Simulation of gravity fingering in porous media using a modified invasion percolation model

We introduce a modified invasion percolation (MIP) model for the immiscible displacement of a nonwetting fluid by a wetting fluid within a porous network. The model includes the influence of gravity and is applicable in the quasi-static limit of infinitesimal flow rate where viscous forces are negligible with respect to gravity and capillary forces. The incorporation of gravity alone creates complicated, pore-scale gravity fingers. To properly model wetting fluid invasion where macroscopic gravity fingers form, we incorporate a pore-scale geometric capillary smoothing function we refer to as ''facilitation.'' Facilitation models the physics of wetting fluid invasion of pores by modifying the capillary pressure required to fill a pore based on the number of adjacent necks connecting the pore to the invading wetting fluid. The wetting fluid invasion facilitation process creates compact clusters and macroscopic fronts in horizontal simulations and in combination with gravity, creates macroscopic, gravity fingers that are in qualitative agreement with physical experiments. The MIP model yields much different imbibition front structures than standard invasion percolation. For MIP, capillary fingering, capillary facilitation, and gravity fingering compete to determine the wetted network structure as a function of pore-size distribution.