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Research Papers: Petroleum Engineering

Development of a New Correlation of Gas Compressibility Factor (Z-Factor) for High Pressure Gas Reservoirs

[+] Author and Article Information
Mohamed Mahmoud

Assistant Professor
Department of Petroleum Engineering,
King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
e-mail addresses: mmahmoud@kfupm.edu.sa and mohnasreldin80@gmail.com

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received February 8, 2013; final manuscript received May 28, 2013; published online September 12, 2013. Assoc. Editor: Sarma V. Pisupati.

J. Energy Resour. Technol 136(1), 012903 (Sep 12, 2013) (11 pages) Paper No: JERT-13-1048; doi: 10.1115/1.4025019 History: Received February 08, 2013; Revised May 28, 2013

Gas compressibility factor or Z-factor for natural gas system can be determined from Standing-Katz charts using the pseudocritical gas pressure and temperatures. These charts give accurate values for Z-factors. Reservoir simulation softwares need accurate correlations to estimate the values of Z-factor; one of the well-known correlations is Dranchuk and Abou-Kassem (DAK) Correlation. This correlation gives large errors at high gas reservoir pressures, this error could be more than 100%. The error in estimating Z-factor will lead to big error in estimating all the other gas properties such as gas formation volume factor, gas compressibility, and gas in place. In this paper a new accurate Z-factor correlation has been developed using regression for more than 300 data points of measured Z-factor using matlab in addition to other data points at low pressure and temperature from Standing-Katz charts and DAK correlation. Old correlations give good estimation of Z-factor at low gas reservoir pressures below 41.37 MPa (6000 psia), at high pressures the error started to appear. The developed correlation is a function of pseudoreduced pressure and temperature of the gas which makes it simpler than the existing complicated correlations. The new correlation can be used to determine the gas compressibility factor at any pressure range especially for high pressures the error was less than 3% compared to the measured data. The developed correlation is very simple to be used, it just needs the gas specific gravity that can be used to determine the pseudocritical properties of the gas and at last the Z-factor can be determined. A new formula of reduced gas compressibility was developed based on the developed Z-factor correlation which in turn can be used to determine the gas compressibility.

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Figures

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Fig. 1

Z-factor as a function of reduced pressure (pr = p/pc) at Tr = 1.5 (after McCain, 27)

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Fig. 2

Z-factor as a function of reduced pressure (pr= p/pc) at different reduced temperatures generated by the new proposed correlation, Eq. (39)

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Fig. 3

Z-factor as a function of reduced pressure (pr = p/pc) at reduced temperature of 1.3. Comparison between the proposed, DAK, Al-Anazi correlations, and Standing-Katz charts

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Fig. 4

Comparison between the different Z-factor correlation with actual measured data for gas mixture 1 at Tpr = 2.438. After ppr value of 10.5 Al-Anazi correlation start to give values less than zero. The proposed correlation is the best one to predict the gas compressibility factor at high pressures. The reservoir pressure for this mixture at ppr = 30 is 137.895 MPa (20,000 psi).

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Fig. 5

Comparison between the different Z-factor correlation with actual measured data for gas mixture 1 at Tpr = 2.155. After ppr value of 9 Al-Anazi correlation start to give values less than zero. The proposed correlation is the best one to predict the gas compressibility factor at high pressures. The reservoir pressure for this mixture at ppr = 30 is 137.895 MPa (20,000 psi).

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Fig. 6

Comparison between the different Z-factor correlation with actual measured data for gas mixture 2 at Tpr = 2.155. After ppr value of 10 Al-Anazi correlation start to give values less than zero. The proposed correlation is the best one to predict the gas compressibility factor at high pressures. The reservoir pressure for this mixture at ppr = 30 is 137.895 MPa (20,000 psi).

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Fig. 7

Gas density for mixture 1 at 422.04 K (300 °F), the proposed correlation gives accurate prediction at high pressures

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Fig. 8

Gas compressibility factor at 377.59 K (220 °F), Tr = 1.93, using the proposed correlation

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Fig. 9

Gas compressibility for mixture 1 at 422.04 K (300 °F) using the proposed correlation and comparing it with charts developed by McCain (27)

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Fig. 10

Comparison between measured gas viscosity and gas viscosity estimated based on the Z-factor from proposed, DAK, and Al-Anzi correlations for methane gas at 422.04 K (300 °F)

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