United States
Environmental Protection
Agency
Hazardous Waste Engineering
Research Laboratory
Cincinnati OH 45268
Research and Development
EPA/600/S2-87/029 Sept. 1987
SER& Project Summary
Effect of Capillarity and Soil
Structure on Flow in Low
Permeability Saturated
Soils at Disposal Facilities
Forest 0. Mixon, Ashok S. Damle, Robert S. Truesdale, and C. Clark Allen
Some permit applications propose to
place hazardous waste land-disposal
facilities in saturated zones of low-
permeability (low-K) soils. Naturally
occurring soils of this type are fre-
quently anisotropic and heterogene-
ous. Heterogeneities may be of lower
or higher permeability than the sur-
rounding soils, and may range from
small, isolated-pockets to large, inter-
connected zones. Low-K heterogene-
ities, particularly those extending long
distances perpendicular to the flow
direction, can retard flow. High-K
heterogeneities, particularly those
extending long distances horizontally
or vertically to a location in or near the
underlying aquifer, can result in rapid
migration of any pollutants reaching
these zones. Anisotropies in hydraulic
conductivity can range across several
orders of magnitude, resulting in rapid
migration of facility releases.
The final report addresses the move-
ment of the leachate after release from
the facility and does not consider those
factors relating to the containment
afforded by the facility proper. Discus-
sions include (1) soil characteristics and
the influence soil-forming mechanisms
have on the types of heterogeneities
and anisotropies to be expected in low-
K soil; (2) the roles played by the
tension-saturated zone, anisotropies,
and heterogeneities in subsurface
leachate movement; and (3) the advan-
tages and disadvantages of various
available computer models to simulate
leachate movement in the saturated.
low-K anisotropic, and heterogeneous
cases.
This Project Summary was devel-
oped by EPA's Hazardous Waste Engi-
neering Research Laboratory, Cincin-
nati, OH, to announce key findings of
the research project that is fully doc-
umented in a separate report of the
same title (see Project Report ordering
information at back).
Introduction
The EPA draft guidance document
prepared to accompany the July 26,
1982, regulations for hazardous waste
management recommends that liner
systems be constructed wholly above the
seasonal high water table, that is, in the
unsaturated soil. The document further
states that "a case-by-case demonstra-
tion of containment will be necessary for
landfills located wholly or partially in the
saturated zone." In all likelihood, permit
applications will be received which
propose to locate hazardous waste
disposal facilities in a saturated zone of
low permeability (low-K) soil.
The objective of this project was to
assess the effects of heterogeneities,
anisotropies, and the tension-saturated
zone with respect to movement of
subsurface leachate releases in satu-
rated low-Ksoils. Soil characteristics and
the influence of soil-forming mecha-
nisms on the types of heterogeneities
and anisotropies to be expected in low-
K soils are discussed. The advantages
and disadvantages of generic types of
computer models for application to
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leachate movement in saturated, low-K
soils are addressed. The basic require-
ments for adequate modeling and the
data input needed to solve the models
are identified and described. Two avail-
able computer programs are used to
obtain sample model simulations and to
generally demonstrate the usability of
these and other codes based on similar
computational techniques for prediction
of contaminant migration in low-K soils.
These models, however, do not consider
the tension-saturated zone. Also, het-
erogeneities considered in the simula-
tions are assumed to be continuous
rather than localized.
The role played by the tension-
saturated zone in subsurface leachate
movement was approached by formula-
ting the hydrodynamics as a modification
of classical free surface techniques. The
equations of motion of ground-water
flow in the vicinity of an excavation were
formulated to permit analytical determi-
nation of the free surface (i.e., the shape
of the top of the capillary fringe) and the
effects of capillarity on this shape and
on the entire flow network.
