Single-Region Flow and Transport
Traditionally, water flow has been assumed to be uniform through relatively
homogeneous layers of the soil profile. Darcy’s law, presented in 1856,
describes flow of water through a homogeneous, saturated soil. It was later
extended to non-steady state, unsaturated flow as:
where q is the flux density (LT-1), i.e., the volume of water
Q (L3) passing through a cross sectional area A (L2)
per unit time t (T). The hydraulic head H (L) is the sum of the gravitational
head z (L) and pressure head h (L). The latter attains positive values
below and negative values above the water table. The hydraulic conductivity
K (LT-1) represents the ability of a soil to conduct water and
is considered to be a constant under saturated conditions. Under unsaturated
conditions, the hydraulic conductivity is a function of h. The rate at
which water is being conducted through the soil is the product of the hydraulic
conductivity and the hydraulic head gradient ¶
H/¶ z (driving force). The negative sign
indicates that the flow of water takes place in the direction of decreasing
H. It should be noted that the flux density q is averaged over a cross
sectional area of soil and does not represent the velocity at which water
moves through the pores. The latter is represented by the average pore
water velocity v (LT-1), which equals the flux density q divided
by the water filled porosity contributing to flow. This is typically taken
as q/q (q is volumetric
water content), which assumes that all water is mobile. Flow through the
vadose zone, i.e., the unsaturated zone from the soil surface to the water
table, is rarely steady state under natural conditions. To fully describe
water flow under transient conditions, Darcy’s law must be combined with
the continuity equation
where Ñ q is the divergence of the
flux, i.e., the difference between inflow and outflow at a given plane.
The left hand side of this equation can be written as
where C(q ), the slope of the water retention
curve, is referred to as the specific water capacity. Combining the continuity
equation with the Darcy equation, results in the Richards equation for
one-dimensional, unsaturated, non-steady state flow of water in the vertical
One-dimensional transport of a nonreactive solute through a homogeneous
soil layer can be described by combining the flux density equation
with the continuity equation
which yields the convective-dispersive equation (CDE)
where Js is the total solute mass flux (ML-2T-1),
JD (ML-2T-1) is the diffusive-dispersive
mass flux, C is the concentration (ML-3), D (L2T-1)
is the effective diffusion-dispersion coefficient expressed as
where Ddif (L2T-1) is the molecular
diffusion coefficient, Ddis (L2T-1) is
the hydrodynamic dispersion coefficient, and all other variables have been
defined before. Hydrodynamic dispersion is the mixing or spreading of the
solute during transport due to differences in velocities within a pore
and between pores. During steady-state flow in a homogeneous porous medium
with uniform water content, Eq. (7) can be simplified to
To describe transport of reactive solutes, i.e., solutes that are sorbed
by the soil, a term representing the amount of solute sorbed, S (MM-1),
needs to be included in Eq. (9). For a representative elementary volume
(REV) of soil, the total amount of a given chemical species c
(ML-3) is represented by the sum of the amount retained by the
soil matrix and that present in the soil solution, i.e.,
As a result, the CDE now becomes
Further rearrangements yield
where Q (ML-3T-1) is a source-sink term, and R,
the retardation coefficient, is defined as
where r b is the bulk density
(ML-3). A key ingredient to the solution of Eq. (10), or and
any other reactive-solute transport equation, is the relationship between
the amount of chemical in solution (C; ML-3) and the amount
sorbed by the solid phase (S; MM-1). This relationship is referred
to as an adsorption isotherm. Sorption is promoted by charged clay minerals,
hydrous oxide coatings on surfaces, and organic matter functional groups
with variable charges. Additionally, some solutes may co-precipitate, volatilize,
Over the last thirty years, several models describing the retention
behavior of various chemical species in the soil have been developed (Selim,
1992). Table 1 provides a listing of commonly
used equilibrium and kinetic retention approaches. A disadvantage of several
of such empirical approaches lies in the basic assumption of local equilibrium
of the governing reactions. Alternatives to equilibrium-based approaches
are the multisite or multireaction models which deal with the multiple
interactions of one solute species in the soil environment. Multiple interaction
approaches assume that a fraction of the total sites is time dependent,
i.e., they are kinetic in nature, whereas the remaining fraction interacts
rapidly or instantaneously with the chemical present in the soil solution.
