Computer Calculation Of Natural Gas Compressibility Factors Using The Standing And Katz Correlation

Abstract

In 1941 Standing and Katz (1) presented a compressibility factor chart based on binary mixtures and saturated hydrocarbon vapor data. This chart is generally reliable for sweet natural gases and correctable for those containing hydrogen sulfide and carbon dioxide (2). It has become one of the most widely accepted correlations in the petroleum industry.

A replot of the original data in the form compressibility versus pseudo-reduced density, with pseudo-reduced temperature as a parameter reveals irregularities at various points, with large departures occurring in portions of the 1.05, 1.10 and 1.15 pseudo-reduced isotherms.

In this work the above mentioned isotherms have been smoothed and the resulting correlation fitted by means of an eight coefficient Benedict-Webb-Rubin type equation. This compact algebraic expression is capable of regenerating the Z, P _r , T _r surface within a standard error of 0.00445 in Z.

Introduction

During the past thirty years, the behavior of natural gas mixtures has been described by means of the modified gas law. The accepted practice has been to employ the compressibility factor correlation proposed by Standing and Katz (3).

The original graphical representation of the correlation was adequatefor hand or desk calculational purposes. However, the advent of the computer brought with it a need for a representation which would lend itself to rapid calculation methods. As a result, a table look-up technique was introduced (4) and the tabulated values Were used to generate a variety of integrals (5). This was followed by a simpler table look-up interpolation method (6). Finally, the correlation was adapted to computational usage by surface fitting of the Z, P _r ,T _r relationship; first by means of Legendre Polynomials (7), and then through the use of general orthogonal polynomials (8).

Although the last three techniques are employed in the petroleum industry at this time, they require considerable computer storage space and execution tinle. In view of the success realized with the expression of compressibility for pure components using reduced density (9), it was decided to examine the possibility of algebraically representing the Standing-Katz correlation in a similar manner.

Compressibility Factors for Natural Gas Mixtures

In 1940, Brown and Halcomb presented a compressibility factor correlation which could be used for natural gas mixtures (10). In their representation, Z was plotted as a function of pseudo-reduced pressure and temperature. They pointed out that the plot was satisfactory for natural gases which were predominantly methane and for binary mixtures containing methane (ll).

This correlation was modified and extended by Standing and Katz, on the basis of data from sixteen saturated multicomponent gases and a comparison with pure methane data (12). This extended correlation, along with correlations for a variety of pure hydrocarbons and blown-up versions for use at low reduced pressures and near atmospheric pressures were presented in a book by Brown, Katz, Oberfell and Alden (13). Thus, despite the widespread belief that the Standing-Katz (sometimes referred to as Katz-Standing) and the Brown, Katz, Oberfell and Alden compressibility factors represented two different correlations, they are in fact one and the same.