Abstract

Forced oil-water displacement and spontaneous counter-current imbibition are the crucial mechanisms of secondary oil recovery.  Classical mathematical models of both these unsteady flows are based on the fundamental assumption of local phase equilibrium.  Thus, the water and oil flows are locally redistributed over their flow paths similarly to steady flows.  This assumption allows one to further assume that the relative phase permeabilities and the capillary pressure are universal functions of the local water saturation, which can be obtained from steady-state flow experiments.  The last assumption leads to a mathematical model consisting of a closed system of equations for fluid flow properties (velocity, pressure) and water saturation.  This model is currently used as a basis for numerical predictions of water-oil displacement.

However, at the water front in the water-oil displacement, as well as in capillary imbibition, the characteristic times of both processes are, in general, comparable with the times of redistribution of flow paths between oil and water.  Therefore, the non-equilibrium effects should be taken into account.  We present here a refined and extended mathematical model for the non-equilibrium two-phase (e.g., water-oil) flows.  The basic problem formulation, as well as the more specific equations, are given, and the results of comparison with experiments are presented and discussed.