Mathematical Structure of the Black-Oil Model for Petroleum Reservoir Simulation

This model incorporates compressibility and general mass transfer between phases. It consists of the conditions of thermodynamic equilibrium, an equation of state for the volume balance between the fluidand the rock void, Darcy’s Law for the volumetric flow rates, and component conservation equations. These relations are manipulated to form a pressure equation and a modified system of component conservation equations. It is shown that the pressure equation is parabolic and that, in the absence of diffusive forces such as capillary pressure and mixing, the component conservation equations are hyperbolic, subject to technical conditions on the relative permeabilities. This sequential formulation of the flow equations forms types of wave structures that occur for the system.