Numerical Methods for Nonlinear System of Hyperbolic Equations Arising in Oil Reservoir Simulation

Abstract

Here, we propose a higher order finite volume scheme by using the idea of discontinuous flux for the numerical study of two-phase flow in a heterogeneous porous media, arising in oil reservoir simulation. To enhance the oil recovery, chemical components called polymers are dissolved in the aqueous phase. This results in studying the Buckley–Leverett model with multicomponent polymer flooding, which is a coupled non-strictly hyperbolic system of conservation laws in the absence of capillary pressure. In the presence of gravity, the flux function is non-monotone and the construction of Godunov type upwind scheme for this system becomes difficult and computationally expensive. To overcome this difficulty, the coupled system is reduced to an uncoupled system of scalar conservation laws with discontinuous coefficients and applied the idea of discontinuous flux to solve these scalar equations.