Nonideal transport of reactive solutes in heterogeneous porous media 6. Microscopic and macroscopic approaches for incorporating heterogeneous rate-limited mass transfer

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 paper, we examine the conceptual framework and model formulation of these two approaches in an attempt to evaluate potential commonality. Numerical solvers are developed for both sets of governing equations, and the performance of these two models is tested for two systems, each incorporating one of two types of mass transfer mechanisms. The results show that despite differences in conceptualization and formulation, the models produce comparable behavior for smaller-scale systems. However, greater deviations are observed at larger scales. This suggests that caution should be exercised when using mathematical modeling for elucidating the specific processes that may be influencing reactive-solute transport for a given system. We also evaluate the impact of microscopic-scale mass transfer heterogeneity on field-scale transport in systems for which hydraulic conductivity is spatially variable. The results show 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 nonequilibrium effects associated with rate-limited mass transfer better than models incorporating locally uniform mass transfer when both pore-scale and field-scale heterogeneity coexist.