Pore-level modeling of immiscible drainage: validation in the invasion percolation and DLA limits

Motivated by a wide-range of applications from ground water remediation to carbon dioxide sequestration and by difficulties in reconciling experiments with previous modeling, we have developed a pore-level model of two-phase flow in porous media. We have attempted to make our model as physical and as reliable as possible, incorporating both capillary effects and viscous effects. After a detailed discussion of the model, we validate it in the very different limits of zero capillary number and zero-viscosity ratio. Invasion percolation (IP) models the flow in the limit of zero capillary number; results from our model show detailed agreement with results from IP, for small capillary numbers. Diffusion limited aggregation (DLA) models the flow in the limit of zero-viscosity ratio; flow patterns from our model have the same fractal dimension as patterns from DLA for small viscosity ratios.