O problema de Riemann para um modelo matemático de um escoamento trifásico em meio poroso.

Abstract

In this work we construct a solution of the Riemann problem for a system of conservation laws arising from the mathematical modeling of a three-phase flow in a porous medium representing the propagation of water-gas-oil mixtures in a recovery project of a petroleum reservoir. Using analytical and computational methods we find the geometry of the wave urves under the viscous profile entropy condition, with the identity as the viscosity matrix. We show that for the right data representing almost pure oil compositions the solution of the Riemann problem generically consists of a sequence of two wave groups, related to the two characteristics families, for any left data considered representing a water-gas mixture. However, for right data representing mixtures with oil still dominant, but with a larger proportion of gas and water, a transitional wave group is required in the sequence for a small subset of left data.