Viscous Transport in Eroding Porous Media

TL;DR

This study investigates how viscous fluid transport in eroding porous media evolves over time, focusing on tortuosity, dispersion, and pore size distribution using advanced numerical simulations.

Contribution

It introduces a comprehensive numerical framework to analyze erosion effects on transport properties in two-dimensional porous geometries, revealing complex tortuosity and dispersion behaviors.

Findings

Tortuosity generally decreases with erosion but can increase transiently.

Porosity-tortuosity relationships vary with erosion dynamics.

Erosion significantly impacts dispersion rates and pore size distribution.

Abstract

Transport of viscous fluid through porous media is a direct consequence of the pore structure. Here we investigate transport through a specific class of two-dimensional porous geometries, namely those formed by fluid-mechanical erosion. We investigate the tortuosity and dispersion by analyzing the first two statistical moments of tracer trajectories. For most initial configurations, tortuosity decreases in time as a result of erosion increasing the porosity. However, we find that tortuosity can also increase transiently in certain cases. The porosity-tortuosity relationships that result from our simulations are compared with models available in the literature. Asymptotic dispersion rates are also strongly affected by the erosion process, as well as by the number and distribution of the eroding bodies. Finally, we analyze the pore size distribution of an eroding geometry. The simulations are performed by combining a high-fidelity boundary integral equation solver for the fluid equations, a second-order stable time stepping method to simulate erosion, and new numerical methods to stably and accurately resolve nearly-touching eroded bodies and particle trajectories near the eroding bodies.