Bioreactive Transport Research Articles

Development and calibration of a bio-geo-reactive transport model for UHS

The increased share of renewable energy sources will lead to large fluctuations in energy availability and increases energy storage’s significance. Large-scale hydrogen storage in the subsurface may become a vital element of a future sustainable energy system because stored hydrogen becomes an energy carrier available on demand. Large hydrogen amounts can be stored in porous formations such as former gas fields or gas storages, while caverns can contribute with high deliverability. However, the storage of hydrogen induces unique processes in fluid-fluid and rock-fluid interactions (for example, bio- and geochemical reactions), which may affect the efficiency of the storage. In the present study, a mathematical model describing the two-phase multicomponent flow in porous media, including bio- and geochemical reactions, is developed to predict these hydrogen-related processes. The proposed model extends an existing model in the open source simulator DuMux describing the bio-reactive transport process considering methanation and sulfate-reduction by geochemical reactions. Significant attention is placed on the reduction from pyrite-to-pyrrhotite coming with the generation of harmful hydrogen sulfide. This reaction is calibrated by developing a kinetic model in DuMux that mimics the observations of reactor experiments from literature. The developed and calibrated model is afterwards used for simulation runs on field scale to assess the impact on Underground Hydrogen Storage (UHS) operations. The developed kinetic model describes the reduction from pyrite-to-pyrrhotite in agreement with the observations in the literature, whereby particular focus was placed on the hydrogen sulfide production rate. The consecutive implementation of the transport model in DuMux on field scale, including the bio- and geochemical reactions, shows the potential permanent hydrogen losses caused by reactions and temporary ones induced by gas-gas mixing with the initial and cushion gas.

Competition within low-density bacterial populations as an unexpected factor regulating carbon decomposition in bulk soil

Bacterial decomposition of organic matter in soils is generally believed to be mainly controlled by the access bacteria have to organic substrate. The influence of bacterial traits on this control has, however, received little attention. Using the substrate-dependent Monod growth model, we develop a bioreactive transport model to screen the interactive impacts of spatial dispersion and bacterial traits on mineralization. Bacterial traits primarily involved in the bacterial response to the substrate concentration, such as the maximum specific uptake rate and efficiency, the adaptation time of the uptake rate and the initial population density, are considered. We compare the model results with two sets of previously performed cm-scale soil-core experiments in which the mineralization of the pesticide 2,4-D was measured under well-controlled initial distributions and transport conditions. Bacterial dispersion away from the initial substrate location induced a significant increase in 2,4-D mineralization. It reveals an increase of specific uptake rates at lower bacterial densities, more than compensating the decrease of specific uptake rates caused by substrate dilution. This regulation of bacterial activities by density, caused by the local depletion of substrate by competing bacteria, becomes dominant for bacteria with an efficient uptake of substrate at low substrate concentrations (a common feature of oligotrophs). Such oligotrophs, commonly found in soils, compete with each other for substrate even at remarkably low population densities. The ratio-dependent Contois growth model, which includes a density regulation in the expression of the uptake efficiency, is more accurate and convenient to calibrate than the substrate-dependent Monod model, at least under these conditions. In view of their strong interactions, bioreactive and transport processes cannot be handled independently but should be integrated, in particular when reactive processes of interest are carried out by oligotrophs.

Exposure-time based modeling of nonlinear reactive transport in porous media subject to physical and geochemical heterogeneity

Transport of reactive solutes in groundwater is affected by physical and chemical heterogeneity of the porous medium, leading to complex spatio-temporal patterns of concentrations and reaction rates. For certain cases of bioreactive transport, it could be shown that the concentrations of reactive constituents in multi-dimensional domains are approximately aligned with isochrones, that is, lines of identical travel time, provided that the chemical properties of the matrix are uniform. We extend this concept to combined physical and chemical heterogeneity by additionally considering the time that a water parcel has been exposed to reactive materials, the so-called exposure time. We simulate bioreactive transport in a one-dimensional domain as function of time and exposure time, rather than space. Subsequently, we map the concentrations to multi-dimensional heterogeneous domains by means of the mean exposure time at each location in the multi-dimensional domain. Differences in travel and exposure time at a given location are accounted for as time difference. This approximation simplifies reactive-transport simulations significantly under conditions of steady-state flow when reactions are restricted to specific locations. It is not expected to be exact in realistic applications because the underlying assumption, such as neglecting transverse mixing altogether, may not hold. We quantify the error introduced by the approximation for the hypothetical case of a two-dimensional, binary aquifer made of highly-permeable, non-reactive and low-permeable, reactive materials releasing dissolved organic matter acting as electron donor for aerobic respiration and denitrification. The kinetically controlled reactions are catalyzed by two non-competitive bacteria populations, enabling microbial growth. Even though the initial biomass concentrations were uniform, the interplay between transport, non-uniform electron-donor supply, and bio-reactions led to distinct spatial patterns of the two types of biomass at late times. Results obtained by mapping the exposure-time based results to the two-dimensional domain are compared with simulations based on the two-dimensional, spatially explicit advection-dispersion-reaction equation. Once quasi-steady state has been reached, we find a good agreement in terms of the chemical-compound concentrations between the two approaches inside the reactive zones, whereas the exposure-time based model is not able to capture reactions occurring in the zones with zero electron-donor release. We conclude that exposure-time models provide good approximations of nonlinear bio-reactive transport when transverse mixing is not the overall controlling process and all reactions are essentially restricted to distinct reactive zones.

