coding
Code Testing
Model Verification
Documentation
Performance
Testing
(range of validity)
Review
Fig. 5. Model development process and feedback.
24
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MANAGEMENT
selection
criteria
design criteria
performance
testing
REAL WORLD
MULTI-ELEMENT
SYSTEMS
selection
REAL WORLD
PROTOTYPE SYSTEM
(Selected Elements)
validation
PROTOTYPE MODEL
CONCEPTS
examination
MATHEMATICAL MODEL
verification
CODE
SAMPLING
selection
criteria
design criteria
correctness
testing
Fig. 6. Model development concepts.
25
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et al. 1986). This stage is often called code verification and is closely
related to the scientific process of model verification in which the
evaluation of the operational characteristics of the code is extended to its
mathematical formulation and solution (assuming a good understanding of the
system, its components, and the interrelationships between the individual
system components). Many research publications report on work done up to this
point in the model development process. Finally, data independently derived
from field sites are used, if available, to establish the code's performance
and validity for particular types of application by assessing the closeness of
the computed results to the system the model is supposed to simulate. In this
case, the selected code is an integral part of the model (concepts,
mathematical descriptions, data) tested. However, for most types of
groundwater models and applications, no such comprehensive, high-quality test
datasets are currently available to confirm the validity of the model in
simulating a particular system of interest (van der Heijde 1987a). A detailed
discussion of the validation process is presented at the end of this chapter.
As a set of simplifying assumptions, equations, and boundary conditions
cast in the form of a computer code, the model may hardly be operational.
Accurate instructions are needed for the preparation of datasets that will
form the input for the code. Therefore, the next stage in the development of
an operational modelthe preparation of documentationis an important step
in the establishment of the code's utility. Documentation should consist of
sections on theory, code structure, operational environment, testing and use.
The instructions contained in the documentation should cover such topics as
hydrogeologic schematization, selection of boundary conditions, gridding and
parameter selection (van der Heijde 1987a). With proper documentation, the
code can be externally evaluated, a quality control procedure that includes
independent review of theory, code, and documentation, audit of the model
development process, and additional performance testing (establishing the
range of parameters, stresses, and scales for which the model can be used
successfully).
When all these steps have been taken, the code is operational and ready
to apply to management problems. In the course of its use, the code gains
confidence by proving its reliability and applicability. This can be further
improved by provisions for continuing support and maintenance. It should be
noted that when changes are made in the code or when model characteristics or
model features are modified, the review and testing process must be repeated
rigorously.
Not all simulation codes resulting from research into the physical and
chemical processes of groundwater systems reach this final stage. This is
partly due to the objectives of the research and development and in part to
the way the project has been launched, or initialized. Basically, three
courses of action are possible: (1) codes can be developed primarily as
research tools (such codes frequently are considered experimental and are not
prepared or released for external use); (2) codes can be developed to provide
practical, descriptive, and predictive management tools for solving field
problems (this type of code is often developed at the special request of
planning, management, or enforcement agencies); and (3) codes can be developed
by consultants as an investment for future consultancy. Codes from the last
two groups are often based on codes of the first category, generally come with
some form of documentation, and have undergone at least limited testing.
26
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MODEL VALIDATION
Successful water management requires that decisions be based on the use
of technically and scientifically sound data collection, information pro-
cessing, and interpretation methods and that these methods are properly inte-
grated. As computer codes are essential building blocks of modeling-based
management, it is crucial that before related computer codes are used as
planning and decision-making tools, their credentials must be established,
independently of their developers, through systematic testing and evaluation
of the codes' characteristics. As in the case of the nuclear industry (Bryant
and Wilburn 1987), software applications in groundwater protection have become
too prominent for the codes to be developed and maintained in the informal
atmosphere that was common in early groundwater modeling software development.
Therefore, determining the validity of a code for modeling well-defined
groundwater systems as part of an analysis of the influence of anthropogenic
stresses on such systems is a crucial step in the development of software to
be used in environmental decisionmaking. It is important at this stage of the
discussion to make the distinction between code testing and model testing.
Code testing is limited to establishing the correctness of the code with re-
spect to the criteria and requirements for which it is designed. Model test-
ing is more inclusive, as it extends to establishing the model's closeness to
the real-world systems it is designed to simulate (Figure 6).
Definitions and Methods
Determining the correctness of a model is basically part of the scien-
tific discovery process and as such is a rather subjective process. When will
a model, or for that matter a theory, be accepted by the scientific community?
Such acceptance is a gradual process. On the other hand, code validation can
be more objective and precise. The proof of a code's correctness in repre-
senting a model of the real system can be obtained by using logic to infer
that an assertion assumed true at program entry is also true at program exit
(Adrion et al. 1986). There are various ways to obtain such a proof, e.g.,
code verification.
Much confusion has resulted from equating model validation with code
validation and model verification with code verification. The term "valida-
tion" is defined according to the discipline in which it is used. In terms of
software engineering such as adopted by the National Bureau of Standards, code
validation is defined as "the determination of the correctness of the final
software product with respect to user needs and requirements" (Adrion et al.
1986). Code validation is sometimes called "functional testing" of software.
In discussing standard practice for evaluating environmental fate models of
chemicals, ASTM (1984) defines model validation as "the comparison of model
results with numerical data independently derived from experiments or obser-
vations of the environment."
A term closely related to validation is verification. In software
engineering, verification is the process of demonstrating consistency,
completeness, and correctness of the software (Adrion et al. 1986). ASTM
(1984) defines verification as the examination of the numerical technique in
the computer code to ascertain that it truly represents the conceptual model
and that there are no inherent problems with obtaining a solution.
27
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Combining code testing with code review provides a more comprehensive
evaluation. In this type of assessment of code quality its actual character-
istics, established through examination and measurement, are compared with
required characteristics. To be conclusive in model review and testing the
code design criteria and the test criteria must be defined explicitly. Soft-
ware engineering distinguishes various methods of examination (Schmidt et al.
1988): (1) static analysis to establish the correctness of the program's
syntax; (2) dynamic analysis to evaluate for correct results, correct
operations, efficiency in time, and efficiency in storage capacity; and (3)
verification and symbolic execution to establish the correctness of algo-
rithms. Quantitative assessment of the quality of the software is normally
done by measuring the code's performance.
The following discussions follow the ASTM definitions as closely as
possible.
Thus, the objective of groundwater model validation is to determine how
well a model's theoretical foundation and computer implementation describe
actual system behavior in terms of the "degree of correlation" between model
calculations and actual measured data for the cause-and-effect responses of
prototype groundwater systems. Various methods exist to quantify or describe
qualitatively this degree of correlation. It should be noted that the actual
measured data of both model input and system response are samples of the real
system and inherently incorporate errors. Thus, model validity established in
this manner is always subjective (measured validity; Figure 7).
To determine the validity of a groundwater model we need to answer such
questions as (Figure 6):
Is the conceptual model valid for the prototype system (as defined in
the beginning of this chapter) it represents? Related to this question
is the purpose for which the model will be used; different levels of
simplification or detail might be sufficient or required to fulfill the
designer's or user's objectives.
Does the mathematical model truly represent the conceptual model, the
processes involved, and the stresses present for the various design
conditions?
Does the code currently represent the mathematical framework?
It should be noted that in applying a model, the validity of^Jts predictions
needs to be established, requiring additional criteria and assessment methods
(see Chapter 4: Model Application).
Four testing approaches are available to determine the validity of a
model in simulating a particular groundwater system: calibration, extended
field comparison (often called field validation), code intercomparison, and
post-audits. ^^
The validity of groundwater models is preferably assessed on the basis of
the simulation of a well-defined field experiment or highly detailed field
exploration study, sometimes backed up with well-conditioned laboratory
experiments. Comparing the predicted with the measured responses may take
28
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Real
Output
Real
Inputs
Real System
real
validity
Measured
Outputs
Measured
Inputs
measured
validity
^.[Predictions
/ \ Model 1
Conceptual
Model 2
measured
validity
comparative
validity
^(Predictions
Model 2
real
validity
Fig. 7. Assessing model validity.
29
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either of two forms. One form, calibration, is sometimes considered the
weaker form of validation insofar as it tests the ability of the code (and the
model) to fit the field data, with adjustments of the physical parameters
(Ward et al. 1984). Some researchers prefer to classify calibration as a form
of verification rather than a form of validation, as calibration does not
provide for testing independently of the model's coding (van der Heijde
1987a). The results of the calibration runs might be influenced by model or
code errors if still present.
A more rigorous form of validation is testing the model's ability to
match the experimental data, using modeling-independent estimates of the para-
meters. In principle, this is the most extensive approach to validation.
However, unavailability and inaccuracy of field data often prevent applying
such a rigid validation approach to actual field systems. Typically, a part
of the field data is designated as calibration data, and a calibrated site-
model is obtained through reasonable adjustment of parameter values. Another
part of the field data is designated as validation data; the calibrated site
model is used in a predictive mode to calculate system responses for compari-
son. The quality of such a test is therefore determined by the extent to
which the site model is "stressed beyond" the calibration data on which it is
based, i.e., represents the same system conditions and stresses for which it
has been calibrated (Ward et al. 1984). The primary value of calibration as a
model testing tool is that failure in calibrating a model to a field site
might indicate for incorrect model formulation or coding errors. In this
report, this type of partial validation is called field testing.
As mentioned before, only a few datasets are currently available for
testing most kinds of groundwater models. These datasets are limited with
respect to the variety of conditions and stresses that occur in the sampled
system. System conditions or stresses needed for a full range of validity
determinations are technically or financially often not feasible to realize or
are restricted by regulation or other legal constraints. Therefore, testing
of models is generally limited to extended verification using existing
analytical solutions, to code intercomparison, and to post-audits of model
applications.
An additional complexity is that often the data used for field validation
are not collected directly from the field by the model development team but
are processed in an earlier study. Therefore, they are subject to inaccu-
racies, loss of information, interpretive bias, loss of precision, and trans-
mission and processing errors, resulting in a general degradation of the data
to be used in the validation process. For these reasons, "absolute" validity
of a model does not exist and only a "limited," "partial" or "relative"
validity can be established.
Another weak form of validation is found in the performance of post-
audits, studies performed after the system is actually stressed according to
simulated scenarios where the observed results are compared with the original
predictions. To use post-audits successfully in determining model validity,
conceptualization, assumptions, and system parameters and stresses should be
updated and the model rerun to facilitate comparison of predictions with
recent, observed system responses. Although post-audits are used primarily to
determine the rate of success of a model application, if a post-audit con-
cludes that the initial predictions were reasonable and that inaccuracies in
30
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the initial predictions were caused primarily by insufficient or inaccurate
data, such a study contributes to the acceptability of the model itself.
Another, weaker form of validation is found in code intercomparison.
This type of testing is often aimed at establishing relative performance
characteristics of various codes, using an existing dataset. However, if such
datasets are not available, a newly developed model might be compared with,
established models designed to solve the same type of problems as the new
model, using hypothetical problems and generic datasets. If the simulation
results from the new code do not deviate significantly from those obtained
with the existing code, a "relative" or "comparative" validity is established
(Figure 7). However, if significant differences occur, in-depth analysis of
the results of simulation runs performed with both codes is called for. If
code intercomparison was used to evaluate a new code, all the models involved
should again be validated as soon as adequate datasets become available.
Whether a model is valid for a particular application can be assessed by
a careful selection process that includes applying predetermined performance
criteria, sometimes called validation or acceptance criteria (see Section 4).
If various uses in planning and decision making are foreseen, different per-
formance criteria might be defined. The user should then carefully check the
validity of the model for the intended use. In this context, acceptance is
sometimes cast in terms of software or model certification. Software
engineering usually considers certification as acceptance of software by an
authorized agent after the software has been validated by the agent or after
its validity has been demonstrated to the agent (Adrion et al. 1986). This
concept has been forwarded by some agencies with respect to environmental
models. However, it is far from being accepted by the scientific community.
It should be noted that acceptance by an agency of software developed under
contract and subsequent public release (e.g., as might be required under the
Freedom of Information Act) does not constitute such certification unless all
criteria, if published, have been satisfied and recorded.
Complete model validation requires testing over the full range of condi-
tions for which the code is designed. Model development is an evolutionary
process responding to new research results, developments in technology, and
changes in user requirements. Model validation needs to follow this dynamic
process and should be applied each time the model (or code) is modified.
Validation Criteria
In describing the degree of validity of a model as discussed above, three
levels of validity can be distinguished (ASTM 1984):
(1) Statistical Validity: using statistical measures to check agreement
between two different distributions, the calculated one and the
measured one; validity is established by using an appropriate per-
formance or validity criterion.
(2) Deviative Validity: if not enough data are available for statis-
tical validation, a deviation coefficient DC can be established,
e.g.,
DC = [(x-y)/x]100£
31
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where x = predicted value and y = measured value. The deviation
coefficient might be expressed as a summation of relative devia-
tions. If ED is a deviative validity criterion supplied by sub-
jective judgment, a model can considered to be valid if DC < ED.
(3) Qualitative Validity: using a qualitative scale for validity levels
representing subjective judgment: e.g., excellent, good, fair, poor,
unacceptable. Qualitative validity is often established through
visual inspection of graphic representations of calculated and
measured data (Cleveland and McGill 1985).
The aforementioned tests apply to single variables and determine local-or-
single variable validity; if more than one variable is present in the model,
the model should also be checked for global validity and for validity consis-
tency (ASTM 1984). For a model with several variables to be globally valid,
all the calculated outputs should pass validity tests (e.g., heads, fluxes and
water balances in flow models). Validity consistency refers to the variation
of validity among calculations having different input or comparison datasets.
A model might be judged valid under one dataset but not under another, even
within the range of conditions for which the model has been designed or is
supposedly applicable. Validity consistency can be evaluated periodically
when models have seen repeated use.
Validation Scenarios
Often, various approaches to field validation of a model are viable.
Therefore, the validation process should start with defining validation
scenarios. Planning and conducting field validation should include the
following steps (Hern et al. 1985):
(1) Define data needs for validation and select an available dataset or
arrange for a site to study;
(2) Assess the data quality in terms of accuracy (measurement errors),
precision, and completeness;
(3) Define model performance or acceptance criteria;
(4) Develop strategy for sensitivity analysis;
(5) Perform validation runs and compare model performance with estab-
lished acceptance criteria;
(6) Document the validation exercise in detail.
Validation Databases
Further development of databases for field validation of models, espe-
cially solute transport models, is necessary. This is also the case for many
other types of groundwater models. These research databases should represent
a wide variety of hydrogeological situations and should reflect the various
types of flow, transport, and deformation mechanisms present in the field.
The databases should also contain extensive information on hydrogeological,
soil, geochemical, and climatological characteristics. With the development
32
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of such databases and the adoption of consistent model-testing and validation
procedures, comparison of model performance and their reliability in ground-
water resource management can be improved considerably.
33
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4. MODEL APPLICATION
THE MODEL APPLICATION PROCESS
The effective application of computer simulation models to field problems
is a qualitative procedure, a combination of science and art. A successful
model application requires knowledge of scientific principles, mathematical
methods, and site characterization, paired with expert insight into the
modeling process. These elements often are provided in a multidisciplinary
team framework. Modeling imposes discipline by forcing all concerned to be
explicit on goals, criteria, constraints, relevant processes, and parameter
values (European Institute for Water, Modeling for Water Management, Workshop
Statements, May 21-22, 1987, Como, Italy).
The preparation of an operational model of a groundwater system can be
divided into three distinct stages: initialization and preparation, calibra-
tion, and problem solving or scenario analysis (sometimes called prediction
stage; Figure 8). Each stage consists of various steps; often, results from a
certain step are used as feedback in previous steps, resulting in a rather
Iterative procedure.
The modeling process is initiated with the formulation of the modeling
objectives and modeling scenarios derived from an analysis of the management
problem under study. Within this context, compilation, inspection, and
interpretation of available data result in a first conceptualization of the
system under study. Often, the technical expert is charged with the task of
making sense of an ill-posed problem with a large amount of mostly irrelevant
data. It is his/her task to rationalize the ill-posed problem into an unam-
biguous question that, to be answered, utilizes a subset of the data available
together with data specifically collected to solve the problem. (Cross and
Moscardini 1985).
Conceptualization of a groundwater system consists of three elements: (1)
Identification of the state of the system; (2) determination of the system's
active and passive controls; and (3) analysis of the level of uncertainty in
the system (Kisiel and Duckstein 1976). To identify the state of the system,
its hydraulic, chemical, thermal, and hydrogeologic characteristics are
defined, and conservation of mass, energy, and momentum are quantified. The
active input refers to such system controls and constraints as pumpage
schedules, artificial recharge, development of new well fields, waste injec-
tion rates, and the construction of impermeable barriers, and clay caps and
liners. If the studied system includes economic or decision-making policy
aspects, active input may also include interest rates, pumping and waste
generation or waste disposal taxes, and policies for conjunctive use. Passive
or uncontrollable inputs include elements of the hydrologic cycle external to
the system under study, such as natural recharge and evapotranspiration, sub-
sidence, and natural water quality. Certain contamination sources such as
leaching landfills, spills, and the leaching of agricultural chemicals present
in soil might also be considered as passive controls. Other passive controls,
such as water demand resulting from population growth, may be external
management factors.
34
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formulate modeling objective and scenarios
compile and interpret available data
conceptualization of system
determine model need and level of complexity
collect more data
improve mode! by
adjusting parameters
(automatically or
manually)
yes
select code and use it initially to prepare a
"simple" scoping model
collect data and observe system
improve model concepts, update input data,
and select more complex code if necessary
prepare or update inpute data for improved
model, using estimated parameters
perform mode! simulations
interpret results and compare with
observed data
sensitivity runs
no
scenario simulation runs
uncertainty analysis
verification of scenario analysis
preparation stage
calibration stage
improve concepts
and parameter
estimates
scenario analysis stage
I
post-audit
Fig. 8. Model application process.
35
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Many modeling studies found to be inadequate were hampered by deficien-
cies in the analysis of the problem to be modeled or in the conceptualization
of the groundwater system (van der Heijde and Park 1986).
Based on the objectives of the study and the characteristics of the sys-
tem, the need for and complexity level of the simulation model must be deter-
mined. Selection of a computer code takes place; if the code is new to the
technical staff, they need some time to become familiar with its operational
characteristics.
The second stage of model application, calibration, starts with the
design or improvement of the model grid and the preparation of an input file
by assigning nodal or elemental values and other data pertinent to the execu-
tion of the selected computer code. The actual computer simulation then takes
place, followed by the interpretation of the computed results and comparison
with observed data. The results of this first series of simulations are used
to further improve the concepts of the system and the values of the para-
meters. Sensitivity runs are performed to assist in the calibration proce-
dure. More data may be needed during the calibration process.
In some cases the code is used initially to design a data collection pro-
gram. The newly collected data are then used both to improve the conceptuali-
zation of the system and to prepare for the predictive simulations.
After the calibration stage has been concluded satisfactorily, it is
followed by the scenario analysis stage, in which the computer code is used to
obtain answers to such management problems as the impacts of proposed
policies, engineering designs, and system alterations. In fact, in this stage
current understanding of the system is extrapolated to evaluate its response
to new or altered stresses. The use of uncertainty analysis in this stage of
the modeling process provides insight into the reliability of the computed
predictions.
In the final stage of a model application project, the computed results
are checked with respect to feasibility and completeness and analyzed in the
context of the management problem being addressed. When the technical expert
has finished the analysis, the key answers obtained in the modeling process
are presented to management. In the modeling process, interaction between
technical experts and management is often an iterative process, with manage-
ment asking new questions based on the results of previous modeling-based
analysis.
Whenever an opportunity exists to obtain further field information
regarding the system being modeled, refinements and improvements in the model
should be made and previous analysis modified. Sometimes, such an opportunity
is offered in the form of post-audits. Post-audits are reviews performed some
time after the model-based predictions were made and often provide an oppor-
tunity for in-depth analysis regarding the inaccuracies in those predictions.
However, not many of such post-audits actually take place, depriving modelers
and managers from important feedback and educational experience.
Often, a major impediment to the efficient use of models in groundwater
management is the lack of data. Data insufficiencies might result from inade-
quate resolution in spatial data collection (e.g., spatial heterogeneities
36
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relevant on smaller scale than sampled), or in temporal sampling of time-
dependent variables (e.g., measured too infrequently), and from measurement
errors (Konikow and Patten 1985).
Many types of problems can occur in the application of models. Some of
these are technical, method-dependent problems such as numerical dispersion
and oscillations in transport models. Conceptual problems, often significant,
can be related to the mechanisms (e.g., dispersion, adsorption, multiphase or
multifluid flow), the heterogeneity of the medium, or the simplifying assump-
tions adopted (e.g., vertical averaging). Finally, problems external to the
model execution can occur, such as those caused by the absence of good data,
model availability, available computer facilities, skilled professionals, and
competent technicians.
CODE SELECTION
In the model application process, code selection is critical in ensuring
an optimal trade-off between effort and result. The result is generally
expressed as the expected effectiveness of the modeling effort in terms of
forecast accuracy. The effort is ultimately represented by the costs. Such
costs should not be considered independently from those of field data acqui-
sition. For a proper assessment of modeling cost, such measures as choice
between the development of a new code or the acquisition of an existing code,
the implementation, maintenance, and updating of the code, and the development
and maintenance of databases, need to be considered.
The Code Selection Process
As code selection is in essence matching a detailed description of the
modeling needs with well-defined characteristics of existing models, selecting
an appropriate model requires analysis of both the modeling needs and the
characteristics of existing models.
Major elements in evaluating modeling needs are: (1) formulation of the
management objective to be addressed and the level of analysis sought (based
among others on the sensitivity of the project for incorrect or imprecise
answers or risk involved); (2) knowledge of the physical system under study;
and (3) analysis of the constraints in human and material resources available
for the study.
To select models efficiently management-oriented criteria need to be
developed for evaluating and accepting models. Such a set of scientific and
technical criteria should include:
Trade-offs between costs of running a model (including data acquisition
for the required level of analyses) and accuracy
A profile of model user and a definition of required user-friendliness
Accessibility in terms of effort, cost, and restrictions
Acceptable temporal and spatial scale and level of aggregation.
37
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If different problems must be solved, more than one model might be needed
or a model might be used in more than one capacity. In such cases, the model
requirements for each of the problems posed have to be clearly defined at the
outset of the selection process. To a certain extent this is also true for
modeling the same system in different stages of the project. Often, a model
is selected in an early stage of a project to assist in problem scoping and
system conceptualization. Limitations in time and resources and in data
availability might initially force the selection of a "simple" model. Growing
understanding of the system and increasing data availability might lead to a
need for a succession of models of increasing complexity. In such cases,
flexibility of the candidate model or the availability of a set of integrated
models of different levels of sophistication might become an important selec-
tion criterion.
The major model-oriented criteria in model selection are: (1) that the
model is suitable for the intended use; (2) that the model is reliable, and
(3) that the model can be applied efficiently (van der Heijde and Beljin
1988). The reliability of a model is defined by the level of quality assur-
ance applied during its development, its verification and field validation,
and its acceptance by users. A model's efficiency is determined by the avail-
ability of its code and documentation, and its usability, portability, modifi-
ability, and economy with respect to human and computer resources required.
As model credibility is a major problem in model use, special attention
should be given in the selection process to ensure the use of qualified models
that have undergone adequate review and testing. However, a standardized
review and testing procedure has not yet been widely adopted, although various
organizations have established their own procedures (van der Heijde 1987a,
Beljin and van der Heijde 1987). In addition, discussions have started within
Subcommittee D-18.21 for Groundwater Monitoring of the American Society for
Testing and Materials (ASTM) as part of their task on design and analysis of
hydrogeologic data systems (J.D. Ritchey, pers. comm. 1987).
Finally, acceptance of a model for decision-support use should be based
on technical and scientific soundness, user friendliness, and legal and
administrative considerations.
In selecting a code, its applicability to the management problem studied
and its efficiency in solving these problems are important criteria. In eval-
uating a code's applicability to a problem, a good description of its operat-
ing characteristics should be accessible. For a large number of groundwater
modeling codes, such information is obtainable from the International Ground
Water Modeling Center (IGWMC), which operates a clearinghouse service for
information and software pertinent to groundwater modeling (van der Heijde
1987b).
Although adequate models are available for analysis of most flow-related
problems, this is less the case for modeling contaminant transport and other
complex processes in the subsurface. For example, computer codes are avail-
able for situations that do not require analysis of complex transport mechan-
isms or chemistry. The use of such programs for groundwater quality assess-
ment is generally restricted to conceptual analysis of pollution problems, to
feasibility studies in design and remedial action strategies, and to data
acquisition guidance. It should be noted that, considering the uncertainties
38
-------
associated with the parameters of groundwater systems, much progress has been
made in determining the probabilities of the arrival of a pollution front
rather than the calculation of concentrations (Bear 1988). Chapter 5 gives a
detailed discussion of the various models currently available for groundwater
evaluations.
A perfect match rarely exists between desired characteristics and those
of available models. Model selection is partly quantitative and partly quali-
tative. Many of the selection criteria are subjective or weakly justified,
often because there are insufficient data in the selection stage of the pro-
ject to establish the importance of certain characteristics of the system to
be modeled. If a match is hard to obtain, reassessment of these criteria and
their relative weight in the selection process is necessary. Hence, model
selection is very much an iterative process.
Finally, as model selection is very closely related to system conceptual-
ization and problem solving, "expert systems" systematically integrating sys-
tem conceptualization and model selection on a problem-oriented basis promise
to be valuable tools in the near future.
Further information on groundwater model selection is presented in (Rao
et al. 1982, Kincaid et al. 1984, Boutwell et al. 1985, Simmons and Cole
1985).
Code Selection Criteria
Acceptance of a model should be based on technical and scientific sound-
ness, its efficiency, and legal and administrative considerations. A model's
efficiency is determined by the availability of its code and documentation,
access to user support, and by its usability, portability, modifiability,
reliability, and economy. A brief discussion of some of these criteria is
given below and follows a more extended treatment in van der Heijde and Beljin
(1988). This latter publication includes also a proposed rating system for
each of these criteria.
Availability
A model is defined as available if the program code associated with it
can be obtained either as source code or as an executable, compiled version or
if the program can be accessed easily by potential users. The two major cate-
gories of groundwater software are public domain and proprietary software. In
the United States, most models developed by federal or state agencies or by
universities through funding from such agencies are available without restric-
tions in their use and distribution, and are therefore considered to be in the
public domain. In other countries the situation is often different, with most
software having a proprietary status, even if developed with government sup-
port or its status is not well-defined. In this case the computer code can be
obtained or accessed under certain restrictions of use, duplication, and
distribution.
Models developed by consultants and private industry are often proprie-
tary. This may also be true of software developed by some universities and
private research institutions. Proprietary codes are in general protected by
copyright law. Although the source codes of some models have appeared in pub-
39
-------
lications such as textbooks, and are available on tape or diskette from the
publisher, their use and distribution might be restricted by the publication's
copyright.
Further restrictions occur when a code includes proprietary third-party
software, such as mathematical or graphic subroutines. For public domain
codes, such routines are often external and their presence on the host-
computer is required to run the program successfully.
Between public domain and proprietary software is a grey area of so-
called freeware or user-supported software. Freeware can be copied and dis-
tributed freely, but users are encouraged to support this type of software
development with a voluntary contribution.
For some codes developed with public funding, distribution restrictions
are in force, as might be the case if the software is exported, or when an
extensive maintenance and support facility has been created. In the latter
case, restrictions are in force to avoid use of non-quality-assured versions,
to prevent non-endorsed modification of source code, and to facilitate
efficient code update support to a controlled user group.
User Support
If a model user has decided to apply a particular model to a problem, he
may encounter technical problems in running the model code on the available
computer system. Such a difficulty may result from (1) compatibility problems
between the computer on which the model was developed and the model user's
computer; (2) coding errors in the original model; and (3) user errors in data
input and model operation.
User-related errors can be reduced by becoming more familiar with the
model. Here the user benefits from good documentation. If, after careful
selection of the model, problems in implementation or execution of the model
occur and the documentation does not provide a solution, the user needs help
from someone who knows the code. Such assistance, called model support,
cannot replace the need for proper training in model use; requests for support
by model developers may assume such extensive proportions that model support
becomes a consulting service or an on-the-job training activity. This poten-
tiality is generally recognized by model developers, but not always by model
users.
Usability-
Various problems can be encountered when a simulation code is implemented
on the user's computer system. Such difficulties may arise from hardware
incompatibilities or coding of user errors in code installation, data input,
or program execution. Programs that facilitate rapid understanding and know-
ledge of their operational characteristics and which are easy to use are
called user-friendly and are defined by their usability (van der Heijde and
Beljin 1988). In such programs, emphasis is generally placed on extensive,
well-edited documentation, easy input preparation and execution, and on well-
structured, informative output. Adequate code support and maintenance also
enhance the code's usability.
40
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Portability--
Programs that can be easily transferred from one execution environment to
another are called portable. To evaluate a program's portability both soft-
ware and hardware dependency need to be considered. If the program needs to
be altered to run in a new computer environment, its modiflability is impor-
tant.
Modifiability
In the course of a computer program's useful life, the user's experiences
and changing management requirements often lead to changes in functional
specifications for the software. In addition, scientific developments,
changing computing environments, and the persistence of errors make it
necessary to modify the program. If software is to be used over a period of
time, it must be designed so that it can be continually modified to keep pace
with such events. A code that is difficult to modify is called fragile and
lacks maintainability. Such difficulties may arise from global, program-wide
implications of local changes (van Tassel 1978).
Reliability
A major issue in model use is credibility. A model's credibility is
based on its proven reliability and the extent of its use. Model users and
managers often have the greatest confidence in those models most frequently
applied. This notion is reinforced if successful applications are peer-
reviewed and published. As reliability of a program is related to the
localized or terminal failures that can occur because of software errors
(Yourdon and Constantine 1979), it is assumed that most such errors originally
present in a widely used program have been detected and corrected. Yet no
program is without programming errors, even after a long history of use and
updating. Some errors will never be detected and do not or only slightly
influence the program's utility. Other errors show up only under exceptional
circumstances. Decisions based on the outcome of simulations will be viable
only if the models have undergone adequate review and testing. However,
relying too much on comprehensive field validation (if present), extensive
field testing or frequency of model application may exclude certain well-
designed and documented models, even those most efficient for solving the
problem at hand.
Extent of Model Use
A model used by a large number of people demonstrates significant user
confidence. Extensive use often reflects the model's applicability to differ-
ent types of groundwater systems and to various management questions. It
might also imply that the model is relatively easy to use. Finally, if a
model has a large user base, many opportunities exist to discuss particular
applications with knowledgeable colleagues.
MULTIPLE SCALES IN MODELING GROUNDWATER SYSTEMS
The scales used in groundwater modeling are determined by the character-
istics of the groundwater system, by the availability of data, by the nature
41
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of the system's management, and by requirements posed by the chosen mathe-
matical technique. These influences often include both natural and human-
induced influences, such as the effects of climate, pumping, deep-well injec-
tion, and agricultural irrigation and drainage.
An important aspect of the scaling problem relates to the difference
between the scale on which processes are mathematically described, and the
subsequent aggregation into larger-scale formulations amenable to field analy-
tical procedures. Small-scale descriptions are aggregated into large-scale
models by applying averaging procedures. Such averaging, when applied to a
statistical description of microscopic processes, is commonly used to obtain
continuous hydrodynamic field equations on the macroscopic scale (e.g., Bear
1972, 1979). Although the resulting model requires less supporting field data
than is required for a problem of the same physical extent, a certain amount
of information regarding the real physical systems is lost. A typical example
is the apparent scale dependency of field dispersion. Recent studies have
related this phenomenon to the area! and vertical variability of other aquifer
characteristics such as hydraulic conductivity (Gelhar and Axness 1983, Molz
et al. 1983, Sudicky et al. 1985). Also, in going to larger spatial and
temporal scales, variations in system characteristics that could be ignored on
the smaller scale may become important. Examples are the increasing impor-
tance of heterogeneities and anisotropy as related to the geology of the sys-
tem for larger spatial scales, and the effects of long-term recharge varia-
tions on the water balance of a system for long time periods. A major problem
in this averaging process lies in evaluating the effects of assumptions made
on the microscopic scale and the effects on the level of uncertainty in the
modeling of a groundwater system. If such assumptions have to be incorporated
in the macroscopic description, their formulation may be problematic. Another
problem that may arise as a result of an averaging approach is that of
defining the physical meaning of the resulting state variables and system
parameters. Thusfar, no systematic evaluation of the consequences of this
aggregation process in groundwater has been published, although an extensive
database is available to carry out such a study.
The essential scaling problem is how to distinguish between the variables
that can be considered as constants or as being uniform across discrete inter-
vals of pertinent dimension (space, time), and the variables that cannot be so
considered (Beck 1985). Problem decomposition in space or time is often
applied to obtain optimal resolution in relation to computational efficiency.
An example of such spatial and temporal decomposition is found in the modeling
of infiltration into the soil and subsequent percolation toward the saturated
zone. A distinction has been made between spatial discretization and connec-
tiveness for local (Figure 9a) and for regional (Figure 9b) scales (van der
Heijde 1988). Runoff from precipitation is split into a surface component
(lumped horizontal segment) and infiltration (one-, two-, or three-dimen-
sional, vertical). The infiltrated water percolates to the groundwater where
a two-dimensional horizontal or three-dimensional model is used. For each of
the submodels a different timestep is used, from hourly for the surface runoff
and daily for the percolation, to weekly or monthly for the flow in the
saturated zone.
In groundwater models, a significant distinction exists between local and
regional discretization of the surface zone. This distinction reflects the
difference in physiographic character between the subsurface and the surface,
42
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LOCAL SCALE
_
r- ->- ->-T -
\ ' ' \
I s / J-
I '
!,_'
/
/- 71
/ ' I
""Lv71
"- -r / /
i / /
/
^ r _
' /
/ /
/
/
/
-»-x
SURFACE ZONE
(SINGLE LAND SEGMENT
REPRESENTATION)
UNSATURATED ZONE
(X - Z, Y - Z
OR X - Y - Z
REPRESENTATION)
SATURATED ZONE
(X - Y - Z REPRESENTATION)
Fig. 9a. Typical dimensionalities used to represent surface, usaturated,
and saturated zones in local-scale groundwater models (after van
der Heijde 1988).
43
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REGIONAL SCALE
SURFACE ZONE
(LARGE LAND SEGMENT
REPRESENTATION)
UNSATURATED ZONE
(LAYERED
Z - REPRESENTATION)
SATURATED ZONE
WATER-TABLE AQUIFER
X-y REPRESENTATION)
CONFINING LAYER
(SINGLE SEGMENT
Z - REPRESENTATION)
SATURATED ZONE
CONFINED AQUIFER
(X- ^ REPRESENTATION)
Fig. 9b. Typical dimensionalities used to represent surface unsaturated
zones in regional groundwater models (from van der Heijde 1988).
44
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resulting in different approaches in aggregating small scale phenomena into
large scale models (Figures 9a,b).
Note the difference in treatment of the vertical components in ground-
water models. In the regional models the flow in soils and between aquifers
is mainly one-dimensional and vertical, to reduce the computational load.
Here, the flow between aquifers is generally represented by a single unit
while the flow in soils might be vertically discretized. In the local model,
second-order effects may be important enough to warrant the use of two-dimen-
sional vertical or three-dimensional simulation in the soil zone.
Another example can be found in simulating solute transport in fractured
porous media where the movement of the solute in the fractures can be two
orders of magnitude greater than in the porous matrix. Here, a split-time
approach, using different time step sizes for simulating the processes that
take place in the fractures and in the porous rock, increases the efficiency
of the simulations (DeAngelis et al. 1984).
With the increasing capacity and decreasing cost of computers, a trend
prevails toward using smaller time scales for the same types of problems,
resulting in higher temporal resolution.
MODEL GRID DESIGN
In the application of numerical models, one of the elements most critical
to the accuracy of the computational results is the spatial and temporal
discretization chosen. Spatial discretization is represented by the grid
overlaying the aquifer and formed by cells (finite-difference method) or ele-
ments (finite-element method) defined by interconnected nodes. These cells
might be one-, two- or three-dimensional in nature, depending on the dimen-
sionality of the model. The discretization in time is represented by the
sequence of time steps selected for the simulation calculations.
Grid Shape and Size
There are various ways to discretize a groundwater system in space, pri-
marily determined by the numerical method chosen. A major distinction exists
between the rather rigid grid required by the common finite-difference method
and the rather flexible grid allowed by many models based on the finite-ele-
ment method, and by such modeling approaches as the polygon-based integrated
finite-difference method. The option to use two-dimensional triangles and
quadrilateral elements and their three-dimensional equivalent in the finite-
element method allows the user to deal efficiently with rather irregular
geometries. In some finite-element models this flexibility is further
enhanced by using internal nodes or so-called "pinch" nodes in selected
elements, e.g. to go from areas the grid needs to provide for a high resolu-
tion, to areas with a low grid density (Voss 1984).
Additional distinctions exists within the major numerical methods, e.g.
between fixed and variable grid spacing in finite-difference grids and between
fixed and variable element shape and size in the finite-element method. Other
numerical methods might have their own specific requirements, such as the
boundary element method with respect to discretization along the boundaries.
45
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The rigid discretization grid for finite-difference models has a major
advantage over the flexibility of the finite-element method in that it allows
efficient nodal and cell-wise ordering of the set of equations, providing for
efficient matrix solution techniques, simple grid design, and relatively easy
input data preparation. However, especially in the case of irregular external
and internal model boundaries, complex hydrogeologic zone boundaries, etc..
the flexibility of the finite-element method allows the user to select many
fewer elements and thus many fewer equations to solve than is needed for a
finite-difference solution obtaining the same accuracy in the computational
results. To closely follow irregular boundaries using a finite-difference
approach requires a rather dense grid, inadvertently resulting in many
inactive cells outside the model area being included in the solution
procedure. This characteristic difference between the two major numerical
modeling approaches is well illustrated by various published modeling studies
of the flow system in the Musquodaboit Harbor Aquifer, Nova Scotia, Canada.
The first numerical modeling study applied a finite-difference model with a
regular square grid having about 2600 nodes (Pinder and Bredehoeft 1968).
According to Pinder and Frind (1972) this number of nodes could be reduced to
approximately 25% by using a variable finite-difference grid. Pinder and
Frind (1972) demonstrated the advantages of the finite-element method by
obtaining a close match with the finite-difference prediction in Pinder and
Bredehoeft (1968), using only 96 nodes and 44 carefully designed and located
deformed isoparametric quadrilateral elements. To reduce the time-consuming
design that such an optimal grid requires, Huyakorn (1984) used 195 automatic,
computer-generated triangular and rectangular elements in the verification
runs of a finite-element flow and transport code. Here, some of the
computational efficiency is given up to achieve an economically optimal grid
design based on computer and personnel costs for both preparation and perform-
ing of the simulation runs.
Design Criteria
Traditionally, designing a grid is a rather intuitive process, increas-
ingly performed with assistance of (semi-)automatic grid generation and inter-
active computer graphics techniques (Sartori et al. 1982, Drolet 1986). Each
grid must be designed for the particular aquifer under study, according to the
purpose of the investigation, the quality of data on geometry, properties, and
boundary conditions, and cost constraints (Townley and Wilson 1980). A major
consideration should be striking a balance between data processing costs (com-
puter, personnel) and required accuracy. Selecting more nodes means solving
more equations, which in turn requires more computer memory and computer time.
A number of general principles apply. Among these, the grid should be
designed to optimally represent:
external and internal boundaries such as recharge, no-flow, geologic
formation boundaries, and low velocity zones (e.g., liners)
external and internal stresses such as river stages, wells (both injec-
tion and discharge), pollution sources (e.g., point sources versus
nonpoint sources), and recharge rates.
46
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Additional considerations include:
aligning where possible the main grid orientation with the principle
direction of flow and transport (or hydraulic parameters, e.g.,
transmissivity)
using a fine grid in areas where results are needed, e.g., in the area
of highest pollution or highest drawdown
using a coarse grid where data are scarce or for parts of the model
area away from the area of interest
spacing nodes close together in areas having large changes in transmis-
sivity or hydraulic head, or where concentration gradients are
significant
where possible, let internal and external boundaries coincide with
element boundaries
locate "well" nodes (both active wells and observation wells) near the
physical location of the well.
To address the need for a fine grid in areas of interest in a large-scale sys-
tem, a modeling technique is used based on successive stages of localization
of scale and adjustment of grid spacing. This stepwise technique is sometimes
referred to as telescoping (Ward et al. 1987). Related to this approach is
the use of different scales for simulating the flow part and the transport
part, using the same modeling software (Konikow 1985). To fulfill the strin-
gent requirements for flow boundary conditions in local transport simulations,
a regional flow model is prepared to provide the required information.
It should be noted that three-dimensional modeling constitutes a signi-
ficant increase in complexity in comparison with two-dimensional modeling. An
important distinction exists between quasi-three-dimensional modeling and
fully three-dimensional modeling. In quasi-three-dimensional modeling the
grid consists of two-dimensional horizontal grids representing the vertically
averaged flow and transport in the individual aquifers connected by a one-
dimensional single cell or element representing the connecting aquitards. In
fully-three-dimensional modeling the cells or elements can be three-dimen-
sional (but also two- or even one-dimensional as in dual porosity systems; see
Chapter 5).
Problems may occur when internal no-flow areas are represented in the
model by cells or elements with zero transmissivity value (Townley and Wilson
1980). In such a case, it may be better to create a hole in the grid, a zone
internal to the modeled area but not included in the model itself.
It should be noted that in using the finite-element method the solution
efficiency depends on node numbering. Modern finite-element codes often
include a node and element-numbering optimization routine, especially if
automatic grid generation is provided for.
47
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Grid Design and Numerical Accuracy
There is a direct relationship between numerical accuracy and stability,
grid density and time step size Huyakorn and Finder 1983). Numerical accuracy
often can be improved by reducing the grid spacing, as the truncation error in
the numerical approximations is proportional to A£2 (where AJ, is grid
spacing). A related numerical problem is the occurrence of oscillations.
Various methods exist to reduce this problem, such as using the Peclet number
Pe = v (At) / D < 2
in reducing grid spacing, or modifying the time step to conform to the Courant
criterion
Cr = v (At)/(Ai) a 1
Oscillations can also be reduced by using spatial or upstream weighting.
To reduce numerical problems when variable grid spacing is present, the
changes in size between neighboring cells or elements should be restricted.
For instance, as a rule-of-thumb in using a finite-difference model, the grid
may be expanded toward distant boundaries by a factor 1.5 to 2. Likewise, in
using a finite-element model, triangular elements should be kept as equila-
teral as possible. Elements with a length-to-width ratio of more than five
tend to give poor accuracy results (Townley and Wilson 1980). The presence of
anisotropy can further restrict this ratio. Another finite-element condition
frequently required to avoid numerical problems limits the size difference
between neighboring elements to less than a factor of five (Townley and Wilson
1980).
Often, in solving non-steady-state problems, one of three finite-differ-
ence approximations for the time variable is used: explicit, fully implicit,
and Crank-Nicolson schemes (Huyakorn and Finder 1983). If the explicit method
is used, a stability criterion applies, dependent on the type of differential
equation solved and the numerical method used. Such a criterion specifies the
maximum value for the time step to avoid uncontrolled growth of the numerical
error during the solution process. The other two time approximation methods
are unconditionally stable.
In simulating multiphase flow using certain five-point finite-difference
approximations (as in a grid with rectangular or square cells: center node and
four surrounding nodes), a numerical difficulty often described as "grid
orientation effect" occurs. The results of computations with a grid diagonal
to the principal direction of fluid movement may be quite different from those
with a parallel grid, both being significant in error with the real answer
(Huyakorn and Finder 1983). Using very refined grids does not reduce the
effects of this problem, as the severity of these effects is a direct result
of the mobility ratio of the two fluid phases. The solution to this kind of
problem is found by using higher-order finite-difference approximations (e.g.,
nine-point methods), or selecting another solution method such as certain
finite-element schemes.
48
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MODEL CALIBRATION
Model calibration is aimed at demonstrating that predictions made with
the model are realistic and to a certain extent "accurate" and "reliable"
(Konikow and Patten 1985). In addition, calibration is often used to obtain
values for parameters that have not been measured or for which no reliable
(field) measurement technique is currently available. The iterative process
of matching calculated values with observed (historical) data by adjusting
model input can take the form of a manual trial-and-error procedure or an
automatized procedure (Figure 10). The calibration process is also known as
history matching and is closely related to parameter estimation. The result
of this process might be in the form of a refinement of initial estimates of
aquifer properties (parameters), the establishment of the location of the
boundaries (areal and vertical extent of aquifer), and the determination of
flow and transport conditions at the boundaries (boundary conditions). Trial-
and-error calibration is a highly subjective, intuitive procedure. As data
quantity and quality is often limited, no unique set of parameters result,
leaving the modeler with a subjective choice. Completion of the calibration
process depends on many factors, including the objectives for analysis, the
complexity of the groundwater system being studied, the length of the observed
history, the accuracy required in the prediction stage, the available budget,
the expertise of the modeler, and the patience of the modeler (or the manager
waiting for answers).
