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The results of potentiometric model studies and numerical computations are described. The purpose of these studies was to determine the influence of the mobility ratio on flooding efficiencies during water encroachment in petroleum reservoirs, in systems of regular well geometry. The direct line drive well pattern having relative spacing distances of one and one-half to one was investigated for water to oil mobility ratios of 10, 1, and 0.1. The results of these studies indicate that the pattern sweep efficiency is very dependent upon the mobility ratio. Introduction The almost universal occurrence of water in the immediate neighborhood of oil-bearing sands lends considerable emphasis to the desirability of having a rational analysis of water encroachment into petroleum reservoirs. This problem has become increasingly important with the accelerated use of water injection for secondary recovery operations. The water encroachment problem has been studied from both the theoretical and experimental viewpoints by Muskat. He has formulated, in a precise manner, differential equations to express flow in a water encroachment system, and rigorous analytical solutions have been developed for the linear, radial, and spherical cases. However, it becomes exceedingly difficult to solve the encroachment problem rigorously for any general two-dimensional system in which the shape of the two-fluid interface is not immediately evident from the geometry of the system. The difficulty lies in the fact that a rigorous analytical solution requires that the shape of the two-fluid interface be known simultaneously with its instantaneous position and with the pressure distribution on both sides of the interface. Although this paper concerns the study of the two-fluid system of oil and water, the methods described in the paper are generally applicable to other systems of incompressible and immiscible fluids in which the displacing fluid sweeps the displaced fluid down to a residual value. In each region it is assumed there is only one mobile fluid and its mobility is constant throughout the region. The same procedure, with minor alterations, is applicable for gas injection systems provided the assumption can be made that both the displaced and displacing gases can be described by steady state formulas.

Mobility Ratio - Its Influence on Flood Patterns During Water Encroachment