United States
Environmental Protection
Agency
Robert S. Kerr Environmental
Research Laboratory
Ada, OK 74820
Research and Development
EPA/600/S2-90/009 Apr. 1990
&EPA Project Summary
Denitrification in
Nonhomogeneous Laboratory
Scale Aquifers: 1. Preliminary
Model for Transport and
Fate of a Single Compound
F.T. Lindstrom and L. Boersma
A two-dimensional mathematical
model for simulating the transport
and fate of organic chemicals in a
laboratory scale, single layer aquifer
is presented. The aquifer can be
nonhomogeneous and anisotropic
with respect to its fluid flow
properties. The physical model has
open inlet and outlet ends and is
bounded by impermeable walls on all
sides. FuMy penetrating injection
and/or extraction wells can be placed
anywhere in the flow field. The inlet
and outlet boundaries have user pre-
scribed hydraulic pressure fields.
The steady state hydraulic pressure
field is obtained first by using the
two-dimensional Darcy flow law and
the continuity equation, with the time
partial derivatives being set to zero.
The transverse and longitudinal com-
ponents of the Darcy velocity are
estimated by using Darcy's law. The
chemical transport and fate equation
is then solved in terms of user stip-
ulated initial and boundary condi-
tions. The model accounts for the
major physical processes of storage,
dispersion, and advection, and also
can account for linear equilibrium
sorption, three first-order loss pro-
cesses, including microbial degrada-
tion, irreversible sorption and/or
dissolution into the organic phase,
metabolism in the sorbed state, and
first-order loss in the sorbed state.
The chemical may be released inter-
nally via distributed leaks, sources
that do not perturb the flow field, or
from fully penetrating injection wells.
Chemical compound may also enter
at the inlet boundary. Chemical mass
balance type inlet and outlet
boundary conditions are used. The
solution to the field equation for
hydraulic pressure is approximated
by a nodal point centered finite
difference method using the strongly
implicit procedure with a user
specified heuristic for choosing the
iteration parameter. A solution to the
transport and fate equations is
approximated with a forward in time
Euler-Lagrange time integrator
applied to the chemical transport and
fate semi-discretization.
This Project Summary was
developed by EPA's Robert S. Kerr
Environmental Research Laboratory,
Ada, OK, to announce key findings of
the research project that is fully
documented in a separate report of
the same title (see Project Report
ordering information at back).
Introduction
Laboratory scale, physical, test
aquifers are increasingly being used for
the study of transport and fate processes.
It is generally less expensive to evaluate
hypotheses for pollutant fate and
transport using laboratory scale aquifers
than to work under field conditions.
Furthermore, numerical models of the
fate and transport of chemicals in
aquifers are now rapidly coming within
the reach of environmental scientists.
These models are even cheaper and
faster to operate than are laboratory
systems. The current investigation will
Printed on Recycled Paper
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analyze the ability of laboratory aquifers
to validate mathematical models. This
interim report presents a mathematical
analysis of two-dimensional horizontal
transport and fate processes in aquifers.
This analysis led to development of a
computerized model. Further develop-
ment (later report) will add microbio-
logical processes to the physical and
chemical processes already addressed in
this report. In addition, results obtained
from the mathematical model will be
compared to the results obtained in a
laboratory test aquifer used to study in
situ denitrification as the first test case.
Aquifer pollution is an emerging and
rapidly growing problem in the United
States. Groundwator contamination is
insidious because measurements of the
problem have only recently been made
on a consistent basis. The magnitude of
mo pollution problem is becoming
increasingly clear as the data base
increases.
Pollution can result from catastrophic
events such as spills of toxic or otherwise
hazardous compounds. Other important
point sources include leaking storage
facilities and waste product disposal. A
growing concern in many areas is the
effect of agricultural practices on ground-
water quality. This form of contamination,
generally described as nonpoint source
pollution, has a cumulative effect both
across a land area and in time. Nitrate
contamination of groundwater is an
example of agricultural pollution. The
problem is increasing and, partly be-
cause the source of pollutant is poorly
defined now, it is likely to continue to
grow in significance as more information
becomes available.
Methods to decrease nitrate levels in
aquifers include decreasing or eliminating
the pollutant source. This approach is
reasonable since loss of nitrate from agri-
cultural systems constitutes an economic
loss to producers. This quantitative factor
and the more qualitative factor of
decreasing environmental pollution have
direct benefits to society. A second, more
expensive method to improve ground-
water quality is to remove the pollutant
from the ground water.