Automatic calibration procedures are based on the use of prescribed algo-
rithms, their completion achieved when preset matching criteria are met.
Because of the formal approach taken in adjusting model input, automatic
procedures are less subjective than trial-and-error procedures. In addition,
they require fewer computer runs and are also more efficient with respect to
staff time required for model output analysis. However, they require the
modeler to be well trained in the use of numerical and statistical techniques.
THE ROLE OF SOFTWARE; STAGES OF DATA PROCESSING
The core of the modeling process is the computer-based simulation of the
behavior of the groundwater system for a particular management scenario. From
the computer software point of view, the simulation is preceded by data acqui-
sition, inspection and storage, data interpretation, and model input prepara-
tion (Figure 11). This data-processing stage is often called (simulation-)
preprocessing. Post-processing involves storage, analysis, and presentation
of the computational results (van der Heijde and Srinivasan 1983). Computer-
based numerical interpolation and statistical techniques as well as graphical
methods might be employed in the pre- and postprocessing stages.
Field data acquisition can be either manual or computer driven. In the
latter case it is often combined with various data handling techniques.
Transfer of data collected in the field to computer-based storage facilities
can be indirect, using data sheets and analog registration and manual computer
data entry, or directly by measurement-linked, on-site storage of data on mag-
netic media or by immediate electronic transfer from a measurement device to
remote storage facilities, often a remote-controlled process. The initial
data storage of unprocessed field data must be followed by data checking and
screening for measurement and transmission errors, after which they are stored
as conditioned data.
49
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c
Start
( Start J
initial parameter estimates
model specification
initial parameter
estimates
e
e
a
E
eo
a
e
E
e
w
eg
a
"3
o
o
E
e
o
a
9
Model
specification
o
a
eo E
= 2
o 5
o a
o
Run model
no
Calculate
criteria
yes
convergence?
Are results
acceptable
no
yes
TRIAL AND ERROR
AUTOMATIC
Fig. 10. History matching/cal ibaration using trial
procedures (after Mercer and Faust 1981).
and error and automatic
50
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GEOMETRY
internal, external
boundaries, zone
information
preprocessing
-DIGITIZED SPATIAL VARIABLES
hydraul.
conduct.
storage
coeff.
regional
recharge
.co
concentr.
dispersiv.
Model Input:
Nodal Information
postprocessing
MANAGEMENT
Fig. 11. Decision-support data stream in modeling.
51
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Interpretation of field data results in an information set on the system
studied, again stored for further use. The next step is the model gridding
followed by nodal or elemental assignment of model input parameters. This
step often requires further interpretation or at least, interpolation of
available data. After appropriate formatting the preprocessing stage is
finished and the simulation runs can start. Many steps in the preprocessing
stage can be computerized. This is especially true for such data handling
activities as error-checking, reformatting, and storing. However, automation
should not limit the modeler's ability to intervene in each stage of the
modeling process.
The simulation program can be run in a batch mode, requiring user-speci-
fied input files. In such a case the model runs independently of any direct
user interaction. A user-prepared file, a so-called batch file containing a
sequence of computer operating system instructions, drives the program execu-
tion. If the user has the option to interact with the program during its
execution, modeling becomes more flexible. Such interaction might facilitate
changing stresses during successive simulation steps, changing such modeling
variables as timestep sequences, or even changing values for system para-
meters. The most common user interaction is a restart option provided by some
software where the latest computed values for the dependent variable are used
as initial values for the new run.
If preprocessing is combined with simulation, three approaches are
possible (Figure 12). First, data can be entered directly into a file from
prepared data sheets, using a generic program such as a word processor or line
editor, followed by a "batch run" of the code, a process in which no user
interaction with the computer is allowed during code execution. The user
needs to ensure that the data formats required by the simulation program are
correctly applied. The second approach uses a dedicated computer program
facilitating interactive data entry, data formatting and storing, followed by
a batch run of the code. Finally, data can be entered interactively, guided
by the same program that contains the simulation algorithms. Some programs
based on this latter approach allow the user to influence program execution
during the simulation runs.
In the interactive use of a computer, a program directs the interaction
between user and computer. The user selects a continuation option at each
decision point in the program. Increasingly, the user might be assisted at
the various decision-making points by expert systems providing decision-making
logic, data options, error-checking, and report facilities.
In using a numerical model, input data preparation is a time-consuming
activity. The user who is unfamiliar with the format specifications of the
model will make many mistakes during data entry: format errors, incorrect data
sequences, and others. Interactive data entry with a dedicated preprocessor
is especially advantageous for a user who is relatively inexperienced in data
formatting, file handling, and running simulation software in general.
Furthermore, preprocessors are often used in local preparation of the input
files for remote computers.
The postprocessing stage includes a variety of data-handling activities.
Computational results are routed to mass-storage devices such as disk drives,
displayed on a video screen or printed (Figure 12). They can be used in
52
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line editor
word-processing
spreadsheet
lield
data file
(mass
storage)
pre-
processec
data file
(mass
storaoeL
dedicated
preprocessor
r
I
i
i
i
interactive
data input
instructions
(core memory)
r
I
i
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Fig. 12. Data preparation and code execution.
53
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subsequent programs for postsimulation analysis or graphic presentation using
a screen terminal or plotter.
Postprocessors might be used to reformat and display or print the results
in textual or graphic form and to analyze the results by means of a variety of
manual and automated techniques (van der Heijde and Srinivasan 1983). For
most models, output for graphic display such as contouring can be obtained by
processing one of the output files directly, using display software, or after
some simple modifications in the simulation code. If the software does not
already have the option to generate time drawdown curves for selected loca-
tions, the code itself has to be changed to facilitate this feature, a
requirement that might not be easily met in the microcomputer environment.
However, this kind of problems are expected to decrease with the next genera-
tion of microcomputers and microcomputer operating systems and new application
software. Display of streamlines and isochrones, among others, requires dedi-
cated software, coupling simulation, and graphics software. Information on
graphic pre- and postprocessing software can be found in Beljin (1985), among
others.
A special form of computerized data processing is provided by computer
graphics. Computer graphics consists of a combination of data structures,
graphic algorithms, and programming languages. The use of graphics is helpful
in presenting information and facilitates the visual inspection and analysis
of certain data structures (e.g., spatial hydrogeologic characteristics and
spatial and temporal distributions of computed results.) Until recently, com-
puter graphics was mainly used to display the results of a simulation. Recent
developments in computer technology have made it possible to digitize large
volumes of mapped data and to use graphics interactively in the design stage
of a model. Generic software such as CAD/CAM programs (Computer Aided
Design/Computer Aided Manufacturing) or dedicated graphic software are
increasingly used for such tasks as the development or alteration of model
grids. Coupled with dedicated software, the digitized data can be automat-
ically transformed into grid-based model input, using interpolation algorithms
and reformatting techniques. Thusfar, these developments have been introduced
in experimental projects (e.g., Fedra and Loucks, 1985) and some proprietary
software (e.g., Kjaran et al. 1986). Currently some of these concepts are
included in software developments projects (P. Bedient, Rice University,
Houston, pers. comm., and C. Cole, Battelle PNL, Richland, WA, pers. comm.)
MODELING SOURCES OF GROUNDWATER POLLUTION
In modeling sources of groundwater pollution, the source must be des-
cribed in terms of its spatial, chemical, and physical characteristics, and
its temporal behavior. The spatial definition of the source includes loca-
tion, depth, and area! extent, and together with the scale of modeling iden-
tifies the source as a point source, a line source, a distributed source of
limited areal or three-dimensional extent, or as a nonpoint source of
unlimited extent (van der Heijde 1986). Figure 13 shows the effect of differ-
ent ways of modeling the leachate of a landfill entering an aquifer as boun-
dary condition on the spreading of a plume in the aquifer. Both the areal and
vertical extent of the plume are influenced by the choice of the spatial
dimensions of the source. Furthermore, the areal extent of the source in
relation to the scale of modeling determines the spatial character of the
54
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a. various ways to represent source.
precipitation
b. horizontal spreading resulting from
various source assumptions.
Fig. 13. Definition of the source boundary condition under a leaking
landfill (numbers 1 4 refer to case 1....4).
55
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c. detailed view of 3D spreading for
various ways to represent source
boundary.
Case 2: vertical 2D-source in aquifer
(for 2D horizontal, vertically
averaged, or 3D modeling)
Case 4: point source at top of aquifer
(for 2D or 3D modeling)
Case 1:
horizontal 2D-areal source at top
of aquifer (for 3D modeling)
Case 3:
1D vertical line source in aquifer
(for 2D horizontal, vertically
averaged, 2D cross-sectional, or
3D modeling)
Fig. 13 (continued).
56
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source in the model. In some cases a nonpoint pollution source for a local
scale model is considered a point pollution source for modeling at a regional
scale (e.g., septic tanks, landfills, feedlots).
The source can be located at the boundary or within the system for which
the model is developed. In this respect, the choice of system boundaries is
important: a source located in the unsaturated zone is an internal source for
a model that includes this zone, but is a boundary source for a model of the
saturated zone alone. Not only are different types of models required (var-
iably saturated versus saturated zone models), but the models need to facili-
tate the source in different mathematical ways, i.e., as an internal source or
as a boundary condition, respectively. An overview of the source types and
their spatial characteristics for modeling is presented in Table 3 (van der
Heijde 1986).
Another source characteristic important to the modeling process is its
history or expected behavior in time. The source can be continuous in time,
either fluctuating or constant in strength (e.g., landfills, impoundments,
feedlots), or in the form of a pulse or series of individual, non-overlapping
pulses (e.g., spills, leaching of agrochemicals during or after a storm).
A conceptual difficulty is that of incorporating the effect of the
unsaturated zone on the concentration and arrival time of contaminants
reaching the groundwater. The heterogeneity of this zone, and the complex
transformations that occur in this soil-plant-water-air environment, con-
tribute to this difficulty.
In certain cases, modeling may be used to trace the source of an existing
pollution plume. For convection-dominated transport, this can be done
directly. However, the irreversibility of some of the chemical and physical
processes (e.g., dispersion) necessitates the use of models for this problem
in an indirect manner. Here, an iterative approach assumes a certain source
in space and time and a certain strength, and predicts the current position of
the plume.
MODELING WASTE DISPOSAL FACILITIES, PROTECTION AREAS,
MONITORING NETWORKS, AND REMEDIAL ACTIONS
Models are used increasingly in evaluating designs for controlled waste
management facilities. Many engineering designs for such facilities are also
useful for restoring a contaminated groundwater system. To this purpose
various technologies have been developed. Restoration or remedial action
technologies can be classified into three groups: surface controls, subsur-
face controls, and waste controls (JRB Associates 1982) (see Table 3). In
addition, models can provide guidance in designing the pollution monitoring
systems required by federal, state, and local regulations.
To use modeling of designed-system alterations and remedial action for
evaluation of performance and efficiency, aspects such as model type and
dimensionality, grid configuration, system stresses and constraints, and para-
meter adjustments, are important (Boutwell et al. 1985). Table 4 provides an
overview of modeling aspects of various engineering activities and remedial
actions in groundwater systems. For each design feature, the effects on the
57
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Table 3. Sources of groundwater pollution and model representations (from van der
Heijde 1986).
Sources
Representation in model
Waste disposal
Solid waste
type:
household, commercial, and industrial
waste
sludge from water-treatment plants
and air-pollution control facilities
mine tailings
disposal facilities
uncontrolled dumps
sanitary and secured landfills
deep-subsurface burial (e.g.,
high-level radioactive waste)
Liquid waste
type:
domestic, municipal and industrial
waste water
disposal facilities:
wastewater impoundments
deep-subsurface injection
land spraying
discharge in surface water bodies
individual sewage disposal systems
point surface or area! surface source
or point or 3-D near-surface source
point or 3-D internal source
point or area! surface source
point or vertical internal line source
nonpoint surface source
line or areal surface source
point or nonpoint surface or near-
surface source
Accidental spills or unforseen leakage
leachate of solid waste
leakage from:
surface storage facilities (e.g.,
impoundments)
subsurface storage facilities (e.g.,
gasoline tanks)
subsurface transport systems (e.g.,
sewers, pipelines)
subsurface disposal facilities (e.g.,
deep well injection)
surface spills
same as for solid waste
point or areal surface source
point or areal near-surface source
near-surface or internal line source
point-internal or vertical line-
internal source
point or areal surface source
58
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Table 3. (continued)
Sources
Representation in model
Agricultural pollution
application of chemicals (fertilizers,
herbicides, pesticides)
production of manure (feedlots, inten-
sively used rangelands)
irrigation with polluted or saline
water
nonpoint surface source
point or areal surface source
areal or nonpoint surface source
Radioactive waste
radiological toxicity or both
radiological and chemical
solid, liquid, or gaseous radioactive
components
high- or low-level waste, with different
ways of controlled disposal
accidental releases
same as for solid and liquid waste
point or areal surface source
Other sources
highway deicing salts
mobilization of heavy metals in soil
by acid rain
infiltration of polluted surface water
saltwater intrusion or upconing
line surface source
nonpoint near-surface source
areal (lake) or line (river) surface
source
boundary source or internal source
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Table 4. Modeling designed-system alterations and corrective action (after
Boutwell et al. 1985).
Design Feature
Effects on Groundwater
Capping, grading, and revegetation
Groundwater pumping (and optional
reinjection of treated water)
Wastewater injection
Interceptor trenches
Impermeable barrier (optional
drainage system to prevent
mounding)
Subsurface drains
Solution mining
Excavation
Reduction of infiltration
Reduction of successive
leachage generation
Changes in heads, direction
of flow, and contaminant
migration
Controlled plume removal
Changes in heads and direction
of flow
Plume generation
Changes in heads, direction of
flow, and contaminant migration
Plume removal
Containment of polluted water
Routing unpolluted groundwater
around site
Changes in heads and direction of
flow
Removal of leachate
Changes in heads, direction of
flow, and contaminant migration
Removal of contaminants after
induced mobilization
Removal of waste material and
polluted soil
Changes in hydraulic characteris-
tics and boundary conditions
Changes in heads and direction
of flow
60
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Table 4. (continued)
Design Feature
Type of Model Required
Capping, grading, and revegetation
Groundwater pumping (and optional
reinjection of treated water
Wastewater injection
Interceptor trenches
Impermeable barrier (optional
drainage system to prevent
mounding)
Subsurface drains
Solution mining
Excavation
Unsaturated zone model, vertical
layered
Saturated zone model, two-
dimensional areal, axisym-
metric or three-dimensional;
Well or series of wells assigned
to individual node
Saturated zone model, two-
dimensional area, axisym-
metric or three-dimensional;
Density-dependent flow;
Temperature difference effects
Saturated zone model, two-
dimensional areal or cross-
sectional, or three-dimen-
sional ;
Trenches are represented by line
of notes with assigned heads
Saturated zone model, two-
dimensional areal or cross-
sectional, or three-dimen-
sional; possibly two-dimen-
sional cross-sectional unsatu-
rated zone model for liners
Saturated or combined unsatu-
rated-saturated zone model,
two-dimensional cross-sec-
tional or three-dimensional
Saturated or combined unsatu-
rated-saturated zone model,
two-dimensional areal, cross-
sectional or three-dimen-
sional ;
Lines of sources (injection)
and sinks (removal)
Unsaturated, saturated, or com-
bined unsaturated-saturated
zone model; for unsaturated
some model minimal one-dimen-
sional vertical, for other
types minimal two-dimensional,
cross-sectional
61
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Table 4. (continued)
Design Feature
Typical Modeling Problems
Capping, grading, and revegetation
Groundwater pumping (and optional
reinjection of treated water)
Wastewater injection
Interceptor trenches
Impermeable barrier liners
(optional drainage systems
to prevent mounding)
Subsurface drains
Solution mining
Excavation
Parameters related to leaching
characteristics of reworked
soil
Representing partial penetration
Representing density-dependent
effects
Representing partial penetration,
resolution near trenches
Representing partial penetration,
flow and transport around end
of barrier(s)
Conductivity liner or barrier
material
Large changes in conductivity
between neighboring elements
Differences in required grid
resolution
Resolution near drain
Parameters related to mobiliza-
tion (sorption coefficient,
retardation coefficient)
Parameters of backfill material
62
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groundwater system, model requirements, and specific modeling problems are
listed.
The selection of the type of model depends on whether surface water,
unsaturated zone, or saturated zone systems are to be modeled, or a com-
bination thereof. In groundwater, each situation is three-dimensional.
However, processes in two directions may be orders of magnitude larger than in
the third direction; then, areal or cross-sectional two-dimensional modeling
is justifiable. Grid configuration reflects spatial characteristics of
source, plume, and designed actions. The engineered modifications may require
parameter adjustments and adjustments of the boundary conditions.
In remedial action modeling one is often confronted with data lacking on
the following aquifer characteristics:
In-place hydraulic conductivities for different impermeable barrier
materials
Changes in chemical mobility caused by injection of chemicals and
solution mining
Hydraulic properties and sorption characteristics of permeable treat-
ment beds
Changes in chemical susceptibility to degradation resulting from
bioreclamation
Alteration of properties by chemical interaction with the barriers.
Other problems encountered that are typical for modeling of remediation
alternatives include code limitations on gridding flexibility, numerical
problems in zones with high-contrast soil or rock properties (heterogeneity),
and inaccuracies where the flow field changes significantly in velocity and
direction (see Table 4). For a more in-depth discussion of these issues see
Boutwell et al. (1985).
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5. MODEL OVERVIEW
TYPES OF MODELS
Groundwater models can be divided into various categories, depending on
the purpose of the model and how the nature of the groundwater system is
described. Apart from spatial resolution (one, two, or three dimensions), and
temporal definition (steady-state flow or transport versus time-dependent
behavior), models can be distinguished by the process they are designed to
simulate (van der Heijde et al. 1985a).
Flow models simulate the movement of one or more fluids in porous or
fractured rock. One such fluid is water; the others, if present, can be air
(1n soil) or immiscible nonaqueous phase liquids (NAPLs) such as certain
hydrocarbons. A special case of multifluid flow occurs when layers of water
of distinct density are separated by a relatively small transition zone, a
situation often encountered when sea water intrusion occurs. Flow models are
used to calculate changes in the distribution of hydraulic head or fluid pres-
sure, drawdowns, rate and direction of flow (e.g., determination of stream-
lines, particle pathways, velocities, and fluxes), travel times, and the posi-
tion of interfaces between immiscible fluids (Mercer and Faust 1981, Wang and
Anderson 1982, Kinzelbach 1986, Bear and Verruijt 1987).
Two types of models can be used to evaluate the chemical quality of
groundwater (e.g., Jennings et al. 1982, Rubin 1983, Konikow and Grove 1984,
Kincaid et al. 1984): (1) pollutant transformation and degradation models,
where the chemical and microbial processes are posed independent of the move-
ment of the pollutants; and (2) solute transport models simulating displace-
ment of the pollutants, often including the effects of transformation and
degradation processes (transport and fate).
Hydrochemical models represent the first type, as they consist solely of
a mathematical description of equilibrium reactions or reaction kinetics
(Jenne 1981, Rice 1986). These models, which are general in nature and are
used for both groundwater and surface water, simulate chemical processes that
regulate the concentration of dissolved constituents. They can be used to
identify the effects of temperature, speciation, sorption, and solubility on
the concentrations of dissolved constituents (Jenne 1981).
Solute transport models are used to predict movement, concentrations, and
mass balance components of water-soluble constituents, and to calculate radio-
logical doses of soluble radionuclides. A solute transport model uses the
(piezometric) head data generated by a flow model to generate velocities for
advective displacement of the contaminant, allowing for additional spreading
through dispersion (Anderson 1984) and for transformations by chemical and
microbial reactions. The transformations considered by so-called nonconser-
vative models are primarily adsorption, radioactive decay, and biochemical
transformations and decay (Cherry et al. 1984, Grove and Stollenwerk 1987).
The inclusion of geochemistry in solute transport models is often based
on the assumption that the reaction rates are limited and thus depend on the
residence time for the contaminant, or that the reactions proceed instan-
taneously to equilibrium. Recently, various researchers have become inter-
64
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ested in a more rigid, kinetic approach to incorporate chemical reactions in
transport models (e.g., Bahr and Rubin 1987). This inclusion of geochemistry
has focused on single reactions such as ion-exchange or sorption for a small
number of reacting solutes (Rubin and James 1973, Valochi et al. 1981, Char-
beneau 1981). Because multicomponent solutions are involved in most contami-
nation cases, there is a need for models that incorporate the significant
chemical interactions and processes that influence the transport and fate of
the contaminating chemicals (Cederberg et al. 1985). This is especially
important in simulating fate and transport of mixed wastes.
In some cases, comprehensive groundwater quality assessment requires the
simulation of temperature variations and their effects on groundwater flow and
pollutant transport and fate. A few highly specialized multipurpose predic-
tion models can handle combinations of heat and solute transport, or either
heat transport or solute transport together with rock matrix displacement (P.
Huyakorn, Hydrogeologic, Inc.; B. Sagar, Rockwell International, Inc.; pers.
comm.). Generally, these models solve the system equations in a coupled
fashion to provide for analysis of complex interactions among the various
physical, chemical, and biological processes involved. None of these models
has yet been released for general use.
As groundwater is part of a larger physical system, the hydrologic cycle,
many models address in one way or another the interaction between groundwater
and the other components of the hydrologic cycle. Some of these models des-
cribe only the interactions, sometimes as a process, sometimes as a dynamic
stress or boundary condition. Increasingly, models are developed that simu-
late the processes in each subsystem in detail, in addition to the inter-
relationships (e.g., Morel-Seytoux and Restrepo 1985). Two types of models
fit this latter category: watershed models and stream-aquifer models
(sometimes called conjunctive use models).
Watershed models customarily have been applied to surface water manage-
ment of surface runoff, stream runoff, and reservoir storage. Traditionally,
these models did not treat groundwater flow in much detail, in part because of
the wide range of temporal scales involved. The subsurface components in
these models were limited to infiltration and to a lumped, transfer function
approach to groundwater (El-Kadi 1983, 1986).
With the growing interest during the 1970s in the conjunctive use and
coordinated management of surface and subsurface water resources by respon-
sible authorities, a new class of models was developed: the stream-aquifer
models, where the flow in both the surface water network and the aquifers
present could be studied in detail. Conjunctive use of water resources is
aimed at reducing the effects of hydrologic uncertainty about the availability
of water. For example, artificially recharged aquifers can provide adequate
water supplies during sustained dry periods when surface water resources run
out and nonrecharged aquifers do not provide enough storage.
For conjunctive use evaluation, models must simulate more processes than
those included in watershed models. Important processes to consider include
canal seepage, deep percolation from irrigated lands, aquifer withdrawal by
pumping, groundwater inflow to or outflow from adjacent aquifers, plant trans-
piration, artificial recharge, bank storage effects, and deep-well injection
(El-Kadi 1986). The inclusion of detailed groundwater flow processes in
65
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watershed models increases significantly the complexity of model computations.
Differences in temporal scale between surface and subsurface processes add to
the complexities.
Recent interest in such multisystem modeling has increased, motivated by
the need to simulate nonpoint pollutant transport such as caused by the wide-
spread use of agricultural chemicals, and by the need to study the contribu-
tion of local soil and groundwater pollution to the quality of surface water
bodies. To model this type of problem, highly detailed descriptions of trans-
port and fate processes are added to the multisystem flow models.
As management is using a multitude of decision criteria to assure the
optimal use of water resources, advanced hierarchical and optimization
modeling of surface and subsurface water resources has been of interest to
researchers for several years in support of management's decision-making
(Halmes 1977).
An overview of watershed models having a significant watershed component
1s given 1n El-Kadi (1986). An overview of management models for conjunctive
use 1s presented in van der Heijde et al. (1985a).
The flow and solute transport models may be embedded in a management
model describing the system in terms of objective function(s) and constraints,
and solving the resulting equations through an optimization technique such as
linear programming (Gorelick 1983, Gorelick et al. 1983, Kaunas and Haimes
1985, Wagner and Gorelick 1987).
As an update of van der Heijde (1984) and van der Heijde et al. (1985a)
the following sections describe in some detail the mathematical basis of flow
and solute transport models and give an overview of the availability and
usability of existing flow and solute transport simulation codes. Appendix A
through G provide a detailed overview of the most prominent simulation codes
currently available.
Several new developments are occurring in groundwater modeling. From the
tables in the Appendices it is evident that recently groundwater flow models
have evolved to a point where a wide range of flow characterizations are
possible. These newer models may include options for various types of
boundary conditions as well as the ability to handle a wide variety of
hydrologic processes such as evapotranspiration, stream-aquifer exchanges,
spatial and temporal variations in recharge, and the more complex characteri-
zation necessary for simulating unsaturated flow. Similarly, recently
developed models for simulation of solute transport or new versions of earlier
models often include increased flexibility in describing the solute source and
simulating transport and fate processes such as radioactive decay or chemical
transformation and effects of both equilibrium and nonequilibrium
adsorption. In some instances, these transport models are coupled with
existing geochemical models to provide a more complete analysis of the solute
chemistry. Such a development is also noticeable with respect to the simu-
lation of biodegradation, e.g., for the analysis of bioremediation schemes
(Borden and Bedient 1986, Borden et al. 1986). Furthermore, important
developments have occurred in the modeling of flow and transport in fractured
rock systems. Here, both improved site characterization and stochastic
analysis of fracture geometry, together with an improved capability to
66
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describe the interactions of chemicals between the active and passive fluid
phases and the rock matrix, have facilitated increasingly realistic simulation
of real-world fractured rock systems. Multiphase flow models have become
increasingly available, especially those designed for studying the movement of
immiscible fluids such as NAPLs. Also, new approaches have been developed for
parameter identification and are increasingly used in practical applications
(Yeh 1986). Finally, optimization-based management models have been applied
to a growing variety of decision problems, especially in the area of ground-
water protection (Wagner and Gorelick 1987). For the purpose of this review,
we consider predictive simulation models that address the processes that
comprise groundwater flow, solute, and heat transport, geochemical interac-
tions, and flow and transport in fractured media. Other important types of
models such as those describing multiphase flow (e.g., immiscible hydrocar-
bons, salt water intrusion), automatic parameter identification, and flow and
solute transport models coupled with optimization techniques (management
models), will be the focus of future evaluation by the IGWMC.
MODEL MATHEMATICS
In terms of spatial orientation, models may be capable of simulating sys-
tems in one, two, or three dimensions. Temporally, they may handle either
transient or steady-state simulations or both. Another distinction in the way
models handle parameters spatially is whether the parameter distribution is
lumped or distributed. Lumped parameter models assume that a system may be
defined with a single value for the primary system variables. The system's
input-response function does not necessarily reflect physical laws. In dis-
tributed-parameter models, the system variables often reflect detailed under-
standing of the physical relationships in the system and may be described with
a spatial distribution. System responses may be determined at various
locations.
Until recently, most groOndwater modeling studies were conducted using
deterministic models based on precise descriptions of cause-and-effect or
input-response relationships. Increasingly, however, models used in ground-
water protection programs reflect the probabilistic or stochastic nature of a
groundwater system to allow for spatial and temporal variability of relevant
geologic, hydrologic, and chemical characteristics (USEPA 1986a, El-Kadi
1987).
Most mathematical models used in groundwater management are distributed-
parameter models, either deterministic or stochastic. Their mathematical
framework consists of one or more partial differential equations called field
or governing equations, as well as initial and boundary conditions and solu-
tion procedures (Bear 1979). Models that adopt the stochastic approach assume
that the processes active in the system are stochastic in nature and that the
variables may be described by probability distributions. Consequently, system
responses are characterized by statistical distributions estimated by solving
the governing equation.
The governing equations for groundwater systems are usually solved either
analytically or numerically. Analytical models contain a closed-form or ana-
lytical solution of the field equations, continuous in space and time. An
important attribute of analytical solutions is the implicit conservation of
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mass (continuity principle). As analytical solutions generally are available
only for relatively simple mathematical problems, using them to solve ground-
water problems requires extensive simplifying assumptions regarding the nature
of the groundwater system, its geometry, and external stresses (Walton 1984,
van Genuchten and Alvas 1982).
In numerical models a discrete solution is obtained in both the space and
time domains by using numerical approximations of the governing partial dif-
ferential equation (PDE). As a result of these approximations the conserva-
tion of mass is not always assured and thus needs to be verified for each
application. Spatial and temporal resolution in applying such models is a
function of study objectives and availability of data. If the governing equa-
tions are nonlinear, linearization often precedes the matrix solution (Remson
et al. 1971, Huyakorn and Pinder 1983); sometimes solution is achieved using
nonlinear matrix methods such as predictor-corrector or Gauss-Newton (Gorelick
1985).
Various numerical solution techniques are used in groundwater models.
They include finite-difference methods (FD), integral finite-difference
methods (IFDM), Galerkin and variational finite-element methods (FE), colloca-
tion methods, boundary (integral) element methods (BIEM or BEM), particle mass
tracking methods (e.g., random walk [RW]), and the method of characteristics
(HOC) (Huyakorn and Pinder 1983, Kinzelbach 1986). Among the most used
approaches are finite-difference and finite-element techniques. In the
finite-difference approach a solution is obtained by approximating the
derivitaves of the PDE. In the finite-element approach an integral equation
is formulated first, followed by the numerical evaluation of the integrals
over the discretized flow or transport domain. The formulation of the solu-
tion in each approach results in a set of algebraic equations which are then
solved using direct or iterative matrix methods (Figure 14).
In semi-analytical models, complex analytical solutions are approximated
by numerical techniques, resulting in a discrete solution in either time or
space. Models based on a closed-form solution for either the space or time
domain, and which contain additional numerical approximations for the other
domain, are also considered semi-analytical models. An example of the semi-
analytic approach is in the use of numerical integration to solve analytical
expressions for streamlines in either space or time (Javandel et al. 1984).
Recently, models have been developed for study of two- and three-dimen-
sional regional groundwater flow under steady-state conditions in which an
approximate analytic solution is derived by superposition of various exact or
approximate analytic functions, each representing a particular feature of the
aquifer (Haitjema 1985, Strack 1988).
No universal model can solve all kinds of groundwater problems; different
types of models are appropriate for solving different types of problems. It
is important to realize that comprehensiveness and complexity in a simulation
do not necessarily equate with accuracy.
68
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Concepts of the
physical system
I
Translate to
Partial differential equa-
tion, boundary and initial
conditions
Subdivide region
into a grid and
apply finite-
difference approx-
imations to space
and time derivatives
Finite-difference
approach
Finite-element
approach
Transform to
Integral equation
Subdivide region
into elements
and integrate
First-order differential
equations
Apply finite-difference
approximation to
time derivative
System of algebraic
equations
Solve by direct or
,, iterative methods
Solution
Fig. 14. Generalized model development by finite-difference
element methods (after Mercer and Faust 1981).
and finite-
69
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FLOW MODELS
Groundwater flow models simulate the movement of one or more fluids in
porous or fractured rock systems. One fluid is always water and the other may
be an immiscible liquid such as a non-aqueous phase liquid (NAPL). Most
existing groundwater models consider only the flow of water in saturated or
variably saturated porous systems. Increasingly, research is concerned with
multiphase flow of immiscible liquids and water and with flow and transport in
fractured media.
The mathematical model for groundwater flow is derived by applying prin-
ciples of mass conservation (resulting in the continuity equation) and conser-
vation of momentum (resulting in the equation of motion; Bear 1972, 1979;
Figure 15). The generally applicable equation of motion in groundwater flow
is Darcy's linear law for laminar flow, which originated in the mid-nineteenth
century as an empirical relationship. Later, a mechanistic approach related
this equation to the basic laws of fluid dynamics (Bear 1972). An increasing
number of models use a nonlinear equation of motion to describe flow around
well bores in large fissures and in very low permeable rocks (non-darcian
flow; Hannoura and Barends 1981, Huyakorn and Finder 1983).
In order to solve the flow equation, both initial and boundary conditions
are necessary (Franke et al. 1984). Initial conditions for saturated flow
systems consist of given values for the piezometric head throughout the model
domain. Initial conditions for variably saturated flow models are usually
expressed in terms of pressure head. For most models, inclusion of initial
conditions is only needed when transient simulations are performed. Boundary
conditions for flow simulation may be any of three types: specified head
(Dirichlet or first type), specified flux (Neumann type or second type), and
head-dependent flux (Cauchy, mixed or third type) conditions. Boundary condi-
tions are specified on the periphery of the modeled domain, either at the
border of the modeled area or at locations within the system where system
responses are fixed (e.g., connections with aquifer penetrating surface water
bodies, or fluxes in/out of the system such as through wells).
Flow models have been developed for flow under both saturated and par-
tially saturated conditions. Variably saturated models handle both condi-
tions, using a single set of equations (the Richards' equation or a variant of
it) (DeJong 1981, El-Kadi 1983). Models that have separate formulations for
simulation of flow in the saturated zone and unsaturated zone are sometimes
called coupled saturated-unsaturated zone models.
Complex liquid wastes often consist of multiple miscible and immiscible
chemical components of varying density and viscosity. Saltwater intrusion is
another density-driven flow phenomenon that impairs parts of many coastal
aquifers and, increasingly, deep continental freshwater aquifers. Extensive
evaluation of methods for analysis of saltwater intrusion is presented in
Jousma et al. (1988). An overview of existing models for the latter type of
use is given by van der Heijde and Beljin (1985).
70
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GROUNDWATER FLOW EQUATION
Rate of change
of mass of
fluid in
reference volume
per time unit
Rate of flow
of fluid mass
into reference
volume
Rate of flow
of fluid mass
out of reference
volume
Water
Mass
Balance
Groundwater
Flow
Equation
Fig. 15. Formulation of the groundwater flow equation.
71
-------
IGWMC has compiled a comprehensive descriptive listing of models that
address saturated, unsaturated, and multiphase flow. Appendix A covers
saturated flow models; Appendix B covers models for unsaturated or variably
saturated flow. The listings have been compiled from the Center's MARS model
referral database, and have been limited to those models that are documented
and readily available for third-party use.
Mathematical Formulation for Saturated Flow
The flow of a fluid through a saturated porous medium can be derived by
combining the mass conservation principle with Darcy's law resulting in (Bear
1979):
Ssl£- "-(K-'h) =0 (1)
in which h is hydraulic head, K is hydraulic conductivity, and Ss denotes
specific storage and is defined as
Ss = Pg(a+nB). (2)
Equation (1) is usually written as
it - "* ss IT <3>
* J
where W* denotes a source term expressed as a volume flow rate per unit volume
with positive sign for outflow and negative for inflow. An overview of
saturated flow models is presented in Appendix B.
Mathematical Formulation for Unsaturated Flow
Because air and water are immiscible fluids, when they coexist a discon-
tinuity takes place between the two phases. The difference in pressure
between the two fluids, called capillary pressure (P ), is a measure of the
tendency of the partially saturated medium to suck irf water or to repel air.
The negative value of the capillary pressure is called suction or tension.
The capillary pressure head (i|>) is defined by (DeJong 1981)
The hydraulic head is given by
h = z - * (5)
in which z is elevation above an arbitrary datum.
72
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The governing equation for unsaturated flow is derived by comsir-rg the
mass balance principal with Darcy's law, ignoring compressibility of matrix,
fluid, and air effects. The resulting equation, known as Richards' equation,
is (DeJong 1981, El-Kadi 1983)
v (Kvh) = F || . (£)
In equation (6), K = K(0) is the hydraulic conductivity, o is volumetric *ate>-
content, h is total head, t is time, and F is moisture capacity defined as
F _ do _ d(9) ana
K(e) , in which 0 is the volumetric water content, is included in these
properties. Hysteresis usually prevails in the relationship 41(0), i.e., a
different wetting and drying curve (Figure 16). Soil air entrapment causes
separation of the boundary drying and wetting curves at zero pressure. In
fine-grained soils, subsidence or shrinking may cause the same effects. In
general, simulation under hysteresis is difficult due to the existence of an
infinite number of scanning, drying, and wetting curves, depending on the
wetting-drying history of the soil. An example of the function 0(41) with no
hysteresis is the form provided by van Genuchten (1978):
(0 - 0 )
0 = 0+ - - - - (8)
r M . I , lwlw
11+ |ai|i| ]
in which 0 and 0 are the saturated and residual water content, respectivel> ,
and a , N, and M are fitting parameters, with M related to N by
M = 1 - £ . (9)
The hydraulic conductivity function K(0)is represented by
0-0 1/2 0-0 l/H M 2
K =
Other forms exist in the literature as well (see, e.g., El-Kadi |1985a,b])
Moisture capacity can be obtained by direct differentiation of equation (8)
Another useful function, especially in the analysis of infiltration, is soil
water diffusivity, defined by
Df = K / F (11)
73
-------
0.3
0
u-
0.1
H
2
LJU
h-
2
O
O
cc
111
g
DC
H
LLJ
-50 -40 -30 -20 -10
PRESSURE HEAD - CM WATER
Fig. 16. Schematic relationships between water content and pressure head for
various draining and wetting cycles (from El-Kadi and Beljin 1987).
74
-------
which can be estimated explicitly from equations (7) and (10) (El-Kadi and
Beljin 1987). An overview of variably saturated models is given in Appendix
B.
Multiphase Flow
Fluids that migrate in the subsurface environment can be grouped with
regard to their migration behavior as either miscible (mixes) with water or
immiscible (does not mix) with water (Morel-Seytoux 1973, Parker et al. 1987).
Miscible fluids form a single phase, while immiscible fluids form two or more
fluid phases (a fluid is either a liquid or a gas). Such a grouping of fluids
is essential for discussion purposes because the movement of two or more
immiscible fluids is distinctly different from the simultaneous movement of
miscible fluids. The flow of immiscible fluids gives rise to two-phase or
multiphase-flow and transport; miscible fluids give rise to single-phase flow
and transport. The following discussion is based primarily on Kincaid and
Mitchell (1986).
Migration patterns associated with immiscible fluids introduced at the
soil surface (e.g., as a chemical spill) are schematically described by
Schville (1984). The extent and character of migration depends on the
chemical characteristics, the source volume, the area covered by the source,
the infiltration rate, and the retention capacity of the porous medium.
Retention capacity is a measure of the volume of immiscible liquid or
nonaquous-phase liquid (NAPL) that can be held in the porous medium without
appreciable movement. This volume is analogous to the volume of water
prevented by the capillary force from draining because of the gravity force.
When the retention of the partially saturated soil column is not
exceeded, the bulk of the liquid chemical contaminant will be retained in the
soil column. Migration of the contaminant to the far-field environment will
occur as a result of its dissolution in water; it may also move in a distinct
vapor phase. Contaminated soil water arriving at the water table will be
carried downgradient in the unconfined aquifer and in the capillary fringe.
Figure 17 shows the ability of heterogeneous sediments within the partially
saturated zone to laterally spread or broaden the contaminant plume with
increasing depth. To estimate the retention capacity of the partially
saturated soil column, the soil profile and moisture content must be known.
When the bulk volume of the chemical entering the soil exceeds the reten-
tion capacity of the partially saturated soil profile, the chemical will reach
the water table in its liquid phase. Chemicals that are less dense than and
immiscible in water, the so-called "floaters," will remain in the capillary
fringe of the partially saturated 2one and near the water table in the satu-
rated zone, as indicated in Figure 18. Examples of this type of pollutant are
gasoline and volatile organic solvents. Immediately beneath the spill chemi-
cals can be forced below the water table and into the saturated zone by the
pressure of the overlying liquid chemical mound (e.g., analogous to ground-
water mound created by water disposal). As the plume migrates downgradient,
the overlying pressure decreases and buoyant forces bring the lighter-than-air
chemical up to the water table. The contamination will spread as a distinct
liquid chemical phase and as a dissolved constituent in the groundwater. Con-
tamination could also spread as a distinct chemical vapor phase. Certainly,
some fraction of the chemical will be held in the porous medium by the reten-
75
-------
Ground Surface
Chemical,
Vapor Phase
Chemical
Spill
Chemical
£?:?:-:5:in Water:
i+xwi'ux-x- -::: :<:::<:
Dissolved
s
Infiltration Rate
Partially Saturated Zone
I
Capillary Fringe
Saturated Zone
Fig. 17. Schematic diagram of a chemical spill of a volume less than the
retention capacity of the partially saturated soil profile (from
Schville 1984).
-------
GroundSurface
Infiltration Rate
Chemical/M,
Vapor Phase :';
Chemical
Spill
Partially Saturated Zone
Capillary Fringe
Water Table-'
Saturated Zone
"*' 18' roTume"'greater than
Schville 1984).
-------
tion capacity mechanism. Release of this fraction, as a dissolved constituent
in soil water and groundwater, will be a long-term process.
As a substantial part of bulk volume of a heavier-than-water immiscible
liquid (e.g., TCE) reaches the water table, the chemical will continue to move
principally in the downward direction by displacing the groundwater. These
liquids are called "sinkers." If the volume of the chemical moving into the
saturated zone is greater than the retention capacity of the unconfined
aquifer formation, the chemical will move through the entire saturated thick-
ness of the unconfined aquifer. Depending on the physical/chemical properties
of the chemical with respect to the impermeable formation, the chemical may
continue its downward migration or form a mound above the impermeable bottom
of the aquifer. Chemicals lying on the aquifer bottom will migrate by follow-
ing the relief of the bedrock. These various aspects of the migration of the
heavier-than-water chemical are shown in Figure 19.
As occurred in the partially saturated zone, heterogeneity within the
saturated zone will cause the contaminant to spread laterally as the migrates
vertically. Note that the slope of the bottom topography (i.e., relief of the
bedrock) may not coincide with the groundwater gradient; the chemical is
driven by its own gradient not the hydraulic gradient of the groundwater, and,
hence, the chemical migration may actually move in a direction opposite to
groundwater flow.
The existence of distinct fluid phases competing for the same pore space
is governed by mass and momentum balance equations and data that uniquely
specify the balance between the fluids in the soil environment. The wetting
fluid is usually water; examples of a nonwetting fluid are mineral oil,
chlorohydrocarbons, and soil air (Parker et al. 1987). Flow of each fluid is
proportional to its potential gradient, the permeability of the medium, the
fluid density and viscosity, and the portion of pore space (i.e., cross-
sectional area) that the fluid occupies.
A fluid mass balance and Darcy's equation can be written for each of the
fluids. When the detailed-flow phenomena in each fluid phase are of interest,
as is the case with two liquids, the mass and momentum balance equations for
each fluid should be solved. Consistent sets of saturation and potential for
each fluid are obtained from such an analysis. However, when flow phenomena
for only one of the two fluid phases are of interest, as is commonly the case
with moisture movement in the partially saturated zone, the saturation and
potential of the fluid of interest should be solved. The saturation of the
second fluid can then be simply calculated given the porosity of the medium
(i.e., given that it occupies the remaining pore space).
The relative permeability of the wetting and nonwetting fluids depends
strongly on the degree of saturation (Dracos 1978, Parker et al. 1987). The
curves describing the permeability of the fluids show the nonlinear behavior
of fluids in a partially saturated environment. Unique curves, exist for
different fluids and media. In general, each fluid must reach' a minimum
saturation before it will flow. In the case of water and air, the minimum
saturation for water is called the irreducible saturation. For moisture
movement in the vadose zone, soil physicists have found that irreducible
saturation is actually a function of the suction pressure applied and the
length of time one is willing to wait for the soil column to respond. Thus,
78
-------
-P .O
-------
irreducible saturation may not necessarily be single-valued. The wetting or
nonwetting fluid must exceed its residual saturation before it will flow.
Residual saturation is the measure of the ability of a soil to retain moisture
and consequently the bulk of a chemical spill.
One of the more complex migration patterns that may occur involves three
phases in the partially saturated zone (Kuppussamy et al. 1987). Water and
chemical would exist as liquid phases and soil air would exist as a gaseous
phase. The flow process is more complicated than the two-phase situation,
although the same principles of mass and momentum balance apply. The indi-
vidual fluids are immobile over relatively large areas of the saturation
triangle, as shown in Figure 20; a relatively small central region exists over
which all three phases are simultaneously mobile.
At low organic fluid saturations, a continuous organic phase may not
exist and the organic fluid might be present as isolated globules surrounded
by water. Such continuity is an essential assumption in virtually all
existing models. In the current generation of models, discontinuity in a
phase means that the relative permeability of the fluid goes to zero and that
the model predicts no flow (Parker et al. 1987). In reality, however, migra-
tion of these isolated parcels of organic fluid can occur, resulting in a
process termed "blob flow." This process is well known in tertiary oil
recovery where the aim is to mobilize such "blobs," using injected surfactants
and gases (e.g., Gardner and Ypma 1984). Existing mathematical models and
codes cannot handle transport by way of globule migration.
