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4
Transport
INTRODUCTION
Ground water contamination occurs when chemicals are detected
where they are not expected and not desired. This situation is a result
of movement of chemicals in the subsurface from some source (per
haps unknown) that may be located some distance away. Ground
water contamination problems are typically advection dominated
(see "Dissolved Contaminant Transport" in Chapter 2), and the pri
mary concerns in defining and treating ground water contamination
problems must initially focus on physical transport processes. If a
contaminant is chemically or biologically reactive, then its migration
tends to be attenuated in relation to the movement of a nonreactive
chemical. The considerations of reaction add another order of mag
nitude of complexity to the analysis of a contamination problem, in
terms of both understanding and modeling. Regardless of the reac
tivity of a chemical, a basic key to understanding and predicting its
movement lies in an accurate definition of the rates and direction of
ground water flow.
The purpose of a mode} that simulates solute transport in ground
water is to compute the concentration of a dissolved chemical species
in an aquifer at any specified place and time. Numerical solute trans
port models were first developed about 20 years ago. However, the
modeling technology did not have a long time to evolve before a
113
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114
GROUND WATER MODELS
great demand arose for its application to practical and complex field
problems. Therefore the state of the science has advanced from the
ory to practice in such a short time (considering the relatively small
number of scientists working on this problem at that time) that a
large base of experience and hypothesis testing has not accumulated.
It appears that some practitioners have assumed that the underly
ing theory and numerical methods are further beyond the research,
development, and testing stage than they actually are.
Most transport models include reaction terms that are math
ematically simple, such as decay or retardation factors. However,
these do not necessarily represent the true complexities of many
reactions. In reality, reaction processes may be neither linear nor
equilibrium controlled. Rubin (1983) discusses and classifies the
chemical nature of reactions and their relation to the mathematical
problem formulation.
Difficult numerical problems arise when reaction processes are
highly nonlinear, or when the concentration of the solute of interest is
strongly dependent on the concentration of numerous other chemical
constituents. However, for field problems in which reactions sig
nificantly affect solute concentrations, simulation accuracy may be
limited less by mathematical constraints than by data constraints.
That is, the types and rates of reactions for the specific solutes and
minerals in the particular ground water system of interest are rarely
known and require an extensive amount of data to assess accurately.
Mineralogic variability may be very significant and may affect the
rate of reactions, and yet be essentially unknown. There are very
few documented cases for which deterministic solute transport mod
els have been applied successfully to ground water contamination
problems involving complex chemical reactions.
Many contaminants of concern, particularly organic chemicals,
are either immiscible or partly miscible with water. In such cases,
processes in addition to those affecting a dissolved chemical may
significantly affect the fate and movement of the contaminant, and
the conventional solute transport equation may not be applicable.
Rather, a multiphase modeling approach may be required to rep
resent phase composition, interphase mass transfer, and capillary
forces, among other factors (see Pinder and Abriola, 1986~. This
would concurrently impose more severe data requirements to de
scribe additional parameters, nonlinear processes, and more complex
geochemical and biological reactions. Faust (1985) states, "Unfortu
nately, data such as relative permeabilities and capillary pressures
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115
for the types of fluids and porous materials present in hazardous
waste sites are not readily available." Welldocumented and efficient
multiphase models applicable to contamination of ground water by
immiscible and partly miscible organic chemicals are not yet gener
ally available.
TRANSPORT OF CONSERVATIVE SOLUTES
Much of the recently published research literature on solute
transport has focused on the nature of dispersion phenomena in
ground water systems and whether the conventional solute transport
equation accurately and adequately represents the process causing
changes in concentration in an aquifer. In discussing the development
and derivation of the solute transport equation, Bear (1979, p. 232)
states, "As a working hypothesis, we shall assume that the dispersive
flux can be expressed as a Fickian type law." The dispersion process
is thereby represented as one in which the concentration gradient is
the driving force for the dispersive flux. This is a practical engineer
ing approximation for the dispersion process that proves adequate
for some field problems. But, because it incorrectly represents the
actual physical processes causing observed dispersion at the scale of
many field problems, which is commonly called macrodispersion, it
is inadequate for many other situations.
