Skip to main content

Numerical procedures for natural gas accurate thermodynamic properties calculation


Natural gas (NG) is a mixture of 21 elements and widely used in the industries and domestics. Knowledge of its thermodynamic properties is essential for designing appropriate process and equipments. In this study, the detailed numerical procedures for computing most thermodynamic properties of natural gas are discussed based on the AGA8 equation of state (EOS) and thermodynamics relationships. To validate the procedures, the numerical values are compared with available measured values. The validations show that the average absolute percent deviation (AAPD) for density calculations is 0.0831%, for heat capacity at the constant pressure is 0.87%, for heat capacity at the constant volume is 1.13%, for Joule-Thomson coefficient is 1.93%, for speed of sound is 0.133%, and for enthalpy is 1.06%. Furthermore, in this work, the new procedures are presented for computing the entropy and internal energy. Due to lack of experimental data for these properties, the validation is done for pure methane. The validation shows that AAPD is 0.078% and 0.0133% for internal energy and entropy, respectively.

This is a preview of subscription content, access via your institution.


  1. 1.

    McCarty, R.D., Extended Corresponding States as a Tool for the Prediction of the Thermodynamic Properties of Mixtures, Int. J. Thermophys., 1986, vol. 7, no. 4.

  2. 2.

    Estela-Uribe, J.F. and Trusler, J.P., Extended Corresponding States Equation of State for Natural Gas Systems, Fluid Phase Equilibria, 2001, vols. 183–184, pp. 21–29.

    Article  Google Scholar 

  3. 3.

    Estela-Uribe, J.F., De Mendozaa, A., and Trusler, J.P., Extended Corresponding StatesModel for Fluids and Fluid Mixtures II. Application toMixtures and Natural Gas Systems, Fluid Phase Equilibria, 2004, vol. 216, pp. 59–84.

    Article  Google Scholar 

  4. 4.

    Jaeschke, M., Audibert, S., van Caneghem, P., Humphreys, A.E., Janssen-van Rosmalen, R., Pellei, Q., Michels, J.P., Schouten, J.A., and ten Seldam, C.A., 1989, MGERG-88, High Accuracy Compressibility Factor for Natural Gases and Similar Mixtures by Use of a Truncated Virial Equation, GERG Tech. Monogr., vol. TM2.

  5. 5.

    Kunz, O., Klimeck, R., Wagner, W., and Jaeschke, M., The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures, Fortschritt-Berichte VDI, ser. 6, no. 557, VDI Verlag.

  6. 6.

    Redlich, O. and Kwong, J.N., On the Thermodynamics of Solutions: V. An Equation of State: Fugacities of Gaseous Solutions, Chem. Rev., 1949, vol. 44, pp. 233–244.

    Article  Google Scholar 

  7. 7.

    Soave, G., Equilibrium Constants from a Modified Redlich-Kwong Equation of State, Chem. Eng. Sci., 1972, vol. 27, pp. 1197–1203.

    Article  Google Scholar 

  8. 8.

    Peng, D.-Y. and Robinson, D.B., A New Two-Constant Equation of State, Ind. Eng. Chem. Fundam., 1976, vol. 15, pp. 59–64.

    MATH  Article  Google Scholar 

  9. 9.

    Valderrama, J.O., A Generalized Patel-Teja Equation of State for Polar and Non-Polar Fluids and Their Mixtures, J. Chem. Eng. Japan, 1990, vol. 23, pp. 87–91.

    Article  Google Scholar 

  10. 10.

    Anderko, A., Cubic and Generalized van der Waals Equation, Equations of State for Fluids and Fluid Mixtures, Sengers, J.V., Kayser, R.F., Peters, C.J., and White, H.J., Eds., Amsterdam: Elsevier, 2000.

    Google Scholar 

  11. 11.

    Neubauer, B., Tavitian, B., Boutin, A., and Ungerer, P., Molecular Simulations on Volumetric Properties of Natural Gas, Fluid Phase Equilibria, 1999, vol. 161, pp. 45–62.