Models and codes of organic chemical migration are commonly categorized
as (1) those for which fluid physics of immiscible organic liquids are empha-
sized, and (2) those for which organics appear as miscible constituents in
which chemical/microbiological reactions for dilute levels of contamination
are emphasized. Existing models and codes can be used to model selected
phases to the extent that vapor phase exchange and transport, geochemical
reactions, and microbiological degradation can be incorporated in existing
codes (i.e., insofar as the mathematical equations are unchanged by the
addition of these processes and reactions). These models are based on the
assumption that for each phase continuous flowpaths exist throughout the
porous medium (Streile and Simmons 1986). A simplified version of such an
approach is presented by Dracos (1978). The proposed model consists of
vertical one-dimensional flow in the unsaturated zone through a column of
radius R, under the source (Fig. 21) and a two-dimensional horizontal model
for the low density liquid atop the watertable. For the miscible component in
the plume a common 2D solute transport model is used, taking the source term
from the ID vertical column model. That it is not easy to make simplified
modeling approaches work successfully for real-world phenomena is demonstrated
by the Bartz and Kass experiment (Fig. 22) in which the bulk oil continues to
advance slowly after 120 days, but the outmost boundary of detectable solutes
is retreating, resulting in a 120-day contour being located outside the 360-
day contour (Dracos 1978).
Petroleum industry models (Aziz and Settari 1979) do not appear to be
readily applicable to organic transport analyses. These codes address only
fluid flow phenomena and neglect entirely transport and attenuation phenomena.
Petroleum industry codes may only be useful in regard to the theory and
methods they embody for simulating multiphase, immiscible-fluid flow.
80
-------
Water
100%
Air
100%
Oil
100%
Fig. 20. Funicular zones for three immiscible fluids.
81
-------
Ground surface
adopted model
Water table
Groundwater flow
Fig. 21. Schematized vertical infiltration and horizontal spreading of the
bulk of a low-density hydrocarbon atop the water table (after
Dracos 1978).
82
-------
00
OJ
360
Zone of dissolved components
OH bulk zone
;F ow direction
Oil infiltration
source
I 1
0 10
-\ 1
50 m
F1g. 22. 011 bulk zone and spreading of dissolved components 1n groundwater
from a field experiment by Bart2 and Kass (after Dracos 1978).
-------
Experimental models for more complex systems, documented recently,
include finite-element formulations by Abriola and Pinder (1985a, 19855) and
Kuppusamy et al. (1987) and a finite-difference formulation by Faust (1985).
For further information on existing multiphase models, see Appendix G.
SOLUTE TRANSPORT MODELS
The groundwater transport of dissolved chemicals and biota such as bac-
teria and viruses is directly related to the flow of water in the subsurface.
Many of the constituents occurring in groundwater can interact physically and
chemically with solid phases such as clay particles, and with various dis-
solved chemicals. As a consequence, their displacement is both a function of
mechanical transport processes such as advection and dispersion, and of
physicochemical interactions such as adsorption/desorption, ion-exchange,
dissolution/precipitation, reduction/oxidation, complexation, and radioactive
decay. Biotransformations taking place during transport can alter the compo-
sition of the groundwater significantly (Ward et al. 1985).
In modeling the transport of dissolved chemicals, the principle of mass
conservation is applied to each of the chemical constituents of interest
(Figure 23). The resulting equations include physical and chemical inter-
actions, as between the dissolved constituents and the solid subsurface
matrix, and among the various solutes themselves (Reilly et al. 1987, Konikow
and Grave 1984). These equations might include the effects of biotic pro-
cesses (Molz et al. 1986, Borden and Bedient 1986, Srinivasan and Mercer
1988). To complete the mathematical formulation of a solute transport prob-
lem, equations are added describing groundwater flow and chemical inter-
actions, as between the dissolved constituents and the solid subsurface
matrix, and among the various solutes themselves. In some cases equations of
state are added to describe the influence of temperature variations and the
changing concentrations on the fluid flow through the effect of these varia-
tions on density and viscosity.
Under certain conditions such as low concentrations of contaminants and
negligible difference in specific weight between contaminant and the resident
water, changes in concentrations do not affect the flow pattern (homogeneous
fluid). In such cases a mass transport model can be considered as containing
two submodels, a flow submodel and a quality submodel. The flow model com-
putes the piezometric heads. The quality submodel then uses the head data to
generate velocities for advective displacement of the contaminant, allowing
for additional spreading through dispersion and for transformations by chemi-
cal and microbial reactions. The final result is the computation of concen-
trations and solute mass balances. In cases of high contaminant concentra-
tions in waste water or saline water, changes in concentrations affect the
flow patterns through changes in density and viscosity, which in turn affects
the movement and spreading of the contaminant and hence the concentrations
(heterogeneous fluid). To solve such problems through modeling, simultaneous
solution of flow and solute transport equations or iterative solution between
the flow and quality submodels is required (Voss 1984, van der Heijde et al.
1985a, Kipp 1987). Mass transport models which handle only convective trans-
port are called immiscible transport models, whereas miscible transport models
handle both convective and dispersive processes. Models that consider both
displacements and transformations of contaminants are called nonconservative.
Conservative models only simulate convective and dispersive displacements.
84
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MASS BALANCE FOR SPECIES:
Rate of change
of mass in control,
volume per time
unit
Rate of transport
of mass into and
out of control,
volume per time
unit
o
TRANSPORT TERM
- inflows
- outflows
Rate of
transformation
of mass in
control, volume
per time unit
O
TRANSFORMATION
TERM
- biological reaction
- chemical reaction
- physical change
Transport Term = Dispersive Flux 4-Advective Flux
Fig. 23. Formulation of the solute transport equation.
85
-------
There are two approaches for modeling multicomponent solutions. In the
first approach, the interaction chemistry may be posed independently of the
mass transport equations. The most widely used form of this approach is the
coupling of the transport equation with an equilibrium phase exchange reaction
such as the Langmuir or Freundlich isotherm (Jennings et al. 1982). An alter-
native approach is to insert all of the interaction chemistry directly into
the transport equations (Jennings 1987).
In general, current solute transport models assume that the reaction
rates are limited and thus depend on the residence time for the contaminant,
or that the reactions proceed instantaneously to equilibrium. Recently,
various researchers have become interested in a more rigid, kinetic approach
to incorporate chemical reactions in transport models.
Several difficulties impair both the credibility and the efficient use of
mass transport models. One such difficulty is "numerical dispersion" in which
the actual physical dispersion mechanism of the contaminant transport cannot
be distinguished from the front-smearing effects of the computational scheme
(Huyakorn and Pinder 1983). For the finite-difference method, this problem
can be reduced by using the central difference approximation. Another numeri-
cal problem occurs as spatial oscillations (overshoot and undershoot) near a
concentration front, especially for advection-dominated transport, sometimes
resulting in negative concentrations. Remedies for these problems are found
in the reduction of grid increments or element size or by using upstream
weighting for spatial derivatives. The use of weighted differences (combined
upstream and central differences) or the selection of other methods (e.g.,
HOC, RW) avoids the occurrence of these numerical problems. A problem
inherent to all numerical techniques, although of a different order of magni-
tude, is numerical inaccuracy. This problem can be mitigated by grid refine-
ment or selection of an alternative method (Huyakorn and Pinder 1983). For
the random walk method, higher accuracies can be obtained by increasing the
number of particles in the system (Uffink 1983, Kinzelbach 1986).
Another problem is related to the general use of mass transport models in
conjunction with flow models. Although a pollution problem is typically
three-dimensional, vertical averaging is frequently used, resulting in the
utilization of a two-dimensional, horizontal mass transport model that is
generally connected with a hydraulic flow model. Such models tend to under-
estimate peak values and thus may fail to predict dangerous concentration
levels and critical arrival times of pollutants in wells that become polluted
by surface or near-surface sources.
Appendix C presents an overview of available solute transport models.
Advection-Dispersion Equation
Processes that control the migration of solute are advection, hydro-
dynamic dispersion, geochemical and biochemical reactions, and radioactive and
biological decay.
In the case of a conservative solute, no reactions such as adsorption
occur between the solute and the solid phase. The rate of transport is equal
to the seepage velocity. If the transport of solute is due only to advection,
a sharp interface will separate the flow domain that contains the solute and
86
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the native groundwater. However, this interface does not remain sharp due to
hydrodynamic dispersion, which causes solute spread over a greater volume of
aquifer than would be predicted by an analysis of groundwater velocity. That
means shorter traveling time for a pollutant from the source of the point of
observation. In the case of an instantaneous release of pollutants and if
dispersion is significant, advective transport relates to the movement of the
center of mass of the spreading (dispersing) plume (Figure 24).
Convection-
Convection, sometimes refered to as advection, is the solute movement
with the bulk flow of the fluid (water). Estimation of convection is based on
determination of fluid flow characteristics, flow paths, and velocity. In
most cases involving unsaturated flow conditions, numerical solutions of the
flow equation are needed to accurately describe the flow field.
Dispersion--
The term hydrodynamic dispersion describes the spreading of a solute at
the macroscopic (Darcy) level by the combined action of mechanical dispersion
and molecular diffusion (Figure 24; Bear 1972, 1979). Mechanical dispersion
is caused by the changes in the magnitude and direction of velocity across any
pore cross-section at the microscopic level. Pores differ in size and shape,
also causing variation in the maximum velocity within individual pores, in
addition to velocity fluctuations in space with respect to the mean direction
of flow. This results in a complex spatial distribution of the flow velocity.
Molecular diffusion results from variation of solute concentration within the
liquid phase. Solute moves by the gradient of concentration from regions of
higher to lower concentration.
In practice, dispersion is considered to be caused by both microscopic
and macroscopic effects (Dagan 1986). The difficulties in quantifying
dispersion are encountered because studies of flow through porous media are
conducted on a macroscopic scale. Darcy's law, for example, is a macroscopic
equation.
In general, flux due to mechanical dispersion is estimated by analogy to
Pick's law, i.e., flux is proportional to concentration gradient (Bear 1972,
1979). Combining the two effects results in the equation
Qc = -0'7C (12)
in which D1 is called the effective diffusion-dispersion coefficient or the
coefficient of hydrodynamic dispersion. D1 is estimated as the sum of the
coefficients of mechanical dispersion, D, and molecular diffusion, D . D is a
tensor usually having longitudinal and transverse components. D ismexpressed
generally as a function of the molecular diffusion coefficient^ a chemical
species in pure water and a tortuosity factor accounting for the nonuniformity
of the pore system and the degree of saturation (Bresler and Sagan 1981, Gupta
and Battacharya 1986), namely,
87
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-source
-Distance-
reginal
flow
B
Fig. 24. Dispersion of a tracer slug in a uniform flow field at various
times; the dispersion coefficients in case B are about 500 times
greater than in case A (A, A2, A3 are traveled distances of center
of mass of plume).
-------
(13)
in which r\1 is the tortuosity factor and D is the diffusion coefficient in
pure water. One model for n is:
1 03
where n is porosity. Equation (14) is similar to that concerning air diffu-
sion, as proposed by Millington and Quirk (1961).
Written in tensor form, the coefficient of hydrodynamic dispersion can be
expressed as:
Dl . = D. . + Dm 6. . (15)
where D^,- is the coefficient of mechanical dispersion, Dm is the coefficient
of molecular diffusion, and 6^. is the unit tensor.
The contribution of molecular diffusion to hydrodynamic
dispersion is small when compared to mechanical dispersion and for
any practical purpose may be neglected. The major ions in
groundwater (Na+, K+, Mg2+, Ca2+, CT, HCOj^SO^') have diffusion
coefficients in the range 1 x 10"9 to 10"9 mVs at 25°C (Robinson and
Stokes 1965). However, its effects cannot be neglected for underground
injection of hazardous wastes where the injection rates are in the order of
centimeters per year for very fine soils (e.g., clays).
The coefficient of mechanical dispersion is usually expressed as a func-
tion of the velocity of groundwater and to the coefficient a. .. , called the
dispersivity of the porous medium (Bear 1972, 1979). The dispersivity is a
property of the geometry of the solid phase.
For isotropic porous media, the following equation can be derived (Bear
1979):
V.V.
Dij = °TV6ij + K - aT> -
89
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where a, and a-r are the longitudinal and lateral dispersivity, 6.. is the
Kronecker delta, V^ and Vj are components of the flow velocity in the i and j
direction respectively, and V = |v|, the magnitude of the flow velocity or in
Cartesian coordinates with velocity components Vx and Vy
_2
D = 0 V 4 (0 - a ) (17a)
xx T L T -
V
D = D = (a - a ) -2L^ (17b)
xy yx L r - ^
_2
D = a V + (a - a ) ^ (17c)
yy T L T -
D = a V. (17d)
zz T
If one of the axes coincides with the direction of the average uniform
velocity V, for example the x-axis, equations (17a-d) become
D = D = a V (18a)
L xx L
D = D = D =a V (18b)
T yy zz T
where D|_ and Dj are the coefficients of longitudinal and transversal disper-
sion, respectively.
Dispersivity is influenced by vertical and horizontal permeability, per-
meability variations, and degree of stratification (Giiven et a. 1984, Black
and Freyberg 1987). Because large solute plumes encounter more permeability
variations than small plumes, dispersivity tends to increase and to approach
some maximum asymptotic value (Gelhar et al. 1979). The difference between
dispersivity values measured in the laboratory and evaluated in the field may
be attributed to the effects of heterogeneity and anisotropy (Pickens and
Grisak 1981a,b, Neuman et al. 1987). The values obtained from tracer tests
are equivalent dispersivities that represent dispersion between the measuring
point and the injection point (Anderson 1984).
90
-------
Because of the difficulties in measuring dispersivity, both longitudinal
and lateral dispersivities are often determined during calibration of the
model. The common assumption is that the medium is isotropic with respect to
dispersivity, which implies isotropy with respect to hydraulic conductivity.
In practice, this is acceptable because most models used for solving field
problems are two-dimensional with vertically averaged hydraulic properties and
because generally the horizontal hydraulic conductivity is much larger than
the vertical hydraulic conductivity. It should be noted that increasingly
stochastic formulations are used to describe the dispersion process (Gelhar
1986, Smith and Schwartz 1980, Uffink 1983).
The partial differential equation for solute transport, including disper-
sion, convection, and a sink/source term may be expressed as (e.g., Anderson
1984)
[dispersion] [convection] [sink/source]
where C is concentration of solute, C1 concentration of solute in the source
or sink fluid, D^j coefficient of dispersion, and V. seepage or pore velocity.
The seepage velocity is calculated as
i n ax. n '
J
The hydraulic head, h, is obtained by solving equation (9) and q by
equation (2).
Adsorption--
Chemicals may partition between volatilized, adsorbed, and dissolved
phases. An adsorbed chemical will migrate away from the source of pollution
at a different rate than a nonsorbed chemical.
If equilibrium-controlled sorption is considered for adsorption/
desorption between solid and liquid phase, equation (19) may be expressed as
(Konikow and Grove 1984)
3X,
where pb is the bulk density of the solid and S is the concentration of solute
adsorbed on the solid surface.
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The relationship between adsorbed concentration (S) and liquid concentra-
tion at equilibrium (C) is called the adsorption isotherm:
S = S(C) . (22)
This relationship is obtained in laboratory experiments where the temperature
is kept constant and the reactions are allowed to reach equilibrium. Several
types of models for adsorption or ion exchange isotherms exist. Most fre-
quently used isotherms are
Linear S = KtC + K2 (23)
Langmuir S = , ! r (24)
1 T ^2^
Freundlich S = KjCK2 (25)
where K4 and K2 are empirically derived constants. All adsorption models
represent reversible adsorption reactions. Generally two or more transport
equations have to be solved for multi-ion transport problems.
The simplest isotherm is given as
S = KdC (26)
where K^ is the distribution coefficient:
., _ mass of solute on the solid phase per unit of solid phase .
d ~ concentration of solute in solution
Distribution coefficients for reactive nonconservative solutes range from
values near zero to 10 ml/g or greater (Mercer et al. 1982).
Incorporating equation (26) into equation (21), the advection-dispersion
equation is given in the form
3 /n \ d /r\7 ^ - R ^ (?7\
,\w \U4 -i ^w / ~ *« {** A i ~ r. ~ " »+ V4-'/
where R, the retardation coefficient is given by
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R = 1 + Kd. (28)
As a result of sorption, solute transport is retarded with respect to
transport by advection and dispersion alone. Sorption reduces _the apparent
migration velocity of the center of a plume or a solute front (v ) relative
to the average groundwater flow velocity (vqw)> °r
> 1 (29)
For Kj values that are orders of magnitude larger than 1, the solute is essen-
tially immobile. Sorption capacity of geologic deposits is given in this
order: gravel < sands < silts < clays < organic material (Mercer et al.
1982). If no sorption occurs, the retardation factor is equal to 1.
It should be noted that a (small) portion of the solute will move signi-
ficantly faster than the plume center due to the heterogeneity of the rock.
Transf ormati on/Degradati on
Transformation and degradation processes determine the fate and persis-
tence of chemicals in the environment. The key processes include biotransfor-
mation, chemical hydrolysis, and oxidation/reduction. The transformation and
degradation processes are generally lumped as a reaction term in the solute
transport equation. Reactions are usually represented by an effective rate
coefficient which depends on a number of variables such as organic matter
content, water content, and temperature. For simplification purposes, how-
ever, a first-order constant rate is usually employed in the analysis. For
decay it is written as (Konikow and Grove 1984)
|f - - yC (30)
in which y is the rate constant.
The solute (tracer) may undergo radioactive or biological decay
|f = - xC (31)
where x is the decay constant and can be calculated if the half-life of the
tracer tO is known:
x - . (32)
k
Including decay and retardation and assuming decay rates are the same for
sorbed and mobile species, equation (27) becomes
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Biodegradation
Biodegradation In groundwater refers to chemical changes in solute or
substrate due to microbial activity. Reactions can occur in the presence of
oxygen (aerobic) or in its absence (anaerobic). Research related to
biodegradation include the work of Troutman et al. (1984), Borden et al.
(1984, 1986), Borden and Bedient (1987), and Barker and Patrick (1985).
Modeling efforts include the work of Sykes et al. (1982), Borden et al.
(1984), Borden and Bedient (1986), Bouwer and McCarty (1984), Molz et al.
(1986), and Srinivasan and Mercer (1988).
Studies indicate that the number of electrons must be conserved in all
biochemical reactions (Srinivasan and Mercer 1988). In such reactions, a
reduced product (called electron acceptor) exists whenever a product has
carbon atoms in a higher oxidized state due to the loss of electrons. For
example, in aerobic reactions oxygen is the electron acceptor and is reduced
to water. In anaerobic systems NO " is the electron acceptor and is reduced
to N02~, N20, or N2.
Modeling approaches can be divided roughly into two: (1) an approach that
uses the biofilm concept to simulate the removal of organics by attached
organisms (e.g., Molz et al. 1986), and (2) an approach that assumes that
microbial population and growth kinetics have little effect on the contaminant
distribution (Borden et al. 1984, Srinivasan and Mercer 1988). Both
approaches apply Monod kinetics (see e.g., Lyman et al. 1982), or a modified
form of them, to reduce the required number of equations.
Application of the first approach by Molz et al. (1986) has resulted in a
set of five coupled nonV',,iear equations that need to be solved simultaneously
to calculate the following:
Concentration of substrate
Concentration of oxygen
Substrate concentration within the colony
Oxygen concentration within the colony
Number of organism colonies per unit volume of aquifer
Three of the five equations are partial differential equations and two
are algebraic equations. Microcolony kinetic parameters are needed for the
analysis. The authors applied their approach to a one-dimensional problem for
illustration purposes and performed a sensitivity analysis. They concluded
that biodegradation can have a major effect on the contaminant transport when
proper conditions for growth exist.
Application of the second approach by Borden and Bedient (1984) and
Borden et al. (1986) has resulted in three partial differential equations
describing contaminant concentration, oxygen concentration, and concentration
of microbes in the solution. The authors solved the system of equations for
one- and two-dimensional problems dealing with hydrocarbon contamination.
They developed a code (BIOPLUME II) that is a modification of an existing two-
dimensional solute transport model based on the method of characteristics
(Konikow and Bredehoeft 1978).
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Volatilization--
Volatilization is defined as the loss of a chemical in vapor from soil
and plant surfaces. This process is controlled by the availability of vapor
at the soil surface and the rate at which this vapor is carried to the atmos-
phere. In addition to the saturated vapor pressure of the chemical under con-
sideration, a number of factors affect the actual volatilization rate from the
soil surface, including soils and atmosphere characteristic, and management
practices. Interaction among these components is also a controlling factor.
Generally, chemicals can partition into adsorbed, dissolved, and vapor
phases. The vapor density is related to solution concentration under an
equilibrium condition by a linear relationship of the form (Hern et al . 1986)
C = KC , (34)
which is known as Henry's law, where K is Henry's constant. A similar
relationship was described earlier regarding partitioning into adsorbed and
dissolved chemicals.
Vapor movement from the soil to the atmosphere is usually modeled by
applying Pick's Law of diffusion (Hern et al . 1986). Chemical movement in
gaseous form through soil is described by an extension of the same law. The
vapor flux is related to concentration gradient by
qv = - i2(a)DGvCG (35)
in which n2 is a tortuosity factor and D is the dispersion coefficient in
air. Millington and Quirk (1961) defined n2 empirically, by
10/3
n2 - -hr- (36)
n
in which a is air content and n is soil porosity. Equation (35) can be added
to the general solute transport equation as a sink term.
Plant Processes--
Vegetation is an integral part of the terrestrial ecosystem. Chemicals
applied to land surfaces may be intercepted by plant leaves where volatili-
zation, photolysis, or biodegradation occur in addition to absorption by the
plant itself. At a later time, the chemicals may be washed off to the soil by
rain or irrigation water, where they contribute to solute transport in the
soil. Plant roots also affect the transport phenomena by uptaking the chemi-
cals into the plant where they can accumulate in different parts of the plant.
Chemicals may move to the leaves where they are subject to transformation and
degradation processes. The remaining chemicals may return to the soil follow-
ing plant death or leaf fall.
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Additional modeling difficulties result from the dynamic nature of
plants, caused by changes in their condition from the time of planting until
harvesting. Also, stem and root penetration can influence the transport
phenomena by changing the hydraulic properties of soil.
Plant models have been introduced by plant and soil scientists (see
Thornley 1976, Tillotson et al. 1980, Campbell 1985). Molz (1981) compiled a
11st of extraction functions used by various researchers to represent water
uptake by plant roots. An exponential depth function adequately describes the
extraction patterns for a number of crops under relatively stable conditions,
such as a fully developed crop under high frequency irrigation (Feddes et al.
1974). However, a simple uniform function may be employed for chemical trans-
port within a large soil depth.
HEAT TRANSPORT MODELS
Analysis of heat transport in soils and groundwater aquifers is an impor-
tant area of research and has many practical applications. Heat transport
affects other transport processes directly and indirectly, e.g., contaminant
transport. Conversely, heat transport might be affected significantly by
other physical and chemical processes. Overlooking such interactive effects
may lead to unacceptable errors. Direct effects on pollutant transport are
attributed to, for example, changes in the soil/groundwater flow field due to
freezing/thawing on the chemical transformation rates due to temperature
changes. The indirect effects are due to the fact that some parameters, e.g.,
hydraulic conductivity, are to a certain extent heat dependent.
Major research activities of heat transport processes in the past con-
cerned high temperature geothermal systems with the best conditions for energy
production. Accordingly, attention has been paid to models for simulation of
complex systems such as water-steam-rock (e.g., Grant et al. 1982). Further
applications of research relevant to heat transport in the subsurface include
aquifer thermal energy storage (Mercer et al. 1982). There, warm waste water
(e.g., from cooling systems) is injected into a confined aquifer during the
warm season. During the cold season, warm water is recovered and utilized for
heating purposes. The resulting cold water is reinjected far enough to pre-
vent accelerating the cooling process of the warm water. An efficiency of
heat recovery of up to 60% has been reported in the literature (Molz et al.
1978).
Another area of growing interest related to heat transport concerns
modeling multiphase transport under freezing/thawing soil conditions. Diffi-
culties in mathematical formulation, in solution approaches, and in parameter
estimation are currently major hurdles toward the development of practical
solutions to this complex problem.
Mathematical formulation of the general transport problem in the subsur-
face involves a coupled system of equations describing the flow of water,
heat, and solutes. The equations are nonlinear in principal, because the
parameters are a function of at least one dependent variable (temperature)
interrelated by equation of state. In such a case, only numerical techniques
might provide a solution. Numerical methods used in heat transport models
were reviewed, e.g., in the report of Pinder (1979); in more general terms,
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heat transport models were described in Bachmat et al. (1978) and van der
Heijde et al. (1985a).
This section reviews briefly the theory of flow of water and solute in
the subsurface under nonisothermal conditions. Details of the formulations
may be found elsewhere (e.g., Lunardini 1981 and Farouki 1986). An up-to-date
list of available models is provided in Appendix D.
The Heat Transport Equation
Groundwater may appear as ice, liquid or steam, interacting with an aqui-
fer. The heat transport equation is derived by applying the energy balance
principles concerning the transport, storage, and external sources/sinks of
heat. Dependent variables in this equation may be temperature or enthalpy.
In general, a state of thermodynamic equilibrium is assumed, i.e., the temper-
ature 1n different constituents (solids and fluids) is equal within the repre-
sentative elementary volume for which the equations are derived. The pro-
cesses that contribute to heat transport include conduction, convection, dis-
persion, radiation, evaporation/condensation, and freezing/thawing. Heat
conduction occurs in all soil constituents, i.e., solids, water in different
phases, and air. In air and vapor, heat conduction is caused by collision
between molecules that increases their mean kinetic energy as heat moves from
wanner to cooler regions. In liquid water, the same process occurs in addi-
tion to energy transfer by breaking and forming of hydrogen bonds. In crys-
talline solids, e.g., quartz, increased atomic vibration at one end will cause
the neighboring atoms in the lattice to follow suit. Heat flux due to conduc-
tion is given by
Qcd - xQ7T (37)
in which T is temperature and x is the thermal conductivity of the porous
medium (water plus solid), defined as the rate which heat energy flows across
a unit area of the soil due to a unit heat gradient, where *0/pC0 is assigned
thermal diffusivity (e.g., W.B. Bird, 1960, p. 246) in a porous matrix.
Free or forced heat convection contributes to heat transfer. Free con-
vection develops due to the existence of a temperature gradient resulting in
density changes. On the other hand, forced convection is due to currents of
fluids that move through pores of soils as a result of head gradients. For a
fluid with velocity V the convective flux is given by
Qcn ' VwCwT <38>
in which PW and Cw are density and specific heat of the fluid, respectively.
Dispersion, sometimes referred to as lateral mixing or turbulent diffu-
sion, is caused by mixing in the pore system. Dispersive heat flux is given
by
(39)
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in which 6 is the heat dispersion coefficient
& = B|VJ, (40)
where e is heat dispersivity analogous to solute dispersivity, although their
magnitudes may differ in the same aquifer, based on field measurement in
France (de Marsily 1986).
Radiation, usually an unimportant process in heat transport in soils, is
the emission of heat from bodies that have temperatures above absolute zero.
Heat energy is emitted in the form of electromagnetic waves and travels across
a vacuum as well as gases, liquids, or solids. The flow of heat depends
mainly on the temperature of the radiating body, namely,
QR = oeAT (41)
which is known as the Stefan-Boltzmann law. In equation (41), A is the sur-
face area, o is a constant, and e the emissivity of the surface (0
-------
Ignoring air movement, the general heat transport equation can thus be
derived by applying the mass balance principal to yield
It tn VCJT} + sh (44a)
or
PWCW 6] VT + Vw PCWT} = |t- {£[0. pCjT} + S, (44b)
in which Sh is a source/sink term that includes radiation, evaporation/conden-
sation, or freezing /thawing effects. The subscript j in equation (44) refers
to unfrozen water and ice (i.e., j=w for water and j=i for ice). Simplified
versions of equation (44b) have been utilized in the analysis, especially in
the absence of phase change processes. For example, for a fully saturated
aquifer, if heat conduction and density changes are neglected, and if heat
capacity was taken as constant, the equation becomes
-ah+Sh (45)
in which a. is the heat capacity of the aquifer.
HYDROCHEMICAL MODELS
Hydrochemical models are used to analyze system geochemistry independent
of physical mass transport processes. The models can simulate chemical pro-
cesses that regulate dissolved species concentrations, including mixing, ad-
sorption, ion-exchange, redox reactions, complexation, and dissolution/preci-
pitation reactions.
The focus of this section is on thermodynamic models for systems at
chemical equilibrium (though EQ3NR/6 and PROTOCOL (listed in Appendix E] con-
tain submodels that do not require equilibrium assumptions). Equilibrium is
rigorously defined for closed systems only, i.e., systems that cannot exchange
matter with their surroundings. Since all natural groundwater systems are
open systems, the time-invariant condition describing the chemical state of
the groundwater system is steady-state, not equilibrium (Rice 1986). There-
fore, application of thermodynamic equilibrium models to groundwater systems
must be done with care. Although chemical equilibrium in some groundwater
environments may be assumed for time scales of tens of hundreds of years
(Morgan 1967), certain processes may not approach equilibrium for much longer
periods of time; additionally, some reactions may be near equilibrium, while
others in the same system are not.
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Although a system may not be at equilibrium, the thermodynamic models may
be used to indicate how close or far a reaction is from equilibrium; there-
fore, although equilibrium models do not indicate the rate at which a reaction
occurs, they do yield a description of the state towards which the system is
tending (Rice 1986).
Equilibrium models can be valuable tools in predicting the behavior of
complex geochemical systems. They do have limitations, however, and only by
understanding the conceptual as well as the computational model can they be
properly applied and interpreted. The following discussion deals with the
theoretical derivation on which the thermodynamic equilibrium models are
based, and limitations of those models; recent articles by Nordstrom et al.
(1979), Jenne (1981), Kincaid et al. (1984), and Nordstrom, Kirk, and Ball
(1984) review the actual models and computer codes. An overview of currently
available computer codes is included as Appendix El and E2.
Gibbs Free Energy and Equilibrium Constants
In any system, a process is determined to be at equilibrium when the
energy function used to describe it is at a minimum. For a closed system at
constant temperature (T) and pressure (P), the energy associated with a geo-
chemical process is described by the Gibbs free-energy function (Denbigh 1971,
Lewis and Randall 1961, Moore 1972), which is defined as the total Gibbs free-
energy of the products (final state) minus that of the reactants (initial
state)
AG = cGc + dGQ - aGA - bGfi (46)
for the general chemical reaction
aA + bB <> cC + dD (47)
where upper case letters represent the species, and lower case letters the
appropriate stochiometric coefficients.
The Gibbs molar free-energy for any individual species is related to the
activity ai of the species by the expression
G. = G? + RT an a. (48)
where G. represents the free-energy of the species in a standard state condi-
tion, and R is the gas constant.
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The expression for AG in equation (46) can be rewritten in terms of equa-
tion (48) as
a ca d
AG = AGO + RT in aC aD . (49)
a aa b
aA aB
At equilibrium, the ratio of activities raised to the power of the respective
stoichiometric coefficients is equal to the equilibrium constant, K (law of
mass action), and the change in total free-energy, AG, is zero; therefore
AG° = -RT fcn K . (50)
Electrolytes and Activity Coefficients
Because equilibrium constants are defined in terms of activities, or
effective solute concentrations, it is necessary to relate these quantities to
experimentally measurable concentrations. The relationship (Moore 1972)
a = y., (51)
where ri is the activity coefficient and m^ the concentration of a component i
considered to be the solute, is based on a standard state that obeys Henry's
Law. The solution becomes ideal (-\. = 1) at low solute concentrations:
11m =r = 1 . (52)
n 0 mi
For the case of more than one solute in solution, all the solutes must simul-
taneously conform to the limit in equation (52).
If the expression for activity in equation (51) is substituted into
equation (48), the result may be written
RT in m + RT in Y , (53)
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o
where the terms G. + RT dn m. represent the free energy of component i in an
ideal solution, i.e., one that follows Henry's Law over the entire range of
concentrations. Thus the term involving the activity coefficient is a measure
of the real solution's deviation from ideality.
It is possible to calculate single-ion activity coefficients from only
electrostatic considerations. This was first done successfully with the
Debye-Huckel theory, which manages to provide surprisingly good results
despite several severe contradictions and physically incorrect assumptions
(Bockris and Reddy 1970). Essentially, the Debye-Huckel theory ignores short-
range interactions between ions of the same charge, and thus its predictions
become poorer for more concentrated solutions in which ions with the same
charge increasingly affect each other, and those with opposite charge form ion
pairs through electrostatic attraction (Robinson and Stokes 1959).
Virtually all current computer models are based on the idea of ion
pairing, which was developed independently by Bjerrum (1926) and Fuoss and
Kraus (1933, Fuoss 1958). With the inclusion of these short-range ionic
interactions, the modified Debye-Huckel equation for species i is
Az?!*8
log Yi = 3LJ , (54)
1 1 + B a.P
Y i
in which A and B are the Debye-Hiickel constants that depend on dielectric
constant and temperature, z^ is the ionic charge, a^ an ion size parameter,
and I the solution's ionic strength, defined by the expression
2
I = % i z.m.. (55)
In equation (54) the numerator accounts for long-range coulombic interactions,
the denominator for short-range interactions that arise from treating the ions
as hard, finite-sized spheres. As a correction for short-range ion-solvent
interactions as well as short-range ion-ion interactions that are not
accounted for by the hard-sphere model, a linear term is often added empir-
ically to equation (54) or to some variation of it. The extended Debye-Huckel
equation which incorporates the linear term, is given by
log y. = Y 1 . + b. I
1 1 + P 1
(56)
where b^ is an ion-dependent empirical constant. The Davies equation (Davies
1967), a modified form of the extended Debye-Huckel equation, given by
log Y = - -JLT - 0.21 (57)
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is frequently used to determine ri since it is supposedly applicable to solu-
tions of ionic strength up to 0.5 M (Stumm et al. 1982); the Debye-Huckel
equation is valid only up to about 0.1 M. Thus computer models that calculate
activity coefficients by either (or both) of these equations are restricted to
fairly dilute ground waters.
Oxidation-Reduction Reactions
Of all the reactions included in any of the computer models, only a small
fraction consists of oxidation-reduction reactions. The model REDEQL-UMD
(Harriss et al. 1984), for example, lists only twenty-two redox couples, and
its authors caution that the kinetics of many oxidation-reduction reactions
may be slow.
The emf or Nernst potential (E) for any reaction involving electron
transfer can be determined from the expression (Moore 1972)
aa ad
RT ar an
E = E°=S*n-rj' {58)
aA aB
where n is the number of electrons transferred, F is the faraday, and the
chemical notation refers to the general reaction in equation (47). The term
E° is the standard emf of the redox reaction and can be calculated from the
standard electrode potentials of the half reactions that sum to the overall
reaction (Latimer 1952).
The fact that oxidation-reduction reactions can be characterized electro-
chemically in this manner has led to the idea that a groundwater system's
"redox state" can be described in terms of a single parameter, either an over-
all Nernst potential, usually designated Eh (Freeze and Cherry 1979), or the
negative logarithm of the electron activity designated pe (Truesdell 1968) in
analogy with pH. The idea that a single parameter like pe or Eh can charac-
terize an entire system is based on the assumption that all the oxidation-
reduction reactions occurring in the system are at equilibrium. That this is
not true has been stated explicitly (Morris and Stumm 1967, Jenne 1981, Wolery
1983), but suggestions that a particular redox couple may be used as an over-
all indicator of the redox state of the system continue (Liss et al. 1973,
Cherry et al. 1979).
Lindberg and Runnel Is (1984) have quantitatively demonstrated the inaccu-
racy inherent in characterizing an entire ground-water system by a single
redox parameter. The field-measured Eh value for each of approximately 600
water analyses was compared with the Nernst potential calculated from the data
on ten different redox couples by means of the computer model WATEQFC (Runnels
and Lindberg 1981). As these same authors (Lindberg and Runnels 1984) state:
"The profound lack of agreement between the data points and the dashed line
[which represents equilibrium points] shows that internal equilibrium is not
achieved. Further, the computed Nernstian Eh values do not agree with each
other. ... If any measured Eh is used as input for equilibrium calcula-
tions, the burden rests with the investigator to demonstrate the reversibility
of the system."
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Because many of the important oxidation-reduction reactions are very slow
and some are even irreversible, it is virtually impossible that any natural-
water system can reach equilibrium with respect to all of its redox couples.
Improvements in this area of computer modeling will require the inclusion of
experimental data for each of the major redox couples in the water system
under study.
Limitations of Hydrochemical Models
Each reaction in the set listed for a particular model must be character-
ized by an equilibrium constant. In any geological environment there is an
extremely large number of possible reactions, and this is reflected by the
databases of many of the models, some of which consist of several hundred
reactions. These include not only reactions occurring solely in the aqueous
phase, but also heterogeneous reactions between dissolved species and solid
phases, such as precipitation/dissolution and ion exchange, as well as oxida-
tion/reduction and degradation reactions that may be catalyzed by microorgan-
isms in the soil.
At least three fundamental problems are associated with such tabulations
of thermodynamic data. A particular species may simply be omitted from the
database, so even though it is present in the physical system being modeled,
it will obviously not appear in the final speciation results nor will its
effect on the speciation of other elements. The program WATEQ3 (Ball et al.
1981), for example, is an extension of WATEQ2 (Ball et al. 1979) through the
addition of several uranium species, but the expanded database does not
include vanadium, which frequently occurs naturally with uranium, and thus the
influence of minerals containing both elements cannot be taken into account.
Even when the database does contain particular minerals, thermochemical
data for them may not be known with very great accuracy. This problem is
frequently compounded by other uncertainties such as nonstoichiometry,
solution-dependent composition with respect to replaceable cations, metastable
forms, and variation in free energy and solubility with the degree of crystal-
linity (Stumm and Morgan 1981).
And third, the tabulated thermodynamic data is also usually not checked
for internal consistency. Because the data for a particular reaction may come
from more than one source, there is no guarantee that all calculations were
made with consistent values of the necessary auxiliary quantities or that the
data satisfies the appropriate thermodynamic relationships. In a study done
by Kerrisk (1981), experimental solubilities of CaC03, CaSCL, and BaS04 in 0-4
M NaCl solutions were compared to those calculated using four different com-
puter models: WATEQF (Plummer et al. 1976), REDEQL.EPA (Ingle et al. 1978),
GEOCHEM (Sposito and Mattigod 1980), and SENECA2, a modification of the
earlier SENECA (Ma and Shipman 1972). Although the ionic strengths exceeded
the limitations of the modified Debye-Huckel and Davies equations, the study
indicated that results for the four models frequently differed even at low
ionic concentrations. Calculations on CaC03 by GEOCHEM differed markedly from
experimental observations even below 0.5 M; one possible explanation for this
is the inclusion of an equilibrium constant of about 4 for the formation of
the ion pair CaCl+. This particular 1on pair is omitted from the other three
computer models, and in fact Garrels and Christ (1965) note that at ordinary
temperatures chloride forms no significant ion pairs with any major cation of
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natural waters. This clearly points to some of the dangers inherent in the
ion-air method employed in equilibrium models, and indicates another potential
problem associated with the thermodynamic databases selected for the different
geochemical models.
Modeling Non-Dilute Solutions
A different approach to the problem of ionic interactions in solution is
the specific-interaction model (Pitzer 1973), which has been applied to sea-
water (Whitfield 1975, Eugster et al. 1980) and hydrothermal brines (Weare
1981, Barta and Bradley 1985). It has been long assumed that the results from
Debye-Hiickel theory could be extended by the addition of power-series correc-
tions (Weare et al . 1982):
DH
log Y. = log Y. + r B...(I)m.. + r
j J
DH
where Y^ is the Debye-Hiickel activity coefficient and 8^(1) and C-j,^ are the
second and third virial coefficients respectively (Lewis and Randall 1961),
the latter of which is required only for solutions of ionic strength greater
than 3 M. Pitzer (1973) has succeeded in modeling the second virial coeffi-
cient B^j as a function of ionic strength and has also developed a Debye-
Hiickel term of the form
z
log Y?H = - Y 1 . + I »n(l + bl%), (60)
1 1 + bP b
which fits experimental data better than the extended Debye-Huckel term given
by equation (56).
Although the specific-interaction model is more complicated mathema-
tically, it has the distinct advantage of not explicitly including ion pairs
for ions that are only weakly associated, such as Ca2+ and Cl~. Instead, the
second virial coefficient accounts for these weak associations through its
dependence on the ionic strength (Weare et al. 1982). Weare and his coworkers
(Harvie and Weare 1980, Eugster et-al. 1980, Harvie et al. 1982, Harvie et al.
1984), have begun applying this model to simple electrolyte systems. The most
complicated thus far is one containing only 11 different ionic species, but
the preliminary results appear to be a significant improvement over calcula-
tions based on ion pairing. There is still considerable work to be done
before the specific-interaction model can be applied to groundwater in
general, but it clearly has the advantage of being able to treat more concen-
trated solutions than ion-pair theory. Pitzer's equations have already been
or are currently being incorporated into at least three geochemical models:
EQ3NR (Wolery 1983), SOLMNEQ (Kharaka and Barnes 1973), and PHREEQE (Parkhurst
et al. 1980).
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STOCHASTIC MODELS
Uncertainty due to the lack of information about the system or to the
variable nature in space and time of certain properties or processes is
increasingly incorporated in the analysis of groundwater systems. Incor-
porating information uncertainty in stochastic analysis can produce a best
estimate of output (the mean) and a measure of the uncertainty of the estimate
(the variance). On the other hand, if intrinsic uncertainty is included, the
model results can describe head (for example) as a stochastic process
resulting from an input (e.g., hydraulic conductivity) represented by a
stochastic process. In other words, head is represented, as is the case with
hydraulic conductivity, as a mean trend with superimposed fluctuations
described by the covariance structure. In addition, questions regarding
spatial structure, statistical homogeneity, and ergodicity of the system (see,
e.g., Bakr et al. 1978) need to be addressed if intrinsic uncertainty is
incorporated.
Recent review of the stochastic approach to analyze uncertainty due to
intrinsic heterogeneity was introduced by Neuman (1982), El-Kadi (1984) and
Freeze et al. (1989). Deterministic models fail because correct parameter
values needed for models are not known at all locations other than those few
available measurements. Recent research in stochastic analysis can be divided
into: (1) a geostatistical approach to estimate uncertainty in input para-
meters (e.g., Hoeksema and Kitanidis 1985), and (2) a simulation approach to
assess the impact of uncertainty of these parameters on model results (e.g.,
Bakr et al. 1978). In addition, the stochastic analysis has been used to
study the physics of flow and transport in fractured and porous media. For
example, it can be used to illustrate how heterogeneities affect flow patterns
(Smith et al. 1989), to analyze the impact of spatial variability on macro-
scopic dispersion (e.g., Gelhar and Axness 1983, Smith and Schwartz 1984), and
to estimate effective parameters that allow the representation of the true
heterogeneous media by an equivalent homogeneous one (e.g., El-Kadi and
Brutsaert 1985).
Two issues stand central in the stochastic approach.
The first issue is describing the spatial variability in probablistic
terms. In general, statistical distributions of model parameters can be esti-
mated through the use of the geostatistical approach to analyze available data
(e.g., Hoeksema and Kitanidis 1985). Given a set of data points located at
random in space, the geostatistical approach (also known as kriging) offers a
best linear unbiased estimation of a regionalized variable (e.g., hydraulic
conductivity) at various locations. A spatial structure is used in the analy-
sis, through the variogram which indicates the degree of correlation between
values of the variable as a function of distance. In general, an assumed
distribution of the variable (e.g., normal or log-normal) is employed and the
first few moments of that distribution are used as input to the stochastic
simulation model. These moments include the expected value and the variance
and covariance of the variable.
The second issue involves mathematical techniques to solve the stochastic
equation. The available approaches can be divided into analytical, quasi-
analytical, and numerical. The analytical techniques include derived distri-
butions (Benjamin and Cornell 1970) that provide an explicit expression of the
106
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probability distribution function (PDF) of the output variable (e.g., hydrau-
lic head) as a function of the PDF for the input variable (e.g., hydraulic
conductivity). This approach also includes the spectral analysis technique
(Bakr et al. 1978, Gelhar and Axness 1983) that estimates the expected value
and covariance of output parameters.
The quasi-analytical techniques include finite-order (first- or second-
order) or perturbation analyses (Sagar 1978, Dettinger and Wilson 1981). They
also provide expressions for the first few moments within a finite-element or
a finite-difference framework. The numerical approach employs the Monte-Carlo
technique, i.e., the repetitive solution of the deterministic problem for a
large number of realizations, each with a set of parameters that is an equally
probable representation of the actual set of parameters. The final product is
a set of answers that can be analyzed to estimate the PDF or the first few
moments of the distribution of the output variable. Example applications of
the technique are presented by Smith and Freeze (1979) and El-Kadi and
Brutsaert (1985).
