Introduction
Heavy metals, including chromium, arsenic, copper, nickel, selenium,
technetium, uranium, and zinc, are widespread and hazardous subsurface
contaminants in groundwater aquifers . For
many heavy metals, their most stable oxidation state is often the most toxic
, and this oxidation state is typically the
highest that occurs under near-surface conditions. Additionally, the chemical
reduction of certain metals is known to reduce their mobility
. This has inspired efforts to manipulate in situ
conditions to stimulate microbial growth and achieve biologically mediated
metal reduction. This technique has been demonstrated, at least in some
settings, for chromium, uranium and selenium ,
nickel , technetium , and copper
, and has been noted as a viable bioremediation
technique by recent critical reviews .
Bioprecipitation, a process by which microbiological exudates react with
metals to produce an insoluble compound, has been widely observed
and has been noted by as
a remediation method. Bio-stimulants have also recently been shown to
effectively reduce chromium through abiotic oxidation–reduction (redox)
pathways and, after fermentation, for other
metals . Naturally, designing a remedial intervention using
one of this family of techniques benefits greatly from the use of a
multi-dimensional/multi-component numerical model of groundwater flow,
contaminant transport, and biogeochemical processes to evaluate different
remediation strategies under varying field conditions. The model should be
capable of capturing the transport behavior of electron donors, biomass, and
other species, dominant biogeochemical reactions, and how these processes
influence, and are influenced by, subsurface flow.
Although the development on in situ bio-reactive transport models goes back to
at least the 1980s, the literature is not vast. Early work focused on in situ
bioremediation of toxic organic compounds through oxidation. A thorough
mathematical and 2-D numerical study representative of this approach is due
to , who presented a three-equation model involving a mobile
electron donor (assumed to be the contaminant), mobile dissolved oxygen, and
immobile biomass. The contaminant was assumed to be consumed only in the
microbial growth reaction, which was linear in biomass,
in electron donor, and Monod in electron acceptor.
subsequently extended a reactive model of this sort to
three dimensions to simulate biodegradation of CH4.
presented a more complicated, unsaturated three-dimensional
model, which introduced Monod dependence on nutrients, and the potential for
two electron donors, with one inhibiting the other. This approach was further
elaborated upon in a study of trichloroethene degradation by
accounting for living and dead microbes, microbial predators, and first-order
kinetic sorption of all aqueous species (microbes were treated as mobile).
Another complex oxidation model was developed by , which
explicitly modeled both mobile and immobile biomass, contained a decay
network, and featured both anaerobic and aerobic oxidation, in competition.
The development of models for metal reduction is comparatively more recent.
For U(VI), field-scale modeling studies have been performed on bio-reduction
under anaerobic conditions at the Old Rifle Site in Colorado
. These conceptions treat the contaminant
as the sole electron acceptor, with an externally applied electron donor, and
the implied equations have a similar form to those devised by
: linear in biomass, Monod in contaminant, and Monod in
electron donor. For clarity, this is expressed symbolically as
∂C∂t∝∂D∂t∝BCKC+CDKD+D,
where t is time, C is the heavy metal (U(VI)) concentration, D is the
electron donor concentration, B is the biomass concentration, KC is
the metal reduction Monod constant, and KD is the electron donor Monod
constant. KC and KD respectively represent the concentration of C
and D at which the reaction rate is halved. Recently,
have published a numerical study of a column experiment with multiple
species, all of whose dynamics are of the above form, but including an extra
chemical inhibition factor. The models of were
implemented at field scale in CrunchFlow , using its
capability to represent single and multiple Monod formulations.
Systems of governing reactive transport equations for enzymatic microbial
Cr(VI) reduction have been presented by , and by
. described the Cr(VI) degradation
reaction slightly differently from :
∂C∂t∝∂D∂t∝BKC′KC′+CDKD+D.
