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CALCULATION OF Z FACTORS FOR NATURAL GASES USING

EQUATIONS OF STATE

P.M. DRANCHUK J.H. ABOU-KASSEM

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JCPT75-03-03 JCPT-19 GAS TECHNOLOGY Calculation of Z Factors For Natural Gases Using Equa tions of State P. M. Dranchuk and J. H. Abou-Kassem, Department of Mineral Engineering, University of Alberta, Edmonton, Alta. 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 generation 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. COMPRESSIBILITYFACTORS have been calculated by means of computer for almost twenty-five years. 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",',',". 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 inthe same region, their application would appear to be restricted to that region. However, there are occasions when Z is required outside this region. Conse quently, 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. Furthermor e, 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, --- 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 Yarboroughfitting of the Starling-Carnahan equ ation of state and the Dranchuk et al. fitting of the BWR with each other with expe rimental data showed that both are reasonably accu rate when extrapolated to P, values in excess of 20. However, neither equation is valid at T@ == 1.0 in the vicinity of the cri tical, and both show marked error increases when extr apolated into the region of T, < I.O. The Starling equation of state may be written as and may, be generalized and rearranged to expres s the Z factor as This equation has been shown to be valid in the extended regions for pur e components andhas been recommended for mixtures 171. In view A, of this and the equation sim ilarity to the BWR equation used in the Dranchuk et al. fitting, it was decided to fit Equation (2) to the 1500 data points used in the Dranchuk et al. fitting. For the purpose of the fitting, the reduced densities as calculated using the expression The Journal of Canadian Petroleum P. M. Dranchuk received his formal training in petroleum engineering at the University of Alberta and Stan- ford University. He has been a member of the academic staff at the Uni- versity of Alberta since 1952,

and is currently Professor of Petroleum En- gineering in the Department of Min- eral Engineering. Dr. Dranchuk has been very active as a Member of the CIM since 1963, and he is currently acting as Program Chairman for the Annual Western Meeting, scheduled for Edmonton in late October. He is also a member of AIME, APEGGA, AAAS, _ the Society of Sigma Xi and the New York Academy of Science. and a Fellow of the Institute of Petroleum. J. H. Abou-Kassem attended the Uni- versity of Cairo as a UNESC@ Scholar and obtained a B.Sc. i,, , troleum engineering from that insti- tution in1970. He then obtained an M.Se. in petroleum engineeri ng from the University of Alberta in 1975. At present, he is a graduate student in chemical engineeri ng at the Univer- sity of Calgary.

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