United States
Environmental Protection
Agency
.Research and Development
Robert S. Kerr Environmental
Research Laboratory
Ada, OK 74820
EPA/600/S2-91/014 May 1991
EPA Project Summary
Denitrification in
Nonhomogeneous Laboratory
Scale Aquifers: 4. Hydraulics,
Nitrogen Chemistry, and
Microbiology in a Single Layer
FT. Lindstrom, L. Boersma, D. Myrold, and M. Barlax
A two-dimensional mathematical
model for simulating the transport and
fete of organic chemicals in a labora-
tory scale, single layer aquifer Is pre-
sented. The aquifer can be
nonhomogeneous and anlsotroplc with
respect to fluid flow properties. The
physical model for which this math-
ematical model has been developed Is
assumed to have open inlet and outlet
ends and to be bounded by Imperme-
able walls on all sides. The mathemati-
cal model allows placement of fully pen-
etrating Injection and/or extraction wells
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-dimen-
sional Darcy flow law and the continu-
ity equation.
Separate dynamic transport and fate
equations are then set up for each of
four dissolved chemicals, which Include
a substrate, nutrients, oxygen, and ni-
trate. Two equations, modeling the lo-
cal growth and decay of two microbial
populations, one operating with either
oxygen or nitrogen, the other only with
oxygen, are coupled to the transport
and fate equations. The four chemical
transport and fate equations are then
solved In terms of user prescribed Ini-
tial conditions. Boundary conditions are
zero flow at the top, bottom, and
sldewalls and accounting of mass at
the inlet and exit ports. The model ac-
counts for the major physical processes
of dispersion and advectlon, and also
can account for linear equilibrium sorp-
tlon, four Hirst order loss processes,
including Irreversible chemical reaction
and/or dissolution Into the organic
phase, and Irreversible binding In the
sorbed state. The loss of substrate, ni-
trate, nutrient, and oxygen Is accounted
for by modified Monod kinetic type rate
rules. The chemical may be released
internally by distributed sources that
do not perturb the flow field, or from
fully penetrating Injection wells. Chemi-
cal compound may also enter at the
inlet boundary. Chemical mass balance
type inlet and outlet boundary condi-
tions are used. The solution to the field
equation for hydraulic pressure Is ap-
proximated by the space centered fi-
nite difference method using the
strongly implicit procedure (SIP) with a
user specified heuristic for choosing
the Iteration parameter. A solution to
the transport and fate equations is ap-
proximated 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 an-
nounce 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 models of
aquifers are increasingly being used for
the study of aquifer processes. Often it is
less expensive to evaluate hypotheses for
Printed on Recycled Paper
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restoration procedures using laboratory
scale models than to work under field
conditions. Aquifer restoration methods are
not without hazards. Biorestoration pro-
cesses may alter the hydraulic properties
of the aquifer.
Furthermore, numerical models of the
transport and fate of chemicals in aquifers
are now rapidly coming within the reach of
environmental scientists. These models,
once validated for the systems they are
designed to simulate, are often cheaper
and much faster to operate In real time
response than the physical models. Thus
the combination of mathematical models
and laboratory scale models presents a
cost effective and time efficient method
for the study of bioremediatbn of con-
taminated aquifers.
In this report a mathematical models for
denMteatton processesin non-homoge-
neous, laboratory scale aquifers is de-
scribed. The nitrogen chemistry and mi-
crobiotogical processes that occur in a
single layer, saturated, aquifer are included
In this model A physical model aquifer is
used at the USEPA Laboratory at Ada,
Oklahoma for testing bforemediatfon pro-
cesses for denitrfficatton. This model will
be used to evaluate data generated by
this aquifer.
The success of biological denHriftoation
methods depends on availability of a fun-
damental understanding of the transport
and fate processes. In add'rtfon, knowl-
edge about the Important limiting factors,
or limiting system properties must be ac-
quired. Therefore, the Immediate objec-
tive was to develop a preliminary math-
ematical model and associated computer
code to describe substrate injection into a
single layer, laboratory scale aquifer and
to use the model In a sensitivity manner
to assess the magnitude of the physical
and biological factors controlling aquifer
denHrificatfon processes and identify those
which can bo manipulated to enhance the
process.
One of the long-term goals of this study
Is development of a mathematical model
of aquifer den'rtrification processes en-
hanced by stimulation of microbial popula-
tions. The experience gained from devel-
oping the preliminary model was used to
develop the two-dimensional model for the
simultaneous transport and fate of nitrate,
and oxygen, substrate, e.g., methanol and
Inorganic nutrients, In the single layer aqui-
fer, deserved in this report. Two indepen-
dently operating microbial pppulations are
Included In the model, both using modi-
fied Monod kinetics. The model, called
LT3VSI, is described in this report.