Linear or nonlinear equilibrium (Freundlich) and first- or n-th order kinetic
reactions are the associated processes (Selim, 1992). Based on the multireaction
approach, adsorption may be regarded simply as consisting of three types
of sites, i.e.,
where Se refers to sorption governed by instantaneous equilibrium
reactions (type 1 sites), Sk refers to sorption governed by
hysteretic kinetic reactions (type 2 sites), and Sir refers
to sorption subjected to irreversible retention (type 3 sites). The instantaneous
equilibrium reaction between the amount of chemical in solution and that
sorbed by the solid phase is generally represented by one of the following
three adsorption isotherms:
1. The simplest chemical reaction model is the linear adsorption equation
where Kd (L3M-1) is referred to as
the distribution coefficient (slope of the adsorption isotherm).
2. Equation (13) is a special case of the Freundlich equation
where Kf is the Freundlich distribution coefficient (L3M-1)N
and N is a fitting parameter.
3. The Langmuir adsorption equation
where a and b are curve fitting parameters.
Incorporation of any of these isotherms into the retardation factor
requires that S be differentiated with respect to C.
Reactive solute transport must also consider chemical non-equilibrium.,
which occurs when the adsorption process is kinetic, i.e., it is not instantaneous
but rate dependent. This may include reversible as well as irreversible
adsorption. The latter includes, e.g., internal diffusion into clay minerals
(Amacher et al., 1988), which may be expressed as a first-order kinetic
where kir is the rate coefficient (T-1) for irreversible
adsorption. The hysteretic kinetic reversible reaction between the solution
and solid phases for Type 2 sites can be represented by
where k1 and k2 are the forward and backward rate
coefficient (T-1), respectively, and n is the reaction order
associated with Sk.
Important aspects to consider in the solution of transport equations
are the different types of concentrations that can be considered and the
application of the appropriate initial and boundary conditions (van Genuchten
and Parker, 1984; Parker and van Genuchten, 1984a). Parker and van Genuchten
(1984a) discussed the importance of distinguishing between a volume-averaged
(C) and a flux-averaged (Cf) concentration in conjunction with
the way an experiment is performed and the results are analyzed (Parker
and van Genuchten, 1984b).
Two-Region Flow and Transport
It is common to observe greater dispersion of solutes during transport
through undisturbed soils than in packed, homogeneous soil columns. This
is typically attributed to soil structural (inter-aggregate pores) pores
and biological channels resulting in water flowing more rapidly in these
large pores than in the soil matrix (inter-aggregate pores). The velocity
through the preferential flow paths may be so much higher than through
the soil matrix that the water in the matrix is considered stagnant or
immobile. For soils of this type, a two-region flow model is warranted,
in which water is partitioned into a mobile and an immobile flow region.
In such a model q m is the water
content of the mobile region (inter-aggregate pores) through which transport
occurs by the CDE (Eq. 7), and q im
is the water content of the immobile region (intra-aggregate pores) through
which solute is transported by diffusion. Solute transfer between mobile
and immobile regions is only by diffusion due to physical nonequilibrium
(concentration gradients). The one-dimensional CDE for two-region flow
and transport is
where Dm (L2T-1) is the hydrodynamic
dispersion coefficient of the mobile region, Sim ( MM-1)
and Sm ( MM-1) are the sorbed amounts in the immobile
and mobile regions, respectively. We further define
where ST ( MM-1) is the total amount sorbed and
fm is the fraction of adsorbed solutes in contact with the mobile
region, i.e., fm = q m/q.
The equation for diffusive transfer between the two regions is
where a is the mass transfer coefficient
(T-1) between the mobile and immobile region, and Qm
and Qim represent the irreversible retention of solute
in the mobile and immobile region, respectively. For single-region flow
and transport with local equilibrium fm = 1 and a
= 0. Independent determinations of fm and a
can be obtained from knowledge of the volume of water drained at a pressure
head value sufficiently negative to drain the mobile pore water. Since
equals the water drained per total soil volume, fm = qm/q,
where q is the initial (saturated) water content.
Using meters for length and days for time, the mobile region dispersion
coefficient, Dm, can be estimated from
where 0.0005 m2/d is the diffusion contribution, lm
is the mobile dispersivity, which is equal to the average diameter of the
aggregates, and vm = q/qm
is the pore water velocity of the mobile region. The mass transfer coefficient,
, can be estimated from
Independent estimates of Dm and a
are necessary because these parameters are auto-correlated.
