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Modeling microbial reactions at the plume fringe subject to transverse mixing in porous media: When can the rates
Modeling microbial reactions at the plume fringe subject
to transverse mixing in porous media: When can the rates
of microbial reaction be assumed to be instantaneous?
M. Chu, P. K. Kitanidis, and P. L. McCarty
Department of Civil and Environmental Engineering, Stanford University, Stanford, California, USA
Received 15 July 2004; revised 14 February 2005; accepted 22 February 2005; published 2 June 2005.
[
1
]
In this research, we investigate the large-time solution behavior of a representative
bioreactive transport model under the conditions that the mixing of two required substrates
occurs only in the directions transverse to groundwater flow. The transport physics is
governed by the commonly used advection-dispersion equations at a steady uniform flow
field. The microbial population dynamics are described by double Monod kinetics and a
linear decay term. Through mathematical analyses we developed useful formulations to
estimate the size of reaction zones and the level of microbial concentrations with the
model parameters. The results show that microbial reaction rates are always limited by the
transverse transport of the substrates at steady state, providing the substrate concentrations
far away from the reaction zone are much larger than a characteristic concentration
determined only by microbial kinetic parameters. Thus the reaction rates can be
considered to be instantaneous. This greatly simplifies the governing equations and allows
us to efficiently solve the steady state solutions for large-scale problems. The method was
applied to a large-scale steady contaminant source problem, in which a dissolved
contaminant was assumed to be biodegraded only at its plume fringe because of transverse
mixing but not inside the plume. The results indicate that the transverse mixing at the
plume fringe may successfully constrain the spread of a plume of high total organic carbon
(TOC) concentrations (TOC = 500 mg/L) generated from a passive bioreactive barrier.
However, the TOC reduction along the plume center line is insignificant even after the
plume has traveled 10 km.
Citation:
Chu, M., P. K. Kitanidis, and P. L. McCarty (2005), Modeling microbial reactions at the plume fringe subject to transverse
mixing in porous media: When can the rates of microbial reaction be assumed to be instantaneous?, Water Resour. Res., 41, W06002,
doi:10.1029/2004WR003495.
1.
Introduction
[
2
] Engineered bioremediation and monitored natural
attenuation have become important options for the clean-
up of the widespread subsurface contamination by organic
compounds. Microbial reactions can be divided into two
categories, those requiring only a single substrate (e.g.,
fermentations), and those requiring two or more sub-
strates. The focus of this study is on the second case.
A groundwater contaminant may, depending upon the
circumstances, serve as either the electron donor (ED)
or the electron acceptor (EA). Because the contaminant
removal occurs only when the ED, the EA, and the
degrading bacteria are present simultaneously, the pro-
cesses that mix the contaminants and substrates can
control the contaminant removal rate [Cirpka et al.,
1999b]. Because of the complex nature of subsurface
environments, in situ bioremediation involves many con-
current physicochemical and biological processes. Thus,
using mathematical modeling coupled with site specific
information is considered to be an effective tool for
understanding the interactions among the various factors
involved and for identifying the rate-controlling processes
[Rittmann et al., 1994]. Mathematical models that account
for key processes can help to predict the environmental
impact of a spill and/or to screen possible remediation
technologies.
[
3
] In the past two decades many mathematical models
have been proposed for studying the fate and transport of
biologically reacting solutes in saturated soils and aquifers
[Baveye and Valocchi, 1989; Kinzelbach et al., 1991;
Murphy and Ginn, 2000]. Since the extent of mixing
may limit the overall reaction rate, especially when the
rate of biodegradation is rather fast compared to transport,
understanding mixing processes may improve our ability
to predict the extent of contaminant plume migration.
Generally, for a steady state flow field, the mixing
processes can be divided into two categories: (1) those
that take place along the groundwater flow direction,
including chromatographic mixing and kinetic mass trans-
fer, and (2) hydrodynamic dispersion and diffusion in the
direction transverse to the principal direction of flow
[Cirpka et al., 1999b]. Coupling an understanding of
the first type of mixing with biodegradation is now well
advanced [Oya and Valocchi, 1997, 1998; Cirpka and
Copyright 2005 by the American Geophysical Union.
0043-1397/05/2004WR003495$09.00
W06002
WATER RESOURCES RESEARCH, VOL. 41, W06002, doi:10.1029/2004WR003495, 2005
1 of 15 Kitanidis, 2000]; however, the second type of transverse
mixing coupled with biodegradation has not been suffi-
ciently studied.
[
4
] Conventional biofilm models used in bioremediation
typically deal with the conditions that the two required
substrates (ED and EA) enter into the biofilm from the same
direction (Figure 1a). However, when two required sub-
strates come together from different directions that are
transverse to groundwater flow (Figures 1b and 1c), the
dynamics of bacterial growth is quite different. Figure 1b
represents the scenario that biodegradation occurring at the
contaminant plume fringe. Figure 1c represents a case
where a long-term stationary substrate source (such as
nonaqueous phase liquids) meets a complementary substrate
(either EA or ED) that can stimulate microbial growth.
Under this condition, possible bacterial growth on one
substrate may be limited by the availability of the other,
and as a result, the microbial reaction zone becomes more
concentrated over time [Chu et al., 2003, 2004]. The
metabolically active bacteria may finally be restricted in a
small region unless their growth is limited by factors other
than the supply of the limiting substrates, such as available
pore space. Thus the reaction timescale in the microbial
reaction zone is likely to be much shorter than the substrate
transport timescale. However, it is not clear when this
hypothesis is valid.
[
5
] The current conventional methodology used to simu-
late bioreactive transport in the saturated subsurface is to
utilize the discretized form of advection-dispersion-reaction
equations, which are coupled partial differential equations
that are numerous and highly nonlinear. The classical
modeling approach can be infeasible due to the large
domain, the long periods, and fine discretizations that are
required [Sun, 2002] at sites where long-term contamination
sources are present and natural attenuation may be a viable
option. Therefore it is important to use innovative
approaches to obtain a better understanding of how biodeg-
radation at a contaminant plume fringe influences plume
migration.
[
6
] In this communication we investigate when the
assumption of instantaneous reactions occurring at a
plume fringe can be justified for the case of a steady
plume emitted from a continuous contaminant source in a
homogeneous steady flow field. We also explore how
biodegradation at a plume fringe may affect the plume
spreading and migration. Transverse diffusive and/or
dispersive mixing at a plume fringe is assumed to be
the only important mixing mechanisms for the contami-
nant and the other rate-limiting substrate. The presentation
is organized in the following manner: we first describe
the mathematical equations that constitute the model
commonly used in bioreactive transport. Subsequently,
we explore the relationships between the characteristics
of microbial reaction zones and the substrate fluxes
consumed by microorganisms by considering a simple
one-dimensional counterdiffusion case.
[
7
] Next, we use the developed formulas to examine the
extent of microbial reactions subject to two parallel streams
of groundwater, one containing only ED and the other
containing only EA, in a two-dimensional domain. Then
we provide a hypothetical source zone contamination prob-
lem to illustrate the impact of transverse mixing coupled
with microbial reactions on the contaminant removal rates at
steady state and present a formula to estimate the plume
length.
2.
Govern