Drainage front width in a three-dimensional random porous medium under gravitational and capillary effects

A theoretical approach to estimating stable drainage front widths in three-dimensional random porous media under gravitational and capillary effects is presented. Based on the frontier of the infinite cluster in gradient percolation, we propose an expression for the 3D front width dependent on the pore-network topology, the distribution of capillary pressure thresholds for the pore throats, the stabilizing capillary pressure gradient, the average pore size, and the correlation length critical exponent from percolation in three dimensions. Theoretical predictions are successfully compared to numerical results obtained with a bond invasion-percolation model for a wide range of drainage flow parameters.