Rather than a single answer that results from a deterministic model, the
stochastic model provides a range of answers that carl be expressed through a
PDF or a number of the distribution moments.
A decision-theory framework based on the probabilistic structure of the
measured variables can be used to assess the worth of data (Massman and Freeze
1987). An objective function that includes benefits, costs, and risks is
optimized, allowing for assessment of the economic consequences of either
planning alternative measurement strategies for a new site, or adding new
measurements to an existing data collection strategy. When additional costs
are no longer balanced by the risk reduction, additional measurements are not
justified. This probabilistic modeling framework can also be used to make
decisions regarding alternative actions, such as selecting between alternative
sites for waste disposal or between alternative engineering designs for a
specific site.
FLOW AND TRANSPORT IN FRACTURED ROCK
Fracture Systems
Metamorphic and igneous rock generally have very low matrix porosities.
As a result, primary permeabilities are so small that they are often regarded
as zero. Significant porosities and permeabilities, however, are developed
through fracturing and weathering of the rock, especially in association with
faults (Davis and DeWiest 1966). This type of permeability is referred to as
secondary permeability. The average porosity of metamorphic rocks decreases
rapidly with depth. Joints, faults and other fractures tend to close at depth
because of the weight of the overlying material. However, some openings exist
at all depths.
Sedimentary rock is often quite porous. Most fine-grained detrital rocks
like shale, claystone, and siltstone have relatively high matrix porosities,
but very low permeabilities (Davis and DeWiest). Coarser-grained sedimentary
rock like sandstone can pair relatively high matrix porosity with a signifi-
cant matrix permeability. Hydraulic properties of both types of sedimentary
107
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rock might be enhanced largely if fractures are present. Furthermore, even in
packed noncemented granular media, major cracks, macropores, and holes may be
present. Such fractures occur over many length scales from microscopic to
regional scale and have a multitude of geometrical characteristics.
As the original porosity and permeability of carbonate rock (mostly lime-
stone and dolomite) are often modified (and reduced) rapidly after deposition,
a wide range of matrix properties might be encountered in the field. Although
original pore space might be retained in older deposits, other forms of poro-
sity are more important such as fractures and solution openings created by
dissolution of the carbonate rock along bedding planes.
Flow in Fractures
The flow behavior of fractured rocks is often characterized in some com-
plex manner by the presence of discontinuities in the rock. These discontin-
uities can consist of cracks, fissures, fractures, joints, and shear zones and
occur usually in sets of families with similar geometries (Witherspoon et al.
1987). Flow in such systems may take place through a channel network of
interconnected fractures. (Streile and Simmons 1986). Flow may also occur
simultaneously through the porous component of the media, if present. In the
latter case, the flow system is often referred to as a dual porosity system
with matrix porosity as primary porosity and fracture porosity as secondary
porosity (Figure 25).
The major issues in analyzing fluid flow through a network of fractures
where the rock matrix is essentially impermeable, are determining the perme-
ability of the fracture system and establishing whether or not such networks
behave more or less as a porous medium. It is often observed in the field
that rock masses contain sets of discontinuous fractures of finite size within
a single plane. As a result, the degree of interconnection between the assem-
blage of discontinuous fracture planes has a major influence on the hydraulic
conductivity of the total system (Witherspoon et al. 1987). The density, or
number of fractures per unit volume of rock, is another important feature.
Finally, the orientation will determine those directions along which the
fluids may flow within the rock mass. Thus, characterization of a fracture
system is considered complete when each fracture can be described in terms of
its size, location, effective aperture and orientation (Figure 26) and the
global geometry of the system in terms of interconnectivity of fractures is
established. It should be noted that the extent of aquifers is commonly one
to three orders of magnitude larger than the aquifer thickness; fractures may
extend over the vertical thickness of the aquifer, but rarely traverse its
length.
To understand fluid flow in rocks of low permeability, it is necessary to
investigate directional characteristics of hydraulic properties. In many of
these hydrogeologic systems, the major channels of mass transport are frac-
tures. Fracture systems can be grouped into continuous and discontinuous
systems. Continuous systems consist solely of conductive fractures that are
very long compared to the region under study. Discontinuous systems consist
of finite-length fractures. The pore region of discontinuous systems consists
of dead-end zones, isolated zones and conductive zones. Part of the pore
region in continuous systems may become nonconductive due to the orientation
of the hydraulic gradient (Endo and Witherspoon 1985) (Figure 27) or local
flow direction might be altered significantly (Figure 28).
108
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porous blocks
Domain of
Porous Media
Continuum
Domain of
Fracture
Continuum
Domain of
Overlapping
Continua
Fig. 25. Dual porosity and scale where continuum approach applies (after
Huyakorn 1987, pers. comm.).
-------
SET 1
SET 2
CENTERS
ORIENTATIONS
LENGTHS
APERTURES
SUPERIMPOSED
RESULT
Fig. 26. Generation of a fracture network (after Long and Billaux 1986)
110
-------
B
Fig. 27. Relationship between directional fracture properties and
orientation of observation or modeling grid (after Long and Billaux
1986).
ill
-------
direction of water movement
predicted on the basis of
water levels in wells
groundwater contours based on
water levels in wells
point of
Tracer injection
angle of
lateral dispersion
actual flow direction
(and tracer movement)
Fig. 28. Two-dimensional fracture pattern and its influence on average flow
direction versus actual flow direction (after Davis and Dewiest
1966).
112
-------
In porous media, the size, shape, and degree of interconnection of the
pores regulate the flow rate. The scale of these pores is small and for most
purposes the medium may be treated as a continuum in which macroscopic flow
properties are considered without regard to the actual flow paths of the indi-
vidual fluid particles. In a fractured rock, however, the scale of the pores
(e.g., fracture space) can be large enough that the continuum approach is not
always appropriate, although often used by applying an equivalent porous
media concept. In such cases, the network of individual fractures must be
analyzed to understand macroscopic flow and transport properties (Endo and
Witherspoon 1985).
Flow in relatively large fissures requires a discrete fracture concept-
ualization where the flow within individual fractures is modeled directly as
flow in an interconnected network of channels. The lack of precise informa-
tion on the configuration of fractures often leads to the necessity of sto-
chastic representation of fracture geometry and distribution (Streile and
Simmons 1986).
It should be noted that in unsaturated fractured porous rock, based on
capillarity and free energy considerations, moisture tends to accumulate in
the porous matrix and only if the flux exceeds the matrix capacity moisture
will move in the fractures.
The velocities in large fissures can be relatively high, sometimes
causing turbulent flow conditions. The effects of turbulent flow are pore
pressures in excess of those resulting from laminar Darcian flow (Elsworth et
al. 1985). As mentioned, conventional porous media concepts may not be appro-
priate. However, the concept of equivalent porous medium is often used for
both continuous and discontinuous fracture systems. This approach is based on
the observation that the more intersections between fractures present in a
fracture network, the more the system is likely to behave as a porous medium
(Long and Witherspoon 1985). Conditions for equivalent porous medium behavior
for fluid flow in fracture networks have been discussed by Long (1983). Endo
and Witherspoon (1985) presented a technique for evaluating porous medium
equivalence for the ratio of fluid flux to mean transport velocity, termed
hydraulic effective porosity. It should be noted that a system that behaves
as a continuum for fluid flux may not behave like a continuum for mechanical
transport.
When fractures or solution channels are primarily developed in a single
direction, the rock will be strongly anisotropic for flow. The direction of
the groundwater flow cannot be predicted by simply drawing orthogonal lines to
the groundwater level contours derived for the equivalent porous media. Some-
times, groundwater flow might occur almost parallel to such groundwater level
contours (Davis and DeWiest 1966). Figure 28 shows an example of anisotropy
in two-dimensional flow in which the head drop in all channels is proportional
to the length of the channel.
The fluid flow in a fracture will vary in a parabolic fashion across the
fracture (aperture = 2b) from a value of zero at the walls to a maximum at the
center of the fracture. This variation is due to the viscous nature of the
fluid and the resistance between fluid and fracture wall (Sudicky 1987,
pers. comm.) (Figure 29). Advection computations are generally based on the
average velocity in the fracture.
113
-------
Hydraulic conductivity used in the Darcy equation as applied to frac-
tures, is based on a hypothetical fracture geometry such as a parallel plate
concept (Figure 29). In reality, the aperture of the fracture might vary
significantly over the length of the fracture (Figure 30). To account for
such a rough-walled fracture system, the constant value of the aperture can be
replaced by a statistical average, based on a schematic asperity model (Figure
30). If only flow in the fracture itself is present, porosity is unity.
In the last ten^years research has been focused on determining the
factors that control the flow of fluids in fractured rocks. It has been shown
that if enough details of the fracture system geometry can be obtained, it is
possible to deduce a great deal about the flow properties of the system
(Witherspoon et al. 1987). However, the field data necessary to characterize
the fracture geometry are not commonly available. An extensive discussion
regarding field techniques for characterization of fractured rock systems can
be found in Nelson (1985).
Transport in Fractured Media
Contaminant and heat transport in fractured rock formations is governed
by the same processes as in granular media: advection, mechanical dispersion,
molecular diffusion, and chemical and biochemical reactions and in the case of
heat transport, conduction. However, there are some notorious differences in
the effects that fractured media can have on these processes due to the need
for a detailed description of the fluid velocities, the sparseness of the flow
channels, their unequal distribution through the rock media, and in porous
rode the interaction between the fluid in the fractures and in the rock
matrix. These effects are especially noticeable in observing dispersion and
diffusion processes (Schwartz et al. 1983, Sudicky et al. 1985).
Although for the study of the head distrbution in a fractured system the
calculation of fluxes is sufficient, for simulation of solute and heat trans-
port the velocity distribution need to be known in detail. The velocities are
determined by the active porosity (that part of the pore space in which the
fluid movement takes place), which is often much smaller than the total
porosity.
Mechanical dispersion in a single fracture consists of longitudinal dis-
persion only. Fracture width is generally too small to show any significant
variation in the distribution of mass across the fracture. A major contri-
butor to macroscopic dispersion in fractured media is the geometry of the
network of interconnected discontinuous fractures (Smith and Schwartz 1984).
The geometry directly determines the variability of the fluid velocity and the
average path length through the interconnecting fractures. In general, the
velocities in fractured rock are not normally distributed, precluding the use
of a Gaussian dispersion model. Macroscopic dispersion is further complicated
by local mixing at the connection between fractures.
114
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assumed velocity
distribution (uniform)
local
coordinates
actual velocity
distribution (parabolic)
solid boundary
Oi =angle between local
and global coordinate system
I X.
(global coordinates)
Fig. 29. Laminar flow in a fracture element bounded by two parallel planes
(after Huyakorn and Finder 1983; Huyakorn et al. 1987).
115
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asperities
macro-roughness
vortices / \
flow lines
mean gap width
Fig. 30. Geometry and schematization of a single fracture (after Elsworth et
al. 1985).
116
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Anderson (1984) concluded that (1) a significant retardation mechanism
for pollutant transport in fractures is diffusion of the contaminants into the
pores of the rock matrix; and (2) an acceleration mechanism for low-velocity
flow in fractures is dispersion within the water phase. Little is known,
however, about the magnitude of the roughness of a fracture. Difficulties in
describing the geometry and hydraulic characteristics of fractured rock in the
field are the major delays in model development and testing.
In dual porosity systems contaminants diffuse from the main fractures
into and out of micropores and dead-end fractures systems (Figures 31 and
32). They penetrate the porous rock from the fracture surfaces, resulting in
considerable broadening of the zone active in transporting contaminants as
compared with transport through equivalent porous media. Unless the source
release occurs over a very long period of time, the resulting broadening of
the zone of contamination can considerably reduce the peak contaminant concen-
tration, such as in the case of the release of a contaminant slug (Figure 33).
Flow in fractured porous media, which is a combination of flow in frac-
tures and flow in porous media, can result in transient chemical concentration
gradients between the water in fractures and pores (Cherry et al. 1984).
Although the bulk of the flow occurs in the fractures, diffusion of trace
organics and other chemicals into and out of the porous matrix can have a
strong influence on contaminant behavior (Tang et al. 1981, Grisak and Pickens
1981). This is caused in part by the fractured surfaces that come into
contact with the flow. Pollutants must come into contact with media surfaces
before chemical interactions, such as adsorption, may occur. Porous media may
also contain organic matter, which enters into reactions (Kincaid and Mitchell
1986).
Cherry et al. (1984) report that the chemical reactions occurring during
contaminant transport can be significantly different in porous media and frac-
tured rock (or fractured, fine-grained, nonindurated porous media). Advection
theory and the isotherm approach to predictive transport modeling have been
specifically developed for porous media. Measurement of adsorption parameters
for predictive modeling of fracture flow in nonporous rock (such as granite)
is very difficult. The distribution coefficient must be defined in terms of
effective surface area of reaction in the fractures instead of in terms of the
mass of solids, as is done for porous media. Cherry et al. (1984) state that
few attempts have been made to determine these properties for undisturbed
surfaces or to validate predictive models under field conditions.
Analysis of dispersion and chemical processes for contaminant transport
in fractured rock, such as shale, granite, basalt, or salt, are in the preli-
minary stage of development (Anderson 1984, Cherry et al. 1984). This type of
analysis may be needed where deep-well injection of hazardous wastes can
result in pollutant transport to the biosphere. Clay, which is also suscep-
tible to fracturing, is used as a disposal medium for municipal, industrial,
and low-level radioactive wastes. Therefore, hazardous chemical movement
caused by the possible increase of flow velocities in fractured porous media
over that seen in a uniformly porous medium is of major concern (Kincaid and
Mitchell 1986).
117
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Solute
Input-
C=C
matrix
diffusion
K\\\VS K ^'XX
KVVSXfracture
N \ \\ xN N \ > >
Fig. 31. Diffusion from fracture into porous matrix for continuous source
(after Huyakorn et al. 1987).
118
-------
t
t
non-p
rock
/
orous
matrix
t
source
diffusion
dead-end
fracture
fracture
advection
Fig. 32. Diffusion from active fracture into dead-end pores and fractures.
119
-------
porous matrix
source* '
affected zone
(molecular diffusion)
porous matrix
C/C,
C/C0 at time t1 in fracture
Fig. 33. Diffusion into and out of porous matrix for a slug source.
120
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Flow and Transport Models for Fractured Rock
Recent developments in mathematical models of flow in fractures have been
based on the concept of a dual porosity medium (Grisak and Pickens 1981,
Huyakorn 1987). A few mathematical models exist for modeling flow and trans-
port in saturated fractured and dual porosity media. Various analytical
solutions for solute transport in simple fractured systems are brought
together in the CRACK package (Sudicky 1986). These solutions include trans-
port in a single fracture with matrix diffusion (but without dispersion along
fracture axis), transport in a system of parallel fractures including matrix
diffusion, and transport in a single fracture with matrix diffusion and radial
diverging flow. A typical numerical model for flow and transport of heat and
nonconservative solutes in fractured rock is the TRAFRAP-WT code developed for
the International Ground Water Modeling Center (Huyakorn 1987) This code is a
two-dimensional finite-element code capable of treating both confined and
water table aquifers. Fractured rock can be modeled as a system of discrete
fractures or as a double porosity system by overlaying the two-dimensional
element grid for the porous medium with one-dimensional line elements
representing discrete fractures (Figure 34). This approach requires that the
geometry of the fracture system is defined on an appropriate scale.
An example of a finite difference model designed to handle solute and
heat transport in fractured porous media is the FRASCL code (Fractured Media -
Advanced Continuous Simulation Language) developed at the Idaho National
Engineering Laboratory (Miller 1983, Clemo and Hull 1986). This code simu-
lates the fractured system as discrete parallel sided channels in the porous
matrix. As with the TRAFRAP model this code allows for diffusion of chemical
compounds from the liquid in the fractures into the matrix blocks. The porous
aquifer is defined by a rectangular finite difference grid of unit thickness.
Fractures connect any two adjacent nodes, vertically, horizontally or diagon-
ally, with a maximum of eight fractures converging at a single node. As in
TRAFRAP, fractures can have any configuration of length, angle, and start and
termination location, constrained only by the connectivity criterion men-
tioned. Aperture is constant between two directly connected nodes, but for
the same fracture can change in the grid section being the fracture's contin-
uation between the next set of nodes. These and other codes that are capable
to simulate fractured systems are listed in Appendix F.
Another example of the dual porosity concept used in transport modeling
in fractured rock is the MINC (Multiple interacting Continua) method developed
by Pruess and Narasimhan (1982a,b). In the double porosity approach the frac-
tured porous reservoir is partitioned into (1) a primary porosity, which con-
sists of small pores in the rock matrix; and (2) a secondary porosity, con-
sisting of fractures and joints (Pruess 1983). Each of the two porosities is
treated as a continuum, whose properties can be characterized by means of the
traditional porous medium properties, i.e., permeability, porosity, and com-
pressibility. The porous matrix is divided in a series of interbedded subsys-
tems such that there is thermodynamic equilibrium in all volume elements at
all time (Figures 35, 36 and 37). The MINC method treats the interporosity
flow (i.e., the exchange between porous matrix and fracture system e.g.,
diffusion of solutes from the fractures into the porous matrix) as a series of
mass exchanges between the nested subsystems. Global flow occurs only through
the network of fractures (Figure 38). An implementation of the MINC concept
in simulating transport of solutes is found in Narasimhan and Pruess (1987)
121
-------
impermeable cover
horizontal fracture
porous matrix
aquifer
vertical
fracture
//////////////////////7 // 7 7 7/ 7 7/ / / 7 777/77/7
impermeable base
.;.;.-. -' ' . .f '
>:. ': :/. :t "-. -
' ' .'-: f ' :
- .> ':i::V"
\
.1 . '
; : >:.!'::
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'' ' ::-:': 1 : ':
:. ;v;;::{:- :
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' "! .'"
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. 1
\
i
} . V (
) ;:! 'i
t .'..:. 1 I
i .' : i i
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- 1 .-.': '-|j
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I 1
\
1
. 1
-I
I
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1
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i i
i i
i ?
1 i
i i
i j
i i
i i
i i
t i
r 1
-1 i .t J
1 .1 -I 1
^
f .
.1
1 > 1 J
1 f 1 t
1 t 1
1 f i
J ( <
i t '
3 ! !
4 l *
1_ * '
1 t \/
3 .( I/
1 t i/
f
t
f
1
t
7/fi~
D fracture I 2D porous
elements matrix
elements
Fig. 34. Treatment of system with intersecting discrete fractures, using
TRAFRAP.WT (after Huyakorn et al. 1987).
122
-------
xx xx xx
xx xx xx
MATRIX
FRACTURES
Fig. 35. Idealized model of a fractured porous medium (from Pruess 1983)
123
-------
\ L^ y /_/__/_/ s / 7 i j L/ y y y y_>!
fractures-
matrix blocks
Fig. 36. Basic computational mesh for a fractured porous medium (from Pruess
1983).
124
-------
Fractures
Connected
fractures
MING partitioning
Fig. 37. MINC concept for an arbitrary two-dimensional fracture distribution
(from Pruess 1983).
125
-------
Node number
Element number
Direction
of flow
Fig. 38. Network approach in modeling interconnected fracture systems (from
Endo et al. 1984).
126
-------
using the Integral Finite Difference Method (IFDM) for solving the governing
equations.
A continuum approach for modeling mass transport in fractured rock based
on the application of a particle tracking method is presented by Schwartz and
Smith (1988). The physical transport is simulated in terms of velocity and
velocity variations using statistics to describe the particle motion in a
representative subdomain of the modeled aquifer region (Figures 39 and 40).
For each of the particles a trajectory is plotted dependent on the statistic
properties of the fracture distribution and the global flow field calculated
with a finite element model using triangular elements and linear basis func-
tions. This approach leads to the definition of an equivalent continuum for
the fractured medium. Dispersion is accounted for by the variability in flow
conditions.
Codes that are well accepted as representing single-phase flow and solute
transport through unsaturated fractured media are presently not available. A
recent discussion on the state-of-the-art of computer modeling flow and trans-
port through unsaturated fractured rock system can be found in Evans and
Nicholson, eds. (1987). While models of single-phase fluid in a porous media
are to some extent applicable to multiphase fluids in porous media, no such
extension of mathematics and numerical methods can yet be made for applica-
tions to fractured media (Kincaid and Mitchell 1986).
As larger fractures often transport a fraction of the solute or heat
dlsappropriately large for its relative pore volume, the presence of such
larger fractures requires special attention in modeling. Simulations con-
ducted 1n a hypothetical fractured porous aquifer with constant overall
porosity but varying rate between pore and fracture porosity and with varying
distribution of fracture size and interconnectivity demonstrated that good
results can be obtained if an adequate active porosity can be determined (Hull
and Clemo 1987). Furthermore Hull and Clemo (1987) found that the success
rate in the simulations of dual porosity systems is directly influenced by the
level to which the most significant discrete fractures are explicitly simu-
lated. It should be noted that in heat transport conduction of heat through
the solids is an important additional process that results in a larger area of
the aquifer participating in the transport than is the case for solute
transport.
127
-------
Step 1) sample for direction
Step 2) sample distribution on fracture
length for distance
Step 3) sample distribution on velocity
in direction 2 and calculate
transport time
Step 4) repeat 1 to 3
and accumulate
times
ii
I'.
.particle trajectory
//////////////////////////////////////////////////////T//////////////
contiuum
(flow domain)
observed subdomain
represented as a
discrete network
Fig. 39. Simulation of transport in a fracture continuum (from Schwartz and
Smith 1988).
128
-------
Fig. 40. Combined trajectories of particles simulating random movement in a
fractured system (from Schwartz and Smith 1988).
129
-------
6. QA IK MODELING
THE ROLE OF QUALITY ASSURANCE
To develop effective software and to apply it in analyzing alternative
solutions to groundwater problems requires a number of steps, each of which
should be taken conscientiously and reviewed carefully. Taking a systematic,
well-defined, and controlled approach to all steps of the model development
and application process is essential for the success of modeling in water
resource management. Quality Assurance (QA) provides the mechanisms and
framework to ensure that decisions are based on the best available data and
(modeling-based) analyses. This does not imply that analyses based on the use
of quality-assured models and modeling projects are guaranteed to provide
correct answers.
Many modeling studies are performed without adequate QA arrangements in
place. QA plans are often lacking and formal QA assessment is frequently
postponed until the project reaches its final stage (van der Heijde and Park
1986). This is especially true for studies where models are applied to site-
specific problems. In contrast, policies based on modeling assessments often
affect large constituencies and thus are more thoroughly scrutinized before
they are adopted. Increasingly, financial and criminal liability require
modelers to implement rigorous QA procedures in all stages of the projects.
Frequently mentioned reasons for deficiencies in QA are lack of specifi-
cations from management with respect to the level of analysis required for
decision making; shortage of time, budget, and experienced staff; unfamil-
iarity with QA procedures; and reluctance to accept additional administrative
duties (van der Heijde and Park 1986).
Program managers in regulatory agencies play a crucial role in QA, as
their decisions rest on the quality of environmental data and data analysis.
They are in a unique position to specify the quality of the environmental data
and the level of problem-solving data analysis required, and to provide suffi-
cient resources to assure an adequate level of QA.
To alleviate the lack of information on QA in groundwater modeling, this
section provides background information on QA and discusses the role of QA in
groundwater modeling. It presents a comprehensive set of procedures together
forming a functional quality-assured modeling methodology. It is written from
the perspective of the model user and the decision maker in need of technical
Information on which to base decisions. Various standards and guidances
applicable to groundwater modeling are given and areas are identified where
additional research and regulation is required. The section is divided in
three parts: (1) model development, (2) model application, and (3) model
selection.
It should be noted that relatively little has been published in the open
literature on QA in software application, as compared with QA in software
development.
130
-------
DEFINITIONS
Quality assurance in groundwater modeling is the procedural and opera-
tional framework put in place by the organization managing the modeling study,
to assure technically and scientifically adequate execution of all project
tasks included in the study, and to assure that all modeling-based analysis is
verifiable and defensible (Taylor 1985). QA in groundwater modeling is
crucial to both model development and model application and should be an
integral part of project planning and be applied to all phases of the modeling
process.
The two major elements of quality assurance are quality control (QC) and
quality assessment. Quality control refers to the procedures that ensure the
quality of the final product. These procedures include the use of appropriate
methodology, adequate validation, and proper usage of the selected methods and
models.
To monitor the implementation of quality control procedures and to eval-
uate the quality of the studies, quality assessment is applied (van der Heijde
1987a). It consists of two elements: auditing and technical review. Audits
are administrative procedures designed to assess the degree of compliance with
QA requirements, commensurate with the level -of QA prescribed for the project.
Compliance is measured in terms of traceability of records, accountability
(approvals from responsible staff), and fulfillment of commitments described
in the QA plan of a project. Technical review consists of independent evalua-
tion of the technical and scientific basis of a project and the usefulness of
its results. In groundwater modeling this latter form of quality assessment
is rather common.
There is a significant difference between software quality assurance
(SQA) and hardware QA (Bryant and Wilburn 1987). Therefor, special SQA pro-
cedures need to be established and detailed. It should be noted also, that
major differences exist between data QA (e.g., EPA 1986b), software QA and
model application QA.
THE QA PLAN
At the beginning of a model development or application project, a project
plan should be made containing a complete set of QA procedures, sometimes
called the QA plan. These QA procedures comprise a list of the measures
required to achieve prescribed quality objectives. The QA plan needs approval
before initiation of technical work. Major elements of such a QA section of
the project plan or QA plan are:
Formulation of QA objectives and required quality level in terms of
validity, uncertainty, accuracy, completeness, and comparability
Development of operational procedures and standards for performing
adequate software development and modeling studies
Establishing a paper trail for QA activities in order to document that
standards of quality have been maintained
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Internal and external auditing and review procedures.
The QA plan should also specify individual responsibilities for achieving
these goals, describe the technical chain-pf-command within the project
organization, and outline procedures for remedial or corrective action in case
problems are detected in the quality assessment stage.
Many modeling studies are performed without adequate QA arrangements in
place. A formal QA plan is often lacking and extensive QA assessment is fre-
quently postponed until the project reaches its final stage (van der Heijde
and Park 1986). This is especially true for studies where models are applied
to solve site-specific problems. In contrast, policies based on modeling
assessments often affect large constituencies and thus are more thoroughly
scrutinized before they are adopted. Increasingly, financial and criminal
liability require modelers to implement rigorous QA procedures in all stages
of the projects.
QA IN CODE DEVELOPMENT AND MAINTENANCE
Software quality assurance (SQA) consists of the application of proce-
dures, techniques, and tools throughout the software life cycle, to ensure
that the products conform to prespecified requirements (Bryant and Mil burn
1987). This requires that in the initial stage of the software development
project appropriate SQA procedures (e.g., developing a QA plan, record keep-
ing, establishing a project QA organization), techniques (e.g., auditing,
design inspection, code inspection, error-prone analysis, functional testing,
logical testing, path testing, reviewing, walk-throughs), and tools (e.g.,
text-editors, software debuggers, source code comparitors, language pro-
cessors) need to be identified and the software design criteria be deter-
mined. Many current groundwater modeling codes have not been subject to such
a rigorous SQA approach. Ideally, SQA should be applied to all codes cur-
rently in use and yet-to-be-developed codes.
The use of the software life cycle concept has proven successful in
determining the QA requirements of the development, use, and operation of
software systems (Bryant and Wilburn 1987). The software development life
cycle consists of three major phases: the initiation phase, the development
phase, and the operation phase (NBS 1976). In the initiation phase the
objectives and requirements for software are defined, and feasibility studies
and cost-benefit analysis performed. In the development phase software and
documentation requirements are determined, program design formulated, coding
implemented, and code testing performed. During this phase, and parallel with
program design and coding, the user's manual, the operations manual, and the
program maintenance manual should be written.
In the operation phase the software is used for the purpose for which it
has been designed. During this phase the software is maintained, evaluated
regularly, and changed as additional requirements are identified. When main-
tenance is no longer justified (e.g., because of changes in computer environ-
ments used, changes in operational requirements, or changes in software design
objectives), the end of the software life cycle is reached. A detailed dis-
cussion of the QA requirements for each of these software life cycle phases is
given by Bryant and Wilburn (1987).
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The most important QA procedures in code development and maintenance are
(van der Heijde 1987a):
Documentation of code development (record keeping)
Verification of program structure and coding
Validation of complete software product (model validation)
Documentation of code characteristics, capabilities and use
Scientific and technical reviews
Administrative auditing.
It should be noted that code testing is generally considered to encompass
verification and validation of the model (Adrion et al. 1982).
To evaluate groundwater models in a systematic and consistent manner, the
International Ground Water Modeling Center (IGWMC) has developed a model
review, verification, and validation procedure (van der Heijde et al. 1985b)
which follows in part the testing approach taken by Nicholson et al. (1987).
If any modifications are made to the model coding for a specific problem,
the code should be tested again; all QA procedures for model development
should again be applied, including accurate record keeping and reporting. All
new input and output files should be saved for inspection and possible reuse.
A detailed discussion of QA requirements for record keeping, program
structure and code verification, model validation, and software documentation,
and the role of scientific and technical reviews is given in the report of the
Committee on Groundwater Modeling Assessment (NRC 1988, in preparation).
QA IN CODE APPLICATION
Quality assurance in model application studies follows the same pattern
discussed for model development projects, and consists of using appropriate
data, data analysis procedures, modeling methodology and technology, adminis-
trative procedures, and auditing. To a large extent, the quality of a
modeling study is determined by the expertise of the modeling and quality
assessment teams.
Quality assurance in code application should address all facets of the
modeling process. It should address such issues as:
Correct and clear formulation of problems to be solved
Project description and objectives
Type of modeling approach to the project
Is modeling the best available approach and if so, is the selected
model appropriate and cost-effective?
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Conceptualization of system and processes, including hydrogeologic
framework, boundary conditions, stresses, and controls
Detailed description of assumptions and simplifications, both explicit
and implicit (to be subject to critical peer review)
Data acquisition and interpretation (including discussion of error and
inaccuracies and of their propagation in the analysis)
Model selection process and justification
Model preparation (parameter selection, data entry or reformatting,
gridding)
The validity of the parameter values used in the model application
Protocols for parameter estimation and model calibration to provide
guidance, especially for sensitive parameters
Level of information in computer output (variables and parameters
displayed, formats, layout)
Identification of calibration goals and evaluation of how well they
have been met
The role of sensitivity analysis
Post-simulation analysis (including verification of reasonability of
results, interpretation of results, uncertainty analysis, and the use
of manual or automatic data processing techniques, as for contouring)
Establishment of appropriate performance targets (e.g., 6-foot head
error should be compared with a 20-foot head gradient or drawdown, not
with the 250-foot aquifer thickness!); these targets should recognize
the limits of the data
Presentation and documentation of results
Evaluation of how closely the modeling results answer the questions
raised by management.
QA for model application should include complete record keeping of each step
of the modeling process. The paper trail for QA should consist of reports and
files that include a description of
Assumptions
Parameter values and sources
Boundary and initial conditions
Nature of grid and grid design justification
Changes and verification of changes made in code
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Actual input used
Output of model runs and interpretation
Validation (or at least calibration) of model.
As is the case with model development QA, all data files, source codes, and
executable versions of computer software used in the modeling study should be
retained for auditing or post-project reuse (in hard-copy and, at higher
levels, in digital form):
Version of source code used
Verification input and output
Validation input and output
Application input and output.
If any modifications are made to the model coding during code application to a
specific problem, the code should be tested again; all QA procedures for model
development should again be applied, including accurate record keeping and
reporting. All new input and output files should be saved for inspection and
possible reuse together with existing files, records, codes, and datasets.
An increasing number of costly decisions are made based in part on the
outcome of modeling studies. In the light of major differences noted in
comparative studies on model application (e.g., McLauglin and Johnson 1987,
Freyberg 1988) and the general lack of confidence in modeling results, effec-
tive quality assurance might go so far as to require the analysis being done
by at least two independent modeling teams. In that case, a third team should
review and compare the results of both modeling efforts and assess the impor-
tance and nature of differences present.
A detailed discussion of QA aspects in model application, including data
collection, model formulation, sensitivity analysis, code implementation and
execution, and the interpretation of results, is given in the report of the
Committee on Groundwater Modeling Assessment (NRC 1988, in preparation).
QA ASSESSMENT
The final stage in quality assurance is quality assessment. Quality
assessment consists of two elements: auditing and technical review (van der
Heijde 1987a). Audits are procedures designed to assess the degree of com-
pliance with QA requirements, commensurate with the level of QA prescribed for
the project. Compliance is measured in terms of traceability of records,
accountability (approvals from responsible staff), and fulfillment of commit-
ments in the QA plan. Technical review consists of independent evaluation of
the technical and scientific basis of a project and the usefulness of its
results.
QA assessment not only involves checking to see if procedures have been
applied correctly, but also establishing quantitatively the overall success of
the project in meeting its original objectives.
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Various phases of quality assessment exist for both model development and
application. First is review and testing in case of software development, or
review and performing control calculations by the responsible researcher, and
sometimes by other staff not involved in the project, or by invited experts
from outside the organization. Also to be considered is the quality assess-
ment by the organization for which the project has been carried out. Again,
three levels can be distinguished: project or product review or testing by the
project officer or project monitor, by technical experts within the funding or
controlling organization, and by an external peer review panel (van der Heijde
1987a).
Quality assessment generally takes the form of technical and administra-
tive reviews. Review comments can be presented in the form of a memorandum or
report, or as annotations in the margin in a certified copy of the reviewed
documents. In case this review should lead to important recommendations for
corrective action or additional studies, follow-up activities by the project
team, and additional review, need to be arranged and documented.
QA ORGANIZATION STRUCTURE
QA is the responsibility of both the project team (quality control and
internal auditing) and the contracting or supervising organization (quality
assessment). QA should not drive or manage the direction of a project nor is
QA intended to be an after-the-fact filing of technical data.
There are two levels in the QA framework within the organization that
carries out a software development or model application study: (1) a permanent
organization complete with QA management policies, goals, and objectives, and
(2) project QA organization where general QA policies and assignments are
detailed towards project objectives. Upper levels of management need to
recognize that QA is a vital part of the software development and modeling
processes. Such recognition by upper management must be translated into a
commitment through policies that set quality goals, establish QA functions,
and authorize necessary resources in terms of people, funding, and equipment
to perform the tasks (Bryant and Wilburn 1987).
The QA organization should have a charter with each element of the organ-
ization defined and its responsibility outlined. The persons responsible for
QA should be independent from those responsible for software development or
model application. The QA organization must not be subordinate in any way to
product development or delivery (Bryant and Wilburn 1987.)
Competent staffing is the key to a successful QA program. QA staff must
have the respect of the project staff with which they work. They must under-
stand how the work whose quality they are assuring is actually accomplished.
Implementation of a successful QA program requires that all individuals
involved understand what QA means, why it is being done, how they will bene-
fit, what is expected of them, what are the responsibilities for each indi-
vidual, and that good QA will help rather than hinder the modeling process
(Bryant and Wilburn 1987). They should be convinced of the usefulness of QA
and the importance given to it by management.
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Closely related to and to a large extent crucial to the success of QA
modeling are the capabilities of the modeling team. A good modeling team is
multidisciplinary, includes highly trained and widely experienced senior
staff, has effective internal communication, is managed by persons who have
overview of the different disciplines involved in the project and who are able
to translate management's questions into technical project objectives, and
modeling results into advice to management. If such a team is well-managed QA
forms an integral part of all its activities.
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7. MANAGEMENT ISSUES IN GROUNDWATER MODELING
MANAGEMENT CONCERNS
Models have become widely accepted and quite useful as tools for drawing
scientific conclusions and making technical decisions. However, models have
not yet achieved great acceptance in the formulation of public policy. There
are several reasons for the failure of policy makers to utilize models (OTA
1982, van der Heijde et al. 1985a). Individuals at higher levels of decision-
making where policies are formulated often have less familiarity with models
than the operation managers who use them for engineering decisions. Further-
more, policy decisions are increasingly contested in court. Evidence require-
ments in the litigation process are often difficult to meet, restricting
management from incorporating modeling in their decision making. Opposing
parties in a court of law frequently arrive at significantly different conclu-
sions, sometimes based on the same model, thus contributing to management's
reluctance to rely on models.
Management's lack of confidence in modeling probably reflects their
experience with unsuccessful model application. Failures have been attributed
to (1) use of insufficient or incorrect data; (2) incorrect use of available
data; (3) inadequate conceptualization of the physical system such as flow in
fractured bedrock; (4) use of invalid boundary conditions; (5) selection of an
inadequate computer code; (6) incorrect interpretation of the computational
results; and (7) providing answers to imprecise or wrongly posed management
problems (OTA 1982, van der Heijde et al. 1985a, van der Heijde and Park
1986).
In some cases, insufficient scientific foundation with respect to basic
processes and methodological principles has contributed to management's
disappointment in model's predictive capabilities.
Groundwater managers have varied interests in model development, selec-
tion, and use, and in training modelers. In discussions with staff of one of
the regulatory agencies, the U.S. EPA, the following major issues surfaced
(van der Heijde and Park 1986):
Limited knowledge of model availability
The need for assistance in selecting and using adequate models for a
specific site or specific use
Guidance in establishing model reliability and interpretation of
simulation results
Improved interaction and communication with other professionals
Training in basic processes (geology, hydrology, fate and transport,
etc.) for the project managers in regulatory agencies as well as
modeling training for the agencies' technical experts.
Hiring and retaining technical staff who have received special training
in modeling
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Need for ground-water modeling policies consistent with those in other
areas of modeling.
Because of the deadlines and workload, project managers, who are often
untrained in groundwater modeling, have no time to keep abreast of develop-
ments in modeling and, therefore, are often not qualified to introduce
modeling into the project or to evaluate modeling done by contractors. Model
application and interpretation of results is very subjective and may be the
core of an expert's testimony in court. The expert's interpretation of
results represents the culmination of months of technical work. Staff in
regulatory agencies must be capable of providing the expert with both policy
and technical oversight, e.g., in the quality assurance of the project. If
this oversight is lacking, the expert's work may be misdirected or poor in
quality. -That this is a significant problem is illustrated by the modeling
deficiencies frequently displayed in reported studies (van der Heijde and Park
1986).
A broad, multidisciplinary team is viewed as mandatory for adequate
modeling of complex problems such as transport of hazardous waste. There is a
tendency to underestimate staffing needs; and, even with breadth, staff tends
to be spread too thin among projects.
High turnover in project managers, together with the inability to review
the degree of success or failure in earlier projects, leaves little institu-
tional memory for learning from previous studies. This leads to serious prob-
lems in the case of groundwater pollution studies, where the modeler or some-
one familiar with the application (e.g., the modeler's supervisor) often is
required to serve as an expert witness. In addition to the familiarity with
the study such a person needs to ensure the quality of the presentation to
management of modeling results, and to the judge in the courtroom, an impor-
tant aspect of the ultimate success of this kind of modeling.
Postmortem analyses of selected cases, with all staff informed, should be
encouraged, so that the lessons learned can be communicated and applied to
current and future site investigations. The results of such analysis should
be made widely available.
The management issues involved are set forth in the final report of a
study group for the EPA Office of Environmental Processes and Effects
Research. The report examines issues related to that Agency's use of ground-
water models and associated constraints (van der Heijde and Park 1986).
According to the report, these issues can be divided into three groups: (1)
the computer model being used, (2) application (conceptualization, data
selection, and simulation), and (3) use of computational results in decision
making. Issues of the first group include the assessment of the validity of
computer codes. Prominent issues of the second group are criteria for selec-
tion of appropriate models for specific applications and review procedures for
establishing model application, adequacy, and validity. The third group of
issues relates only in part to modeling, as decision making is often based
extensively on nontechnical considerations. A major limitation in addressing
these issues is the scarcity of trained staff at all levels of management and
technical services, both in government agencies and in private industry. To
resolve many of the problems identified, the study group recommended that the
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Agency adopt rigorous, well defined quality assurance procedures and establish
extensive technology transfer and training programs.
Review of the important issues of the late 1970s and mid-1980s shows that
despite many efforts to make improvements a significant number of problems
still exist today (Bachmat et al. 1980, van der Heijde et al. 1985).
Major issues still of concern include inadequacies in models (formula-
tion, testing, documentation), inadequacies in modeling (application, review),
in communication betwee'n managers and technical personnel, and in training of
model users and education of managers.
To further explore these issues, the Water Science and Technology Board
recently established the Committee on Ground Water Modeling Assessment to
examine the current state of knowledge concerning groundwater models and the
role of contaminant models in the regulatory community (WSTB 1988). The 18-
month study will address issues such as (1) the representation of physical,
chemical, and biological processes in models of groundwater quality; (2) model
formulation as related to observation of real groundwater systems; (3) model
application procedures; (4) scientific, engineering, and policy trends influ-
encing the future of modeling; (5) the role of models in decision making; and
(6) the formulation of modeling guidelines and recommendations.
TECHNOLOGY TRANSFER AND TRAINING
As modeling for groundwater protection has become a rapidly growing area
of technology and research, a vast body of information on technological and
scientific advances is becoming increasingly available for groundwater manage-
ment. Furthermore, the revolutionary advancement in computer software and
hardware and the marked reduction in its cost has stimulated rapid adoption of
groundwater modeling among groundwater professionals. The goal of technology
transfer is to improve the systematic dissemination of information on ground-
water modeling through communication and education. In its broadest sense,
technology transfer includes development of application-oriented methods and
models, the distribution of modeling codes and documentation, and training and
assistance in model use (van der Heijde 1987b).
In 1982 the Office of Technology Assessment of the U.S. Congress (OTA)
published a report on the use of models for water resources management,
planning, and policy. Many of OTA's conclusions and recommendations on tech-
nology transfer and training apply to groundwater modeling today. The
following OTA findings still apply:
Levels of communication between decision makers and modelers are low,
and little coordination of model development, dissemination, or use
occurs within individual federal agencies.
Developing and using models is a complex undertaking, requiring per-
sonnel with highly developed technical capabilities, as well as
adequate budgetary support for computer facilities, collecting and
processing data, and such support services as user assistance.
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In general, technology transfer means dissemination of information on
technological advances through communication and education. When applied to
ground-water modeling, technology transfer includes dissemination of infor-
mation about the role of modeling in water resource management, model theory,
the process and management of modeling, availability and applicability of
model software, information on quality assurance, model selection, and model
testing and verification. It also pertains to the distribution of computer
codes and documentation, and includes assistance in transferral, implementa-
tion, and use of codes.
The OTA report considers specific education and training of model de-
velopers, users, and managers in aspects of water resources modeling, as a
critical component of technology transfer. Other technology transfer mech-
anisms include the distribution of published, printed, or electronically
stored materials, such as reports, newsletters, papers, computer codes, data
files, and other communications, and discussions and information exchanges in
meetings, workshops, and conferences.
Effective communication forms the basis of technology transfer. Com-
munication is often hampered because of insufficient communication channels,
incompatible language or jargon, existence of different concepts, and adminis-
trative impediments.
Despite recent examples of successful modeling use in developing ground-
water protection policies in the United States and abroad, managers still do
not rely widely on modeling for decision making. One of the major obstacles
is the inability of modelers and program managers to communicate effectively.
An ill-posed problem yields answers to the wrong questions. Sometimes, this
is the result of managers and modelers speaking different jargon.
On another level of communication, managers should appreciate how dif-
ficult it is to explain the results of complicated models to nontechnical
audiences such as in public meetings and courts of law. Audio-visual aids are
one useful means of overcoming these limitations in communication.
Training in Groundwater Modeling
Groundwater and groundwater modeling expertise often is disjunct within
the groundwater community. Many inconsistencies in groundwater modeling have
resulted.
The EPA Study Group (van der Heijde and Park 1986) concluded that among
the modeling issues addressed during its meetings, improving the expertise of
technical personnel deserves a high priority. Because it is expected that
model use will increase in the future, the development of expertise on various
levels of decision-making and technical assistance, by whatever means, appears
to be a major priority.
A major impediment to meeting modeling needs is the inadequacy of current
levels of model-related training and information exchange. If models are to
be used effectively in water resources analysis, training in basic concepts of
modeling and in proper interpretation of model results must be offered to
decision makers at all levels of water resources management and environmental
protection. Further, there is a need for specific training in the use of
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individual models, and a need for continuingly informing and educating users
and managers in research developments, new regulations and policies, and field
experience.
