Transition to steady-state solutions of the equations of multicomponent flow through porous media

Abstract

The question of the dynamics of the approach to steady-state solutions is examined in relation to the system of equations of equilibrium multicomponent two-phase flow through porous media [1, 2]. The equations are analyzed in the linear approximation for the case of small fluctuations. An expression is obtained for the characteristic transition time. Numerical modeling is carried out for substantial deviations from the steady-state solution. The problem of the plane linear displacement of a ten-component gas-condensate mixture by an enriched gas with subsequent transition to the extraction regime is solved. It is shown that the change in phase compositions and pressure proceeds with characteristic times of the order of the time required to create a spatially nonuniform distribution of the mixture properties during injection. However, the change in the saturations and overall composition takes place in times approximately 200 times greater than the injection time. The question of the existence of discontinuous steady-state solutions of the system of equations investigated is considered, and in the case of a binary mixture it is shown that such solutions cannot be realized.