A Reduced Equation of State Applied to Generalized Compressibility Factor Tablest

Abstract

Abstract This paper reviews the general problem of finding an equation of state for a pure substance, and discusses the various ways of analyzing the isochores. The approach used was to replace the conventional isometric diagram showing the vapour pressure curve with either a ZT, versus Tr isometric diagram or a P r/Z versus Pr isometric diagram. The latter diagrams show the two-phase envelope which permits use of the saturated state for the origin of individual isochors. This results in the density implicit formulations. (Equation Available In Full Paper) which may be conveniently solved with a digital computer. To demonstrate the method, analytical expressions were developed to represent the compressibility factor tables of Lydersen et a1. For reduced densities greater than one, in the reduced temperature range from 0.3 to 3.0, and the pressure range from saturation to Pr = 30, a standard relative error of 0.65 per cent was obtained with only five constants. The approach is also applicable for reduced densities of less than one, but, at the present time, owing to an inability to 6accurately describe the saturated vapour curve in terms of density, the results are only qualitatively Correct. The sparsity of data for Ze values of 0.25 and 0.29 in this region prevented development of a cross-correlation with Z. INTRODUCTION COMPUTER PROGRAMS used for modelling the performance of petroleum reservoirs, or for describing chemical other industrial processes, frequently require a method for calculating fluid densities. This is usually accomplished through the use of a suitable equation of state or through corresponding states correlations, The latter are often used to estimate the density of pure substances, and they can be extended to mixture through the use of the concept of pseudocritical properties. In order to use corresponding states correlations, a suitable method must be found to adapt the information to computer use. This may be accomplished by applying interpolation techniques to tabular data which have been read into memory, by fitting empirical functions to all or part of the data or by using the reduced form of an equation of state. Of these three possibilities, the use of interpolation techniques is considered to be the least desirable, because large-scale data storage and subsequent retrieval is an inefficient computer operation. The well-known equations of Beattie and Bridgeman(14), and Benedict, Webb and Rubin(15) have been applied in reduced form to generalized correlations by Su and Viswanath(18) Good accuracy has been achieved using these equations in the gaseous region, but unfortunately it has not been possible to find a single set of coefficients that will give satisfactory results over the entire liquid, gaseous and saturated regions. Hirschfolder, Buehler, McGee and Sutton(7) have developed a generalized equation of state in which different functions are used for the three regions defined as:gas, where the reduced density is less than one;