Multi-Region Flow and Transport
Luxmoore (1981) proposed that soils consists of a continuous distribution
of pore sizes which may be separated into pore size classes of macro-,
meso-, and micropores analogously to particle size distribution. It is
common for dye staining patterns to reveal preferential flow through a
secondary pore region. The pores of this region are too small to be considered
macropores and are morphologically not distinguishable from the soil matrix
which contains the immobile water (Omoti and Wild, 1979; Hornberger et
al., 1991; Seyfreid and Rao, 1987; Germann and Beven, 1981). The pores
in the secondary pore region are called mesopores in Luxmoore’s scheme
(1981). Jury and Fluhler (1992) concurred by stating that "substantial
water flow may occur in the surrounding matrix as well as in the preferential
flow region." They further stated that "solutes partition into a rapid
or preferential flow region and a slower, but still mobile matrix flow
region, each of which may embody a small but significant degree of water
flow." They concluded that "the model is unsatisfactory for representing
media wherein transport occurs both in preferential flow regions and in
the bulk matrix." If a secondary pore class significantly contributes to
flow and transport, a multi-region model may be needed. Jardine et al.
(1990) conducted field-scale transient flow tracer experiments on a 2 m
x 2m x 3 m deep, in situ soil block in Eastern Tennessee. They reasoned
that hydraulic (hydraulic head gradients) and physical (solute concentration
gradients) nonequilibrium between pore classes near the soil surface, shortly
after tracer application, caused convective and diffusive transfer, respectively,
from the solute rich mesopores into the macropores. They observed significant
movement through the mesopores, which was more continuous than transport
through the macropores. The latter responded to storm events much like
discrete flow pulses.
A generic description of multi-region media is one in which soils are
highly structured such that macropores occur as voids between macroaggregates
(peds), which themselves are highly permeable due to smaller voids between
microaggregates. Radulovich et al. (1992) called these inner-macroaggregate
voids, interpedal pores. Under the multi-region flow concepts developed
by researchers at the Oak Ridge National Laboratory (Wilson, Jardine, Gwo,
and Luxmoore), preferential flow includes the secondary pore size class
containing mesopores. These pores are capable of high flow for extended
periods following drainage events. Flow and transport through each region
were described by the Richards and convective-dispersive equation, respectively.
A key mechanism in solute transport through multi-region media under
transient flow conditions is the mass transfer among regions. It has often
been thought that only diffusion is responsible for mass transfer between
regions. Once macropore flow is initiated, the unsaturated macroaggregates
(mesopores and micropores) at subsequent depths are by-passed due to the
high velocity in the macropore region. This variably-saturated preferential
flow scenario explicitly means that hydraulic nonequilibrium exists, i.e.,
hydraulic gradients exist between flow regions. Thus, convective transfer
of solutes between regions must be incorporated with the diffusive transfer
due to physical nonequilibrium, i.e., concentration gradients between regions.
The mathematical development and application of these multi-region flow
and transport processes can be found in Gwo et al. (1995).
Application and Parameterization
To solve the Richards equation (Eq. 4), the hydraulic conductivity
function, K(h), and the water retention function, q
(h), must be known in continuous form. Experimental and numerical techniques
for determining these hydraulic functions can be found in Klute (1986).
The water retention function or water characteristic curve is a fundamental
soil property that reflects the pore-size distribution of the soil. Whereas
the wet end predominately reflects soil structure, the dry end is more
a reflection of soil texture and mineralogy. Water retention functions
are empirical relationships determined by fitting mathematical expressions
through experimentally determined data points using least-squares fitting
techniques. To be properly applied, such expressions require measured values
over the entire h range of the application. The two most common expressions
in use today are the Brooks-Corey (1964) and van Genuchten (1980) models.
The Brooks-Corey (1964) model is:
where q r is the residual
volumetric water content, q s
is the saturated volumetric water content, ha is the air-entry
value, and l is considered a pore-size distribution
index. One of the strengths of the Brooks-Corey expression is that no air
will displace water as long as the pressure head value is greater than
the air entry value. The same expression applies if two liquids are present
in a porous medium. Equation (25) then states that the nonwetting liquid
will not displace the wetting liquid unless the displacement or entry pressure
head value has been reached. Van Genuchten (1980) developed the following
where a and n are curve fitting parameters.