The return on investments made in applying mathematical models to ground-
water problems depends a great deal on the training and experience of the
technical support staff involved in their use. Managers should be aware that
specialized training and experience are necessary to develop and apply mathe-
matical models, and that relatively few technical support staff can be
expected to have such s"kills. This is due in part to the need for familiarity
with a number of scientific disciplines, so that the model may be structured
to faithfully simulate real-world problems. Managers should have some working
knowledge of the sciences involved so that they might put appropriate ques-
tions to specialists. In practice this means that groundwater modelers,
technical staff, and their supervisors should become involved in continuing
education efforts, and managers should expect and encourage this. They should
be sensitive to the financial and time requirements necessary for adequate
training. (One does not become a competent modeler in a course of a week;
that takes years and is a combination of training and experience.)
Mission-oriented organizations such as the USGS traditionally have given
high priority to training and expertise. In regulatory agencies most
technical and managerial personnel do not need to become modeling "experts,"
but should have sufficient training to be knowledgeable users or at least
competent judges of the appropriateness of models used by third parties.
Information Exchange on Groundwater Modeling
There is an urgent need for expanding existing and developing new mech-
anisms to disseminate and exchange technical information. Two different
approaches exist to information exchange: (1) the receiver actively seeks the
required information or technology; (2) the receiver has a passive role inso-
far as supervisors or internal or external specialists bring the information
or technology to the potential user.
When particular models are applied at particular sites, the experience
needs to be institutionalized. A central clearinghouse should be created for
keeping records on models used in a regulatory framework. The clearinghouse
should have readily available information on: (1) where and under what condi-
tions the models have been used; (2) what results were provided in terms of
usefulness to management; and (3) what administrative, technical, and legal
problems were encountered. This information should include contact persons,
site descriptions, model modifications, and details on QA procedures.
A major impediment to meeting modeling needs is the inadequacy of model-
related training and information exchange. Despite many efforts to resolve
this obstacle, information from research projects often is not disseminated
effectively to potential users. Recent legislation has demonstrated the
renewed attention given to this problem (Section 209 of the Superfund Amend-
ments and Reauthorization Act [SARA] of 1987).
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PROPRIETARY CODES VERSUS PUBLIC DOMAIN CODES AND OTHER ACCEPTANCE CRITERIA
Is the use of proprietary codes in solving groundwater problems for or by
government agencies acceptable, or should they be banned in favor of publicly
accessible codes? Deciding this policy issue has become imperative in recent
years, as an increasing number of modeling-based analyses performed by consul-
tants or regulatory agencies in regulatory compliance cases are contested in
the courtroom, and envrionmental decision-making processes in general are
subject to increasing public scrutiny.
A proprietary code consists of computer software that is sold, leased, or
used on a royalty basis, which generally conditions its use and limits its
distribution. Some proprietary codes are publicly accessible, but restricted
1n transfer and use. According to this definition, proprietary codes used for
solving groundwater problems could include: (1) groundwater simulation codes,
(2) databases, (3) statistical packages, and (4) graphical packages. Public
domain codes consist of software and documentation that can be used, copied,
transferred, distributed, modified, or sold without any legal restrictions
such as violation of copyrights.
There are various reasons why the use of proprietary codes is regarded
problematic by the government (van der Heijde and Park 1986): lack of peer
review and validation; problems with intercomparison and reproducability of
results; administrative complications; and lack of access to software and
theoretical basis. On the other hand, owners of proprietary code rights often
promote the use of these codes for commercial, scientific, and other reasons.
Banning the Use of Proprietary Codes
Some agencies or their individual offices prefer the use of public codes
if litigation is anticipated, assuming such code is available, even if the
code is less efficient than an alternative proprietary code. Banning of
proprietary codes is expected to eliminate some of the problems encountered in
court cases. One of these problems is related to the notion that the code
itself and its theoretical foundation might become contested. Unrestricted
access to the computer code and documentation is considered crucial in such
cases. However, if adequate model selection guidelines existed, including
requirements for code review, validation, and documentation, and were applied
consistently, such problems might be less significant.
Another issue is the inaccessibility of some proprietary codes and docu-
mentation. For example, EPA regulations (40 CFR 124.11 and 124.12) provide a
mechanism for formal public hearings during the RCRA permit process. All
aspects of EPA's decision making, including the use of groundwater models, are
subject to public scrutiny. EPA use of models not accessible to the public
may complicate the proceedings and result in EPA having to duplicate the
modeling effort with a publicly accessible model. EPA's continued use of non-
publicly accessible models increases the likelihood of Federal Open Informa-
tion Act litigation. EPA policy restricting the use of nonpublicly accessible
models may reduce this likelihood.
Furthermore, regulatory staff often does not have enough time and exper-
tise to evaluate models or to go through a proper model selection process
without support from model experts. However, this support can be provided
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indirectly by establishing a list of reviewed and validated models and through
various forms of guidance such as reports, and by expert systems. In such a
certification process, public agencies tend to focus on public domain
software.
Not all proprietary codes are publicly inaccessible. The private sector
may control the use and dissemination of its computer models through copyright
protection, patent protection, trade secret protection, or through a con-
tractual or license agreement. Most of the issues discussed above result from
attempts by some companies to maintain tight controls over their models
through trade secret protection. The rationale is that a given model contains
some formulation that makes it superior to those generally available, and that
this formulation gives the company an advantage over its competitors. Exer-
cising control through copyright protection and contractual agreements might
be more difficult to enforce than trade secret protection. However, they
allow for greater and quicker acceptance of the model by the technical
community.
Continuing the Use of Proprietary Codes
Several reasons have been brought forward for the continued use of
proprietary groundwater simulation codes:
Use of proprietary codes encourages code development for solving new
problems. If proprietary codes are banned, this incentive will be
removed, greatly inhibiting future code development in the private
sector. Because it is difficult for private companies to obtain
funding for code development, the main justification for investing
corporate funds in code development is the anticipation that some
development costs will be recovered through code sales or value-added
use. Capital gain is a major incentive for code development.
Use of proprietary codes encourages private companies to enhance codes
originally developed in the public domain. Many research-oriented
codes developed in universities have been generalized, made user-
friendly, and have been documented more fully by enterprising private
developers. If the profit incentive is removed, further development
and enhancement of public domain codes for applied purposes will be
discouraged.
Proprietary codes provide solutions to some problems that publicly
available codes cannot solve. In some casesfor example, complex
three-dimensional transport problemspublicly available codes are not
adequate. Banning proprietary codes would eliminate the use of some of
the more sophisticated codes. An alternative is to bring such a code
into the public domain through outright purchase, and installing a
service and support agreement with the code developers.
Proprietary codes are often subject to rigorous internal QA. This is
not always the case with public domain codes. If a code has problems
(bugs), it will develop a bad reputation and will not sell, or will
compromise the reputation of the company; a company is not likely to
profit by selling inferior codes. In practice, however, many distri-
butors of proprietary groundwater modeling software are relatively
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small companies, some of which do not apply QA to model development and
documentation. A model review and validation policy or procedural
guidance should cull out the inferior models.
User support might be available for proprietary codes. Once a proprie-
tary code has been sold, it is in the interest of the seller to help
the user apply the code in the best possible manner. Again, this does
not always accur, as the smaller groundwater modeling software distri-
butors often have limited resources for support and maintenance of
their software. Often, consistent user support is not available for
public domain codes.
The use of proprietary databases, statistical packages, and graphical
packages is rather widely accepted; the current regulatory questions
focus specifically on the use of groundwater simulation codes.
Policies applied to groundwater modeling software should be consistent
with those established for other software.
It is necessary to establish consistent policies concerning selection and
use of well tested and validated groundwater models. Such a policy should
address the issues of model acceptance and use of proprietary codes and should
be consistent with policies regarding surface water and air models. With
respect to proprietary codes opinions vary from outright banning to ensuring a
proper place for them in public policy (van der Heijde and Park 1986). In
general, the following elements for such a policy regarding model acceptance
are considered important:
Establish a formal mechanism to review and validate models and define
model acceptance criteria. This approach should be restricted to
publicly available, noncopyrighted codes.
Regulatory agencies should identify proprietary codes that it regards
important to their mission; such codes should be brought into the
public domain, after passing a review and validation process.
A special list should be compiled of those proprietary codes that have
passed a comparable review and validation process.
Wherever possible the regulatory agency should advocate the use of
publicly accessible groundwater modeling software.
The ,EPA Study Group (van der Heijde and Park 1986) recommended that a
general framework of nondiscriminatory criteria should be established to apply
to both public domain and proprietary codes. These criteria should include:
Publication and peer review of the conceptual and mathematical
framework
Full documentation and visibility of the assumptions
Testing of the code according to prescribed Agency methods; this should
include verification (checking the accuracy of the computational algo-
rithms used to solve the governing equations), and validation (checking
the ability of the theoretical foundation of the code to describe the
actual system behavior)
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Trade secrets (unique algorithms that are not described) should not be
permitted if they might affect the outcome of the simulations; proprie-
tary codes are already protected by the copyright law.
In case an agency policy includes acceptance of proprietary codes, provi-
sions should be made regarding distribution of program copies of licensed
software and documentation for purposes of regulatory compliance, as well as
provisions for reasonable use by third parties (at reasonable cost) of code
documentation and an executable version of the program code, or, at a minimum,
access to the use of the code. Unreasonable cost to a group, such as a public
interest group, could violate the provisions of the Freedom of Information
Act.
For proprietary codes, an agency might also require from a contractor
proof of copyright, ownership, or license to perform, display, and use the
code. In case the agency intends to use the software internally, a license
should be obtained to perform, display, use, and reproduce the code and
related documentation in all parts of that agency.
In standardizing model selection, three major approaches are employed in
characterizing the validation of numerical models. In one, the model is
tested according to established procedures; when accepted, the model is
prescribed in regulations for use in cases covered by those regulations. This
approach does not leave much flexibility for incorporating the advances of
recent research and technological development. The second approach includes
the establishment of a list of groundwater simulation codes as "standard"
codes for various generic and site-specific management puposes. To be listed,
a code should pass a widely accepted review and test procedure. However,
establishing "standard models" will not prevent discussion of the appropriate_
ess of a selected model for analysis of a new policy or of its use in a~
particular decision-making process.
The question is, should standard models be established for an agency,
such as EPA, or should criteria or guidelines be developed by which analysts
can evaluate use of models. In considering this issue, questions have been
raised such as:
Are there legal liabilities for setting up certain models as accept-
able? (For instance, if EPA certifies a model for a particular use,
can the Agency no longer criticize an industry's selection of that
model for other identical problems, or for that matter, even for
solving non-identical problems?)
Does certification squelch the development of new, better models?
What balance should there be between using the newer, faster models and
using mature models already subjected to peer review?
Another approach is to prescribe a review-and-test methodology in the
regulations and require the model development team to show that the model code
satisfies the requirements. This approach leaves room to update the codes as
long as each version is adequately reviewed and tested. An example of this
last approach is the quality assurance program for models and computer codes
of the U.S. Nuclear Regulatory Commission (Silling 1983).
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8. CURRENT LIMITATIONS OF MODELING; RECOMMENDATIONS FOR IMPROVEMENT
This report has focused on the principles of groundwater modeling and the
status of modeling related software.
During the present decade a rapidly increasing number of sophisticated
simulation models have become available for the evaluation of groundwater
problems. These models are based on mathematical descriptions of the physi-
cal, chemical, and biological processes that take place in a complex hydrogeo-
logical environment. The extensive need for these models in assessing current
and potential water management problems has resulted in two groups of
modelers: (1) researchers who propose a conceptual representation of a ground-
water system of interest and who generate computer codes to verify the mathe-
matical descriptions derived from the modeled system and to evaluate the be-
havior of such a modeled system, and (2) model users who apply models rou-
tinely to actual groundwater management problems.
Accurate modeling of groundwater systems, especially where pollution is
present, is limited by some fundamental problems. In the first place, not all
processes involved are well understood and adequately described mathematically
(Bear 1988). This is especially true for chemical and biological processes.
For the most complex mechanisms, such as described by systems of coupled,
highly non-linear equations, available numerical techniques are not always
adequate (Pinder 1988). Finally, in most cases, lack of quantity or quality
of data restricts model utility (Bear 1988, Konikow 1988).
Although major advances have been made in predicting the behavior of
individual contaminants, studies of the interactions among contaminants are
still in their infancy. Among others, these studies have focused on the
ability of certain solvents to increase dramatically the mobility of ordi-
narily slow-moving pesticides, of polynuclear aromatic hydrocarbons, and of
other substances.
Other areas where substantial progress is needed lie in understanding the
immiscible flow and transport considerations so crucial to solving the prob-
lems of leaking underground storage tanks, and the manner in which contaminant
transport in fractured rocks differs from transport through porous sediment.
Improvements are required, concurrently, in several other major areas.
Data acquisition methods and interpretive models are needed that can examine
to an unprecedented degree the physical, chemical, and biological processes
controlling the transport and fate of groundwater contaminants. Unfor-
tunately, few of the constants and coefficients needed to incorporate chemical
and biological processes into contaminant transport evaluations are available.
THE ROLE OF DATA
Modeling provides a framework to order and interpret data within the
decision-making process. The effectiveness of any model is dependent on the
accuracy of the data acquired. In many applications, the lack of data
inflicts a severe constraint upon obtaining useful model results. Therefore,
the use of computer models in groundwater resource development and protection
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will continue to be limited mainly by the time and costs incurred in collect-
ing sufficient and accurate hydrologic and geologic data for proper descrip-
tion of groundwater systems and their functional characteristics. This does
not mean, however, that some indication of the relative contribution of var-
ious processes to a groundwater system's total response cannot be estimated;
much of the existing information can be used in a semiquantitative manner
(i.e., sensitivity analyses and "worst-case" scenarios).
Efforts to collect field data and to estimate natural-process parameters
must be expanded and improved so that model applications will be more physic-
ally based and thereby capable of more accurate predictions. For example, so
few data are available concerning the exact location, volume, composition, and
timing of chemical releases at existing sites that it is very difficult for
modelers to determine the appropriate configuration of what is referred to as
the "source term" in modeling. One prevailing misconception in this regard is
the idea that additional chemical sampling of monitoring wells can provide
definitive clues to the missing historical data; this is true only superfi-
cially. Although indication of the source term can be obtained from the
patterns of chemical movement, there is no guarantee that causal relationships
can be discovered or that the patterns will remain constant.
A common misconception is that all field methods and tools necessary for
obtaining data to run the models are available, if not in optimal form, at
least in a useful form. In fact, however, direct measurements are unreliable
or cannot be obtained for a number of parameters such as groundwater flow
velocity and direction, rates of sorption and desorption (retardation) of
organic chemicals, and the potential for biotransformation. This misconcep-
tion parallels the mistaken idea that all necessary theories have been worked
out and that further refinements are needed only to provide precision and
accuracy.
The integration of geologic, hydrologic, chemical, and biological pro-
cesses into usable subsurface flow and transport models is possible only if
the data and concepts invoked are sound. The data must be representative as
well as accurate and precise. The degree to which the data are representative
is relative to the scale of the problem and the concepts guiding data collec-
tion and interpretative efforts. Careful definition of these concepts is cru-
cial; special attention should be given to the spatial and temporal variations
involved.
The use of newly developed theories to help solve field problems is often
a frustrating exercise. Most theoretical advances call for some data not yet
practically obtainable (e.g., chemical interaction coefficients and relative
permeabilities of immiscible solvents and water). In addition, the incorpora-
tion of theoretical relationships into mathematical models typically is made
possible by invoking certain assumptions and simplifications that alter the
intended relationship. Therefore, theoretical advances in modeling ground-
water problems must be accompanied by improvements in data collection and
mathematical representation efforts.
Large numerical models are particularly data-hungry. Incorporating new
geochemical, hydrological, and biochemical processes often stretches existing
data collection capabilities beyond a practical limit. In many cases generic
data are required, obtained from laboratory batch experiments or controlled
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field experiments. Centralized management of such datasets and efficient
dataset referral services are of great importance to the groundwater modeling
community.
MANAGEMENT ISSUES IN MODELING
Although the precise formulation of a management problem can be quite
thorny, it is prerequisite to the solution. The manner in which a problem is
defined bears heavily on how the professional approaches a solution. Improved
problem definition is likely to result from more interactive participation of
managers and technical personnel in model design and application, both in a
project's initial stage, as is usually the case, and during the modeling
effort itself. Code output is often a barrier to more effective utilization
of the code. Program managers and decision makers need to have model results
presented in a way that is both meaningful and compatible with decisions that
must be made. The uncertainties contained in various decision alternatives
are especially important to assess.
The economic consequences of model predictions and the potential lia-
bilities incurred by their use have brought quality guarantees and code credi-
bility to the forefront as major issues in groundwater modeling. Hence,
quality assurance (QA) needs to be defined and implemented for both model
development and model application. There is a significant difference between
these two: the first is designed to result in a generally reliable code, and
the second to obtain reliable predictions for existing field conditions under
prevailing management constraints. Both require stringent QA procedures. To
further increase the applicability of the models, good documentation and user-
friendliness of the computer coding involved should receive close attention.
Parallel with, and to a significant extent responsible for the rapid
increase in groundwater modeling capabilities, is the technological advance in
computer hardware and software. This is especially noticeable in the inte-
grated approach to computer-based decision-support systems in groundwater
management. In these hardware-software systems, data acquisition and control
is combined with analytical, optimization, and presentational techniques,
resulting in an efficient management tool. The recent introduction of arti-
ficial-intelligence-based expert system technology promises further advances
in the utility and sophistication of decision-support technology.
Managers should require computer-processible data; a protocol for data-
base management systems, improved data-processing techniques, and standardized
formats for I/O (input-output) should be adopted. This will significantly
improve the efficiency of modeling-based data analyses needed for the resolu-
tion of many groundwater issues.
RESEARCH NEEDED
The earlier-quoted EPA Study Group has identified a variety of new models
and modeling approaches as important to groundwater protection (van der Heijde
and Park 1986):
Simulation of flow and transport in multimedia (e.g., coupled models
for surface water/ground-water interaction)
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Representation of stochastic processes in predictive modeling, and
improving the applicability of geostatistical models
Improved modeling of hydrochemical speciation
Simulation of flow and transport in fractured and dual-porosity media,
including diffusion in dead-end pores
Simulation of flow and transport in soils containing macropores
Determination of effects of concentration-dependent density on ground-
water flow and pollutant transport
Determination of effects of alteration of geologic media on hydro-
logical and chemical characteristics (e.g., dehydration of clay when
attacked by solvents, change in sorptive capacity of material when
heated)
Representation of the three-dimensional effects of partially pene-
trating wells on water table aquifers
Development of models for management of groundwater contamination
plumes
Development of expert systems (artificial intelligence) for such tasks
as selecting appropriate submodels or subroutines for specific problems
Application of parameter identification models to be used with site
studies
Further development of pre- and postsimulation data processors
Continued development of risk assessment and management models
Modeling of volatilization, multiphase flow, and immiscible flow
Incorporation of economic factors to improve estimation of cleanup
costs
Development of generic and site-specific parameter databases.
Fundamental research supporting groundwater modeling is considered
necessary in such areas as:
Transient behavior of process parameters (e.g., retardation, hydraulic
conductivity)
Desorption for nonhydrophobic chemicals
Multicomponent transport and chemical interaction
Enhanced transport mechanisms (e.g., piggy-backing on more mobile
chemicals)
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Transport of silt with sorbed chemicals in aquifers
Improved numerical accuracy, stability, and efficiency.
Modeling the transport and fate of chemicals in groundwater is a major
subject of several research programs (DOE 1985, EPA 1987). These programs
focus on immiscible flow associated with organic and oil-like liquids (DOE
1986, EPA 1987). Other topics currently being studied include simulation of
flow and transport in fractured and dual-porosity media, representation of
stochastic processes in predictive modeling, multimedia risk assessment,
incorporation of volatilization in multiphase transport models, and simulation
of density-dependent flow.
CLOSURE
Current and near-future research on geochemical, hydrological, and bio-
physical mechanisms, including large- intermediate- (e.g., artificial aqui-
fers), and field-scale experiments, will probably lead to increasingly
sophisticated mathematical tools for analysis of a variety of groundwater
problems, taking into consideration the stochastic nature of many of the
processes involved. Such problems will not be restricted to water supply and
water pollution issues, but may include other aspects of subsurface use, as
for geothermal energy generation, subsurface energy storage, in-situ ore
processing, and foundation engineering. The complexity of the resulting
models will require a significant increase in computer resources, validation
opportunities, and user expertise. Datasets generated in field-scale experi-
ments will be particularly useful for retrospective model validation. Along
with the growing complexity of groundwater models and methodologies, user
expertise must expand through education and training.
In many respects, modeling will be made easier and "flashier" by the
rapidly evolving computer hardware and software technologies. The mechanics
of entering data, running simulations, and creating high-quality graphics will
become less time-consuming and less complex. Such a reduction of time and
effort may lead to the dangerous assumption that modeling seems to be simple.
In fact, however, modeling will become more and more challenging as ground-
water specialists deal with increasingly complex natural systems and manage-
ment problems, and as the gap widens between our capabilities to characterize
the real world by measuring and simulating simplified images of real-world
systems. Ultimately, it should be the multidisciplinary team representing the
combined knowledge of several fields of expertise that passes judgment on a
management issue, and not the modeler and certainly not "the model." A model
is not more than a tool, albeit a complex one, and a model user should be more
than someone who knows how to handle the tool. As the role of models in
decision making increases, the consequences of incorrect model use become more
critical. To draw on a common metaphor: it seems easy to hit a nail with a
hammer, but no one wants to be the person who misses the nail while someone
else holds it!
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172
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APPENDIXES A-H
The following appendixes contain descriptive listings of selected models
from the IGWMC MARS database. The IGWMC model information databases are
accessible through the IGWMC offices in Indianapolis, Indiana, and Delft, The
Netherlands. The models listed are considered by the authors to be relevant,
available (as defined in the section on model selection of Chapter 4), and
current. Model categories are saturated groundwater flow (Al, A2), variable
saturated flow (Bl, B2), solute transport (Cl, C2), heat transport (Dl, D2),
hydrogeochemical speciation (El, E2), flow and transport in fractured rock
(Fl, F2), and multiphase flow (61, G2). Two tables are provided for each
category. The first table (e.g., Al) identifies the models, provides
contacts, and describes the capabilities of each model. The second table
(e.g., A2) for a given category provides additional information for evaluating
a model's usefulness and reliability.
As discussed in the section on model selection in Chapter 4, an important
aspect of a model's use 1n ground-water management is its efficiency, which is
determined by the human and computer resources required for its proper
operation. A model's efficiency can be described by its usability,
availability, modiflability, portability, and economy of computer use.
Another important issue is the model's reliability. In the appendixes,
usability and reliability are qualified by the following descriptors.
USABILITY
Pre- and Postprocessors
The presence of pre- and postprocessors is rated as: not present [none,
N], dedicated [model-dependent, D], generic [can be used for a class of
models, might include separate reformatter for specific models or display
software, G], used for interactive runs [I], or status unknown [Ul.
Documentation
As part of assessing the adequacy of the documentation, the presence of
an adequate description of user's instructions and example datasets is
indicated by yes [Y] or no [N]. Models having no published description of
their theoretical basis are not listed in these appendices.
Support
Software support and maintenance is rated as: none [N], limited with
respect to level of support [L], unlimited [Y], and unknown [U].
Hardware Dependency
In this report a model's hardware and/or software dependency is indicated
as present [Y] or not [N]. Hardware dependency may be due to the size of the
source code, the way it has been designed and compiled, the use of specific
peripherals, and graphics calls in the program. In addition, programs may be
software-dependent, requiring specific program purchases to reside on the
user's computer (e.g., graphics or mathematical routines).
173
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RELIABILITY
Review
This report identifies peer-review of theory and coding. For each
category the rating is: peer-reviewed [Y}, not peer-reviewed IN], and unknown
[U]. A model is considered to be peer-reviewed if theory and code has been
subject to a formal review process such as established by certain agencies
(eg., U.S. EPA, U.S. Geological Survey). In addition, a model's theory is
considered to be peer-reviewed if it has been published in a peer-reviewed
journal (e.g., Water Resources Research).
Verification
A model's verification status is rated as extensive IY], not verified
[N], or unknown {U]. Models verified only with respect to segments of their
coding or for only a part of the tasks for which they were designed are rated
to have undergone partial or limited verification {LJ.
Field Testing
In this report, model field testing, the application of models to site-
specific conditions for which extensive datasets are available (see Chapter
3), is rated as extensive [y], partial or limited [L], not validated [N], or
unknown [U].
Extent of Model Use
This report evaluates the extent of a model's use in four classes: many
[M, >10], few [1-10], none [N], and unknown [U].
Appendix H is a list of principle references for the models listed in
A-G. Note that model reference numbers are listed under the author entry in
tables A1-G1. Similarly, each reference in Appendix H includes the appendix
number and IGWMC key number of the model to which that reference applies.
For additional information contact IGWMC-Indianapolis, Holcomb Research
Institute, Butler University, 4600 Sunset Avenue, Indianapolis, Indiana 46208,
or IGWMC-Oelft, TNO-DGV Institute of Applied Geoscience, P.O. Box 285, 2600
AG, Delft, The Netherlands.
174
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APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
NO.
i.
2.
3.
4.
5.
6.
Author(s)
S.P. Neunan
P. A.
Wither spoon
Ref: 116
S.P. Neuman
P. A.
Witherspoon
Ret: 117
T.R. Narasimhan
Ref: 112
R.I. Cooler
J. Peters
Ref: 26
R.L. Coo ley
J. Peters
Ref: 26
R.L. Coo ley
R.L. Naff
Ref: 27
Contact Address
Department of Hydrology
and Water Resources
University of Arizona
Tucson, A2 85721
Department of Hydrology
and Water Resources
University of Arizona
Tucson. A2 85721
National Energy Software
Center (NESC)
Argonne National Lab.
9700 South Cass Avenue
Argonne, IL 60439
Hydro logic Engineering
Center
U.S. Army Corps of
Eng i neers
609 Second Street
Davis, CA 95616
Hydro logic Engineering
Center
U.S. Army Corps of
Engineers
609 Second Street
Davis, CA 95616
U.S. Geological
Survey
Water Resources Division
Box 25046, MS 413
Federal Center
Denver, CO 80225
Model Name
(last update)
FREE SURF 1
(1979)
FREESURF 1 1
(1979)
TERZAGI
(1981)
ECPL 723-G2-
L2440
(1981)
FINITE
ELEMENT
SOLUTION OF
STEADY -STATE
POTENTIAL
FLOW
PROBLEMS
(1981)
NON-LINEAR
REGRESSION
GROUNDWATER
FLOW MODEL
(1985)
Model
Description
A finite-element model
to simulate two-dimen-
sional vertical or axi-
symmetric, steady-state
flow in an anisotropic,
heterogeneous , conf i ned
or water-table aquifer.
A finite-element model
to simulate two-dimen-
sional vertical or axi-
symmetric, transient
flow in anisotropic.
heterogeneous porous
media with free
surfaces.
An integrated-f inite-
difference approach to
compute steady and non-
steady pressure head
distributions., and one-
dimensional compaction
in saturated, hetero-
geneous, anisotropic
porous media with
complex geometry.
A finite-element solu-
tion for determining
head distributions in
confined, sen '-confined,
or uncon f i ned , an i so-
tropic, heterogeneous
aquifer systems. The
node! can handle hori-
zontal , cross-sectional.
or axisymnetric configu-
rations for steady-state
flow.
A finite-element solu-
tion to simulate steady-
state ax i symmetric flow
through a heterogeneous
anisotropic, leaky
aquifer.
An interactive inverse
groundwater flow model
using non- linear regres-
sion and finite-element
simulation. It esti-
mates source/sinks,
boundary fluxes and best
fit hydraulic head dis-
tribution for steady-
state, horizontal
groundwater flow in an
anisotropic, hetero-
geneous aquifer.
Model
Processes
consol idation
expansion
leaKage
compaction
leakage
cap! 1 lary
forces
leakage
leakage
delayed yield
IGWMC
Key
0020
0022
0121
0140
0141
0195
175
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APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
F
8.
9.
10.
11.
12.
13.
14
Author(s)
H.J. Morel-
Seytoux
C. Rodriguez
C. Daly
T.
1 1 langasekare
G. Peters
Ref: 111
T.A. Prickett
C.G. Lonnquist
Ref: 137
G.F. Pinder
E.O. Frind
Ref: 132
G.F. Pinder
C.I . Voss
Ref: 135
P.S. Huyakorn
Ref: 81
T.R. Knowles
Ref : 164
C.R. Faust
T. Chan
B.S. Ramada
B.M. Thompson
Ref: 82
S.B. Pahwa
B.S. Rama Rao
Ref: 83
Contact Address
Colorado State
University
Engineering Research
Center
Fort Col 1 ins, CO 80523
Consulting Water
Resource Engineers
6 G.H. Baker Drive
Urbana, IL 61801
Department of Civil
Engineering
Princeton University
Princeton, NJ 08540
U.S. Geological Survey
Water Resources Division
National Center, MS 431
Reston, VA 22092
Performance Assessment
Department
Office of Nuclear Waste
Isolation
Battel le Project
Management Division
505 King Avenue
Columbus, OH 43201
Texas Department of
Water Resources
P.O. Box 13087
Austin, TX 78758
Performance Assessment
Department
Office of Nuclear Water
Isolation
Battel le Project Mgmt.
Division
505 King Avenue
Columbus, OH 43201
Performance Assessment
Department
Office of Nuclear Waste
Isolation
Battelle Project Mgmt.
Division
505 King Avenue
Columbus, OH 43201
Model Name
( last update)
DELTA
(1981)
PLASM
(1971)
1 SOQUAD
(1982)
AOUIFEM
(1979)
STAFAN 2
(1982)
GWSIM
(1981)
STFLO
(1982)
NETFLO
(1982)
Model
Description
A two-dimensional areal
model to simulate tran-
sient groundwater flow
in a confined or uncon-
fined heterogeneous,
isotropic aquifer con-
nected with a river.
using stream-aquifer
response coefficients.
A finite-difference two-
dimensional or quasi -
three-d i mens i ona 1 ,
transient, saturated
f low model for single
layer or multi-layered
confined, leaky
confined, or water-table
aquifer systems with op-
tional evapotranspi ra-
tion and recnarge from
streams.
Finite-element model to
simulate three-dimen-
sional groundwater flow
in confined and uncon-
f ined aqui f ers.
A finite-element model
to simulate transient,
areal groundwater flow
in an isotropic, hetero-
geneous, confined,
leaky-confined or water
table aqui fer.
A finite-element model
for simulation of tran-
sient two-dimensional
flow and stress in de-
formabie fractured and
unfractured porous
media.
A transient, two-dimen-
sional, horizontal model
for prediction of piezo-
metric head in an an iso-
tropic, single- layer
aquifer.
A linear finite-element
code for simulation of
steady-state, two-dimen-
sional (areal or verti-
cal ) plane or axisy-
metric groundwater flow
in an isotropic, hetero-
geneous, confined, leaky
or water-table aquifers.
To simulate steady-state
three-dimensional flow
in a heterogeneous
medium by an equivalent
network of series and
parallel flow members.
Model
Processes
inf i Itrat ion
evapotrans-
piration
leakage
leakage
leakage
inf i Itrat ion
deformation
compaction
leakage
GHMC
ey
0260
0322
0510
0514
0584
0681
0694
0695
176
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APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
15.
16.
17.
18.
19.
20.
21.
Author (s)
T. Haddock 1 1 1
Ref: 165
P.C. Trescott
S.P. Larson
Ref: 171 *
P.C. Trescott
G.F. Pinder
S.P. Larson
Ref: 172
V. Guvanasen
Ref: 65
K.R. Rushton
L.M. Toml inson
Ref: 148
M. Clouet
D' Or vat
M. Clouet
D'Orval
Contact Address
Water Resources
Development and
Management Service
Land and Water
Development
Organization
Food and Agriculture
Organization of U.N.
Via Delle Terme de
Caracella, 00100
Rome Italy
U.S. Geological Survey
Branch of Groundwater
MS 411, National Center
Res ton, VA 22092
U.S. Geological Survey
Branch of Groundwater
MS 411, National Center
Reston, VA 22092
Department of Civil and
System Engineering
James Cook University of
North Queensland
Queensland, 481 1
Austral ia
Department of Civi 1
Engineering
University of Birmingham
P.O. Be* 363
Birmingham, B15 2TT
United Kingdom
Burgeap
70, Rue Mademoiselle
75015 Paris
France
Burgeap
70, Rue Mademoiselle
75015 Paris
France
Model Name
(last update)
LEAKY
AQUIFER
SIMULATION
(1982)
USGS-3D-FLOW
(1982)
USGS-2D-FLOW
(1976)
1 .D.P.N.G.M.
(1979)
AGU-1
(1979)
BURGEAP
7600 HYSO
PACKAGE
(1982)
BURGEAP
7600 HYSO
(TRABISA
MODEL)
(1981)
Model
Description
To calculate the re-
sponse of an isotropic,
heterogeneous, confined
or leaky aquifer to
pumping from one or more
wells, based on horizon-
tal two-dimensional,
unsteady-state flow
simulation.
A f inite-dif ference
model to simulate
transient, three-
dimensional and quasi -
three-dimensional ,
saturated flow in an iso-
tropic, heterogeneous
groundwater systems.
A finite-difference
model to simulate
transient, two-
dimensional horizontal
or vertical flow in an
an isotropic and
heterogeneous, confined,
leaky-confined or »ater-
table aquifer.
Finite-difference
approach for the direct
inverse problem of para-
meter identification in
a confined or unconfined
heterogeneous isotropic
aquifer with transient
two-dimensional horizon-
tal groundwater flow.
Finite-difference model
for transient single
layered two-dimensional
horizontal groundwater
flow.
A program package to
simulate two-dimension-
al, hor izontal /vert i ca 1 ,
steady/transient, satu-
rated flow in confined/
unconfined, homogeneous/
heterogeneous aquifer
systems with multiple
immiscible fluids, and
connection with surface
water.
To simulate two-dimen-
sional , horizontal ,
transient, saturated
flow of two immiscible
f luids of different
densities, in uncon-
fined, homogeneous/
heterogeneous aquifers.
Model
Processes
leakage
evapotrans-
pirat ion
leakage
leakage
evapotrans-
piration
leakage
IGWMC
Key
0756
0770
0771
0951
1230
1370
1371
177
-------
APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
22.
23.
24.
25.
26.
27.
28.
Author (s)
M. Clouet
D'Orval
A. Levassor
P. Prudhomme
J.L. Henry
F. Biesel
P. Prudhomme
J.L. Henry
F. Biesel
B. Boehm
Y. Bachmat
A. Oax
O.A. Blank
Contact Address
Burgeap
70, Rue Mademoisel le
75015 Paris
France
Centre D1 Informatique
Geologique
Ecol Des Mines De Paris
35, Rue Saint-Honore
77305-Fontainbleau
France
Laboratoire Central
D'Hydraul ique De France
10, Rue Eugene-Renault
94700 Maisons-Alfort
France
Laboratoire Central
D'Hydraul ic De France
10, Rue Eugene-Renault
9700 Maisons-Alfort
France
Abtei lung
Wasserwirtschaft
Rheinbraun
Stuttgenweg 2
5000 Koln 41
Federal Republ ic of
Germany
Hydro logical Service of
Israel
P.O. Box 6381
Jerusalem, Israel
Tahal Consulting
Engineers Ltd.
P.O. Box 11170
Tel Aviv, Israel
Model Name
(last update)
BURGEAP
7600HYSO
(TRABICO
MOOED
(1981)
PL IN
(1981)
BIDAT-HS2
(1981)
TRIGAT-HS1
OR AXYZ-HS5
(1981)
GW 1
(1981)
ITERATIVE
ALGORITHM
FOR SOLVING
THE INVERSE
PROBLEM IN A
MULT 1 CELL
AQUIFER
MODEL
(1979)
AQSIM
(1981)
Model
Description
Simulation of two-dimen-
sional, vertical tran-
sient flow in hetero-
geneous, confined or
unconfined aquifers with
representation of free
surface to determine the
hydraulic coefficients
pertaining to the rela-
tion between a river and
the aquifer.
Optimization of well
field exploitation in
single or multi -layered
aquifer system using
influence coefficients.
A finite-difference
model for prediction of
piezometric heads and
flow in anisotropic.
heterogeneous, confined,
semi -con f ined, or
unconf ined aqui fers.
A finite-difference
model for prediction of
piezometric heads for
unsteady three-dimen-
sional flow in confined,
sem i -con f i ned or uncon-
fined, anisotropic,
heterogeneous aquifers.
A transient, two-dimen-
sional finite-difference
groundwater model to
simulate dewatering in
isotropic, heterogeneous
aqui fers, using
polygons.
This model solves the
inverse problem in a
two-dimensional water-
table aqui fer with
varying pumping and
replenishment.
A two-dimensional
finite-difference model
to solve transient
horizontal groundwater
problems in isotropic,
heterogeneous , con f i ned
or phreatic aquifers
connected with a stream;
optional simulation of
salt-fresh water
interface.
Model
Processes
leakage
inf i 1 tration
leakage
dewatering
inf i 1 tration
IGWMC
Key
1372
1470
1481
1482
1531
1631
1651
178
-------
APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
29.
30.
31.
32.
33.
34.
35.
36.
Author(s)
H.M. Haitjema
O.D.L. Strack
T.N. Olsthoorn
C. van den
Akker
Ref: 175
C. van den
Akker
Ref: 175
C. van den
Akker
Ref: 175
P. van der Veer
A. Verruijt
J.B.S. Gan
Ref: 186
D.E. Evenson
Ref: 47
Contact Address
School of Publ ic and
Environmental Affairs
10th Street
Indiana University
Bloom ing ton, IN 47405
Nansenlaen W.
9641 XW Pynacker
The Netherlands
National Institute for
Water Supply
P.O. Box ISO
2260 AD Leidschendam
The Netherlands
National Institute for
Water Supply
P.O. Box 150
2260 AO Leidschendam
The Netherlands
National Institute for
Water Supply
P.O. Box 150
2260 AO Leidschendam
The Netherlands
Ri jkswaterstaat
Data Processing Division
P.O. Box 5809
2280 HV Rijswijk (2.H.)
The Netherlands
Department of Civil
Engineering
Delft Technical
University
Sterinweg 1
2628 CM Delft
The Netherlands
COM water Resources
Engineers
710 South Broadway
Walnut Creek, CA 94596
Model Name
(last update)
SYLENS
(1985)
TOFEM-N
C1985)
FLOP
(1981)
FLOP-2
(1981)
FRONT
(1981)
MOTGRO
(1981)
SWIFT
(1982)
PEP
(1981)
Model
Description
An analytical solution
for steady-state
groundwater flow in
regional double aquifer
systems with local
interconnections.
Multi-layer finite-
element groundwater flow
Model.
A finite-difference
model for calculation of
pathl ines in confined
aquifers without storage
and residence times of
water particles.
To generate pathl ines
for steady-state flow in
a semi -con f ined, i so-
tropic, homogeneous
aquifer without storage
and to calculate resi-
dence times for a number
of water particles.
Calculation of path lines
for steady-state and
transient f low in a
confined, isotropic,
heterogeneous aquifer
and computation of
residence times for a
number of water
particles.
Prediction of ground-
water head and stream
function for two-dimen-
sions using analytical
function method;
vertical, steady and
unsteady, single or
multi-fluid flow in
homogeneous , an i sotro-
pic, confined or uncon-
fined aquifers or
arbitrary shapes.
A cross-sectional
finite-element model for
transient horizontal
flow of salt and fresh
water and analysis of
upconing of an interface
in a homogeneous
aquifer.
To calibrate steady or
unsteady, confined or
water-table flow models
for an isotropic heter-
ogeneous aquifer systems
automatically by non-
1 inear programming
techniques.
Model
Processes
inf i Itration
evapotrsns-
pi rat ion
buoyancy
leakage
inf i Itration
IGWMC
Key
1791
1814
1820
1821
1822
1830
1852
1940
179
-------
APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
Ho.
37.
38.
39.
40.
41.
42.
43.
44.
Author(s)
K. Ueshita
K. Sato
Ref: 173
H.J. Morel-
Seytoux
T.
1 1 langasekare
Ref: 79
H.J. Morel-
Seytoux
C.J. Daly
6. Peters
Ref: 130
S.K. Gupta
C.R. Cole
F.W. Bond
Ref: 61
A.E. Reisenauer
C.R. Cole
Ref: 15
A.E. Reisenauer
C.R. Cole
Ref: 15
A.E. Reisenauer
C.R. Cole
Ref: 15
j.W. Mercer
C.R. Faust
Ref: 109
Contact Address
Department of
Geotechnical Eng.
Nagoya University
Chikusa, Nagoya 464
Japan
Engineering Research
Center, A3 15
Colorado State
University
Fort Collins, CO 80523
Engineering Research
Center, A315
Colorado State
University
Fort Coll ins, CO 80523
Water and Land Resources
Division
Battel le Pacific NW Lab.
P.O. Box 999
Rich land, MA 99352
Mater and Land Resources
Division
Battel le Pacific NW Lab
P.O. Box 999
Richland, WA 99352
Water and Land Resources
D i v i s i on
Battel le Pacific NW Lab
P.O. Box 999
Richland, WA 99352
Water and Land Resources
Division
Battel le Pacific NW Lab
P.O. Box 999
Richland, WA 99352
Geotrans, Inc.
250 Exchange PI .
Suite A
Herdon, VA 22070
Model Name
(last update)
CONSOL-I
(1981)
DELTIS-
STREAM-
AQUIFER
DISCRETE
KERNEL
GENERATOR
(1981)
DELPET-
DISCRETE
KERNEL
GENERATOR
(1977)
FE3DGW
(1985)
VTTSS3
(1979)
VTTSS2
(1979)
VTT
U979)
SWSOR
(1980)
Model
Description
A non-steady-state
finite-element model to
simulate one-dimensional
vertical groundwater
flow and soil displace-
ment in order to calcu-
late the groundwater
levels necessary for the
prevention of land
subs i dence .
A stream-aquifer dis-
crete kernel generator
for horizontal confined
or uncon fined, transient
grounduater flow in i so-
tropic, heterogeneous
aquifers.
A discrete kernel
generator for transient
horizontal flow in an
isotropic, hetero-
geneous, confined or
unconfined aquifer to
simulate drawdowns and
return flows.
Transient or steady-
state, finite-element
three-dimensional
simulation of flow in a
large multi-layered
groundwater basin.
A finite-difference
model to predict steady-
state hydraulic head in
uncon fined or confined
multi-layered aquifer
systems and to generate
stream! ines and
travel times.
A finite-difference
model to predict steady-
state hydraulic head in
conf ined aquifers
systems w i th up to f i ve
layers.
A f inite-di f ference
node! to calculate
transient hydraulic head
distributions in
confined or unconfined
multi-layered aquifer
systems, and to generate
travel times.
A finite-difference
model to simulate the
areal, unsteady flow of
saltwater and freshwater
separated by an inter-
face in an isotropic.
heterogeneous porous
media.
Model
Processes
consol idation
evapotrans-
piration
leakage
delayed yield
compaction
inf i 1 tration
leakage
inf i Itration
leakage
inf i Itration
leakage
inf i Itration
1 eakage
inf i Itration
GHMC
Key
2021
2060
2061
2072
2090
2091
2092
2140
180
-------
APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
45.
46.
47.
48.
49.
50.
51.
52
Author (s)
J.B. Weeks
Ref: 18
L.R. Town ley
J.L. Wilson
A.S. Costa
Ref: 168
L.K. Kuiper
Ref: 99
R.H. Page
Ref: 126
D.R. Posson
G.A. Hearne
J.V. Tracy
P.P. Frenzel
Ref: 136
C.J. Oaly
Ref: 29
J. Boonstra
Ref: 16
0. Berney
Ref: 12
Contact Address
U.S. Geological Survey
Water Resources Division
Box 25046, MS 412
Denver Federal Center
Lakewood, CO 80225
Ralph M. Parsons
Laboratory for Water
Resources and
Hydrodynamics
Room 48-211
Massachusetts Institute
of Technology
Cambridge, MA 02139
U.S. Geological Survey
SW Tower, 3rd floor
211 East 7th Street
Austin, TX 78701
Water Resources Program
Department of Civi 1
Engineering
Princeton University
Princeton, NJ 08540
U.S. Geological Survey
P.O. Box 26659
Albuquerque, NM 87125
U.S. Array Corps of
Engineers
Cold Regions Research 4
Engineering Lab
Hanover, NH 03755
Intern M Inst. for
Land Reclamation and
Improvement
P.O. Box 45
Wageningen
The Netherlands
Land and Water
Development Division
Food and Agriculture
Organization
Via Del le Terme Dl
Caracal la
00100-Rome
Italy
Model Name
(last update)
QUASI THREE-
DIMENSIONAL
MULT 1 AQUIFER
MODEL
(1978)
AQUIFEM-1
(1979)
VARIABLE
DENSITY
MODEL
(1984)
INTERFACE
(1979)
N.M.F.D 3D
(1980)
CRREL
(1984)
S.G.M.P.
