Predicting Phase and Thermodynamic Properties of Natural Gases With the Benedict-Webb-Rubin Equation of State
Authors: Wolfe J.F. 
Published: December 2007

Abstract
The Benedict-Webb-Rubin equation of state was used in digital computer programs to make rapid determinations of natural gas equilibrium phase compositions. Mixture components were the nine hydrocarbons, methane through heptane. Comparative tests were made with data from field separators, plant exchangers and literature sources. For most tests made, the B-W-R equations predicted component K-values, mixture enthalpies and phase densities within the accuracy of available correlations for nine-component mixtures; significant deviations were noted when mixtures contained components heavier than heptane.
Introduction
Rapid, accurate methods for calculating the properties of hydrocarbon mixtures are needed for predicting the behavior of natural gas processes. For example, because of the common use of two-phase separation methods in gas processing, calculations must be made for the density and composition of equilibrium vapor and liquid phases. In addition, predictions must often be made for the temperature and pressure changes associated with the flow of single- and two-phase natural gas fluids through heat exchangers, chokes and turbines. The complex nature of non-ideal mixtures makes rigorous calculations for these natural gas properties difficult and time-consuming. Natural gas properties have conventionally been determined with generalized data correlations. These correlations, such as the K-values presented in the NGAA Equilibrium Ratio Data Book, are usually based on some average property of the mixture and have proven to give satisfactory estimates for the properties of most oil and gas systems. Digital computers, however, have not only increased the utility of these correlations, but also have made practical the use of equations of state for calculating the properties of natural gases. Potentially, if basic pure component data are available, all the desired thermodynamic properties of mixtures can be derived from a single equation of state describing the mixture. Currently, the best equation of state for describing the behavior of pure, light hydrocarbons over single- and two-phase regions, both below and above critical pressure, is that of Benedict, Webb and Rubin. The equation contains eight constants which are determined by empirically fitting the equation to pure-component PVT data. Benedict and his co-workers presented the development of their equation as early as 1940. The B-W-R equation is a modification of the Beattie-Bridgeman equation of state and gives better PVT predictions than the Beattie equation at densities above the critical density. Benedict et al. made the equation applicable to mixtures by relating the mixture constants to composition and the constants for pure compounds. These authors, in a series of articles in 1951, showed the accuracy of the B-W-R equation when applied to light hydrocarbons and their simple mixtures, and demonstrated the equation's utility for making vapor-liquid equilibria calculations. Since its inception, the B-W-R equation has been the subject of many papers. Numerous additions and modifications have been proposed, the purpose of most being to improve the equation's ability to predict PVT properties of specific mixture systems. In 1959, Opfell, Pings and Sage summarized much of the work on the B-W-R equation in their book on equations of state. Since natural gases are primarily mixtures of light hydrocarbons, the B-W-R equation is a natural choice for an equation of state to compute both phase equilibria and thermodynamic properties of natural gases.
JPT
P. 364ˆ