The disadvantage of this model is that it predicts drainage even at h values
close to zero, which implies displacement by some other fluid (either air
or another liquid) and an associated hydraulic conductivity value. This
has important consequences for the prediction of contamination by, e.g.,
Similarly to water retention curves, empirical equations exist for K(h)
1986). One of the most commonly used expressions used in unsaturated flow
problems is the Gardner (1958) equation:
where b is a curve fitting parameter and
Ks is the saturated hydraulic conductivity, both of which vary
from soil to soil. Equation (27) should only be used for that portion of
the curve where measurement points exist.
Physically-based K(h) models require knowledge of a soil property that
is related by some physical law or numerical expression to the ability
of the soil to conduct water. According to Poiseuille’s law, the flux density
through a tube is directly related to the radius of the tube to the power
4. The hydraulic conductivity should, therefore, be related to the pore-size
distribution. Given that the shape of the water retention function reflects
the pore-size distribution, the shape parameters for q
(h) can be used to predict K(h). The proposed Brooks-Corey (1964) equation
Another frequently used model was presented by van Genuchten (1980),
where m is assumed to equal to 1 - 1/n. The parameters a,
and m are determined from the q (h) parameterization.
One of the problems with predicting K(h) from water retention data is
that q (h) is typically derived from laboratory
core samples which deviate from field situations. Laboratory samples generally
exhibit higher water contents at the wet end than field measurements at
the same pressure head (Cassel, 1985) due to more entrapped air in the
field. Additionally, laboratory measurements of retention are rarely measured
to the field residual water content. Kunze et al. (1968) documented how
the accuracy of the K(h) function depends upon having a complete q
It should be noted that the hydraulic relationships are highly site
specific and spatially variable. Data for these hydraulic properties for
some of the important soils of the southeastern United States can be found
in Cassel (1985), Dane et al. (1983), and Romkens et al. (1985, 1986).
Because of the difficulty in directly measuring these functions for field
conditions, attempts have been made to derive these functions from knowledge
of other, more easily determined soil properties using pedotransfer functions
(Puckett et al., 1985), fractal theory approaches (Rieu and Sposito, 1991;
Hatano and Booltink, 1992), and inverse procedures (Dane and Hruska, 1983;
Zijlstra and Dane, 1995). As yet, there is no consensus on how to best
obtain these functions. The existence of two- or multi-region flow requires
that the K(h) and q (h) functions be determined
for each flow region. Additionally, mass transfer coefficients between
the regions need to be determined. Various methods (Smettem et al., 1991;
Jarvis et al., 1991; Wilson et al., 1992; Mohanty et al., 1997) have been
proposed to describe the hydraulic functions for either one-, two-, or
multi-region soils. Diffusive mass transfer between regions can be obtained
by the flow interruption miscible displacement technique (Reedy et al.,
1996), while Gwo et al. (1996) estimated the convective transfer coefficients
from measurements of fracture spacing. The adequacy of such estimates is,
however, completely speculative.
Although a wealth of data is available in the literature on solute transport
parameters, the authors know of no document that assimilates this information
for soils in the southeastern United States in a manner similar to the
assimilation of the soil hydraulic properties. Methods for experimental
determination of the instantaneous and single-site kinetic adsorption coefficients
may be found in (Van Genuchten and Wierenga, 1986; Leij and Dane, 1989a,b).
However, the difficulty remains in being able to separate the contributions
of the various type sites. Considerable less information is available for
multi-reaction adsorption coefficients (Wilson et al., 1998).
Land use Effects on Flow and Transport
In addition to the complexities of determining the pertinent flow and
transport properties for the various soils of the southeastern United States,
these properties often vary with time as they are strongly effected by
land use and soil management practices. A good example is the effect of
no-tillage (NT), compared to conventional tillage (CT), on the flow of
water and transport of chemicals through macropores. Because the soil remains
mostly undisturbed under NT, macropore (cracks between aggregates and biological
pores) formation and organic matter accumulation at the surface are enhanced.