A variety of methods have been used
to restore the quality of groundwater. The
two major categories are physical
containment and chemical and/or biologi-
cal treatment. Physical methods,
including placement of barriers or
hydrodynamic control by pumping, have
been used with some success but are
most effective when used to isolate point
sources of pollution. Removal of the
pollutant from the groundwater is a more
reasonable strategy for pollutants
contributed by nonpoint sources or by
widely distributed sources. Chemical and
biological methods are commonly used in
situations where water is pumped out,
treated, and used. This class of methods
is used extensively for drinking water
supplies where the end product is
important enough to justify the expense.
A significant advantage of chemical
and biological methods is the possibility
of in situ aquifer restoration. A number of
chemical techniques have been used in
situ, and there is considerable interest in
the rapidly growing field of biorestoration.
The challenge of in situ methods is
maintaining appropriate conditions in the
aquifer itself. For biorestoration, the
important factors affecting rate and
efficiency of-contaminant degradation are
1) presence of microbes suitable for
degrading the pollutants; 2) energy
sources and electron acceptors to sustain
adequate microbial growth; 3) distribution
of pollutant, substrate, and organisms in
the aquifer; and 4) flow properties of the
aquifer, including well locations and flow
rates.
A number of studies have
demonstrated that there is microbial
activity in aquifers. Such organisms are
generally considered to be substrate lim-
ited, particularly in anaerobic environ-
ments. In fact, pollutants have probably
stimulated microbial activity by increas-
ing substrate concentrations. Biological
denitrification has been observed in
aquifers and in saturated sediments.
Findings from low temperature environ-
ments indicate that denitrifiers can
function under normal aquifer conditions.
There are also limited data that suggest
that carbon substrate additions may
increase nitrate utilization. Several stud-
ies provide evidence that biorestoration
processes, occur in aquifers.. The evid-
ence is clear for degradation of hydro-
carbons in aerobic aquifer environments
where microbial counts, oxygen con-
sumption and hydrocarbon loss all
increase. Denitrification has been ob-
served in aquifers, artificial aquifers, and
in microcosms constructed of aquifer
materials. In addition, biological denitrifi-
cation is commonly observed in reactors
designed to treat groundwater after it has
been pumped to a surface treatment site.
The experiments listed above indicate
the potential for aquifer restoration by
biological denitrification. The utility of
biorestoration methods depends on
establishing the proper conditions for
microbial population growth. In addition,
field scale restoration depends on the
distribution of microbes, substrate, and
nitrate. The limiting factor among these is
usually substrate concentration. There-
fore, effective biorestoration methods
require injection of a carbon source.
Aquifer injection and plume movement
have been studied extensively,
particularly using solute transport models.
Models have been useful for developing
an understanding of basic processes
affecting solute distribution in aquifers but
are generally not precise enough to
predict field situations reliably.
The common failing of models for field
situations is the treatment of dispersion. If
inadequate data are available to
characterize aquifer hydraulic conductiv-
ity, the dispersion coefficient must be
increased to include the apparent
dispersion caused by variation in aquifer
material ptop'ertieSTThisTe~sTiltsiri^"sc"ale
dependent dispersion coefficient based
on the specific properties of the flow
system under investigation rather than
the properties of the porous medium.
Predictions of substrate spreading are
only as good as the theoretical
understanding and the field data that are
available. This includes understanding
dispersion and availability of hydraulic
conductivity coefficients applicable to
field situations. Understanding of the flow
field at an aquifer restoration site is
critical because methods for spreading
added constituents throughout the aquifer
depend on reliable prediction of the
effects of injection rate and concentration,
injection pulsing, and pumping from
adjacent wells..
If biological denitrification is to be
used as an effective technique for
restoration, a fundamental understanding
of the transport and fate processes is
required. In addition, knowledge about
the important limiting factors, or limiting
system properties must be acquired.
Theiefpre,,_tf)p JmjTie.diate, ,pbjective,,,vyas
to develop a preliminary mathematical
model and associated computer code to
describe substrate injection into an
aquifer and to use the model in a
sensitivity fashion to assess the mag-
nitude of the physical and biological
factors controlling aquifer denitrification
processes and identify those which can
be manipulated to enhance the process.
The preliminary mathematical model
addresses primarily aquifer fluid transport
phenomena including perturbations due
to presence of injection and withdrawal
wells. Solute movement includes advec-
tion, dispersion, molecular diffusion, and
simple first-order chemical and/or biologi-
cal reactions in the aquifer. The math-
ematical modeling effort presented here
is part of an ongoing study of aquifer
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restoration being conducted by the
Environmental Protection Agency at the
Robert S. Kerr Environmental Research
Laboratory, Ada, Oklahoma.
