United States
Environmental Protection
Agency
Office of
Research and
Development
Office of Solid Waste
and Emergency
Response
August 1989
SEPA
Superfund
Ground Wafer Issue
Contaminant Transport in Fractured Media: Models for Decision Makers
Stephen G. Schmelling and Randall R. Ross
The Regional Superfund Ground Water Forum is a group of
ground-water technical specialists, representing EPA's Regional
Superfund Offices, organized to exchange up-to-date information
related to ground-water remediation at Superfund sites. Site
characterization of fractured rock sites, and modeling ground-
water flow and contaminant transport in fractured media, have
been identified by the EPA Regional Superfund Ground Water
Forum as major issues of concern for decision-makers at many
Superfund sites. The ability to reliably predict the rate and
direction of ground-water flow and contaminant transport in
fractured rock systems would be of great value in planning and
implementing the remediation of contaminated aquifers. This
paper summarizes the current status of modeling ground-water
flow and contaminant transport in fractured rock systems. A
companion paper summarizing the status of site characterization
at fractured rock sites is in preparation.
For further information contact Stephen G. Schmelling, RSKERL-
Ada, FTS 743-2434; Randall R. Ross, RSKERL-Ada, FTS 743-
2355.
Summary
Mathematical models have a potentially useful role to play in
arriving at a decision on the remedial action to be taken at a
contaminated site. Where there Is a need for a quantitative
estimate of the threat to public health resulting from a particular
course of action, of the estimated cost and time of clean-up for
a particular remediation strategy, or of the results of other
actions to be taken at a contaminated site, mathematical
models have a greater potential to provide the needed information
than any other approach to the problem. For contaminated
sites in fractured rock, however, this potential has yet to be real-
ized.
The development of predictive models for ground-water flow
and contaminant transport in fractured rock systems is an active
area of research, but field-validated models that are directly
applicable to the remediation of contaminated sites are not yet
available. Nonetheless, when used with appropriate site
characterization data, the available models can be helpful in
developing a qualitative understanding of the behavior of the
fractured rock system and the interactions of contaminants with
the system.
Selection of a suitable model requires the model userto have a
specific objective in mind. For example, is the purpose of the
modeling eff ortto determine the location of additional monitoring
wells, to design optimal well placement for hydraulic control
during site remediation, to interpret existing data, ortodetermine
sources or predict the fate of a pollutant? No single model will
serve all purposes. The choice of model will depend on the
system conditions, the decision to be made, and the extent and
availability of site characterization data.
Before ground-water models can be applied to any system,
fractured or not, it is necessary to have extensive data about
that system. Data are needed to (1) select or develop an ap-
propriate model based on the processes acting on the system;
(2) define boundaries in space and time of the domain in which
these processes are acting; (3) determine the state of the
system at some point In time from which predictions, either
forward or backward In time, can be made; and (4) estimate the
effects of future stresses or inputs to the system (Konikow and
Mercer, 1988). Modeling and data collection are complementary
activities, neither being a substitute for the other. Not only are
data necessary for successful modeling, but modeling results
may be used to guide data collection efforts.
Superfund Technology Support Centers for Ground Water
Robert S. Kerr Environmental
Research Laboratory
Ada, OK
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Because of the heterogeneous and anisotropto nature of fractures
In the subsurface, the data requirements for modeling the
movement of water and contaminants In fractured media are
somewhat different than the requirements for modeling more
homogeneous unconsolidated porous media. The development
of techniques to characterize the hydrogeologic properties of
fractured rock systems has proceeded in parallel with the
development of models. These techniques are often more
complex and more difficult to interpret than analogous techniques
used In unconsolidated media.
