How fluid-mechanical erosion creates anisotropic porous media

TL;DR

This study uses boundary integral equations to simulate erosion in porous media, revealing how microscopic grain changes lead to large-scale anisotropic structures that favor flow in certain directions.

Contribution

It introduces a boundary integral simulation method for erosion of multiple grains, showing how erosion induces anisotropy in porous media.

Findings

Erosion causes significant anisotropy, favoring flow along the longitudinal direction.

Flow in the longitudinal direction can be up to six times easier than in the transverse.

Microscopic erosion processes lead to large-scale structural features like channelization.

Abstract

Using a Cauchy integral formulation of the boundary integral equations, we simulate the erosion a porous medium comprised of up to 100 solid bodies embedded in a Stokes flow. The grains of the medium are resolved individually and erode under the action of surface shear stress. Through nonlinear feedback with the surrounding flow fields, microscopic changes in grain morphology give way to larger-scale features in the medium such as channelization. The Cauchy-integral formulation and associated quadrature formulas enable us to resolve dense configurations of nearly contacting bodies. We observe substantial anisotropy to develop over the course of erosion; that is, the configurations that result from erosion generally permit flow in the longitudinal direction more easily than in the transverse direction by up to a factor of six. These results suggest that the erosion of solid material from groundwater flows may contribute to previously observed anisotropy of natural porous media.