Estrutura de ondas para um modelo de escoamento trifásico com viscosidades das fases assimétricas.

Abstract

In this work we consider the Riemann probíem for a system of conservation laws modeling the oil recovery for a three-phase flow in a porous médium by the injection of a mixture of water and gas in a reservoir whieh is initially filled with a mixture of water and oil. Using the theory of conservation laws, the solution of the Rieman problem is determined considering ali possibilities for the production data. For each of these production data. ali possible cases for the injected gas/ water mixture are considered as well. For each production case it is shown the existence of some special injection data separating distinct constmctions of Solutions in the state space. Moreover, among these special injection data one of them is criticai in the sense that the wave sequence that describes the solution can be represented by two or three distinct paths in the state space, but consisting of the same solution in the physical space - xi. In general the solution of the Riemann problem consists of a sequence of two waves separated by one intermediate constant state when the production data are closed to the extreme situations where the initial water or oil saturations are maximal. For production data with a more homogeneous initial water and oil proportion, the solution may consists up to three waves separated by two constant intermediate states for some injected mixtures containing a hígher proportion of gas than water. In such cases a nonelassical wave, i. e. a transitional wave, must be used.