Stochastic pore-scale growth models of DNAPL migration in porous media

Stochastic models that account for a wide range of pore-scale effects are discussed in the context of two-phase, immiscible displacement problems in natural porous media. We focus on migration of dense, nonaqueous phase liquids (DNAPLs) through water-saturated geological materials. DNAPL movement is governed by buoyancy, capillary, and viscous forces, as well as by the details of the porous medium. We examine key issues relevant to development of stochastic growth models. We then present a particular stochastic growth model, based on a generalization of invasion percolation and Eden growth approaches, which realistically simulates two-phase flows in a computationally efficient manner. Fingering patterns are shown to depend critically on the competing buoyancy, capillary, and viscous forces between the DNAPL and the water, and their interactions with the porous medium at the local scale. We conclude with recommendations for future research.