Oil displacement by water and gas in a porous medium: the Riemann problem

In this work we present the construction of the Riemann solution for a system of two conservation laws representing displacement in immiscible three-phase flow. The porousmedium is initially filled with oil and small amounts of water and gas; then a fixed proportion of water and gas is injected. We use the wave curve method to determine the wave sequences in the Riemann solution for arbitrary initial and injection data in the above mentioned class. We show the L_Loc¹-stability of the Riemann solution with variation of data. We do not verify uniqueness of the Riemann solution, but we believe that it is valid.