Phase equilibrium calculations play an important role in a wide variety of applications in chemical and petroleum engineering. In this work, we focus on CO₂-hydrocarbon mixtures, with applications ranging from enhanced oil recovery processes to CO₂ storage. In compositional reservoir simulation, both robustness and efficiency are of utmost importance. The conventional approach for multiphase equilibrium consists of a sequence of phase stability and flash calculations. At each level of the stepwise process, stability testing is performed starting from several initial guesses; therefore, reducing the number of stability calls and using judiciously the information from stability to initialize a phase split are key points in developing an efficient stability-flash algorithm. Two new initialization strategies for multiphase flash calculations are proposed. The first one (improved stepwise initialization) follows the conventional procedure, but uses additional initial guesses. In the second one (improved multiple initialization), a three-phase split is initiated if at least three minima of the tangent plane distance (TPD) function are detected by stability analysis of feed composition. Both proposed methods are using all information from phase stability testing at each stage. Unlike in previous formulations, compositions at all minima of the TPD function, including trivial and positive TPDs are used to generate initial equilibrium constants. Highly robust routines are used, based on successive substitution iterations (SSI) in early iteration stages, followed by Newton iterations with modified Cholesky factorization and line search, in both stability and flash calculations. The proposed methods are tested and compared with the conventional procedure for several benchmark mixtures from the literature, containing hydrocarbon components and CO₂. Phase diagrams are constructed in the P-Z plane, focusing on the number of stationary points of the TPD functions found in each step of the multiphase stability-flash algorithm and on how they must be efficiently used in initialization. For all the test mixtures, in the proposed stability-flash strategy, the number of calls of the stability and flash routines and the number of iterations in flash calculations are significantly reduced as compared to previous approaches, recommending the new approach as a useful tool in compositional simulation.

Three-phase equilibrium calculations for water-CO2-hydrocarbon mixtures are required in the compositional simulation of various applications in CO2 storage, geothermal systems, and enhanced oil recovery. The very low solubility of hydrocarbon components in water leads to a special mathematical structure of the problem. Several techniques were suggested, such as the free-water flash (FWF) and the augmented free-water flash (AFWF); in the former, the aqueous phase is pure water, while in the latter only certain components, CO2 or methane for example, are dissolved in the aqueous phase. However, only the first-order successive substitution method was used in the previous published approaches, making them unattractive for compositional simulations in which a significant number of phase equilibrium calculations are performed. In this work, a robust and efficient AFWF method is proposed, using combined successive substitutions-modified Newton iterations. The new method is general, allowing partial solubility of any selected component in the water-rich phase, depending on the specific compositions and operating conditions. A detailed description of second-order methods in a Gibbs energy minimization framework for the general AFWF is presented. In the AFWF, the dimension of the problem and the number of function evaluations (thus the computation time) are significantly reduced. Moreover, it is shown that the augmented method always has better convergence properties than its conventional multiphase flash counterpart, in both first- and second-order methods. The new AFWF method is tested for various hydrocarbon-water-CO2 mixtures and proved to be robust and efficient, systematically outperforming the conventional approach. Unlike in previous AFWF formulations, the number of components soluble in water is not limited, leading to a controlled accuracy with respect to a full three-phase equilibrium, even at high pressures and/or large amounts of CO2.