Approach
Modeling of Leachate
Migration in Saturated
Low-K Soils
In general, contaminants that are
soluble in ground water migrate by
miscible transport processes. Transport
mechanisms such as convective trans-
port, mechanical dispersion, and molec-
ular diffusion as well as physico-
chemical interactions between the soil
and the contaminant species are impor-
tant in determining the quality of ground
water. The interactions include adsorp-
tion/desorption of the contaminant
species on soil particles as well as
chemical reactions between soil chem-
icals and contaminants (e.g., ion
exchange). Aqueous leachates gener-
ated by land disposal of liquid and solid
wastes migrate by such miscible trans-
port mechanisms and form a large class
of typical ground-water contamination
problems. Liquid contaminants that are
insoluble in ground water are trans-
ported by immiscible (or multiphase)
transport processes. The present discus-
sion is limited to miscible contaminant
transport processes.
In saturated environments, ground-
water flow generally obeys Darcy's law,
which states that flow velocity is propor-
tional to both the hydraulic gradient and
hydraulic conductivity of the soil. Com-
plications arise from the heterogeneous
and anisotropic nature of soils because
the hydraulic conductivity is usually
variable in space and also dependent on
the flow direction. The dispersion and
diffusion of the contaminant species are
expressed by Pick's law, which, when
combined with convective flux, give the
net migration flux of the contaminant
species. The governing conservation
equations, when combined with flux
relations, reduce to a set of coupled,
nonlinear, second-order partial differen-
tial equations—one describing the
ground-water and flow and the other
characterizing the migration of chemical
species.
These equations are then solved using
appropriate initial and boundary condi-
tions and system parameters to obtain
flow and concentration profiles. The
boundary conditions are usually of two
types: (1) specified functional values
(e.g., head or concentration values at
specified locations); and (2) specified flux
values (e.g., water flow rate or mass flux
of solute). To solve the transient equa-
tions, initial functional values of head or
concentration over the entire region are
also required. For dilute solutions, the
ground-water density may be assumed
to be constant and independent of solute
concentration, thus uncoupling the flow
and transport equations.
Available computer simulation codes
are based on either analytical or numer-
ical solutions to the above equations in
one-, two-, three-dimensional form. The
level of complexity is a function of
geometry, heterogeneity of the porous
matrix, anisotropy, and transport mech-
anisms represented. Generally, the
energy transport equation is ignored,
although it may be significant in a few
special cases. The flow and solute
transport equation are generally
assumed to be uncoupled, and most
chemical transport models assume a
binary system (i.e., one contaminant of
importance in ground water).
The accuracy of any solution depends
on the accuracy of various parameters
incorporated into the equations. For flow
problems, the critical parameters are soil
hydraulic conductivity and porosity. To
account for heterogeneities and anisot-
ropies, vertical and horizontal compo-
nents of the hydraulic conductivity need
to be provided over the entire flow region.
Compressibility of the soil and fluid are
combined in a single parameter, specific
storage. The critical parameters in solu
transport problems are the hydrodynam
dispersivities and molecular diffusk
coefficients for the solute species
interest. The hydrodynamic dispersivi
is essentially a property of the flu
velocity and the porous matrix, and it
often dependent on flow direction.
addition, the attenuation mechanism
such as adsorption and chemical rea
tions, if important, need to be expressf
by suitable attenuation coefficients. (
all these parameters, the attenuatic
coefficients are the most difficult
obtain. However, this problem may I
avoided by considering the worst cas
of no attenuation. This is applicable •
the conservative specie that is expectf
to migrate the farthest.
Most computer simulations treat th
dispersion coefficient the same as tr
diffusion coefficient. Although the diffi
sion and dispersion terms are added 1
obtain overall dispersion coefficient
there is a significant difference betwee
them. Diffusion is a molecular phenort
enon and allows the flow of contam
nants against the direction of grounc
water flow. Mechanical or hydrodynam
dispersion arises from the uneven flo<
and division of flow of water as it move
through soil particles. The dispersio
depends on flow velocity and soil matr
and may mathematically be expressed b
diffusion-type equations. But unlik
molecular diffusion, the mechanic!
