United States
Environmental Protection
Agency
Robert S Kerr Environmental
Research Laboratory
Ada OK 74820
Research and Development
EPA/600/8-87/003 Jan. 1987
4>EPA The Use of
Models in
Managing
Ground-Water
Protection
Programs
Li
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EPA/600/8-87/003
January 1987
THE USE OF MODELS IN MANAGING
GROUND-WATER PROTECTION
PROGRAMS
Joseph F. Keely, Ph.D, P.Hg.
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
Ada, Oklahoma 74820
U.S. Environmental v-' ' '' ;i -c-lC '
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60604 ,#
Office of Research and Development
U.S. Environmental Protection Agency
Ada, Oklahoma 74820
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DISCLAIMER
The information in this document has been funded wholly or in
part by the United States Environmental Protection Agency. It has
been subjected to the Agency's peer and administrative review, and
it has been approved for publication as an EPA document.
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FOREWORD
The U.S. Environmental Protection Agency was established to
coordinate administration of the major Federal programs designed
to protect the quality of our environment.
An important part of the Agency's effort involves the search for
information about environmental problems, management
techniques and new technologies through which optimum use of the
Nation's land and water resources can be assured and the threat
pollution poses to the welfare of the American people can be
minimized.
EPA's Office of Research and Development conducts this search
through a nationwide network of research facilities.
As one of the facilities, 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 transformation
rates of pollutants in the soil, the unsaturated zone and the
saturated zones of the suburface environment; (b) define the
processes to be used in characterizing the soil and 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 the soil and subsurface environment, for the protection of this
resource.
This report contributes to that knowledge which is essential in
order for EPA to establish and enforce pollution control standards
which are reasonable, cost effective and provide adequate
environmental protection for the American public.
Clinton W. Hall
Director
Robert S. Kerr Environmental
Research Laboratory
111
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ABSTRACT
Because ground-water quality protection is emerging as a
major National environmental problem of this decade, there is
increasing pressure on regulators and the regulated to identify,
assess or even anticipate situations involving ground-water
contamination. Site-specific and generic mathematical models are
increasingly being used by EPA to fulfill its mandates under a
number of major environmental statutes which call for permit
issuance, investigation of potential problems, remediation
activities, exposure assessment and a myriad of other policy
decisions.
Mathematical models can be helpful tools to managers of
ground-water protection programs. They may be used for testing
hypotheses about conceptualizations and to gather a fuller
understanding of important physical, chemical and biological
processes which affect ground-water resources. The possible
outcomes of complex problems can be addressed in great detail, if
adequate data are available. The success of these efforts depends
on the accuracy and efficiency with which the natural processes
controlling the behavior of ground water, and the chemical and
biological species it transports, are simulated. Success also depends
heavily on the expertise of the modeler and the communication
with management so that the appropriateness, underlying
assumptions, and limitations of specific models are appreciated.
IV
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CONTENTS
Foreword iii
Abstract iv
Figures vii
Tables ix
Acknowledgments x
1. The Utility of Models 1
Introduction 1
Management Applications 3
Modeling Contaminant Transport 6
Categories of Models 7
Chapter Summary 8
2. Assumptions, Limitations, and Quality Control 9
Introduction 9
Physical Processes 9
Advection and Dispersion 10
Complicating Factors 13
Considerations for Predictive Modeling 14
Chemical Processes 15
Chemical/Electronic Alterations 15
Nuclear Alterations 16
Chemical Associations 16
Surface Interactions 17
Biological Processes 19
Surface Water Modeling Analogy 19
Ground-Water Biotransformations 20
A Ground-Water Model 20
Analytical and Numerical Models 22
Quality Control 23
Chapter Summary 25
3. Applications in Practical Settings 29
Stereotypical Applications 29
Real-World Applications 29
Field Example No. 1 30
Field Example No. 2 32
Practical Concerns 44
Chapter Summary 52
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4. Liabilities, Costs, and Recommendations for Managers 55
Introduction 55
Potential Liabilities 55
Economic Considerations 56
Managerial Considerations 64
Chapter Summary 66
References 69
VI
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FIGURES
Number Page
1-1 Small 'sand tank' physical aquifer model 2
1-2 Laboratory column housed in constant-temperature
environmental chamber 2
1-3 Electric analog aquifer model constructed by Illinois
State Water Survey 3
1-4 Typical ground-water contamination scenario and a
possible contaminant transport model grid design
for its simulation 4
2-1 The influence of natural processes on levels of
contaminants downgradient from continuous and
slug-release sources 11
2-2 Examples of plots prepared with the Jacob's
approximation of the Theis analytical solution to
well hydraulics in an artesian aquifer 24
2-3 Mathematical validation of a numerical method of
estimating drawdown, by comparison with an
analytical solution 26
3-1 Location map for Lakewood Water District wells
contaminated with volatile organic chemicals 31
3-2 Schematic illustrating the mechanism by which a
downgradient source may contaminate a
production well 33
3-3 Location map for Chem-Dyne Superfund Site 35
3-4 Chem-Dyne geologic cross-section along NNW-SSE
axis 36
3-5 Chem-Dyne geologic cross-section along WSW-ENE
axis 37
3-6 Shallow well ground-water contour map for
Chem-Dyne 38
Vll
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Number Page
3-7 Typical arrangement of clustered, vertically-
separated wells installed adjacent to Chem-Dyne
and the Great Miami River 39
3-8 Estimates of transmissivity obtained from shallow
and deep wells during Chem-Dyne pump test 41
3-9 Distribution of total volatile organic chemical
contamination in shallow wells at Chem-Dyne
during October 1983 sampling 42
3-10 Distribution of tetrachloroethene in shallow wells
at Chem-Dyne during October 1983 sampling 45
3-11 Distribution of trichloroethene in shallow wells at
Chem-Dyne during October 1983 sampling 46
3-12 Distribution of trans-dichloroethene in shal low
wells at Chem-Dyne during October 1983 sampling 47
3-13 Distribution of vinyl chloride in shallow wells at
Chem-Dyne during October 1983 sampling 48
3-14 Distribution of benzene in shallow wells at Chem-
Dyne during October 1983 sampling 49
3-15 Distribution of chloroform in shallow wells at Chem-
Dyne during October 1983 sampling 50
3-16 General relationship between site characterization
costs and clean-up costs as a function of the
characterization approach 54
4-1 Average price per category for ground-water
models from the International Ground Water
Modeling Center 57
4-2 Price ranges for IBM-PC ground-water models
available from various sources 59
4-3 Costs of sustaining ground-water modeling
capabilities at two different computing levels, for
a five-year period 61
Vlll
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TABLES
Number Page
2-1 Natural processes that affect subsurface
contaminant transport 10
3-1 Chem-Dyne pump test observation network 43
3-2 Conventional approach to site characterization
efforts 51
3-3 State-of-the-art approach to site characterization
efforts 52
3-4 State-of-the-science approach to site characterization
efforts 53
4-1 Desired backgrounds and salary ranges advertised
for positions requiring ground-water modeling 60
4-2 Screening-level questions to help ground-water
managers focus mathematical modeling efforts 65
4-3 Conceptualization questions to help ground-water
managers focus mathematical modeling efforts 66
4-4 Sociopolitical questions to help ground-water
managers focus mathematical modeling efforts 67
IX
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ACKNOWLEDGMENTS
The author is indebted to the many fine scientists, engineers,
and support staff at the Robert S. Kerr Environmental Research
Laboratory for their assistance. In particular, Dr. Marvin D. Piwoni
and Dr. John T. Wilson made substantial contributions to Chapter 2
in the chemical and biological sections, respectively. Ms. Carol
House and Ms. Renae Daniels typed many drafts of the document.
Ms. Kathy Clinton prepared most of the illustrations.
The author is grateful to Drs. William F. McTernan and Douglas
C. Kent of Oklahoma State University for their technical reviews of
the manuscript. Thanks also go to Ir. Paul van der Heijde of the
International Ground Water Modeling Center for his readings of
early drafts of many sections, and for the use of certain photographs.
Mr. Marion R. (Dick) Scalfs guidance and encouragement as EPA
Project Officer on this project are deeply appreciated. Comments and
suggestions from the readers are welcome; the author assumes all
responsibility for any errors, omissions, or misstatements.
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CHAPTER 1
THE UTILITY OF MODELS
INTRODUCTION
Every time man attempts to simulate the effects of natural
phenomena, he is engaging in the scientific art of modeling. Models
are nothing more than simplified representations of reality, and
their creation and use involves a considerable degree of subjective
judgment, as well as an attempt to incorporate known scientific
facts. There are many forms of models, each having specific
advantages and disadvantages compared with the remainder.
Physical models, such as sand-tanks used to simulate aquifers
(Figure 1-1) and laboratory columns used to study the relative
motion of various contaminants flowing through aquifer materials
(Figure 1-2), provide an element of reality which is enlightening and
satisfying from an intuitive viewpoint. Their main disadvantage
relates to the extreme efforts and time required to generate a
meaningful amount of data. Other difficulties relate to the care
required to obtain samples of subsurface material for construction of
these models, without significantly disturbing the natural condition
of the samples.
Analog models are also physically based, but their operating
principle is one of similarity, not true-life representation. A typical
example is the electric analog model (Figure 1-3), in which
capacitors and resistors are able to closely replicate the effects of the
rate of release of water from storage in aquifers. The clear
disadvantage is that "a camel is not a horse', even if both can carry a
load. As is the case with other physically based models, data
generation is slow and there is little flexibility for experimental
design changes.
Mathematical models are non-physical, relying instead on the
quantification of relationships between specific parameters and
variables to simulate the effects of natural processes (Figure 1-4). As
such, mathematical models are abstract and provide little in the
way of a directly observable link to reality. Despite this lack of
intuitive grace, mathematical models can generate powerful
insights into the functional dependencies between causes and effects
in the real world. Large amounts of data can be generated quickly,
and experimental modifications can be made with minimal effort, so
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Figure 1-1. Small "sand tank" physical aquifer model. Three
Pumping wells (A,B,C) penetrate the homogeneous
sand to study the effects of well hydraulics on plume
movements. Vials in foreground contain various
concentrations of water-active dyes.
Figure 1-2. Laboratory column housed in constant-temperature
environmental chamber. Contaminated solutions are
injected into column through inlet tubing in top, by
action of hydraulic press in foreground. Samples of
the advancing front are withdrawn through ports
visible on right-hand side and bottom of column.
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51 It:!!
Figure 1-3. Electric analog aquifer model constructed by Illinois
State Water Survey. The regular array of resistors and
the two electric "pumps" shown are hard-wired into
a board covered with the appropriate geologic maps.
that many possible situations can be studied in great detail for a
given problem.
MANAGEMENT APPLICATIONS
Mathematical models can and have been used to help organize
the essential details of complex ground-water management
problems so that reliable solutions are obtained (Holcomb Research
Institute, 1976; Bachmat and others, 1978; U.S. Office of Technology
Assessment, 1982; van der Heijde and others, 1985). Some principal
areas where mathematical models are now being used to assist in
the management of ground-water protection are:
(1) appraising the physical extent, and chemical and biological
quality, of ground-water reservoirs (e.g., for planning
purposes),
(2) assessing the potential impact of domestic, agricultural, and
industrial practices (e.g., for permit issuance),
(3) evaluating the probable outcome of remedial actions at
waste sites, and aquifer restoration techniques generally,
and
(4) providing health-effects exposure estimates.
The success of these efforts depends on the accuracy and
efficiency with which the natural processes controlling the behavior
of ground water, and the chemical and biological species it
transports, are simulated (Boonstra and de Ridder, 1976; Mercer
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Figure 1-4. Typical ground-water contamination scenario and a
possible contaminant transport model grid design for
its simulation. Values for natural process parameters
would be specified at each node of the grid in
performing simulations. The grid density is greatest
at the source and at potential impact locations.
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and Faust, 1981; Wang and Anderson, 1982). The accuracy and
efficiency of the simulations, in turn, are heavily dependent on
subjective judgements made by the modeler and management.
