Non-negative entropy production criteria for numerical simulations of flows in porous media

The problem of constructing finite-difference schemes for non-isothermal multiphase flows in porous media is investigated. We consider the general case where the filtration of a mixture with an arbitrary number of components and phases is calculated. We derive the non-negative entropy production criteria for the upwind numerical scheme and propose the approximations of fluxes satisfying the criteria. It is shown that the sign of the entropy production is strongly affected by the consistency of mixture properties with the laws of thermodynamics.