Summary Flash calculations for use in compositional simulation are more difficult and time-consuming as the number of equilibrium phases increases beyond two. Because of its complexity, many simulators do not even attempt to incorporate three or more hydrocarbon phases, even though such cases are important in many low-temperature gasfloods or for high temperatures where hydrocarbons can partition into water. Multiphase flash algorithms typically use successive substitution (SS) followed by Newton's method. For NP-phase flash calculations, (NP–1) Rachford-Rice (RR) equations are solved in every iteration step in SS and, depending on the choice of independent variables, in Newton's method. Solution of RR equations determines both compositions and amounts of phases for a fixed overall composition and set of K-values. A robust algorithm for RR is critical to obtain convergence in multiphase compositional simulation and has not been satisfactorily developed, unlike the traditional two-phase flash. In this paper, we develop an algorithm for RR equations for multiphase compositional simulation that is guaranteed to converge to the correct solution independent of the number of phases for both positive and negative flash calculations. We derive a function whose gradient vector consists of RR equations. This correct solution to the RR equations is formulated as a minimization of the nonmonotonic convex function using the independent variables of (NP–1) phase mole fractions. The key to obtaining a robust algorithm is that we specify nonnegative constraints for the resulting equilibrium phase compositions, which are described by a very small region with no poles. The minimization uses Newton's direction with a line-search technique to exhibit superlinear convergence. We show a case in which a previously developed method cannot converge while our algorithm rapidly converges in a few iterations. We implement the algorithm both in a standalone flash code and in UTCOMP (Chang et al. 1990), a multiphase compositional simulator, and show that the algorithm is guaranteed to converge when a multiphase region exists as indicated by stability analysis.

Supercritical CO 2 injection is a promising way to hydraulically fracture tight/shale gas formations as well as enhance gas recovery from these formations. Understanding of phase behavior and interfacial tension (IFT) of CO 2 /CH 4 /brine (NaCl) systems is important, because they affect the performance of such a process in tight/shale gas formations. In this study, we employ the axisymmetric drop shape analysis (ADSA) method to measure the IFT between CO 2 / CH 4 mixtures and brine over the temperature range from 77.0 to 257.0 °F and the pressure range from 15 to 5027 psia. Test results show that the presence of CO 2 decreases the IFT of CH 4 /H 2 O or CH 4 /brine (NaCl) systems, while the degree of reduction depends on the molar fraction of CO 2 in the gas mixture. Salinity tends to cause an increase in IFT of CO 2 /CH 4 /brine (NaCl) systems; a higher salinity leads to an increased IFT for a given system. On the basis of the Parachor model (Weinaug and Katz J. Ind. Eng. Chem. 1943, 35, 239) and Firoozabadi's model (Firoozabadi and Ramey J. Can. Pet. Technol. 1988, 27, 41), we propose an improved IFT model to represent the measured IFT data for CO 2 /CH 4 /brine systems. The new IFT model preserves the principle of zero IFT at a critical point. Comparison of the new IFT model with four commonly used IFT correlations presented in the literature shows the superiority of the new model.

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Summary Mixtures of oil with solvent gas can exhibit three-hydrocarbon-phase behavior at reservoir conditions, where the solvent-rich liquid (L2) phase coexists with the gaseous (V) and oleic (L1) phases. Three-hydrocarbon-phase behavior has been studied in the literature for carbon dioxide (CO2) floods and enriched-gas floods at relatively low temperatures. Prior research on heavy-oil displacement with enriched gas presented that displacement efficiency at a given throughput can be nonmonotonic with respect to gas enrichment. Slimtube experiments for such displacements showed that oil recovery increased first, then decreased, and increased again with increasing gas enrichment. An optimum displacement with a high efficiency of more than 90% was observed when three-hydrocarbon-phase flow was present. However, detailed mechanisms for such an optimum displacement with three phases have not been explained in the literature. In this research, we investigate mass transfer on multiphase transitions between two and three phases for three-hydrocarbon-phase displacements. Simple conditions are derived for the multiphase transitions that yield high local displacement efficiency by three hydrocarbon phases. The derivation is based on the generalized mass conservation for a multiphase transition in 1D gas injection. The conditions derived are applied to explain nonmonotonic oil recovery in quaternary displacements and the West Sak oil displacements. Oil recovery at a given throughput can be nonmonotonic with respect to pressure or gas enrichment. Such a nonmonotonic trend can occur when local oil displacement by three hydrocarbon phases becomes more efficient, but slower, with decreasing pressure or decreasing gas enrichment. An optimum pressure or enrichment can occur as a consequence of the balance between the local displacement efficiency and the propagation rate of three hydrocarbon phases. The West Sak oil displacement with enriched gas studied in this research yields a high displacement efficiency of more than 90% at 1.5 hydrocarbon pore volumes (PV) injected at 53% methane (C1) dilution.