A New Approach for Determining Equation-of-State Parameters Using Phase Equilibria Data
Authors: Starling K.E. 
Published: December 2007

Abstract
Phase equilibria data were used to develop an equation-of-state correlation for complex hydrocarbon mixtures, thereby circumventing difficulties associated with use of pressure-volume-temperature data. Equilibrium phase data for two condensate reservoir fluids were used to determine equation-of-state parameters for hydrocarbons as heavy as C22H46 in a modified form of the Benedict-Webb-Rubin equation of state. Comparative tests of K-values from the resultant correlation were made with data for condensate reservoir, separator and gas plant absorber mixtures. Generally, for temperatures above 0F and computed liquid densities below 0.55 lb-mole/cu ft, the modified BWR equation predicted K-values in close agreement with the experimental data.
Introduction
Accurate predictions of thermodynamic behavior for complex hydrocarbon mixtures are necessary for many calculations k the petroleum industry. Because of the relatively high cost of extensive experimental data, many correlations for prediction of phase behavior have been developed. Some of these, such as the correlation of K-values presented in the NGAA Equilibrium Ratio Data Book, are totally empirical. Others, such as the Benedict-Webb-Rubin (BWR) equation-of-state method, are semitheoretical. Unfortunately, published correlation methods often do not accurately predict the phase behavior of complex hydrocarbon mixtures, principally because of inadequate representation of the effects of components heavier than decane. This paper presents a new approach to this problem in which basic equation-of-state relations including heavy hydrocarbon effects are applied. Equilibrium phase data for two condensate reservoir fluids containing hydrocarbons as heavy as C22H46 are used to correlate component K-values. The BWR equation was chosen as the prototype equation of state for this study because of its proven capability for accurately predicting phase behavior and thermodynamic properties of light-hydrocarbon mixtures. Research was directed toward development of BWR parameters for the heavy hydrocarbons and modifications of the mathematical form of the BWR equation for application to complex hydrocarbon mixtures. The new equation-of-state approach presented differs considerably from previous methods in that phase equilibria rather than PVT data are used for determination of equation-of-state parameters. It is an explicit approach since the parameters are determined directly from mixture data. As such, it does not encounter problems inherent in the implicit method used by Benedict, Webb and Rubin and numerous other investigators-one in which mixture parameters were postulated to be functions of the pure component parameters. The pure component BWR parameters, in turn, were determined from experimental PVT data. This method has been limited to mixtures containing components lighter than decane because of lack of vapor phase PVT data. Studies have been reported in which BWR parameters have been determined explicitly from PVT data for binary mixtures. However, since small concentrations of heavier components have only a minor effect on PVT behavior, it is doubtful that these explicit methods would yield useful results for condensate systems. Ellington and Eakin have shown that the accuracy of K-values predicted by an equation of state developed from mixture PVT data probably would be more than an order of magnitude lower than the accuracy of the PVT data. On the other hand an equation of state utilizing parameters developed from phase equilibria data should predict K-values with accuracy comparable to be accuracy of the experimental phase compositions. This work applies this explicit approach with the objective of improving hydrocarbon mixture phase behavior predictions.
SPEJ
P. 363ˆ