In the current philosophy of ground-water protection programs,
the value of a ground-water resource is bounded by the most
beneficial present and future uses to which it can be put (U.S. EPA,
1984). In most instances, physical appraisals of ground-water
resources are conducted within a framework of technical and
economic classification schemes. Classification of entire ground-
water basins by potential yield is a typical first step (Domenico,
1972). After initial identification and evaluation of a ground-water
resource, strategies for its rational development need to be devised.
Development considerations include the need to protect
vulnerable recharge areas and the possibility of conjunctive use
with available surface waters (Kazmann, 1972). Ground-water
rights must be fairly administered to assure adequate supplies for
domestic, agricultural, and industrial purposes. Because basinwide
or regional resource evaluations normally do not provide sufficent
resolution for water allocation purposes, more detailed
characterizations of the properties and behavior of an aquifer, or of a
subdivision of an aquifer, are usually needed. Hence, subsequent
classifications may involve local estimation of net annual recharge,
rates of outflow, and the pumpage which can be substained without
undesirable effects.
The consequences of developments which might affect ground-
water quality may be estimated initially by employing generalized
classification schemes; for example, classifications based on regional
hydrogeologic settings have been presented (Heath, 1982; Aller and
others, 1985). Very detailed databases, however, must be created
and molded into useful formats before decisions can be made on how
best to protect and rehabilitate ground-water resources from site-
specific incidents of natural and manmade contamination.
The latter are ordinary ground-water management functions
which benefit from the use of mathematical models. There are other
uses, however, which ought to be considered by management. The
director of the International Ground Water Modeling Center
discussed the role of modeling in the development of ground-water
protection policies recently, noting its success in many policy
formulation efforts in the Netherlands, the United States, and
Israel. Nevertheless, he concluded that modeling was not widely
relied upon for decision-making by managers; the primary obstacle
has been an inability of modelers and program managers to
communicate effectively (van der Heijde, 1985). The top executives
of a leading high-tech ground-water contamination consulting firm
made the same point clearly, going on to highlight the need for
qualified personnel appreciative of the appropriateness, underlying
assumptions, and limitations of specific models (Faust and others,
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1981). Because these views are widely held by technical
professionals, it will be emphasized herein that mathematical
models are useful only within the context of the assumptions and
simplifications on which they are based. If managers are mindful of
these factors, however, mathematical models can be a tremendous
asset in the decision- making process.
MODELING CONTAMINANT TRANSPORT
Associated with most hazardous waste sites is a complex array
of chemical wastes and the potential for ground-water
contamination. The hydrogeologic settings of these sites are usually
quite complicated when examined at the scale appropriate for
technical assessments and remediation efforts (e.g., 100's of feet). As
a result, data acquisition and interpretation methods are needed
that can examine to an unprecendented degree the physical,
chemical, and biological processes that control the transport and
fate of ground-water contaminants. The methods and tools that have
been in use for large-scale characterizations (e.g., regional water
quality studies) are applicable in concept to the specialized needs of
hazardous waste site investigations; however, the transition to
local-scale studies is not without scientific and economic
consequences. In part, this stems from the highly variable nature of
contaminant distributions at hazardous waste sites; but it also
results from the limitations of the methods, tools, and theories used.
Proper acknowledgement of the inherent limitations means that one
must project the consequences of their use within the framework of
the study at hand.
Assessments of the potential for contaminant transport require
interdisciplinary analyses and interpretations. Integration of
geologic, hydrologic, chemical, and biological approaches into an
effective contaminant transport evaluation can only be possible if
the data and concepts invoked are sound. The data must be accurate,
precise, and appropriate at the intended problem scale. Just because
a given parameter (e.g., hydraulic conductivity) has been measured
correctly at certain points with great reproducibility, is no
guarantee that those estimates represent the volumes of aquifer
material assigned to them by a modeler. The degree to which the
data are representative, therefore, is not only relative to the
physical scale of the problem, it is relative to the conceptual model
to be used for interpretation efforts. It is crucial, then, to carefully
define and qualify the conceptual model. In so doing, special
attention should be given to the possible spatial and temporal
variations of the data that will be collected.
To circumvent the impossibly large numbers of measurements
and samples which would be needed to eliminate all uncertainties
regarding the true relationships of parameters (e.g., hydraulic
conductivity) and variables (e.g., contaminant concentrations and
rates of movement), more comprehensive theories are constantly
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under development. The use of newly developed theories to help
solve field problems, however, is often a frustrating exercise. Most
theoretical advances call for some data which are not yet practically
obtainable (e.g., chemical interaction coefficients, relative
permeabilities of immiscible solvents and water, etc.). The 'state-of-
the-art1 in contaminant transport assessments is necessarily a
compromise between the sophistication of "state-of-the-science1
theories, the current limitations regarding the acquisition of specific
data, and economics. In addition, the best attempts to obtain
credible data are limited by natural and anthropogenic variabilities;
and these lead to the need for considerable judgement on the part of
the professional.
Despite these technical limitations, how well the problem is
conceptualized remains the most serious concern in modeling
efforts. For example, researchers recently produced dramatic
evidence to show that, in spite of detailed field measurements,
extrapolations of two-dimensional model results to a truly three-
dimensional problem lead to wildly inaccurate projections of the
actual behavior of the system under study (Molz and others, 1983).
Therefore, it is incumbent on model users to recognize the difference
between an approximation and a misapplication. Models should
never be used strictly on the basis of familiarity or convenience; an
appropriate model should always be sought.
CATEGORIES OF MODELS
The foregoing is not meant to imply that appropriate models
exist for all ground-water problems, because a number of natural
processes have yet to be fully understood. This is especially true for
ground-water contaminant transport evaluations, where the
chemical and biological processes are still poorly defined. For,
although great advances have been made concerning the behavior of
individual contaminants, studies of the interactions between
contaminants are still in their infancy. Even the current
understanding of physical processes lags behind what is needed,
such as in the mechanics of multiphase flow and flow through
fractured rock aquifers. Moreover, certain well-understood
phenomena pose unresolved difficulties for mathematical
formulations, such as the effects of partially penetrating wells in
unconfined (water-table) aquifers.
The technical-use categories of models are varied, but they can
be grouped as follows (Bachmat and others, 1978; van der Heijde
and others, 1985):
(1) parameter identification models,
(2) prediction models,
(3) resource management models, and
(4) data manipulation codes.
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Parameter identification models are most often used to estimate
the aquifer coefficients determining fluid flow and contaminant
transport characteristics, like annual recharge (Puri, 1984),
coefficients of permeability and storage (Shelton, 1982; Khan, 1986a
and b), and dispersivity (Guven and others, 1984; Strecker and Chu,
1986). Prediction models are the most numerous kind of model, and
abound because they are the primary tools for testing hypotheses
about the problem one wishes to solve (Andersen and others, 1984;
Mercer and Faust, 1981; Krabbenhoft and Anderson, 1986).
Resource management models are combinations of predictive
models, constraining functions (e.g., total pumpage allowed) and
optimization routines for objective functions (e.g., optimization of
wellfield operations for minimum cost or minimum
drawdown/pumping lift). Very few of these are so well developed and
fully supported that they may be considered practically useful, and
there does not appear to be a significant drive to improve the
situation (van der Heijde, 1984a and 1984b; van der Heijde and
others, 1985). Data manipulation codes also have received little
attention until recently. They are now becoming increasingly
popular, because they simplify data entry ('preprocessors') to other
kinds of models and facilitate the production of graphic displays
('postprocessors') of the data outputs of other models (van der Heijde
and Srinivasan, 1983; Srinivasan, 1984; Moses and Herman, 1986).
Other software packages are available for routine and advanced
statistics, specialized graphics, and database management needs
(Brown, 1986).
CHAPTER SUMMARY
Mathematical models can be helpful tools to managers of
ground-water protection programs. They may be used for testing
hypotheses about conceptualizations and to gather a fuller
understanding of important physical, chemical, and biological
processes which affect ground-water resources. The possible
outcomes of complex problems can be addressed in great detail, if
adequate data are available. Mathematical modeling is neither
simple nor impossible, but its successful application relies heavily
on the expertise of the modeler and the degree of communication
with management.
The merits of any problem solving technique need to be judged
by many criteria, the most important of which may not relate to
mathematical sophistication. Qualitative judgements by prior
experience, "back of the envelope1 calculations, analytical models,
and other non-numerical modeling methods should be considered for
a reason which deserves emphasis; the data available or obtainable
may not justify extensive numerical model analyses (Javendel and
others, 1984). After all, it is neither pretty nor efficient to 'use a
silver sledgehammer to drive a thumbtack'.
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CHAPTER 2
ASSUMPTIONS, LIMITATIONS, AND QUALITY
CONTROL
INTRODUCTION
There are many natural processes that affect chemical transport
from point to point in the subsurface. These natural processes can be
arbitrarily divided into three categories: physical, chemical, and
biological (Table 2-1). Conceptually, contaminant transport in the
subsurface is an undivided phenomenon composed of these processes
and their interactions (Figure 2-1). At this level the transport
process may be gestalt: the sum of its parts, measured separately,
may not equal the whole because of interactions between the parts.
In the theoretical context, a collection of scientific laws and
empirically derived relationships comprise the overall transport
process. The universally shared premise that underlies theoretical
expressions is that there are no interactions, measureable or
otherwise.
Significant errors may result from the discrepancy between
conceptual and theoretical appproaches. Also the simplifications of
theoretical expressions used to solve practical problems can cause
substantial errors in the most careful analyses. Assumptions and
simplifications, however, must often be made in order to obtain
mathematically tractable solutions. Because of this, the magnitude
of errors that arise from each assumption and simplification must be
carefully evaluated. The phrase, "magnitude of errors", is
emphasized because highly accurate evaluations usually are not
possible. Even rough approximations are rarely trivial exercises
because they frequently demand estimates of some things which are
as yet ill-defined.
PHYSICAL PROCESSES
Until recently, ground-water scientists studied physical
processes to a greater degree than chemical or biological processes.
This bias resulted in large measure from the fact that, in the past,
ground-water practitioners dealt mostly with questions of adequate
water supplies. As quality considerations began to dominate
ground-water issues, the need for studies of the chemical and
biological factors, as well as more detailed representations of the
physical factors, became apparent.
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Table2-1. Natural processes that affect subsurface
contaminant transport.
PHYSICAL PROCESSES
Advection (porous media velocity)
Hydrodynamic Dispersion
Molecular Diffusion
Density Stratification
Immiscible Phase Flow
Fractured Media Flow
CHEMICAL PROCESSES
Oxidation-Reduction Reactions
Radionuclide Decay
Ion-Exchange
Complexation
Co-Sol vati on
Immiscible Phase Partitioning
Sorption
BIOLOGICAL PROCESSES
Microbial Population Dynamics
Substrate Utilization
Biotransformation
Adaptation
Co-metabolism
There are two complimentary ways to view the physical
processes involved in subsurface contaminant transport: the
piezometric (pressure) viewpoint and the hydrodynamic viewpoint.
Ground-water problems of yesterday could be addressed by the
former, such as solving for the change in pressure head caused by
pumping wells. Contamination problems of today also require
detailed analyses of wellfield operations, for example, pump-and-
treat plume removals. However, solutions to such problems depend
principally on hydrodynamic evaluations, such as computing
ground-water velocity (advection) distributions and dispersion
estimates for migrating plumes.
Advection and Dispersion
Ground-water velocity distributions can be approximated if the
variations in hydraulic conductivity, porosity, and the strength and
location of recharge and discharge sources can be estimated.
While there are several field and laboratory methods for
estimating hydraulic conductivity, these are not directly
comparable because different volumes of aquifer material are
10
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(T) Advcctlon
Dispersion
Sorptlon
Blotr«n«form«tlon
DISTANCE FROM CONTINUOUS CONTAMINANT SOURCE
DISTANCE FROM SLUG-RELEASE CONTAMINANT SOURCE
Figure2-1. The Influence of natural processes on levels of
contaminants downgradient from continuous and
slug-release sources.
11
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affected by different tests. Laboratory permeameter tests, for
example, obtain measurements from small core samples and thus
give point value estimates. These tests are generally reliable for
consolidated rock samples, such as sandstone, but can be highly
unreliable for unconsolidated samples, such as sands, gravels, and
clays. Pumping tests give estimates of hydraulic conductivity that
are averages over the entire volume of aquifer subject to the
pressure changes induced by pumping. These give repeatable
results, but they are often difficult to interpret. Tracer tests are also
used to estimate hydraulic conductivity in the field, but are difficult
to conduct properly.
