Effects of Compressibility and Solution Gas on The Gas Drive Mechanism for Linear and Radial Systems

Abstract

A numerical model was constructed to investigate the effects of compressibility, and solution on the immiscible gas drive mechanism. Based on the results of this model, these effects can be predicted using a modification of the Buckley-Leverett and Kern solutions. Introduction A theory describing linear displacement of one fluid by another in porous media was developed in 1941 by Buckley and Leverett. The validity of two of the simplifying assumptions made in their development would seem to depend on the type of fluid used as the displacing phase. The first assumption is that the density of each phase remains constant throughout the reservoir. This supposition is realistic when the oil is displaced by water owing to the relative incompressibility of the two phases. However, when the oil is displaced by gas, this assumption becomes somewhat incredible owing to the fact that the gas is extremely compressible. The other assumption, peculiar only to the displacement of oil by gas, is the constancy of the solution gas during the period of injection. This conjecture would seem unreasonable, inasmuch as when gas is injected at a pressure greater than the saturation pressure of the oil, an pressure greater than the saturation pressure of the oil, an increase in the amount of solution gas per volume of oil undoubtedly occurs. Recognizing these limitations of the Buckley-Leverett theory, Kern presented a modification that takes into account a change in solution gas when gas is injected into an undersaturated reservoir. In this derivation, gas is assumed to be compressed to the volume it would occupy at the injection pressure, and it is postulated that gas remains in this compressed state until breakthrough of the gas. The saturation pressure of the oil is considered to change from the initial bubble-point pressure to a new value equivalent to the injection pressure. Pirson offered a graphical technique for solving Kern's equations. Using this method, saturation at the front and average saturation behind the front can be found in a manner similar to that proposed by Welge. Consequently, the object of this study is to demonstrate with the aid of a numerical model the effect of compressibility and changing fluid properties on the gas displacement mechanism. Complete details of this study can be found elsewhere. A digital computer is used to solve the finite-difference representations of the partial differential equations of motion for the simultaneous flow of oil and gas through porous media. Results from the solutions of Buckley-Leverett, Kern, and the numerical model are contrasted. Suggestions are made as to the reasons for the differences in the three solutions. A variation to the Kern solution for both linear and radial systems is presented for estimating recoveries at breakthrough when injection, production, and initial bubble-point pressures are known. JPT P. 1079