Pore-scale simulation of intragranular diffusion: Effects of incomplete mixing on macroscopic manifestations

Diffusive mass transfer into and out of intragranular micropores ("intragranular diffusion") plays an important role in the transport of some groundwater contaminants. We are interested in understanding the combined effect of pore-scale advection and intragranular diffusion on solute transport at the effective porous medium scale. We have developed a 3-D pore-scale numerical model of fluid flow and solute transport that incorporates diffusion into and out of intragranular pore spaces. A series of numerical experiments allow us to draw comparisons between macroscopic measures computed from the pore-scale simulations (such as breakthrough curves) and those predicted by multirate mass transfer formulations that assume complete local mixing at the pore scale. In this paper we present results for two model systems, one with randomly packed uniform spherical grains and a second with randomly packed spheres drawn from a binary grain size distribution. Non-Fickian behavior was observed at all scales considered, and most cases were better represented by a multirate mass transfer model even when there was no distinct secondary porosity (i.e., no intragranular diffusion). This suggests that pore-scale diffusive mass transfer processes between preferential flow paths and relatively immobile zones within the primary porosity may have significant impact on transport, particular in low-concentration tails. The application of independently determined mass transfer rate parameters based on an assumption of well-mixed concentrations at the pore scale tends to overestimate the amount of mass transfer that occurs in heterogeneous pore geometries in which preferential flow leads to incomplete pore-scale lateral mixing.