Using travel times to simulate multi-dimensional bioreactive transport in time-periodic flows

In travel-time models, the spatially explicit description of reactive transport is replaced by associating reactive-species concentrations with the travel time or groundwater age at all locations. These models have been shown adequate for reactive transport in river-bank filtration under steady-state flow conditions. Dynamic hydrological conditions, however, can lead to fluctuations of infiltration velocities, putting the validity of travel-time models into question. In transient flow, the local travel-time distributions change with time. We show that a modified version of travel-time based reactive transport models is valid if only the magnitude of the velocity fluctuates, whereas its spatial orientation remains constant. We simulate nonlinear, one-dimensional, bioreactive transport involving oxygen, nitrate, dissolved organic carbon, aerobic and denitrifying bacteria, considering periodic fluctuations of velocity. These fluctuations make the bioreactive system pulsate: The aerobic zone decreases at times of low velocity and increases at those of high velocity. For the case of diurnal fluctuations, the biomass concentrations cannot follow the hydrological fluctuations and a transition zone containing both aerobic and obligatory denitrifying bacteria is established, whereas a clear separation of the two types of bacteria prevails in the case of seasonal velocity fluctuations. We map the 1-D results to a heterogeneous, two-dimensional domain by means of the mean groundwater age for steady-state flow in both domains. The mapped results are compared to simulation results of spatially explicit, two-dimensional, advective-dispersive-bioreactive transport subject to the same relative fluctuations of velocity as in the one-dimensional model. The agreement between the mapped 1-D and the explicit 2-D results is excellent. We conclude that travel-time models of nonlinear bioreactive transport are adequate in systems of time-periodic flow if the flow direction does not change.

On the validity of travel-time based nonlinear bioreactive transport models in steady-state flow

Travel-time based models simplify the description of reactive transport by replacing the spatial coordinates with the groundwater travel time, posing a quasi one-dimensional (1-D) problem and potentially rendering the determination of multidimensional parameter fields unnecessary. While the approach is exact for strictly advective transport in steady-state flow if the reactive properties of the porous medium are uniform, its validity is unclear when local-scale mixing affects the reactive behavior. We compare a two-dimensional (2-D), spatially explicit, bioreactive, advective–dispersive transport model, considered as “virtual truth”, with three 1-D travel-time based models which differ in the conceptualization of longitudinal dispersion: (i) neglecting dispersive mixing altogether, (ii) introducing a local-scale longitudinal dispersivity constant in time and space, and (iii) using an effective longitudinal dispersivity that increases linearly with distance. The reactive system considers biodegradation of dissolved organic carbon, which is introduced into a hydraulically heterogeneous domain together with oxygen and nitrate. Aerobic and denitrifying bacteria use the energy of the microbial transformations for growth. We analyze six scenarios differing in the variance of log-hydraulic conductivity and in the inflow boundary conditions (constant versus time-varying concentration). The concentrations of the 1-D models are mapped to the 2-D domain by means of the kinematic (for case i), and mean groundwater age (for cases ii & iii), respectively. The comparison between concentrations of the “virtual truth” and the 1-D approaches indicates extremely good agreement when using an effective, linearly increasing longitudinal dispersivity in the majority of the scenarios, while the other two 1-D approaches reproduce at least the concentration tendencies well. At late times, all 1-D models give valid approximations of two-dimensional transport. We conclude that the conceptualization of nonlinear bioreactive transport in complex multidimensional domains by quasi 1-D travel-time models is valid for steady-state flow fields if the reactants are introduced over a wide cross-section, flow is at quasi steady state, and dispersive mixing is adequately parametrized.