Physical Aquifers at RSKERL
Two large (4 ft wide, 4 ft high, 16 ft long)
physical aquifers were constructed at the
USEPA Robert S. Kerr Environmental Re-
search 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 f tow. These systems can be used
for validation of mathematical models that
simulate the hydrodynamic pressure dis-
tribution for the study of transport and fate
of chemicals, and for evaluation of the
growth characteristics of indigenous mi-
crobial populations. The physical aquifers
are also used for the study of proposed
physical and biological remediation
schemes.
Long-term Goals of the
Mathematical Modeling Effort
The goal of the present mathematical
modeling effort is to describe the fate and
transport of contaminants in the physical
models. This work includes two-dimen-
sional mathematical modeling of the steady
state hydraulics and simultaneous trans-
port and fate of the dissolved oxygen,
nutrients (such as phosphorus), a carbon
based substrate (for example methanol),
and dissolved nitrate. Also included are
two microbial populations which change
in space and time. The mathematical
model will be used to study scenarios for
biorestoration of aquifers contaminated
with nitrates.
The procedures being followed to
achieve these goals include several steps.
The first step was development of a pre-
liminary model of the transport and fate of
chemical compounds, with constant first-
order toss processes and linear equilib-
rium sorptton assumptions. This model is
for two space dimensions and simulates
only the 'aquifer" slab of the physical
model. The second step was to use the
preliminary, two-dimensional model, called
LT2VSI, for preliminary numerical studies
of several scenarios for injection and/or
extraction well placement. The third step
was to expand LT2VSI by including four
chemical compounds and two microbial
populations. This model, referred to as
LT3VSI, is the subject of this report.
Assumptions Underlying Model
LT3VSI
The RSKERL physical models have
been constructed in such a way that ho-
mogeneous and isotropic soil slabs were
obtained. They have impermeable (no f tow)
side walls, an open top, partially open
ends, and an impermeable lower or bot-
tom boundary. The assumptions regard-
ing the walls and the bottom made in the
preliminary mathematical model LT2VSI
reflect these conditions with the exception
that the top boundary was assumed to be
a "no flow" boundary. The hydraulic head
distributions at the completely open inlet
and exit boundaries are prescribed in
model LT2VSI and fully penetrating injec-
tion and extraction wells may be present.
Model LT2VSI was developed for a single-
layer of soil representing the aquifer part
of the three soil layers making up the
RSKERL aquifers.
This report describes an extension of
the preliminary model which is referred to
as LT3VSI. The hydraulics in LT3VSI are
the same as in LT2VSI. LT3VSI uses a
Two-dimensional, horizontal, steady state,
fluid flow field defined by a hydraulic head
field which depends on appropriate
Dirtohlet and Neumann boundary condi-
tions and characterizing the spatial de-
pendency of the longitudinal and trans-
verse components of the hydraulic con-
ductivity tensor at saturation. The model
determines simultaneous two-dimensfona/
transport and fate of four dissolved chemi-
cals, i.e.: oxygen, substrate, nutrient, and
nitrate in the nonhomogeneous aquifer.
The distribution of chemicals is affected
by advectton and dispersion in both the
longitudinal and transverse directions. Lin-
ear equilibrium adsorption/desorption pro-
cesses on each of the porous medium
fractions is permitted. Three different first-
order toss processes 1) chemical reaction
with other soil components in the frae
phase, 2) other irreversible processes in
the free phase, 3) chemical reaction in the
sorbed phase. Modified Monod microbial
degradation kinetics of the substrate sys-
tem including oxygen, nutrients, and ni-
trate in addition to two microbial popula-
tions is also permitted. Zero order sources
of the chemicals can be simulated. Appro-
priate Dirichlet and no flux Neumann
boundary conditions with a provision for
nonzero initial distribution of the chemi-
cals is another feature of the model. Fully
penetrating injection and/or extraction wells
are allowed.
H is assumed that most, if not all, of the
chemical and biological process coeffi-
cients are at least once continuously djf-
ferentiable functions of the transverse co-
ordinate x and the longitudinal coordi-
nate y.
Fluid Flow Field
The porous medium may be
nonhomogeneous and anisotropic with re-
spect to fluid flow properties and has im-
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pervious wails on all sides. These condi-
tions allow evaluation of two-dimensional
transport and fate. It is assumed that the
fluid flow field operates at steady state
conditions at all times. Also it is assumed
that any fluid flow perturbations introduced
at the flow boundaries propagate extremely
rapidly throughout the flow field, so that a
new steady state is achieved instantly.
Under these conditions the fluid storath/rty
term in the fluid flow model may be ne-
glected as shown for aquifers of the size
considered here. The aquifer material can
be nonhomogeneous as well as anisotro-
pte, with the principal components of the
saturated hydraulic conductivity tensor as-
sumed to be once continuously differen-
tiable over the interior of the flow domain.
