Horizontal one-dimensional redistribution of oil and water with hysteresis due to oil entrapment

Redistribution of oil and water in a long horizontal column, including oil entrapment by water, is described by a nonlinear diffusion problem with a spatially varying diffusion coefficient. This problem admits a similarity solution that was found previously for redistribution of water with capillary hysteresis. The distributions of both the free and the trapped oil saturations are computed and additionally the effect of initially trapped oil on the solution is demonstrated.