Multiphase Equilibrium Calculation Framework for Compositional Simulation of CO2 Injection in Low-Temperature Reservoirs

Abstract

CO₂ injection into an oil reservoir at low temperature can lead to the formation of three hydrocarbon phases. Key challenges persist in the development of phase equilibrium calculations for three-phase hydrocarbon–CO₂ systems. One challenge is the identification of a third equilibrium phase via stability testing of a two-phase mixture. Stability testing requires initial estimates of phase equilibrium ratios (K-values). Existing methods for estimating K-values for the identification of three-phase behavior are unable to detect the whole three-phase region. In addition, many of the initial K-value estimates are redundant, wherein convergence is to the same composition. In this work, we present systematic procedures for single-phase and two-phase stability testing using optimized sets of initial K-value estimates. We show that two-phase stability testing requires one to test both of the equilibrium phases in the system. We reveal that three-phase hydrocarbon–CO₂ behavior cannot be resolved across the pressure–composition parameter space with existing methods for the estimates of the initial K-value. We introduce a new initial K-value estimate for two-phase stability testing to resolve three-phase behavior. Our approach significantly improves the reliability and reduces the cost of phase stability testing. Reservoir simulation requires fast and reliable algorithms for stability testing and flash calculations. Failure of the phase equilibrium kernel leads to time-step cuts and the potential cessation of the simulator. We have implemented a combined successive substitution, Newton, and trust-region optimization algorithm for both stability testing and multiphase flash calculations. We have also developed a novel optimization algorithm to solve the multiphase Rachford–Rice equations. We present the performance of our phase equilibrium framework using nine characterized fluid systems from the literature. Rigorous testing across a wide parameter space demonstrates the robustness of our framework. We show specific instances of quantification of phase equilibrium in challenging scenarios, including near the stability test limit locus in stability testing and the critical region in multiphase flash calculations. The results in this work address the most prominent difficulties in equation of state modeling of CO₂ flooding. In sum, this work provides the comprehensive detailed algorithms for phase equilibrium calculations for simulation of CO₂ flooding in low-temperature reservoirs.