Calculation of Z Factors For Natural Gases Using Equations of State

Abstract

The generalized Starling equation of state has been fitted to the Standing and Katz Z-factor correlation and a computer program is presented for the ge11eration of Z factors by means of this equation. A comparison is made of the performance of the Hall and Yarborough, Dranchuk et al. and above-mentioned methods, and the results are discussed.

COMPRESSIBILITY FACTORS have been calculated by means of computer for almost twenty-five years ^(l). During this period, the techniques available for effecting such calculations have been gradually improved and refined. In the recent past, experimental data have been fitted with various equations of state and these fitted equations have been used to generate Z factors ^(2,3,4,5). These equations represent a significant step forward in that they may be used as algebraic expressions for Z in dealing with its functions.

As most of these fittings have been made using the Standing and Katz correlation or data in the same region, their application would appear to be restricted to that region. However, there are occasions when Z is required outside this region. Consequently, the object of this study was to examine the extent to which these equations could be extrapolated and to try modified fittings which would extend the region of application.

Preliminary examination showed that the Redlich Kwong equation could not be generally compared with the Standing and Katz correlation, because it is not expressed in reduced form. Furthermore, this equation could not be tested against experimental data where critical properties rather than gas analyses are reported. In view of these problems, this equation was eliminated from further study.

It was observed that the Hankinson et al. fitting of the BWR equation was restricted to the region 1.1 ≤ T _r ≤3.0 and that the manner of fitting was such that errors in Z in the fitted region were considerably higher than those produced by either the Hall and Yarborough or Dranchuk et al. methods. On the basis of this observation, the Hankinson et al. fitting was eliminated from further examination.

A comparison of the Hall and Yarborough fitting of the Starling-Carnahan equation of state and the Dranchuk et al. fitting of the BWR with each other and with experimental data showed that both are reasonably accurate when extrapolated to P _r values in excess of 20. However, neither equation is valid at T _r = 1.0 in the vicinity of the critical, and both show marked error increases when extrapolated into the region of T _r < 1.0.

The Starling equation of state may be written as

(Equation in full paper)

and may be generalized and rearranged to express the Z factor as

(Equation in full paper)

This equation has been shown to be valid in the extended regions for pure components and has been recommended for mixtures ⁽⁷⁾. In view of this and the equation''s similarity to the BWR equation used in the Dranchuk et at fitting, it was decided to fit Equation (2) to the 1500 data points used in the Dranchuk et al. fitting.