Modeling substrate-bacteria-grazer interactions coupled to substrate transport in groundwater

Models of microbial dynamics coupled to solute transport in aquifers typically require the introduction of a bacterial capacity term to prevent excessive microbial growth close to substrate-injection boundaries. The factors controlling this carrying capacity, however, are not fully understood. In this study, we propose that grazers or bacteriophages may control the density of bacterial biomass in continuously fed porous media. We conceptualize the flow-through porous medium as a series of retentostats, in which the dissolved substrate is advected with water flow whereas the biomasses of bacteria and grazers are considered essentially immobile. We first model a single retentostat with Monod kinetics of bacterial growth and a second-order grazing law, which shows that the system oscillates but approaches a stable steady state with nonzero concentrations of substrate, bacteria, and grazers. The steady state concentration of the bacteria biomass is independent of the substrate concentration in the inflow. When coupling several retentostats in a series to mimic a groundwater column, the steady state bacteria concentrations thus remain at a constant level over a significant travel distance. The one-dimensional reactive transport model also accounts for substrate dispersion and a random walk of grazers influenced by the bacteria concentration. These dispersive-diffusive terms affect the oscillations until steady state is reached, but hardly the steady state value itself. We conclude that grazing, or infection by bacteriophages, is a possible explanation of the maximum biomass concentration frequently needed in bioreactive transport models. Its value depends on parameters related to the grazers or bacteriophages and is independent of bacterial growth parameters or substrate concentration, provided that there is enough substrate to sustain bacteria and grazers.

Numerical simulation of isotope fractionation in steady-state bioreactive transport controlled by transverse mixing

Compound-specific stable isotope analysis (CSIA) has increasingly been used as a tool to assess intrinsic biodegradation at contaminated field sites. Typically, the Rayleigh equation is used to estimate the extent of biodegradation from measured isotope ratios of the contaminant. However, if the rate-limiting step in overall degradation is not the microbial reaction itself, the Rayleigh equation may no more be applicable. In this study we simulate biodegradation of continuously emitted petroleum hydrocarbons in groundwater systems. These contaminants are effectively degraded at the plume fringe where transverse dispersion makes them mix with dissolved electron acceptors present in the ambient groundwater. We simulate reactive transport to study the coupled effects of transverse mixing and biodegradation on the spatial patterns of carbon isotope signatures and their interpretation based on depth-integrated sampling which represents the most common setup in the assessment of contaminated sites. We present scenarios mimicking a hydraulically uniform laboratory experiment and a field-scale application considering heterogeneous conductivity fields. We compare cases in which isotopologue-specific transverse dispersion is considered to those where this additional fractionation process is neglected. We show that these effects cause significant shifts in the isotopic signals and may lead to overestimation of biodegradation. Moreover, our results provide evidence that the rate-limiting effect of transverse mixing on the overall degradation spatially varies along the length of a steady-state contaminant plume. The control of biodegradation by transverse dispersion and the fractionating effect of dispersion modulate the fractionation caused by the microbial reaction alone. As a consequence, significantly nonlinear isotopic patterns are observed in a Rayleigh plot. Simulations in heterogeneous flow domains show that these effects persist at larger field scales and are sensitive to the degree of mixing enhancement, determined by the heterogeneity of the hydraulic conductivity fields, and to the groundwater flow velocity.

Modeling Dehalococcoides sp. Augmented Bioremediation in a Single Fracture System

A numerical reactive transport model was developed to simulate the bioremediation processes in a perchloroethene (PCE) contaminated single fracture system augmented with Dehalococcoides sp. (DHC). The model describes multispecies bioreactive transport processes that include bacterial growth and detachment dynamics, biodegradation of chlorinated species, competitive inhibition of various reactive species, and the loss of daughter products because of back‐partitioning effects. Two sets of experimental data, available in the study by Schaefer et al. (2010b), were used to calibrate and test the model. The model was able to simulate both datasets. The simulation results indicated that the yield coefficient and the DHC maximum utilization rate coefficient were the two important process parameters. A detailed sensitivity study was completed to quantify the sensitivity of the model to variations in these two parameter values. The results show that an increase in yield coefficient increases bacterial growth and thus expedites the dechlorination process, whereas an increase in maximum utilization rate coefficient greatly increased dechlorination rates. The proposed model provides a mathematical framework for simulating remediation systems that employ DHC bioaugmentation for restoring chlorinated‐solvent contaminated groundwater aquifers.

