The propagation of weak concentration discontinuities in the isothermal flow of a multicomponent mixture in a porous medium with phase transitions

It is shown that for the general case of a system of non-linear equations, describing multicomponent isothermal flow in a porous medium with phase transitions, as in hyperbolic systems, weak concentration discontinuities propagate with finite velocities, which are determined by solving an eigenvalue problem. If the seeping phases are incompressible and there are no phase transitions, the results obtained for weak discontinuities transfer into the well-known formulae for the Buckley – Leverett model. The results are demonstrated for the case of two-component seepage with phase transitions.