The dispersion coefficient is considered to be a function both
of the intrinsic properties of the aquifer (such as heterogeneity in
hydraulic conductivity and porosity) and of the fluid flow (as rep
resented by the velocity). Scheidegger (1961) showed that the dis
persivity of a homogeneous, isotropic porous medium can be defined
by two constants. These are the longitudinal dispersivity and the
transverse dispersivity of the medium. Most applications of trans
port models to ground water contamination problems documented
to date have been based on this conventional formulation, even when
the porous medium is considered to be anisotropic with respect to
flow.
The consideration of solute transport in a porous medium that
is anisotropic would require the estimation of more than two disper
sivity parameters. For example, in a transversely isotropic medium,
as might occur in a horizontally layered sedimentary sequence, the
dispersion coefficient would have to be characterized on the basis
of six constants. In practice, it is rare that field values for even
the two constants longitudinal and transverse dispersivity can be
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116
GROUND WATER MODELS
defined uniquely. It appears to be impractical to measure as many
as six constants in the field. If just single values of longitudinal and
transverse dispersivity are used in predicting solute transport in an
anisotropic medium when the flow direction ~ not always parallel to
the principal directions of anmotropy, then dispersive fluxes will be
either overestimated or underestimated for various parts of the flow
system. This can sometimes lead to significant errors in predicted
concentrations.
Dispersion and advection are actually interrelated and are de
pendent on the scale of measurement and observation and on the
scale of the model. Because dispersion is related to the variance of
velocity, neglecting or ignoring the true velocity distribution must
be compensated for in a mode! by a correspondingly higher value
of dispersivity. Domenico and Robbins (1984) demonstrate that a
scaling up of dispersivity will occur whenever an (nl) dimensional
mode} is calibrated or used to describe an edimensional system.
Davis (1986) used numerical experiments to show that variations in
hydraulic conductivity can cause an apparently large dispersion to
occur even when relatively small values of dispersivity are assumed.
Similarly, Goode and Konikow (1988) show that representing a tran
sient flow field by a mean steaclystate flow field, as is commonly
done, inherently ignores some of the variability in velocity ancI must
also be compensated for by increased values of dispersivity.
The scale dependence of dispersivity coefficients (macrodisper
sion) is recognized as a limitation in the application of conventional
solute transport models to field problems. Anderson (1984) and
Gelhar (1986) show that most reported values of longitudinal dis
persivity fall in a range between 0.01 and 1.0 on the scale of the
measurement (see Figure 4.~. Smith and Schwartz (1980) conclude
that macrodispersion results from largescale spatial variations in
hydraulic conductivity and that the use of relatively large values of
dispersivity with uniform hydraulic conductivity fields is an inapt
propriate basis for describing transport in geologic systems. It must
be recognized that geologic systems, by their very nature, are com
plex, threedimensional, heterogeneous, and often anisotropic. The
greater the degree to which a mode! approximates the true hetero
geneity as being uniform or homogeneous, the more must the true
variability in velocity be incorporated into larger dispersion coeffi
cients. We will never have so much hydrogeologic data available that
we can uniquely define all the variability in the hydraulic properties
of a geologic system; therefore, assumptions and approximations are
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117
Sand, Gravel,
Sandstone
Limestone, Basalt
· Granite, & Schist
100
Oh
llJ
In
10
z
At
o
1
.
I`
· / ~
/
/
/ ·
·~.
By
a/ ·
~/
~
.
A_
·,
/
in)/
· /
· /
.
/ 
.
1 0 1 00 1 ,000
DISTANCE (m)
FIGURE 4.1 Variation of dispersivity with distance (or scale of measurement).
SOURCE: Modified from Anderson, 1984.
always necessary. Clearly, the more accurately and precisely we can
define spatial and temporal variations in velocity, the lower will be
the apparent magnitude of dispersivity. The role of heterogeneities
is not easy to quantify, and much research is in progress on this
problem.
