Transport of reactive solutes in heterogeneous porous media: Heterogeneous rate-limited mass transfer

The transport of reactive solutes in the subsurface is influenced by a variety of physical and chemical processes. The processes are characteristically heterogeneous and often operate simultaneously at different temporal and spatial scales. In modeling reactive solute transport different models take different approaches, dependent on the scale of the system and the objective of the study. Two major approaches have been used to incorporate heterogeneous rate-limited mass transfer into mathematical models for solute transport. One focuses on processes operative at the microscopic scale and associated grain-scale heterogeneity, while the other stresses the macroscopic variability of the medium and the field-scale behavior of solute transport. In this work, I first examine the conceptual framework and model formulation of these two approaches in an attempt to evaluate potential commonality, then present a two dimensional numerical model that integrates the first approach with traditional stochastic modeling for reactive transport. In this model multiple processes are explicitly accounted for, including spatially variable flow, spatially variable sorption, locally heterogeneous diffusive mass transfer, locally heterogeneous rate-limited sorption, and locally heterogeneous first-order degradation. Finally, the model is used to (1) examine the individual and concurrent effects of multiple heterogeneous processes on reactive transport, and (2) evaluate the impact of microscopic-scale mass transfer heterogeneity on field-scale transport in systems for which hydraulic conductivity is spatially variable. The comparison of the two approaches shows that despite differences in conceptualization and formulation, both microscopic and macroscopic based models produce comparable behavior for smaller-scale systems. However, greater deviations are observed at larger scales. This suggests that caution should be taken when using mathematical modeling for elucidating the specific processes that may be influencing reactive-solute transport for a given system. Results from 2-D simulations of the new model reveal that inclusion of locally heterogeneous mass transfer does not appear to significantly influence the mean transport behavior for systems with field-scale heterogeneity. However, it does appear to influence low-concentration tailing. For simulations of reactive transport over extended distances, models with locally heterogeneous mass transfer may "preserve" the non-equilibrium effects associated with rate-limited mass transfer better than the models incorporating locally uniform mass transfer when both pore-scale and field-scale heterogeneity coexist