Upscaling transport of a sorbing solute in disordered non periodic porous domains

Spatial Markov random walk models (SMM) have been demonstrated to accurately predict conservative solute transport across a wide range of hydro-geological systems, with recent advances enabling the SMM to model systems with linear kinetic reactive processes. However, the proposed reactive SMM's applicability is limited to systems that can be partitioned into a series of identical periodic cells where travel times across cells are highly correlated to the solute's entrance position at the cell inlet. In real geologic settings, the spatial layout and size of grains varies through space, decorrelating the relationship between travel time and transverse position. Here, we generalize previous SMM implementations and implement a Bernoulli CTRW, where transport behavior can be captured in disordered and non-periodic porous media. We validate our upscaled model predictions with results from direct numerical simulation of transport in a 2D porous column that cannot be partitioned into identical periodic elements. We parameterize our model based on a subset of simulation statistics and explore how model accuracy changes due to our sampling method. This finding yields important insights for optimizing efficiency of the upscaled transport model parameterization and can guide field sampling of geological structures as well as multiscale investigation of laboratory observations.