KC′ is the concentration of Cr(VI) at which the reaction rate is halved,
which is similar to KC. However, although Eq. () appears
superficially similar to Eq. (), the C factor represents
entirely different behavior – not as an energy source but rather as an
inhibitor. Interestingly, since the right-hand side of Eq. () is a proxy
for the biomass growth reaction, C consumption is modeled as proportional
to biomass growth, but the biomass growth rate is modeled as independent of
C. Biomass dynamics are governed by a growth term proportional to donor
consumption and a first-order decay term, accounting for eventual biomass
die-off. Other authors e.g., have used a similar
approach. presented a relatively complex model which included
transport with both mobile and immobile biomass, and also included two
enzymes (both created due to biomass growth, but one conserved, and one
irreversibly consumed during bio-reduction). Neglecting the
irreversibly consumed enzyme and the mobile–immobile behavior, this model
shares its electron donor and biomass dynamics with the model of
. It differs significantly from other models that we are
aware of by treating the Cr(VI) degradation reaction in this model as an
incidental enzymatic process, and is governed by the following Monod
equation:
∂C∂t∝BCKC+C.
There is strong experimental support for this approach
e.g.,, and this is arguably more defensible in a real,
complex geochemical system in which there are multiple competing donors and
receptors, and given that there is evidence for indirect reduction pathways,
e.g., by metabolites . All of the models of Cr(VI)
bio-reduction discussed above appear to be one-dimensional only.
A general three-dimensional bio-reactive transport model (not specifically
focused on heavy metals) which models biomass as a separate species, and
explicitly models electron donors and acceptors, was presented by
. Biomass growth is taken to be proportional to biomass
concentration, with arbitrary user-selectable Monod and inhibition terms, and
biomass decay is taken to be a first-order process with no positive floor
value. Unlike the models discussed above, donor and acceptor consumption
rates are taken to be proportional to the biomass concentration growth rate,
rather than its magnitude. A more recent code, GeoSysBRNS
, also models general three-dimensional
multi-species transport processes with bio-mediated A+B→C
reactions, but with somewhat simpler biomass dynamics than that presented by
.
Our literature review did not reveal discussion of field-scale bio-reduction
models for heavy metal species besides uranium. It thus appears that the
primary example of a bio-reduction model applicable to modeling a real-world
remediation scheme is the CrunchFlow model of uranium treatment at the Rifle
site, which was discussed above. We set out to develop a new model, dubbed
chrotran, which is optimized for modeling bioremediation of Cr(VI),
but of sufficient generality that it may be used for bioremediation of other
metals, or for abiotic reduction, with ease. The key features of the model we
developed are as follows:
Abiotic reaction of electron donor and contaminant
Recent experimental results
have established a rapid direct redox reaction when molasses is used as
an electron donor and Cr(VI) is the contaminant, rather than the bio-mediated reaction previously posited.
It is thus crucial to include this behavior in a model aimed at remediation design.
Indirect Monod kinetics
On account of the evidence
for modeling Cr(VI) degradation with Eq. (), we implemented this general formulation as opposed to one which ties all contaminant degradation to a single biomass growth equation.
Bio-fouling/bio-clogging
It is well known in practice that one of the problems afflicting bioremediation schemes is build-up of biological material near the amendment injection point.
This reduces the hydraulic conductivity, interfering with amendment injection, and may rapidly consume any amendment that does manage to pass through it.
The model thus contains feedback between local biomass concentration and flow parameters such as porosity and hydraulic conductivity.
Biomass crowding
Similarly, if biomass becomes overly dense, this causes cell stress, which reduces the rate of further growth.
Since clogging is enabled, this behavior was added as well.
Modeling of amendment additives
To address clogging or to attempt to spread electron donors farther from the well before
they are consumed, additional chemicals may be injected to reduce biomass concentrations, and their reactive transport behavior is incorporated.
Multiple donor consumption pathways
The best model of electron donor consumption by biomass may be proportional to biomass
concentration or biomass growth, and the model can handle any such combination.
Building this functionality required custom programming beyond what is
embedded in existing reactive transport codes . To
accomplish our goal, we turned to pflotran , which is open source and has a modular structure
featuring a “reaction sandbox” interface that
allows derivative versions with custom reaction behavior to be developed and
compiled. We developed chrotran based on the existing
pflotran code, taking advantage of the reaction sandbox interface to
implement complex model features not included in its basic microbial packages
while leveraging other aspects of pflotran, such as its
high-performance computing capabilities. No changes to the flow and transport
part of pflotran were needed.
