On the Riemann problem for the foam displacement in porous media with linear adsorption

Motivated by the foam displacement in porous media with linear adsorption, we extended the existing framework for two-phase flow containing an active tracer described by a non-strictly hyperbolic system of conservation laws. We solved the global Riemann problem by presenting possible wave sequences that composed this solution. Although the problems are well-posedness for all Riemann data, there is a parameter region where the solution lacks structural stability. We verified that the model implemented on the most used commercial solver for geoscience, CMG-STARS, describing foam displacement in porous media with adsorption satisfies the hypotheses to apply the developed theory, resulting in structural stability loss for some parameter regions.