Regardless of the estimation technique used, the best that can
be expected is order-of-magnitude estimates for hydraulic
conductivity at the field scale appropriate for site-specific work.
Conversely, porosity estimates that are accurate to better than a
factor of two can be obtained. Estimation of the strength of nonpoint
sources of recharge to an aquifer, such as infiltrating rainfall and
leakage from other aquifers, is another order-of-magnitude effort.
Similarly, nonpoint sources of discharge, such as aquifer losses to
gaining streams, are difficult to quantify. Estimation of the strength
of point sources of recharge or discharge (injection or pumping wells)
can be highly accurate.
Consequently, it is not possible to generalize the quality of
velocity distributions. They may be accurate to within a factor of
two for very simple aquifers, but are more often accurate to an
order-of-magnitude only. This situation has changed little over the
past 20 years because better field and laboratory methods for
characterizing velocity distributions have not been developed. This,
however, is not the primary difficulty associated with defining the
advective part of contaminant transport in the subsurface. The
primary difficulty is that field tests for characterizing the physical
parameters that control velocity distributions are not incorporated
into contamination investigations on a routine basis. The causes
seem to be: a perception that mathematical models can "back-out1 an
approximation of the velocity distribution (presumably eliminating
the need for field tests); unfamiliarity with field tests by many
practitioners; and a perception that field tests are too expensive. A
more field oriented approach is preferable because the non-
uniqueness of modeling results has been amply demonstrated, and
this leads to uncertain decisions regarding the design of remedies.
Dispersion estimates are predicated on velocity distribution
estimates and their accuracy is therefore directly dependent on the
accuracy of the estimated hydraulic conductivity distribution.
Tracer tests have been the primary method used to determine
dispersion coefficients until recently. Presently there are
suggestions that any field method capable of generating a detailed
understanding of the spatial variability of hydraulic conductivity,
which in turn could give an accurate representation of the velocity
12
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distribution, may be used to derive estimates of dispersion
coefficients. The manner in which data from field tests should be
used to derive estimates of dispersion coefficients, however, is a
controversial issue. There are both deterministic and stochastic
schools of thought, and neither has been conclusively demonstrated
in complex hydrogeological settings.
Complicating Factors
Certain subtleties of the spatial variability of hydraulic
conductivity must be understood because of its key role in the
determination of velocity distributions and dispersion coefficients.
Hydraulic conductivity is also known as the coefficent of
permeability because it is comprised of fluid factors as well as the
intrinsic permeability of the stratum in question. This means that a
stratum of uniform intrinsic permeability (which depends strictly on
the arrangement of its pores) may have a wide range of hydraulic
conductivity because of differences in the density and viscosity of
fluids that are present. The result is a dramatic downward shift in
local flow directions near plumes that have as little as a 1% increase
in density relative to uncontaminated water. Such density contrasts
frequently occur at landfills and waste impoundments. It is often
necessary to correct misimpressions of the direction of a plume
because density considerations were not addressed.
Many solvents and oils are highly insoluble in water, and may
be released to the subsurface in amounts sufficient to form a
separate fluid phase. Because that fluid phase will probably have
viscosity and density different from freshwater, it will flow at a rate
and, possibly, in a direction different from that of the freshwater
with which it is in contact. If an immiscible phase has density
approximately the same or less than that of ground water, this
phase will not move down past the capillary fringe of the ground
water. Instead, it will flow along the top of the capillary fringe in the
direction of the maximum water-level elevation drop. If the density
of an immiscible phase is substantially greater than the ground
water, the immiscible phase will push its way into the ground water
as a relatively coherent blob. The primary direction of its flow will
then be down the dip of the first impermeable stratum encountered.
There is a great need for better means of characterizing such
behavior for site-specific applications. Currently, estimation
methods are patterned after multiphase oil reservoir simulators.
One of the key extensions needed is the ability to predict the
transfer of trace levels of contaminants from the immiscible fluid to
ground water, such as xylenes from gasoline.
Anisotropy is a subtlety of hydraulic conductivity which relates
to structural trends of the rock or sediments of which an aquifer is
composed. Permeability and hydraulic conductivity are
directionally dependent in anisotropic strata. When molten
material from deep underground crystallizes to form granitic or
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basaltic rocks, for instance, it forms cleavage planes which may
later become the preferred directions of permeability. Marine
sediments accumulate to form sandstone, limestone, and shale
sequences that have much less vertical than horizontal
permeability. The seasonal differences in sediments that
accumulate on lakebeds, and the stratification of grain sizes
deposited by streams as they mature, give rise to similar vertical-to-
horizontal anisotropy. Streams also cause anisotropy within the
horizontal plane, by forming and reworking their sediments along a
principal axis of movement. These structural variations in
permeability would be of minimal concern except that ground water
does not flow at right angles to water-level elevation contours under
anisotropic conditions. Instead, flow proceeds along oblique angles,
with the degree of deviation from a right-angle pathway
proportional to the amount of anisotropy. This fact is all too often
ignored and the causes again seem to be a reluctance to conduct the
proper field tests, combined with an over-reliance on mathematical
modeling.
If the pathways created by cleavage planes and fractures begin
to dominate fluid flow through a subsurface stratum, the directions
and rates of flow are no longer predictable by the equations used for
porous rock and sediments. There have been a number of attempts
to represent fractured flow as an equivalent porous medium, but
these tend to give poor predictions when major fractures are present
and when there are too few fractures to guarantee a minimum
degree of interconnectedness. Other representations that have been
studied are various dual porosity models, in which the bulk matrix
of the rock has one porosity and the fracture system has another.
Further development of the dual porosity approach is limited by the
difficulty in determining a transfer function to relate the two
different porosity schemes. Research in this area needs to be
accelerated because there is a great likelihood of fractured flow in
just those situations commonly believed to be the most suitable for
disposal of hazardous wastes, such as building landfills on
'impermeable1 bedrock.
Considerations for Predictive Modeling
Equations for the combined advection-dispersion process are
used to estimate the time during which a nonreactive contaminant
will travel a specific distance, the pathway it will travel, and its
concentration at any point. The accuracy of most predictions is only
fair for typical applications, because of the complexity of the
problems and the scarcity of site-specific hydrogeologic data. The
lack of such data can be improved on with much less effort than is
commonly presumed, especially when the cost of another round of
chemical sampling is compared with the costs of additional borings,
core retrievals, geophysical logging, or permeability testing.
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Equations that assume a nonreactive contaminant have limited
usefulness, because most contaminants react with other chemical
constituents in subsurface waters and with subsurface solids in a
manner that affects the rate at which they travel. Nevertheless,
nonreactive advection-dispersion equations are often used to
generate 'worst-case' scenarios, on the presumption that the
maximum transport velocity is obtained (equal to that of pure
water). This may not be as useful as it first seems. Remedial action
designs require detailed breakdowns of which contaminants will
arrive at extraction wells and when, how long contaminants will
continue their slow release from subsurface solids, and whether the
contaminants will be transformed into other chemical species by
chemical or biological forces. To address these points, special terms
must be added to the advection-dispersion equations.
CHEMICAL PROCESSES
As difficult as the foregoing complications may be, predicting
how chemical contaminants move through the subsurface is a
relatively trivial matter when the contaminants behave as ideal,
nonreactive substances. Unfortunately, such behavior is limited to a
small group of chemicals. The actual situation is that most
contaminants will, in a variety of ways, interact with their
environment through biological or chemical processes. This section
focuses on the dominant chemical processes that may ultimately
affect the transport behavior of a contaminant. As with the physical
processes previously discussed, some of the knowledge of chemical
processes has been translated into practical use in predictive
models. However, the science has, in many instances, advanced well
beyond what is commonly practiced. Furthermore, there is
considerable evidence that suggests that numerous undefined
processes affect chemical mobility. Most of the deviation from ideal
nonreactive behavior of contaminants relates to their ability to
change physical form by energetic interactions with other matter.
The physical-chemical interactions may be grouped into: alterations
in the chemical or electronic configuration of an element or
molecule, alterations in nuclear composition, the establishment of
new associations with other chemical species, and interactions with
solid surfaces.
Chemical/Electronic Alterations
The first of these possible changes is typified by oxidation-
reduction or redox reactions. This class of reactions is especially
important for inorganic compounds and metallic elements because
the reactions often result in changes in solubility, complexing
capacity, or sorptive behavior, which directly impact on the mobility
of the chemical. Redox reactions are reasonably well understood, but
there are practical obstacles to applying the known science because
15
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it is difficult to determine the redox state of the aquifer zone of
interest and to identify and quantify the redox-active reactants.
Hydrolysis, elimination, and substitution reactions that affect
certain contaminants also fit into this classification. The chemistry
of many organic contaminants has been well defined in surface
water environments. The influence of unique aspects of the
subsurface, not the least of which is long residence time, on such
transformations of important organic pollutants is currently under
investigation. There is also a need to investigate the feasibility of
promoting in-situ abiotic transformations that may enhance the
potential for biological mineralization of pollutants.
Nuclear Alterations
Another chemical process interaction, which results in internal
rearrangement of the nuclear structure of an element, is well
understood. Radiodecay occurs by a variety of routes, but the rate at
which it occurs is always directly proportional to the number of
radioactive atoms present. This fact seems to make mathematical
representation in contaminant transport models quite
straightforward because it allows characterization of the process
with a unique, well defined decay constant for each radionuclide.
A mistake that is often made when the decay constant is used in
models involves the physical form of the reactant. If the decay
constant is applied to the fluid concentrations and no other chemical
interactions are allowed, then incorporation of the constant into the
subroutine which computes fluid concentrations will not cause
errors. If the situation being modeled involves chemical interactions
such as precipitation, ion-exchange, or sorption, which temporarily
remove the radionuclide from solution, then it is important to use a
second subroutine to account for the non-solution-phase decay of the
radionuclide.
Chemical Associations
The establishment of new associations with other chemical
species is not as well understood. This category includes ion-
exchange, complexation, and co-solvation. The lack of
understanding derives from the nonspecific nature of these
interactions which are, in many instances, not characterized by the
definite proportion of reactants to products (stoichiometry) typical of
redox reactions. While the general principles and driving
mechanisms by which these interactions occur are known, the
complex subsurface matrix in which they occur provides many
possible outcomes and renders predictions uncertain.
Ion-exchange and complexation reactions heavily influence the
mobility of metals and other ionic species in the subsurface in a
reasonably predictable fashion. Their influence on organic
contaminant transport, however, is not well understood. Based on
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studies of pesticides and other complex organic molecules, natural
organic matter (such as humic and fulvic materials) can complex
and thereby enhance the apparent solubility and mobility of
synthetic organic chemicals. Research is needed to define the
magnitude of such interactions, not only with naturally occurring
organic molecules but also with man-made organics present in
contaminated environments. Research is also needed to determine if
these complexes are stable and liable to transport through the
subsurface. Examination of the degree to which synthetic organic
chemicals complex toxic metals is also necessary. There is no
theoretical objection to such interactions, and there is ample
evidence that metals are moving through the subsurface at many
waste sites.
Co-solvation occurs when another solvent is in the aqueous
phase at concentrations that enhance the solubility of a given
contaminant. This occurs in agricultural uses, for example, where
highly insoluble pesticides and herbicides are mixed with organic
solvents to increase their solubility in water prior to field
application. There is every reason to expect similar behavior at
hazardous waste sites, where a variety of solvents are typically
available. At present, prediction of the extent of the solubility
increases that might occur at disposal sites in the complex mixture
of water and organic solvents is essentially impossible. Researchers
have started examining co-solvation as an influence on pollutant
transport, by working on relatively simple mixed solvent systems.
This research will be extremely useful, even if the results are
limited to a qualitative appreciation for the magnitude of the effects.
At the extreme, organic solvents in the subsurface may result in
a phase separate from the aqueous phase. In addition to movement
of this separate phase through the subsurface, contaminant mobility
that involves partitioning of organic contaminants between the
organic and aqueous phases must also be considered. The
contaminants will move with the organic phase and will, depending
on aqueous phase concentrations, be released into the aqueous
phase to a degree roughly proportional to their octanol-water
partition coefficients. An entire range of effects is possible, from
increasing to slowing the mobility of the chemical in the subsurface
relative to its migration rate in the absence of the organic phase.