(1981)
Dl SI FLAG
(1980)
Model
Description
A finite-difference
model to simulate
transient or steady-
state groundwater flow
in isotropic, hetero-
geneous multi-aquifer
systems .
A two-dimensional ,
finite-element model for
transient, horizontal
groundwater flow.
1 ntegrated-f i n i te-d i f -
ference model for the
simulation of variable
density groundwater flow
in three dimensions.
To simulate transient
flow of fresh and saline
water as immiscible
fluids separated by an
interface in an iso-
tropic, heterogeneous,
water table aqui fer
using the finite-element
method .
A finite-difference
model for simulation of
unsteady two-dimensional
horizontal groundwater
flow in multi-layered
heterogeneous
an isotropic aquifer
systems or unsteady
three-d i nens i ona 1
saturated flow systems.
Analytical model to
calculate and plot
streamlines for flow in
anisotropic, hetero-
geneous aquifers.
Uses i ntegrated-f inite-
dif ference approach for
simulation of steady-
state or transient, two-
dimensional, horizontal
flow in a saturated.
anisotropic, and hetero-
genous, confined,
semi confined or phreatic
aquifer.
A finite-difference
model for steady-state
or transient simulation
of two-dimensional ,
horizontal groundwater
flow in a two-layered,
isotropic, heterogeneous
aquifer system.
Model
Processes
leakage
leakage
evapotrans-
pi rat ion
leakage
leakage
leakage
GMMC
ey
2510
2630
2663
2720
2740
2791
2800
2870
181
-------
APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
53.
54.
55.
56.
57.
58.
59.
60.
Author (s)
H.N. Tyson
Ref: 12
A. P.M. Broks
D. Dijkstra
J.W. Wesseling
Ref: 19
B.H. Gi Iding
J.W. Wessel ing
Ref: 55
J. Moor i shad
P. A.
Witherspoon
J. Noorishad
M.S. Ayatollahi
P. A.
Witherspoon
Ref: 124
G. Schmid
Ref: 155
P.M. Cobb
C.O. Meet wee
M.A. Butt
Ref: 108
B. Sagar
Contact Address
Water Resources
Development and
Management Service
Land and Water
Development Division
Food and Agriculture
Organization of the
United Nations
Via Delle Terrae 01
Caracal la, 00100
Rome , 1 ta 1 y
Delft Hydraul ics Lab
P.O. Box 152
8300 AD Emmeloord
The Netherlands
Delft Hydraulics Lab
P.O. Box 152
8300 AO Emmeloord
The Netherlands
Earth Sciences Division
Lawrence Berkeley Lab
University of California
Berkeley, CA 94720
Earth Sciences Division
Lawrence Berkeley Lab
University of California
Berkeley, CA 94720
Ruhr-University Bochum
Institute F. Konst.
Ingenleubau A6 IV
D-4630 Bochum
Federal Republic of
Germany
Kansas Geological Survey
1930 Avenue A, Campus W
University of Kansas
Lawrence, KS 66044
Analytic and
Computational
Research, Inc.
3106 Inglewood Blvd.
Los Angeles, CA 90066
Model Name
(last update)
KRGW
(1982)
GROMULA
(1981)
GROMAGE
(1982)
ROCMAS-H
(1976)
ROCMAS-HM
(1981)
SICK 100
(1981)
TSSLEAK
(1982)
AQUIFER
(1982)
Model
Description
A finite-difference
odel to simulate
steady-state or
transient, two-dimen-
sional horizontal flow
in a single confined or
uncon fined, or a two-
layered, leaky, i so-
tropic, heterogeneous
aquifer systea.
A user-oriented finite-
element model to
simulate steady-state or
transient, two-dimen-
sional groundwater flow
in anisotropic, hetero-
geneous, multi-layered
aquifer systens.
Finite-element solution
for transient simulation
of two-dimensional
horizontal groundwater
flow and drainage in
anisotropic hetero-
geneous multi-layered
aquifer systems.
A finite-element model
for two-dimensional
simulation of transient
groundwater flow 'in
porous fractured rock.
A finite-element two-
dimensional model for
analysis of quasi -static
coupled stress and fluid
flow in porous fractured
rock.
Simulation of vertical
and horizontal steady
and non-steady ground-
water flow, using
potential and stream
function approach.
Automated analysis of
pump ing-test data for a
leaky-artesian aquifer.
Analysis of steady and
non-steady-state, two-
dimensional areal or
cross-sect i ona ! , rad i a 1
flow in heterogeneous.
anisotropic multi-
aquifer systems.
Model
Processes
leakage
leakage
evapotrans-
piration
drainage
consol idation
fracture
deformation
delayed yield
leakage
leakage
inf i Itration
IGHMC
Key
2930
2980
2981
3080
3082
3110
3160
3230
182
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APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
61.
62.
63.
64.
65.
66.
Author (s)
B. Sagar
Ref: 150
J.A. Liggett
Ref: 103
P.J.T. van
Bakel
Ref: 174
G.T. Yeh
C.W. Francis
Ref: 196
G.T. Yeh
D.O. Huff
Ref: 197
D.N. Contractor
Ref: 194
Contact Address
Analytic and
Computational
Research, Inc.
3106 Inglewood Blvd.
Los Angeles, CA 90066
School of Civil and
Environmental
Engineering
Ho) lister Hall
Cornel 1 University
Ithaca, NY 14853
Institute for Land and
Water Management
Research
P.O. Box 35
6700 AA Mageningen
The Netherlands
Environmental Sciences
Division
Oak Ridge National
Laboratory
Oak Ridge, TN 37830
Environmental Sciences
Division
Oak Ridge National Lab
Oak Ridge, TN 37830
Water and Energy
Research Institute of
the Western Pacific
University of Guam
Col lege Station,
Hangilao, Guam 96913
Model Name
(last update)
DEWATER
(1962)
GM5
(1982)
FEMSAT
(1981)
AOU 1 FLOW
(1984)
FEWA
(1983)
SWIGS2D
(1982)
Model
Description
Uses i ntegrated-f inite-
difference approach for
two-d i mens i ona 1 , area 1
or cross-sectional ,
radial simulation of
steady or unsteady flow
in anisotropic and
heterogeneous, confined
or water table aquifers;
predicts drawdown due to
pumping during surface
and subsurface mining
and building construc-
tion operations.
Uses boundary integral
equation modified for
steady-state simulation
of three-dimensional
saturated groundwater
flow in an anisotropic,
heterogeneous multi-
aquifer system.
A finite-element model
to simulate transient
two-dimensional horizon-
tal flow in a saturated
heterogeneous, anisotro-
pic multi -layered
aqui fer system.
A two-dimensional
finite-element model to
simulate transient flow
in horizontal ,
anisotropic,
heterogeneous aquifers
under confined, leaky or
unconfined conditions.
A two-dimensional
finite-element model to
simulate transient flow
in confined, leaky con-
fined, or water table
aquifers.
A two-dimensional
finite-element model to
simulate transient.
horizontal salt and
fresh water flow
separated by a sharp
interface in an
anisotropic, hetero-
geneous, confined, semi-
con fined or water table
aquifer.
Model
Processes
dewater i ng
leakage
leakage
leakage
leakage
leakage
IGWMC
Key
3231
3240
3350
3372
3373
3600
183
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APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
67.
66.
69.
70.
71.
72.
73.
Author(s)
R.I . Al layla
1 . Herrera
J.P. Hennart
R. Yates
Ref: 68
F.T. Tracy
Ref: 169
C.S. Desai
C.S. Desai
C.S. Desai
C.S. Desai
Ref: 37
Contact Address
Civil Engineering
Department
Colorado State
University
Fort Coll ins, CO 80523
Intituto De Geofisiea
Ciudad Universitaria
04510 Mexico, D.F.
U.S. Army Engineer
Waterways
Experiment Station
Automatic Data
Processing Division
P.O. Box 631
Vicksburg, MS 39180
Department of Civi I
Engineering
University of Arizona
Tuscon, AZ 85721
Department of Civil
Engineering
University of Arizona
Tuscon, AZ 85721
Department of Civil
Eng i neer i ng
University of Arizona
Tuscon, AZ 85721
Department of Civil
Engineering
University of Arizona
Tuscon, AZ 85721
Model Name
(last update)
SEAWTR/
SEACONF
(1980)
LAFTID
(1983)
ECPL 704-F3-
RO-011
(1983)
DFT/C-10
(1984)
FIELD-2D
SEEP2(VM)-2D
(1984)
SEEP(VM)-3D
(1983)
Model
Description
A finite-difference
odel for two-dimen-
sional horizontal
simulation of simul-
taneous flow of salt and
fresh water in a con-
fined or water table
aquifer with anisotropic
and heterogeneous pro-
perties, including
effects of cap! 1 lary
flow.
A finite-element quasi -
three-dimensional model
for transient leaky
aquifer flow including
predictions of land
subsidence.
A finite-element model
for steady-state
simulation of cross-
sectional and
ax i symmetric flow in
confined or uncon fined,
anisotropic, hetero-
geneous porous media.
A finite-element model
for 1 inear stress-
deformation, and steady
or transient fluid flow
analysis of one-dimen-
sional problems;
calculation of dis-
placement, fluid head,
temperature or pore
water pressure.
A finite-element model
for 1 inear steady
analysis of two-
dimensional problems in
torsion, potential flow.
seepage and heat flow.
A finite-element model
for two-dimensional
planar or ax i symmetric
simulation of steady
confined, steady free
surface and transient
free surface seepage in
structures such as dams,
river banks, hillslopes
and wei is.
Three-dimensional simu-
lation of confined, and
steady and transient
free surface seepage in
porous bodies (dams.
ells, slopes, drains,
edia with cracks) ,
using a finite-element
technique with variable
and moving mesh.
Model
Processes
capi I lary
forces
influence
capil lary
region on
spec i f i c
yield
consol idation
leakage
conduct i on
consol idation
campaction
conduction
IGWMC
Key
3640
3700
3810
3860
3861
3862
3863
184
-------
APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
74.
75.
76.
77.
78.
79.
80.
81.
Author (s)
C.S. Desai
C.S. Desai
C.S. Desai
C.S. Desai
D.G. Jorgensen
H. Grubb
C.H. Baker, Jr.
G.E. Hi lines
E.D. Jenkins
Ref: 86
J.V. Tracy
Ref: 167
W.I .H.
E 1 derhorst
M.G. McDonald
A.W. Harbaugh
Ref: 107
Contact Address
Department of Civi 1
Engineering
University of Arizona
Tuscon, AZ 85721
Department of Civi 1
Engineering
University of Arizona
Tuscon, AZ 85721
Department of Civil
Eng i neer i ng
University of Arizona
Tuscon, A2 85721
Department of Civi 1
Engineering
University of Arizona
Tuscon, AZ 85721
U.S. Geological Survey
Water Research Dept.
1950 Ave. A-Campus West
University of Kansas
Lawrence, KS 66044-3897
U.S. Geological Survey
Water Resources Dept.
National Center
Reston, VA 22092
Institute for Appl ied
Geosciences
TNO/DGV
P.O. Box 285
2600 AG Delft
The Netherlands
Ground Water Branch, WRD
U.S. Geological Survey
WGS-MS 433
Reston, VA 22092
Model Name
(last update)
STRESEEP-2D
(1984)
CONS2-1D
(1984)
CONSPU/NL)-
20
(1984)
CONSA(L)-2D
(1984)
GWM03-
APPROPRIA-
TION MODEL
(1982)
PARAMETER
ESTIMATION
PROGRAM
(1980)
INVERS
(1983)
MOOFLOW
(1988)
Model
Description
A finite-element model
for combined stress,
seepage and slope
stabi 1 ity analysis of
dans, embankments and
slopes using the resid-
ual flow method.
A f i n i te-e 1 ement node 1
for consolidation and
settlement analysis of
foundations idealized as
one-dimensional with
linear variation of pore
water pressures.
A finite-element model
for consolidation and
settlement analysis of
foundations, dans and
embankments idealized as
plane strain.
A finite-element model
for consolidation and
settlement analysis of
foundations, piles,
tanks and other struc-
tures, ideal ized as
ax i symmetr i c .
An ax i symmetric finite-
difference model to cal-
culate dra«do«n due to a
proposed «el 1 , at all
existing wel Is in the
section of the proposed
well and in the adjacent
8 sections and to com-
pare drawdowns with
al lowable 1 imits.
An automated calibration
procedure to calculate
transmissivities, verti-
cal conductivities,
storage coefficients and
specific storages of
confining layers in the
head results from a
quasi -three-dimensional
flow system, using a
finite-difference flow
model as input.
A direct inverse model
to calculate hydraulic
resistance of confining
layers in a multi-
layered aquifer with
steady-state groundwater
flow.
A nodular three-dimen-
sional finite-difference
groundwater model to
simulate transient flow
in anisotropic, hetero-
geneous, layered aquifer
systems .
Model
Processes
consol idation
consol idation
consol idation
evapotrans-
pi rat ion
drainage
IGWMC
Key
3864
3865
3866
3867
3870
3880
3950
3980
185
-------
APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
82.
83.
84.
85.
86.
87.
Author(s)
C.R. Kolterman
Ref: 95
A.I. El-Kadi
Ref: 43
D.N. Contractor
S.M.A. El Oidy
A.S. Ansary
Ref: 25
P.R. Schroeder
J.M. Morgan
T.H. Walski
A.C. Gibson
Ref: 153
P.K.M. van der
Heijde
Ref: 177
P.K.M. van der
Heijde
Ref: 178
Contact Address
Water Resources Center
Desert Research Inst.
University of Nevada
System
Reno, NV
International Ground
Mater Modeling Center
Hoi comb Research Inst.
Butler University
4600 Sunset Avenue
Indianapolis, IN 46208
Department of Civ! 1
Engineering
Universtiy of Arizona
Tuscon, AZ 85721
International Ground
Water Modeling Center
Hoi comb Research
Institute
4600 Sunset Ave.
Indianapol is, IN 46208
International Ground
Mater Model ing Center
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapolis, IN 46208
International Ground
Water Model ing Center
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapolis, IN 46208
Model Name
(last update)
GWUSER/
CONJUN
(1983)
ST2D
(1985)
MAOWF
(1987)
HELP
(1987)
THWELLS
(1988)
GWFLOW
(1987)
Model
Description
A combined simulation-
optimization model to
determine optimal pump-
ing locations and rates
for confined aquifer
with or without artifi-
cial recharge or for
conjunctive use of
aquifer stream system;
uses finite-differences
and linear programming.
This is a two-dimen-
sional model to solve a
stochastic gravity
drainage problem via the
Monte-Carlo technique.
The flow problem is
solved, using the
f inite-element
technique.
A finite-element model
for simulation of tran-
sient two-dimensional
horizontal flow in a
ultiple aquifer
system. The model
provides velocities to
be used as input for
transport model .
A water budget model for
the Hydro logic Evalua-
tion of Landf i 1 1
Performance.
An analytical model to
calculate drawdown or
buildup in an isotropic
homogeneous non- leaky
confined aquifer with
ultiple pumping and
injection wel Is.
A package of seven
analytical solutions for
groundwater flow prob-
lems. The package
includes solutions for
partial penetration,
leaky confined systems,
layered systems, ground-
water mounding, and
stream depletion due to
punping.
Model
Processes
aqui fer-
stream
interaction
surface
storage,
runoff,
inf i Itration,
percolation,
evapotrans-
piration.
sol 1 moisture
storage ,
lateral
drainage
stream
depletion.
mounding,
leakage
GWHC
Key
4070
4160
4530
4680
6022
6023
186
-------
APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
88.
89.
90.
91.
92.
93.
94.
Author(s)
P.K.M. van der
Heijde
A. Verruijt
Ref: 187
K.S. Rathod
K.R. Rushton
Ref: 142
P.K.M. van der
Heijde
Ref: 180
M.A. Butt
C.D. McElwee
Ref: 21
M.S. Beljin
Ref: 10
L.A. Abriola
G.F. Pinder
Ref: 1
Contact Address
International Ground
Hater Modeling Center
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
International Ground
Water Modeling Center
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
International Ground
Water Modeling Center
Holcomb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
International Ground
Water Modeling Center
Holcomb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
International Ground
Water Modeling Center
Holcomb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
International Ground
Water Modeling Center
Holcomb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
International Ground
Water Model ing Center
Holcomb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
Model Name
(last update)
THCVFIT
(1987)
BASIC GWF
(1987)
RADFLOW
(1984)
TSSLEAK
(1988)
VARQ
(1986)
PUMPTEST
(1986)
TETRA
(1985)
Model
Description
An interactive program
to determine trans-
it) issivity and storage
coefficient from pump
test data. This node I
replaces traditional
curve-fitting by a
graphics routine to
natch the The is well
function with field
drawdown data.
A finite-element model
for analysis of plane,
steady or unsteady
groundwater flow in an
isotropic, hetero-
geneous, confined or
unconfined aquifer.
A finite-difference
model for transient
radial flow towards a
well in a homogeneous.
isotropic aquifer.
RAOFLOW a 1 lows for
changing conf ined/
unconfined conditions in
time, and it can handle
variable pumping
schedules.
A least-squares pro-
cedure for fitting the
Hantush and Jacobs
equations to experi-
mental pump test data to
obtain estimates for
storage coefficient,
transmissivity, leakage
coefficient, and
aquitard permeability.
A program to calculate
aquifer parameters by
automat ically fitting
pump test data with
Theis-type curve. The
program al lows for
variable discharge rates
during the test.
An interactive, menu-
driven program package
to calculate trans-
missivity and storage
coefficient from time-
drawdown , d i stance-
drawdown, or recovery
pump test data. Jacob's
method and regression
analysis are applied to
a user-specified portion
of the data curve.
A simple program to cal-
culate velocity compo-
nents in three dimen-
sions from hydraulic
head measurements.
Model
Processes
leaKage
IGWMC
Key
6025
6030
6064
6081
6082
6382
6430
187
-------
APPENDIX Al
SATURATED FLOW MODELS: SUMMARY LISTING
No.
95.
96.
97.
Author(s)
K.R. Bradbury
E.R. Rothschild
Ref: 17
D.B. Thompson
Ref: 166
J.M. Shafer
Ref: 158
Contact Address
International Ground
Mater Modeling Center
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
International Ground
Water Modeling Center
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapolis, IN 46206
Illinois State Water
Survey
Ground Hater Section
2204 Griffith Drive
Champaign, 11 61820-7495
Model Name
(last update)
TGUESS
(1986)
TIMELAG
(1987)
GWPATH
(1987)
Model
Description
A program for estimating
transnissivity from spe-
cific capacity data.
TGUESS corrects for par-
tial penetration and
veil loss.
A program to estimate
hydraulic conduct i v i ty
from time-lag slug
tests.
An interactive software
package for estimating
horizontal fluid path-
lines and travel times in
ful ly saturated media.
GWPATH is appl i cable to
heterogeneous an i so-
tropic flow systems, and
it features forward and
reverse pathl ine
tracking, time-related
capture zone analysis.
and multiple pathl ine
capture detection
mechanisms.
Model
Processes
nonun i form
flow
GWMC
Key
6450
6580
6650
188
-------
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-------
APPENDIX A2
SATURATED FLOW MODELS: USABILITY AND RELIABILITY
No.
47.
48.
50.
51.
52.
53.
C/1
04.
CR
93.
56.
57.
58.
en
59.
60.
61.
62.
63.
64.
65.
66.
Author(s)
L.K. Kuiper
R.H. Page
DD D A^ c/\rt A^ al
.K. rosson, et ai.
C.J. Daly
J. Boonstra
0. Berney
H.N. Tyson, et al.
A.r.M. Broics , et ai.
BU P 4 1 A \ nn
.n. fai laing
J.W. Wesseling
J. Noorishad
P. A. Witherspoon
J. Noorishad et al.
G. Schmid
PU /***UK n^ *1
.N. IODD, et ai.
B. Sagar
B. Sagar
J.A. Liggett
P.J.T. van Badel
G.T. Yeh
C.W. Francis
G.T. Yeh
D.D. Huff
D.N. Contractor
Model Name
Variable
Density
Model
INTERFACE
Nu c n ?n
.n.r.u. i\i
CRREL
SGMP
DISIFLAQ
KRGW
CDDMIII A
uKUnULn
ROCMAS-H
ROCMAS-HM
SICK 100
AQUIFER
DEVIATE R
GM5
FEMSAT
AQUIFLOW
FEWA
SWIGS2D
USABILITY
§
n
§
i.
a
0
a.
U
U
U
N
N
U
U
U
U
U
U
N
U
N
N
U
Ifl
«
8
a
1
U
u
Y
U
N
U
U
U
Y
U
U
N
U
G
G
U
M
§
.1
L ^
« in
0.
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
u
SI
B C
0 0
11
U
L
Y
N
N
U
U
U
L
N
N
N
L
N
N
U
4-
U
O
1
(A
N
N
Y
Y
Y
N
N
N
Y
U
Y
N
Y
Y
Y
Y
RELIABILITY
X
l>
L
1!
Y
Y
Y
Y
U
Y
Y
Y
Y
U
Y
Y
U
U
U
Y
I
la
e
11
U
u
u
u
u
u
u
u
Y
U
U
N
U
U
U
U
0
i
Y
Y
Y
Y
Y
U
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
o
v a
5?
u. t-
L
L
i
L
L
U
U
Y
i
L
U
u
L
L
L
L
L
L
L
L
ID
U
0
Ul
i
F
F
F
F
M
F
U
U
U
U
Y
F
F
U
F
F
IGWMC
KEY
2663
2720
2791
2800
2870
2930
3080
3082
3110
OlCfl
jiOU
3230
3231
3240
3350
3372
3373
3600
KEY: Y * YES
NO
U * UNKNOWN
6 ' GENERIC
D ' DEDICATED L * LIMITED M ' MANY
F * FEW
192
-------
APPENDIX A2
SATURATED FLOW MODELS: USABILITY AND RELIABILITY
No.
67.
eg
DO.
69.
70.
71.
72.
70
/ j
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
Author(s)
R.I. Allayla
F.T. Tracy
C.S. Desai
C.S. Desai
C.S. Desai
C.S. Desai
C.S. Desai
C.S. Desai
C.S Desai
D.G. Jorgensen, et al.
J.V. Tracy
W.I.M. Elderhorst
M.G. McDonald
A.M. Harbaugh
C.R. Kolterman
A.I. El-Kadi
D.M. Contractor, et al .
Model Name
SEAWTR/
SEACONF
i amn
Lnr 1 1U
ECPL 704-
F3-RO-011
DFT/C-1D
FIELD-2D
SEEP2(VM)-
20
crcp/yux on
jLLr ^Vrl}-jU
STRESEEP-2D
CONS2-10
CONSP
(L/NL)-2D
CONSA(L)-2D
GWMD3
Parameter
Estimation
Program
INVERS
MODFLOW
GWUSER/
CONJUN
ST2D
MAQWF
USABILITY
8
in
|
1
Y
U
U
U
u
u
u
u
u
N
U
U
Y
U
N
U
8
10
I
a.
I
Y
D
U
U
U
U
U
U
U
U
U
U
Y
U
N
U
IA
C
O
u
(A 3
- L.
k +
ss
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
.1
ti
GL
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
sl
fe£
U
U
U
U
U
U
U
U
U
N
U
Y
N
Y
L
Y
t
a
3
in
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
N
RELIABILITY
13
t
O
11
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
U
U
Y
U
Y
Y
o
o
1
Ic
e
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II
U
u
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u
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u
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Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
U
U
Y
Y
Y
U
o 1
+
«
U. h-
U
L
L
L
L
L
L
L
L
L
L
L
Y
L
L
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in
u
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L
F
U
U
U
U
U
U
U
U
U
U
M
U
U
U
IGWMC
KEY
3640
*n\f\
3/00
3810
3860
3861
3862
3864
3865
3866
3867
3870
3880
3950
3980
4070
4160
4530
KEY: Y » YES
N * NO
U * UNKNOWN
6 GENERIC
D * DEDICATED
L LIMITED
MANY
F « FEW
193
-------
APPENDIX A2
SATURATED FLOW MODELS: USABILITY AND RELIABILITY
NO.
85.
86.
87.
88.
89.
90.
91.
92.
94.
95.
QC
yo.
97.
Author(s)
P.R. Schroeder, et al.
P.K.M. van der Heijde
P.K.M. van der Heijde
P.K.M. van der Heijde
A. Verruijt
K.S. Rathod
K.R. Rushton
P.K.M. van der Heljde
M.A. Butt
MC D<*1 44m
.0. Be 1 Jin
L.A. Abriola
G.F. Plnder
K.R. Bradbury
E.R. Rothschild
D.B. Thompson
J.M. Shafer
Model Name
HELP
THWELLS
GWFLOW
THCVFIT
BASIC GWF
RADFLOW
TSSLEAK
VARQ
DIIUDTCCT
rUMr 1 til
TETRA
TGUESS
TTkin lif
\ IMtLAo
GWPATH
USABILITY
3
M
g
a
£
D
D
0
0
0
D
D
D
D
D
D
8
M
41
8
a
I
N
D
N
0
N
N
0
N
N
N
D
I/I
S
u
ID 3
- U
U +
4* «/)
IA c
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
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1!
a c
a. H
U
Y
U
U
Y
Y
Y
U
Y
U
U
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N
U
U
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N
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U
Y
Y
Y
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Y
Y
Y
Y
Y
o «
4-
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U. K
U
L
L
L
U
L
L
L
L
L
U
U)
L.
4)
U)
O
M
M
M
M
F
M
M
M
M
M
F
IGWMC
KEY
4680
6022
6023
6025
6030
6064
6081
6082
6430
6450
ccori
D3OU
6650
KEY: Y » YES
N « NO
U * UNKNOWN
GENERIC
D » DEDICATED
L « LIMITED
MANY
f * FEW
194
-------
APPENDIX Bl
VARIABLY SATURATED FLOW MODELS: SUMMARY LISTING
NO.
l.
2.
V
3.
4.
5.
6.
Author(s)
S.P. Neuman
Ref: 31
T.N. Narasimhan
Ref: 145
T.N. Narasimhan
S.P. Neuman
Ref: 113
A. Vandenberg
Ref: 176
P.J.M. DeLaat
Ref: 35
R. W. Skaggs
Ref: 159
Contact Address
Dept. of Hydrology and
Mater Resources
Univ. of Arizona
Tuscon, AZ 85721
Water and Land Resources
0 i v i s i on
Battellle Pacific NM Lab
P.O. Box 999
Richland, WA 99352
Earth Sciences Division
Lawrence Berkeley
Laboratory
University of California
Berkeley, Ca 94720
National Hydrology
Research Institute
Inland Waters
Directorate
Ottawa, K1A OE7
Ontario, Canada
International Inst. for
Hydraulic and Environra.
Eng.
Delft, The Netherlands
P.O. Box 5906
Dept. of Biological and
Agricultural Eng.
North Carolina State
University
Raleigh, NC 27650
Model Naae
(last update)
UNSAT2
(1979)
TRUST
(1981)
FLUMP
(1981)
FLO
(1985)
MUST
(1985)
DRAINMOO
(1980)
Node!
Description
A two-dimensional
finite-element node! for
horizontal, vertical or
ax i symmetric simulation
of transient flow in a
variably saturated, non-
uniform, anisotropic
porous medium.
To compute steady and
nonsteady pressure head
distributions in multi-
dimensional, heterogen-
eous, variably satur-
ated, deformable porous
edia with complex geo-
metry; uses integrated-
f inite-differece method.
A finite-element model
for computation of
steady and nonsteady
pressure head distri-
butions in two-dimen-
sional or ax i symmetric,
heterogeneous, aniso-
tropic, variably
saturated porous media
with complex geometry.
FLO simulates the ele-
ments of the hydrologic
cycle which are directly
influenced by soi 1 and
surface drainage im-
provements. Total dis-
charge from a drained
plot is estimated.
Detai led accounts of
unsaturated flow are
considered.
A finite-difference
odel which simulates
one-dimensional ver-
tical , unsaturated
groundwater flow, evapo-
transpiration, and
interception of
precipitation by plants.
An analytical model for
unsteady, one-dimen-
sional, horizontal /ver-
tical, saturated/unsat-
urated problems; simu-
lates water table posi-
tion and soil water
regime above water table
for artificially drained
soils.
Model
Processes
cap! 1 larity
evapo-
transpiration
plant uptake
cap! 1 larity
diffusion
consol idation
hysteresis
cap! 1 larity
diffusion
evapo-
transpiration
capi 1 larity
evapo-
transpiration
capi 1 larity
evapo-
transpi ration
plant uptake
cap! 1 larity
evapo-
transpiration
IGWMC
Key
0021
0120
0122
1092
1771
1950
195
-------
APPENDIX Bl
VARIABLY SATURATED FLOW MODELS: SUMMARY LISTING
No.
7.
8.
9.
10.
11.
12.
13.
14.
Author (s)
O.L. Ross
H.J. Morel-
Seytoux
Raf: 146
S.K. Gupta
C.S. Simmons
Ref: 60
R.A. Feddes
Ref: 11
L.A. Davis
Ref: 32
J.W. Wessel ing
G.T. Yeh
O.S. Ward
Ref: 195
G.T. Yeh
R.J. Luxmoore
Ref: 198
J.I. Neiber
Ref: 118
Contact Address
Dept. of Civil Eng.
Colorado State Univ.
Fort Collins, CO 80523
Battelle Pacific NW Labs
P.O. Box 999
Richland, WA 99352
Inst. for Land and Water
Management Research
P.O. Box 35
6700 AA Wageningen
The Netherlands
Water, Waste and Land,
Inc.
1311 S. Collins Ave.
Fort Collins, CO 80524
Delft Hydraul ics
Laboratory
P.O. Box 152
8300 AD Emneloord
The Netherlands
Environmental Sciences
Division
Oak Ridge National Lab
Oak Ridge, TN 37830
Environmental Sciences
Division
Oak Ridge National lab
Oak Ridge, TN 37830
Dept of Agricultural Eng
Cornell University
Ithaca, New York 14853
Model Naoe
(last update)
SOILMOP
(1982)
UNSAT1D
(1981)
SWATRE,
SWATR-CROPR
(1981)
SEEPV
(1980)
SOMOF
(1982)
FEMWATER/
FECHATER
(1987)
MATTUM
(1983)
FEATSMF
(1979)
Model
Description
An analytical model to
predict ponding time.
Inf i Itration rate and
amount, and water
content profiles under
variable rainfal 1
conditions. The model
solves a one-dimensional
flow equation in a homo-
geneous soil. Air phase
is also included.
A finite-difference
model for one-
dimensional simulation
of unsteady vertical
unsaturated flow.
A finite-difference
model for simulation of
the water balance of
agricultural soil.
A finite-difference
transient flow model to
simulate vertical
seepage fron a tailings
impoundment in variably
saturated flow systems;
considers interactions
between a 1 iner and the
underlying aqui fer.
A f i n i te-d i f f erence
model for simulation of
transient unsaturated
soil moisture flow in a
vert i ca 1 prof i 1 e .
A two-dimensional
finite-element model to
simulate transient,
cross-sectional flow in
saturated-unsaturated
anisotropic, heteroge-
nous porous media.
This is a three-dimen-
sional model for simula-
ting moisture and ther-
mal transport in unsat-
urated porous media.
The model solves both
the flow equation and
the heat equation under
unsaturated water condi-
tions, using the inte-
grated compartment
method.
A transient finite-
element 2-D soil mois-
ture flow model for
homogeneous, isotropic
h i 1 1 s 1 opes where the
moisture is supplied by
rainfall.
Model
Processes
capillarity
capil larity
evapo-
transpiration
plant uptake
precipitation
capi 1 larity
evapo-
transpiration
inf i Itration
capi I larity
evapo-
transpiraton
precipitation
capillarity
evapo-
transpiration
gravity
drainage
plant uptake
ponding
capillarity
inf i Itration,
ponding
capil larity
capi I larity
evapo-
transpiration
IGWMC
Key
2062
2071
2550
2890
2983
3370
3375
3420
196
-------
APPENDIX Bl
VARIABLY SATURATED FLOW MODELS: SUMMARY LISTING
No.
15.
16.
17.
18.
19.
20.
21.
Author(s)
M. Th. van
Genuchten
Ref: 162
J.B. Kool
J.C. Parker
M.Th. van
Ganuchten
Ref: 97
H. Vaucl in
Ref: 40
P. Christopher
D. Hilly
Ref: 110
O.K. Sunada
Ref: 88
M.J. Payer
G.W. Gee
Ref: 50
P.M. Craig
E.C. Davis
Ref: 28
Contact Address
U.S. Salinity Lab
U.S. Oept. of
Agrigulture
4500 Glenwood Drive
Riverside, CA 92501
245 Smyth Hall
Va. Polytechnic Inst.
Blacksburg, VA. 24061
Institute De Mecanique
De Grenoble - BP 68
38402 St. Martin O'Heres
- Cedex, France
Oept. of Civil Eng.
Princeton University
Princeton, NJ 08544
Dept. Civil Eng.
Colorado State
University
Fort Col 1 ins, CO 80523
Battel le Pacific
Northwest Lab
Rich land, WA 99352
Environmental Science
Division
Oak Ridge Nat' I.
Laboratory
Oak Ridge, TN
Model Name
(last update)
DNS ATI
(1978)
ONESTEP
(1985)
INFIL
(1983)
SPLASHWATR
(1983)
GRWATER
(1981)
UNSAT-H
(1985)
INFGR
(1985)
Model
Description
A finite-element
solution to Richards'
equation to simulate
one-dimensional
saturated-unsaturated
flow in heterogeneous
soils.
A non 1 i near parameter
estimation model for
evaluating soil
hydraulic properties
from one-step outflow
experiments in one-
dimensional flow.
The finite-difference
model solves for one-
dimensional infiltration
into a deep homogeneous
soil. Output includes
water content profile
and amount and rate of
infiltration at differ-
ent simulation tines.
Simulation of coupled
heat and moisture fields
in the unsaturated zone.
A finite-difference
model to predict the
decline of ground-water
mounds developed under
recharge in an
isotropic, heterogeneous
aquifer with transient
saturated or unsaturated
flow conditions.
UNSAT-H is a finite-
difference one-dimen-
sional, unsaturated flow
model. It simulates
infiltration, drainage.
redistribution, surface
evaporation, and plant
water uptake from
soil. The model is de-
signed for arid zones
similar to the Han ford
Site (Washington).
1-D vertical model to
estimate infiltration
rates, using the Green
and Ampt equation. The
compression method is
used to estimate infil-
tration during low rain-
fall periods.
Model
Processes
capillarity
evapo-
transpiration
capillarity
capillarity
inf i Itration
evapo-
transpiration
cap! 1 larity
evapo-
transpiraton
convection
conduction
diffusion
change of
phase
hysteresis
adsorption
infiltration
cap! 1 larity
evapo-
transpiration
cap! 1 larity
evapo-
transpiration
infiltration
drainage
plant uptake
capil larity
IGWMC
Key
3431
3433
3570
3590
3660
4340
4380
197
-------
APPENDIX Bl
VARIABLY SATURATED FLOW MODELS: SUMMARY LISTING
No.
22.
23.
24.
25.
26.
27.
28.
Author(s)
R-M LI
K.G. Eggert
K. Zachmann
Ref: 102
G.P. Korfiatis
Ref: 98
E.R. Perrier
A.C. Gibson
Ref: 129
E.G. Lappala
R.M. Healy
E.P. Weeks
Ref: 100
A.I. El-Kadi
Ref: 42
A.I. El-Kadi
Ref: 41
D.L. Nofziger
Ref: 121
Contact Address
Simons, Li , 4
Associates, Inc.
P.O. Box 1816
Fort Collins, CO 80522
Civil and
Environmental
Engineering
Rutgers University
The State University of
New Jersy
New Brunswick, NJ
Sol id and Hazardous
Waste Research Oiv.
Municipal Environmental
Research Laboratory
Cincinnati, OH 45268
U.S. Geological Survey
Box 25046, M.S. 413
Denver Federal Center
Denver, CO 80225
International Ground
Water Modeling Center
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
International Ground
Water Model ing Center
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapolis, IN 46208
Institute of Food and
Agricultural Sciences
University of Florida
Gainesville, FL 32611
Model Name
(last update)
FLOWVEC
(1983)
LANDFIL
(1984)
HSSWOS
(1982)
VS2D
(1987)
SOIL
(1987)
INFIL
(1987)
WATERFLO
(1985)
Model
Description
A finite-difference
model which uti I izes a
vector processor for
solutions to three-
dimensional variably
saturated flow problems.
Model simulates the
transport of moisture
through the unsaturated
zone, using a finite-
difference solution for
the 1-0 flow equation.
1-0 analytical water
budget model to estimate
the amount of moisture
percolation through
different types of
landfills.
2-D finite-difference
code for the analysis of
flow in variably satur-
ated porous media. Model
considers recharge.
evaporation, and plant
root uptake.
A model to estimate soil
hydrau 1 i c propert I es ,
using a non- linear least
squares analysis.
An analytical solution
to calculate infiltra-
tion rate and water con-
tent profile at differ-
ent times, using the
Philip series solution
of a one-dimensional
form of the Richards
equation.
A one-dimensional
finite-difference
solution for the
Richards equation to
Simulate water Movement
through soils.
Model
Processes
capi 1 lary
forces
capillarity
evapotrans-
piration
capi 1 larity
evapotrans-
piration
runoff
snowme 1 t
evaporation
recharge
plant uptake
inf i Itration
IGWMC
Key
4390
4400
4410
4570
6330
6335
6630
198
-------
APPENDIX B2
VARIABLY SATURATED FLOW MODELS: USABILITY AND RELIABILITY
No.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
.
12.
13
A J
14.
15.
16.
Author(s)
S.P. Neuman
T.N. Narasimhan
T.N. Narasimhan
S.P. Neuman
A. Vandenberg
P.J.M, DeLaat
R.W. Skaggs
D.L. Ross
H.J. Morel -Seytoux
S.K. Gupta
C.S. Simons
R.A. Feddes
L.A. Davis
JU Uaeeal-inn
H. rfcSSe 1 IrKJ
D.W. Green
H. Dablri
C.F. Wienaug
R. Prill
GT Yph
1 . 1 CM
D.S. Ward
G.T. Yeh
R.J. Luxmoore
J.L. Neiber
M.Th. van Genuchten
Model Name
UNSAT2
TRUST
FLUMP
FLO
MUST
ORAINMOO
SOILMOP
UNSAT10
SWATRE
SWATR-CROPR
SEEPV
enunc
iunur
TWO- PHASE
UNSATURATED
FLOW
FFMUATPR /
r trinn i LI\/
FECWATER
MATTUM
FEATSMF
UNSAT1
USABILITY
Y
U
U
U
U
U
U
U
U
U
N
U
U
U
G
D
U
U
U
U
U
U
U
U
N
U
U
U
Y
U
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
T
Y
Y
Y
Y
U
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
I
u
Y
Y
L
N
U
Y
U
Y
Y
Y
Y
Y
Y
N
Y
N
Y
Y
U
N
Y
N
N
Y
N
N
N
Y
N
Y
RELIABILITY
Y
Y
Y
U
Y
Y
U
Y
Y
Y
N
U
Y
Y
Y
U
Y
U
U
U
U
U
U
U
N
U
U
Y
Y
Y
Y
U
Y
Y
U
Y
Y
Y
Y
Y
Y
Y
L
L
L
U
L
Y
U
Y
L
L
Y
U
L
L
M
F
F
F
F
F
F
F
F
F
F
F
F
M
IGWMC
KEY
0021
0120
0122
1092
1771
1950
2062
2071
2550
2890
OOQI
£70J
3280
307(1
Jj/U
3375
3420
3431
KEY: V - YES
N * NO
U « UNKNOWN
6 ' GENERIC
D ' DEDICATED
L * LIMITED
M > MANY
F * FEW
199
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-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
NO.
1.
2.
3.
4.
5.
6.
7.
Author(s)
P.S.C. Rao
Ref: 30
H.H. Selim
J.M. Davidson
Ref: 154
G.F. Finder
Ref: 133
P. Huyakorn
Ref: 78
P. Huyakorn
Ref: 70
P. Huyakorn
Ref: 75
P. Huyakorn
Ref: 72
Contact Address
2169 McMarthy Hall
Soi 1 Science Dept.
University of Florida
Gainesville, FL 3261)
Louisiana Agricultural
Experiment Station
Agronomy Dept.
Louisiana State Univ.
Baton Rouge, LA 70803
Dept. of Civi 1 Eng.
Princeton Univ.
Princeton, NJ 08540
IGWMC
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapolis, IN 46208
GeoTrans, Inc.
250 Exchange Place
Suite A
Herndon, VA 22070
GeoTrans, Inc.
250 Exchange Place
Suite A
Herndon, VA 22070
GeoTrans, Inc.
250 Exchange Place
Suite A
Herndon, VA 22070
Model Name
(last update)
NITROSIM
(1981)
NMODEL
(1976)
ISOQUAO 2
(1977)
TRAFRAP-WT
(1987)
GREASE2
(1982)
SATURN2
(1982)
SEFTRAN
(1985)
Model
Description
A finite-difference
solution for simulation
of transport and plant
uptake of nitrogen and
transformations of
nitrogen and carbon in
the root zone.
A finite-difference
model for steady or
unsteady simulation of
one-dimensional ,
vertical Hater and
nitrogen transport and
nitrogen transformations
in unsaturated mult i lay-
ered homogeneous soils.
A finite-element model
to solve the transport
equation in nonsteady,
. confined, areal, two-
dimensional groundwater
flow systems.
A finite-element model
to study transient, two-
dimensional, saturated
ground water flow and
chemical or radionuclide
transport in fractured
and unfractured, an i so-
tropic, heterogeneous,
mu 1 1 i 1 ayered porous
media.
A finite-element node!
to study transient.
multidimensional ,
saturated ground water
flow, solute and/or
energy transport in
fractured and unfrac-
tured, anisotropic,
heterogeneous, multi-
layered porous media.
A finite-element model
to study transient, two-
dimensional variably
saturated f 1 ow and so-
lute transport in
anisotropic, hetero^
geneous porous media.
A two-dimensional
f inite-element model for
simulation of transient
flow and transport of
heat or solutes in ani-
sotropic, heterogeneous
porous media.
Model
Processes
cap! 1 larity
precipitation
evapo-
transpiration
convection
d i spers i on
diffusion
adsorption
ion exchange
decay
capi 1 larity
convect i on
dispersion
di f fusion
adsorption
nitrification
plant uptake
advection
dispersion
diffusion
advection
dispersion
diffusion
adsorption
decay
chemical
reactions
advection
conduction
dispersion
diffusion
buoyancy
adsorption
advection
conduction
dispersion
diffusion
adsorption
decay
chemical
reactions
advection
dispersion
diffusion
adsorption
decay
IGWMC
Key
0280
0290
0511
0589
0582
0583
0588
201
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
8.
9.
10.
11.
12.
13.
14.
Author (s)
T.R. KnoMles
Ret: 163
INTERA
Environmental
Consult., Inc.
Ref: 84
L.F. KonikOM
J.O. Bredehoeft
Ref: 96
S.P. Garabedian
L.F. Konikow
Ref: 53
S.W. Ah 1 Strom
H.P. Foote
R.J. Serne
Ref: 2
F.E. Kaszeta
C.S. Simmons
C.R. Cole
Ref: 192
V. Guvanasen
Ref: 24
Contact Address
Texas Oept. of Water Res
P.O. Box 13087
Capitol Station
Austin. TX 78758
K. Kipp
U.S.. Geological Survey
Box 25046, nail Stop 411
Denver Federal Center
Lakewood, CO 80225
L.F. Konikou
U.S. Geological Survey
12201 Sunrise Valley Dr.
Reston, VA 22092
L.F. Konikow
Water Resources Division
U.S. Geological Survey
12201 Sunrise Val ley Dr.
Reston, VA 22092
Battelle Pacific NW
Laboratories
P.O. Box 999
Rich land, WA 99352
Battel le Pacific NW Labs
P.O. Box 999
Rich land, WA 99352
Applied Geoscience
Branch
Whiteshell Nuclear
Research
Atomic Energy of
Canada
Pinawa, Manitoba ROE HO
Model Name
(last update)
GWSIH-II
(1981)
SWIPR
(1985)
USGS-2D-
TRANSPORT/
HOC
(1988)
FRONTTRACK
(1983)
MMT-DPRW
(1976)
HMT-10
(1980)
MOTIF
(1986)
Model
Description
A transient, two-dimen-
sional, horizontal model
for prediction of water
levels and water quality
in an anisotropic,
heterogeneous, confined
or uncon fined aquifer
based on finite-differ-
ence method.
A finite-difference
model to simulate
nonsteady, three-
dimensional ground water
flow and heat and
contaminant transport in
a heterogeneous aquifer.
To simulate transient,
two-d i mens i ona 1 , nor i -
zontal ground water flow
and solute transport in
con f i ned/sem i con fined
aqui fers using f inite
differences and method
of characteristics.
