Flow-induced channelization in a porous medium

Abstract

Flow through a saturated, granular, porous medium can lead to internal erosion, preferential flow enhancement and the formation of channels within the bulk of the medium. We examine this phenomenon using a combination of experimental observations, continuum theory and numerical simulations in a minimal setting. Our experiments are carried out by forcing water through a Hele-Shaw cell packed with bidisperse grains. When the local fluid flow-induced stress exceeds a critical threshold, the smaller grains are dislodged and transported, thus changing the porosity of the medium and thence the local hydraulic conductivity and the development of erosional channels. The erosion is ultimately arrested due to the drop in the mean pressure gradient, while most of the flow occurs through the channels. These observations are consistent with a simple theoretical model for channelization in terms of a macroscopic multiphase description of erosion. We model a dynamical porosity field that evolves along with the volume fraction of the mobile and immobile grains in response to fluid flow. Numerical solutions of the resulting initial boundary value problem yield results for the dynamics and morphology that are in qualitative agreement with our experiments. In addition to providing a basis for channelization in porous media, our study highlights how heterogeneity in porous media may arise from flow as a function of the erosion threshold, and thus potentially offers the ability to control channelization.