The equilibrium partitioning process increases the total volume of
ground water affected by contaminants, by releasing a portion of the
organic phase constitutents into adjacent waters. It may also
interfere with transformation processes by affecting pollutant
availability for reaction, or by acting as a biocidal agent to the
native microflora.
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Surface Interactions
Of those interactions that involve organic chemicals in the
environment, none has been as exhaustively studied as sorption.
Sorption studies relate, in terms of a sorption isotherm, the amount
of contaminant in solution to the amount associated with the solids.
Most often the sorption term in transport models is estimated for
simplicity from the assumption that the response is linear. This
approximation can produce serious mass balance errors. Typically,
the contaminant mass in the solution phase is underestimated and
contaminant retardation is thereby overestimated. In practical
applications, this means that high contaminant levels can be
detected at a monitoring well long before they were predicted. To
resolve the discrepancy between predicted and actual transport,
most practitioners arbitrarily adjust some other poorly-
characterized model parameter, for example, dispersion. This leads
to the creation of a model that does not present various natural
process influences in proper perspective. The predictions from such
models are likely to be qualitatively, as well as quantitatively,
incorrect. More widespread consideration should be given to
accurate representation of non-linear sorption, particularly in
transport modeling at contaminated sites.
The time dependency of the sorption process is a related
phenomenon that has also been largely ignored in practical
applications of sorption theory. Most models assume that sorption is
instantaneous and completely reversible. A growing body of
evidence argues to the contrary, not only for large organic molecules
in high-carbon soils and sediments, but also for solvent molecules in
low-carbon aquifer materials. Additionally, there must be some
subtle interplay between sorption kinetics and ground-water flow
rates which gains significance in pump-and-treat remediation
efforts, where flow rates are routinely substantially increased.
Constant pumpage at moderate-to-high flow rates may not allow
contaminants that are sorbed to solids sufficient times of release to
increase solution concentrations to maximum (equilibrium) levels
prior to their removal from the aquifer. Hence, treatment costs may
rise substantially due to the prolonged pumping required to remove
all of the contaminants and due to the lowered efficiency of
treatment of the less contaminated pumped waters.
Evidence from Superfund sites and ongoing research activities
suggests that contaminant association with a solid surface does not
preclude mobility. In many instances, especially in glacial tills that
contain a wide distribution of particle sizes, fine aquifer materials
have accumulated in the bottom of monitoring wells. Iron-based
colloids have been identified in ground water downgradient from a
site contaminated with domestic wastewater. If contaminants can
associate with these fine particles, their mobility through the
subsurface could be markedly enhanced. To determine the
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significance of particle transport to pollutant movement, studies
must be performed at such contaminated sites.
Although knowledge about chemical processes that function in
the subsurface has been significantly expanded in recent years, this
information is only slowly finding its way into practical
interpretations of pollutant transport at contaminated sites.
Evidence from field sites suggests that much remains to be learned
about these processes.
BIOLOGICAL PROCESSES
Many contaminants that enter the subsurface environment are
biologically reactive. Under appropriate circumstances they can be
completely degraded to harmless products. Under other
circumstances, however, they can be transformed to new substances
that are more mobile or more toxic than the original contaminant.
Quantitative predictions of the fate of biologically reactive
substances are at present very primitive, particularly compared to
other processes that affect pollutant transport and fate. This
situation resulted from the ground-water community's choice of an
inappropriate conceptualization of the active processes: subsurface
biotransformations were presumed to be similar to
biotransformations known to occur in surface water bodies. Only
very recently has detailed field work revealed the inadequacy of the
traditional view.
Surface Water Model Analogy
As little as five years ago ground-water scientists considered
aquifers and soils below the zone of plant roots to be essentially
devoid of organisms capable of transforming contaminants. As a
result, there was no reason to include terms for biotransformations
in transport models. Recent studies have shown that water-table
aquifers harbor appreciable numbers of metabolically active
microorganisms, and that these microorganisms frequently can
degrade organic contaminants. It became necessary to consider
biotransformation in transport models. Unfortunately, many
ground-water scientists adopted the conceptual model most
frequently used to describe biotransformations in surface waters.
The presence of the contaminant was assumed to have no effect
on microorganism populations that degrade it. It was also assumed
that contaminant concentration does not influence transformation
kinetics, and that the capacity to transform the contaminant is
uniformly distributed throughout the body of water under study.
These assumptions are often appropriate for surface waters:
contaminant concentration is usually too low and the residence time
too short to allow adaptation of the microbial community to the
contaminant, and the organisms that are naturally pre-adapted to
the contaminant are mixed throughout the water body by
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turbulence. Consequently, utilization kinetics can conveniently be
described by simple first-order decay constants. In surface waters
these constants are usually obtained by monitoring contaminant
disappearance in water samples.
Ground-Water Biotransformations
These circumstances rarely apply to biotransformation in
ground water. Contaminant residence time is usually long, at least
weeks or months, and frequently years or decades. Further,
contaminant concentrations that are high enough to be of
environmental concern are often high enough to elicit adaptation of
the microbial community. As a result, the biotransformation rate of
a contaminant in the subsurface environment is not a constant, but
increases after exposure to the contaminant in an unpredictable
way. Careful field work has shown that the transformation rates in
aquifers of typical organic contaminants, such as alkylbenzenes, can
vary as much as two orders of magnitude over a meter vertically and
a few meters horizontally. This surprising variability in
transformation rates is not related in any simple way to system
geology or hydrology.
It is difficult to determine transformation rates in subsurface
material. Most microbes in subsurface material are firmly attached
to solid surfaces; usually less than 1% of the total population is truly
planktonic. As a result, the microbes in a ground-water sample
grossly underrepresent the total microbial population in the aquifer.
Thus, contaminant disappearance kinetics in a ground-water
sample do not represent the behavior of the material in the aquifer.
It is therefore necessary to do microcosm studies with samples
representative of the entire aquifer system - a formidable technical
challenge.
A Ground-Water Model
These concerns have prompted re-examination of assumptions
about biotransformation implicit or explicit in traditional modeling
approaches, with the realization that no one qualitative description
of biotransformation can be universally applicable. Field experience
has shown that the relationships that describe the biological fate of
contaminants actually change within aquifers in response to
geochemical constraints on microbial physiology. Rather than
describing biotransformation with a continuous function applicable
at all points in the aquifer, it may be more realistic to examine key
geochemical parameters and to use that information to identify the
relationship for biotransformation that applies at any particular
point. These key parameters could include the contaminant
concentration, oxygen or other electron-acceptor concentration,
redox state, pH, toxicity of the contaminant or co-occurring
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materials, and temperature. One such model has been evaluated in
the field.
The model described an alkylbenzene and polynuclear aromatic
hydrocarbon plume in a shallow water-table aquifer. Microcosm
studies showed that organisms in the aquifer had adapted to these
contaminants, and would degrade them very rapidly when oxygen
was available. As a result of this adaptation, the hydrocarbon
biodegradation rate was not controlled by any inherent property of
the organisms. Rather, the physical transport processes of diffusion
and dispersion seemed to dominate by controlling oxygen
availability to the plume.
Because the biotransformation rate was controlled by physical
processes, the actual model was very simple. Oxygen and
hydrocarbon transport were simulated as conservative solutes using
the U.S. Geological Survey method-of-characteristics code. A
subroutine examined oxygen and hydrocarbon concentrations at
each node (point located at interesecting grid lines of the model) and
generated new concentrations based on oxidative metabolism
stoichiometry. When the model was used to simulate the growth of
the plume over time, it illustrated an important property of many
such plumes. The plume grew until the rate of admixture of oxygen
balanced the rate of release of hydrocarbons from the source.
Afterward, the extent of the plume was at steady-state (stopped
growing).
The body of field experience that can be drawn on to properly
assign laws for biotransformation is growing rapidly. Transport-
limited kinetics may commonly apply to releases of petroleum
hydrocarbons and other easily degradable materials such as ethanol
or acetone in oxygenated ground water. On the other hand,
materials that can support a fermentation may follow first-order
kinetics. Unfortunately, many important biotransformations in
ground water are still mysteries.
Rapid field methods to determine if adaptation has occurred at a
site are needed. Tools to predict whether adaptation can be expected,
and to estimate the time required for adaptation if it does occur, are
also needed. For systems that are limited by transport processes,
field methods to estimate the aquifer processes that control mixing,
such as transverse dispersion and exchange processes across the
water table, are required. For systems that are limited by the
intrinsic biotransformation rate, new laboratory test methods
(possibly, improved microcosms) that will provide reliable estimates
of the kinetic parameters are required.
In addition to being sufficiently accurate and precise, these new
methods should provide estimates that are truly representative of
the hydrologic unit being simulated. Because contaminants
typically have long residence times in aquifers, slow transformation
rates can have environmental significance. The test methods should
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therefore be sufficiently sensitive to measure transformation rates
that are significant in the hydrologic context being simulated.
Finally, there is a need for models that go beyond simple prediction
of contaminant concentrations at points in the aquifer, and forecast
the concentrations produced by production wells.
ANALYTICAL AND NUMERICAL MODELS
One of the more subtly involved decisions that must be made is
whether to use an analytical or a numerical model to solve a
particular problem. Analytical models provide exact solutions, but
many simplifying assumptions must be made for the solutions to be
tractable. This places a burden on the user to test and justify the
underlying assumptions and simplifications (Javendel et al, 1984).
For example, the Theis equation is an analytical expression which is
used to predict the piezometric head changes for pumping or
injection wells in confined aquifers (Freeze and Cherry, 1979; Todd,
1980):
s = [Oy(4*n*T)] * [-0.5772 - ln(u) + u - (u2/(2*2!)) + (u3/(3*3!))
- (u*/(4*4!))..]
where: 's1 is the change in piezometric head,
'Q' is the flowrate of the well,
T' is the transmissivity of the aquifer, and
1u' = (r2*s)/(4*T*t);
V is the radial distance from the well,
'S1 is the storage coefficient of the aquifer, and
't1 is the length of time the well has been operating.
Here the principal assumptions are (Lohman, 1972):
(1) the aquifer is homogenous and isotropic,
(2) the aquifer is of infinite areal extent, relative to the effects
of the well (no nearby boundaries),
(3) the well is screened over the entire saturated thickness of
the aquifer,
(4) the saturated thickness of the aquifer does not vary as a
result of the operation of the well,
(5) the well has an infintesimal diameter so that waters in
storage in the casing represent an insignificant volume, and
(6) water is removed from or injected into the aquifer with an
instantaneous change in the piezometric head.
Evaluation of the foregoing equation, which incorporates an
infinite Taylor series representing the well function integral, can be
accomplished graphically using type curves (Walton, 1962; Lohman,
1972). Alternatively, a simplification can be made so that the Theis
equation is directly solvable (Cooper and Jacob, 1946). This is done
by dropping all terms in the Taylor series with powers greater than
one, and is strictly valid for cases where 'u1 has a value less than 0.01
(e.g., Figure 2-2). Physically, this corresponds to a limitation on the
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predictive power of the modified Theis equation; head changes
predicted at locations far from the well are inaccurate, except for
long durations of pumpage (i.e., approaching equilibrium or steady-
state conditions).
Numerical models are much less burdened by these assumptions
and are therefore inherently capable of addressing more
complicated problems, but they require significantly more data and
their solutions are inexact (numerical approximations). For
example, the assumptions of homogeneity and isotropicity are
unnecessary due to the ability to assign point (nodal) values of
transmissivity and storage. Likewise, the capacity to incorporate
complex boundary conditions obviates the need for the 'infinite area
extent' assumption. There are, however, difficult choices facing the
user of numerical models; i.e. time steps, spatial grid designs, and
ways to avoid truncation errors and numerical oscillations must be
chosen (Remson and others, 1971; Javendel and others, 1984). These
choices, if improperly made, may result in errors unlikely to be
made with analytical approaches (e.g.; mass imbalances, incorrect
velocity distributions, and grid-orientation effects).
