Permeability Estimation Based on the Geometry of Pore Space via Random Walk on Grids

In the literature, the mean penetration depth (MPD) calculated by “walk on spheres“ or “walk on cubes“ was used to quickly estimate the intrinsic permeability of digitized porous media. However, these two methods encounter difficulties such as irregular boundaries and the determination of arrivals at a boundary. In this study, an MPD method that is based on a more flexible “random walk on grid“ (WOG) is explored. Moreover, the accurate MPDs for the pores of simple shapes are derived with Green’s functions to validate the WOG-based MPD. The results suggested that MPDs based on Green’s functions and WOG are consistent with each other; the factor in the permeability expression is slightly dependent on roundness of the cross sections and is approximately 1.125 on average, according to analytical and numerical results. In a synthetic complex pore, the permeability estimated by WOG is comparable to, but greater than, the estimate based on the pore-scale dynamics simulation in COMSOL.