A finite-difference
nodel for simulation of
convective transport of
a conservative tracer
dissolved in groundwater
under steady or tran-
sient flow conditions.
The model calculates
heads, velocities and
tracer particle posi-
tions.
To predict the transient
three-dimensional move-
Bent of radionucl ides
and other contaminants
in unsaturated/saturated
aquifer systems.
A finite-difference
model to simulate
transient, one-
dimensional movement of
radionucl ides and other
contaminants in
saturated/un saturated
aquifer systems.
Finite-element model for
one, two, and three-di-
mensional saturated/un-
saturated groundwater
flow, heat transport,
and solute transport in
fractured porous media;
facilitates single-spe-
cies radionucl ide trans-
port and solute diffu-
sion from fracture to
rock matrix.
Model
Processes
advection
dispersion
d i f f us i on
advection
conduction
dispersion
diffusion
adsorption
advection
dispersion
diffusion
adsorption
decay
advection
convection
dispersion
adsorption
absorption
ion exchange
decay
reactions
cap i 1 1 ar i ty
convection
dispersion
adsorption
absorpt i on
ion exchange
decay
convection
dispersion
diffusion
adsorption
decay
advect i on
Key
0680
0692
0740
0741
0780
0781
0953
202
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
15.
16.
17.
18.
19.
20.
21.
Author (s)
1. Miller
J. Marlon-
Lambert
Ref: 105
S.K. Gupta
C.T. Kinkaid
P.R. Meyer
C.A. Newbill
C.R. Cole
Ref: 59
H.C. Burkholder
M.O. Cloninger
W.V. Dernier
G. Jansen
P.j. Liddell
J.F. Washburn
Ref: 36
R.W. Kelson
Ref: 114
R.D. Schmidt
Ref: 157
T.A. Prickett
T.G. Naymik
C.G. Lonnquist
Ref: 138
B. Ross
C.M. Kopl ik
Ref: 4
Contact Address
Golder Associates
2950 Northup Way
Bellevue, MA 98004
C.R. Cole
Batten e Pacific NW Labs
P.O. Box 999
Rich land, HA 99352
Natl. Energy Software
Center
Argonne Natl. Laboratory
9700 S. Cass Avenue
Argonne, IL 60439
Battel le Pacific NW Labs
P.O. Box 999
Rich land, MA 99352
U.S. Dept. of the
Interior
Bureau of Mines
P.O. Box 1660
Twin Cities, MN 55111
III. State Water Survey
P.O. Box 5050, Sta. A
Chanpaign, IL 61820
Analytic Sciences Corp.
Energy i Environment
Div.
One Jacob Way
Reading, MA 01867
Model NOK
(last update)
Golder
Groundwater
Computer
Package
(1983)
CFEST
(1987)
GETOUT
(1979)
PATHS
(1980)
ISL-50
(1979)
Random Walk
(1981)
WASTE
(1981)
Model
Description
A transient finite-ele-
ment model to simulate
hydraulic and solute
transport characteris-
tics of two-dimensional.
horizontal or axi-
symmetric ground Hater
flow systems with
layered geometry.
A three-dimensional fi-
nite-element model to
simulate coupled tran-
sient flow, solute- and
heat-transport in satu-
rated porous media.
A one-dimensional
analytical model for
radionucl ide transport.
To evaluate contamina-
tion problems in un-
steady, two-dimensional
ground water flow sys-
tems, using an analy-
tical solution for the
flow equation and the
Runge-Kutta method for
the path line equation.
A three-dimensional
semi -analytical model to
describe transient flow
behavior of leachates
and ground water, in-
volving an arbitrary
pattern of injection and
recovery wel Is.
To simulate one- or two-
dimensional, steady/non-
steady flow and solute
transport problems in a
heterogeneous aqu i f er
with water table and/or
confined or semi con fined
conditions, using a
"random-walk" technique.
An analytical solution
to compute one- or two-
dimensional horizontal,
or one-dimensional ver-
tical, steady/unsteady
transport of radio-
nucl ides in confined or
semiconf ined, an i so-
tropic, heterogeneous
multi-aquifer systems.
Model
Processes
advection
dispersion
diffusion
adsorption
decay
chemical
reaction
advection
dispersion
diffusion
adsorption
decay
advection
dispersion
di f fusion
adsorption
ion exchange
(chain) decay
advection
adsorption
ion exchange
advection
advection
dispersion
di f fusion
adsorption
decay
chemical
reaction
advection
dispersion
diffusion
adsorption
ion exchange
decay
1GWMC
Key
1010
2070
2080
2120
2560
2690
2810
203
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
22.
23.
24.
25.
26.
27
Author (s)
L.A. Davis
G. Segol
Ret: 33
L.A. Davis
G. Segol
Ref: 33
J.W. Wesseling
J. Noorishad
M. Mehran
Ref: 123
J.W. Warner
Ref: 191
S. Haji-Ojafar
T.C. Wells
Ref: 67
Contact Address
Water, Waste and
Land, Inc.
1311 S. Col lege Avenue
Fort Collins, CO 60524
Water, Waste, and
Land, Inc.
1311 S. College Avenue
Fort Collins, CO 80524
Delft Hydraulics Lab.
P.O. Box 152
8300 AD Emmet oord
The Netherlands
Earth Sciences Division
Lawrence Berkeley Lab.
Un i v . of Ca I i f orn i a
Berkeley, CA 94720
Civil Engineering Dept.
Colorado State Univ.
Ft. Collins, CO 80523
O'Appo Ionia Waste
Mngmt. Services, Inc.
10 Duff Rd.
Pittsburgh, PA 15235
Model Nue
(last update)
6S2
(1985)
GS3
(1985)
GROWKWA
(1982)
ROCMAS-HS
(1981)
RESTOR
(1981)
GEOFLOW
(1982)
Model
Description
6S2 is a two-dimensional
finite-element code for
the analysis of flow and
contaminant transport in
partially saturated me-
dia. Either vertical or
horizontal plane simula-
tion is possible. Mass
transport analysis in-
cludes convection, dis-
persion, radioactive
decay, adsorption.
GS3 is a three-dimen-
sional finite-element
code for analysis of
fluid flow and contam-
inant transport in
partially saturated me-
dia. The code is parti-
cularly useful for simu-
lation of anisotropic
systems with strata of
varying thickness and
continuity.
Transient finite-element
simulation of two-dimen-
sional , horizontal
ground water flow and
transport of noncon-
servative solutes in a
ulti -layered, aniso-
tropic, heterogeneous
aquifer system.
A transient finite-
element model to solve
for two-dimensional
d i spers i ve-convect i ve
transport of non-conser-
vative solutes in
saturated, fractured
porous media for a given
velocity field as gener-
ated by ROCMAS-H.
A finite-element model
to calculate the dual
changes in concentration
of two reacting solutes
subject to binary cation
exchange in flowing
ground water; two-
dimensional simulation
of areal transient or
steady ground water flow
and transient coupled
transport of two solutes
In an anisotropic,
heterogeneous confined
aquifer.
A three-dimensional fi-
nite-element model to
simulate coupled tran-
sient flow, solute- and
heat-transport in satu-
rated porous media.
Model
Processes
evapo-
transpiration
convection
dispersion
diffusion
adsorption
decay
infiltration
evapo-
transpiration
convection
dispersion
diffusion
inf i Itration
advect i on
dispersion
diffusion
adsorption
ion exchange
decay
chemical
reactions
convection
dispersion
diffusion
adsorption
decay
reactions
advect ion
dispersion
diffusion
ion -exchange
adyection
dispersion
diffusion
GWMC
ey
2891
2892
2982
3081
3100
3220
204
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
28.
29.
30.
31.
32.
Author (s)
B. Sagar
Ref: 52
A.K. Runchal
Ref: 46
B. Sagar
Ref: 151
B. Sagar
G.T. reh
D.S. Ward
Contact Address
Analytic & Computational
Research, Inc.
3106 Inglewood Blvd.
Los Angeles. CA 90066
Analytic 4 Computational
Research, Inc.
3106 Inglewood Blvd.
Los Angeles, CA 90066
Analytic & Computational
Research, Inc.
3106 Inglewood Blvd.
Los Angeles, CA 90066
Analytic & Computational
Research, Inc.
3106 Inglewood Blvd.
Los Angeles. CA 90066
Environmental Sciences
Division
Oak Ridge National Lab
Oak Ridge, TN 37830
Model Name
(last update)
FRACFLOW
(1981)
PORFLOW
II & III
(1988)
VADOSE
(1982)
FLOTRA
(1982)
FEMWASTE/
FECWASTE
(1981)
Model
Description
An integrated-f inite-
difference approach for
steady and unsteady
state analysis of den-
sity-dependent flow,
heat and mass transport
in fractured confined
aquifers. Two-dimen-
sional simulation of the
processes in the porous
medium and one-dimen-
sional simulation of the
fractures.
An integrated-f in ite-
difference model for
steady or transient, 2-0
hor i zonta 1 , vert i ca 1 or
radial and 3-0 simula-
tion of density-depen-
dent flow, heat and mass
transport in an i so-
tropic, heterogeneous,
nondeformable saturated
porous media with time-
dependent aquifer and
fluid properties.
Steady or transient.
two-dimensional, areal,
cross-sectional or
radial simulation of
density-dependent trans-
port of moisture, heat
and mass in variably
saturated, hetero-
geneous, anisotropic
porous media.
Steady or transient,
two-dimensional, areal,
cross-sectional or
radial simulation of
density-dependent flow.
heat and mass transport
in variably saturated,
anisotropic, hetero-
geneous defornable
porous media.
A two-dimensional
finite-element model for
transient simulation of
areal or cross-sectional
transport of dissolved
constituents for a given
velocity field in a
anisotropic, heter-
ogeneous porous medium.
Model
Processes
convect i on
conduction
dispersion
diffusion
consol idation
adsorption
decay
reactions
convection
conduction
dispersion
diffusion
change of
phase
adsorption
decay
reactions
convection
conduction
dispersion
diffusion
hysteresis
adsorption
decay
reactions
convection
conduction
dispersion
d i f f us i on
consol idation
hysteresis
adsorption
decay
reactions
capi 1 larity
convection
dispersion
diffusion
adsorption
decay
IGWMC
Key
3232
3233
3234
3235
3371
205
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
33.
34.
35.
36.
37.
38.
Author(s)
G.T. Yeh
D.D. Huff
Ref: 199
D.I. Deangel is
S.T. Yeh
0.0. Huff
Ref: 34
J.C. Parker
M. Th. van
Genuchten
Ref: 183
H. Fluhler
W.A. Jury
Ref: 51
H. Fluhler
W.A. Jury
Ref: 51
Walter G.
Knisel
Ref: 90
Contact Address
Environmental Scl. Oiv.
Oak Ridge National Lab.
Oak Ridge, TN 37830
Envionmental Sci. Div.
Oak Ridge National Lab.
Oak Ridge. TN 37830
Dept. of Agronomy
Virginia Polytechn.
Inst. and State Univ.
Blacksburg, VA' 24061
Swiss Federal Inst. of
Research
CH 8903 Brimensdorf
Switzerland
Swiss Federal Inst. of
Research
CH 8903 Birmensdorf
SH i tzer I and
U.S. Dept. of
Agriculture
Agricultural Research
Serv i ce
Southeast Watershed
Research Lab.
P.O. Box 946
Tifton, GA 31793
Model Name
(last update)
FEMA
(1985)
FRACPORT
(1984)
CXTFIT
(1984)
PISTON
(1983)
DISPEQ
/DISPER
(1983)
CREAMS
(1982)
Model
Description
A two-dimensional
finite-element model to
simulate solute trans-
port Including radio-
active decay, sorption,
and biological and
chemical degradation.
This model solves only
the solute transport
equation and velocity
field must be generated
by a flow model .
An integrated compart-
ments 1 model for des-
cribing the transport of
solute in three-dimen-
sional fractured porous
medium.
To determine values for
one-dimensional analy-
tical solute transport
parameters, using a
nonlinear least-squares
inversion method.
A finite-difference
approach to simulate
transport of reactive
solute species through
soi 1 columns by mass
flow (convective
transport) including
instantaneous equili-
brium and rate-dependent
solute exchange between
liquid and solid phase.
Finite-difference
approach to simulate
transport of reactive
solute species through
soil columns, including
dispersion, instan-
taneous equ i 1 i br i urn
adsorption (DISPEQ) and
rate-dependent adsorp-
tion (DISPER).
CREAMS is a general
watershed model designed
to evaluate nonpoint
source pollution from
alternate management
practices for field-size
areas. It consists of
three main components:
hydrology, erosion/sedi-
mentation, and
chemistry.
Processes
dispersion
di f fusion
adsorption
decay
advection
advection
dispersion
adsorption
decay
dispersion
di f fusion
decay
zero-order
production
advection
adsorption
ion exchange
reactions
dispersion
adsorption
ion exchange
react i ons
precipitation
evapo-
transpiration
adsorption
decay
IGWMC
Key
3376
3374
3432
3450
3451
3540
206
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
39.
40.
41.
42.
43.
44.
Author (s)
N.W. Kline
R.I. England
R.C. Boca
Ref: 34
C.I. Voss.
"
Ref: 188
F.M. Lewis
C.I. Voss
J. Rubin
Ref: 101
R.T. Dillon
R.M. Cranwel 1
R.B. Lant2
S.B. Pahwa
H. Reeves
Ref: 144
A.B. Gureghian
Ref: 62
B.J. Travis
Ref: 170
Contact Address
Rockwell International
Rock we 1 1 Han ford
Operations
P.O. Box 800
Rich land, HA 99352
U.S. Geological Survey
National Center
12201 Sunrise Valley Dr.
Reston, VA 22092
U.S. Geological Survey
National Center
12201 Sunrise Valley Dr.
Reston, VA 22092
Natl. Energy Software
Center
Argonne Natl. Laboratory
9700 S. Cass Avenue
Argonne, IL 60439
ONWI, Battelle Memorial
Institute
505 King Avenue
Columbus, OH 43201
Earth and Space Sciences
Division
Los Alamos National Lab.
Los Alaaos, NM 87545
Model Naae
(last update)
CHAINT
(1985)
SUTRA
(1984)
SATRA-CHEM
(1986)
SWIFT
(1981)
TRIPH
(1983)
TRACR3D
(1984)
Model
Description
A general purpose two-
dimensional, finite-ele-
ment model for radionu-
cl ide transport in a
fractured porous Medium.
CHAINT includes advec-
tion, dispersion, diffu-
sion, retardation and
chain-decay. It
requires output of the
finite-element flow
model MAGNUM. 2D as
i nput .
A finite-element simula-
tion model for two-di-
mensional, transient or
steady-state, saturated-
unsaturated, density-
dependent ground water
flow with transport of
energy or chemical ly
reactive single species
solutes.
A two-dimensional inte-
grated-f i n i te-d i f f erence
model for flow and
solute transport in
saturated porous media.
The model is a modifi-
cation of SATRA, a sim-
plified version of
SUTRA. It incorporates
aqueous equ i 1 i br i um-
controlled reactions,
and either 1 inear
adsorption or binary ion
exchange.
A three-dimensional fi-
nite-difference model
for simulation of coup-
led, transient, density-
dependent flow and
transport of heat.
brine, tracers or ra-
dionuclides in an i so-
tropic, heterogeneous
saturated porous media.
A two-dimensional
f inite-eleoent model for
the simultaneous
transport of water and
reacting solutes through
saturated and
unsaturated porous
media.
A three-dimensional
finite-difference model
of transient two-phase
flow and mu 1 t i component
transport in deformable,
heterogeneous, porous/
fractured media.
Model
Processes
diffusion
adsorption
decay
advection
buoyancy
chain-decay
(two
daughters)
cap! 1 larity
convection
d i spers i on
diffusion
adsorption
reactions
advection
dispersion
adsorption
ion exchange
complexation
advection
dispersion
diffusion
adsorption
ion exchange
decay
chemical
reactions
capillarity
dispersion
adsorption
decay
advect i on
capi 1 larity
dispersion
diffusion
adsorption
decay
advection
IGWMC
Key
3791
3830
3831
3840
4081
4270
207
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
45.
46.
47.
48.
49.
50.
51.
52.
Author(s)
C.J. Emerson
B. Thomas
R.J. Luxmoore
Ref: 44
1 .L. Nwaogazie
Ref: 125
H.J. Martinez
Ref: 106
A.J. Russo
Ref: 149
R.M. Li
Ref: 20
A.L. Baehr
Ref: 7
G.A. Cederberg
R.L. Street
J.O. Leckie
Ref: 23
D.N. Contractor
S.M.A. El Didy
A.S. Ansary
Ref: 25
Contact Address
Computer Sciences
Oak Ridge National Lab.
Oak Ridge, TN 37831
1 .L. Nwaogazie
Dept. of Civi 1 Eng.
Univ. of Port Harcourt
PMB 5323
Port Harcourt, Nigeria
Fluid Mechanics and Heat
Transfer Division
Sandia National
Laboratories
Albuquerque, NM 87185
Fluid Mechanics and Heat
Transfer Division
Sandia National
Laboratories
Albuquerque, NM 87185
Simous, Li & Assoc.,
Inc.
P.O. Box 1816
Ft. Collins, CO 80522
U.S. Geological Survey
National Center
12201 Sunrise Valley Dr.
Reston, VA 22092
Los Alamos National Lab
MS F665
Los Alamos, NM 87544
Department of Civil and
Mechanical Engineering
University of Arizona
Tucson, AZ 85721
Model Name
(last update)
CAD 11
(1984)
SOTRAN
(1988)
FEMTRAN
(1984)
IONMIG
(1984)
SBIR
(1984)
GASOLINE
(1985)
TRANQL
(1985)
MAQWQ
(1986)
Model
Description
CAD 11 simulates chemical
transport through soils
and the effect of soi 1
temperature on chemical
degradation.
A finite-element solute
transport model for two-
dimensional unconfined
aquifer systems, using
1 inear or quadratic
isoparametric quadri-
lateral elements
A two-dimensional
finite-element model to
simulate cross-sectional
radionuclide transport
in saturated/unsaturated
porous media. The model
considers chain-decay of
the radionucl ides. It
requires user-prescribed
heads.
A finite-difference
model to calculate two-
dimensional transport of
decaying radionucl ides
through a saturated
porous medium.
A three-dimensional
finite-difference model
for simulation of flow
and mass transport in a
variably saturated
porous medium.
A one-dimensional model
to solve a system of
equations defining the
transport of an immisci-
ble contaminant immobi-
lized in the unsaturated
zone, with or without
biodegradation.
TRANQL is a finite-
element, coupled
geochem i ca 1 /transport
model for a multicom-
ponent solution system
with equilibrium inter-
action chemistry coupled
with one-dimensional
advect i ve-d i spers i ve
transport.
A finite-element model
for simulation of tran-
sient nonconservative
transport of contami-
nants in a multiple
aquifer system, using
velocities generated by
the code MAQWF.
Model
Processes
diffusion
adsorption
deposition
chemical
degradation
d i spers i on
adsorption
advect ion
biodegra-
dation
radioactive
decay
cap! 1 larity
advect ion
decay
dispersion
diffusion
adsorption
decay
cap! 1 larity
convection
dispersion
advect ion
dispersion
biodegra-
dation
immiscible
flow
convection
dispersion
adsorption
ion exchange
reactions
dispersion
diffusion
adsorption
decay
advect ion
Key
4290
4320
4350
4360
4391
4420
4450
4531 .
208
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
53.
54.
55.
56.
57.
58.
59.
Author (s)
C.H. King
E.L. Mflhite
R.W. Root Jr.
O.J. Fauth
K.R. Routt
R.H. Emslie
R.R. Beckmeyer
Ref: 89
0.0. Nielsen
P. Bo. L.
Car (sen
Ref: 119
K.L. Kipp
Ref: 91
A.B. Gureghian
Ref: 63
P.S. Huyakorn
Ref: 74
P.S. Huyakorn
Ref: 73
P.S. Huyakorn
Ref: 76
Contact Address
E.I. Oupont de Nemours
and Corp.
Savannah. River Lab.
Aiken, S.C.
Chew is try Oept.
Rlso National Laboratory
P.O. Box 49
OK-4900, Denmark
IGWMC
Hoi comb Research
Institute
4600 Sunset Ave.
Indianapol is, IN 46208
Office of Crystalline
Repository Development
Battel le Memorial
Institute
505 King Avenue
Columbus, Ohio 43201
GeoTrans, Inc.
250 Exchange Place
Suite A
Herndon, VA 22070
HydroGeoLogic, Inc.
503 Carl isle Dr.,
Suite 250
Herndon, VA 22070
HydroGeoLogic, Inc.
503 Carlisle Dr.,
Suite 250
Herndon, VA 22070
Model Name
(last update)
OOSTOMAN
(1985)
COLUMN2
(1985)
HST30
(1988)
MASCOT
(1986)
FLAMINGO
(1985)
VAM2D
(1988)
VAM3D
(1988)
Model
Description
A finite-difference
compartments 1 model for
estimation of long-term
dose to humans from
buried waste.
One-dimensional simu-
lation of solute trans-
port in column experi-
ments, using a finite-
difference approach
combined with the method
of characteristics to
solve the transient
nonconservat i ve trans-
port equation.
A density-dependent,
three-dimensional ,
finite-difference model
for simulation of heat
and solute transport.
Analytical solutions for
multidimensional trans-
port of a four-member
radionuclide decay chain
in groundMater.
A three-dimensional
finite-element code for
analyzing water flow and
solute transport in
saturated-unsaturated
porous media.
A two-dimensional
finite-element model to
simulate flow and con-
taminant transport in
variably saturated
porous media. This code
can perform simulations
in an areal plane, a
cross-section, or an
ax i symmetric configura-
tion. It can also
handle highly nonlinear
soil moisture relations.
A three-dimensional
f i n i te-e 1 ement mode 1
that simulates flow and
contaminant transport in
variably saturated por-
ous media. It is cap-
able of steady-state and
transient simulations in
an areal plane, a cross-
section, an ax i symmetric
configuration, or as
fully three-dimensional.
Model
Processes
diffusion
adsorption
ion exchange
decay
reactions
advect i on
dispersion
adsorption
ion exchange
decay
reactions
advect ion
hydrolysis
complexation
advect ion
dispersion
diffusion
retardation
decay
diffusion
decay
reactions
advect ion
dispersion
evapotrans-
piration
dispersion
diffusion
adsorption
decay
advect ion
recharge
infiltration
evapotrans-
pi rat ion
advect ion
dispersion
adsorption
degradation
advect ion
dispersion
adsorption
degradation
IGWMC
Key
4540
4560
4610
4620
4630
4690
4691
209
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
60.
61.
62.
63.
64.
Author (s)
P.S. Huyakorn
Ref: 77
R.F.Carsel
C.N. Smith
I. A. Mulkey
J.D. Dean
P. Jowise
Ref: 22
M. Bonazountas
J.M. Wagner
Ref: 14
P.K.M. van der
Heijde
Ref: 179
H.Th. van
Genuchten
W.J. Alves
Ref: 184
Contact Address
HydroGeoLogic, Inc.
503 Carlisle Dr.,
Suite 250
Herndon, VA 22070
Environmental Research
Lab
Office of Research and
Development
U.S. EPA
Athens, GA 306)3
Off ice of Toxic
Substances
U.S. EPA
Washington, DC
IGWMC
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapolis, IN 46208
IGWMC
Ho 1 comb Research
Institute
4600 Sunset Avenue
Indianapolis, IN 46208
Model Name
(last update)
DSTRAM
(1988)
PR2M
(1984)
SESOIL
(1984)
PLUME2D
(1986)
ONE-D
(1985)
Model
Description
A three-dimensional
finite-element model
that simulates density-
dependent single-phase
fluid flow and solute or
energy transport in sat-
urated porous xedia.
This model can perform
steady-state or tran-
sient simulations in a
cross-section, an axi-
symmetric configuration,
or a ful ly 3-D model ,
and it is designed
specif ical ly for situ-
ations (there groundwater
flow is inf luenced by
variations in solute
concentration or
temperature.
The Pesticide Root Zone
Model simulates the ver-
tical movement of pesti-
cides in the unsaturated
zone. The model con-
sists of hydrologic and
chemical transport com-
ponents to simulate run-
off, erosion, plant up-
take, leaching, decay.
fol iar washof f , and
volati 1 ization.
A user-friendly model
for long-term environ-
mental pollutant fate
simulations. SESOIL is
designed to describe
flow, sediment trans-
port, pollutant trans-
port and transformation,
pollutant migration to
groundwater , and soil
qual ity.
An analytical solution
to calculate concentra-
tion distribution in a
homogeneous non leaky.
confined aquifer with
uniform regional flow.
The model uses the wel 1
function for solute
convection and disper-
sion in a system with
continuously injecting.
fully penetrating wells.
A package of five analy-
tical solutions to the
one-dimensional convec-
tion-dispersion equation
with linear adsorption,
zero-order production,
and first-order decay.
Model
Processes
inf i Itration
aquitard
leakage
advection
dispersion
adsorption
degradation
conduction
heat storage
runoff
erosion
plant uptake
leaching
decay
foliar
washof f
volati I iza-
tion
convection
dispersion
retardation
decay
convection
dispersion
adsorption
decay
GWHC
Key
4700
4720
4730
6024
6220
6221
6222
6223
6224
210
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
65.
66.
67.
68.
69.
70.
71.
Author(s)
M.Th. van
Genuchten
Ref: 185
1. Javandel
L. Doughty
C.F. Tsang
Ref: 85
W.C. Walton
Ref: 190
M.S. Beljin
Ref: 9
J. Bear
A Verruijt
Ref: 8
J.P. Sauty
M. Kinzelbach
Ref: 152
P. Srinivasan
J.W. Mercer
Ref: 160
Contact Address
IGWMC
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
IGWMC
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
IGWMC
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
IGWMC
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
IGWMC
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
IGWMC
Hoi comb Research
Institute
4600 Sunset Avenue
Indianapol is, IN 46208
GeoTrans, Inc.
250 Exchange Place,
Suite A
Herndon, VA 22070
Model Name
(last update)
CFITIM
(1985)
AGU-10
(1988)
WALTON 35
(1985)
SOLUTE
(1985)
BEAVERSOFT
(1987)
CATTI
(1988)
BIO-ID
(1988)
Model
Description
A program for estimation
of non-equilibrium sol-
ute transport parameters
from miscible disp lace-
Bent experiments.
A package of analytical
and semi -analytical
solutions for solute
transport which includes
one-and two-dimensional
solutions (ODAST,
TDAST), a semi -analyti-
cal solution for radial
dispersion (LTIRD), and
a streamline-tracking
solution (RESSQ).
A series of analytical
and simple numerical
ode Is to analyze flow
and solute and heat
transport in confined,
leaky confined, and
water table aquifers
with simple geometry.
A package of eight
analytical models for
solute transport. The
ode Is vary according to
dimensional capabilities
and boundary conditions.
A package of analytical
and numerical solutions
for groundwater flow and
solute transport. The
package includes models
for steady and unsteady
two-dimensional flow in
heterogeneous aquifers,
for flow through dams,
contaminant transport by
advection and dispersion
and for salt water
intrusion.
A program for the inter-
pretation of tracer test
data. CATTI computes
breakthrough curves
based on instantaneous
or continuous injection
of tracer into a homo-
geneous aquifer with
either 1D-2D uniform
flow or ax i symmetric
flow for one or two
layers. The package
includes a parameter
optimization procedure.
A one-dimensional solute
transport model which
simulates aerobic and
anaerob i c degradat i on
with or without adsorp-
tion for both substrate
and oxygen.
Model
Processes
convection
dispersion
decay
adsorption
convection
dispersion
stream
depletion
upconing
conduction
induced
inf i Itration
convection
dispersion
adsorption
decay
convection,
dispersion
convection
adsorption
biodegrada-
tion
IGWMC
Key
6227
6310
6311
6312
3940
3941
6350
6380
6590
6600
6610
211
-------
APPENDIX Cl
SOLUTE TRANSPORT MODELS: SUMMARY LISTING
No.
72.
73.
Author (s)
D.I. Nofziger
J.R. Williams
I.E. Short
Ref: t20
D.L. Nofziger
P.S.C. Rao
A.G. Hornsby
Ref: 122
Contact Address
Robert S. Kerr
Environmental Research
Lab
U.S. EPA
Ada, OK 74820
Institute of Food and
Agricultural Sciences
University of Florida
Gainesville, FL 32611
Model Nwe
(last update)
RITZ
(1988)
CHEHRANK
(1988)
Model
Description
The Regulatory and
Investigative Treatment
Zone Model is an Inter-
active aodel for simula-
tion of the movement and
fate of hazardous chemi-
cals during land treat-
ment of oily wastes.
A package which utilizes
four schemes for screen-
ing of organic chemicals
relative to their poten-
tial to leach into
groundwater systems.
The schemes are based on
rates of chemical move-
ment or relative rates
of mobility and degrada-
tion of the chemicals
within the vadose zone.
Model
Processes
volati I iza-
tion
degradation
leaching
leaching
degradation
mobility
GWHC
ey
6620
6640
212
-------
APPENDIX C2
SOLUTE TRANSPORT MODELS: USABILITY AND RELIABILITY
No.
1.
2.
3.
4.
5.
6.
7.
8.
.
1 n
10.
11.
12.
1 O
13.
14.
15.
16.
17.
18.
Author(s)
P.S.C. Rao
H.M. Selim
J.M. Davidson
G.F. Pinder
P.S. Huyakorn
P.S. Huyakorn
P.S. Huyakorn
P.S. Huyakorn
T.R. Knowles
INTERA Env. Cons., Inc.
LC V f\*\ 4 U ni i
.r. Komkow
J.O. Bredehoeft
S.P. Gar abed i an
L.F. Konikow
S.W. Ahl strom
FC ^A«»'*/*+* M^ »1
. t. Kaszeta, et ai.
V. Guvanasen
I. Miller
S.K. Gupta, et al.
H.C. Burkholder, et al.
R.W. Nelson
Model Name
NITROSIM
NMODEL
ISOQUAD 2
TRAFRAP-WT
GREASE 2
SATURN 2
SEFTRAN
GWSIM-II
CU TDD
iWirK
IICPC on
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TRANSPORT/
MOC
FRONTTRACK
MMT-DRPW
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Golder
Groundwater
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-------
APPENDIX C2
SOLUTE TRANSPORT MODELS: USABILITY AND RELIABILITY
No.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
Author(s)
P.S. Huyakorn
P.S. Huyakorn
R.F. Carsel, et al.
M. Bonazantas
J.M. Wagner
P.K.M. van der Heijde
M.Th. van Genuchten
W.J. Alves
M.Th. van Genuchten
I. Javandel, et al.
W.C. Walton
M.S. Beljin
J. Bear
A. Verruijt
J.P. Sauty
W. Kinzelbach
P. Srinivasan
J.W. Mercer
D.L. Nofzlger, et al.
D.L. Hofziger, et al.
Model Name
VAM3D
OSTRAM
PRZM
SESOIL
PLUME2D
ONE-0
DFITIM
AGU-10
WALTON 35
SOLUTE
BEAVER-
SOFT
CATTI
BIO- ID
RITZ
CHEMRANK
USABILITY
N
N
D
D
0
0
N
N
D
D
0
D
D
D
D
N
N
N
U
N
N
N
Y
N
0
D
0
D
N
U
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
N
K
U
U
L
N
N
L
L
L
L
L
L
U
U
Y
Y
L
N
Y
L
L
Y
L
Y
L
L
Y
L
L
RELIABILITY
Y
Y
U
U
Y
Y
U
Y
Y
Y
Y
U
U
U
U
U
U
U
U
N
N
U
N
U
N
U
U
U
U
U
Y
Y
Y
U
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
U
L
L
L
U
L
U
L
L
L
L
L
U
L
L
U
F
F
F
F
M
F
F
M
M
M
M
F
F
F
F
IGWMC
KEY
4691
4700
4720
4730
6024
6220-
6224
6227
6310
6311
6312
3940
3941
6350
6380
6590
6600
6610
6620
6640
KEY:
YES
N = NO
U « UNKNOWN
6 > GENERIC
DEDICATED
L * LIMITED
M * MANY
FEW
216
-------
APPENDIX 01
HEAT TRANSPORT MODELS: SUMMARY LISTING
No.
i.
2.
3.
4.
5.
6.
7.
Author(s)
M.J. Lippman
T.N. Narasimhan
D.C. Mangold
6.S. Bodvarsson
Ref: 104
M.L. Sorey
M.J. Lippman
Ref: 39
G.F. Finder
P.E. Kinnmark
C.I. Voss
Ref: 134
P.S. Huyakorn
P.S. Huyakorn
Ref: 70
P.S. Huyakorn
Ref: 78
J.E. Reed
Ref: 143
Contact Address
Nat'l Energy Software
Center
Argonne Nat'l Lab.
9700 S. Cass Ave.
Argonne, IL 60439
Nat'l Energy Software
Center
Argonne Nat'l Lab.
9700 S. Cass Ave.
Argonne, IL 60439
Oept. of Civi 1
Engineering
School of Engineering i
Appl ied Science
Princeton Univ.
Princeton, NJ 05844
GeoTrans, Inc.
250 Exchange Place
Suite A
Herndon, VA 22070
GeoTrans, Inc.
250 Exchange Place
Suite A
Herndon, VA 22070
IGWMC
Hoi comb Research
Institute
4600 Sunset Ave.
Indianapol is, IN 46208
M.S. Bedinger
U.S. Geological Survey
Box 25046, MS 417
Federal Center
Denver, CO 80225
Model Name
(last update)
PT/CCC
(1981)
SCHAFF
(1974)
GAFETTA
(1980)
SEFTRAN
(1985)
GREASE2
(1982)
TRAFRAP-WT
(1987)
HOTWTR
(1985)
Model
Description
Model uses integrated-
f inite-dif ference method
to calculate steady and
unsteady temperature and
pressure distributions.
and vertical compaction
in multidimensional
heterogeneous systems
with complex geometry
and a single phase, non-
isothermal liquid.
A three-dimensional
finite-difference model
to simulate unsteady
heat and fluid flow in
si i ght 1 y compress i b 1 e
porous media.
Prediction of heads and
temperatures by finite-
element simulation of
two-dimensional, hori-
zontal f low and heat
transport (steady-state
or transient) in iso-
tropic, heterogeneous
aqui fers.
A two-dimensional
finite-element model for
simulation of transient
flow and transport of
heat or solutes in ani-
sotropic, heterogeneous
porous media.
The finite-element model
simulates heat and/or
solute transport in
fractured porous media.
The flow field is multi-
dimensional, density-
dependent, transient or
steady-state in an i so-
tropic heterogeneous,
confined, or uncon fined
aquifers.
Two-dimensional finite-
element model to simu-
late fluid flow and
transport of radionu-
cl ides in fractured
porous media.
A finite-difference
model to simulate
steady-state coupled
fluid and heat flow in
an isotropic hetero-
geneous aquifer system
with uniform thermal
properties and
v i scos i ty-dependent
hydrau 1 i c conduct i v i ty .
Model
Processes
Heat convec-
tion
conduction.
consol idation
expansion
Heat
convection
conduction
Heat convec-
tion
conduction
dispersion
advection
dispersion
di f fusion
adsorption
decay
Heat convec-
tion
conduction
dispersion
solute con-
vection.
diffusion
adsorption
Heat convec-
tion
conduction in
fluid
dispersion
Heat convec-
tion and
conduction
coupled with
flow
IGWMC
Key
0100
0160
0513
0588
0582
0589
0612
217
-------
APPENDIX Dl
HEAT TRANSPORT MODELS: SUMMARY LISTING
No.
8.
9.
10.
11.
12.
13.
Author (s)
INTERA, Inc.
Ref: 64
K.L. Kipp
Ref: 91
C.R. Faust
J.W. Mercer
Ref: 48
S.W. Ahlstrom
H.P. Foote
R.J. Serne
Ref: 2
F.E. Kaszeta
C.S. Simmons
C.R. Cole
Ref: 192
V. Guvanasen
Ref: 24
Contact Address
INTERA Technologies,
Inc.
6850 Austin Ctr. Blvd.
Suite 300
Austin, TX 78731
K. Kipp
U.S. Geological Survey
Box 25046, Mail Stop 411
Denver Federal Center
Lakewood, CO 80225
ONWI
Battel le Project
Hgmnt. Division
505 King Avenue
Columbus, OH 43201
Battel le Pacific NW Labs
P.O. Box 999
Rich land, WA 99352
Battel le Pacific NW Labs
P.O. Box 999
Richland, WA 99352
Applied Geoscience
Branch
Mhiteshell Nuclear Res.
Atonic Energy of Canada
Pinawa, Manitoba
Canada ROE 1LO
Model Name
(last update)
SWENT
(1983)
HST30
(1988)
GEOTHER
(1983)
MMT-DPRW
(1976)
MMT-1D
(1980)
MOTIF
(1986)
Model
Description
Multidimensional finite-
difference model to
simulate fluid flow,
heat, and radioactive
contaminant transport in
heterogeneous porous
media.
A finite-difference
ode) to simulate non-
steady three-dimensional
groundwater flow, heat,
and contaminant trans-
port in a heterogeneous
aquifer.
Finite-difference simu-
lation of transient,
three-dimensional ,
single and two-phase,
heat transport in an i so-
tropic, heterogeneous.
porous media.
Model using discrete
parcel random walk
method to predict
transient, three-
dimensional movement of
radionucl ides, heat and
other contaminants in
saturated/unsaturated
aquifer systems.
A discrete parcel random
walk model to simulate
transient, one-dimen-
sional movement of
radionucl ides, heat and
other contaminants in
saturated/unsaturated
aquifer systems (1-0
version of HMT-DPRW).
A finite-element model
for one-, two-, and
three-dimensional
saturated/unsaturated
groundwater flow, heat
transport, and solute
transport in fractured
porous media. The model
considers single-species
radionucl ide transport
and solute diffusion
from fracture to rock
matrix.
Model
Processes
Heat convec-
tion
conduction
dispersion
vertical heat
loss
Heat convec-
tion, conduc-
tion, and
dispersion;
pressure
effects on
enthalpy;
solute con-
vection,
diffusion.
dispersion,
adsorption/
desorption.
and decay
Heat convec-
tion, conduc-
tion, disper-
sion, and
di f fusion;
condensation;
change of
phase
advection
dispersion
di f fusion
adsorption
decay
chemical
reactions
ion exchange
dissolution
precipitation
advection
dispersion
diffusion
sorption
decay
chemical
reactions
Capi 1 larity;
heat convec-
tion; solute
convection,
dispersion.
diffusion.
adsorption.
and decay
IGWMC
Key
0692
4610
0730
0780
0781
0953
218
-------
APPENDIX Dl
HEAT TRANSPORT MODELS: SUMMARY LISTING
No.
14.
15.
16.
17.
18.
Author(s)
J.F. Pickens
6.E. Grisak
Ref: 131
S.K. Gupta
C.R. Cole
C.T. Kincaid
A.M. Monti
Ref: 59
K. Pruess
R.C. Schroeder
Ref: 140
K. Pruess
Ref: 141
O.K. Gartl ing
Ref: 54
Contact Address
INTERA Technologies Inc.
6850 Austin Ctr. Blvd.
Suite 300
Austin, TX 78731
Water and Land Resources
Division
Battel le Pacific NW Lab
P.O. Box 999
Rich land, WA 99352
Nat'l Energy Software
Center
Argonne Nat'l Lab
9700 S. Cass Ave.
Argonne, IL 60439
Mail Stop 50E
Lawrence Berkeley Lab
Berkeley, CA 94720
Sand i a Nat'l Labs
Division 5511
Albuquerque, NM 87185
Model Name
(last update)
SHALT
(1980)
CFEST
(1987)
SHAFT79
(1980)
MULKOM
(1985)
MAR 1 AH
(1980)
Model
Description
The model simulates heat
and solute transport in
a fractured, saturated
or unsaturated, two-
dimensional aquifer.
The finite-element tech-
nique is used in the
solution of the equation
describing density-
dependent, compressible
fluid, steady-state or
transient situations.
Two- or three-dimension-
al finite-element simu-
lation of steady-state
or transient flow.
energy and solute trans-
port in anisotropic
heterogeneous multi-
layered aquifers.
Transient simulation of
simultaneous three-
dimensional heat and
fluid transport in
porous media using
finite-difference and
i ntegrated-f inite-
difference methods.
An i ntegrated-f inite-
difference model to
simulate heat and
multiphase fluid flow in
multidimensional frac-
tured porous media; the
method adopted is a
generalization of the
doub 1 e-poros i ty
approach.
A finite-element model
to simulate unsteady
two-dimensional vertical
flow in anisotropic
heterogenous porous
media with heat
transfer.
Model
Processes
Heat convec-
tion, conduc-
tion, and
dispersion;
solute
convection.
dispersion,
adsorption,
radioactive
decay, and
cheaical
reactions
Heat convec-
tion, conduc-
tion, solute
convection,
dispersion.
and
diffusion
condensation;
heat convec-
tion, and
conduction;
change of
phase
Heat convec-
tion and
conduction;
Fluid (water
and gas)
transport;
change of
phase;
solute
convection;
dissolution
and precipi-
tation.
transport of
dissolved
solids
Heat convec-
tion, conduc-
tion, and
dispersion
1GWMC
Key
2034
2070
2580
2581
2620
219
-------
APPENDIX 01
HEAT TRANSPORT HODELS: SUMMARY LISTING
No.
19.
20.
21.
22.
23.
Author(s)
J.W. Pritchett
Ref: 139
J.W. Pritehett
Ref: 139
A.K. Runchal
J. Treger
G. Segal
Ref: 147
C.B. Andrews
Ref: 6
M.R. Walker
J.D. Sabey
Ref: 189
Contact Address
Systems, Science and
Software
P.O. Box 1620
La Jolla, CA 92038
Systems, Science and
Software
P.O. Box 1620
La Jolla, CA 92038
Dames and Moore
Advanced Technology
Group
1100 Gelndon Ave.,
Suite 1000
Los Angeles, CA 90024
Woodward-Clyde Cnslt.
Three Embarcadero
Center, Suite 700
San Francisco, CA 94111
Water Resources Research
Center
Virginia Polytechnic
Institute
617 North Main St.
Blacksburg, VA 24060
Model Name
(last update)
MUSHRM
(I960)
CHARGR
(1980)
EP21-GWTHERM
(1979)
UWIS-2D-
TRANSPORT
(1980)
TRANS
(1981)
(
Model
Description
Multi species hydrother-
mal reservoir model to
simulate unsteady multi-
phase fluid and heat
flow in multidimensional
geometries by means of
finite-difference
method.
Hydrothernal reservoir
model using finite-
difference method to
predict pressures and
temperatures in an i so-
tropic, heterogeneous
confined aquifers with
matrix deformation;
simulation of three-
dimensional transient
multiphase flow of a
compressible fluid with
dissolved incondensible
gases and heat trans-
port.
An integrated-f inite-
difference model to
simulate fluid flow and
heat and solute trans-
port in an anisotropic,
heterogeneous, water-
table aquifer. The flow
field is two-dimen-
sional, density-depen-
dent and steady-state or
transient.
Model using finite-ele-
ment method to simulate
two-dimensional, ares I
or cross-sectional.
steady or transient,
single-phase, heat or
conservative solute
transport in a confined
or phreatic, aniso-
tropic, heterogeneous
aquifer.
The finite-element model
predicts heads, flow
rates, moisture contents
and temperatures by sim-
ulating two-dimensional
horizontal or vertical.
transient flow and heat
transport in anisotro-
pic, heterogeneous,
variably saturated soil.
Model
Processes
Heat convec-
tion, and
conduction;
degass i ng ,
consol ida-
tion;
expansion;
change of
phase
(flow is
coupled)
Heat convec-
tion and
conduction;
change of
phase (flow
is coupled)
Heat convec-
tion and
dispersion;
solute
convection.
dispersion,
diffusion,
retardation
and radio-
active decay
Heat convec-
tion, conduc-
tion, and
dispersion;
solute
convection.
dispersion.
diffusion,
adsorption,
and absorp-
tion
Heat convec-
tion, conduc-
tion, and
dispersion
(coupled with
flow)
GUMC
Key
2760
2761
2830
2860
2950
220
-------
APPENDIX 01
HEAT TRANSPORT MODELS: SUMMARY LISTING
No.
24.
25.
26.
27.
28.
Author(s)
B. Sagar
B. Sagar
A.K. Runchal
6.T. Yeh
R.J. Luxmoore
P.C.D. Hilly
Ref: 110
Contact Address
Analytic & Computational
Research, Inc.
3016 Inglewood Blvd.
Los Angeles, CA 90066
Analytic & Computational
Research, Inc.
3106 Inglewood Blvd.
Los Angeles, CA 90066
Analytic 4 Computational
Res. Inc.
3106 Inglewood Blvd.
Los Angeles, CA 90060
Environmental Sci. Oiv.
