EOS Predictions of Compressibility and Phase Behavior in Systems Containing Phase Behavior in Systems Containing Water, Hydrocarbons, and CO2
Two cubic equations of state (EOS) have been adopted to compute multicomponent two-phase compressibility, CO2/water and hydrocarbon/water phase behavior, and gas- and liquid-phase densities. The equations used in phase behavior, and gas- and liquid-phase densities. The equations used in this paper are the Schmidt-Wenzel (SW) EOS and the Peng-Robinson (PR) EOS, While these cubic equations have the same form, the SW is reported to be more accurate for predicting hydrocarbon gas- and liquid-phase densities. Density predictions are compared with experimental data to confirm the superiority of the SW EOS. The use of EOS to predict equilibrium phase compositions of water/hydrocarbon and water/CO2 systems is discussed. For the water/hydrocarbon systems, the aqueous-phase interaction coefficient between water and the dissolved component shows a strong temperature dependency, while in the gas phases, a constant value of interaction coefficient is adequate. In the case of the CO2/water systems, the interaction coefficients for both the aqueous and gas phases show temperature dependency.A scheme to compute the two-phase compressibility of multicomponent reservoir fluid systems is also introduced. Our results show the expected sharp change in the compressibility during phase change. Such computations are required in some reservoir simulators.
Much progress has been made in predicting the phase behavior of reservoir fluid systems since cubic EOS were first used. In the earliest two papers published on the subject, the emphasis was on phase equilibrium ratios (K values) of hydrocarbons, nitrogen, and CO2 components of crude systems. Later it was recognized that while the phase-density predictions by the PR EOS were superior to those by the Soave-Redlich-Kwong equation (SRK EOS), further improvements were needed. In the area of waterphase behavior with hydrocarbons and nonhydrocarbons, the conventional use of cubic EOS showed large deviations between measured and computed solubility of hydrocarbons and CO2 in water. Several investigators have proposed procedures to improve both the density and the water/hydrocarbon and water/CO2 phase-behavior predictions by the PR and SRK equations. phase-behavior predictions by the PR and SRK equations. Peneloux et al. introduced a third parameter (in addition to the a and b parameters) to the SRK EOS to improve phase-density predictions. The third parameter, however, does not influence K-value predictions. The third parameter, however, does not influence K-value predictions. Peneloux et al. showed that the additional parameter predictions. Peneloux et al. showed that the additional parameter improves volumetric prediction of single-component liquids, liquid and gas phases of binary systems, and pipeline condensates. Later Jhaveri and Youngren applied the same method to the PR EOS. They demonstrated that the third parameter enhances the volumetric predictions of crude oil and gas-condensate systems. Some predictions of crude oil and gas-condensate systems. Some investigators have proposed the use of cubic equations other than the commonly used PR and SRK equations. Still another group has suggested more complicated mixing rules for the a and b parameters of the PR and SRK equations. For example, Lawal et al. parameters of the PR and SRK equations. For example, Lawal et al. presented results of density predictions made with a four-parameter presented results of density predictions made with a four-parameter EOS. With this EOS, these authors reported an average absolute deviation of 6% between the computed and measured densities of 140 reservoir fluid systems. Schmidt and Wenzel proposed a three-parameter cubic EOS (the SW EOS), which yields a component-dependent critical compressibility factor. This EOS has the same data requirements as the PR and SRK equations: the critical temperatures and pressures and the acentric factors of all components. Schmidt and Wenzel demonstrated that their EOS predicted the density of pure components more accurately than either the PR or SRK equations. Clancy et al. have shown that the SW EOS prediction of natural gas density is in excellent agreement with prediction of natural gas density is in excellent agreement with experimental data. Recently, cubic EOS have also been used to predict the phase behavior of water/hydrocarbon and water/CO2 systems. Li et al. have shown that aqueous-phase-behavior predictions made with standard cubic EOS deviate substantially from measured data. They showed that the computed component solubilities in the aqueous phase could be an order of magnitude lower than the corresponding phase could be an order of magnitude lower than the corresponding experimental values. These authors used a fixed hydrocarbon/water interaction coefficient to make their predictions. Robinson et al. made two modifications to the PR EOS to improve phase-behavior predictions for systems containing water. One modification was to predictions for systems containing water. One modification was to calculate (see Eq. A-7) for the water component with a different equation than is normally used for the PR EOS. This in turn changes the a parameter in the EOS. The other change was to use temperature-dependent interaction coefficients for the aqueous-phase components. These modifications resulted in drastic improvements in the phase behavior of water/methanol and water/methane systems examined by Robinson et al. In a recent paper, Enick et al. discussed making substantial modifications to both pure-component and mixture a and b parameters of the PR EOS. One of the changes involved the use of different values for interaction coefficients and for various binary pairs. Another change was to introduce two new variables in the conventional definition of the a and b parameters for pure components, which were suggested to be parameters for pure components, which were suggested to be temperature-dependent for water. The purpose of these changes was to improve predictions of water/hydrocarbon and water/CO2 phase behavior and phase densities. Enick et al. did not, however, compare predicted and measured CO2/water and hydrocarbon/water phase predicted and measured CO2/water and hydrocarbon/water phase behavior in their paper. In this paper, we examine the use of cubic EOS, and in particular the SW EOS, to predict reservoir fluid densities and the phase behavior of water/CO2 and water/hydrocarbon systems. In addition, we introduce a scheme for predicting multi-component two-phase compressibility with cubic EOS. These compressibilities arise naturally in some reservoir models and well-test 15 equations.