Numerical Simulations of Gravity-Driven Fingering in Unsaturated Porous Media Using a Non-Equilibrium Model

TL;DR

This computational study models gravity-driven fingering in unsaturated porous media using a non-equilibrium approach, analyzing parameter sensitivity and validating results against experimental data.

Contribution

Introduces a non-equilibrium model for fingering in porous media, incorporating hysteresis and non-monotonic saturation profiles, with validation against experiments.

Findings

Model captures realistic fingering patterns

Sensitivity analysis reveals key parameter impacts

Validation shows good agreement with experimental data

Abstract

This is a computational study of gravity-driven fingering instabilities in unsaturated porous media. The governing equations and corresponding numerical scheme are based on the work of Nieber et al. [Ch. 23 in Soil Water Repellency, eds. C. J. Ritsema and L. W. Dekker, Elsevier, 2003] in which non-monotonic saturation profiles are obtained by supplementing the Richards equation with a non-equilibrium capillary pressure-saturation relationship, as well as including hysteretic effects. The first part of the study takes an extensive look at the sensitivity of the finger solutions to certain key parameters in the model such as capillary shape parameter, initial saturation, and capillary relaxation coefficient. The second part is a comparison to published experimental results that demonstrates the ability of the model to capture realistic fingering behaviour.