Predictions of K-Values for Ternary Hydrocarbon Systems: Conditions up to the Critical Point
Authors: Smialek R.J. , Thodos George 
Published: December 2007

Abstract
A method has been developed that permits the correlations of Mehra and Thodos and Dastur and Thodos for binary systems to be used for the prediction of the vapor-liquid equilibrium constants of the light and heavy constituent, Kl and Kh, of a ternary hydrocarbon mixture. Furthermore, the unique relationship observed in this study, i.e., a plot of log Kl/Ki vs log Kl/Kh is linear and passes through the origin, permits the calculation of the K-value for the intermediate component. This approach has been used to establish K-values for the constituents of the three ternary hydrocarbon systems used to develop this method and has also been applied to two additional ternary hydrocarbon systems to yield an average deviation of 7.7 per cent resulting from a total of 294 points for the five ternary systems considered.
Introduction
The rigorous calculation of vapor-liquid equilibrium constants for systems containing two or more components is a difficult problem and becomes extremely complex at elevated pressures and for conditions approaching critical point. Although thermodynamic relationships can be developed to account for the vapor-liquid equilibrium behavior of simple systems, their use is limited because the necessary PVT data for these systems are not generally available. To establish a method for calculating K constants directly, without any recourse to the PVT behavior of a system, Mehra and Thodos applied the principle of corresponding states to the vapor-liquid equilibrium constants of binary hydrocarbon systems. They developed a series of charts which made possible the prediction of K-values for all binary hydrocarbon systems not containing methane. This work has been extended by Dastur and Thodos to include binary hydrocarbon systems containing methane. The charts developed in these two studies cover the high-pressure region and are applicable to conditions in the vicinity of the critical point. The ability of this approach to predict vapor-liquid equilibrium constants of binary hydrocarbon systems suggests that this method may be extended to the prediction of the K-values of the components of ternary hydrocarbon systems. In this investigation, the charts developed for both the methane and non-methane binary systems, together with mixture rules developed in this study, have been used to predict the K- values of the light and heavy components of a ternary hydrocarbon system. These calculated values are then used to establish the K-value of the intermediate component through the use of a novel relationship developed in the present study.
DEVELOPMENT OF METHOD FOR PREDICTING K-VALUES OF TERNARY SYSTEMS
The application of the corresponding state charts developed for binary hydrocarbon systems is restricted to those systems containing two components. The extension of these correlations to three-component systems requires that the ternary system be reduced to an equivalent binary, which can be treated in a manner consistent with the corresponding state development. To establish such an approach, the vapor-liquid equilibrium constant of the light component Kl is first calculated by assuming that the ternary mixture consists of the light component and a pseudo- heavy component of the intermediate and heavy constituents of the original ternary. To establish the vapor-liquid equilibrium constant of the heavy component Kb, the light and intermediate constituents of the ternary are combined to form a pseudo-light component of another equivalent binary system. The calculated values Kl and Kb are then utilized to calculate the vapor-liquid equilibrium constant of the intermediate component Ki.
SPEJ
P. 329ˆ