In Sect. , we present the mathematical details of
chrotran and justify some of the decisions underlying the model. In
Sect. , we present two numerical studies which
illustrate chrotran and also suggest an interesting conclusion
regarding Cr(VI) remediation. In Sect. , we briefly
summarize what has been presented. The chrotran 1.0 user manual is
presented in Appendix , which gives instructions on how
to install and use the software.
Model description
We consider flow and transport at aquifer scale. Conceptually, the aquifer is
modeled as saturated, with incompressible water moving in accordance with
Darcy's law. We note that, since chrotran is built on top of
pflotran, it inherits all of pflotran's groundwater flow
modeling capabilities. This includes the ability to consider unsaturated and
otherwise multiphase flow conditions, which are beyond the scope of the present
discussion. Please see the pflotran user manual
for details on its complete capabilities. Two
transport processes are considered – namely, advection with Darcy flow and
Fickian dispersion. Multiple reaction terms are then added in order to
capture the complex chemical dynamics during remediation. As the model is
intended to be used for remedial design, every effort was made to simplify
the formulation to use the smallest number of explanatory variables and
parameters, and to keep the equations at a high level of abstraction, so they
are not tied to one particular set of chemical species.
The following are the several species whose dynamics are captured by the
system of reaction equations, each with their own symbols:
Biomass, B(molmb-3),
representing the concentration of all microbes and their associated extracellular material.
The concentration of biomass is expressed in terms of bulk volume (mb3), which includes both the volume of the porous medium and the solution.
The quantification of biomass as a “molar” rather than a mass concentration is unusual, and was done for two reasons: (i) to avoid hard-coding units in which biomass
concentration is to be specified, and (ii) to simplify presentation of the model, so all governing equations have the same units. A mole of biomass should be understood
as an equivalent mass: any quantity can be used, as long as one uses a consistent definition throughout the model. In the examples in this paper, we use the definition 1 mol ≡ 1 g of biomass.
Aqueous contaminant, C(molL-1),
which we here assume is a heavy metal ion in its oxidized state, such as Cr(VI) or U(VI).
Electron donor,
which is part of the chemical amendment, and may be
immobile, represented by Di(mol:mb-3), or
mobile, represented by Dm(molL-1),
with exchange of mass between the two states.
Nonlethal biomass-growth inhibitor, I(molL-1),
such as ethanol, which is modeled as a conservative species but acts to slow microbial growth.
Biocide, X(molL-1),
which reacts directly with biomass and is consumed.
For convenience, we also define a total species aqueous concentration of the
electron donor, D, according to the formula D=Diθ(x,t)103+Dm[molL-1], where θ(x,t) [–] is the current porosity at x. For
simplicity, we assume that both the mobile and immobile donor participate
equally in all reactions. In reality, of course, bio-availability may differ
between mobile and immobile species. However, as long as the two phases are
near equilibrium, we may calibrate effective reaction rates that ostensibly
utilize both phases equally. This is what we have done.
Flow and transport
Groundwater flow equations
Flow may be modeled using the balance of water mass given by
ddtρwθ+∇⋅q=qM(x,t),
with the water mass fluxes related to head via Darcy flux q:
q=-∇ρwK(x,t)h(x,t),
where ρw [kg m-3] is the density of water,
qM(x) [kg m-3 s-1] is the local mass injection rate
into the system, K(x) [m s-1] is the local hydraulic
conductivity, and h(x,t) [m] is the local hydraulic head.
The hydraulic conductivity is continually updated in accord with the relation
K(x,t)=K(x,0)θ(x,t)θ0,
where θ0 [–] is the spatially uniform initial porosity, and
θ(x,t) is calculated according to
θ(x,t)=θ0-B(x,t)ρB,
where ρB [mol L-1] is the intrinsic biomass density. (Note that,
using our proposed definition of 1 mol of biomass as 1 g of biomass,
1 mol L-1=1 kg m-3.)
Advective–dispersive transport operator
We define T{⋅} to be an advective–dispersive transport
operator, which characterizes the hydrodynamic effects on solute transport.
For c, the concentration of an arbitrary mobile species,
T{c}≡-q⋅∇c+∇⋅(θD(q)∇c),
where D is a dispersion tensor that depends on the longitudinal
and transverse dispersivities, molecular diffusion as well as the Darcy flux.