    Article  Google Scholar 

  12. 12.

    Elsharkawy, A.D, Yousef, S.Kh., Hashem, S., and Alikhan, A.A., Compressibility Factor for Gas Condensates, Energy Fuels, 2001, vol. 15, pp. 807–816.

    Article  Google Scholar 

  13. 13.

    Elsharkawy, A.M., Efficient Methods for Calculations of Compressibility, Density and Viscosity of Natural Gases, Fluid Phase Equilibria, 2004, vol. 218. pp. 1–13.

    Article  Google Scholar 

  14. 14.

    Wendland, M., Saleh, B., and Fischer, J., Accurate Thermodynamic Properties from the BACKONE Equation for the Processing of Natural Gas, Energy Fuels, 2004, vol. 18, pp. 938–951.

    Article  Google Scholar 

  15. 15.

    Nasrifar, Kh. and Bolland, O., Prediction of Thermodynamic Properties of Natural Gas Mixtures Using 10 Equations of State Including a New Cubic Two-Constant Equation of State, J. Petroleum Sci. Eng., 2006, vol. 51, pp. 253–266.

    Article  Google Scholar 

  16. 16.

    Martinez, S.A. and Hall, R.K., Thermodynamic Properties of Light Synthetic Natural Gas Mixtures Using the RK-PR Cubic Equation of State, Ind. Eng. Chem. Res., 2006, vol. 45, pp. 3684–3692.

    Article  Google Scholar 

  17. 17.

    Huber, M.L., Smith, B.L., Ott, L.S., and Bruno, T.J., Surrogate Mixture Model for the Thermophysical Properties of Synthetic Aviation Fuel S-8: Explicit Application of the Advanced Distillation Curve, Energy Fuels, 2008, vol. 22, pp. 1104–1114.

    Article  Google Scholar 

  18. 18.

    AGA8-DC92 EoS (1992): Compressibility and Super Compressibility for Natural Gas and Other Hydrocarbon Gases, Transmission Measurement Committee Report, no. 8, AGA Catalog no. XQ 1285, Arlington, VA.

  19. 19.

    ISO-12213-2 (1997), Natural Gas-Calculation of Compression Factor, pt. 2: Calculation Using Molar Composition Analysis, ISO, Ref. no. ISO-12213-2:1997(E).

  20. 20.

    Marić, I., Galović, A., and Šmuc, T., Calculation of Natural Gas Isentropic Exponent, Flow Meas. Instrum., 2005, vol. 16, no. 1, pp. 13–20.

    Article  Google Scholar 

  21. 21.

    Marić, I., The Joule-Thomson Effect in Natural Gas Flow-Rate Measurements, Flow Meas. Instrum., 2005, vol. 16, pp. 387–95.

    Article  Google Scholar 

  22. 22.

    Marić, I., A Procedure for the Calculation of the Natural GasMolar Heat Capacity, the Isentropic Exponent, and the Joule-Thomson Coefficient, Flow Meas. Instrum., 2007, vol. 18, pp. 18–26.

    Article  Google Scholar 

  23. 23.

    Farzaneh-Gord, M., Khamforoush, A., Hashemi, Sh., and Pourkhadem, N.H., Computing Thermal Properties of Natural Gas by Utilizing AGA8 Equation of State, Int. J. Chem. Eng. Appl., 2010, vol. 1, no. 1.

  24. 24.

    Steven, C., Chapra, and Raymond, P., Numerical Method for Engineers, McGraw-Hill, 2005.

  25. 25.

    Capla, L., Buryan, P., Jedelsky, J., Rottner, M., Rottner, M., and Linek, J., Isothermal pVTMeasurements on GasHydrocarbon Mixtures Using a Vibrating-Tube Apparatus, J. Chem. Therm., 2002, vol. 34, pp. 657–667

    Article  Google Scholar 

  26. 26.