dispersion does not allow flow of cor
taminants against the ground-wate
flow. This problem is less significant fc
convection-dominant solute transpo
processes. For dispersion-dominate
cases, any prediction of contaminar
migration against the ground-water flo\
direction should by viewed with cautior
In low-K soils, where flow velocitie
are low, molecular diffusion may becom
a dominant solute transport mechanisrr
Theoretically, the hydrodynamic
dispersion coefficient is proportional t
the flow velocity, the proportionalit
constant being called dispersivity, a. (I
a simple form, the longitudins
hydrodynamic-dispersion coefficient, D
= BL |V|, and the transverse hydrc
dynamic-dispersion coefficient, DT = a
|V|.) Thus, at sufficiently low velocitie!
the molecular diffusion coefficient ma
become greater than DL and DT.
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Special Considerations
The primary concern in modeling the
flow and solute transport in saturated
low-K soils is the presence of heteroge-
neities in these soils. Because of the high
resistance of low-K soils to ground-water
flow, the effects of nonuniformities such
as stratified permeable sand layers,
fractures, and fissures become very
important as these provide the low-
resistance path to leachate flow. For very
low-K soils with hydraulic conductivity
less than 1 Cf9 cm/sec, almost all the flow
may be expected through such
nonuniformities.
Any applicable model must be able to
represent these nonuniformities ade-
quately. Finite element models offer an
advantage in this respect, as they can
better accommodate uneven distribution
of heterogeneities. Simulation of frac-
tures present special problems as these
represent extreme discontinuity in the
soils with porosity equal to unity, and the
ground-water flow equation may not be
strictly applicable in such a case.
A second important consideration in
low-K soils is the contribution of the
molecular diffusion process to solute
transport. For very low flow velocities,
such as 10"* cm/sec (e.g., with K = 10~7
cm/sec and hydraulic gradient = 0.01),
the hydrodynamic dispersion coefficient
may become smaller than the molecular
diffusion coefficient which is usually in
the range of 10"5to 10"8cm2/sec. In such
cases, molecular diffusion may represent
a dominant transport mechanism over
advection and hydrodynamic dispersion.
Applicable models should, therefore,
include a molecular diffusion term in the
solute transport equation, along with
advection and hydrodynamic dispersion
contributions. Also, the hydrodynamic
dispersivity data for low-K soils are
generally not available, and data on other
soils may indicate higher values. Based
on laboratory experiments, low values of
dispersivities may be expected for uni-
form low-K soils.
Another aspect of simulations of low-
K soils is the large time increment and
time scales involved. Long time periods
may be required for significant advance-
ment of the concentration front. Over
such long periods, the boundary condi-
tions may become variable and time-
dependent. Examples of these boundary
conditions are the concentration and flux
of solute species at the source and the
prevailing hydraulic gradients in the flow
region. In such situations, models incor-
porating variable, time-dependent boun-
dary conditions may be desirable.
Sample Model Simulations
Two available computer programs
were used to obtain sample model
simulations and to demonstrate gener-
ally the usability of these and other codes
based on similar computational tech-
niques for predicting contaminant migra-
tion in low-K, saturated soils:
1. SEFTRAN—Simple and Efficient
Flow and Transport—code deve-
loped by Huyakorn of Geotrans, Inc.
This model is based on finite element
techniques and can allow rectangu-
lar or triangular elements for flexible
geometry.
2. Two-dimensional U.S. Geological
Survey Model developed by Konikow
and Bredehoeft of USGS. This model
is based on finite difference tech-
niques and uses the method of
characteristics to solve the solute
transport equation.
Both programs provided analyses of
two-dimensional fluid flow and contam-
inant transport in areal/cross-sectional
configuration of saturated heterogene-
ous and anisotropic media. The solute
transport part can take into account
convection, hydrodynamic dispersion,
equilibrium adsorption, and first-order
decay processes. The SEFTRAN model
takes into account molecular diffusion,
whereas this term is ignored in the
USGS-2D model.