There are at least four categories of models to describe flow
and transport In fractured rock systems. (1) Models developed
foruse In unconsolidated porous media have been successfully
applied to certain fractured rock systems. These models consider
the fractured rock system as an equivalent porous medium
(EPM). EPM models are more likely to accurately predict
ground-water flux than to correctly predict solute transport
(Endo, et al. 1984). (2) A second category of fractured rock
models explicitly considers discrete fractures. The extensive
data required by discrete fracture models for fracture system
characterization limit their use to sites with a relatively small
numberof well defined fractures. (3) Athird category of models
represents the fractured system by aset of matrix blocks of well
defined geometry. Such models are largely research tools that
are useful for enhancing our conceptual understanding of
pollutant transport In fractured rock. (4) A fourth category of
models uses a stochastic approach to describe the fracture
distribution. At the present time these are research models. It
Is Important to note again that the choice of an appropriate
model depends on the conditions present at the site, and on the
decision to be reached by using the model.
Before discussing models In more detail, Section II provides
some basic Information on ground-water flow and contaminant
transport In f ractu red rock systems. Section III briefly discusses
methods of characterizing contaminated fractured rock sites.
SRe characterization and modeling are complementary activities
and each Is essential to the other. The last part of the paper
discusses the conceptual basis of ground-water models and
gives some specific examples of the types of models that are
publicly available.
Fractured Rock Systems
Development of the theory of flow through porous media began
with experimental work by Henri Darcy, published in 1857. The
study offluld flow through fractured rock was first developed in
the petroleum industry. These studies resulted from observations
that oil and gas production could be significantly increased by
fracturing the producing formations near the well bore (Duguld
and Lee, 1977). Gale (1982) notes thatthe first comprehensive
experiments on flow through artificial fractures were conducted
In the early 1950's. During the past decades, the amount of
research onflow and transport In unconsolidated porous media
has greatly exceeded that devoted to fractured media. This is
due In part to the complexity of fractured rock systems and the
lack of economic Incentives.
Most fractured rock systems consist of rock blocks bounded by
discrete discontinuities comprised of fractures, joints, and
shear zones, usually occurring in sets with similar geometries
(Witherspoon, et al., 1987). Fractures may be open, mineral-
filled, deformed, or any combination thereof (Nelson, 1985).
Open fractures may provide conduits for the movement of
ground water and contaminants through an otherwise relatively
impermeable rock mass. Mineral-fllledfractures are filled either
partially or completely by secondary cementing materials such
as quartz orcarbonate minerals, thereby reducing oreliminating
fracture porosity and permeability. Deformed fractures may be
infilled with permeability-reducing gouge, a finely abraded material
produced by the cataclasis of grains In contact across a fault
plane during displacement of the rock masses. Other deformed-
fracture features include slickensides, which are striated surfaces
formed by frictional sliding along a fault plane. Slickensides
reduce permeability perpendicularto the fracture plane, but the
mismatch of fracture surfaces may increase permeability along
the fracture plane. Very little displacement is necessary to
produce gouge or slickensides. The deposition of a thin layer
of low permeability material, fracture skin, may prevent the free
exchange of fluids between the rock matrix and fracture (Moench,
1984).
Major factors affecting ground-water flow through fractured
rock include fracture density, orientation, effective aperture
width, and the nature of the rock matrix. Fracture density
(number of fractures per unit volume of rock) and orientation
are Important determinants of the degree of interconnection of
fracture sets, which is a critical feature contributing to the
hydraulic conductivity of afractured rock system (Witherspoon,
et al., 1987). Only interconnected fractures provide pathways
for ground-water flow and contaminant transport. Fractures
oriented parallel to the hydraulic gradient are more likely to
provide effective pathways than fractures oriented perpendicular
to the hydraulic gradient. Fractured rock systems simulate
equivalent porous media when the fracture apertures are
constant, the fracture orientations are randomly distributed and
the fracture spacing is small relative to the scale of the system
(Long, etal., 1982).
The cross-sectional area of a fracture will have an important
effect on flow through the fracture. Fracture-flux is proportional
to the cube of the fracture aperture (distance between rock
blocks). The relationship between flux and aperture appears to
be true for fractures with apertures greater than 10 microns
(Witherspoon, et al., 1987). Fracture apertures, and therefore
flow through fractures, are highly stress-dependant, and generally
decrease with depth (Gale, 1982).