    Patil, P., Ejaz, S., Atilhan, M., Cristancho, D., Holste, J., and Hall, K.R., Accurate Density Measurements for a 91% Methane Natural Gas-LikeMixture, J. Chem. Therm., 2007, vol. 39, pp. 1157–1163.

    Article  Google Scholar 

  27. 27.

    Hwang, C.-A., Simon, P.P., Hou, H., Hall, K.R., Holste, J.C., and Marsh, K.N., Burnett and Pycnometric (p, V, T) Measurements for Natural GasMixtures, J. Chem. Therm., 1997, vol. 29, pp. 1455–1472.

    Article  Google Scholar 

  28. 28.

    DIPPR®801, Evaluated Standard Thermophysical Property Values, Design Institute for Physical Properties, 2004.

  29. 29.

    Mayrath, J.E. and Magee, J.W., Measurements ofMolar Heat Capacity at Constant Volume: C v,m{xCH6 + (1 − x)C2H6}, J. Chem. Therm., 1989, vol. 21, pp. 499–5I3.

    Article  Google Scholar 

  30. 30.

    Ernst, G., Keil, B., Wirbser, H., and Jaeschke, M., Flow-Calorimetric Results for the Massic Heat Capacity cp and the Joule-Thomson Coefficient of CH4, of 0.85CH4 + 0.15C2H6, and of aMixture Similar to Natural Gas, J. Chem. Therm., 2001, vol. 33, pp. 601–613.

    Article  Google Scholar 

  31. 31.

    Barreau, A., Janneteau, P., and Gaillard, K., Isobaric Heat Capacity of Natural Gases. Measurements and Modeling, Fluid Phase Equilibr., 1997, vol. 127, pp. 155–171.

    Article  Google Scholar 

  32. 32.

    Trusler, J.P., The Speed of Sound in (0.8CH4 +0.2C2H6) at Temperature between 200 K and 375 K, J. Chem. Therm., 1994, vol. 26, pp. 751–763.

    Article  Google Scholar 

  33. 33.

    Costa Gomes, M.F. and Trusler, J.P., The Speed of Sound in Two Methane-Rich Gas Mixtures at Temperatures between 250 K and 350 K and at Pressures up to 20 MPa, J. Chem. Therm., 1998, vol. 30, pp. 1121–1129.

    Article  Google Scholar 

  34. 34.

    Estela-Uribe, J.F, Trusler, J.P., Chamorro, C.R., Segovia, J.J., Martin, M.C., and Villamanan, M.A., Speeds of Sound in {(1 − x)CH4 + xN2} with x = (0.10001, 0.19999, and 0.5422) at Temperatures between 170 K and 400 K and Pressures up to 30 MPa, J. Chem. Therm., 2006, vol. 38, pp. 929–937.

    Article  Google Scholar 

  35. 35.

    Day, C., Stephan, M., and Oellrich, L.R., A New Flow Calorimeter for the Measurement of the Isobaric Enthalpy Increment and the Insenthalpic Joule-Thomson Effect Results for Methane and “Methane-Ethane,” J. Chem. Therm., 1997, vol. 29, pp. 949–971.

    Article  Google Scholar 

  36. 36.

    Ashton, G.J. and Haselden, G.G., Measurements of Enthalpy and Phase Equilibrium for Simulated Natural Gas Mixtures and Correlation of the Results by a Modified Starling Equation, Cryogenics, 1980.

  37. 37.

    Setzmann, U. and Wagner, W., A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures up to 1000 MPa, J. Phys. Chem. Ref. Data, 1991, vol. 20, no. 6, pp. 1061–1155.

    ADS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to M. Farzaneh-Gord.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Farzaneh-Gord, M., Rahbari, H.R. Numerical procedures for natural gas accurate thermodynamic properties calculation. J. Engin. Thermophys. 21, 213–234 (2012).

Download citation


  • Molar Enthalpy
  • Compressibility Factor
  • Binary Interaction Parameter
  • Molar Entropy