Dirichlet boundary conditions hold at both
the inlet and outlet ends. Hydraulic heads
at the inlet and outlet ends are specified.
No-flow Neumann or flux type boundary
conditions are specified along the walls.
The Darcy velocity field components of
the flow vector are defined by the trans-
verse and longitudinal components of the
saturated hydraulic conductivity in the aqui-
fer. For isotropic and homogeneous po-
rous media an analytical representation of
the hydraulics in terms of a double sum
infinite series of trigonometric functions,
i.e., an eigenfunction solution procedure
is possible. However, even in the very
special isotropic case, the solutions are
usually very slow to converge. Thousands
if not millions of terms are necessary to
achieve the required number of significant
digits in each velocity component. Thus,
the hydraulic head field on the interior of
the flow domain, is usually approximated
by means of finite difference or finite ele-
ment methods.
Approximation of the Fluid Flow
Equations
The method chosen for the solution of
the flow equations is the Strongly Implicit
Procedure (SIP). A heuristic for choosing
the "cancellation of terms" parameter is
included in the models SIP subroutine.
Velocity Components
Once all components of hydraulic head
are known, the x and y components of the
Darcy fluid velocity field, and also the ef-
fective pore velocities, can be estimated.
However, since the hydraulic head field is
known only approximately and only on a
finite set of grid points, the two velocity
components must be numerically estimated
by interpolation.
Chemical Transport and Fate
Model
The assumptions, which form the basis
for the transport and fate model and which
hold for each one of the four chemical
compounds., i.e., substrate, nutrient, oxy-
gen, and nitrate are: 1) Mass transport is
via advection (convection) and dispersion.
2) The x and y dispersion components
are linearly dependent upon the moduli of
the velocity components of the flow field
for two-dimensional flow in an isotropic
and nonhomogeneous aquifer. 3) The po-
rous medium can be partitioned into three
distinct fractions sorbing particles (clay
minerals and small silt particles), weakly
sorbing particles (large silt and sand par-
ticles), and strongly sorbing organic mat-
ter with linear equilibrium sorptton rule as-
sumed for the porous medium. 4) Chemi-
cals 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 enough 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 of the porous medium do not
occur in time. 5) Water containing chemi-
cals can be introduced via fully penetrat-
ing injection wells or extracted from simi-
lar wells by pumping. 6) Loss of chemical
can occur via first order irreversible loss
processes such as chemical transforma-
tions and precipitation in both the free and
sorbed phases in addition to loss via mi-
crobial degradation. 7) Microbiological pro-
cesses are modeled using modified Monod
kinetics. The model developed here in-
cludes two microbial populations, utilizes
substrate under both aerobic and anaero-
bic conditions.
Consideration of the balance of chemi-
cal mass leads to the coupled system of
four nonlinear, two-dimensional, transport
and fate equations as the generic trans-
port and fate equation. This equation is
used to describe the transport and fate of
each compound in the aquifer. Closed form
solutions such as combinations of elemen-
tary functions or eigenfunctions do not
exist for the system of equations. There-
fore an approximate solution must be ob-
tained using numerical procedures. The
procedure used here is a type of finite
difference Euler-Lagrange procedure,
which is a modification of the method of
characteristics.
Conclusions for the Model
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 heteroge-
neous or homogeneous and anisotropic
or isotropic with respect to the water flow
field and heterogeneous or homogeneous
but isotropic with respect to the chemical
transport field properties.
The two-dimensional transport and fate
model can be used for study of the impor-
tant aspects of bioremediation of aquifers
contaminated with nitrogen. A broad range
of aquifer remediation scenarios may be
considered. These scenarios could include
studies of placement of injection/extrac-
tion wells to induce plume spreading or
plume shaping and the effects of regions
of varying hydraulic conductivity on the
shape of the plumes. The comprehensive
treatment of the inlet and exit port in-
duced lx>undary conditions, included with
the analysis represents a significant step
forward in modeling the transport and fate
of chemicals in laboratory scale physical
aquifers. .
•&U.S. GOVERNMENT PRINTING OFFICE: 1992 - 648-000/40223
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F.T. Undstrom, L Boersma, D. Myrold, and M. Bartaz are with Oregon State
University, Corvallis, OR 97331.
Thomas £ Short is the EPA Project Officer (see below).
TTi&complotereport, entitled **Dentrffication in Nonhomogeneous Laboratory Scale
Aquifers: 4. Hydraulics, Nitrogen Chemistry, and Microbiology in a Single Layer,"
(OrdorNo.PB91-182345/AS; Cost: $17.00, subject to change) will be available
onfyfrom:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Off her 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
BULK RATE
POSTAGE & FEES PAID
EPA
PERMIT No. G-35
Official Business
Penalty for Private Use $300
EPA/600/S2-91/014
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