One of the long-term goals of this
study is development of a mathematical
model of aquifer denitrification processes
enhanced by stimulation of microbial
population. The experience gained from
developing the preliminary model is
currently being used to develop a two-
dimensional model for the simultaneous
transport and fate of oxygen, substrate
(methanol), nutrients, and nitrate in the
single layer aquifer. Two independently
operating microbial populations are
included in the model, both using
modified Monod kinetics.
-Physieal-Aquifers-at-RSKERb—
Two large (4 ft wide, 4 ft high, 16 ft
long) physical aquifers were constructed
at the USEPA Robert S. Kerr Environ-
mental Research Laboratory in Ada,
Oklahoma. Each aquifer contains three
horizontal layers of material, with each
layer assumed to be homogeneous and
isotropic with respect to water flow.
These systems can be used for validation
of mathematical models that simulate the
hydrodynamic pressure distribution, for
the study of transport and fate of chem-
icals, and for evaluation of the growth
characteristics of indigenous microbial
populations. The physical aquifers will
also be used for the study of proposed
physical and biological remediation
schemes.
Long-term Goals of the
Mathematical Modeling Effort
The goals of the present mathematical
modeling effort are to describe the fate
and transport of the physical models.
Mathematical modeling will include three
space dimensions for steady state hy--
draulics and simultaneous transport and
fate. Dissolved oxygen, nutrients (phos-
phorus), a carbon based substrate
(methanol), and dissolved nitrate, as well
as two spatially and temporally changing
microbial populations are all factors that
are to be included. The model will be
used to study scenarios for biorestoration
of aquifers contaminated with nitrates.
The procedures followed to achieve
these goals are to first develop a
preliminary model of the transport and
fate of chemical compounds. Constant
first-order loss processes and linear
equilibrium sorption are to be assumed.
This model is for two space dimensions
and simulates the "aquifer" slab only.
The preliminary two-dimensional mod-
el, called LT2VSI, will be used to make
preliminary numerical studies of several
scenarios for injection and/or extraction
well placement. LT2VSI will be expanded
to include four chemical compounds and
two microbial populations. This will be
LT3VSI. Next, LT3VSI will be expanded
to the full three-dimensional space. The
last model, LT4VSI will simulate the
physical aquifers and will allow for a
nonhomogeneous flow field and nonho-
mogeneous chemical and biological
conditions.
Detailed Assumptions in the
Preliminary Model
The preliminary mathematical model is
the first step in the model development.
With Vne^ Jong-term_gpal being the_
"descripfion~b"f the transport~arid "1 afe of~
chemicals in the full three-dimensional,
laboratory scale, physical aquifers at the
Robert S. Kerr Environmental Research
Laboratory (RSKERL). An intermediate
objective was to develop a preliminary,
two-dimensional model for horizontal
water and chemical transport and fate.
LT2VSI was developed for a situation
which consists of a single layer rep-
resenting the aquifer part of the three soil
layers making up the RSKERL aquifers.
The RSKERL physical models have
been constructed in such a way that
homogeneous and isotropic soil slabs
were obtained. They have impermeable
(no flow) side walls, an open top, partially
open ends, and an impermeable lower or
bottom boundary. The same assumptions
regarding the walls and the bottom are
made in the preliminary mathematical
model. However, the top boundary is
assumed to be a "no flow" boundary.
The hydraulic head distributions at the
open inlet and exit boundaries are
prescribed. Fully penetrating injection
and extraction wells may be present.
The model, hereafter referred to as
LT2VSI, makes it possible to evaluate
and validate a large number of the
relevant individual transport and fate
process laws. The important features of
LT2VSI are: 1) two-dimensional, horizon-
tal, steady state, fluid flow field defined
by a hydraulic head field which depends
on appropriate Dirichlet and Neumann
boundary conditions and the charac-
terizing spatial dependency of the
longitudinal and transverse components
of the hydraulic conductivity tensor at
saturation and 2) two-dimensional trans-
port and fate of chemicals in the
nonhomogeneous aquifer.
The distribution of chemicals is
affected by 1) advection and dispersion
in both the longitudinal and transverse
directions, 2) linear equilibrium adsorp-
tion/desorption processes on each of the
porous medium fractions, 3) three dif-
ferent first-order loss processes either
metabolism by soil microbes or chemical
reaction with other soil components in the
free phase, 4) other irreversible
processes in the free phase, either
metabolism or chemical reaction in the
sorbed phase, 5) the presence of zero
order sources of chemical, 6) appropriate
Dirichlet and Neumann boundary
conditions with a provision for nonzero
initial distribution of the chemical, and 7)
presence of fully penetrating injection
and/or extraction wells.
