Stochastic analysis of oxygen‐limited biodegradation in three‐dimensionally heterogeneous aquifers

Abstract

Abstract. A three-dimensional analytical model is developed to quantify the process of oxygen-limited biodegradation as it occurs at field scales. The model incorporates the effects of chemical and microbiological heterogeneities inherent to the biodegradation process in a stochastic analysis of the coupled transport equations for a system consisting of a contaminant and an oxidizing agent, that is, oxygen, in heterogeneous and anisotropic aquifers. Natural aquifer variability, equilibrium linear sorption and Monod-type kinetics for the microbial population constitute the sources of these heterogeneities. Calculations for hypothesized field conditions show that longitudinal macrodispersivities for the contaminant and dissolved oxygen are considerably affected by biodegradation. The effective contaminant decay rate is fundamentally found to be moderately less than the mean, while the effects are lesser for the effective retardation factor. The usual assumption of equal dispersivities for both components is found to be inadequate over most concentration ranges.

Toward efficiency in heterogeneous multispecies reactive transport modeling: A particle‐tracking solution for first‐order network reactions

“…Even though model predictions can be strongly affected by the spatial variability of both hydraulic and biochemical properties [Rehfeldt et al, 1992;Miralles-Wilhelm and Gelhar, 1996;Miralles-Wilhelm et al, 1997;Cunningham and Fadel, 2007;Maxwell and Kastenberg, 1999;Maxwell et al, 2007], reactive transport codes based on Eulerian methods such as finite-difference or finite elements [e.g., Saaltink et al, 2004;Clement, 1997] still undergo computational burden and numerical problems when modeling strong heterogeneities and complex biochemical systems at high resolution. In this context, Particle Tracking Methods (PTMs) offer a convenient numerical solution particularly efficient in dealing with heterogeneities [e.g., Wen and GomezHernandez, 1996;LaBolle et al, 1996;Salamon et al, 2007;Riva et al, 2008] and a large variety of complex transport processes such as non-Fickian transport [Delay and Bodin, 2001;Cvetkovic and Haggerty, 2002;Berkowitz et al, 2006;Zhang and Benson, 2008;Dentz and Castro, 2009] and multiple porosity systems [Salamon et al, 2006b;Benson and Meerschaert, 2009;Tsang and Tsang, 2001;Huang et al, 2003;Willmann et al, 2013].…”

Traveltime‐based descriptions of transport and mixing in heterogeneous domains

“…A particular challenge lies in predicting mixing-controlled reactive transport in heterogeneous domains. If mean concentrations of reactive species are predicted by solving macroscopic advective-dispersive-reactive transport, calibrated by fitting mean conservative concentrations, the degree of mixing and related reaction rates will be overestimated [Molz and Widdowson, 1988;Semprini and McCarty, 1991;Ginn et al, 1995;Sturman et al, 1995;Miralles-Wilhelm et al, 1997;Cirpka et al, 1999b]. Bimolecular reactive transport experiments, conducted by Raje and Kapoor [2000] and Gramling et al [2002], demonstrated that even in nearly homogeneous porous media the reaction rates were overestimated by mean advectivedispersive-reactive transport models with transport parameters fitted from average concentration breakthrough curves (BTCs) of conservative tracers.…”

Statistical analysis of a semilinear hyperbolic system advected by a white in time random velocity field

“…We mention in passing that similar semilinear systems also arise in bioremediation and transport in porous media [18], [19]. In [21], system (1.3) was derived in a fast reaction limit of microbial reaction when the substrate retardation factor is equal to one.…”

“…In [21], system (1.3) was derived in a fast reaction limit of microbial reaction when the substrate retardation factor is equal to one. However, the velocity v in that particular application is spatially random and independent of time [18].…”