Isotopic Fractionation by Transverse Dispersion: Flow-through Microcosms and Reactive Transport Modeling Study

Flow-through experiments were carried out to investigate the role of transverse dispersion on the isotopic behavior of an organic compound during conservative and bioreactive transport in a homogeneous porous medium. Ethylbenzene was selected as model contaminant and a mixture of labeled (perdeuterated) and light isotopologues was continuously injected in a quasi two-dimensional flow-through system. We observed a significant fractionation of ethylbenzene isotopologues during conservative transport at steady state. This effect was particularly pronounced at the plume fringe and contrasted with the common assumption that physical processes only provide a negligible contribution to isotope fractionation. Under the experimental steady state conditions, transverse hydrodynamic dispersion was the only process that could have caused the observed fractionation. Therefore, the measured isotope ratios at the outlet ports were interpreted with different parameterizations of the transverse dispersion coefficient. A nonlinear compound-specific parameterization showed the best agreement with the experimental data. Successively, bioreactive experiments were performed in two subsequent stages: a first oxic phase, involving a single strain of ethylbenzene degraders and a second phase with aerobic and anaerobic (i.e., ethylbenzene oxidation coupled to nitrate reduction) degradation. Significant fractionation through biodegradation occurred exclusively due to the metabolic activity of the anaerobic degraders. We performed analytical and numerical reactive transport simulations of the different experimental phases which confirmed that both the effects of physical processes (diffusion and dispersion) and microbially mediated reactions have to be considered to match the observed isotopic fractionation behavior.

Simplified simulation of steady state bioreactive transport with kinetic solute uptake by the biomass

Biodegradation of continuously emitted compounds that need a dissolved reaction partner, which is not jointly introduced with the contaminant into the subsurface, is mainly controlled by transverse dispersive mixing. Previous analytical approaches of evaluating mixing‐controlled bioreactive transport in steady state have been based on the assumption that the bulk aqueous‐phase concentration of the reactants is directly available to the specific biomass catalyzing the reaction. These models predict a very narrow stripe of active biomass with high specific biomass concentration. Experimental studies have indicated that such behavior may be unrealistic, particularly for anaerobic biodegradation. I extend the previous analysis to include kinetic solute uptake by the biomass, expressed as a first‐order mass‐transfer process coupled to dual Monod kinetics in the bio‐available domain. The approach is based on the evaluation of conservative components undergoing advective‐dispersive transport, the solution of a quadratic speciation problem within the immobile bio domain, and iterative simulation of linear transport of a single reactive constituent in steady state. Convergence is typically achieved within less than ten iterations. The comparison with simulations assuming instantaneous solute uptake by the biomass indicate that mass‐transfer kinetics may explain larger overlap of reactive constituents and a wider spatial distribution of specific biomass observed in experiments. Depending on the rate coefficient of mass transfer, the overall transformation of the contaminant may be significantly reduced or only slightly shifted to a region farther downstream.

GeoSysBRNS—A flexible multidimensional reactive transport model for simulating biogeochemical subsurface processes

The description of reactive transport processes in subsurface environments requires a sound understanding of both the biogeochemical complexity of the system and the spatially resolved transport of reactive species. However, most existing reactive transport models, for example in the field of contaminant hydrology, are specialized either in the simulation of the reactive or of the flow and transport processes. In this paper, we present and test the coupling of two highly flexible codes for the simulation of reactive transport processes in the subsurface: the Biogeochemical Reaction Network Simulator (BRNS), which contains a solver for kinetically and thermodynamically constrained biogeochemical reactions, and GeoSys/RockFlow, a multidimensional finite element subsurface flow and transport simulator. The new model, named GeoSysBRNS, maintains the full flexibility of the original models. The coupling is handled using an operator splitting scheme, which allows the reactive solver to be compiled into a problem specific library that is accessed by the transport simulator at runtime. The accuracy of the code coupling within GeoSysBRNS is demonstrated using two benchmark problems from the literature: a laboratory experiment on organic carbon degradation in a sand column via multiple microbial degradation pathways, and a dispersive mixing controlled bioreactive transport problem in aquifers, assuming three different reaction kinetics.