Contaminant migration through low-K
soils may be described as a two-step
process. In the first step, the contaminant
migrates vertically through saturated
low-K soils to an underlying aquifer or
a more permeable zone. In the second
step, the contaminant entering the more
permeable zone or aquifer is transported
horizontally away from the source. These
two steps were simulated with the above
mentioned codes.
The first sample model simulation
studied vertical migration of a contam-
inant from a hazardous waste land
disposal facility to an underlying aquifer
through saturated low-K soil. The SEF-
TRAN code was used for this case, and
the effects of heterogeneity and aniso-
tropy of the soil were examined in this
simulation. The heterogeneity was sim-
ulated by introducing a thin, highly
permeable, continuous sand layer in an
otherwise homogeneous low-K soil. Also
simulated was the case of very low-K of
soils with and without molecular
diffusion.
In the second sample model simula-
tion, horizontal migration of contami-
nants from the landfill site through an
underlying aquifer was simulated using
the USGS2D model. Here also the effects
of heterogeneity and anisotropy of the
permeable aquifer were studied.
Conformal Mapping
As stated previously, of particular
interest is that situation where a landfill,
surface impoundment, or waste pile
would be located in saturated low-K soil.
A facility so located would tend to
influence local flow dynamics, including
the water table and the capillary fringe
(tension-saturated zone).
The problem to be addressed is a
disposal facility sited such that its lower
surface is beneath the normal water
table. As in a well, there is a tendency
for ground water to flow into the exca-
vation. A complicating factor, however,
is capillary attraction, which draws fluid
into the soil interstices and creates a
zone of negative pressure, the capillary
fringe or tension-saturated zone.
In the capillary fringe, the region
between the water table and free sur-
face, the physical picture is that of
individual granules whose interstices
contain no significant vapor bubbles. This
zone is normally referred to as the
tension-saturated zone or the negative
pressure zone. Within this zone the
pressure ranges from atmospheric (P =
0) at the water table to some negative
value (P = -Hc) at the free surface, where
P = Manometer pressure in head
units, L
Hc = Equilibrium capillary rise, L.
Above the top of the capillary fringe,
the physical appearance is that of
individual granules whose interstices are
filled primarily with vapor or gas bubbles.
This region is referred to as the unsat-
urated zone and its moisture content
normally decreases with elevation or
increases with depth. Fluid motion in the
unsaturated zone is not addressed in this
report.
In order to assess the effects of the
capillary fringe on the fluid flow patterns
in the neighborhood of the excavation,
the equations of motion for the flow field
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are formulated and solved with the
capillary pressure, Hc, as an adjustable
parameter. Comparative analysis of the
solutions for various values of the
capillarity reveal and quantify its effects.
Classical potential theory, which app-
lies here, in which the flow is propor-
tional to the gradient of some potential,
provides a relatively easily visualizable
and familiar representation of the flow
field in the form of the flow net. This net
is comprised of lines of constant potential
and orthogonal, or perpendicular, lines
of constant stream function. The lines of
constant stream function, or stream
lines, represent particle tracks in steady
flow; hence no fluid flows across these
lines. Any two such lines form a stream
tube, through which the total flow is
constant.
Imagine that the lines of constant
potential and flow lines are drawn on an
infinitely stretchable thin sheet of rubber.
Imagine moreover that this rectangular
piece of rubber is positioned and
deformed so that the lateral edges
correspond to the centerline of the
excavation, the bottom of the pit, and the
free surface. If this stretching is done in
such a way that angles are preserved,
e.g., conformally, then the resulting
curvilinear network comprising the (now
deformed) lines of constant potential and
constant stream function represents a
new flow field, the one sought in this
study.
Conformal mapping is a mathematical
formalism for accomplishing this stretch-
ing. In a typical application, a simple flow
configuration (a rectangle) is mapped
onto a more complicated geometry (the
disposal facility) in such a way that the
important mathematical features of the
flow net are preserved and the resulting
curvilinear flow net is a theoretically
accurate representation of the flow field
in the more complex geometry. The
mathematical formalisms are developed
and solutions presented from which the
behavior at various values of the capil-
larity can be compared.
