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A Simplified Method For Computing Oil Recovery By Gas Or Water Drive

Henry J. Welge

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Abstract The approximate methods which are now in use for calculating oil displacement from reservoirs by gas-cycling or gravity-drainage at constant gas pressure, or by water flooding, make use of fundamental relationships derived by Leverett and Buckley and Leverett. The mathematical equations needed are derived by applying Darcy's law to the flowing phases, and by material balance considerations. In general, any treatment of this type gives, for any particular exploitation time considered, a plot of oil saturation against distance in the reservoir. The oil recovery must then be obtained by integrating in some manner the area under the plot. A useful analytical method has been derived for computing the average saturation, and hence the oil recovery. Use of this method simplifies the calculations because it makes unnecessary any numerical integrations, and even the saturation distribution plots are not needed. A further advantage of the method is that knowledge of the relative permeabilities is required only for a limited and intermediate saturation range. In both the Buckley and Leverett method and the method discussed here, a linear sand section is assumed, and in the case of gas drive the gas pressure is assumed sufficiently constant both with respect to reservoir position and time so that changes in gas density, solubility, or reservoir volume factor are negligible. Thus, the exploitation contemplates oil displacement as by an immiscible phase. Examples are given to illustrate how the new method can be used. Introduction and Theoretical Background This paper treats a simplified method for computing oil recovery when the oil is displaced from the reservoir sand by a fluid which, within the limits of accuracy desired, can be assumed to be incompressible and immiscible with the oil. The method makes use of two basic relations originally developed for the case of water displacing oil. However, the case of gas displacing oil saturated with gas at a constant (or nearly constant) pressure may also be considered a displacement by an immiscible fluid. This is possible for the reason that the concentration of the gas in the oil never changes if the pressure is fixed. Consequently, any additional free gas must remain undissolved in the oil, and so must act essentially as an immiscible phase. For convenience, the case of gas drive will be considered first.