Flow-induced channelization in a porous medium

We propose a theory for erosional channelization induced by fluid flow in a saturated granular porous medium. When the local fluid flow-induced stress is larger than a critical threshold, grains are dislodged and carried away so that the porosity of the medium is altered by erosion. This in turn affects the local hydraulic conductivity and pressure in the medium and results in the growth and development of channels that preferentially conduct the flow. Our multiphase model involves a dynamical porosity field that evolves along with the volume fraction of the mobile and immobile grains in response to fluid flow that couples the spatiotemporal dynamics of the three phases. Numerical solutions of the resulting initial boundary value problem show how channels form in porous media and highlights how heterogeneity in the erosion threshold dictates the form of the patterns and thus the ability to control them.