Experimental and Numerical Studies of Three-Phase Relative Permeability Isoperms for Heavy Oil Systems
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There is a great deal of interest in obtaining reliable three-phase relative permeability data given recent developments in enhanced heavy oil recovery processes associated with multiphase flow in porous media. Experimental measurement of threephase relative permeability data for heavy oil systems is prohibitively difficult. Such data and research is scarce in the literature since the implementation of steady state experiment is onerous and time consuming. Still results from unsteady state technique do not really coincide with those from steady state experiments. Empirical correlations, such as Stone’s models, which are widely used in modern commercial simulators, carry along uncertainties with two-phase relative permeabilities. In addition, their applicability to heavy oil systems has not been proven. This work proposes a procedure to utilize two- and three-phase unsteady state displacements in order to estimate three-phase relative permeability isoperms. Using residual oil and irreducible water saturations obtained from two-phase heavy oil/water floods, a three-phase flow zone in a ternary diagram was found. Three-phase displacement was conducted in the form of gas injection into a consolidated Berea core saturated with heavy oil and water. A lab-scale three-phase one-dimensional simulator was developed and validated to simulate three-phase displacement experiments. Appropriate three-phase relative permeability data was then selected according to a saturation path drawn across the three-phase flow zone in the ternary diagram. This relative permeability data was continuously fine-tuned until differential pressure, heavy oil production, and water production from the numerical simulator match those from the three-phase displacement experiment. Repeating this procedure for different saturation paths provides a set of relative permeability data which were used to plot relative permeability isoperms for each phase in ternary diagrams. The procedure was validated using steady state experiment and, then, used to study the effect of temperature, oil viscosity, and different gas phase on the relative permeability isoperms for heavy oil systems. Results from this study showed that limited three-phase flow zones exist for heavy oil fluid systems due to high values of residual oil saturation. Different curvatures were observed with relative permeability isoperms of all phases. It was observed that, due to significant contrast between viscosities, oil relative permeability values are higher than those for water and carbon dioxide in order of magnitude of three and five, respectively. It was found that relative permeabilities is no longer a function of saturations as they tend to vary with change in the temperature, oil viscosity, and gas phase. The effect of such parameters on relative permeabilities was shown to be different for each phase. In some cases, opposite and even reversal trends were observed. For instance, oil relative permeability in the presence of carbon dioxide was higher compared to methane, while relative permeability to water phase was higher in presence of methane. The proposed method takes advantage of the practicability of the unsteady state method to provide three-phase relative permeability isoperms in a fast and reliable way. It minimizes the uncertainties that exist with the unsteady state method, such as inaccurate end-face saturation calculation and erroneous derivatives. Also, extensive study of relative permeabilities in different conditions helps us to improve our understating of three-phase relative permeabilities in simulation of processes such as thermal techniques, Steam Assisted Gravity Drainage (SAGD), Cyclic Steam Stimulation (CSS) etc.