The effect of soil management practices on macroporosity and organic matter
has important impacts that must be considered. For example, NT usually
increases the hydraulic conductivity due to macropore development, decreases
reactivity of dissolved chemicals in macropores due to their low pore-surface
area and short residence time, and increases the reactivity of chemicals
in the soil matrix due to the increase in organic matter. Consequently,
NT can shift a soil from behaving as a single-region, one-site reactivity
soil, to a multi-region, multi-reaction site soil. Failure to recognize
this shift can result in improper characterization of the flow and transport
parameters. For example, increases in organic matter provide kinetic adsorption
sites for some solutes which, if ignored, would be inappropriately lumped
into the instantaneous equilibrium adsorption terms.
Failure to fully understand the impact of soil management on flow and
transport properties has led to much confusion of the significance of tillage
on, and how to sample for, water quality. Research by Thomas and Phillips
(1979) in Kentucky demonstrated greater nitrate leaching with NT than with
CT. They concluded that NT increased the preferential leaching of nitrate
through macropores. However, Kanwar et al. (1991) concluded that increased
macroporosity under NT results in decreased nitrogen leaching if the nitrogen
source was located within the soil micropores. They proposed that macropores
facilitate the bypassing of water-filled micropores, thereby reducing nitrate
leaching relative to displacement of the nitrogen rich micropore water.
This is a good example of the importance of mass transfer between regions
as a result of physical and hydraulic nonequilibrium in response to preferential
flow. Yet failure to recognize the shift in flow and transport processes
can lead to inaccurate assessment of the impact of NT on water quality.
Essington et al. (1995) documented the importance of this for pesticide
movement in long-term tillage plots. Depth incremented soil sampling in
a NT soil revealed that the pesticide had not moved below 60-cm depth.
Traditional pesticide degradation analysis would have assumed that all
loss of mass (pesticide not accounted for) was due to degradation. However,
tension-free pan lysimeters at the 90-cm depth, which collected drainage
water through preferential flow paths, revealed that as much as 50% of
the applied pesticide had leached out of the root zone and was, therefore,
not detected by soil sampling. Failure to account for the shift in flow
and transport processes in the sampling methods would have resulted in
the inaccurate conclusion that this pesticide had limited mobility due
to high degradation rates, when in fact the opposite was true. Another
important finding by Essington et al. (1995) was that between 68 and 100%
of the pesticide transport occurred during the first two storm events following
application. They concluded, as have Shipitalo et al. (1990), that rainfall
timing relative to application is a key factor to pesticide mobility. Thus,
while characterizing a soil’s chemical and hydraulic properties is important,
the timing and intensity of rainfall events following chemical (fertilizer,
pesticides, etc.) applications play a significant role due to their control
of the hydrological processes. A light rainfall following chemical applications
may not be sufficient to initiate macropore flow. Consequently, infiltration
into micropores occurs and the soil behaves as a single-region flow system.
The result is that much of the chemical becomes slowly mobile to immobile
in the micropores. Subsequent heavy rainfalls, which result in macropore
flow, cause the soil to then behave as a two-region flow system. The preferential
flow region may either enhance or reduce chemical leaching, depending upon
the degree of mass transfer between the chemical rich micropores of the
soil matrix and the preferential flow paths.
A logical extension of the previously discussed flow and transport
is the study of transport of immiscible fluids. Multi-phase transport usually
involves the gas phase and one or more liquid phases. There is a need to
study these processes in order to predict the movement of (volatile) substances
such as pesticides, oil products, and other (organic) compounds.
Jury et al. (1980) determined the loss of pesticide via volatilization
and diffusion in the vapor phase and via advection and diffusion in the
liquid phase. Their investigation involved the movement of triallate in
soil samples at different values of the relative humidity. The total concentration
of the solute in the soil was given by
where Ct is the total concentration expressed as mass of
solute per volume of soil (ML-3), S is the adsorbed concentration
expressed as mass of solute per mass of soil (MM-1), C and Cg
are the concentrations in mass of solute per volume of liquid and gas phase
(ML-3), respectively, and q and qg
are the liquid and gas content, respectively, expressed as volume of fluid
per volume of soil (L3 L-3). The solute flux was
where Jt is the total solute flux, Dg is the gas
diffusion coefficient (L2T-1), Ddif is
the liquid diffusion coefficient (L2T-1), and all
other variables have been defined before. It should be noted that advective
transport in the vapor phase was considered to be negligible. Equation
(33) differs, therefore, only from Eq. (5) by the gas diffusion term. Under
some circumstances, such as non-isothermal flow, this might not be justified.