QUALITY CONTROL
These latter points signify a greater need for quality control
measures when contemplating the use of numerical models. Three
levels of quality control have been suggested previously (Huyakorn
and others, 1984):
(1) validation of the model's mathematics by comparison of its
output with known analytical solutions to specific problems,
(2) verification of the general framework of the model by
successful simulation of observed field data, and
(3) benchmarking of the model's efficiency in solving problems
by comparison with other models.
These levels of quality control address the soundness and utility
of the model alone, and do not treat questions of its application to a
specific problem. Hence, at least two additional levels of quality
control appear justified:
(4) critical review of the problem conceptualization to ensure
that the modeling effort considers all physical, chemical,
and biological processes which may affect the problem, and
(5) evaluation of the specifics of the application; e.g.,
appropriateness of the boundary conditions, grid design,
time steps, etc.
Validation of the mathematical framework of a numerical model
is deceptively simple. The usual approach for ground-water flow
models involves a comparison of drawdowns predicted by the Theis
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Drawdown, ft
16
14
12
10
8
6
4
2
0
Flow rate = 100,000 cu. ft./d
Transmissivity = 10,000 sq. ft./d
Storage coefficient = 0.0001
200 400 600 800 1,000
Radius of Observation, ft
Figure2-2. Example of plots prepared with the Jacob's
approximation of the Theis analytical solution to well
hydraulics in an artesian aquifer.
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analytic solution to those obtained by using the model, such as
depicted in Figure 2-3. The 'deceptive1 part is the foreknowledge
that the Theis solution can treat only a very simplified situation as
compared with the scope of situations addressable by the numerical
model. In other words, analytical solutions cannot test most of the
capabilities of the numerical model in a meaningful way; this is
particularly true with regard to simulation of complex aquifer
boundaries and irregular chemical distributions.
Field verification of a numerical model consists of first
calibrating the model using one set of historical records (e.g.,
pumping rates and water levels from a certain year), and then
attempting to predict the next set of historical records. In the
calibration phase, the aquifer coefficients and other model
parameters are adjusted to achieve the best match between model
outputs and known data; in the predictive phase, no adjustments are
made (excepting actual changes in pumping rates, etc.). Presuming
that the aquifer coefficients and other parameters are known with
sufficient accuracy, a mismatch means that either the model is not
correctly formulated or that it does not treat all of the important
phenomena affecting the situation being simulated (e.g., does not
allow for leakage between two aquifers when this is actually
occurring).
Field verification exercises usually lead to additional data
gathering efforts, because existing data for the calibration
procedure are often insufficient to provide unique estimates of key
parameters. This means that a "black box1 solution may be obtained,
which may be good only for the records used in the calibration. For
this reason, the blind prediction phase is an essential check on the
uniqueness of the parameter values used. In this regard, field
verification of models using datasets from controlled research
experiments may be much more achievable practically.
Benchmarking routines to compare the efficiency of different
models in solving the same problem have only recently become
available (Ross and others, 1982; Huyakorn and others, 1984). Much
more needs to be done in this area, because some unfair perceptions
continue to persist regarding the ostensibly greater utility of certain
modeling techniques. For example, it has been said many times that
finite element models (FEM's) have an inherent advantage over
finite difference models (FDM's) in terms of the ability to
incorporate irregular boundaries (Mercer and Faust, 1981); the
number of points (nodes) which must be used by FEM's is
considerably less due to the flexible nodal spacings that are allowed.
Benchmarking routines, however, show that the much longer
computer time required to evaluate FEM nodes causes there to be
little, if any, cost advantage for simulations of comparable accuracy.
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Drawdown, ft
2
1.8
1.6
1.4
1.2
1
.8
.6
Flow rate = 100,000 cu.ft./d
Transmissivity = 10,000 sq. ft/d
Storage coefficient = 0.00003
Observation radius = 2000ft.
Analytical
(Jacob's Approx.)
D Numerical
(Alt. Direct.
Implicit.)
_L
_L
_L
I
I
234 56789
Duration of Pumpage, days
10
Figure 2-3. Mathematical validation of a numerical method of
estimating drawdown, by comparison with an
analytical solution.
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CHAPTER SUMMARY
Mathematical models of subsurface contaminant transport are
simplified representations of reality that incorporate a number of
theoretical assumptions about the natural processes governing the
transport and fate of contaminants. In order for solutions to be made
tractable, further simplifications are made in applications of theory
to practical problems. Hence, mathematical models produce
representions that are not faithful to the true complexities of real
world situations. This limitation can be partially compensated for,
however, by detailed mathematical testing to determine the
magnitude of errors generated by the assumptions and
simplifications involved.
The application of mathematical models is also subject to
considerable error in practical situations due to the lack of
appropriate field determinations of natural process parameters.
This source of error is not adequately addressed by sensitivity
analyses or stochastic techniques for estimating uncertainty,
contrary to popular beliefs. Rather, the high degree of
hydrogeologic, chemical, and microbiological complexity typically
present in field situations demands characterization of the
magnitude of influences from various natural processes by actual
field determinations.
Both the mathematics describing models and the parameter
input to models must be subjected to rigorous quality control
procedures. Otherwise, results from field applications of models are
likely to be qualitatively, as well as quantitatively, incorrect.
Quality control methodologies must recognize that accuracy and
precision determinations are insufficient measures of quality. The
correctness of the problem conceptualization, and the
representativeness of parameter values are essential quality
considerations.
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CHAPTER 3
APPLICATIONS IN PRACTICAL SETTINGS
STEREOTYPICAL APPLICATIONS
As stated in proceeding sections, models are simplifications of
reality that may or may not faithfully simulate the actual situation.
Typically, attempts are made to mimic the effects of hydrogeologic,
chemical, and biological processes in practical applications of
models. These almost always involve idealizations of known or
suspected features of the problem on hand. For example, the
stratification of alluvial, fluvial, and glacial deposits may be
assumed to occur in uniformly thick layers, despite the great
variability of stratum thicknesses found in actual settings. Large
blocks of each stratum are assumed to be homogeneous. Sources of
chemical input are commonly assumed to have released
contaminants at constant rates over the seasons and years of
operational changes that the sources were active. The areal
distribution of rainfall and the actual schedules of pumpage from
production wells are also artificially homogenized in most modeling
exercises.
All these idealizations are made necessary by a lack of the
appropriate historical records and field-derived parameter
estimates, and all reduce the reliability of predictions made with
models. The degree of usefulness of a model is therefore directly
dependent on the subjective judgements that must be made in data
collection and preparation efforts prior to attempting mathematical
simulations. This is true not only in a quantitative sense, but also in
a qualitative sense because it is the data gathering phase of a project
that begets the conceptualization on which the model will be based.
REAL-WORLD APPLICATIONS
To illustrate this point, the highlights of two very different
contamination problems will be described. The first involves a
relatively limited contamination incident arising from a very small
source and having few contaminants. The second involves a major
contamination incident arising from the operation of a chemical
reprocessing facility that handled dozens of different contaminants
in large amounts. The common theme that is shared by the two
cases, as should also apply to virtually all cases, is one of seeking to
define the relative influences of natural processes affecting
contaminant transport in order to optimize the assessment
29
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and remediation of the problem. It is the validity of the conceptual
model of what is happening at these sites that is most important, not
the application of a particular mathematical model.
Field Example No. 1
The Lakewood Water District in Lakewood, Washington
operates a number of wells for drinking water supply purposes.
Some of the wells operated by the District, such as the two primary
wells at its Ponders' Corner site (Figure 3-1), have been
contaminated with low levels of volatile organic chemicals (VOC's).
During the course of the investigations at the Ponder's Corner site, a
number of cost-saving sampling alternatives were chosen. These
related principally to the field use of a portable gas chromatograph
(Organic Vapor Analyzer) for the screening of water samples and
soil extracts taken while drilling monitoring wells, and to the use of
selective analyses (VOCs only) of ground-water samples when
initial results showed only a narrow group of contaminants to be
present. The lowered analytical costs, in part, allowed for increased
expenditures for geotechnical characterization of the site (Wolf and
Boateng, 1983).
The geotechnical efforts, particularly the pump tests that were
conducted, led to a realization that the source of the contaminants
was to be found regionally downgradient (Keely and Wolf, 1983).
The pumping strength of the water-supply wells, when operating,
was sufficient to pull contaminants over 400 feet back upgradient of
the wells they affect. This behavior was somewhat unexpected. A
unique feature of the field investigation was the taking of the
ground-water samples from the pumping wells concurrent with
drawdown measurements obtained during pump tests (Keely, 1982).
The pump tests yielded estimates of local transmissivity and
storage coefficients. They also confirmed the presence of a major
aquifer boundary nearby; a buried glacial till drumlin just west of
the site parallels the general direction (northwest) of regional flow.
The pump tests clearly showed some anisotropy of the sediments as
well; drawdown contours produced an elliptical cone of drawdown,
the major axis of which was aligned with the regional flow to the
north. This information resulted in modifications to the original
plans, which called for drilling and constructing several monitoring
wells west of the site. Instead, more monitoring wells were drilled
along the north-south axis. Chemical analysis of the samples taken
concurrent with drawdown measurements formed a time-series of
contaminant concentrations that provided a clue to where the
contaminant source was located (Keely, 1982). The time-series
showed that the well nearest the downgradient edge of the wellfield
was exposed to increasing contaminant levels as pumping
continued, whereas the upgradient pumping well remained largely
unaffected (Keely and Wolf, 1983).
30
-------
South Tacoma Way/Pacific Highway
Natural
Flow
Not Drawn to Scale
Figure3-1. Location map for Lakewood Water District wells
contaminated with volatile organic chemicals.
31
-------
The hydrogeologic parameter estimates obtained from the pump
tests strengthened the conceptualization of contaminants being
drawn back against the regional flow because the capture zones of
the pumping wells were sufficiently distorted by the local anisotropy
to more than encompass the contaminant source. Without
considering the anisotropic bias along the regional flow path, the
estimated boundaries of the capture zone for either of the two wells
marginally reached the distance to the contaminant source. The
mechanism by which the two wells became contaminated seemed to
be understood from a hydraulic point of view (Figure 3-2), but the
chemical information did not seem to provide a consistent picture.
The source of contamination, a septic tank at a dry-cleaning
facility, was found to have received large amounts of
tetrachloroethylene and trichloroethylene, but no known amounts
of cis- or trans-dichloroethylene; whereas the contaminated wells
had relatively high concentrations of dichloroethylene. Initially it
was thought that other sources might also be present and would
explain the high concentrations of dichloroethylene. However, it
soon became clear that recent research results regarding the
potential for biotransformation of tetrachloroethylene and
trichloroethylene (Wilson and McNabb, 1981) would more
satisfactorily explain the observations.
Simulations of this kind of problem could be adequately
performed only by contaminant transport models capable of
incorporating the effects of the pumping wells on the regional flow
field. More sophisticated approximations would also require the
ability to account for the anisotropic and heterogeneous character of
the site, the retardation of the VOC's by sorption, and their possible
biotransformations. Given the highly localized nature of the
contaminant source and limited extent of the plume, however, there
was insufficient justification for pursuing such efforts. The
resolution of the problem was possible by relatively simple source
removal techniques (excavation of the septic tank and elimination of
discharges).
Field Example No. 2
Similar experience with special use of geotechnical methods and
state-of-the-art research findings occurred at the 20-acre Chem-
Dyne solvent reprocessing site in Hamilton, Ohio (Figure 3-3).
During operation of the site (1974-1980), poor waste handling
practices such as onsite spillage of a wide variety of industrial
chemicals and solvents, direct dischage of liquid wastes to a
stormwater drain beneath the site, and mixing of incompatible
wastes were engaged in routinely. These caused extensive soil and
ground-water contamination, massive fish kills in the Great Miami
River, and major onsite fires and explosions, respectively. The
stockpiling of liquid and solid wastes resulted in thousands of badly
32
-------
1
Well
H-2
Well
H-1
Water Table
Q: 1175gpm
Water Table
Q: 1175gpm
Figure 3-2. Schematic illustrating the mechanism by which a
downgradient source may contaminate a production
well, and by which a second well may isolate the
source through hydraulic interference.