For the work in this paper, we will only consider isotropic diffusion, and
thereby we set D=DmI, although chrotran can
handle more general dispersion tensors. Note that, while this is not shown
explicitly for compactness, all symbols in Eq. () are
functions of x and t.
Biogeochemical reactions
We define one governing equation for each species, mobile or immobile, as
well as two equations defining reaction rate expressions for algebraic
convenience. The governing equations include kinetically limited redox
reactions. These reactions are often non-instantaneous with redox-sensitive
species remaining in thermodynamic disequilibrium
, and a kinetic formulation is a fair
representation of this type of behavior . The
equations involve numerous parameters, whose symbols, units, and long-form
name in the chrotran input file are summarized in
Table . The parameter symbols follow a scheme in
which the first letter encodes the physical interpretation of the parameter
and the subscript specifies the governing equation in which they participate.
A symbol beginning with Γ is a second-order mass action rate constant,
with units of Lmol-1s-1. A symbol beginning with K is a
Monod or inhibition constant with units of concentration,
mol mb-3 or mol L-1, and represents the concentration
at which a process rate becomes 50 % of its maximum rate, all other
parameters being equal. A symbol beginning with λ has units of
s-1 and is interpreted as a pure first-order reaction rate
constant. A symbol beginning with S is dimensionless, and represents a
stoichiometric relationship between a reaction rate and the consumption rate
of a certain species.
chrotran parameter values used in the bio-fouling example in Sect. .
Symbol
Value
Units
α
1
–
Bmin
10-10
mol mb-3
ΓB
2.6×10-2
Lmol-1s-1
ΓCD
1
Lmol-1s-1
ΓX
2.6×10-5
Lmol-1s-1
λB1
10-5
s-1
λB2
10-15
s-1
λC
10-10
s-1
λD
0
s-1
λDi
1.5
s-1
λDm
10-2
s-1
KB
5×102
mol mb-3
KC
10-7
molL-1
KD
10-6
molL-1
KI
1
molL-1
ρB
103
molL-1
SC
3.3×10-1
–
SD1
10-5
–
SD2
2.0833×10-2
–
Before presenting the equations, it is useful to review all of the
biochemical processes that are incorporated into the model:
Abiotic reduction
This is an aqueous-phase bimolecular reaction between the electron donor, D, and the contaminant, C.
It is modeled with a classical second-order mass action rate law.
Bio-reduction
This represents the removal of the contaminant, C by the biomass, B.
The process is assumed to be linear in B and Monod in C.
Note that we are not assuming that reduction of C is directly tied to any particular cell metabolic process.
This form is sufficiently general that it can capture other bio-remediation processes besides bio-reduction of heavy metals.
Biocide reaction
This is an inter-phase bimolecular reaction between the biocide, X, and the biomass, B.
It is modeled with a classical second-order mass action rate law, with the added condition that B cannot fall below a specified minimum concentration Bmin.
Biomass growth
The core biomass growth reaction irreversibly consumes electron donor, D, to increase biomass, B.
As a biologically catalyzed reaction, it is assumed to be linear in B and Monod in D.
Two inhibition effects are assumed: a biomass crowding term, tunable with exponent α, attenuates growth rate as the biomass concentration rises.
The nonlethal inhibitor concentration, I, also reduces the reaction rate as its concentration increases.
Mobile–immobile mass transfer (MIMT)
This is a process with first-order kinetics, which models sorptive retardation of the electron donor.
Natural decay
This is an empirical process reflecting the idea that, if left unstimulated, both the amount of living cells and the amount of
extracellular material in the aquifer will ultimately return to their natural background level (i.e., Bmin).
This is modeled as a first-order process. Our model assumes that reduction is occurring as a dissimilatory reaction that occurs extracellularly, so biomass decay does not directly release heavy metal.
Respiration
This represents consumption of the electron donor for purposes of life maintenance, unrelated to biomass growth.
This is described by a first-order rate law which is proportional to biomass concentration, B.
The explanations of the operative processes and of parameter interpretation
above help the descriptions of factors and terms in the governing equations
presented below.