An extreme but common example of heterogeneity is rocks that
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118
GROUND WATER MODELS
exhibit a dominant secondary permeability, such as fractures or so
lution openings. In these types of materials, the secondary perme
ability channels may be orders of magnitude more transmissive than
the porous matrix of the bulk of the rock unit. In these settings,
the most difficult problems are identifying where the fractures or so
lution openings are located, how they are interconnected, and what
their hydraulic properties are. These factors must be known in or
der to predict flow, and the flow must be calculated or identified in
order to predict transport. Anderson (1984) indicates that where
transport occurs through fractured rocks, diffusion of contaminants
from fractures to the porous rock matrix can serve as a significant
retardation mechanism, as illustrated in Figure 4.2. Modeling of flow
and transport through fractured rocks is an area of active research,
but not an area where practical and reliable approaches are readily
available. Modeling the transport of contaminants in a secondary
permeability terrain is like predicting the path of a hurricane with
out any knowledge of where land masses and oceans are located or
which way the earth is rotating.
Because there is not yet a consensus on how to describe, account
for, or predict scaledependent dispersion, it is important that any
conventional solute transport mode} be applied to only one scale
of a problem. That is, a single model, based on a single value of
dispersivity, should not be used to predict both nearfield (near the
solute source) and farfield responses. For example, if the clispersivity
value that is used in the mode} is representative of transport over
distances on the order of hundreds of feet, it likely will not accurately
predict dispersive transport on smaller scales of tens of feet or over
D I f FU
POROU S
ROCK MATRIX
FRACTURE
F LOW
FIGURE 4.2 Flow through fractures and diffusion of contaminants from frac
tures into the rock matrix of a dualporosity medium. SOURCE: Anderson,
1984.
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TRANSPORT
C
nJection
well
Land surface
A C
{B+D
1
Flow ~
B
1
o
119
Fully
penetrating
observation
well
/A
_ ~

`. Point',
samples
C ~ C: D:Br
FIGURE 4.3 Effect of sampling scale on estimation of dispersivity. SOURCE:
L. F. Konikow, U.S. Geological Survey, Ralston, Va., written communication,
1989.
larger scales of miles. Warning flags must be raised if measurements
of parameters such as dispersivity are made or are representative of
some scale that is different from that required by the mode! or by
the solution to the problem of interest.
Similarly, the sampling scale and manner of sampling or measur
ing dependent variables, such as solute concentration, may affect the
interpretation of the data and the estimated values of physical pa
rameters. For example, Figure 4.3 illustrates a case in which a tracer
or contaminant is injected into a confined and stratified aquifer sys
tem. It is assumed that the properties are uniform within each layer
but that the properties of each layer differ significantly. Hence, for
injection into a fully penetrating injection well, as shown at the left
of Figure 4.3, the velocity will differ between the different layers.
Arrival times will then vary at the sampling location. Samples col
lected from a fully penetrating observation well will yield a gentle
breakthrough curve indicating a relatively high dispersivity. How
ever, breakthrough curves from point samples will be relatively steep,
indicating low dispersivity in each layer. The finer scale of sampling
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120
GROUND WATER MODELS
yields a more accurate conceptual mode} of what is really happening,
and an analogous mode! should yield more reliable predictions.
Because advective transport and hydrodynamic dispersion de
pend on the velocity of ground water flow, the mathematical simu
lation mode! must solve at least two simultaneous partial differential
equations. One is the flow equation, from which velocities are calcu
lated, and the other ~ the solute transport equation, which describes
the chemical concentration in ground water. If the range in concen
tration throughout the system is small enough that the density and
viscosity of the water do not change significantly, then the two equa
tions can be decoupled (or solved separately). Otherwise, the flow
equation must be formulated and solved in terms of intrinsic per
meability and fluid pressure rather than hydraulic conductivity and
head, and iteration between the solutions to the flow and transport
equations may be needed.