33
-------
Icorroded caking drums that posed a long-term threat to the
environment (CH2M-Hill, 1984).
The seriousness of the ground-water contamination problem
became evident during the initial site survey (1980-1981), which
included the construction and sampling of over twenty shallow
monitoring wells (Ecology and Environment, 1982). The initial
survey indicated that the contaminant problem was much more
limited than was later shown to be the case (Roy F. Weston Inc.,
1983, CH2M-H111, 1984). A good portion of the improvement in
delineating the plume was brought about by an improved
understanding of the natural processes controlling transport of
contaminants at the site.
The initial site survey indicated that ground-water flow was
generally to the west of the site, toward the Great Miami River, but
that a shallow trough paralleled the river itself as a result of weak
and temporary stream influences. The study concluded that
contaminants would be discharged from the aquifer into the river
(Ecology and Environment, 1982). That study also concluded that
the source was limited to highly contaminated surface soils, and
that removal of the uppermost three feet of the soil would
essentially eliminate the source.
That conclusion was, however, based on faulty soil sampling
procedures. The soil samples that were taken were not preserved in
air-tight containers, so that most of the VOC's leaked out prior to
analysis. That the uppermost soil sample showed high VOC levels is
probably explained by the co-occurrence of viscous oils and other
organic chemicals that may have served to entrap the VOC's. The
more viscous and highly retarded chemicals did not migrate far
enough into the vertical profile to exert a similar influence on
samples collected at depths greater than a few feet.
Subsequent studies of the site corrected these
misinterpretations by producing data from proper soil samplings
and by incorporating a much more detailed characterization of the
fluvial sediments and the natural flow system. In those studies
vertical profile characterizations were obtained from each new
borehole drilled by continuous split-spoon samples of subsurface
solids; and clusters of vertically-separated monitoring wells were
constructed. The split-spoon samples helped to confirm the general
locations of interfingered clay lenses and clearly showed the high
degree of heterogeneity of the sediments (Figures 3-4 and 3-5).
While an extensive network of shallow wells confirmed earlier
indications of general ground-water flow toward the river (Figure 3-
6), the clusters of vertically separated wells revealed that dramatic
downward gradients existed adjacent to the Great Miami River
(Figure 3-7). This finding indicated that the migrating plume would
not be discharged to the river, but would instead flow under the
river.
34
-------
IQ
c
S
U)
U)
o
Q)
6"
3
a>
T3
3-
-n
n
Q.
L
]| CHEM-DYNE SUPERFUND SITE
Hamilton, Ohio
LEGEND
• monitoring well locations
MW1 monitoring well identity
• • • site boundary
LOCATION MAP
-------
(Q
C
Ul
S.S
*/» n>
• 3
6
(Q
o
(Q
IV
r>
6DD
590 -
5BQ
NNW
SSE
(0
2 570
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560
_ 550
— 540
^ 530
UJ
—I 520
LU
510
500
- 5
.( Water Level Elevation" ]
1 Approximately 563 ft. MSL I
^ ^^;
CO
csj
"October 3D, 1983
Fill (sandy gravel)
DATA SOURCE: U.S. EPA, 1984
Sand
Silty sand
/j;; Clayey silt, silty clay
Sandy gravel, gr. sand
Clayey gravel, glacial till
-------
ClSW
NOI1VA313
Figure3-5. Chem-Dyne geologic cross-section along WSW-ENE
dXfS.
37
-------
Figure 3-6. Shallow well ground-water contour map for Chem-
Dyne. Flow is generally to the river (west) and down
the valley (southwest).
38
-------
GROUND
SURFACE
SHALLOW
WELL
I
INTERMEDIATE
WELL
DEEP
WELL
Figure3-7. Typical arrangement of clustered, vertically-
separated wells installed adjacent to Chem-Dyne and
the Great Miami River.
39
-------
The presence of major industrial wells on the other side of the
river supported this conclusion. The plume would be drawn to
greater depths in the aquifer by the locally severe downward
gradient, but whether the industrial wells would actually capture
the plume could not be determined. That determination would
require careful evaluation of the hydrogeologic features beneath the
river; something that has not been attempted because of the onset of
remedial actions designed to stop the plume from reaching the river.
The field characterization efforts did, however, include the
performance of a major pump test so that the hydrogeologic
characteristics of the contaminated portion of the aquifer could be
estimated. The pump test was difficult to arrange, because the
pumping well had to be drilled onsite for reasons of potential
liability and lack of property access elsewhere. The drillers were
considerably slowed in their work by the need to don air-tanks when
particularly contaminated subsoils were encountered because the
emission of volatile fumes from the borehole presented unacceptable
health risks. Since the waters which would be pumped were
expected to be contaminated, it was necessary to construct ten large
temporary holding tanks (100,000 gallons each) onsite to impound
the waters for testing and possible treatment prior to being
discharged to the local sewer system (CH^M-Hill, 1984).
The costs and difficulty of preparing for and conducting the test
were worth the effort, however. The water levels in thirty-six
monitoring wells were observed during the test and yielded a very
detailed picture of transmissivity variations (Figure 3-8), which has
been used to help explain the unusual configuration of the plume
(Figure 3-9) and which were used to guide the design of a pump-and-
treat system. Storage coefficients were also estimated; and though
the short duration of the test (14 hours) did not allow for definitive
estimates to be obtained, it was clear that qualitative confirmation
of the generally non-artesian (water-table) nature of the aquifer
beneath the site was confirmed. An automated data acquisition
system (computer-controlled pressure transducer system) was used
to monitor the water levels and provide real-time drawdown plots of
19 of the 36 wells (Table 3-1), greatly enhancing the information
obtained with only minimal manpower requirements. The benefits
from conducting the pump test cannot be overemphaiszed;
qualitative confirmation of lithologic information and semi-
quantitative estimation of crucial parameters were obtained.
Finally, the distribution patterns of contaminant species that
emerged from the investigations at Chem-Dyne were made
understandable by considering research results and theories
regarding chemical and microbiological influences. Once again
there seemed to be evidence of transformation of tetrachloroethene
(Figure 3-10) to less halogenated daughter products such as
trichloroethene (Figure 3-11), dichloroethene (Figure 3-12), and
vinyl chloride / monochloroethene (Figure 3-13). The relative rates
40
-------
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to m
0.
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(B -K
QL 0)
C D
-i v*
5" 3
10 Ł'
6°
•<
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o
3
o
LEGEND
* monitoring well locations
MW1 monitoring well identity
• • • site boundary
CHEM-DYNE SUPERFUND SITE
Hamilton, Ohio
Transmissivity Estimate from October
1983 Pump Test
(values in thousands of square feet per day)
-------
Suunp
•6ui|diuesŁ86l
;e S||a/v\ MO||eqs ui
\eioi ±
o <
O o
-------
Table 3-1. Chem-Dyne Pump Test Observation Network.
Obs.
Well No.
MW1
MW2
MW3
MW4
MW5
MW6
MW7
MW8
MW9
MW10
MW11
MW12
MW13
MW14
MW15
MW16
MW17
MW18
MW19
MW20
MW21
MW22
MW23
MW24
MW25
MW26
MW27
MW28
MW29
MW30
MW31
MW32
MW33
MW34
MW35
MW36
Pumping
Well
Radial
Dist.
(feet)
957
965
848
537
313
420
480
740
487
186
502
232
232
701
611
1275
1518
692
1204
1225
1259
1261
298
398
53
62
272
248
167
993
465
1236
690
454
651
696
0
(ref. pt.)
Init. Wtr.
Level
(ft, MSL)
563.68
563.74
563.96
563.27
563.31
564.40
563.30
563.01
563.08
563.29
562.90
562.39
563.19
-
563.10
562.47
560.03
562.67
559.80
562.10
561.29
559.95
563.07
563.07
563.04
562.96
563.13
562.99
563.23
561.25
562.78
559.56
562.06
562.29
562.93
562.69
562.97
Method of
Measurement
(type, field unit)
manual, electric probe
manual, electric probe
automatic, float-type
manual, electric probe
manual, electric probe
manual, electric probe
manual, electric probe
manual, electric probe
manual, electric probe
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
dry - no data collected
auto., pressure transducer
manual, electric probe
manual, electric probe
manual, electric probe
automatic, float-type
auotmatic, float-type
manual, electric probe
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
manual, electric probe
automatic, float-type
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
auto., pressure transducer
manual, electric probe
auto., pressure transducer
43
-------
of movement of these contaminants, as well as other common
solvents like benzene (Figure 3-14) and chloroform (Figure 3-15),
generally conformed to predictions based on sorption principles. The
remediation efforts also made use of these contaminant transport
principles in estimating the capacity of the treatment system
needed and the length of time necessary to remove residuals from
the aquifer solids (CH2M-Hill, 1984).
During the latter stages of negotiations with the Potentially
Responsible Parties (PRP's), government contractors prepared
mathematical models of the flow sytem and contaminant transport
at Chem-Dyne (GeoTrans, 1984). These were used to estimate the
possible direction and rate of migration of the plume in the absence
of remediation, the mass of contaminants removed during the
various remedial options, and the effects of sorption and dispersion
on those estimates. Because of the wide range of sorption properties
associated with the variety of VOC's found in significant
concentrations, it was necessary to select values of retardation
constants that represented the likely upper- and lower-limits of
sorptive effects. It was also necessary to estimate or assume the
values of other parameters known to affect transport processes, such
as dispersion coefficients.
While the developers of the models would be the first to
acknowledge the large uncertainties associated with those modeling
efforts due to lack of information about the actual history of
chemical inputs and other important data, there was agreement
between the government and PRP technical experts that the
modeling efforts had been very helpful in assessing the magnitude
of the problem and in determining minimal requirements for
remediation. Consequently, modeling efforts will continue at Chem-
Dyne. Data generated during the remediation phase will be used to
refine models in an ongoing process so that the effectiveness of the
remedial action can be evaluated properly.
PRACTICAL CONCERNS
In many ways, there may be too much confidence among those
not directly involved in ground-water quality research regarding
current abilities to predict transport and fate of contaminants in the
subsurface. The discussions in the preceeding sections should place
in proper perspective the admittedly remarkable advances that
have been made in recent years by illustrating the practical and
conceptual uncertainties that remain unresolved. Continuing
research efforts will eventually resolve these uncertainties, but
those efforts will be considerably slower if existing results are not
routinely incorporated into practical situations. Research results
must be tested in real-world settings because there is no alternative
mechanism for validating them. Just as importantly, there are
economic arguments for incorporating research findings and state-
44
-------
UJ
Figure 3-10. Distribution of tetrachloroethene in shallow wells at
Chem-Dyne during October, 1983 sampling.
45
-------
Figure 3-11. Distribution of trichloroethene in shallow wells at
Chem-Dyne during October, 1983 sampling.
46
-------
Figure 3-12. Distribution of trans-dichloroethene in shallow wells
at Chem-Dyne during October, 1983 sampling.
47
-------
Figure3-13. Distribution of vinyl chloride in shallow wells at
Chem-Dyne during October, 1983 sampling.
48
-------
Figure 3-14. Distribution of benzene in shallow wells at Chem-
Dyne during October, 1983 sampling.
49
-------
IQ
c
3
en
O O
D r-f
n 2.
I'S
8 5'
3 .
S
I
*/r
o>
r*
n
LEGEND
• monitoring well locations
MW1 monitoring well identity
... site boundary
O^X^ Isopleth in parts per billion
(shallow wells only)
CHEM-DYNE SUPERFUND SITE
Hamilton, Ohio
CHLOROFORM
OCTOBER 1983 SAMPLING
-------
of-the-art techniques into routine contaminant investigations and
remediations.
Additional effort devoted to site-specific characterizations of
natural process parameters, rather than relying almost exclusively
on chemical analyses of ground-water samples, can significantly
improve the quality and cost effectiveness of remedial actions at
such sites. To underscore this point, condensed summaries are
provided of the principal activities, benefits, and shortcomings of
three possible site characterization approaches: conventional (Table
3-2), state-of-the-art (Table 3-3), and state-of-the-science (Table 3-4).
To further illustrate this, a qualitative assessment of desired trade-
offs between characterization and clean-up costs is presented in
Figure 3-16.
