Equilibrium Calculations for Coexisting Liquid Phases

Modeling of reservoir processes like gas miscible flooding may require consideration of phase equilibrium between multiple liquid phases. Under certain conditions two hydrocarbon liquid phases may form; one may also want to account for mass transfer between the hydrocarbon and the aqueous phases. This paper describes a refined successive substitution (SS) method for calculating multiphase flash equilibrium. The phase behavior procedure proceeds in a stepwise manner, and additional phases are introduced by a special testing scheme based on phase fugacities. This is to avoid trivial solutions and to ensure continuity across phase boundaries. The method has been tested on various three- and four-phase systems, and examples of application show that the method performs well. Introduction Fluid phase behavior constitutes a very important aspect of more sophisticated oil recovery processes such as gas miscue flooding. In such processes mixtures of the reservoir fluids and the injected gas typically may approach critical conditions, and laboratory experiments have shown that the oil phase may in some cases split into two or more coexisting hydrocarbon liquid phases. In addition, interaction with the water phase may become important as the dissolution of gas components in water may affect the overall process performance significantly. The complexity of phase behavior during gas miscible flooding makes modeling and predictions a demanding task. Cubic Redlich-Kwong type EOS's have proved applicable for both gaseous and liquid phases. Thus, because of their simplicity, their reasonable accuracy, and their consistency near critical points, they have received much recent attention as a tool for describing compositional hydrocarbon reservoir phenomena. Various schemes for flash equilibrium calculations based on an EOS have been proposed. Broadly, they may be categorized as variants of the widely applied SS method or as second-order Newton-type methods. Most applications deal with two-phase problems, but extensions to multiphase problems have been reported. A basic solution scheme for multiphase cases was presented by Peng and Robinson. In addition, an extension of the minimum variable Newton technique was described by Fussell, and a combination of both first- and second-order methods was considered by Mehra and Mehra et al. One main problem with flash equilibrium calculations band on EOS's convergence toward trivial solutions and a proper delineation of phase boundaries. This is so for two-phase problems but even more so for multiphase problems, where phase boundaries may be very close to each other and good estimates of equilibrium K-values are more difficult to obtain. The work described here is part of a research project aimed at development of numerical modeling tools for EOR processes. The method for multiphase equilibrium calculations presented is an extension of the refined SS method previously developed for two-phase problems. The method has been incorporated into a fluid phase behavior package (COPEC). In developing the method, special emphasis has been put on computational efficiency and continuity across phase boundaries. Calculation Steps of Multiphase Flash The basis for our approach to the multiphase flash equilibrium problem is the SS method, which consists of the following steps.1. Assume equilibrium K-values.2. Calculate the phase distribution and compositions corresponding to the given K-values.3. Calculate component fugacities in each phase and check forequality.4. If equality is not achieved. correct the K-values on the basis of the fugacities and repeat from Step 2. We assume that fugacities are given from a cubic EOS (Redlich-Kwong, Peng-Robinson), but the problem of selecting suitable parameters, especially for lumped and/or heavy components, is considered beyond the scope of this paper. If the initial K-value estimates are sufficient, simultaneous handling of mi phases is probably the most efficient method. Frequently this is not the case, however, and the method then easily, becomes unstable and leads to trivial solutions. We have found it advantageous, therefore, to develop a more stepwise approach. Existence of the different phases is tested explicitly, and the sets of equilibrium constants are developed phase by phase before all phases are handled simultaneously. SPEJ P. 87^