Upscaling of transport processes in porous media with biofilms in equilibrium and non-equilibrium conditions

Transport of biologically reactive dissolved solutes in a saturated porous medium including a biofilm-phase occurs in various technological applications such as in biochemical or environmental engineering. It is a complex process involving a wide variety of scales (from the bacteria-scale to the aquifer-heterogeneities-scale in the case of groundwater remediation) and processes (hydrodynamic, physicochemical and biochemical). This work is devoted to the upscaling of the pore-scale description of such processes. Firstly, one-equation macroscopic models for bio-reactive transport at the Darcy-scale have been developed by using the volume averaging method; they will be presented below. These one-equation models are valid for different limit cases of transport; their validity domains in terms of hydrodynamic and biochemical conditions will also be discussed. Finally, in order to illustrate such a theoretical development, an example of application to the operation of a packed bed reactor will be studied.

Two-dimensional flow-through microcosms – Versatile test systems to study biodegradation processes in porous aquifers

A fundamental prerequisite of any remedial activity is a sound knowledge of both the biotic and abiotic processes involved in transport and degradation of contaminants. Investigations of these aspects in situ often seem infeasible due to the complexity of interacting processes. A simplified portrayal of nature can be facilitated in laboratory-based two-dimensional (2D) sediment flow-through microcosms. This paper describes the versatility of such simple aquifer model systems with respect to biodegradation of aromatic hydrocarbons, i.e. toluene and ethylbenzene, under various environmental conditions. Initially constructed to study non-reactive and bioreactive transport of organic contaminants in homogeneous porous media under steady state hydraulic conditions, experimental setups developed towards more realistic heterogeneous sediment packing and transient hydraulic conditions. High-resolution spatial and temporal sampling allowed to obtain new insights on the distribution of bioactivities in contaminant plumes and associated controlling and limiting factors. Major biodegradation activities in saturated porous sediments are located at the fringes of contaminant plumes and are driven by dispersive mixing. These hot-spots of contaminant biotransformation are characterized by steep physical–chemical gradients in the millimeter to centimeter range. Sediment heterogeneity, i.e. high-conductivity zones, was shown to significantly enhance transverse mixing and subsequently biodegradation. On the contrary, transient hydraulic conditions may generate intermediate disturbances to biodegrader populations and thus may interfere with optimized contaminant conversion. However, a bacterial strain aerobically degrading toluene, i.e. Pseudomonas putida F1, was shown to adapt to vertically moving contaminant plumes, in the way that it regained full biodegradation potential two-times faster in areas with a mid-term (days to weeks) contamination history than in areas not contaminated before. The 2D flow-through microcosms facilitated to combine a number of physicochemical and microbiological methods, such as high-resolution non-invasive oxygen measurements, conservative tracer tests, compound-specific isotope analysis (CSIA), fluorescence in situ hybridization (FISH), and numerical transport modelling, to name a few. Moreover, due to the defined and well-controlled operating conditions, these bench-scale flow-through systems allow to investigate theoretical concepts and to develop and test predictive models. They represent a valuable tool in helping to bridge the current knowledge gap concerning transport and degradation of contaminants in groundwater from the small-scale (i.e. oversimplified batch systems, disregarding transport processes) to the highly complex field conditions. The promising potential of applications is by far not exhausted. Further possibilities include testing ecological theories such as the resource-ratio theory, island biogeography, area-species richness relationships and relations between community structure, microbial abundance and process rates as well as the importance and effects of bacterial chemotaxis.

Discontinuous Galerkin methods for simulating bioreactive transport of viruses in porous media

Primal discontinuous Galerkin (DG) methods are formulated to solve the transport equations for modeling migration and survival of viruses with kinetic and equilibrium adsorption in porous media. An entropy analysis is conducted to show that DG schemes are numerically stable and that the free energy of a DG approximation decreases with time in a manner similar to the exact solution. Combining results for free and attached virus concentrations, we establish optimal a priori error estimates for the coupled partial and ordinary differential equations of virus transport. Numerical results suggest that DG can treat bioreactive transport of viruses over a wide range of modeling parameters, including both advection- and dispersion-dominated problems. In addition, it is shown that DG can sharply capture local phenomena of virus transport with dynamic mesh adaptation.

Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady state

Under steady-state conditions, the degradation of contaminant plumes introduced continuously into an aquifer is controlled by transverse dispersion when the other reacting compound is provided from ambient groundwater. Given that the reaction is instantaneous and longitudinal dispersion can be neglected, the length of the plume is inversely proportional to the transverse dispersion coefficient. In typical scenarios of natural attenuation, however, the considered reaction is biotic and kinetic. The standard model of bioreactive transport relies on double-Monod kinetics and pseudo first-order biomass decay. Under these conditions, a fraction of the injected mass flux remains beyond the length of the plume determined for the instantaneous reaction. We present an analytical framework to derive the steady-state concentration distributions of the dissolved compounds and the biomass from the concentration distribution of a conservative compound, assuming double-Monod kinetics and two different models describing biomass decay. The first biomass-decay model assumes a constant first-order decay coefficient, while the second assumes that the decay coefficient depends upon the electron-acceptor concentration. We apply the method to the case of a line-injection in two-dimensional uniform flow. In general, the bioreactive concentration distributions are similar to the distributions computed for an instantaneous reaction. The similarity is greater when the biomass decay coefficient is assumed to depend on the electron-acceptor concentration rather than being constant.

Stochastic analysis of nonlinear biodegradation in regimes controlled by both chromatographic and dispersive mixing

Nonlinear biodegradation in natural porous media is affected by the heterogeneity of the formation and dispersive mixing processes. We analyze these coupled effects by combining recent advances in analytical one‐dimensional modeling of bioreactive transport with stochastic concepts of dispersive mixing in heterogeneous domains. Specifically, we model bioremediation of a sorbing contaminant undergoing nonlinear biodegradation in heterogeneous aquifers applying the stochastic‐convective and the advective‐dispersive stream tube approaches, in which we use a semianalytical traveling wave solution for one‐dimensional reactive transport. The results of numerical simulations agree excellently with both models, which establishes that the traveling wave solution is an efficient and accurate way to evaluate the development of intrastream tube concentration distributions and that the advective‐dispersive stream tube approach is suitable to describe nonlinear bioreactive transport in systems controlled by local‐scale dispersion. In contrast with conservative transport the mean contaminant flux is shown to be significantly influenced by transverse dispersion, even for realistic Peclet values. Furthermore, asymptotic front shapes are shown to be neither Fickian nor constant (traveling wave behavior), which raises questions about the current practice of upscaling bioreactive transport. The error caused by neglecting local dispersion was found to increase with time and to remain significant even for large retardation differences between electron acceptor and contaminant. This implies that, even if reaction rates are dominated by chromatographic mixing, the dispersive mixing process cannot be disregarded when predicting bioreactive transport.

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?

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.

Travel-time based model of bioremediation using circulation wells.

Vertical circulation wells can efficiently provide microorganisms with substrates needed for enhanced bioremediation. We present a travel-time based approach for modeling bioreactive transport in a flow field caused by a series of circulation wells. Mixing within the aquifer is due to the differences in sorption behavior of the reactants. Neglecting local dispersion, transport simplifies to a single one-dimensional problem with constant coefficients for each well. Recirculation is characterized by the discharge densities over travel time. We apply the model to the stimulation of cometabolic dechlorination of trichloroethene (TCE) by alternate injection of oxygen and toluene into the circulation wells. Mixing within the wells can be minimized by interposing sufficiently long breaks between the oxygen and toluene pulses. In our simulation, the proposed injection scheme stimulates biomass growth without risking biofouling of the aquifer.

Stochastic‐Convective Transport with Nonlinear Reaction: Biodegradation With Microbial Growth

The representation of subsurface flow and reactive transport as an ensemble of one‐dimensional stream tubes is extended to account for nonlinear biodegradation with coupled microbial growth. The Stochastic‐convective reaction (SCR) model is derived for bioreaction of a single solute by a single class of microorganisms coupled with dynamic microbial growth. A new global variable, the integral of the solute degraded per unit length of system traversed, accounts for degradation. Dimensionless scaling and the method of characteristics are used to reduce the model, written for a single convecting reactor (stream tube), to a pair of coupled nonlinear functional equations for solute concentration and microbial biomass. Existence of a solution to the stream tube system is shown, both numerical and approximate analytical approaches to the solution are given, and example computations using both methods are presented. Conditions under which the stream tube solution is “canonical,” or scalable to fit any permissible stream tube travel time function, arise from requirements for invariance (over the stream tube ensemble) of effective one‐dimensional stream tubes used to represent transport along real stream tubes in three‐dimensional space. Averaging of the stream tube solution over travel time and reaction properties representative of physical and chemical heterogeneities is described as a way to separate and upscale the processes of macrodispersion and microbiological reaction. The approach is exercised to simulate Monte Carlo average behavior of bioreactive transport in physically heterogeneous two‐dimensional media. Results show that the method captures the ensemble average large‐scale effects of the nonlinear reactions more accurately than done in the classical reactive convection‐dispersion equation (CDR), even when the appropriate scale dependent dispersion coefficient is afforded to the CDR.