The continuity equation for one-dimensional transport in the absence of
a source/sink term is
Substitution of Eq. (32) and (33) into Eq. (34) results in the equation
that describes the total mass transport. To solve the resulting equation,
it should contain only one dependent variable, viz., a concentration in
a particular phase. The following relationships are useful for this purpose:
Gas and liquid concentration are related by Henry’s law
where KH (-) is the partition coefficient. Equation
(35) is only valid for dilute solutions. A linear adsorption isotherm in
the form of
Jury et al. (1980) made some additional assumptions to rewrite Eq. (34)
in terms of Cg
where e = r bKdKH-1
+ q KH + qg,
De = q gDg
+ KH-1q Ddif
and ve = qKH-1. For appropriate boundary
and initial conditions, Eq. (37) can be solved analytically for Cg.
Of course, due to hysteresis and non-equilibrium, Eq. (35) and (36) might
not be representative. This would subsequently influence the accuracy of
the solutions of Eq. (37).
Jury et al. (1980) considered two cases, viz., transport by diffusion
only (q = 0) and transport by advection-diffusion (q ¹
0), which obviously led to different solutions for Cg. An expression
for the solute flux at the surface, Jt(0,t), was found by using
Eq. (33), in conjunction with the solution for Cg and
Eq. (7). The cumulative loss was then obtained via integration of the flux
over time. The experimentally measured cumulative loss was used to determine
the effective diffusion coefficient, De. Knowledge of this De
enables one to make theoretical predictions of the mass flow. It was shown
that advection (evaporation) caused the vapor loss to increase slightly.
Loss of the pesticide was mainly due to depletion from the upper soil layer.
Because of the increase in the concentration gradient, diffusion becomes
more important close to the soil surface.
As pointed out earlier, multi-phase transport usually involves the gas
phase and one or more liquid phases. Thus far we concentrated our discussion
on the movement of a chemical which occurred in two immiscible fluids,
viz., water and the gas phase. Flow and transport processes become even
more complicated when we deal with the simultaneous movement of two immiscible
liquids, with or without the presence of a gas phase, as it occurs during
spills of nonaqueous phase liquids (NAPLs). NAPLs which are denser than
water are known as dense NAPLs (DNAPLs) and NAPLs which are lighter than
water are known as light NAPLs (LNAPLs) (Mercer and Cohen, 1990; Schwille,
1988). DNAPLs include solvents such as trichloroethylene (TCE; specific
gravity = 1.46) and tetrachloroethylene or perchloroethylene (PCE; specific
gravity = 1.63). LNAPLs include petroleum products such as gasoline (specific
gravity = 0.73) and toluene (specific gravity = 0.87) (Hunt et al., 1988a;
Mercer and Cohen, 1990). Although NAPLs are essentially immiscible with
water, they are slightly soluble or contain components which are soluble
in water. Consequently, large volumes of groundwater may become contaminated
by dissolved NAPLs or their dissolved components if NAPLs enter the subsurface
through leaks in underground storage tanks or through spills at the ground
surface (Freeze and Cherry, 1979; Fetter, 1988; Pinder and Abriola, 1986;
Schwille 1988). NAPL components may also occur in gaseous form mixed with
air in the unsaturated zone due to the volatility of many NAPL components
(Schwille, 1988; Abriola, 1988).
A major source of NAPLs in the subsurface is leakage from underground
storage tanks used by many industries to store petroleum and chemical products
(Tyler et al., 1987; Mercer and Cohen, 1990). Other sources or waste-producing
processes involving NAPLs include coal tars disposed of in pits, ponds
or landfills at gas production sites, steel industry coking operations
and wood treating operations (see, e.g., Villaume, 1985; Moore, 1989).
