Numerical simulation of immiscible two-phase flow in porous media

Nonlinear evolution of viscous and gravitational instability in two-phase immiscible displacements is analyzed with a high-accuracy numerical method. We compare our results with linear stability theory and find good agreement at small times. The fundamental physical mechanisms of finger evolution and interaction are described in terms of the competing viscous, capillary, and gravitational forces. For the parameter range considered, immiscible viscous fingers are found to undergo considerably weak interaction as compared to miscible fingers. The wave number of nonlinear fingers decreases rapidly due to the shielding mechanism and scales uniformly as t(-1) at long times. We have observed that even a small amount of density contrast can eliminate viscous fingers. The dominant feature for these flows is the gravity tongue, which develops a "ridge instability" when capillary and gravity effects are of similar magnitude.