An asymptotic analysis and an integral equation method approach for erosion in porous media

Abstract

In nature, erosion caused by water or air flow is one of the most prevalent geological and mechanical processes. This phenomenon occurs at the fluid–solid interface when the total shear stress induced by the flow exceeds a specific critical threshold that depends on the properties of the solid material. This research project focuses on the mathematical modeling and simulation of the erosion process in a porous medium characterized by axisymmetric channels. We employ an integral equation method (IEM), which enables an efficient and accurate analysis of the erosion process within the porous medium. In addition, we present a detailed comparison between the numerical solutions from our model and a reduced mathematical model using asymptotic analysis. This comparison provides critical insights into erosion patterns and validates the proposed computational approach for sufficiently small pore geometries. Our results demonstrate that while the asymptotic model provides a highly efficient approximation for slender channels, the IEM is favorable for comparably wider pores.