A Continuous-Time Random Walk Approach for Upscaling Anomalous Transport in Vesicular Porous Media

The emergence of non-Fickian transport in heterogeneous fractured porous media has been widely investigated in the literature. These studies typically report an early breakthrough and long tailing at late times mainly as a result of the formation of preferential pathways of fluid within the heterogeneous porous medium. However, transport in vesicular porous media with multi-modal pore size distributions, consisting of a porous matrix and fluid-filled cavities is an ongoing area of research.

The anomalous transport in a vesicular media originates from the occurrence of non-Gaussian and multiscale velocity distributions caused by local flow instabilities, vorticities, and stagnant zones. These local features of fluid flow result in a significantly different velocity distribution for the tracer compared to the fluid. We simulate the inert tracer transport in a porous cell problem with one cavity located at the center. Main features of transport, including the tracer time transitions, are extracted within a continuous-time random walk (CTRW) framework. We use breakthrough curves to derive the upscaled CTRW memory term for a vesicular media with cavities of high degree disorder. We quantify the effect of Peclet number, cavity shape, and cavity volume fraction on the transport process.