Three-phase immiscible displacement in heterogeneous petroleum reservoirs

We describe a fractional-step numerical procedure for the simulation of immiscible three-phase flow in heterogeneous porous media that takes into account capillary pressure and apply it to indicate the existence of a so-called “transitional” wave in at least some multi-dimensional flows, thereby extending theoretical results for one-dimensional flows. The step procedure combines a second-order, conservative central difference scheme for a pertinent system of conservation laws modeling the convective transport of the fluid phases with locally conservative mixed finite elements for the associated parabolic and elliptic problems.