The oil-water flow in a heterogeneous porous medium was studied numerically, with special emphasis on the interface between two homogeneous layers of the porous matrix. The heterogeneity considered consists of a discontinuous capillary pressure on the interface. The differential equation was solved using a fully implicit scheme based on the upwind finite volume method. The unknown was the water saturation. This study evaluated the impact of changes in: the porosity of the entire domain, the initial water saturation, the water injection rate, the gravitational force, and the material grain size, on the water saturation at the interface. Experiments have improved the understanding of hydrodynamics on the interface. A full characterization of the porous matrix is an essential condition before defining conditions of oil extraction. The studied algorithm has great potential for use in earlier stages of design and planning for oil extraction.