Reactive transport equations
Definitions of convenience reaction variables
The biomass growth reaction is linear in biomass concentration, has a Monod
dependence on electron donor, a tunable inhibition factor due to biomass
crowding, and a classic inhibition factor describing the impact of the
nonlethal growth inhibitor (as indicated by comment braces):
μB=λB1BDKD+D︷e-donorKBKB+Bα︷crowdingKIKI+I︷inhibitionmolmb3s.
The direct, abiotic reduction reaction is represented by a classical
second-order mass action law:
μCD=ΓCDCDmolLs.
Partial differential equations for mobile chemical components
The mobile components are all governed by the advection–dispersion operator,
T, defined previously, and also affected by extra terms
implementing the chemical processes outlined earlier (as indicated by comment
braces):
∂θC∂t=T{C}-λCBCKC+C︷bio-reduction-SCμCD︷abioticreductionmolmb3s,∂θDm∂t=T{Dm}-SD1DmDμB︷biomassgrowth-λDDmDB︷respiration-SD2θμCDDmD︷abioticreduction-λDiθDm+λDmDi︷MIMTmolmb3s,∂θI∂t=T{I}molmb3s,∂θX∂t=T{X}-ΓXBX︷biocidereactionmolmb3s.
Partial differential equations for immobile chemical components
The immobile component concentrations are affected only by the reactive
processes outlined above (again, indicated by comment braces):
∂B∂t=μB︷biomassgrowth-λB2(B-Bmin)︷naturaldecay-ΓB(B-Bmin)X︷biocidereactionmolmb3s,∂Di∂t=-SD1DiDμB︷biomassgrowth-λDDiDB︷respiration-SD2θμCDDiD︷abioticreduction+λDiθDm-λDmDi︷MIMTmolmb3s.
<sc>chrotran</sc> validation and remediation case studies
Relationship between the parameter names in the CHEMISTRY
card (Fig. ) and the mathematical symbols shown in
Sect. .
Symbol
Units
Name in CHEMISTRY card
α
–
EXPONENT_B
Bmin
mol mb-3
BACKGROUND_CONC_B
ΓB
Lmol-1s-1
MASS_ACTION_B
ΓCD
Lmol-1s-1
MASS_ACTION_CD
ΓX
Lmol-1s-1
MASS_ACTION_X
KB
mol mb-3
INHIBITION_B
KC
molL-1
INHIBITION_C
KD
molL-1
MONOD_D
KI
molL-1
INHIBITION_I
λB1
s-1
RATE_B_1
λB2
s-1
RATE_B_2
λC
s-1
RATE_C
λD
s-1
RATE_D
λDi
s-1
RATE_D_IMMOB
λDm
s-1
RATE_D_MOBIL
ρB
molL-1
DENSITY_B
SC
–
STOICHIOMETRIC_C
SD1
–
STOICHIOMETRIC_D_1
SD2
–
STOICHIOMETRIC_D_2
Maps of Cr(VI) concentrations (ppb) in the aquifer 470 days after injection ceased in each of the four scenarios discussed in Sect. .
Injection well location is denoted by a black X.
![]()
A sequence of snapshots of the cell-center groundwater seepage
velocity fields and biomass concentration distributions in the example of
Sect. . Velocity magnitude is indicated by arrow
length and direction by arrow orientation; the arrow tails are located at the
cell center; biomass concentration (g m-3) is indicated by green
intensity in each superimposed map. The initial condition snapshot is shown
in the upper left corner, with time increasing in the clockwise direction,
until the initial condition is reached again at day 416. The same scale is
used in each snapshot.
![]()
The pflotran software from which chrotran derives its
numerical flow and reactive transport solvers has gone through extensive
quality assurance testing , has been benchmarked against other reactive transport
solvers , and is used inside and outside the US
Department of Energy for mission-critical analytical work
e.g.,.
The new bio-reactive transport model that is constitutive of
chrotran is not available in any other software, so direct
benchmarking is not possible. However, extensive quality testing has been
performed by the developers. We have validated the code through batch and
multi-dimensional simulations that chrotran does satisfy the
governing equations we present for chemistry and permeability, and also that
it gives plausible, physically consistent results for a wide range of
scenarios. In particular, the repository includes batch regression tests which
cover abiotic reaction, abiotic reaction with sorption (MIMT), microbial
growth and decay, as well as interaction with biocide and nonlethal
inhibitor. In addition, a non-batch reference simulation featuring
bio-clogging is included. These benchmarks are located in subdirectories of
the chrotran_benchmarks directory in the developer branch
(dev) of the chrotran repository. In the top-level
directory resides a bash script, chrotran_benchmarks.sh that runs
all the regression tests.
