Modification of the Redlich-Kwong-Aungier Equation of State to Determine the Main Thermodynamic Parameters in the Pure Liquid CO2 Region

Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Pidhornyi Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN  2709-2984 (Print), 2709-2992 (Online)
Issue Vol. 25, no. 2, 2022 (June)
Pages 6-13
Cited by J. of Mech. Eng., 2022, vol. 25, no. 2, pp. 6-13



Hanna S. Vorobieva, National Aerospace University “Kharkiv Aviation Institute” (17, Chkalov str., Kharkov, 61070, Ukraine), e-mail:, ORCID: 0000-0002-4181-8269



The most important parameters for determining the state of real gas and the thermodynamic properties of the working fluid in a pure liquid region are pressure, specific volume, enthalpy and entropy. The paper presents a modified Redlich-Kwong-Aungier equation of state for determining pressure, specific volume, enthalpy and entropy in the pure liquid phase of real gas. CO2 was selected as the studied working fluid. When solving this problem, the author identified the main parameters of liquid carbon dioxide thermo-dynamics with the least error in comparison with experimental data in a wide range from 220 K to 300 K. It is possible to calculate pressure, specific volume, density, enthalpy and entropy of liquid CO2 with the help of the proposed method, for which the initial data are temperature, density, critical properties, molar mass and acentric factor of the working fluid. In particular, a modified Redlich-Kwong-Aungier equation is used to calculate the pressure of the working fluid. The author proposes a correlation equation of the scale correction, which is used in the Redlich-Kwong-Aungier equation for CO2 in the region of pure liquid phase. The results obtained for the pressure, enthalpy and entropy of liquid CO2 showed good agreement with the basic values, which provides the application of the proposed method in the field of pure liquid CO2, limited by the temperature range from 220 K to 300 K. The simplicity of the equation of state and the small number of empirical coefficients allows to use this method to solve practical problems of computational gas dynamics without spending a lot of time on calculations.


Keywords: pure liquid CO2 region, Aungier-modified Redlich-Kwong Equation of State, pure liquid pressure, pure liquid enthalpy, pure liquid entropy.


Full text: Download in PDF



  1. Redlich, O. & Kwong, J. N. S. (1949). On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions. Chemical reviews, vol. 44, no. 1, pp. 233–244.
  2. Soave, G. (1972). Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical engineering science, vol. 27, iss. 6, pp. 1197–1203.
  3. Peng, D.-Yu. & Robinson, D. B. (1976). A new two-constant equation of state. Industrial & Engineering Chemistry Fundamentals, vol. 15, no. 1, pp. 59–64.
  4. Span, R. & Wagner, W. (1996). A new equation of state for carbon dioxide covering the fluid region from the triple‐point temperature to 1100 K at pressures up to 800 MPa. Journal of Physical and Chemical Reference Data, vol. 25, iss. 6, pp. 1509–1596.
  5. Wagner, W. & Kretzschmar, H.-J. (2008). IAPWS industrial formulation 1997 for the thermodynamic properties of water and steam. International Steam Tables: Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97, pp. 7–150.
  6. Povodyrev, A. A. (1995). Krossovernoye povedeniye termodinamicheskikh i transportnykh svoystv binarnykh rastvorov [Crossover behavior of thermodynamic and transport properties of binary solutions]: Cand. Sci. (Phys.-Math.) dissertation. Institute of Oil and Gas Problems of Russian Academy of Sciences and the State Committee of the Russian Federation for Higher Education. Moscow, 118 p. (in Russian).
  7. Pakravesh, A., Fatemeh, Z., & Hosseinali, Z. (2021). PρT parameterization of SAFT equation of state: Developing a new parameterization method for equations of state. Fluid Phase Equilibria, vol. 538, paper ID 113024.
  8. Saali, A., Sakhaeinia, H., & Shokouhi, M. (2021). Modification of Peng–Robinson cubic equation of state with correction of the temperature dependency term. Journal of Solution Chemistry, vol. 50, no. 3, pp. 402–426.
  9. Kumar, A. & Upadhyay, R. (2021). A new two-parameters cubic equation of state with benefits of three-parameters. Chemical Engineering Science, vol. 229, paper ID 116045.
  10. Vorobiova, H. S. (2021). Modification of the Redlich-Kwong-Aungier equation of state to determine the degree of dryness in the CO2 two-phase region. Journal of Mechanical Engineering – Problemy mashynobuduvannia, vol. 24, no. 4, pp. 17–27.
  11. Aungier, R. H. (1995). A fast, accurate real gas equation of state for fluid dynamic analysis applications. Journal of Fluid Engineering, vol. 117, iss. 2, pp. 277–281.
  12. Woodcock, L. V. (2018). Thermodynamic fluid equations-of-state. Entropy, vol. 20, no. 1, paper ID 22.


Received 09 May 2022

Published 30 June 2022