Ground water transport equations, in general, are more diffi
cult to solve numerically than are the ground water flow equations,
largely because the mathematical properties of the transport equa
tion vary depending upon which terms in the equations are dominant
in a particular situation (Konikow and Mercer, 1988~. The transport
equation has been characterized as "schizophrenic" in nature (Pin
der and Shapiro, 1979~. If the problem is advection dominated, as
it is in most cases of ground water contamination, then the govern
ing partial differential equation becomes more hyperbolic in nature
(similar to equations describing the propagation of a shock front
or wave propagation). If ground] water velocities are relatively low,
then changes in concentration for that particular problem may re
sult primarily from diffusion and dispersion processes. In such a
case, the governing partial differential equation is more parabolic in
nature. Standard finitedifference and finiteelement methods work
best with parabolic and elliptic partial differential equations (such as
the transient and steadystate ground water flow equations). Other
approaches (including method of characteristics, random walk, and
related particletracking methods) are best for solving hyperbolic
equations. Therefore no one numerical method or simulation mode!
will be ideal for the entire spectrum of ground water contamination
problems encountered in the field. Mode! users must take care to use
the mode} most appropriate to their problem.
Further compounding this clifficulty is the fact that the ground
water flow velocity within a given multidimensional flow field will
normally vary greatly, from near zero in lowpermeability zones or
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121
near stagnation points, to several feet per day in highpermeability
areas or near recharge or discharge points. Therefore, even for a
single ground water system, the mathematical characteristics of the
transport process may vary between hyperbolic and parabolic, so that
no one numerical method may be optimal over the entire domain of
a single problem.
A comprehensive review of solute transport modeling is pre
sented by Naymik (1987~. The mode! survey of van der Heij~e et
al. (1985) reviews a total of 84 numerical mass transport models.
Currently, there is much research on mixed or adaptive methods
that aim to minimize numerical errors and combine the best features
of alternative standard numerical approaches because none of the
standard numerical methods is ideal over a wide range of transport
problems.
In the development of a deterministic ground water transport
mode! for a specific area and purpose, an appropriate level of com
plexity (or, rather, simplicity) must be selected (Konikow, 1988~.
Finer resolution in a mode} should yield greater accuracy. However,
there also exists the practical constraint that even when appropriate
data are available, a finely subdivided threedimensional numerical
transport mode] may be too large or too expensive to run on available
computers. This may also be true if the mode! incorporates nonlinear
processes related to reactions or multiphase transport. The selection
of the appropriate mode} and the appropriate level of complexity will
remain subjective and dependent on the judgment and experience
of the analysts, the objectives of the study, and the level of prior
information on the system of interest.
In general, it is more difficult to calibrate a solute transport
mode! of an aquifer than it is to calibrate a ground water flow model.
Fewer parameters need to be defined to compute the head distribu
tion with a flow mode} than are required to compute concentration
changes using a solute transport model. A mode} of ground water
flow is often calibrated before a solute transport mode} is developed
because the ground water seepage velocity is determined by the head
distribution and because advective transport ~ a function of the
seepage velocity. In fact, in a field environment, perhaps the single
most important key to understanding a solute transport problem
is the development of an accurate definition (or model) of the flow
system. This is particularly relevant to transport in fractured rocks
where simulation is based on porousmedia concepts. Although the
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122
GROUND WATER MODELS
head distribution can often be reproduced satisfactorily, the required
velocity field may be greatly in error.
It is often feasible to use a ground water flow mode} alone to
analyze directions of flow and transport, as well as travel times,
because contaminant transport in ground water ~ so strongly (if
not predominantly) dependent on ground water flow. An illustrative
example is the analysis of the Love Canal area, Niagara Fails, New
York, described by Mercer et al. (1983~. Faced with inadequate
and uncertain data to describe the system, Monte CarIo simulation
and uncertainty analysis were used to estimate a range of travel
times (and the associated probabilities) from the contaminant source
area to the Niagara River. Similarly, it is possible and often useful
to couple a particletracking routine to a flow mode! to represent
advective forces in an aquifer and to demonstrate explicitly the travel
paths and travel times of representative parcels of ground water. This
ignores the effects of dispersion and reactions but may nevertheless
lead to an improved understanding of the spreading of contaminants.