A simple mathematical transformation
converts the isotropic solution to an
anisotropic one through coordinate
stretching. The effects of anisotropy are
examined. Heterogeneities can also
influence flow. A local heterogeneity can
be of two types, either more or less
conducting than the adjacent soil struc-
ture. Conformal mapping techniques are
used in this project to examine flow paths
in the neighborhood of both types of
structure.
Findings
1. Soils frequently exhibit anisotropic
flow behavior in that the horizontal
hydraulic conductivity is greater
than the vertical. This phenomenon
can increase the net flow substan-
tially at a given hydraulic gradient
as a result of the more open horiz-
ontal flow path for liquid motion. For
example, a fourfold full force
increase in horizontal conductivity
can increase the net flow at a given
hydraulic gradient by approximately
fourfold over the isotropic situation.
2. Heterogeneities and anisotropy are
common in naturally occurring low-
K soils. The heterogeneities can
range from small, isolated pockets
to large, continuous or connected
regions with high hydraulic
conductivities.
3. Since interconnected secondary
porosity can significantly increase
the average hydraulic conductivity of
a low-K soil, these zones must be
mapped if subsurface leachate
migration is to be adequately
modeled or a landfill sited with any
assurance of contaminant contain-
ment by the natural low-K soil (in
the event of a failure in the primary
liner).
4. Several ground-water transport
models applicable to movement of
leachate releases in saturated low-
K soils that are heterogeneous and/
or anisotropic are available. Numer-
ical models that employ finite ele-
ment and/or method of character-
istics are the most applicable. None
of the models have been verified for
this case by comparison to actual
field conditions.
5. The analysis shows that the effect
of capillarity is to drawfluid vertically
into the soil interstices and thence
to open the area through which fluid
can flow into the excavation. Capil-
larity thus causes the flow into an
excavation to increase over the no
capillarity case; the magnitude of the
increase can be on the order of 10
to 20 percent of the total flow and
is higher for higher hydraulic gra-
dients.
6. Heterogeneities, such as joints,
fissures, animal and root holes, and
silt and sand seams can occur in a
soil and can cause an increase
several orders of magnitude in tl
average hydraulic conductivity of
low-K soil. Heterogeneities wi
high hydraulic conductivity, e.i
sand lenses, root holes and fissure
are of most significance when th
extend for a large distance, allowii
rapid migration of pollutants th
reach the heterogeneity. Heterog
neities with low hydraulic condu
tivities, e.g., rocks, are of mo
significance when they extend for
large distance perpendicular to tl
direction of flow. In this configur
tion, migration is retarded.
7. Conformal mapping is capable
providing the details of the f low fiel
e.g., the velocities at all locatioi
surrounding the disposal facilil
This velocity field can be used
conjunction with other numeric
models in the analysis of othi
phenomena of interest; namel
diffusional transport superimpose
upon the convective flow fiel
adsorptive and desorptive intera
tion of contaminants in the grour
water with local soils, reactiv
degradation of possible contam
nants catalyzed by mineral matti
within the soil or otherwise, ar
contaminant transport times fro
the disposal facility to the surface i
to adjacent bodies of water.
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Forest O. Mixon, Ashok S. Damle, Robert S. Truesdale, and C. Clark Allen
are with Research Triangle Institute. Research Triangle Park, NC 27709.
Jonathan G. Herrmann is the EPA Project Officer (see below).
The complete report entitled "Effect of Capillarity and Soil Structure on Flow
in Low Permeability Saturated Soils at Disposal Facilities," (Order No. PB
87-180 576/AS; Cost: $18.95, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Hazardous Waste Engineering Research Laboratory
U.S. Environmental Protection Agency
Cincinnati, OH 45268
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300
EPA/600/S2-87/029
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