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 semi-analytical 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 intra-stream 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 can not be disregarded when predicting bioreactive transport.