Nonclassical Solutions for Three-Phase Flow in Porous Media

We consider a strictly hyperbolic model for three-phase flow in porous media and solutions of its associated Riemann problem. Juanes and Patzek showed that solutions of such a system, in the absence of gravity and capillarity, include rarefaction waves and shocks which satisfy the Liu entropy criterion. By incorporating capillary pressure, as given by thermodynamically constrained averaging theory (TCAT), the model gains dissipation and dispersion terms, the latter of which is rate-dependent. This extends the framework developed by Hayes and LeFloch in which the presence of shocks which do not satisfy the Liu entropy criterion can be determined with an entropy dissipation function. These shocks are undercompressive and contribute to nonclassical solutions of the Riemann problem. In this talk, we give the regularized model and discuss the implications for the catalogue of solutions of the Riemann problem.