Three-Phase Relative Permeability Measurements by Unsteady-State Method

Abstract

For the performance prediction of multiphase oil recovery processessuch as steam stimulation, there is an acute need for three-phaserelative permeability data. No fast and simple experimental technique,such as the unsteady-state method proposed by Welge for two-phaseflow, is available for the three-phase flow.In this paper, an unsteady-state method is presented for obtainingthree-phase relative permeability data; this method is as fast andeasy as Welge's method for two-phase flow. Analytical expressionsare derived by extension of the Buckley-Leverett theory to three-phaseflow to express the saturation at the outflow face for all threephases in terms of the known parameters. It is assumed that the fractionalflow and relative permeability of each phase are a function of thesaturation of that phase. Other simplifying assumptions made includethe neglect of capillary and gravity effects. The effect of saturationhistory upon relative permeability is acknowledged and attainmentof similar saturation history in laboratory and field is recommended.The required experimental work and computations are simple to perform.The test core is presaturated with oil and water, then subjectedto gas drive. During the test, required data are the rates of oil,water, and gas production, together with pressure drop and temperature.The ordinary gas-oil unsteady-state relative permeability apparatuscan be readily modified to measure the required data. The proposedtechnique was applied to samples of a Berea and a reservoir core.The effect of saturation history upon relative permeability was studiedon one Berea core. It was found that increase in initial water saturationhas a similar effect upon three-phase relative permeability as itdoes in two-phase flow.