New empirical scaling equations for oil recovery by free fall gravity drainage in naturally fractured reservoirs

Abstract

Gas-oil gravity drainage is a recognized major contributor to production in fractured reservoirs. While various empirical and analytical methods have been proposed to model this process, many of them contain assumptions that are questionable or require parameters that are not accessible at the field level. The aim of this work is to provide new, easy-to-use scaling equations for estimating the recoverable oil through gravity drainage in naturally fractured reservoirs, considering the effects of resistance capillary pressure. To accomplish this, data from four oilfields undergoing gravity drainage, including rock properties (eight sets), block height (three sets), and fluid properties (four sets), were used to generate a wide range of recovery curves using a single porosity numerical simulation model. Aronofsky's and Lambert's functions were then utilized to match the generated recovery curves. Statistical analysis revealed that the Aronofsky's function is more accurate in replicating the recovery patterns, while the Lambert's function tends to overestimate the early-time oil recovery and underestimate the oil recovery at a later stage in the majority of cases. A sensitivity analysis was subsequently performed, revealing that parameters such as absolute permeability, viscosity of oil, height of block, gas and oil density, characteristics of relative permeability and capillary pressure curves and interfacial tension (IFT) influence the amount of time taken to achieve the final recovery. Of these parameters, absolute permeability has the most significant effect on the amount of time needed to attain the final recovery, while the effect of difference between oil and gas densities is the lowest. Consequently, two different expressions were developed using nonlinear multiple regression analysis of simulated gravity drainage data which can be combined with the Aronofsky model to substitute the rate convergence constant. The new scaling equations include the effects of capillary pressure and other relevant factors in gravity drainage simulations. Both forms show satisfactory accuracy, as evidenced by the statistical parameters obtained (R2 = 0.99 and MSE = 0.0019 for both established correlations). The new correlations were verified using a wide range of oilfield data and are expected to provide a better understanding of the recovery process in naturally fractured reservoirs.