Table 3-2. Site Characterization Conventional Approach.
ACTIONS TYPICALLY TAKEN
Install a few dozen shallow monitoring wells
Sample and analyze numerous times for 129+ pollutants
Define geology primarily by driller's log and cuttings
Evaluate hydrology with water level maps only
BENEFITS
Rapid screening of problem
Moderate costs involved
Field and lab techniques standardized
Data analysis relatively straightforward
Tentative identification of remedial options possible
SHORTCOMINGS
True extent of problem often misunderstood
Selected remedial alternative may not be appropriate
Optimization of remedial actions not possible
Clean-up costs unpredictable and excessive
Verification of compliance uncertain and difficult
As illustrated there, some investments in specialized equipment
and personnel will be necessary to make transitions to more
sophisticated approaches, but those investments should be more
than paid back in reduced clean-up costs. The maximum return on
increased investments is expected for the state-of-the-art approach,
and will diminish as the state-of-the-science approach is reached
because highly specialized equipment and personnel are not widely
available. It is vitally important that this philosophy be considered,
51
-------
Table 3-3. Site Characterization State-of-the-Art Approach.
RECOMMENDED ACTIONS
Install depth-specific well clusters
Sample and analyze for 129+ pollutants
Analyze selected contaminants in subsequent samplings
Define geology by extensive coring/split-spoon samples
Perform limited tests on solids (grain size, clay content)
Conduct geophysical surveys (resistivity soundings, etc.)
BENEFITS
Conceptual understanding of problem more complete
Better prospect for optimization of remedial actions
Predictability of remediation effectiveness increased
Clean-up costs lowered, estimates improved
Verification of compliance soundly based, more certain
SHORTCOMINGS
Characterization costs somewhat higher
Detailed understanding of problem still difficult
Full optimization of remedial actions not likely
Field tests may create secondary problems
Demand for specialists increased
because the probable benefits in lowered total costs, health risks,
and time for effective remediations can be substantial.
CHAPTER SUMMARY
It is well understood that models may be used to examine the
significance of various natural processes controlling the behavior of
ground water and the chemical and biological species it transports.
Literally thousands of laboratory and field experiments have been
conducted and interpreted with the assistance of mathematical
models. Virtually all of these, however, are performed in idealized
settings and are tightly controlled. There still exists the need to
truly evaluate the predictive accuracy and utility of mathematical
models for real-world contamination problems.
Managers are increasingly asking technical support staff to use
models to interpret field data within the context of developing and
optimizing alternative solutions to their problems. That this cannot
be done in a meaningful way, without serious efforts to characterize
natural process parameters at actual sites, must also be fully
appreciated.
52
-------
Table3-4. Site Characterization State-of-the-Science
Approach.
IDEALIZED APPROACH
Assume 'State-of-the-Art Approach' as starting point
Conduct tracer-tests and borehole geophysical surveys
Determine % organic carbon, exchange capacity, etc. of
solids
Measure redox potential, pH, DO, etc. of fluids
Evaluate sorption-desorption behavior using select cores
Identify bacteria and assess potential for
biotransformation
BENEFITS
Thorough conceptual understanding of problem
obtained
Full optimization of remedial actions possible
Predictability of remediation effectiveness maximized
Clean-up costs lowered significantly, estimates reliable
Verification of compliance assured
SHORTCOMINGS
Characterization costs significantly higher
Few previous field applications of advanced theories
Field and laboratory techniques not yet standardized
Availability of specialized equipment low
Demand for specialists dramatically increased
53
-------
f'S
•ipeojddc uojiezuspejeip
jo uoipunj e se S;SOD dn-ueap pue SISOD
aiis uaa/v\;aq
o
*
RELATIVE COSTS
-------
CHAPTER 4
LIABILITIES, COSTS, AND
RECOMMENDATIONS FOR MANAGERS
INTRODUCTION
There are many texts available that describe the derivation of the
theories underlying mathematical models, the technical
applications of models, and related technical topics (e.g., data
collection and parameter estimation techniques). Few texts treat
the nontechnical issues that managers face when evaluating the
possible uses of models, such as potential liabilities, costs, and
communications between the modeler and management. These are,
however, important considerations because many modeling efforts
fail as a consequence of insufficient attention to them. This section
is therefore directed to those issues.
POTENTIAL LIABILITIES
Some of the liabilities attending the use of mathematical models
relate to the degree to which predictive models are relied on to set
conditions for permitting or banning specific practices or products. If
a model is incapable of treating specific applications properly, there
may be substantially incorrect decisions made. Depending on the
application, unacceptable environmental effects may begin to
accumulate long before the nature of the problem is recognized.
Conversely, unjustified restrictions may be imposed on the
regulated community. Inappropriate or inadequate models may also
cause the 're-opening clause1 of a negotiated settlement agreement
to be invoked when, for instance, compliance requirements that
were guided by model predictions of expected plume behavior are
not met.
Certain liabilities relate to the use of proprietary codes in legal
settings, where the inner workings of a model may be subject to
disclosure in the interests of justice. The desire for confidentiality by
the model developer would likely be subordinate to the public right
to full information regarding actions predicated on tnodelingresults.
The mechanisms for protection of proprietary rights do not currently
extend beyond extracted promises of confidentiality by reviewers or
other interested parties. Hence, a developer of proprietary codes still
assumes some risk of exposure of innovative techniques, even if the
code is not pirated outright.
55
-------
Yet other liabilities may arise as the result of misapplication of
models or the application of models later found to be faulty.
Frequently, the choices of boundary and initial conditions for a
given application are hotly contested; misapplications of this kind
are undoubtedly responsible for many of the reservations expressed
by would-be model users. It has also happened many times in the
past that a widely used and highly regarded model code was found to
contain errors that affected its ability to faithfully simulate
situations for which it was designed. The best way to minimize these
liabilities is to adopt strict quality control procedures for each
application.
ECONOMIC CONSIDERATIONS
The nominal costs of the support staff, computing facilities, and
specialized graphics' production equipment associated with
numerical modeling efforts can be high. In addition, quality control
activities can result in substantial costs; the determining factor in
controlling these costs is the degree to which a manager must be
certain of the characteristics of the model and the accuracy of its
output.
As a general rule, costs are greatest for personnel, moderate for
hardware, and minimal for software. The exception to this ordering
relates to the combination of software and hardware purchased. An
optimally outfitted business computer (e.g., VAX 11/785 or IBM 3031)
costs upwards of $100,000; but it can rapidly pay for itself in terms of
dramatically increased speed and computational power. A well
complimented personal computer (e.g., IBM-PC/AT or DEC
Rainbow) may cost $10,000; but the significantly slower speed and
limited computational power may infer hidden costs in terms of the
inability to perform specific tasks. For example, highly desirable
statistical packages like SAS and SPSS are unavailable or available
only with reduced capabilities for personal computers; many of the
most sophisticated mathematical models are available in their fully
capable form only on business computers.
Figure 4-1 gives a brief comparison of typical costs for software
for different levels of computing power. Obviously, the software for
less capable computers is cheaper, but the programs are not
equivalent; so managers need to thoroughly think through what
level is appropriate. If the decisions to be made are to be based on
very little data, it may not make sense to insist on the most elegant
software and hardware. If the intended use involves substantial
amounts of data and sophisticated analyses are desired, it would be
unwise to opt for the least expensive combination.
Based on experience and observation, there does seem to be an
increasing drive away from both ends of the spectrum and toward
the middle; that is, the use of powerful personal computers is
56
-------
Ave. Price
U.S. Dollars
100
80
60
40
20
Ground-Water Modeling Software Categories
1 = Mainframe/business computer models
2 = Personal computer versions of mainframe models
3 = Original IBM-PC and compatibles'models
4 = Handheld microcomputer models (e.g., Sharp PC1500)
5 = Programmable calculator models (e.g., HP41-CV)
Note: Prices include software and all available
documentation, reports, etc.
Source of data: International Ground Water Modeling
Center
Figure 4-1. Average price per category for ground-water models
from the International Ground-water Modeling
Center.
57
-------
increasing rapidly, whereas the use of small programmable
calculators and large business computers alike is declining.
In part, this stems from the significant improvements in the
computing power and quality of printed outputs obtainable from
personal computers. In part, it is due to the improved
telecommunications capabilities of personal computers; they are
now able to emulate the interactive terminals of large business
computers so that vast computational power can be accessed and the
results retrieved with no more than a phone call. Most importantly
for ground-water managers, many of the mathematical models and
data packages have been 'down-sized* from mainframe computers to
personal computers; many more are being written directly for this
market.
Since it is expected that most managers will want to explore this
situation a bit more, Figure 4-2 has been prepared to provide some
idea of the costs of available software and hardware for personal
computers. Table 4-1 lists salary ranges and desired backgrounds
for the technical support staff needed to operate such systems, based
on advertisements posted in the past two years. Figure 4-3 is an
attempt to place all of the nominal costs in perspective.
The technical considerations discussed in previous sections
indicate that the desired accuracy of the modeling effort directly
affects the total costs of mathematical simulations. Thus managers
will want to determine the incremental benefits gained by increased
expenditures for more involved mathematical modeling efforts.
There are many economic theories which can be helpful in
determining the incremental benefits gained per increased level of
investment. The most straightforward of these are the cost-benefit
approaches commonly used to evaluate the economic desirability of
water resource projects. There are two generalized approaches in
common practice: the "benefit/cost ratio1 method and the 'net benefit*
method.
The benefit/cost ratio method involves tallying the economic
value of all benefits and dividing that sum by the total cost involved
in generating those benefits (i.e.; B/C = ?). A ratio greater than one
is required for the project to be considered viable, though there may
be sociopolitical reasons for proceeding with projects that do not
meet this criterion. Consider the example where a project is about to
get underway and has gained considerable social or political
momentum when the initial cost estimates begin to prove too low.
Not proceeding or substantially altering the work may be
economically wise; however, such a decision may be viewed as a
breach of faith by the public. Regardless of how this kind of situation
evolves, it is not uncommon for certain costs to be forgiven or
subsidized and this muddies the picture for incremental benefits or
trade-off analyses.
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Ave. Price
U.S. Dollars
2,000
1,500
1,000
500
1 23 4 56 78 9 10 11 12 13 14 15
Vendors of Ground-Water Models
1. International Ground
Water Model ingCtr.
2. ComputapipeCo.
3. Data Services, Inc.
4. GeoTrans, Inc.
5. Hydrosoft, Inc.
6. In Situ, Inc.
7. Irrisco Co.
8. Koch and Assoc.
9. KRS Enterprises, Inc.
10. Michael P. Spinks Co.
11.RockWare, Inc.
12. Sol utech Corp.
13.T.A. Prickett & Assoc.
14. JamesS. UlrickCo.
15. Watershed Research, Inc.
Figure4-2. Price ranges for IBM-PC ground-water models
available from various sources.
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Table 4-1. Desired backgrounds and salary ranges advertised
for positions requiring ground-water modeling.
Position Title:
Salary Offered:
Desired Bkgrnd:
Position Title:
Salary Offered:
Desired Bkgrnd:
Position Title:
Salary Offered:
Desired Bkgrnd
Position Title:
Salary Offered:
Desired Bkgrnd:
Position Title:
Salary Offered:
Desired Bkgrnd:
Position Title:
Salary Offered:
Desired Bkgrnd:
Position Title:
Salary Offered:
Desired Bkgrnd:
Hydrogeologist(Argonne Nat'l. Lab.)
$31,619-$48,876
familiarity and experience in field testing and
monitoring of ground-water flow and the use
of numerical models
Hydrologic Modeler (Univ. of Wisonsin)
$23,000-$25,000
primary strength in application of numerical
models to ground-water flow and chemical
transport; strong chemical background
Soil Scientist (U.S. EPA)
$31,619-$41,105
knowledge of (i) soil physics, (ii) processes
governing transport and fate of chem. and
bio. species, (iii) math, statistics and geostat;
and the ability to develop computer codes
Ground-Wtr .Hydrol. (Inyo Co. Wtr .Dept., CA)
starting up to $32,000
at least three years experience including field
work, surface/ground-water resource eval.,
environ, assess., flow modeling, FORTRAN
Hydrogeologist (S.W. Texas State Univ.)
