Validation and application of probabilistic simulation for fluid flow through porous media

The non-linear partial differential equations describing oil- water displacement in porous media can be solved using a probabilistic simulation technique. Results have been presented by various authors. However, an elaborate proof of the technique has as yet not been presented. The results of a probabilistic simulator, are validated using a one dimensional solution in closed of the Buckley-Leverett problem including capillary forces. Subsequently the simulator is applied to study the effect of permeability heterogeneity on displacement characteristics. Both one and two dimensional examples are presented.