A representation of the equations of multicomponent multiphase seepage

A mathematical model of non-isothermal multicomponent flows in a porous medium is investigated. A general case is considered when the model can be used to describe processes with an arbitrary number of components and phases. A general form of the system of mixed-type equations describing the flow, which is similar to the Godunov form for hyperbolic systems is proposed. The equations obtained are applicable to flows with gas, liquid and solid phases. The thermodynamic properties of the medium are determined solely by a single multivalued function, by changing which one can obtain models of different flows in a porous medium. A clear geometrical interpretation of the solutions of the equations is proposed. An equation for the entropy is obtained, and it is shown that in order that the model should not contradict the second law of thermodynamics, it is necessary to take into account, in the energy equation, the work of the gravity force, which is often neglected when investigating seepage.