The nature of the rock matrix plays an important role in the
movement of water and contaminants through fractured rock
systems. Metamorphic and Igneous rocks generally have very
low primary porosity and permeability. Fractures may account
for most of the permeability in such systems and the movement
of water and contaminants into and out of the rock matrix may
be minimal. Sedimentary rocks generally have higher primary
porosity and varying permeability. Coarse-grained materials
such as sandstone have relatively high primary porosity and
significant matrix permeability. Fine-grained materials such as
shale have high primary porosity and low permeability. Fractures
may enhance the permeability of all types of materials. High
porosity allows significant storage of water and contaminants in
the rock matrix. Authigenic clays formed during the weathering
of certain rock-forming minerals may significantly reduce the
porosity and permeability of the fractures and rock matrix.
Rates of contaminant migration into and out of the rock matrix
will depend on the permeability of the matrix, the presence of
low-permeability fracture skins, and the matrix diffusion coefficient
of the contaminant.
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A completedescription of a contaminated fractured rocksystem
would include data on the dimensions of the system, the length,
aperture width, location, and orientation of each fracture, the
hydraulic head throughout the system, the porosity and
permeability of the rock matrix, the sources of water and
contaminants, the nature and concentrations of the contaminants
throughout the system, and the chemical interactions between
the contaminants and rock matrix. Presently, collection of such
detailed information is neither technically possible, nor
economically feasible on the scale of most contaminated sites.
However, most ground-water models, especially those describing
contaminant transport, require this type of information as input.
In general, the more detailed the site characterization, the
greater the probability of success in modeling the site. The
accuracy of flow and transport modeling in fractured rock
systems is highly dependent on the accuracy and extent of site
characterization data.
Hydrogeologic Characterization Methods
Hydrogeologic characterization methods are usually most
successful when used in conjunction with one another. These
methods may include coring, aquifertests, tracertests, surface
and borehole geophysical techniques, borehole flowmeters,
and othertools. Important information may be gathered before,
during, and after drilling operations.
Coring
Core material obtained during drilling operations can yield
information onthedensity, location, and orientation of fractures,
and provide samples for physical and chemical testing. Information
concerning fracture roughness and mineral precipitation on
fracture surfaces can also be obtained from core samples.
Information collected during air hammerdrilling operations with
open hole completions includes the location of major water
bearing fractures, changes in hydraulic head with depth, and
changes in the ground-water geochemistry. In certain instances,
cores may be taken diagonally to intercept near vertical fractures
and determine fracture azimuth. A major drawback of coring is
the relatively high cost. However, the information obtained
from coring operations often makes this characterization technique
cost-effective.
Aquifer Tests
Aquifertests, including constant rate pumping tests and slug
tests, can provide hydraulic conductivity and anisotropy information
for fractured formations. These tests also allow the estimation
of average fracture apertures of a medium. The same tests that
are commonly used for unconsolidated porous media can be
used for fractured media. The test results, however, will
generally be more difficult to interpret. Barker and Black (1983)
note that transmissivity values will always be overestimated by
applying standard type curve analysis to fissured aquifers.
Other more complextests, such as cross-hole packertests, are
particularly applicable to fractured media.
Hsieh, et al. (1985a,b) describe a method of determining the
three-dimensional hydraulic conductivity tensor. The method
consists of injecting fluid into, or withdrawing fluid out of,
selected intervals isolated by inflatable packers and monitoring
the transient response in isolated intervals of neighboring wells.
This method is applicable to situations where the principal
directions of the hydraulic conductivity tensor are not neces-
sarily vertical and horizontal. A minimum of six cross-hole tests
is required to determine the six Independent components of the
hydraulic conductivity tensor. In practice, scatter in the data Is
likely to be such that more than six cross-hole tests will be
required. Hsieh, et al. conclude that failure to fit data to an
ellipsoidal representation indicates that the rock cannot be
represented by an equivalent, continuous, uniform, anisotroplc
medium on the scale of the test. Depending on the application
to be made, the test may be repeated on a larger scale, orthe
data may be interpreted in terms of discrete fractures of the
system.
