Brian D. Wood

Processes in microbial transport in the natural subsurface

This is a review of physical, chemical, and biological processes governing microbial transport in the saturated subsurface. We begin with the conceptual models of the biophase that underlie mathematical descriptions of these processes and the physical processes that provide the framework for recent focus on less understood processes. Novel conceptual models of the interactions between cell surface structures and other surfaces are introduced, that are more realistic than the oft-relied upon DLVO theory of colloid stability. Biological processes reviewed include active adhesion/detachment (cell partitioning between aqueous and solid phase initiated by cell metabolism) and chemotaxis (motility in response to chemical gradients). We also discuss mathematical issues involved in upscaling results from the cell scale to the Darcy and field scales. Finally, recent studies at the Oyster, Virginia field site are discussed in terms of relating laboratory results to field scale problems of bioremediation and pathogen transport in the natural subsurface.

Diffusion and reaction in biofilms

In the development of models for diffusion and reaction in biofilms, one often begins with the assumption that the biofilm is a continuum. This approach leads to equations for which the domain of validity is not clearly defined, and it provides no theoretical foundation for the prediction of the effective coefficients that appear in the postulated equations. In this paper we treat the intracellular phase and the extracellular phase as continua and use the method of volume averaging to develop the spatially smoothed transport equations for diffusion and reaction in biofilms. This allows us to identify three regimes in which the spatially smoothed transport equations take on special forms. The first of these is the one-equation model that is valid when the principle of local mass equilibrium is satisfied; the second is the two-equation model that is not constrained by the principle of local mass equilibrium; and the third is a pseudo one-equation model. The latter occurs when the reaction in the intracellular phase can be treated as instantaneous. Constraints that identify the domain of validity of these three models are given.

Stochastic-convective transport with nonlinear reaction: Mathematical framework

A stochastic-convective reactive (SCR) transport method is developed for one-dimensional steady transport in physically heterogeneous media with nonlinear degradation. The method is free of perturbation amplitude limitations and circumvents the difficulty of scale dependence of phenomenological parameters by avoiding volume-averaged specifications of diffusive/dispersive fluxes. The transport system is conceptualized as an ensemble of independent convective-reactive streamlines, each characterized by a randomized convective velocity (or travel time). Dispersive effects are treated as a component of the randomness in the streamline velocity ensemble, so no explicit expression for hydrodynamic dispersive flux is written in the streamline transport equation. The expected value of the transport over the stream tube ensemble is obtained as an average of solutions to the reactive convection equation according to the stream tube (travel time) probability distribution function. In this way, transport with reaction can be expressed in terms of global-scale random variables, such as solute travel time and travel distance, which are integrals of the stochastic variables such as velocity. Derivations support the hypothesis that via the SCR the decay process can be factored out of the mechanical transport behavior (as reflected by movement of a passive tracer) and scaled independently. Solution strategies are presented for general linear and nonlinear kinetic reactions. Demonstration simulations show that for Fickian transport with nonlinear reactions the SCR and convection dispersion equation can give different results. Ginn et al. (this issue) extend the SCR solution to coupled nonlinear equations, to accommodate Michaelis-Menten biodegradation of solute with an accounting of microbial growth.

In situ measurement of microbial activity and controls on microbial CO2 production in the unsaturated zone

Carbon dioxide COncentrations were measured at various depths and times in the unsaturated zones of two hydraulically and geochemically contrasting field sites, one in southeastern Washington state, and the other in south central Saskatchewan. In situ CO, production rates were calculated from a mass balance that accounted for diffusive fluxes and partitioning of CO[sub 2] into an advecting aqueous phase. Production rates were compared with (1) microbial abundance and (2) subsurface temperature to determine whether subsurface CO[sub 2] production rates could be expressed as a simple function of these two variables. At the Washington site, subsurface production was successfully expressed as a function of microbial abundance and temperature for a large portion of the year, but not near the end of the growing season. Although subsurface microbes and organic carbon were more abundant at the Saskatchewan site, subsurface CO[sub 2], production rates were generally several orders of magnitude lower than at the Washington site, and no correlation could be established between microbial numbers, temperature, and production rate. The cases where production rates could not be expressed as a function of microbial numbers and temperature suggested conditions in which some other factor, such as nutrient limitations, was controlling.

Modeling contaminant transport and biodegradation in a layered porous media system

The transport and biodegradation of an organic compound (quinoline) were studied in a meter-scale system of layered porous media. A two-dimensional laboratory experiment was conducted in a saturated system with two hydraulic layers with a ratio of conductivities of 1:13. A solution containing dissolved quinoline was injected as a front at one end of the system, and the aqueous-phase concentrations of quinoline, its first degradation product (2-hydroxyquinoline), and oxygen were monitored over time at several spatial locations. Results from a set of ancillary batch and small-column experiments were used to generate a mathematical model for the microbial kinetics; these kinetics described the time rate of change of the concentrations of the two organic compounds (quinoline and 2-hydroxyquinoline), the electron acceptor (oxygen), and microbial biomass. This independently developed kinetic model was incorporated into a two-dimensional numerical model for flow and transport, so that simulations of the laboratory system could be conducted and the results compared with observed data. An analysis of the applicability of single-phase and multiple-phase models for the description of the microbial kinetics was conducted. The results of this analysis indicated that for some cases, it is not necessary to explicitly model the mass transfer between the aqueous phase and the biomass phase. A single-phase model was used for simulating the laboratory system described here. Favorable comparisons between the laboratory and simulation data suggested that a single-phase model was appropriate for describing the microbially mediated reactions in this system. A method for incorporating the effects of metabolic lag into microbial kinetics is described. Metabolic lag was explicitly accounted for in the degradation kinetics for this system; the inclusion of metabolic lag proved to be important for describing transient concentration pulses that were observed in the low-conductivity layer.

