Flow-induced channelization in a porous medium

¹ Woods Hole Oceanographic Institution - Woods Hole, MA 02543-1050, USA
² Chemical Engineering Division, National Chemical Laboratory - Pune 411008, India
³ Department of Physics, Clark University - Worcester, MA 01610, USA
⁴ School of Engineering and Applied Sciences, Department of Physics, Harvard University Cambridge, MA 02138, USA

^a lm@seas.harvard.edu

Received: 5 December 2011
Accepted: 29 April 2012

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 flow-induced stress exceeds a critical threshold, the smaller grains are dislodged and transported. This changes the porosity of the medium, thence, the local hydraulic conductivity, and leads to the development of erosional channels. Erosion is ultimately arrested due to the drop in the mean pressure gradient, while most of the flow occurs through the channels. We describe this using a minimal multiphase description of erosion where the volume fraction of the fluid, mobile, and immobile, grains change in space and time. 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.