Aquifer tests can provide information on aquifer anisotropy,
heterogeneity and boundary conditions, but do not provide
information on the range of fracture apertures or surface
roughness. One of the major drawbacks associated with long-
term aquifer testing is storage and treatment of the large
volume of water discharged during the test.
Tracer Tests
Tracer tests can provide information on effective porosity,
dispersion and matrix diffusion, generally unobtainable from
other hydrogeologic methods. Tracer tests can either be con-
ducted under natural gradient or forced gradient conditions.
The primary disadvantages of tracer tests include the time,
expense, numberof necessary sampling points, and difficulties
associated with data interpretation. However, the Important
information provided by tracertests is difficult to obtain by any
other means. Davis, et al. (1985) provide a good Introduction
to the use of tracers in ground-water investigations.
Geophysical Tools
Both surface and borehole geophysical methods can be used
to characterize fractured rock systems. Application of surface
geophysical methods such as ground-penetrating radar,
magnetometer surveys, and seismic and remote sensing
techniques should be evaluated before a drilling program is
initiated. These techniques may provide Insight to potential
monitoring well locations by revealing the orientation of major
fracture systems. However, the correlation of major surface
geophysical features with contaminant transport processes in
fractured media has yet to be thoroughly characterized.
Borehole walls are usually less susceptible to fractures Induced
during drilling operations than cores. Borehole geophysical
techniques can usually provide a more reliable estimate of
fracture density than cores. However, as Indicated by Nelson
(1985) in a review of down-hole techniques, responses used to
detect fractures on well logs are non-unique and require
detailed knowledge of the tool and the various rock property
effects, which could cause fracture-like responses. Borehole
geophysical methods include acoustic, electrical resistivity,
caliper, gamma and other high energy borehole logging
techniques. The acoustic televiewer presents a continuous
image of the acoustic response of the borehole face, and can
detect fracture apertures as small as one millimeter. This
oriented tool also allows the determination of fracture orientations.
Caliper logs are best suited for determining relative fracture
intensity in continuous, competent rock. Advances In electronic
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and desorptlon assumes that the processes are described by
linear Isotherms and Ignores sorptlon kinetics. Some models
account separately for sorptlon processes In the fractures and
within the rock matrix. In porous rocks, the available surface
area within the matrix Is likely to be so much greater than that
In the fractures that sorptlon within the matrix will probably be
more Important than sorptlon in the fractures, assuming that the
contaminants have time to diffuse Into the matrix.
None of the available models appear to explicitly account for
Ion-exchange processes. While many of the organic chemicals
of concern are not Ionized In solution, other contaminants such
as heavy metals could be, depending on the pH of the system.
Little experimental or theoretical work has been done In this
area; more work Is needed.
Radioactive Decay
Much of the work on modeling flow and transport in fractured
systems has been motivated by concerns about the disposal of
radioactive waste. Consequently, there are a number of
models that account for the radioactive decay of single
radtonuclldes and radlonucllde chains.
Chemical Reactions and Biological Processes
Very little work has been done that deals specifically with
chemical reactions and biological processes in fractures. None
of the models account forthese processes. This is an important
topic, and more work needs to be done on It.
Multiphase Row
Models forf low and transport In fractured systems appear to be
limited to single-phase flow. That Is, they can simulate the flow
of water alone, or the transport of contaminants that are
dissolved In water. The models cannot simulate the flow of a
system of water and an Immiscible phase such as an oily waste,
nor the transport of a contaminant dissolved in an Immiscible
phase. At the present time neither the capability of modeling
multiphase flow In homogeneous media, nor the capability of
modeling solute transport In fractured systems Is advanced
enough to Implement a practical code for modeling multiphase
flowlnfracturedsystems(Streile and Simmons, 1986). Schwille
(1988) has studied the qualitative behavior of dense non-
aqueous liquids In laboratory models. His book contains a
number of Interesting photographs. This is another area where
more research Is needed.