To demonstrate the novel capabilities of our software, we present two example
studies, which together illustrate the interactions of all the types of
chemical species it permits to be modeled, along with its treatment of
bio-clogging. The input and auxiliary files for these two examples can be
found in the chrotran_examples directory in the chrotran
repository.
Case study: remediation of Cr(VI) by molasses and ethanol co-injection
This study concerns the co-injection of molasses (electron donor, D) and
ethanol (nonlethal bio-inhibitor, I) into a single well drilled in a
heterogeneous aquifer with an appreciable background Cr(VI) concentration.
The competition between direct abiotic reduction of Cr(VI) by molasses and
bio-reduction of Cr(VI), which exists since both reduction pathways consume
the electron donor, along with the impact of suppressing the biomass growth
is explored. The basic parameters used are those shown in
Figs. and , with changes as
indicated below.
Four related simulations are performed on the same 100 m × 100 m
two-dimensional heterogeneous hydraulic conductivity field, with geometric
mean conductivity Kg=10-4 m s-1, a multi-Gaussian
correlation structure with exponential semivariogram with correlation length
of 4 m, and σlnK2=2. Each simulation takes place over a span
of 500 days and begins with ϵ=10-20 mol L-1 initial
concentrations of all species, except C=1.923×10-5 mol L-1
(1000 ppb Cr(VI)), B=Bmin=10-10 mol mb-3, and
Di=10-20 mol mb-3. In all cases, there are no
flow boundaries at the north and south of the domain (y=0 m and
y=100 m), and constant head boundaries are imposed at the west and east of
the domain (x=0 m and x=100 m), such that there is a drop of head of
0.28 m between these faces. A single injection well exists at
(x,y)=(25 m, 50 m). For the first 10 days of the simulation, there
is no injection into the well. From day 10 to day 30, injection is performed at
the well with constant volumetric flow rate 272.55 m3 d-1 with
species concentrations discussed below. From day 30 to day 500, there is again no
injection at the well. A very large (arbitrary) ρB is assumed, so as
to eliminate the effect of biomass clogging from this simulation.
The four simulations differ in their chemistry only. Two direct abiotic
reduction rates are considered (ΓCD=1 L mol-1 s-1
and ΓCD=0 L mol-1 s-1) as are two different ethanol
concentrations in the injection fluid (I=1 mol L-1 and
I=ϵ mol L-1) in all four possible combinations. The injection
fluid chemistry always has Cr(VI) concentration equal to the initial
concentration (C=1.923×10-5 mol L-1), ensuring that no
chromium disappearance is due to dilution, and molasses concentration D=1×10-2 mol L-1.
Concentrations of Cr(VI) for each scenario are shown in
Fig. . It is apparent that little persistent reduction due to
biomass alone occurs, although ethanol co-injection does increase biomass
footprint, which has a noticeable and persistent effect. By contrast, the
rapid abiotic reaction between Cr(VI) and a constituent of molasses has more
impact. This is attributable to the fact that molasses has a large reducing
capacity, background concentrations of Cr(VI) are relatively low, and it has
a retardation factor of around 150 (obtained from ),
meaning that it has the potential to form a persistent permeable reactive
barrier around the well. The better performance in the presence of ethanol is
attributable to the fact that ethanol co-injection prevented consumption of
molasses by the biomass during the injection phase, and so molasses persists
over a larger area.
Case study: biomass clogging/unclogging due to acetate/dithionite injection
chrotran has the capability to model hydraulic conductivity
reduction due to bio-fouling and the use of biocide as a remediation
strategy. To illustrate model capabilities, we perform a simulation of
constant-head injection into a homogeneous aquifer in which the injection
fluid is amended initially with the biostimulant acetate (D=10-2 mol : L-1) for the first 400 days. The acetate amendment is
subsequently replaced with the biocide dithionite (X=3.5 mol L-1), for the remainder of the simulation. The basic
structure of the chrotran input file is the same as in the study
outlined in Sect. (this is to say, as shown in
Figs. and ), but with different
chrotran parameter values, as shown in Table .
