Mathematical Modeling of Gravity Drainage After Gas Injection into Fractured Reservoirs

Abstract

Abstract This paper addresses mathematical modeling of free-fall gravity drainage which is believed to occur in naturally fractured reservoirs after depletion of oil in the fractures or gas injection into the fractured system. Comparison of wetting phase recoveries calculated using existing math-ematical models with experimental data indicates the in-accuracy of these models. The causes of error are identified to be the unrealistic assumptions made in formulation of the models. Based on Darcy's law and film flow theory, we have developed a new mathematical model to describe the free-fall gravity drainage process, A simple non-linear governing equation for phase demarcator in dimensionless form was formulated and solved numerically as a function of dimensionless time. Based on the dimensionless demarcator, fluid recovery during free-fall gravity drainage is calculated. Comparisons of wetting phase recoveries given by the new model with 20 sets of experimental data obtained under thermodynamic equilibrium conditions for a variety of fluids and cores show much better accuracy of the model over the existing models. Using the dimensionless time, tD — ke∆𝜌gt/𝜇L, fluid recovery obtained from laboratory studies can be scaled to field applications for estimation of projected oil recoveries in oil fields. We have also applied the new model to simulation of free-fall gravity drainage under non-equilibrium conditions where molecular diffusion between phases is considered. Experimental oil recovery data obtained from CO2 injection into a Berea core and a reservoir sandstone core, which were saturated with separator oil, have been matched by the model using empirical correlations for fluid properties. The objective of this paper is to provide reservoir engineers with a useful tool for estimating the oil recovery from fractured reservoirs after gas injection.