Available Models
This section describes types of models that are available to
describe flow and transport In fractured rock systems. Specific
models will not be mentioned by name because the Information
Is likely to become outdated In a short period of time. A good
starting place for obtaining Information on publicly available
models is the International Ground Water Modeling Center,
located at Butler University In Indianapolis, Indiana. They can
provide a list of available models and Information on specific
models on the list.
Freeze and Cherry (1979) describe the development and use of
a mathematical ground-water model as "a four-step process,
involving (1) examination of the physical problem, (2) replace-
ment of the physical problem by an equivalent mathematical
problem, (3) solution of the mathematical problem with accepted
techniques of mathematics, and (4) interpretation of the mathe-
matical results in terms of the physical problem." Successful
modeling of a ground-watercontamination problem, whether in
fractured rock or not, requires that all four of these steps be
carried out correctly. While step (3), solution of the mathe-
matical problem, could conceivably be carried out by a person
who knew almost nothing about ground water, successful
completion of the other three steps requires a thorough knowledge
of hydrogeology in general, along with specific knowledge of the
hydrogeology of the site to which the model Is to be applied.
Fractured systems present several difficulties which hinderthe
replacement of the physical problem by an equivalent mathe-
matical problem - step (2). One difficulty is that the spatial
distribution of the fractures and the way in which they control the
flow is usually not known, nor Is it even knowable In a practical
sense. A second difficulty is that even if this Information were
available, including it in the mathematical problem would make
the mathematical problem so complex that a solution could not
be found. As a result, all mathematical models Include certain
assumptions about, and simplifications of, the actual physical
problem. Forexample.the model may assume thatthefractures
are of uniform width with parallel sides, and/or that they form a
regular geometric pattern. Comparable assumptions are also
made about other physical, chemical, and biological processes.
Consequently, the mathematical model provides only an
approximate description of the physical system under study.
The model can still be very useful, but anyone using a mathematical
model should be fully aware of these assumptions and
simplifications and their effect on the appropriateness of the
model for the problem of interest.
Mathematical models that describe ground-water systems are
usually written in terms of partial differential equations. If the
equations are simple enough, the solution to the equations can
be expressed in a closed mathematical form (e.g., a formula).
This type of solution is called an analytical solution. More
generally, the equations in the model are too complex to find an
analytical solution, and a numerical method must be used to
solve the problem. Models forfractured systems include those
with analytical solutions as well as those with numerical solutions.
For either type of solution, the product available to the model
user is a computer code in a high level language such as
FORTRAN. The hardware requirements to run the code will
vary from a personal computer (PC) to a main-frame type of
computer. As expected, the more complex models usually have
greater hardware requirements.
Models with Analytical Solutions
Models for which analytical solutions have been obtained are
basically one dimensional. An example of this type of solution
is a model describing solute transport in a single fracture or a set
of parallel fractures. Processes that are included In the model
include diffusion in and out of the rock matrix along a direction
perpendicular to the plane of the fracture, adsorption on the
fracture face and in the rock matrix, and radioactive decay. The
solution to this problem has been published in the open literature
(Sudicky and Frind, 1982) and is simple enough that the
computer code can run on a personal computer.
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To arrive at an analytical solution for this problem, the parallel
fracture model assumes that the fracture or set of fractures has
a uniform aperture and is in a homogeneous rock matrix, and
that the fractures in a set of parallel fractures are uniformly
spaced. To use this model, one must have an estimate or
measurement of the following parameters: the flow velocity in
the fracture, the longitudinal dispersivity in the fracture, the
fracture aperture or width, the fracture spacing for a set of
fractures, the matrix porosity, the matrix tortuosity, the diffusion
coefficient of the solute in water, the fracture retardation factor
or partition coefficient, the matrix retardation factor or partition
coefficient, and the half-life if the solute is a radioactive species.