The main reason for distinguishing between LNAPLs and DNAPLs is that
a LNAPL plume tends to "float" in the vicinity of the groundwater table
whereas a DNAPL plume tends to "sink" into the aquifer (Schwille, 1984;
Mackay et al., 1985). While LNAPLs and DNAPLs behave quite differently
near the capillary fringe and below the groundwater table, their general
behavior in the unsaturated zone is quite similar. Both types of NAPLs
generally migrate downward in the unsaturated zone under the actions of
gravity and capillarity (surface tension effects), and may even spread
out over lenses of low-hydraulic-conductivity materials. As the spill progresses
downward through the unsaturated zone, some residual NAPL is retained around
the soil grains and trapped in the pore spaces due to surface tension effects.
If a sufficiently large quantity of NAPL enters the subsurface, it will
eventually reach the capillary fringe. In case of a LNAPL, the liquid will
accumulate at the water table, while in case of a DNAPL, the spilled liquid
will penetrate the water table, if its pressure exceeds the required displacement
pressure, and accumulate over less permeable lenses or layers or at the
bottom of the aquifer (Schwille, 1984). In either case, a certain amount
of NAPL will be immobilized in the unsaturated and saturated zones as residual
NAPL. The residual NAPL will then act as a source of subsurface contamination
due to the dissolution of the residual NAPL into the flowing groundwater
or into the recharge water infiltrating at the surface. The mobile (free-phase)
NAPL, which accumulates on the water table or over layers or lenses of
low permeability material, will also act as a source of groundwater contamination
due to dissolution of the NAPL (Schwille, 1984, 1988; Hunt et al., 1988a;
Feenstra and Cherry, 1988; Mercer and Cohen, 1990). Unless the NAPL is
removed from the subsurface, it may act as a source of contamination for
many years (Mercer and Cohen, 1990). It may be useful to note that, while
the mobile (free-phase) NAPLs may be pumped out of an aquifer by means
of wells, the immobile residual NAPLs can only be removed by special means
such as steam injection or surfactant-aided mobilization (Hunt et al.,
1988b; Mercer and Cohen, 1990; Ang and Abdul, 1991).
Schwille (1984) and Hunt et al. (1988a) pointed out that the spatial
distribution of a LNAPL plume will be greatly affected by the fluctuations
of the water table. The distribution of the LNAPL in turn affects its rate
of dissolution and the behavior of the resulting dissolved contaminant
plume (Fried et al., 1979; Pfankuch, 1984; Schwille, 1984). The spatial
variations of the aquifer material properties also play an important role
in the behavior of both LNAPL and DNAPL plumes (Schwille, 1984, 1988; Osborne
and Sykes, 1986; Feenstra and Cherry, 1988; Faust et al., 1989; Mercer
and Cohen, 1990; Oostrom et al., 1997; Hofstee et al., 1998).
As with the movement of a single liquid, usually water, the simultaneous
movement of two liquids is described by Darcy type equations and corresponding
continuity equations, which requires knowledge of retention and permeability
relations. The penetration of a NAPL into water saturated porous media,
either at the surface or at layers in the subsurface, is extremely sensitive
to the values of the displacement pressure. Hence, when predicting NAPL
behavior in soils and aquifers, the Brooks-Corey representations of the
hydraulic properties are to be preferred over those of van Genuchten (Oostrom
et al., 1997). Predictive models for the constitutive relations in multifluid
flow systems have been proposed based on retention curves of water-air
systems and values of the interfacial tensions (Lenhard and Parker, 1987a,b).
Measurement techniques to directly measure the retention properties were
developed by Lenhard and Parker (1988), Lenhard (1992), and Hofstee et
al. (1997). But it was not until very recently that a technique was developed
to directly measure the permeability of a NAPL at different saturations
in the presence of water (Dane et al., 1998).
Researchers in the southeastern United States have significantly contributed
to the increased capabilities of numerically modeling solute transport
during the past decade through the development of multi-region and multi-reaction
site transport models. However, practical use of such approaches is still
highly speculative and must be used with caution. The limiting factor to
the proper prediction of flow and transport is typically considered to
be the lack of or uncertainty in parameter values. While this report seeks
to alleviate that problem to some degree, we hope that this bulletin will
caution users to the fact that false information may be generated by using
inappropriate physical or chemical models. One may have access to excellent
data to determine the model parameters, but if the model is not based on
the appropriate flow regime and sorption type, then the results will be
of limited value and may even be erroneous. This bulletin points out the
different processes associated with different kinds of soils. One should
also keep in mind that these processes are temporally variant due to the
land use practices.
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