Anisotropy of flow in stochastically generated porous media

Models of porous media are often applied to relatively small systems, which leads not only to system-size-dependent results, but also to phenomena that would be absent in larger systems. Here we investigate one such finite-size effect: anisotropy of the permeability tensor. We show that a nonzero angle between the external body force and macroscopic flux vector exists in three-dimensional periodic models of sizes commonly used in computer simulations and propose a criterion, based on the ratio of the system size to the grain size, for this phenomenon to be relevant or negligible. The finite-size anisotropy of the porous matrix induces a pressure gradient perpendicular to the axis of a porous duct and we analyze how this effect scales with the system and grain sizes. We also analyze how the size of the representative elementary volume (REV) for anisotropy compares with the REV for permeability.