Problema de Riemann para um sistema de leis de conservação não estritamente hiperbólico modelando o deslocamento de espuma

Abstract

Motivated by the foam displacement in porous media with linear adsorption, we extended the existing framework for the two-phase flow containing an active tracer described by a non-strictly hyperbolic system of conservation laws. We solved the corresponding Riemann problem by presenting possible wave sequences that composed this solution. We presented necessary and sufficient conditions to guarantee the compatibility of such waves demonstrating the existence of a global solution. We classify the solutions in the phase plane containing all possible left and right states connected by a compatible wave sequence. We point out where the solution is unique and where two different compatible wave sequences exist. We present the CMG-STARS model describing foam displacement in porous media with adsorption and verify that it satisfies the properties necessary for the developed theory. All analytical solutions presented in this model match with direct numerical simulation results. We show parameter regions where the CMG-STARS model presents a lack of solution uniqueness in the phase-plane, yielding the loss structural stability. We also show that this model is well-posed in the Hadamard sense, being able to presents numerical oscilations due to structual instability. We present conditions to establish a chemical optimal slug composed by two Riemann problems, and evaluating the impact of the adsorption in it.