Development of an Efficient Algorithm for the Calculation of Two-Phase Flash Equilibria

Abstract

Summary. This paper details the development of an efficient algorithm for the calculation of two-phase equilibrium in multicomponent hydrocarbon systems with an equation of state (EOS). A number of numerical solution algorithms are evaluated for speed and robustness. To ensure generality, the compositions used in the study range from a synthetic 3-component fluid to a real 20-component reservoir fluid, and the calculations are performed at different positions on the fluid-phase diagram. The results of the study are used in the construction of a stable and efficient algorithm. Although the method was developed with reservoir engineering applications in mind, it should also be applicable in chemical, process, and petroleum engineering. Introduction The determination of phase equilibrium in multicomponent hydrocarbon systems is of great interest in many different branches of petroleum engineering. The simulation of gas condensate and volatile oil reservoir performance with compositional reservoir models requires an accurate knowledge of the phase and volumetric behavior of the reservoir fluids. The calculation of fluid properties and phase equilibria is also used as a general reservoir properties and phase equilibria is also used as a general reservoir engineering tool, with applications ranging from the study of reservoir fluids to the design of pipelines or surface facilities, such as separators. EOS's have been used widely for the calculation of multicomponent hydrocarbon phase equilibria. This represents a relatively simple thermodynamic model but is found to be reasonably accurate and offers the advantage of consistency near the critical point, a region of particular interest in simulations of processes involving gas miscible flooding. For compositional reservoir simulation, it is estimated that 75 % or more of the total computing time may be related to the phase-behavior part of the program. This rules out the use of more phase-behavior part of the program. This rules out the use of more complex EOS's than cubic and indicates the need for speedy and robust solution. In recent years, many numerical solution algorithms have been proposed for the determination of two-phase and multiphase proposed for the determination of two-phase and multiphase equilibria, as well as calculation of saturation points. This paper compares methods proposed for two-phase flash equilibrium calculations. The comparison is based on two criteria: robustnessthe algorithm must be capable of finding solutions in difficult regions, such as the retrograde condensation and near-critical regions, and speed-the algorithm should have the property of rapid convergence. Results of the comparison are used in the construction of an algorithm that is both more robust and faster than the alternatives. Full details of the new algorithm are presented. Two-Phase Flash Equilibrium Equations In an isothermal flash equilibrium calculation, a fluid of fixed total composition is equilibrated at a given temperature and pressure. Consider a fluid containing n components of total composition z that separate into a liquid-phase fraction, F, with composition × and a vapor-phase fraction, F, with composition v . The thermodynamic criterion for equilibrium between the two phases is that the total Gibbs free energy should be a minimum. phases is that the total Gibbs free energy should be a minimum. This yields the condition that the fugacities of each component in the two phases must be equal: (1) The overall material balance is given by (2) while material balance for each component gives (3) The phase compositions × and v are mole fractions and are constrained by the restrictive equation (4) In practice, it is usual to define equilibrium ratios or K values: (5) The material balance equations can then be written as (6) and (7) The value of F corresponding to a given set of K values can be found by solving the Rachford-Rice equation: (8) In the EOS approach, the fugacities, f, are calculated with the chosen EOS for each phase. The general form of an EOS is (9) where Z is the phase compressibility (Z=pv,/RT) and × (or y ) are the phase compositions. SPERE