Wave Structure in WAG Recovery

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Abstract For linear immiscible three-phase flow, potentially three-quarters of the oil recovered through a WAG process can be caused by a non-Buckley-Leverett " transitional " shock wave. This nonclassical kind of wave is common in three-phase flow. In this paper, we show how transitional waves arise in WAG flow and how they can be calculated by semi-analytic methods, which are helpful in the design of effective WAG recovery strategies. 1. Introduction In secondary oil recovery, water or gas is injected into a well to displace in situ oil to the producing well. It is well established that oil recovery can be improved by alternately injecting gas and water (Water-Alternating-Gas, or WAG, injection) rather than injecting pure water or gas. The purpose of this work is to understand the wave structure of three-phase WAG flow in a core sample. We show that, in addition to classical Buckley-Leverett shock waves and auxiliary slow waves, there occur two significant features: a new type of shock wave, of intermediate speed; and a fast, decaying, oscillatory injection wave. The elementary wave structure can be understood semi-analytically by solving a Riemann problem, and the oscillatory wave can be calculated numerically, facilitating the design of WAG strategies that maximize recovery with minimal cost. An outline of the paper is as follows. The class of three-phase flow models we study is described in Sec. 2. An important feature of the model is the existence of an umbilic point. Section 3 discusses elementary wave solutions: rarefaction fans and shock waves. It …