Relevance of analytical Buckley\u2013Leverett solution for immiscible oil displacement by various gases

Abstract

To generate the valid numerical simulation model, the sufficient amount of gathered data from the oil field is required. However, it is not always possible to acquire such data at the initial stage of project development. Buckley and Leverett (Pet Trans AIME 146(01):107–116, 1942) developed the analytical solution allowing to easily assess the oil displacement efficiency. One of the main assumptions of this model is incompressibility of oil and injected fluid. For slightly compressible water and oil such assumption is rational. However, that is not always the case when the gas is injected. This research aims to identify the conditions at which the usage of the incompressible gas model is appropriate. Likewise, the cases when the model of compressible gas is required are also evaluated. To accomplish the goals of this research, the comparative analysis between the injection of compressible and incompressible gases was undertaken using the numerical solution of the correspondent reservoir engineering problems. The validation of the numerical model was performed showing that it matches the analytical Buckley–Leverett solution. The findings of this research indicate that the relative and absolute density change with the pressure of the injected gas has the profound impact on the convergence between two models under consideration. With the increase in the injection pressure, the discrepancy between the models of compressible and incompressible gas raises for all the considered injection fluids (CO_2, CH_4 and N_2). Due to a steep slope of density–pressure curve for CO_2 at low initial reservoir pressure, the incompressible model cannot accurately predict the oil displacement efficiency by this gas at any reasonable injection pressure. All one-dimensional results are also representative for two-dimensional simulations (2D). However, the mismatch between two models increases considerably for 2D simulation scenarios. This study might be beneficial for those considering or researching the possibility of immiscible gas flooding by various gases at the particular oil field. Knowing some basic reservoir and technological parameters, the presented results might be used as simple screening criteria allowing to estimate the relevance of analytical Buckley–Leverett solution.