Solution of Riemann problems for hyperbolic systems of conservation laws modeling two-phase flow in general stream tube geometries

Abstract

This paper describes a procedure for the analytical solution of Riemann problems for multi-component, two-phase flow in general stream tube geometries in porous media. The procedure is first described for a scalar hyperbolic conservation law modeling waterflooding of an oil reservoir. Thereafter, it is easy to generalize the procedure to Riemann problems for multi-component, two-phase systems of hyperbolic conservation laws, for which the associated 1D Riemann problem has a known solution. The procedure is described for both constant flow rate and constant boundary pressures as imposed Riemann data. In the latter case, the flow rate is time-dependent and its novel analytical solution is constructed in this paper, clearly demonstrating a non-trivial impact of the flow geometry on the solution.