Anisotropy of flow in stochastically generated porous media

TL;DR

This paper investigates how finite-size effects in simulated porous media cause anisotropy in permeability, leading to perpendicular pressure gradients, and provides criteria for when this anisotropy is significant.

Contribution

It introduces a criterion based on system size to grain size ratio to determine the relevance of anisotropy in porous media simulations.

Findings

Finite-size anisotropy causes a non-zero angle between force and flux.

Anisotropy induces perpendicular pressure gradients in porous ducts.

Scaling of anisotropy with system and grain sizes is analyzed.

Abstract

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 non-zero 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 system size to the grain size ratio, 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.