Oak Ridge National Lab
Oak Ridge, TN 37830
Massachusetts Inst.
of Technology
Dept. of Civil Eng.
Cambridge, HA 02139
Model Name
(last update)
VAOOSE
(1982)
FLOTRA
(1982)
PORFREEZE
(1981)
HATTUH
(1983)
SPLASHWATR
(1983)
Model
Description
Steady or transient,
two-dimensional, area),
cross-sectional or
radial simulation of
density-dependent trans-
port of moisture, heat
and mass in variably
saturated, hetero-
geneous, anisotropic
porous media.
Steady or transient,
two-dimensional, area),
cross-sectional or
radial simulation of
dens i ty-dependent f 1 ow ,
heat and mass transport
in variably saturated.
anisotropic, hetero-
geneous deformable
porous media.
The model simulates
dens i ty-dependent f 1 ow
and heat transport in
two-dimensional
freezing-soil domains.
The coupled equations
represent saturated
steady-state or
transient conditions and
are solved using the
finite-difference
approach. The system
modeled is anisotropic
and heterogeneous.
A three-dimensional
model for simulating
moisture and heat
transport in unsaturated
porous media. The model
solves both the flow and
heat equation using the
integrated compartment
method.
One-d i mens i ona 1 , vert i -
cal finite-element simu-
lation of steady or
transient saturated/
unsaturated flow and
heat transport in i so-
tropic, heterogeneous
soils to predict heads.
flow rates and tempera-
tures.
Model
Processes
convection
conduction
dispersion
diffusion
hysteres i s
adsorption
decay
reactions
convection
conduction
dispersion
diffusion
consol idation
hysteresis
adsorption
decay
reactions
Heat convec-
tion and
conduction
Capil larity
heat convec-
tion, conduc-
tion, and
latent trans-
fer due to
evaporation
Heat convec-
tion, conduc-
tion, and
dispersion
IGUMC
Key
3234
3435
3236
3375
3590
221
-------
APPENDIX Dl
HEAT TRANSPORT MODELS: SUMMARY LISTING
NO.
29.
30.
31.
32.
33.
Author(s)
N.W. Kline
A.K. Runchal
R.G. Baca
Ref: 93
C. 1 . Voss
Ref: 188
R.T. Dillon
R.M. Cranwell
R.B. Lantz
S.B. Pahwa
H. Reeves
Ref: 144
A.S. Bodvarsson
Ref: 13
E.K. Grubaugh
D.L. Reddell
Ref: 58
Contact Address
Rockwell Hanford
Operations
Energy Systems Group
Rockwell International
P.O. Box 800
Rich land, NA 99352
U.S. Geological Survey
National Center
12201 Sunrise Valley Or.
Reston, VA 22092
National Energy
Software Center
Argonne National Lab.
9700 S. Cass Ave.
Argonne, IL *>0439
Earth Sciences Oiv.
Lawrence Berkeley Lab.
University of California
Berkeley, CA 94720
E.K. Grubaugh
Texas Water Res. Inst.
Texas A4M Univ.
College Station, TX
77843
Model Naae
(last update)
PORFLOW
(1983)
SUTRA
(1985)
SWIFT
(1981)
PT
(1983)
TEXASHEAT
(1980)
Model
Description
An integrated-f inite-
difference model for
simulating transient.
two-dimensional or axi-
symmetric transfer and
transport of radionu-
clides In layered geo-
logic systems.
A finite-element simula-
tion model for two-
dimensional, transient
or steady-state, satu-
rated-unsaturated ,
dens i ty-dependent
groundwater flow.
Transport of either
energy or dissolved
substances is also
included.
A three-dimensional
finite-difference model
for simulating coupled,
transient, density-de-
pendent flow and trans-
port of heat, brine.
tracers or radionucl ides
in anisotropic, hetero-
geneous confined
aquifers.
Model using finite-dif-
ference and integrated-
f inite-dif ference meth-
ods to simulate tran-
sient three-dimensional
fluid flow and heat
transport and one-dimen-
sional subsidence in
isotropic, hetero-
geneous, porous media.
A three-dimensional,
transient finite-element
model for solution of
simultaneous flow and
heat transport through
anisotropic, hetero-
geneous porous media.
Model
Processes
Heat convec-
tion and
conduction;
solute
dispersion,
diffusion,
adsorption.
decay, and
retardation
Cap i 1 1 ar i ty ;
heat convec-
tion, disper-
sion, and
conduction;
solute
convection,
dispersion,
diffusion.
adsorption,
and
reactions
(flow is
coupled with
either heat
or solute
transport)
Heat convec-
tion and
conduction;
solute
convection,
dispersion.
diffusion.
adsorption,
ion exchange,
and decay,
reaction, and
buoyancy;
salt
dissolution
Heat convec-
tion, and
conduction;
consol ida-
tion;
expansion
Heat convec-
tion and
conduction;
coupled with
flow
GWMC
Key
3790
3830
3840
3890
3970
222
-------
APPENDIX Dl
HEAT TRANSPORT MODELS: SUMMARY LISTING
No.
34.
35.
36.
Author(s)
A.I. Edwards
A. Rasnuson
1. Neret nicks
T.N. Narasimhan
Ref: 38
C.A. Anderson
Ref: 5
R.I. England
M.M. Kline
K.J. Ebb lad
R.6. Baca
Ref: 49
Contact Address
Oept. of Chemical Eng.
Royal Inst. of Tech.
S- 100 44 Stockholm,
Sweden
Los Alamos Nat'l Lab.
Los Alamos, NH 6754$
Rockwel 1 Han ford
Operations
P.O. Box 800
Rich I and, WA 99352
Model Name
(last update)
TRUMP
(1980)
SANGRE
(1986)
MAGNUM-2D
(1985)
Model
Description
A multidimensional
mode 1 , based on the
i ntegrated-f i n i te-d i f -
ference method, to sim-
ulate steady-state or
transient flow and heat
or solute transport in
fractured rock.
Two-dimensional finite-
element program to
simulate groundwater
flow, heat transport and
faulting in highly
deformable porous
aquifers.
Two-d imens iona 1 mode 1 ,
based on finite-element
method, to simulate
groundwater flow and
heat transfer in
fractured porous medium.
Model
Processes
Heat convec-
tion, disper-
sion, and
conduction;
solute
dispersion.
convection.
diffusion.
and decay
(flow is
coupled with
either heat
or solute
transport)
Heat
convection,
conduction
Heat convec-
tion, conduc-
tion, and
dispersion
IGWMC
Key
4030
4600
4590
223
-------
APPENDIX 02
HEAT TRANSPORT MODELS: USABILITY AND RELIABILITY
No.
1
3
5
6
7
0
o
9
11
12
13
14
1C
19
16
17
18
19
20
Author(s)
M.J. Lippman, et al.
Ml ^nr*av
u o u i c j
M.J. Lippman
G.F. Pinder, et al.
P.S. Huyakorn
P.S. Huyakorn
J.E. Reed
TNTFRA Tnr
llilLI\/^, JLIlC.
K. Kipp
CD Panet
. t\ . r dU SI
J.W. Mercer
S.W. Ahl strom, et al.
F.E. Kaszeta, et al.
V. Guvanasen
J.F. Pickens
G.E. Grisak
SV Cunta at al
. K. QUpta, et al.
K. Pruess
R.C. Schroeder
K. Pruess
O.K. Gartling
J.W. Pritchett
J.W. Pritchett
Model Name
PT/CCC
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KEY: Y * YES
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U « UNKNOWN
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D * OEOICATEO
L > LIMITED
M - MANY
F * FEW
224
-------
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Model Users
si
m
-------
APPENDIX El
HYDROCHEMICAL MODELS: SUMMARY LISTING
No.
i.
2.
3.
4.
5.
6.
7.
Author(s)
D.I. Parkhurst
L.N. Pluiwer
D.C.
Thorstenson
Ref: 128
T.J. Nolery
J.R. Morrey
O.W. Shannon
6. Sposito
S.V. Hattigod
J.C. Nestall
J.I. Zachary
F.M.M. Morel
A.R. Felmy
O.C. Girvin
E.A. Jenne
D.L. Parkhurst
D.C.
Thorstenson
L.N. Plumper
Ref: 127
Contact Address
L.N. Plunmer
U.S. Geological Survey
Water Resources Division
12201 Sunrise Valley
Drive
Reston, VA 22092
T.J. Wolery
Lawrence Livernore
National Laboratory
P.O. Box 808, L-204
Livermore, CA 94550
Vase) W. Roberts
Electric Power Research
Institute
3412 Nil (view Avenue
Palo Alto, CA 94304
G. Sposito
Department of Soi 1 and
Environmental Sciences
University of California
Riverside, CA 92521
F.M.M. Morel
Dept. of Civil
Engineering
Hassachusetss Institute
of Technology
Cambridge, HA 02139
David Disney
ADP Section
Environmental Research
Lab.
U.S. Environmental
Protection Agency
College Station Road
Athens, GA 30613
L.N. Plummer
U.S. Geological Survey
Water Resources Division
12201 Sunrise Valley
Drive
Reston, VA 22092
Model Name
(last update)
BALANCE
(1982)
EQ3NR/6
(1983)
EQUILIB
(1978)
GEOCHEM
(1980)
MINEQL2
(1980)
HINTEO
(1987)
PHREEQE
(1980)
Model
Description
Using the chemical com-
positions of water
samples from two points
along a flow path and a
set of Mineral phases
hypothesized to be the
reactive constituents in
the system, the program
calculates the mass
transfer necessary to
account for the observed
changes in composition
between the two water
samp I es .
EQ3NR is a geochemical
aqueous spec! at ion/
solubility program that
can be used alone or in
conjunction with EQ6,
which per fonts reaction-
path calculations. Ac-
comodates up to 40
elements, 300 aqueous
species, 15 gases, and
275 minerals.
Models chemical equi-
libria in geothermal
brines at various ele-
vated temperatures.
Contains 26 elements.
200 aqueous species, 7
gases, and 186 minerals.
A program for predicting
the equilibrium distri-
bution of chemical
species in soil solution
and other natural water
systems. Includes 45
elements, 1853 aqueous
Species, 42 organic
ligands, 3 gases, and
250 minerals and solids.
A program for the calcu-
lation of chemical equi-
libria in aqueous
systems.
A program for calcula-
ting geochemical equi-
libria, containing the
WATEQ3 database.
Includes 31 elements,
373 aqueous species, 3
gases, and 328 solids.
An equil i far i urn model
that can calculate mass
transfer as a function
of stepwise temperature
change or dissolution.
Includes 19 elements.
120 aqueous species, 3
gases, and 21 minerals.
Model
Processes
ass balance
on elements
mixing end-
member waters
redox reac-
tions
i sotope
balance
no thermo-
dynamic con-
straints on
the reactions
redox reac-
tions need
not be at
equi I ibrium
redox
reactions
mass balance
for each
species
redox
reactions
cation
adsorption
and exchange
mass balance
redox reac-
tions
surface
adsorption
mass balance
for each com-
ponent
redox
reactions
ion exchange
six surface
coop lexat ion
models
ass balance
redox reac-
tions for 3
elements
ion exchange
IGWMC
Key
3400
2610
226
-------
APPENDIX El
HYDROCHEMICAL MODELS: SUMMARY LISTING
No.
8.
9.
to.
11.
12.
13.
14.
Author (s)
6. Pickrel 1
D.D. Jackson
S.E. Ingle
H.O. Schuldt
D.W. Schults
O.K. Karri ss
S.E. Ingle
O.K. Taylor
V.R. Magnuson
Y.K. Kharaka
1 . Barnes
B.W. Goodwin
M. Hunday
J.W. Bal 1
E.A. Jenne
O.K. Nordstrom
J.W. Ball
E.A. Jenne
M.W. Cantrell
Contact Address
0.0. Jackson
Lawrence Livermore
National Laboratory
P.O. Box 808, L-329
Livermore, CA 94550
D.W. Schults
Hatfield Marine Sci.
Cntr.
U.S. Environmental
Protection Agency
Newport, OR 97365
V.R. Magnuson
Department of Chemistry
University of Minnesota
Duluth, MN 55812
r.K. Kharaka
U.S. Geological Survey,
MS/427
345 Middlefield Road
Men lo Park, CA 94025
B.W. Goodwin
Atomic Energy of
Canada Ltd.
Whiteshell Nuclear
Research Establishment
Pinawa, Manitoba ROE ILO
Canada
J.W. Ball
U.S. Geological Survey,
MS/21
345 Middlefield Road
Menlo Park. CA 94025
J.W. Ball
U.S. Geological Survey
MS/21
345 Middlefield Road
Menlo Park, CA 94025
Model Nave
(last update)
PROTOCOL
(1984)
REDEQL.EPA
(1978)
REDEQL-UMD
(1984)
SOLMNEQ
(1973)
SOLMNQ
(1983)
WATEQ2
(1980)
WATEQ3
(1981)
Model
Description
A coupled kinetic/equi-
librium program for cal-
culating dissolution
reactions of inorganic
solids in aqueous solu-
tion, with specif ic
application to corrosion
of vitrified nuclear
waste by groundwater.
1 ncorporates equ i 1 i br i um
routines from MINEQL.
A program to compute
aqueous equilibria for
up to 20 metals and 30
ligands in a system.
Includes 46 elements, 94
aqueous species, 2
gases, and 13
minerals/sol ids.
A program to compute
equi 1 ibrium distri-
butions of species
concentrations in
aqueous systems.
Standard version
includes 53 elements.
109 aqueous species, 2
gases, and 27 mixed
sol ids
A program for computing
the equilibrium distri-
bution of species in
aqueous solution.
Includes 26 elements,
162 aqueous species, and
158 minerals.
An interactive chemical
spec! at ion program that
calculates equilibrium
distributions for inor-
ganic aqueous species
often found in ground-
water, a FORTRAN version
of SOLMNEQ. Includes 28
elements, 239 aqueous
species, and 181 solids.
A chemical equilibrium
model for calculating
aqueous spec! at ion of
major and minor elements
among natural ly
occurring ligands. _
The MATE02 model with
the addition of uranium
species.
Model
Processes
kinetic sub-
models
-empirical
-dissolution
of s i 1 i ca
-surface
coverage
mass balance
redox
reactions
ccnp 1 exat i on
redox
reactions
surface com-
pl exat ion
adsorption
model
mass balance
of each
element
redox
reaction
ass balance
of each
element
aqueous
species of
uranium and
Plutonium
added
redox
react i ons
ass balance
redox
reactions
ass. balance
redox
reactions
IGWMC
Key
Z27
-------
APPENDIX El
HYDROCHEMICAL MODELS: SUMMARY LISTING
No.
15.
Author(s)
L.N. Plumner
B.F. Jones
A.H. Truesdel 1
Contact Address
L.N. PluMwr
U.S. Geological Survey
Water Resources Division
12201 Sunrise Valley
Drive
Reston, VA 22092
Model Name
(last update)
WATEQF
(1984)
-
Model
Description
A program to model the
thermodynamic spec! at ion
of inorganic ions and
complex species in
solution for a given
water analysis. A
FORTRAN version of the
original MATEQ (1973) in
PL/1.
Model
Processes
mass balance
redox
reactions
IGWMC
Key
228
-------
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-------
APPENDIX Fl
FRACTURED ROCK MODELS: SUMMARY LISTING
No.
i.
2.
3.
4.
5.
Author(s)
P.S. Huyakorn
H.O. White
T.O. Wadsworth
Ref: 78
P.S. Huyakorn
Ref: 70
P.S. Huyakorn
Ref: 81
S.B. Pahwa
B.S. Rama Rao
Ref: S3
V. Guvanasen
Ref: 24
Contact Address
IGWMC
Hot comb Research
Institute
4600 Sunset Ave.
Indianapolis, IN 46208
GeoTrans, Inc.
250 Exchange Place
Suite A
Herndon, VA 22070
Code Custodian
Performance Assessment
Dept.
Office of Nuclear Waste
Isolation
Battelle Project Mgmt.
Oiv.
505 King Avenue
Columbus, OH 43201
Code Custodian
Performance Assessment
Oept.
Office of Nuclear Waste
Isolation
Battelle Project Manage-
ment Div.
505 King Avenue
Columbus, OH 43201
Applied Geoscience
Branch
Whi resell Nuclear
Research
Atomic Energy of Canada
Pinawa, Manitoba
Canada ROE 110
Model Name
(last update)
TRAFRAP-WT
(1987)
GREASE2
(1982)
STAFAN2
(1982)
NETFLOW
(1982)
MOTIF
(1986)
Model
Description
A two-dimensional
finite-element model to
simulate transient.
saturated groundMater
flow and chemical or
radionuclide transport
in fractured or unfrac-
tured, anisotropic,
heterogeneous, multi-
layered porous media;
fractures handled by
either the dual porosity
or the discrete fracture
approach.
A finite-element model
to study transient.
multidimensional, satu-
rated groundwater flow,
solute and/or energy
transport in fractured
and unfractured, aniso-
tropic, heterogeneous.
mu 1 1 i 1 ayered porous
media.
A finite element model
for simulation of tran-
sient two-dimensional
flow and stress in
deformable fractured and
unfractured porous
media.
A finite-element model
to simulate steady-state
three-dimensional flow
in a heterogeneous
medium by an equivalent
network of series and
parallel flow members
Finite-element model for
one, two, and three-
dimensional saturated/
unsaturated groundwater
flow, heat transport.
and solute transport in
fractured porous media.
faci 1 States single-
species radionuclide
transport and solute
diffusion from fracture
to rock matrix.
Processes
Convection,
dispersion.
diffusion,
adsorption.
absorption.
decay.
reactions
Convection,
conduction.
dispersion,
diffusion,
adsorption
Deformation
Convection,
dispersion.
diffusion.
adsorption,
decay.
advection
IGWMC
Key
0589
0582
0584
0695
0953
230
-------
APPENDIX Fl
FRACTURED ROCK MODELS: SUMMARY LISTING
No.
6.
7.
a.
9.
10.
n.
Author(s)
J.F. Pickens
Ref: 56
J.F. Pickens
Ref: 57
K. Pruess
Ref: 141
K. Pruess
Y.W. Tsang
J.S.Y. Wang
J. Moor i shad
P.A.
Wither spoon
J. Noorishad
M. Menran
Ref: 123
Contact Address
INTERA Technologies,
Inc.
6850 Austin Center
Blvd., #300
Austin, TX 78731
INTERA Technologies, Inc
6850 Austin Center
Blvd., /300
Austin, TX 78731
Mai (stop 50E
Lawrence Berkeley Lab
Berkeley, CA 94720
Earth Sciences Division
Lawrence Berkeley
Laboratory
University of California
Berkeley, CA 94720
Earth Sciences Division
Lawrence Berkeley
Laboratory
Univ. of Cal i form' a
Berkeley, CA 94720
Earth Sciences Division
Lawrence Berkeley
Laboratory
Univ. of Cal ifornia
Berkeley, CA 94720
Model Name
(last update)
FRACT
(1981)
FRACSOL
(1981)
MULKOM
(1985)
TOUGH
(1984)
ROCMAS-H
(1976)
ROCMAS-HS
(1981)
Model
Description
A finite-element model
for simulation of
advect J ve-d i spers i ve
solute transport in
linear fractures with
solute diffusion into
the adjacent matrix
blocks.
Analytical solution for
simulation of solute
transport in fractured
media.
Mult {component, multi-
phase fluid and heat
flow in porous or frac-
tured media; MINC con-
cept, separate equations
for flow through matrix
and fractures. Frac-
tures are represented by
one-dimensional cells.
An integrated-f inite-
difference model for
transient simulation of
two-phase flow of water
and air with simul-
taneous heat transport
in fractured unsaturated
porous media.
A finite-element model
for two-dimensional
simulation of transient
ground water flow tn
porous fractured rock.
A transient model to
solve for two-dimension-
al di spers i ve-con vect ive
transport of nonconser-
vative solutes in satu-
rated, fractured porous
media for a given velo-
city field as generated
by ROCMAS-H.
Model
Processes
Convect i on ,
dispersion,
diffusion,
adsorption,
ion exchange,
decay
Convection,
diffusion
Convection,
change of
phase, disso-
lution and
precipitation
of silica,
equi I i brat ion
of nonconden-
sible gases.
transport of
noncon den-
si ble gases
and dissolved
sol ids.
Condensation,
capil lary
forces,
evapotrans-
pi rat ion,
conduction.
diffusion,
change of
phase,
adsorption,
compression.
dissolution
of air in
1 iquid.
advect ion.
buoyancy
Convection,
dispersion,
diffusion.
adsorption.
decay.
reactions
IGWMC
Key
2032
2037
2581
2582
3080
3081 .
231
-------
APPENDIX Fl
FRACTURED ROCK MODELS: SUMMARY LISTING
No.
12.
13.
14.
15.
16.
17.
IB.
Author(s)
J. Moor i shad
M.S. Ayatollahi
P.A.
Wither spoon
Ref: 124
J. Noorishad
P.A.
Witherspoon
Ref: 193
B. Sagar
Ref: 52
O.L. Deangel is
G.T. Yen
O.D. Huff
Ref: 34
O.D.L. Strack
Ref: 161
N.W. Kl ine
R.L. England
R.C. Boca
Ref: 94
A.L. Edwards
A. Rasnuson
1. Neretnieks
T.N. Narasinha
Ref: 38
Contact Address
Earth Sciences Division
Lawrence Berkeley
Laboratory
Univ. of Cal ifornia
Berkeley, CA 94720
Earth Science Div.
Lawrence Berkeley Lab.
Univ. of California
Berkeley, CA 94720
Analytic & Computational
Research, Inc.
3106 Inglewood Blvd.
Los Angeles, CA 90066
Environmental Sciences
Division
Oak Ridge National
Laboratory
Oak Ridge, TN 37630
R.W. Nelson
Battelle Pacific
Northwest Laboratories
Hydro logic Systems
Section
Rich land, MA 99352
Rockwe 1 1 1 nternat i ona 1
Rockwell Hanford
Operations
P.O. Box 800
Rich land, HA 99352
Dept. of Chenical
Engineering
Royal Inst. of
Technology
S-IOO 44 Stockholm,
Sweden
Model Name
(last update)
ROCMAS-HH
(1981)
ROCMAS-THM
FRACFLOW
(1981)
FRACPORT
(1984)
8ACRACK
(1982)
CHAINT
(1985)
TRUMP
(1980)
Model
Description
Two-dimensional finite-
element node) for
analysis of quasi -static
coupled stress and fluid
flow in porous fractured
rock.
Two-dimensional finite-
element model for
coupled hydraul ic-
therma 1 -mechan i ca 1
analysis of porous
fractured rock.
Integrated-f inite-
difference model for
steady and unsteady
State analysis of den-
sity-dependent flow.
heat and mass transport
in fractured confined
aquifers; two-dimen-
sional simulation of the
processes in the porous
medium and one-dimen-
sional simulation of the
fractures.
An integrated compart-
nental model for des-
cribing the transport of
solute in a fractured
porous medium.
A boundary element model
to simulate two-dimen-
sional steady flow
through f i ssured porous
media.
* general purpose two-
dimensional, finite-ele-
ment model for radionu-
cl ide transport in a
fractured porous medium.
Requires output of the
finite-element flow
model MAGNUM 2D as
input.
A multidimensional model
based on the integrated-
f inite-difference
method, to simulate
steady-state or tran-
sient ground water flow
and heat or solute
transport in fractured
rock.
Model
Processes
Con sol ida-
tion,
fracture
deformation
Convection,
conduction,
consol idation
Convection,
conduction,
dispersion,
diffusion.
consol idation
adsorption,
decay.
reactions
Dispersion,
adsorption.
decay,
advection
Dispersion,
diffusion,
adsorption,
decay,
advection.
buoyancy ,
chain-decay
(two
daughters)
Conduction,
dispersion,
diffusion,
decay,
advection
GUMC
Key
3082
3083
3232
3374
3440
3791
4030
232
-------
APPENDIX Fl
FRACTURED ROCK MODELS: SUMMARY LISTING
No.
19.
20.
21.
22.
23.
24.
Author(s)
A. Rasmuson
1. Neretnieks
Ref: 115
B.J. Travis
Ref: 170
K. Karasaki
Ref: 87
S.A. Holditch
and Associates
Ref: 69
L. Kiraly
Ref: 92
V. Guvanasen
Ref: 66
Contact Address
Oept. of Chemical
Engineering
Royal Institute of
Technology
S-100 44 Stockholm,
Sweden
Earth and Space Sciences
Division
Los Alamos National
Laboratory
Los Alamos. NM 87545
Earth Sciences Division
Lawrence Berkeley Lab.
University of California
Berkeley. CA 94720
U.S. Department of
Energy
Office of Fossil Energy
Morgantown Energy
Techno Igy Center
P.O. Box 880
Morgantown, MV 26505
National Cooperative for
Storage of Radioactive
Waste-NAGRA
Parkstrasse 23
CH-5401 Baden
S« i tzer 1 and
Tin Chan
AECL Wiiteshell Nuclear
Research Establishment
Pinawa, Maintoba
Canada
Model Name
(last update)
TRUCHN/ZONE
(1984)
TRACR30
(1984)
FRACTEST
(1986)
SUGARHAT
(1983)
FEM301
(1985)
MOTIF
(1987)
Model
Description
Advect ion-dispersion of
radionucl ides in
strongly fissured zones
including diffusion into
the rock matrix with
strongly varying velo-
city and block sizes
along the flow path.
A three-dimensional
finite-difference model
of transient two-phase
flow and multicomponent
transport in deformabie,
heterogeneous, reactive
porous/fractured media.
Simulation of flow in
fractured rock for we 1 1
test analysis. The
model consists of a mesh
generator to produce a
representative fractured
system and a finite-ele-
ment model for calcula-
tion of transient
hydraulic heads using a
parallel processor.
A two-dimensional, two-
phase finite-difference
model to simulate the
transient flow of both
gas and water in dual
porosity reservoirs.
A three-dimensional
finite-element model for
simulation of steady-
state flow in an equi-
valent anisotropic por-
ous medium intersected
by I inear or planar
discontinuities.
A finite-element model
to simulate the coupled
processes of saturated
or unsaturated flu-id
flow, conductive and
convective heat trans-
port, brine transport
and single species
radionucl ide transport
in a compressible rock
of low permeabil ity
intersected with
fractures.
Model
Processes
advection.
dispersion,
diffusion
into rock
Dispersion,
diffusion,
adsorption.
decay,
advection
Gas desorp-
tion from
pore wel Is
Cap! 1 lary
forces,
convection.
conduction.
dispersion,
diffusion.
consol ida-
t i on ,
hysteresis,
adsorption,
ion exchange,
decay ,
reactions
Key
4031
4270
4470
4490
4500
4550
233
-------
APPENDIX Fl
FRACTURED ROCK MODELS: SUMMARY LISTING
No.
25.
26.
27.
Author(s)
J.D. Hi Her
P.S. Huyakorn
Ref: 71
E.A. Sudicky
Ref: 162
Contact Address
Hydrology Unit
Idaho National
Engineering Lab
Idaho Falls, ID 83415
HydroGeoLog i c , Inc.
503 Carlisle Dr.,
Suite 250
Herndon, VA 22070
Institute for
Groundwater Research
Oept. of Earth Sciences
University of Waterloo
Waterloo, Ontario
Canada N21 3G1
Model Name
(last update)
FRACSL
(1986)
STAFF20
(1988)
CRACK
(1986)
Model
Description
A steady-state two-
dimensional finite-
difference model to
simulate flow and solute
and heat transport in a
porous rock with
discrete fractures.
A two-dimensional
finite-element model to
simulate flow and solute
transport in fractured
or granular porous
Media. The model can
address both confined
and unconfined forma-
tions, and it can handle
fracture systems con-
taining an intricate
network of fractures
and/or a few discrete
fractures.
A package of four analy-
tical models for mass
transport in fractured
porous media. The
models address transport
in a single fracture
with matrix diffusion
and transport in a
network of paral lei
fractures.
Model
Processes
advection,
diffusion,
dispersion,
conduction
inf i Itration,
aquitard
leakage,
advection,
dispersion,
adsorption,
degradation
dispersion
along
fracture
axis; matrix
diffusion
IGWMC
Key
4670
4710
6660
234
-------
APPENDIX F2
FRACTURED ROCK MODELS: USABILITY AND RELIABILITY
No.
.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Author(s)
P.S. Huyakorn, et al.
P.S. Huyakorn
P.S. Huyakorn
S.B. Pahwa
B.S. Rama Rao
V. Guvanasen
J.F. Pickens
J.F. Pickens
K. Pruess
K. Pruess, et al.
J. Noorishad
P. A. Witherspoon
J. Noorishad
M. Menran
J. Noorishad
M.S. Ayatollahi
P. A. Witherspoon
J. Noorishad
P. A. Witherspoon
B. Sagar
D.L. Deangelis, et al.
O.D.L. Strack
N.W. Kline, et al.
A.L. Edwards
Model Name
TDACDAD LIT
TRAFRAP-WT
GREASE 2
STAFAN2
NETFLOW
MOTIF
FRACT
FRACSOL
MULKOM
TOUGH
ROCMAS-H
ROCMAS-HS
ROCMAS-HM
ROCMAS-THM
FRACFLOW
FRACPORT
BACRACK
CHAINT
TRUMP
USABILITY
fc
M
I/I
a
0
L.
a.
N
N
U
U
N
N
N
N
U
U
U
U
N
N
N
U
U
8
a
I
a
1
N
N
U
U
N
N
N
N
U
U
U
U
N
N
N
U
U
e
o
+^
U
in 3
. +>
O VI
ft C
Y
Y
Y
Y
N
N
N
N
Y
Y
Y
Y
Y
Y
N
Y
Y
.1
ll
Y
Y
Y
Y
N
N
N
N
Y
Y
Y
Y
Y
Y
N
Y
Y
X
U
SS
a T>
t c
l&
L
L
L
N
L
L
L
U
U
U
U
U
N
L
Y
Y
U
U
O
a.
a.
3
L
L
L
L
N
N
N
N
L
L
L
L
L
L
L
L
N
RELIABILITY
1
U
!»
i_
sl
Y
Y
U
U
U
U
U
U
Y
Y
Y
Y
U
U
Y
U
U
o
$
o
Jo,
e
u
Y
Y
U
U
U
U
U
U
Y
Y
Y
Y
U
U
Y
U
U
o
o
L.
C
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
o
+
H t-
L
U
U
L
U
U
U
U
U
U
U
U
U
U
L
L
U
10
9
(ft
i.
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
IGWMC
KEY
A CQQ
w WO ?
0582
0584
0695
0953
2032
2037
2581
2582
3080
3081
3082
3083
3232
3374
3440
3791
4030
KEY:
YES
N » NO
UNKNOWN
6 > GENERIC
D DEDICATED
L * LIMITED
M MANY
F - FEW
235
-------
APPENDIX F2
FRACTURED ROCK MODELS: USABILITY AND RELIABILITY
No.
19.
in
ZU.
21.
22.
23.
24.
25.
26.
27.
Author(s)
A. Rasmuson
I. Neretnicks
B.J. Travis
K. Karasaki
S.A. Holditch &
Associates
L. Kiraly
V. Guvanasen
J.D. Miller
P.S. Huyakorn
E.A. Sudicky
Model Name
TRUCHN/
ZONE
TO Aroon
IKALKjl)
FRACTEST
SUGARWAT
FEM301
MOTIF
FRACSL
STAFF2D
CRACK
USABILITY
\
I
t
t
U
N
U
U
U
U
N
D
)
1
in
t
t
>
L
i
>
u
N
U
U
U
U
N
Y
(A
U
3
L,
in
c
Y
N
Y
N
N
Y
Y
Y
w
E
5
o
*
Y
N
Y
N
N
Y
Y
Y
X
u
c
o
o
t c
o
&
u
Y
u
u
U
U
N
L
L
s
"»
L
N
U
U
U
L
Y
L
RELIABILITY
D
)
t
I
- 0
u
u
u
u
u
Y
Y
Y
>
t
i
i
: 01
c
i?
a.0
U
u
u
u
u
u
u
u
«
c
*
Y
Y
Y
Y
Y
Y
Y
Y
*
> »
U. h-
U
L
L
L
L
U
L
L
U)
U
(A
=1
^J
"g
*
F
F
F
F
F
F
F
F
IGWMC
KEY
4031
4470
4490
4500
4550
4670
4710
6660
KEY:
YES
HO
UNKNOWN
6 * GENERIC
D « DEDICATED
L * LIMITED
MANY
F « FEW
236
-------
APPENDIX 61
MULTIPHASE FLOW MODELS: SUMMARY LISTING
No.
i.
2.
3.
4.
5.
6.
Author(s)
C.R. Faust
J.W. Mercer
Ref: 48
J.H. Guswa
O.K. LeBlanc
Ref: 64
M. Clouet
D'Orval
M. Clouet
O'Orval
W. Giesel
G. Schmidt
K. Trippler
Ref: 156
P. van der Veer
Ref: 181
Contact Address
Performance Assessment
Oept
Office of Nuclear Waste
Isolation
Battell e Project Mgmnt.
Oiv.
505 King Avenue
Columbus, OH 43201
U.S. Geological Survey
150 Causeway St.
Suite 1001
Boston, HA 02114
Burgeap
70, Rue Mademoiselle
75015 Paris
France
Burgeap
70, Rue Mademoiselle
75015 Paris
France
Bundesanstalt fur
Geowissenschaften und
Rohstoffe
P.O. Boy 510153
3000 Hannover 51
West Germany
Ri jkswaterstaat.
Data Processing Division
P.O. Box 5809
2280 HB Rijswijk (2.H.)
The Netherlands
Model Name
(last update)
GEOTHER
(1983)
Cape Cod
Aquifer
System
Models
(1981)
BURGEAP
7600HYSO
PACKAGE
(1982)
BURGEAP
7600HYSO
(TRABISHA
MODEL)
(1981)
Aquifer
Simulation
Subroutines
Package
(1976)
MOTGRO
(1981)
Model
Description
A finite-difference
model for simulation of
transient, three-dimen-
sional , single and two-
phase heat transport in
anisotropic, hetero-
geneous, permeable
media.
Steady-state simulation
of three-dimensional
flow in a heterogeneous,
anisotropic aquifer with
a sharp static interface
between fresh and salt
water .
A program package to
simulate two-dimension-
al, her izontal /vert i ca 1 ,
steady/transient, satu-
rated flow in confined/
uncon fined, homogeneous/
heterogeneous aquifer
systems with multiple
imiscibie fluids, and
connection with surface
water .
To simulate two-dimen-
sional , horizontal ,
transient, saturated
flow of two imiscibie
fluids of different
densities, in uncon-
f ! ned , homogeneous/
heterogeneous aquifers.
Finite-difference simu-
lation of steady-state
or transient groundwater
flow in an anisotropic,
heterogeneous, multi-
aquifer system, includ-
ing a saltwater/fresh-
water interface.
Prediction of ground-
water head and stream
function for two-dimen-
sional, vertical, steady
and unsteady single or
multiple fluid flow in
inhomogeneous, aniso-
tropic, confined or
uncon fined aquifers of
arbitrary shapes; uses
analytical function
method.
Model
Processes
Condensation,
convection,
conduction,
dispersion,
diffusion,
change of
phase
interface
IGWMC
Key
0730
0770
mod.
1370
1371
1550
1830
237
-------
APPENDIX Gl
MULTIPHASE FLOW MODELS: SUMMARY LISTING
No.
7.
8.
9.
10.
11.
Author (s)
A. Verruijt
J.B.S. Can
Ref: 186
J.W. Mercer
C.R. Faust
Ref: 109
K. Pruess
Ref: 141
K., Y.W. Pruess
J.S.Y. Wang
A. A. 6. Sada
Costa
J.L. Wilson
Contact Address
Techn. Univ. Delft
Oept. Civil Engineering
Stevinweg 1
2628 CN Delft
The Netherlands
GeoTrans, Inc.
250 Exchange Place
Suite A
Herndon, VA 22070
Mail stop 50E
Lawrence Berkeley Lab
Berkeley, CA 94720
Earth Sciences Division
Lawrence Berkeley
Laboratory
University of California
Berkeley, CA 94720
Director, R.M. Parsons
Laboratory for Water
Resources and
Hydrodynamics
Dept. of Civil
Engineering
MIT
Cambridge, MA 02139
Model Name
(last update)
SWIFT
(1982)
SWSOR
(I960)
MULKOM
(1985)
TOUGH
(1984)
SWIM
(1981)
Model
Description
A cross-sectional
finite-element model for
transient, horizontal
flow of salt and fresh
water and analysis of
upconing of an interface
in a homogeneous
aquifer.
A two-dimensional
finite-difference solu-
tion to simulate the
area 1 , unsteady f 1 ow of
saltwater and freshwater
separated by an inter-
face In anisotropic.
heterogeneous porous
media.
Mult {component, multi-
phase fluid and heat
flow in porous or
fractured media.
An Integrated-f inite-
difference model for
transient simulation of
two-phase flow of water
and air with simultan-
eous heat transport in
fractured unsaturated
porous media.
A versatile finite-
element model to simu-
late transient, hori-
zontal salt and fresh
water flow in porous
media, separated by a
sharp interface.
Model
Processes
upconing
Convection,
change of
phase,
dissolution
and precipi-
tation of
si 1 ica.
equi 1 i brat ion
of noncon-
densible
gases,
transport of
nonconden-
sible gases
and dissolved
sol ids.
Condensation,
cap! I lary
forces,
evapotrans-
pi rat ion,
conduction,
diffusion.
change of
phase,
adsorption.
compress i on ,
dissolution
of air in
1 iquid.
advection.
buoyancy
IGMMC
Key
1852
2140
2581
2582
2631
238
-------
APPENDIX Gl
MULTIPHASE FLOW MODELS: SUMMARY LISTING
No.
12.
13.
14.
15.
16.
17.
Author (s)
R.H. Page
Ref: 126
J.W. Pritchett
Ref: 139
.
J.W. Pritchett
D.N. Contractor
Ref: 194
R.I. Allayla
Ref: 3
A.I. Baehr
Ref: 7
Contact Address
Water Resources Program
Dept. of Civil
Engineering
Princeton University
Princeton, NJ 08540
Systems, Science and
Software
P.O. Box 1620
La Jolla, CA 92038
Systems, Science and
Software
P.O. Box 1620
La Jolla, CA 92038
Water and Energy
Research
Inst. of The Western
Pacific
University of Guam
College Station,
Mangilao, Guam 96913
Civil Eng. Dept.
Colorado State Univ.
Fort Col tins, CO 80523
U.S.G.S.
Water Resources Oiv.
National Center
12201 Sunrise Valley Dr.
Reston, VA 22092
Model Name
(last update)
INTERFACE
(1979)
MUSHRH
(1980)
CHARGR
(1980)
SWIGS2D
(1982)
SEAWTR/
SEACONF
(1980)
GASOLINE
(1984)
Model
Description
A finite-element model
to simulate transient
flow of fresh and saline
water as immiscible
fluids separated by an
interface in an i so-
tropic, heterogeneous,
water-table aquifer.
A finite-difference
multi -species hydrother-
mal reservoir model to
simulate unsteady multi-
phase fluid and heat
flow in nut i dimensional
geometr i es .
Multi species hydrother-
mal reservoir model to
simulate unsteady multi-
phase fluid and heat
flow in multi-
dimensional geometries
by means of f inite-
difference method.
A two-dimensional
finite-element model to
simulate transient,
horizontal salt and
fresh water flow
separated by a sharp
interface in an
anisotropic, hetero-
geneous, confined, semi-
con fined or water-table
aquifer.
A two-dimensional
finite-difference model
for horizontal simula-
tion of simultaneous
flow of salt and fresh
water in a confined or
water-table aquifer with
anisotropic and hetero-
geneous properties.
Including effects of
cap i 1 1 ary f 1 ow .
A one-dimensional model
to solve a system of
equations defining the
transport of an immis-
cible contaminant immo-
bil ized In the unsatu-
rated zone, with or
without biodegradation.
Model
Processes
Convection,
conduction,
change of
phase,
degass i ng
phenomena
Heat
convection
and
conduction;
degassing;
consol ida-
tion;
expansion;
change of
phase (flow
is coupled)
Capil lary
forces,
influence of
cap! 1 lary
region on
specific
yeild
Capil lary
forces,
dispersion,
diffusion.
adsorption,
reactions,
advection.
buoyancy.
biological
activity
IGWMC
Key
2720
2760
2761
3600
3640
4420
239
-------
APPENDIX Gl
MULTIPHASE FLOW MODELS: SUMMARY LISTING
No.
IB.
19.
Author(s)
S.A. Holditch
And Associates
Ref: 69
C.R. Faust
J.O. Rumbaugh
Ref: 49
Contact Address
Office of Fossil Energy,
Morgan town Energy
Technology Center,
P.O. 880,
Morgantown. WV 26505
GeoTrans, Inc.
250 Exchange Place
Suite A
Herndon, VA 22070
Model Nane
(last update)
SUGARWAT
(1983)
SWANFLOW
(1986)
Model
Description
A two-dimensional, two-
phase f i n i te-d i f f erence
odel to si nutate the
transient flow of both
gas and water in dual
porosity reservoirs.
Three-dimensional simu-
lation of flow of water
and inniscible non-
aqueous phase liquids
within and below the
vadose zone with a
finite difference
solution.
Model
Processes
Gas
desorption
from pore
wells
Cap! 1 lary
forces
Key
4490
4650
240
-------
APPENDIX G2
MULTIPHASE FLOW MODELS: USABILITY AND RELIABILITY
No.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Author (s)
C.R. Faust
J.W. Mercer
J.H. Goswa
D.R. LeBlanc
M. Clouet D'Orval
M. Clouet D'Orval
W. Giesel, et al.
P. van der Veer
A. Verruijt
J.B.S. Gan
J.W. Mercer
C.R. Faust
K. Pruess
K. Pruess, et al.
A.A.G. Sada Costa
R.H. Page
J.W. Pritchett
J.W. Pritchett
D.N. Contractor
R.I. Allayla
Mode
GEOTJ
Cape
/
Name
]
Cod
Aquifer
Systems
Model
BURGEAP
7600
HYSO
PACKAGE
TRABISA
Aquifer
Simulation
Subroutines
Package
MOTGRO
SWIFT
SWSOR
MULKOM
TOUGH
SWIM
INTERFACE
MUSHRM
CHARGR
SWIGS2D
SEAWTR/
SEACONF
USABILITY
fc
g
N
N
N
N
N
N
N
N
N
N
N
N
U
U
U
N
8
i
a
1
N
N
N
N
N
N
N
N
N
N
N
N
U
U
U
N
2
u
a 9
- i.
L. 4-
SC/I
e
3
Y
Y
Y
Y
N
Y
Y
Y
N
N
U
Y
Y
Y
Y
Y
.1
11
via.
Y
Y
Y
Y
N
Y
Y
Y
N
N
U
Y
Y
Y
Y
Y
fel
ft
£2
L
N
Y "
Y
U
L
N
N
L
U
U
L
U
N
U
L
+.
3
L
U
N
N
N
U
L
L
N
N
U
N
U
Y
L
N
RELIABILITY
o
8
9
!>.
u O
|J
U
u
u
u
u
u
Y
Y
U
U
U
U
U
Y
U
U
1
i?
II
u
u
u
u
u
u
u
Y
U
U
u
u
u
u
u
u
a
9
L.
Y
Y
Y
U
U
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
o
o
+
L
U
Y
Y
L
L
U
L
U
U
L
L
L
U
L
L
A
0
M
i
F
F
M
M
F
F
F
F
F
F
F
F
U
F
F
F
IGWMC
KEY
0730
0770
mod.
1370
1371
1550
1830
1852
2140
2581
2582
2631
2720
2760
2761
3600
3640
KEY:
rES
N « NO
UNKNOWN
6 * GENERIC
0 - DEDICATED
L « LIMITED
M > MANY
F * FEW
241
-------
APPENDIX 62
MULTIPHASE FLOW MODELS: USABILITY AND RELIABILITY
No.
17.
18.
19.
Author (s)
A.L. Baehr
S.A. Holdltch
& Associates
C.R. Faust
J.D. Rumbaugh
Model Name
GASOLINE
SUGARWAT
SWANFLOW
USABILITY
*
(A
Preproce
N
U
Y
L.
8
a
Postproc
N
U
Y
m
s
«z
!l
Y
Y
Y
Sample
Problems
Y
Y
Y
>
u
Hardware
Oependen
U
U
L
Support
L
U
L
RELIABILITY
o
?
?i
ll
Y
U
U
o
*
o
*z
21
Y
U
U
Verified
Y
Y
Y
o
o o
4-
8
u. (-
L
L
L
UNKNOWN G * GENERIC 0 > DEDICATED L « LIMITED M « MANY F » FEW
242
AU.S.GOVERNMENTPRINTINGOFnCE: i989-6i»e -163/87110
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