  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.