Figure 4.4 illustrates in a general manner the role of models
in providing input to the analysis of ground water contamination
problems. The value of the modeling approach lies in its capability
to integrate sitespecific data with equations describing the relevant
processes as a basis for predicting changes or responses in ground
water quality. There is a major difference between evaluating existing
contaminate sites and evaluating new or planned sites. For the
former, if the contaminant source can be reasonably well defined,
the history of contamination itself can, in effect, serve as a surrogate
longterm tracer test that provides critical information on velocity
and Aspersion at a regional scale. However, it is more common
that when a contamination problem is recognized and investigated,
the locations, tinning, and strengths of the contaminant sources are
for the most part unknown, because the release to the ground water
system occurred in the past when there may have been no monitoring.
In such cases it is often desirable to use a mode} to determine the
characteristics of the source on the basis of the present distribution of
contaminants. That is, the requirement is to run the mode! backward
in time to assess where the contaminants came from. Although this is
theoretically possible, in practice there is usually so much uncertainty
in the definition of the properties and boundaries of the ground water
system that an unknown source cannot be uniquely identified. At
new or planned sites, historical data are commonly not available
to provide a basis for mode! calibration and to serve as a control
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P NN NO FOR FUTURE ASSESSMENTS OF EXISTING
WASTE DISPOSAL 1  CONTAM NATED S TES.
· SITE SELECTION · SOURCES OF CONTAMINATION
· OPERATIONAL DESIGN · FUTURE CONTAMINATION
· MONITORING NETWORK · MANAGEMENT OPTIONS
~1 ~
1
1
L
123
 MODEL PREDICTIONS
rid   MODEL APPLICATION AND CALIBRATION ~
1
NUMERICAL MODEL' I OF GROUND WATER 1
FLOW AND CONTAMINANT TRANSPORT I I
COLLECTION AND
INTERPRETATION OF
SITESPECIFIC DATA
CONCEPTUAL MODELS
OF GOVERNING
PHYSICAL, CHEMICAL,
AND BIOLOGICAL
PROCESSES
~1
FIGURE 4.4 Overview of the role of simulation models in evaluating ground
water contamination problems. SOURCE: Konikow, 1981.
On the accuracy of predictions. As indicated in Figure 4.4, there
should be allowances for feedback from the stage of interpreting
mode! output both to the data collection and analysis phase and
to the conceptualization and mathematical definition of the relevant
governing processes.
NONCONSERVATIVE SOLUTES
The following sections assess the state of the art for modeling
abiotic transformations, transfers between phases, and biological pro
cesses in the subsurface. Descriptions of all of these processes are
provided in Chapter 2. The focus for this assessment is an examina
tion of what reactions are important and to what extent they can be
described by equilibrium and kinetic models.
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V
SEA
149
Accretion
Fresh water ~
Ground Surface
Water Table
/~e ~Impervious
Seawater =~ c ~Boundary
"'a_
Toe
FIGURE 4.9 Seawater intrusion in an unconfined aquifer. SOURCE: After Sa
da Costa and Wilson, 1979.
then the problem scale is such that an interface approximation is
valid and saltwater and fresh water may be treated as immiscible.
The analysis of aquifers containing both fresh water and salt
water may be based on a variety of conceptual models (doss, 1984~.
The range of numerical models includes dispersed interface mod
els of either crosssectional or fully threedimensional fluiddensity
dependent flow and solute transport simulation. Sharp interface
models are also available for crosssectional or areal applications.
Of the sharp interface models, some account for the movement of
both fresh water and saltwater, while others account only for fresh
water movement. The latter models are based on an assumption of
instantaneous hydrostatic equilibrium in the saltwater environment.
In the majority of cases involving seawater intrusion, water qual
ity is viewed as good or bad; either it is fresh water or it is not a
resource. Therefore many studies seek to determine acceptable lev
els of pumping or appropriate remediation or protection strategies.
These resource management questions are resolved through fluid flow
simulation and do not require solute transport simulations.
