Three-phase fluid displacements in a porous medium

Oil in a reservoir is usually found together with water and gas. Often a mixture of water and gas is used to displace such oil. In this work, we present the Riemann solution for such three-phase flow problem. This solution encodes the dependence of recovery on the injected proportion, the proportion initially present, and the viscosity of the several fluids. We use the wave curve method to determine the Riemann solution for initial and injection data in the above-mentioned class. We verify the L-loc(1)-stability of the Riemann solution with variation of data. We do not establish uniqueness of the Riemann solution, but we believe that it is valid.