Organizing structures in the Riemann solution for thermal multiphase flow in porous media
Julio Daniel Silva
systems of conservation laws | Riemann problem | thermal multiphase flow.
The aim of this work is to construct the solution to a nonlinear system of conservation laws arising in petroleum engineering for a model that describes the injection of a mixture of gas and oil, in any proportion, into a porous medium filled with a similar mixture, at different temperatures. The model allows the existence of fluids in three thermodynamical configurations, namely: a single phase gas configuration, a single phase liquid configuration and a two-phase configuration. The solutions are constructed around two organizing structures. The first is a singular point, intrinsically associated to most bifurcations in the Riemann solutions for this class of models. The second is the interface between the two-phase configuration and the single-phase liquid configuration in state space; the change of thermodynamical configuration introduces a new pattern in the Riemann solutions.