Organic FIllid Contamination
The migration and fate of organic compounds in the subsurface
are of significant interest because of the potential health effects of
these compounds at relatively low concentrations. A significant body
of work exists within the petroleum industry regarding the move
ment of organic compounds, e.g., of} and gas resources. However,
this capability has been developed for estimating resource recovery
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150
GROUND WATER MODELS
or production and not contaminant migration. To compound prob
lems, the petroleum industry's computational capability is largely
proprietary and is oriented toward deep geologic systems, which typ
ically have higher temperatures and higher pressure environments
than those encountered in shallow contamination problems.
Within the past decade, a considerable effort has been made
to establish a capability to simulate immiscible and miscible or
ganic compound contamination of ground water resources. Migration
patterns associated with immiscible and miscible organic fluids are
schematically described by Schwille (1984) and Abriola (1984~. Fig
ure 4.10 depicts one possible organic liquid contamination event. If
not remediated, the migration of an immiscible organic liquid phase
is of interest because it could represent an acute or chronic source of
pollution. Movement of the organic liquid through the vadose zone is
governed by the potential of the organic liquid, which in turn depends
upon the fluid retention and relative permeability properties of the
air/organic/water/solid system. As an organic liquid flows through
a porous medium, some Is adsorbed to the medium or trapped within
the pore space. Specific retention defines that fraction of the pore
space that will be occupied by organic liquid after drainage of the
bulk organic liquid from the soil column. This organic contamina
tion held within the soil column by capillary forces (at its residual
saturation) represents a chronic source of pollution because it can be
leached by percolating soil moisture and carried to the water table.
If the organic liquid is lighter than water, it may migrate as a
distinct immiscible contaminant (the acute source) within the cap
ilIary fringe overlying the water table. The soluble fraction of the
organic liquid will also contaminate the water table aquifer and mi
grate as a miscible phase within ground water. This is the situation
shown in Figure 4.10. If the organic liquid is heavier than water, it
will migrate vertically through the vadose zone and water table to
directly contaminate the ground water aquifer. It may also pene
trate waterconfining strata that are permeable to the organic liquid
and, consequently, contaminate underlying confined aquifers. The
organic contaminant may form a pool on the bedrock of the aquifer
and move in a direction defined by the bedrock relief rather than
by the hydraulic gradient. Contamination of ground water occurs
by dissolution of the soluble fraction into ground water contacting
either the main body of the contaminant or the organic liquid held
by specific retention within the porous medium.
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Ground Surfacer
Capillary Fringe
Water Table
151
'my
,.::::.. i. :$...//////
Oil Zone ~
l   .' lo,!. . of ~
CUnsaturated Zone
Gas Zone (evaporation envelope)
~ ", ~.~;,
Oil Core
\ Diffusion Zone
(soluble components)
Figure 4.10 Organic liquid contamination of unsaturated and saturated porous
media. SOURCE: After Abriola, 1984.
Governing Equations for M~tiphase Flow
The region of greatest interest in seawater intrusion problems is
the front between fresh water and seawater. The problem of salinity
as a miscible contaminant in ground water is addressed with standard
solute transport models. In reality, seawater is miscible with fresh
water, and the front between the two bodies of water Is really a
transition zone. The density and salinity of water across the zone
gradually vary from those of fresh water to those of seawater (Bear,
1979~. A sharp or abrupt interface Is assumed if the width of the
transition zone is relatively small. Fresh water is buoyant and will
float above seawater. The balance struck among fresh water (i.e.,
ground water) moving toward the sea, seawater contaminating the
approaching fresh water by miscible displacement, and fresh water
overlying seawater results in a nearly stationary saline wedge. Figure
4.9 illustrates the stationary saline wedge conceptual model. This
wedge will change if influenced by pumping or changes in recharge.
While one can pose and solve the seawater intrusion problem as
a single fluid having variable density (e.g., Begot et al., 1975; Voss,
1984), the most common approach has been to simulate fresh water
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152
GROUND WATER MODELS
and seawater as distinct liquids separated by an abrupt interface.
