Reduced variables method for four-phase equilibrium calculations of hydrocarbon-water-CO₂ mixtures at a low temperature

Carbon dioxide (CO₂) flooding has been widely applied to enhance oil recovery. In low temperature reservoirs, CO₂ injection may result in the formation of three hydrocarbon phases at thermodynamic equilibrium. In addition, an aqueous phase is always present in the reservoir. The aqueous phase can coexist with three hydrocarbon phases to form a four-phase equilibrium system. To evaluate CO₂ utilization and storage in these low temperature petroleum reservoirs, a robust and efficient four-phase equilibrium calculation framework involving water is necessary for a compositional reservoir simulator. This is challenging not only because the number of variables increases but also because stability analysis becomes much complicated as the number of phases increases. In this research a novel four-phase equilibrium calculation framework is proposed for compositional reservoir simulation. A reduced variables method is used to solve four-phase flash problems efficiently and robustly. Multiphase flash calculations using reduced variables (RV) can converge to the equilibrium solution faster than formulations using conventional variables (Petitfrere and Nichita, 2015). Secondly, RV does not suffer from numerical problems in the Newton iterations when trace components are present in the aqueous phase. In addition to the implementation of the RV formulation, a systematic procedure consisting of stability analysis and flash calculations is proposed without any prior knowledge of initial K-values. Sets of different initial K-values are appropriately tested in each stability analysis. We performed comprehensive testing using characterized fluids found in the literature in order to validate the robustness of the proposed procedure. The four-phase regions in pressure-composition (Px) space could be accurately identified using our procedure. On the other hand, in some instances mixtures were incorrectly evaluated as three-phase when using existing approaches such as Li and Firoozabadi (2012). Our approach proposed in this paper is a promising four-phase equilibrium calculation framework for compositional reservoir simulation. The procedure achieved excellent robustness and efficiency with minimal modification to the conventional two or three-phase equilibrium calculation framework.