$24.444-$30,096
academic training in hydrogeology, min. 2
years experience, knowledge of limestone
aquifers and computer operations
Geochemist (U.S. Nuclear Regulatory Comm.)
$23,170-$41,105
knowledge of solute and radionuclide
transport, including speciation, attenuation
(sorption) numerical modeling
Hydrogeol./Civil.Engr. (typical consulting firm)
'conmmensurate with experience'
strong background in applied ground-water
flow and contaminant transport modeling,
knowledge of federal/state regulations
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Ground-Water
Models ($5K)
Benefits -
25% Salary,
Service,
Expendables,
and Optional
Software
($10K)
IBM-PC/AT &
Accessories
w/Financing
($15K)
Salary: 1.0 FTE
-$40K/yr
Service,
Expendables,
and Optional
Software
($25K)
Benefits -
25% Salary
Ground-Water
Models ($15K)
Salary: 1.0 FTE
- $40K/yr
VAX 11'785
&Accesories
w/Financing
($125K)
Figure4-3. Costs of sustaining ground-water modeling
capabilities at two different computing levels for a
five-year period.
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The 'net benefit' method involves determining the arithmetic
difference of the total benefits and total costs (i.e.; B-C = ?). Here
the obvious criterion is that the proposed work result in a situation
where total benefits exceed total costs. This approach is most often
adopted by profit-making enterprises, because they seek to
maximize the difference as a source of income. The ratio method, by
contrast, has long been used by government agencies and other non-
profit organizations because they seek to show the simple viability
of their efforts irrespective of the costs involved.
In a very real sense, then, these two general economic
assessment methods stem from different philosophies. They share
many common difficulties and limitations, however. For example,
there is a need to predict the present worth of future costs and to
amortize benefits over the life of a project. The mechanics of such
calculations are well known, but they necessarily involve
substantial uncertainties. For example, the present worth of a series
of equal payments for equipment or software can be computed by
(White and others, 1984):
where: P is the present worth,
A is the series payment each interest period,
i is the interest rate per period, and
n is the number of interest periods.
Note, however, that the interest rate must be estimated; this has
fluctuated widely in the past two decades as a result of inflationary
and recessionary periods in our economy. The significance of this is
that a small difference in the interest rate results in tremendous
differences in the present worth estimate because of the exponential
nature of the equation.
It is also possible to compute the future worth of a present
investment, to calculate the percentage of worth annually acquired
through single payments or serial investments, and so on. One
should be aware that these methods of calculating costs belong to
the general family of 'single-objective', or 'mutually-exclusive
alternative' analyses which presuppose that the cost of two actions
is obtained by simple addition of their singly-computed costs. In
other words, the efforts being evaluated are presumed to have no
interactions. For some aspects of ground- water modeling efforts this
assumption may not be valid; e.g., one may not be able to specify
software and hardware costs independently. In addition, these
methods rely on the 'expected value concept1, wherein the expected
value of an alternative is viewed as the single product of its effects
and the probability of their occurence. This means that high-risk,
low-probability alternatives and low-risk, high-probability
alternatives have the same expected value.
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To overcome these difficulties it is necessary to use methods
which can incorporate functional dependencies between various
alternatives and which do not rely on the expected value concept,
such as multi-objective decision theories (Asbeck and Haimes, 1984;
Haimes and Hall, 1974; Haimes, 1981). A conceivable use would be
the estimation of lowered health risks associated with various
remedial action alternatives at a hazardous waste site. In such a
case the output of a contaminant transport model would be used to
provide certain inputs (i.e., water levels, contaminant
concentrations, etc.) to a health effects model, and it would convert
these into the inputs for the multiobjective decision model (e.g.,
probability of additional cancers per level of contaminant). The
primary difficulty with these approaches to cost-benefit analyses is
in clearly formulating the overall probabilities of the alternatives,
so that the objectives which are to be satisfied may be ranked in
order of importance. A related difficulty is the need to specify the
functional form of the inputs (e.g., the 'population distribution
function' of pumpage rates or contaminant levels). Historical
records about the inputs may be insufficient to allow their
functional forms to be determined.
Another problem compounding the cost-benefit analysis of
mathematical modeling efforts relates to the need to place an
economic value on intangibles. For example, the increased
productivity a manager might expect as a result of rapid machine
calculations replacing hand calculations may not be as definable in
terms of the improved quality of judgements made as it is in terms of
time released for other duties. Similarly, the estimation of improved
ground-water qaulity protection benefits may necessitate some
valuation of the human life and suffering saved (rather nebulous
quantities). Hence, there is often room for considerable 'adjustment'
of the values of costs and benefits. This flexibility can be used
inappropriately to improve otherwise unsatisfactory economic
evaluations. Lehr (1986) offers a scathing indictment of the
Tennessee Valley Authority for what he described as an 'extreme
injustice', perpetrated by TVA in the form of hydroelectric projects
which have 'incredibly large costs and negative cost benefit ratios'.
Finally, some costs and benefits may be incorrectly evaluated
because the data on which they are based are probabilistic and this
goes unrecognized. For instance, we often know the key parameters
affecting ground-water computations (i.e., hydraulic conductivity)
only to within an order-of-magnitude due to data collection
limitations. In these situations great caution must be exercised.
On the one hand, excessive expenditures may be made to ensure
that the model 'accurately1 simulates observed (though inadequate)
data. On the other, the artistic beauty of computer generated results
sometimes generates its own sense of what is 'right1, regardless of
apparent clashes with common sense. The reason the basic data are
uncertain is very important. Costs are not uncertain just because of
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lack of information about future interest rates; many times
expectations are not realized because of societal and technological
changes. Miller (1980) noted that EPA overestimated the cost of
compliance with its proposed standard for vinyl chloride exposure by
200 times the actual costs.
MANAGERIAL CONSIDERATIONS
The return on investments made to use mathematical models
rests principally with the training and experience of the technical
support staff applying the model to a problem and on the degree of
communication between those persons and management. In
discussing the potential uses of computer modeling for ground-
water protection efforts, Faust and others (1981) summarized by
noting that 'the final worth of modeling applications depends on the
people who apply the models'. Managers should be aware that a fair
degree of specialized training and experience are necessary to
develop and apply mathematical models, and relatively few
technical support staff can be expected to have such skills presently
(van der Heijde and others, 1985). 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.
What levels of training and experience are necessary to apply
mathematical models properly? Do we need 'Rennaissance1
specialists or can interdisciplinary teams be effective? The answers
to these questions are not clear-cut. From experience it is easy to see
that the more informed an individual is, the more effective he or she
can be. It is doubtful, however, that any individual can master each
discipline with the same depth of understanding that specialists in
those fields have. What is clear is that some working knowledge of
many sciences is necessary so that appropriate questions may be put
to specialists, and so that some sense of integration of the various
disciplines can evolve. In practice this means that ground-water
modelers have a great need to become involved in continuing
education efforts. Managers should expect and encourage this
because the benefits to be gained are tremendous, and the costs of
not doing so may be equally large. An ability to communicate
effectively with management is essential also.
Just as is the case with statistical analyses, an ill-posed problem
yields answers to the wrong questions ('I know you heard what I
said, but did you understand what I meant?'). Some of the questions
managers should ask technical support staff, and vice versa, to
ensure that the solution being developed is appropriate to the actual
problem are listed in Tables 4-2 through 4-4. Table 4-2 consists of
'screening level' questions, Table 4-3 addresses the need for correct
conceptualizations, and Table 4-4 is comprised of sociopolitical
concerns.
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Table 4-2. Screening-level questions to help ground-water
managers focus mathematical modeling efforts.
General Problem Definition
(1) What are the key issues; quantity, quality, or both?
(2) What are the controlling geologic, hydrologic, chemical and
biological features?
(3) Are there reliable data (proper field scale, quality
controlled, etc.) for preliminary assessments?
(4) Do we have the model(s) needed for appropriate
simulations?
Initial Responses Needed
(1) What is the time-frame for action (imminent or long-term)
(2) What actions, if taken now, can significantly delay the
projected impacts?
(3) To what degree can mathematical simulations yield
meaningful results for the action alternatives, given
available data?
(4) What other techniques or information (generic models, past
experiences, etc.) would be useful for initial estimates?
Strategies for Further Study
(1) Are the critical data gaps identified; if not, how well can
simulations determine the specific data needs?
(2) What are the trade-offs between additional data and
i ncreased certai nty of the si mulations?
(3) How much additional manpower and resources are
necessary for further modeling efforts?
(4) How long will it take to produce useful simulations,
including quality control and error-estimation efforts?
On another level of communication, managers should appreciate
how difficult it will be to explain the results of complicated models to
non-technical audiences such as in public meetings and courts of
law. Many scientists find it a trying exercise to discuss the details of
their labors without the convenience of the jargon of their discipline.
Some of the more useful means of overcoming this limitation involve
the production of highly simplified audio-visual aids, but this
necessarily involves a great deal of work. The efforts which will be
required to sell purportedly self-explanatory graphs f-om computer
simulations may rival the efforts spent on producing the
simulations initially.
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Table 4-3. Conceptualization questions to help ground-water
managers focus mathematical modeling efforts.
Assumptions and Limitations
(1) What are the assumptions made, and do they cast doubt on
the model's projections for this problem?
(2) What are the model's limitations regarding the natural
processes controlling the problem; can the full spectrum of
probable conditions be addressed?
(3) How far in space and time can the results of the model
simulations be extrapolated?
(4) Where are the weak spots in the application, and can these
be further minimized or eliminated?
Input Parameters and Boundary Conditions
(1) How reliableare the estimates of theinput parameters; are
they quantified within accepted statistical bounds?
(2) What are the boundary conditions, and why are they
appropriate to this problem?
(3) Have the initial conditions with which the model is
calibrated been checked for accuracy and internal
consistency?
(4) Are the spatial grid design(s) and time-steps of the model
optimizedforthis problem?
Quality Control and Error Estimation
(1) Have these models been mathematically validated against
other solutions to this kind of problem?
(2) Has anyone field verified these models before, by direct
applications or simulation of controlled experiments? Have
these models been mathematically validated against other
solutions to this kind of problem?
(3) How do these mdoels compare with others in terms of
computational efficiency, and ease of use or modification?
(4) What special measures are being taken to estimate the
overall errors of the simulations?
CHAPTER SUMMARY
Mathematical models can be helpful tools to managers of
ground-water resource programs. Models may be used for testing
hypotheses about conceptualizations and to generate better
understanding of important physical, chemical, and biological
processes which affect ground-water resources. The possible
outcomes of complex problems can be addressed in great detail, if
66
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Table4-4. Sociopolitical questions to help ground-water
managers focus mathematical modeling efforts.
Demographic Considerations
(1) Is there a larger population endagered by the problem
than we are able to provide sufficient responses to?
(2) Is it possible to present the model's results in both non-
technical and technical formats, to reach all audiences?
(3) What role can modeling play in public information efforts?
(4) How prepared are we to respond to criticism of the
model(s)?
Political Constraints
(1) Are there non-technical barriers to using this model, such
as 'tainted by association' with a controversy elsewhere?
(2) Do we have the cooperation of all involved parties in
obtaining the necessary data and implementing the
solution?
(3) Are similar technical efforts for this problem being
undertaken by friend or foe?
(4) Can the results of the model simulations be turned against
us; are the results ambiguous or equivocal?
Legal Concerns
(1) Will the present schedule allow all regulatory requirements
to be met in a timely manner?
(2) If we are dependent on others for key inputs to the
model(s), how do we recoup losses stemming from their
non-performance?
(3) What liabilities are incurred for projections which later
turn out to be misinterpretations originating in the model?
(4) Do any of the issues relying on the application of the
model(s) require the advice of attorneys?
adequate data are available. Mathematical modeling is neither
simple nor impossible. Its successful application, however, relies
heavily on the expertise of the modeler and the degree of
communication with management.
The use of mathematical models in the decision-making process
means that the user will inevitably incur certain liabilities.
Anticipation of problem areas and some sensitivity to the possible
misuses of models will greatly minimize potential liabilities, as will
rigorous quality control programs. A number of direct and indirect
67
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costs attend the use of models, not the least of which involve efforts
to obtain and retain specialized experts.
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