Along the interface, the pressures of both liquids must be identical.
Sharp interface methods are applied to both vertical cross sections
(e.g., Volker and Rushton, 1982) and areal models (e.g., Sa da Costa
and Wilson, 1979~. The equations used to formulate the problem are
the same as those used for the standard ground water flow problem.
The only differences are that two equations are used (i.e., freshwater
and seawater versions) and that their joint solution is conditioned to
the pressure along the interface. Assuming that the response of the
seawater domain is instantaneous and hence that hydrostatic equi
librium exists in the seawater domain, one can mode} the intrusion
problem with a stanciard transient ground water flow mode} (doss,
1984~.
Pinder and Abriola (1986) provide a broad overview of the prob
lem of modeling multiphase organic compounds in the subsurface.
Abriola (1984) grouped models of multiphase flow and transport
into two categories, those that address the migration of a miscible
contaminant in ground water and those that address two or more
distinct liquid phases. The former category of models addresses the
farfield problem of chronic miscible contamination. Standard ground
water flow and solute transport codes can be applied to these organic
compound contamination problems. However, standard codes may
require modifications to address biodegradation or sorption charac
teristics of a specific organic compound.
As in the case of seawater intrusion, the region of greatest interest
is the region exhibiting multiphase behavior. The problem of organic
contamination is more complex for two reasons: (~) in general, a
stationary interface will not exist, and (2) one is often interested in
contamination of unsaturated soil deposits as a precursor to contam
ination of a ground water aquifer. Interest in the migration and fate
of organic compounds has required that transient analysis methods
be developed. Such methods enable one to simulate the movement
of bulk contamination through the vadose zone and into a ground
water aquifer. One is also able to estimate the mass of contamina
tion held in the media by specific retention. Because the front is
not stationary, one must mode} liquid/solid interactions that govern
the movement of each fluid in the presence of others. The equations
describing multiphase flow and transport are similar to those previ
ously described for simulating water movement and solute transport
in unsaturated soils. One fluid flow (e.g., fluid mass conservation)
equation is required for each fluid phase simulated (e.g., gas, organic
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153
liquid, water). Rather than simulate distinct fluid regions separated
by abrupt interfaces, one simulates a continuum shared by each of the
fluids of interest. The equation set is coupled by the fluid retention
and relative permeability relationships of the multiphase system.
Miscible displacement of trace quantities of an organic fluid can
occur within the water and gas phases. This is a common occurrence;
however, it greatly complicates the ma" balance equation for the
organic fluid. The statement of mass conservation must now account
for organic mass entrained in the water and gas phases as well as the
organic mass held in the immiscible fluid phase. Transport processes
are introduced into the conservation equations, and the exchange of
organic mass between fluid phases must be accounted for through
partition coefficients.
Abriola (1988) and Allen (1985) review models available for the
simulation of multiphase problems. A variety of solutions have been
published for multiphase contamination problems. This is due to the
complexity of the overall problem and the variety of approaches that
can be taken to provide an approximate solution. A useful hierarchy
of modeling approaches is as follows: sharp interface approxima
tions, immiscible phase flow modem incorporating capiliarity, and
compositional models incorporating interphase transfer.
Examples of models based on sharp interface approximations
are those of Hochmuth and Sunada (1985), Schiegg (1986), and van
Dam (1967~. Immiscible phase models incorporating capilIarity al
low a more realistic sunulation of the specific retention phenomena
but do not address hysteresis in the fluidsoi! interaction. Examples
of these models are presented by Faust (1985), Kuppusamy et al.
(1987), and Osborne and Sykes (1986)0 Compositional models in
corporating interphase transfer are extremely complex and require
the most data, many of which are not routinely available for con
taminants of interest. Examples of these models are presented by
Abriola and Pinder (1985a,b), Baehr and Corapcioglu (1987), and
Corapcioglu and Baehr (1987~.
