Miscible Displacement - A Multilayer Technique for Predicting Reservoir Performance
Authors: Doepel G.W. , Sibley W.P. 
Published: December 2007

Abstract
A three-dimensional, multilayer, mathematical model has been developed for predicting performance by miscible displacement. Areal and vertical coverage, total gas-oil ratio, propane-oil ratio and oil-recovery factor for the multilayer system are computed as functions of hydrocarbon pore volumes of solvent injected. The technique has been programed for use on the IBM–7090 digital computer and was used in calculating performance for continuous miscible displacement of a five-spot, 50-layer system. Results reported are based on the use of published laboratory data for a single, uniform five-spot layer. However, the technique is sufficiently generalized to calculate performance of any system of layers of any pattern configuration and mobility ratio, provided data are available to describe performance of a single layer. The technique has also been adapted for predicting oil recovery resulting from various gas-driven slug sizes. The results presented for both continuous and slug-type injection show that permeability variation has a significant effect on oil recovery but that solvent composition, within the range studied, has a lesser effect on oil recovery.

Introduction
Experience from many of the miscible-phase displacement projects currently in operation indicates that the injected solvent flows preferentially through the more permeable zones in the reservoir. This preferential solvent flow in the high-permeability streaks results in a reduction of vertical coverage (Cv) and an attendant decrease in oil recovery. The multilayer technique presented in this paper uses areal coverage (C A) data for a single layer from the literature and from laboratory measurements of displacement efficiency (herein referred to as microscopic coverage, C M) to calculate areal coverage (C A) and vertical coverage (C V) for the multilayer system. Oil recovery for the multilayer system is obtained as the product of (C A) (C M) (C V). It is assumed that C V in a single layer is 100 per cent; therefore, (C A) (C M) is a measure of oil recovery from that layer. Data presented in the literature for a single layer generally deal only with areal coverage and/or microscopic coverage - but seldom specifically with oil recovery. Nevertheless, this technique is flexible in that either C A and C M of an individual layer or a direct measurement of oil recovery for the layer may be used. In developing this technique, the problem arose concerning a method of determining the relative amounts of solvent that will enter each layer during any increment of solvent injected. To solve the problem, a dimensionless equation was derived for expressing solvent injected into each layer as a fraction of total injection. A finite-difference method was applied in integrating the equation to determine oil recovery for the system of layers as a function of pore volumes injected. The technique subsequently was programed for solution on a digital computer. The method was applied to predict performance of a deep California reservoir under continuous miscible displacement and has been extended for calculating oil recovery as a function of slug size for gas-driven slug injection. The technique may be applied to any petroleum reservoir that can be adequately represented as a layered system, by considering permeability variation, permeability range and average permeability. Each layer is then assigned its appropriate permeability, porosity and hydrocarbon saturation.

RESERVOIR VOLUME CONTACTED BY SOLVENT
It has been recognized for some time that high microscopic coverage (C M) can be obtained by injecting a miscible agent, such as propane, into an oil reservoir. These high values of C M have been demonstrated in the laboratory and are normally between 80 and 100 per cent, depending on solvent and reservoir oil composition as well as on reservoir temperature and pressure. In miscible-phase displacement, because there is no interface between solvent and oil, effective permeability to solvent is the same as that to oil. (This assumes that oil saturation has not changed and that water is immobile.) Consequently, mobility ratio (M) simply reduces to that of viscosity ratio (o/ s).
JPT
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