On the Riemann problem for the foam displacement in porous media with linear adsorption. (English) Zbl 1537.35234
Summary: 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-posed 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.
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35L45 | Initial value problems for first-order hyperbolic systems |
| 35L60 | First-order nonlinear hyperbolic equations |
| 35Q35 | PDEs in connection with fluid mechanics |
| 74S20 | Finite difference methods applied to problems in solid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
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