We here make the reasonable p. 361 assumption that
biomass has the same density as water (recall that we everywhere use the
interpretation that 1 mol of biomass is defined as 1 g of biomass).
The simulation is performed on a 50 m square homogeneous hydraulic
conductivity field, with constant hydraulic conductivity K=9.8×10-5 m s-1 and initial porosity θ=0.15. Each simulation
takes place over a span of 500 days, and begins with
ϵ=10-20 mol L-1 initial concentrations of all species,
except C=1.923×10-5 mol L-1 (1000 ppb Cr(VI)),
B=Bmin=10-10 mol mb-3 and
Di=10-20 mol mb-3. No-flow boundaries are
imposed at the north and south of the domain (y=0 m and y=50 m), and
constant head boundaries are imposed at the west and east of the domain (head
0.28 m at x=0 m and head 0 m at x=50 m). A single injection well
exists at (x,y)=(25 m, 25 m), and constant head of 0.28 m is imposed at
its location.
A sequence of quiver plots representing the velocity field at nine points in
time, superimposed on the intensity of biomass concentration are shown in
Fig. . During the first 400 days of the simulation, biomass
concentration grows in the vicinity of the well, until hydraulic conductivity
drops to zero at the well and no influx occurs there; only ambient flow is
apparent, flowing around the impermeable biomass barrier near the well. At
this point, the biomass has become useless for bioremediation, as
contaminated aquifer water no longer travels through it. However, at day 400,
dithionite is introduced into the injection fluid and effectively
eliminates biomass in the vicinity of the well.
The region containing dithionite is relatively sterile and grows outwards
until the biomass concentration approaches background, and the initial flow
regime is recovered at day 416. Because initial and final conditions are the
same, this cycle may be performed indefinitely.
Summary and conclusions
For modeling in situ remediation of aqueous groundwater contaminants by
injection of aqueous amendment, we recognized the importance of mathematical
formulations and numerical codes that can represent multi-dimensional fluid
flow and multi-species contaminant transport in heterogeneous aquifers with
arbitrary injection regimes. For the particularly important case of heavy
metal remediation, a number of contaminant remediation processes (pathways)
are amenable to a unified modeling framework: bio-reduction,
bio-precipitation, and direct reduction by the chemical amendment. There have
previously existed no general tools appropriate for modeling such
interventions. With this background in mind, we developed a mathematical
model that describes the reactive transport dynamics of an amendment
(containing any combination of electron donor, non-lethal bio-inhibitor, and
biocide) with biomass and aqueous heavy metal contaminant. We also
implemented the mathematical model in a novel computational framework, called
chrotran, that is based on the open-source code pflotran.
pflotran's modularity and the reaction sandbox capability allowed us
to implement the model easily without making any changes to the flow and
transport code of pflotran. chrotran can harness the
existing capabilities of pflotran, which allows for simulations of
complex models with a large number of computational cells and degrees of
freedom. We described our computer implementation and explained how to use
chrotran to solve practical problems.
We also considered two demonstration studies related to chromium remediation.
The presented synthetic problems were formulated to be consistent with
real-world groundwater contamination problems and illustrate the capability
of chrotran to aid in the engineering design process. In one of the
studies, we discovered that, contrary to much existing theory, Cr(VI)
reduction was maximized by injecting molasses and suppressing biomass growth
to maximize the direct, abiotic reduction reaction. In the other, we showed
the feasibility of pulsed injection of bio-stimulant and biocide to alleviate
bio-fouling in the context of ongoing bioremediation.
We observe that because of the abstraction of our model and its parametric
flexibility, the chrotran equations can be used to model other
reactive transport behaviors besides the heavy metal bio-reduction that we
have focused upon, including basic advection–dispersion reaction interaction
(between C and D, in the absence of B). The bio-reduction model
captures any biodegradation that can be represented using a Monod equation,
as long as the contaminant represented by C is non-sorbing, and it does not
explicitly require the contaminant to be reduced. This potentially allows for
modeling the biodegradation of a wide range of organic contaminants, which
include but are not limited to hydrocarbons, chlorinated solvents,
pesticides, and volatile organic compounds.