Parameters and Titian and Boundary Conditions for
Multiphase Flow
The physical complexity exhibited by multiphase flow models
consumes all available computer resources. This strain on computer
resources has precluded acknowledgment, in models, of the com
plexities of heterogeneous media that are spatially distributed in
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GROUND WA173R MODELS
the real environment. At the present time, computational resources
restrict fully threedimensional problems to homogeneous, porous
media. Realistically, currently available computational resources are
best suited to addrem conceptual modem
Mode} parameters necessary for the simulation of seawater in
trusion are basically identical to those required for the simulation of
ground water flow; however, twofluid models require duplicate pa
ran~eters for fresh water and saltwater. A great many more mode} pa
rameters are necessary for a complete analysis of immiscible organic
contaminant migration in the subsurface. While the seawater intru
sion problem is restricted to saturated porous media, organic fluid
migration often occurs in the unsaturated zone. Consequently, fluid
retention and relative permeability properties are required for the
air/organic/water/solid system. Other standard data requirements
for multiphase fluid flow simulation include porosity, compressibility
of liquids and porous media (or storage coefficient), fluid densities
and viscosities, and the intrinsic permeability tensor.
As in the case of the fluid flow simulations, mode} parameters
for transport simulations are more detailed for the organic fluid mi
gration problem than for the seawater intrusion problem. Mode}
parameter requirements for solute migration within variabledensity
seawater intrusion are very similar to the requirements of any single
phase saturated zone model; however, duplicate data sets are re
quired for freshwater and seawater domains. Parameters necessary
for detailed analysis of organic liquid transport phenomena include
macroscopic diffusion and dispersion coefficients for each fluid phase
(e.g., gas, water, or organic liquid), partition coefficients for watergas
and waterorganic phases, sorption mode} parameters for alternative
sorption models, and degradation mode! parameters for the organic
fluid.
Certainly, the more complex and complete models of multiphase
contaminant problems require more data. If one considers only the
immiscible flow problem in an attempt to estimate the migration
of the bulk organic plume, then one will not require any of the
miscible displacement (transport) parameters. If one assumes that
the gas phase is static, one greatly reduces the data requirement
in terms of both flow and transport phenomena. Key data for any
analysis of multiphase migration are the fluid retention and relative
permeability characteristics for the fluids and media of interest. The
media porosity and intrinsic permeability, as well as fluid densities
and viscosities, are also essential.
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All comments made regarding boundary and initial conditions
for flow and transport of a singlephase contamination analysis also
apply to a multiphase analysis. Aspects of transient analysis can
be important in seawater intrusion problems because of seasonal
pumping stresses. Transient analyses are also essential for organic
fluid migration simulation because of interest in the migration and
fate of these potentially harmful substances.
Spatial dunensionality of a multiphase analysis can influence re
sults. For example, in the real, fully threedimensional environment,
a heavierthanwater organic fluid can move vertically through the
soil profile and form a continuous distinct fluid phase from the wa
ter table to an underlying impermeable medium. Ground water will
simply move around the immiscible organic fluid as though it were an
impermeable object. Attempts to analyze such a situation in a ver
tical cross section with a twodimensional multiphase model will fad!
because the organic fluid will act as a dam to laterally moving ground
water. Thus only an intermittent source of immiscible organic fluid
can be analyzed. Note that such an analysis will be flawed for most
realworId applications because it will represent a laterally infinite
intermittent source rather than a point source of pollution.
Problems Associated with Mult~phase Flow
The problems associated with modeling multiphase flow include
the following:
.
complexities;
magnitude of computational resources required to address all
data requirements of the multiphase problem that are inde
pendent of consideration of spatial variability, paucity of data specific
to soils and organic contaminants of interest, and no way to address
the problem of mixtures of organics;
. absence of hysteresis submodels needed to address retention
capacity of porous media and to enable one to simulate purging of
the environment;
. virtual orn~ssion of any realistic surface geochemistry or mi
crobiology submodels necessary to more completely describe the as
sim~lative or attenuative capacity of the subsurface environment; and
. viscous fingering and its relationship to spatial variability
occurring in the natural environment.
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GROUND WATER MODELS
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