Computation of Multiphase Equilibrium For Compositional Simulation

Abstract

Abstract A numerical scheme has been developed for calculation of multiphase equilibria. The scheme is applied to a thermodynamic model that employs a modified version of the Peng-Robinson equation for all phases except possibly an aqueous phase. Henry's constants are used for computation of solute fugacities in the water phase. The numerical scheme makes "optimal" use of first- and second-order iterative schemes and circumvents the problems reported by previous investigators. An outline of the scheme is presented with references to other sources where complete details are available. Examples of two-, three-, and four-phase separations are presented to demonstrate the range of the proposed scheme. Limited comparison with experimental data also is provided. The scheme may be embedded in compositional reservoir simulators for the modeling of oil recovery by such processes as hydrocarbon gas injection, nitrogen injection, and CO2 floods. Introduction Injection of a fluid into a petroleum reservoir that causes some of the phases to disappear and/or new phases to appear is a difficult problem to simulate. The problem becomes even more difficult when the injected fluid contains nonhydrocarbons such as CO2 or H S and when interactions with the water phase are significant. Models that permit large changes in the amount and composition of various phases in the reservoir are known as compositional models (e.g.. Coats and Nghiem et at. ). A key step in the development of such models is the correct representation of the thermodynamics of the in-situ fluids, injected fluids and their mixtures. Two-parameter equations of state with adjustable parameters to account for binary interactions provide relatively simple and reasonably accurate thermodynamic models that, in principle, can be embedded in the compositional reservoir model. Existing thermodynamic models suffer from problems of two types:Phase behavior predictions may not represent real phenomena with sufficient accuracy because of improper characterization of heavy components, existence of multiple liquid phases and lack of data for determination of binary interaction parameters.Computational problems associated with iterative solution of the thermodynamic equations may range from slow rate of convergence to no convergence near phase boundaries or the critical point. Under certain conditions apparent convergence may be to an incorrect solution. This paper presents general features of an efficient computational scheme for the prediction of multiphase equilibria. Although the proposed approach is particularly suitable for reservoir compositional models. It should also Find applications in many other chemical and petroleum engineering problems. Thermodynamic Model In this work the hydrocarbon phases are represented by the Peng-Robinson equation of state and solutes in the aqueous phase are treated by Henry's constants using the Cysewski and Prausnitz correlation. A water-water interaction parameter is introduced to improve water-vapor pressure calculations. A similar modification for the Redlich-Kwong equation of state was proposed by Evelein et al. The pseudocomponents (C +) are characterized through the correlation of Bergman for fractions with a boiling point of less than 75 deg. C and through the correlation of Cavett for fractions with a higher boiling point. Equilibrium State The equilibrium state is characterized by a minimum in the Gibbs free energy. SPEJ P. 61^