Stochastic analysis of oxygen-limited biodegradation in heterogeneous aquifers with transient microbial dynamics

A stochastic theory of multiple species transport and transformation is developed for the problem of oxygen-limited biodegradation of contaminants in aquifers, considering the presence of transient microbial growth dynamics. The theory incorporates the effects of physical, chemical and microbiological heterogeneities into a stochastic analysis of the coupled transport/transformation equations for a system consisting of a contaminant, an oxidizer, i.e., dissolved oxygen, and active biomass in heterogeneous and anisotropic aquifers. The developed theory is used to quantify the effects of mean concentrations on the field scale coefficients of decay, retardation and macrodispersion, and to evaluate the assumption of a steady-state biomass, previously reported in the literature. A comparison between the steady state assumption [Miralles-Wilhelm, F., Gelhar, L.W., Kapoor, V., 1997. Stochastic analysis of oxygen-limited biodegration in three dimensionally in heterogeneous aquifers. Water Resour. Res., 33 (6)] and this work for hypothesized field conditions shows that the effects of transient microbial growth on the effective retardation factor and macrodispersivities are minor, while the effects are modest for the effective decay rate. Transient microbial growth dynamics are found to occur over most contaminant and dissolved oxygen mean concentration ranges, and therefore a transient mean balance equation for biomass should be included in modeling efforts directed at quantifying oxygen-limited biodegradation at field scales. As in previous research, the effective decay rate is found to be less than the mean, which results in a larger field scale contaminant half-life in a heterogenous aquifer, compared to that in a homogeneous aquifer.