Multi-species diffusion and reaction in biofilms and cellular media

In this paper we examine the problem of diffusion and reaction in biofilms and cellular systems when the reaction rate is limited by both a substrate and an electron acceptor. The intercellular kinetics is represented by a conventional multiplicative expression for the reaction between the substrate and oxygen, and by a first-order endogenous respiration rate. The membrane transport process for substrate and oxygen occurs through two different mechanisms. The transport of the electron acceptor is described by a permeability model while the transport of the substrate is treated in terms of a simple carrier model. The microscopic (sub-cellular) description is used to develop an upscaled version of diffusion and reaction in biofilms and other cellular media. The effective diffusivity that appears in the macroscopic description is predicted by a closure problem. Solutions to this closure problem are presented for simplified geometries, and the effective diffusivity predicted by the theory is compared with experimental values.

Volume averaging for determining the effective dispersion tensor: Closure using periodic unit cells and comparison with ensemble averaging

In this work, we use the method of volume averaging to determine the effective dispersion tensor for a heterogeneous porous medium; closure for the averaged equation is obtained by solution of a concentration deviation equation over a periodic unit cell. Our purpose is to show how the method of volume averaging with closure can be rectified with the results obtained by other upscaling methods under particular conditions. Although this rectification is something that is generally believed to be true, there has been very little research that explores this issue explicitly. We show that under certain limiting (but mild) assumptions, the closure problem provides a Fourier series solution for the effective dispersion tensor. When second-order spatial stationarity is imposed on the velocity field, the method yields a simple Fourier series that converges to an integral form in the limit as the period of the unit cell approaches infinity. This limiting result is identical to the quasi-Fickian forms that have been developed previously via ensemble averaging by Deng et al. [1993] and recently by Fiori and Dagan [2000] except in the definition of the averaging operation. As a second objective we have conducted a numerical study to evaluate the influence of the size of the averaging volume on the effective dispersion tensor and its volume averaged statistics. This second objective is complimentary in many ways to recent research reported by Rubin et al. [1999] (via ensemble averaging) and by Wang and Kitanidis [1999] (via volume averaging) on the block-averaged effective dispersion tensor. The variability of the effective dispersion tensor from realization to realization is assessed by computing the volume-averaged effective dispersion tensor for an ensemble of finite fields with the same (ensemble) statistics. Ensembles were generated using three different sizes of unit cells. All three unit cell sizes yield similar results for the value of the mean effective dispersion tensor. However, the coefficient of variation depends strongly upon the size of the unit cell, and our results are consistent with those developed by Fiori [1998] from the ensemble averaging perspective. This implies that in applications the actual value of the effective dispersion tensor may be significantly different than expected on the basis of unconditioned hydraulic conductivity statistics, and this variation should be considered when applying macrodispersion to real-world systems.

Occupation and local times for skew Brownian motion with applications to dispersion across an interface

This research was partially supported by the grant GrantCMG EAR-0724865 from the National Science Foundation.

Multidimensional, multicomponent, subsurface reactive transport in nonuniform velocity fields : code verification using an advective reactive streamtube approach

Abstract High performance computing has made possible the development of high resolution, multidimensional, multicomponent reactive transport models that can be used to analyze complex geochemical environments. However, as increasingly complex processes are included in these models, the accuracy of the numerical formulation coupling the nonlinear processes becomes difficult to verify. Analytical solutions are not available for realistically complex problems and benchmark solutions are not generally available for specific problems. We present an advective reactive streamtube (ARS) transport technique that efficiently provides accurate solutions of nonlinear multicomponent reactive transport in nonuniform multidimensional velocity fields. These solutions can be compared with results from Eulerian-based advection–dispersion-reaction models to evaluate the accuracy of the numerical formulation used. The ARS technique includes mixed equilibrium and kinetic complexation and precipitation–dissolution reactions subject to the following assumptions: (1) transport is purely advective (i.e., no explicit diffusion or dispersion), and (2) chemistry is described by a canonical system of reactions that evolves with time and is unaffected by position in space. Results from the ARS technique are compared with results from the massively parallel, multicomponent reactive transport model MCTRACKER on a test problem involving irreversible oxidation of organic carbon and reaction of the oxidation products with two immobile mineral phases, gypsum and calcite, and fifteen aqueous complexes. Truncation error, operator splitting error, and the nonlinear transformation of these errors in the high-resolution reactive transport model are identified for this problem.

Cellular growth in biofilms

In this paper we develop a macroscopic evolutionary equation for the growth of the cellular phase starting from a microscopic description of mass transport and a simple structured model for product formation. The methods of continuum mechanics and volume averaging are used to develop the macroscopic representation by carefully considering the fluxes of chemical species that pertain to cell growth. The concept of structured models is extended to include the transport of reacting chemical species at the microscopic scale. The resulting macroscopic growth model is similar in form to previously published models for the transport of a single substrate and electron donor and for the production of cellular mass and exopolymer. The method of volume averaging indicates under what conditions the developed growth model is valid and provides an explicit connection between the relevant microscopic model parameters and their corresponding macroscopic counterparts.