This model obviously describes a highly idealized situation and
would not be a suitable predictive tool for dealing with a real
contamination problem. However, it could have some use in
building an understanding of the system and the interactions of
the pollutants within the system. It is easy to vary the effect of
the fracture apertures, fracture spacing, matrix porosity, and so
forth, and see the effect that each of these parameters has on
the rate at which pollutants move through the system. Used
with the proper degree of professional judgement, the results of
the model could provide guidance in making a decision. One
possible application would be in comparing solute transport in
two fractured systems from which cores had been collected to
provide information on the parameters that are included in the
model.
Analytical solutions have also been published in the open
literature for dual-porosity, or "two-region" models of one-
dimensional flow through systems composed of porous blocks
with well-defined geometry (van Genuchten and Dalton, 1986).
Those geometries for which solutions are available include
close-packed spheres, hollow cylindrical macropores, close-
packed solid cylinders, and rectangular blocks. Data and
hardware requirements for running these codes are similar to
those for the parallel crack model.
Models with Numerical Solutions
Models for which only numerical solutions are available are
often referred to as numerical models. Codes forthese models
are likely to require more input data and greater computer
power than those for analytical models. The reward for this
extra work is that one can investigate more complicated problems
using numerical models than one can using only analytical
models.
One example of a numerical model for fractured rock systems
is a two-dimensional model that can simulate both ground-
water flow and contaminant transport in a fractured aquifer.
The step up from a one-dimensional system to a two-dimensional
system allows one to model a more complex situation, but it
also requires a more complex set of differential equations and
a more complex code. The model uses a dual porosity
approach and allows for some specific fracture geometries.
Processes that are included in the model include advective-
dispersive transport in the fractures, diffusion in the matrix
blocks, sorption in the fractures and in the matrix, and radionuclide
decay chains.
This two-dimensional code requires data on the system
dimensions, the transmissivity, the storage coefficient, and the
fracture aperture and spacing if it is to be used to predict
ground-water fipw. The input data requirements for predicting
solute transport include all of those listed for the one-dimensional
analytical model described above plus values for the solute
concentrations at the system boundaries.
Whi'e codes like this have utility for understanding system
behavior, they should not be used as predictive tools. Like all
ground-water models, they will be most useful when applied by
a person with the necessary training and experience-typically,
a professional hydrogeologist. To quote a recent report (van
der Heijde, et al., 1988), "The application of computersimulation
models to field problems is a qualitative procedure, a combination
of science and art."
There are a number of numerical models that have been written
to model flow and transport through systems of randomly
oriented fractures and compare the results with experimental
data. Theresultsofthisworkhavebeenof use in understanding
the nature of flow and transport in fractured media, but this type
of modeling is a research effort at this time.
Summary Remarks
The development of models to enhance understanding of and to
predict contaminant transport in fractured rock systems continues
to be an active area of research. Reliable, field-validated
models that can be used to predict the results of clean-up
scenarios at contaminated sites are not yet available. The
models that are available help in developing an understanding
of the behavior of the fractured rock system.
The application of mathematical models to contamination in
fractured rock systems is hampered by difficulties in at least two
major areas. The first problem is site characterization - the
collection of the necessary data to adequately describe the
geologic and hydrologic properties of the system. Mathematical
modeling is not a substitute for collecting data. In fact, data
collection is an essential part of modeling the behavior of a site.
Collecting the data required by existing models is difficult and
expensive, and in many cases not possible with present techniques.
More research Is needed to find better ways to measure the
properties of fractured rock systems. Conversely, there maybe
value in developing models that require data that can be
collected.
The second problem is model validation-comparing the results
of modeling to results obtained in the field. Validation of models
is necessary if decision makers are to have confidence in them
and be able to use them in planning and carrying out remedial
work. Research is being doneto validate models of contaminant
transport in fractured rock systems, but more work is needed.
One problem with model validation studies is the shortage of
data sets for sites with a variety of geological and hydrogeological
characteristics. This is where cooperation and coordination
between those in the research community and those charged
with remediating contaminated sites could prove mutually
beneficial.
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