Analytical Models of Water-Flooding of Stratified Reservoirs

Abstract

In this chapter, the asymptotic behaviour of the system of equations of two-dimensional two-phase flow in a porous medium is analyzed in order to evaluate the effect of capillary and gravitational forces on vertical redistribution of the fluids. It is shown that, in a large-scale approximation, the pressures in the phases are equal, and are constant over the vertical. Nevertheless, there is some vertical crossflow. The dimensionality of the problem can be reduced in some cases, for which pseudo phase permeabilities and capillary pressure are used [5,71,72,87,107,129,158,159,162,269,270,271,272], and the appropriate conditions are obtained. The structure of the transition zones, which are the large-scale equivalent of saturation jumps, is explored following [146]. Models of oil displacement by water are derived for the two most common cases of viscous domination [5,87,107,159] and capillary-gravitational equilibrium [71,72,158,270].