Method of Negative Saturations for Modeling Two-phase Compositional Flow with Oversaturated Zones

We examine the two-phase flow through porous media of multicomponent partially miscible fluids. The composition of both the phases is variable in space and time and is assumed to be in local thermodynamic equilibrium. One of the basic problems in modeling such systems is related to the appearance of single-phase zones occupied by the fluid which is over- (or under-) saturated, i.e., it is significantly remote from the equilibrium two-phase region. In an oversaturated zone, the two-phase flow equations degenerate and can no longer be used, which provokes serious numerical problems. We propose to describe the two-phase and oversaturated single-phase zone by a uniform system of classic two-phase equations while extending the concept of the phase saturation so that it may be negative and higher than one. Physically this means that we consider the oversaturated single-phase states as the pseudo two-phase states which are characterized by a negative saturation of the imaginary phase. Such an extension of the concept of the phase saturation requires the development of some consistence conditions that ensure the equivalence between the pseudo two-phase equations and the true single-phase flow model in the oversaturated zones. This method allows using the existing numerical simulators of two-phase flow for modeling single-phase zones by adding a simple plug-in with no modification of the structure of the simulators. The method is illustrated by several examples of hydrogene-water flow in a waste radioactive storage and of CO₂ injection in an oil reservoir.