Finite-size anisotropy in statistically uniform porous media

TL;DR

This paper investigates how finite system size induces anisotropy in permeability in statistically uniform porous media, affecting transport properties and providing estimates for anisotropy-related errors in simulations.

Contribution

It reveals the dependence of permeability anisotropy on system size and obstacle ratio, offering a quantitative framework for assessing anisotropy effects in simulations.

Findings

Permeability anisotropy increases with obstacle-to-system size ratio.

The angle distribution between force and flow is approximately normal.

Standard deviation of the angle decays as (a/L)^{d/2} with system size.

Abstract

Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic permeability can give rise to significant changes of transport parameters such as permeability and tortuosity. The main parameter controlling the anisotropy is $a/L$, being the ratio of the obstacle to system size. Distribution of the angle $\alpha$ between the external force and the volumetric fluid stream is found to be approximately normal, and the standard deviation of $\alpha$ is found to decay with the system size as $(a/L)^{d/2}$, where $d$ is the space dimensionality. These properties can be used to estimate both anisotropy-related statistical errors in large-scale simulations and the size of the representative elementary volume.