It is assumed that most, if not all, of
the chemical and biological process
coefficients are at least once
~continuously different'iable~~fDricffons" of"
the transverse coordinate and the
longitudinal coordinate.
Fluid Flow Field
The porous medium may be
nonhomogeneous and anisotropic with
respect to fluid flow and has impervious
walls on all sides. These conditions allow
evaluation of .two-dimensional transport
and fate. The assumptions concerning
the fluid flow field are: 1) the fluid flow
field operates at steady state conditions
at all times and 2) any fluid flow
perturbations introduced at the flow
boundaries propagate extremely rapidly
throughout the flow field, so that a new
steady state is achieved rapidly. Under
these conditions the fluid storativity term
in the fluid flow model may be neglected
for aquifers of the size we are con-
sidering; 3) the aquifer material can be
nonhomogeneous as well as anisotropic,
with the principal components of the
saturated hydraulic conductivity tensor
assumed to be once continuously differ-
entiable over the interior of the flow
domain; 4) Dirichlet boundary conditions
hold at both the inlet and outlet ends. The
hydraulic head at the inlet end and at the
outlet end are specified. No flow
Neumann or flux type boundary con-
ditions are specified along the walls.
Chemical Transport and Fate
Model
This model provides for unsteady
transport and fate of chemicals either
present initially at low concentrations or
injected at low concentrations into the
aquifer. Mass transport is via advection
(convection) and dispersion. The disper-
sion components are assumed to be
linearly dependent upon the moduli of the
velocity components of the flow field. The
longitudinal and transverse dispersivities
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as well as the tortuosity are assumed to
be once continuously differentiable
functions. The porous medium is
partitioned into three distinct fractions:
sorbing particles (clay minerals and small
silt particles), mildly sorbing particles
(large silt and sand particles), and
strongly sorbing organic matter.
Chemical can be introduced into the
aquifer with the "feed stream" at the inlet
end or from constantly emitting sources
in the aquifer. Fluids added by these
methods must have a low volumetric
concentration and the flow rates must be
low so that the previously established
fluid flow field is not disturbed. It is
assumed that density gradients, density
stratification, or local changes in the
transport and/or fate.. properties_ .ot-Jtbe, _
porous medium do not occur in time.
Water containing chemicals can be
introduced via fully penetrating injection
wells or extracted from similar wells by
pumping. Loss of chemical can occur via
first-order loss processes including
microbial and/or irreversible processes
such as chemical transformations and
precipitation in both the free and sorbed
phases. All the above chemical first-order
loss process coefficients are assumed to
be continuous functions.
Analytical solutions could not be found
for the initial and boundary conditions of
the problem stated here. This made it
necessary to approximately solve the
transport equations. The method used for
this in this report is a type of finite
difference Euler-Lagrange procedure
which is a modification of the method of
characteristics.
Conclusions „ ^^
Methods were developed for solving
equations that describe transport and fate
of chemicals in laboratory scale models
of aquifers. The mathematical model is
for aquifers consisting of a single layer of
material, which can be either hetero-
geneous or homogeneous and either
anisotropic or isotropic with respect to
the water flow field and can be either
heterogeneous or homogeneous but
isotropic with respect to the chemical
transport field properties.
The two-dimensional, horizontal depth-
averaged, transport and fate model can
be used for study of the important
physical aspects of remediation of
contaminated aquifers. A broad range of
remediation scenarios may be consid-
ered, including placement of injection/
extraction wells to induce plume spread-
ing or plume shaping and the effects of
regions of varying hydraulic conductivity
on the shape of the plumes. A
..^-comprehensive^ treatment ofJheJrjIet-and
exit port induced boundary conditions,
included with the analysis, represents a
significant step forward in modeling the
transport and fate of chemicals in
laboratory scale physical aquifers.
F.T. Lindstrom and L Boersma are with Oregon State University, Corvallis, OR
97331.
Thomas £ Short /s the EPA Project Officer (see below).
The complete report, entitled "Denitrification in Nonhomogeneous Laboratory
Scale Aquifers: 1. Preliminary Model for Transport and Fate of a Single
Compound," (Order No. PB90-186 305/AS; Cost: $17.00, subject to
change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
Ada, OK 74820
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use S300
EPA'600'S2-90/009
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