Miscible gas flooding is a common method for enhanced oil recovery. Reliable design of miscible gas flooding requires compositional reservoir simulation that can accurately predict the fluid properties resulting from mass transfer between reservoir oil and injection gas. Drawbacks of compositional simulation are the efficiency and robustness of phase equilibrium calculations consisting of flash calculations and phase stability analysis. Simulation of multicontact miscible gas flooding involves a large number of phase equilibrium calculations in a near-critical region, where the calculations are time-consuming and difficult. Also, mixtures of reservoir oil and solvent such as CO₂ and rich gas can exhibit complex phase behavior at temperatures typically below 120°F, where three hydrocarbon-phases can coexist. However, most compositional simulators do not attempt to solve for three hydrocarbon-phases because three-phase equilibrium calculations are more complicated, difficult, and time-consuming than traditional two-phase equilibrium calculations. Due to the lack of robust algorithms for three-phase equilibrium calculations, the effect of a third hydrocarbon-phase on low-temperature oil displacement is little known. We develop robust and efficient algorithms for phase equilibrium calculations for two and three phases. The algorithms are implemented in a compositional reservoir simulator. Simulation case studies show that our algorithms can significantly decrease the computational time without loss of accuracy. Speed-up of 40% is achieved for a reservoir simulation using 20 components, compared to standard algorithms. Speed-up occurs not only because of improved computational efficiency but also because of increased robustness resulting in longer time-step sizes. We demonstrate the importance of three-phase equilibrium calculations, where simulations with two-phase equilibrium approximations proposed in the literature can result in complete failure or erroneous simulation results. Using the robust phase equilibrium algorithms developed, the mechanism is investigated for high efficiency of low-temperature oil displacements by CO₂ involving three hydrocarbon-phases. Results show that high displacement efficiency can be achieved when the composition path goes near the critical endpoint where the gaseous and CO₂-rich liquid phases merge in the presence of the oleic phase. Complete miscibility may not be developed for three-phase flow without considering the existence of a tricritical point. / text