Modification of the Redlich-Kwong-Aungier Equation of State to Determine the Degree of Dryness in the CO2 Two-phase Region

image_print
DOI https://doi.org/10.15407/pmach2021.04.017
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. 24, no. 4, 2021 (December)
Pages 17-27
Cited by J. of Mech. Eng., 2021, vol. 24, no. 4, pp. 17-27

 

Author

Hanna S. Vorobieva, National Aerospace University “Kharkiv Aviation Institute” (17, Chkalov str., Kharkov, 61070, Ukraine), e-mail: vorobyovaanna1610@gmail.com, ORCID: 0000-0002-4181-8269

 

Abstract

The degree of dryness is the most important parameter that determines the state of a real gas and the thermodynamic properties of the working fluid in a two-phase region. This article presents a modified Redlich-Kwong-Aungier equation of state to determine the degree of dryness in the two-phase region of a real gas. Selected as the working fluid under study was CO2. The results were validated using the Span-Wanger equation presented in the mini-REFPROP program, the equation being closest to the experimental data in the CO2 two-phase region. For the proposed method, the initial data are temperature and density, critical properties of the working fluid, its eccentricity coefficient, and molar mass. In the process of its solution, determined are the pressure, which for a two-phase region becomes the pressure of saturated vapor, the volumes of the gas and liquid phases of a two-phase region, the densities of the gas and liquid phases, and the degree of dryness. The saturated vapor pressure was found using the Lee-Kesler and Pitzer method, the results being in good agreement with the experimental data. The volume of the gas phase of a two-phase region is determined by the modified Redlich-Kwong-Aungier equation of state. The paper proposes a correlation equation for the scale correction used in the Redlich-Kwongda-Aungier equation of state for the gas phase of a two-phase region. The volume of the liquid phase was found by the Yamada-Gann method. The volumes of both phases were validated against the basic data, and are in good agreement. The results obtained for the degree of dryness also showed good agreement with the basic values, which ensures the applicability of the proposed method in the entire two-phase region, limited by the temperature range from 220 to 300 K. The results also open up the possibility to develop the method in the triple point region (216.59K-220 K) and in the near-critical region (300 K-304.13 K), as well as to determine, with greater accuracy, the basic CO2 thermodynamic parameters in the two-phase region, such as enthalpy, entropy, viscosity, compressibility coefficient, specific heat capacity and thermal conductivity coefficient for the gas and liquid phases. Due to the simplicity of the form of the equation of state and a small number of empirical coefficients, the obtained technique can be used for practical problems of computational fluid dynamics without spending a lot of computation time.

 

 

Keywords: CO2 two-phase region, saturated vapor pressure, Aungier-modified Redlich-Kwong equation of state, Lee-Kesler and Pitzer method, Yamada-Gann method, degree of dryness.

 

Full text: Download in PDF

 

References

  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, iss. 1, pp. 233–244. https://doi.org/10.1021/cr60137a013.
  2. Soave, G. (1972). Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science, vol. 27, iss. 6, pp. 1197–1203. https://doi.org/10.1016/0009-2509(72)80096-4.
  3. Peng, D. Y. & Robinson, D. B. (1976). A new two-constant equation of state. Industrial & Engineering Chemistry Fundamentals, vol. 15, iss. 1, pp. 59–64. https://doi.org/10.1021/i160057a011.
  4. Haghtalab, A., Mahmoodi, P., & Mazloumi, S. H. (2011). A modified Peng–Robinson equation of state for phase equilibrium calculation of liquefied, synthetic natural gas, and gas condensate mixtures. The Canadian Journal of Chemical Engineering, vol. 89, iss. 6, pp. 1376–1387. https://doi.org/10.1002/cjce.20519.
  5. Thamanavat, K., Sun, T., & Teja, A. S. (2009). High-pressure phase equilibria in the carbon dioxide+ pyrrole system. Fluid Phase Equilibria, vol. 275, iss. 1, pp. 60–63. https://doi.org/10.1016/j.fluid.2008.09.019.
  6. Chapoy, A., Ahmadi, P., de Oliveira Cavalcanti Filho, V., & Jadhawar, P. (2020). Vapour-liquid equilibrium data for the carbon dioxide (CO2)+ carbon monoxide (CO) system. The Journal of Chemical Thermodynamics, vol. 150, paper 106180. https://doi.org/10.1016/j.jct.2020.106180.
  7. Renon, H. & Prausnitz, J. M. (1968). Local compositions in thermodynamic excess functions for liquid mixtures. AIChE Journal, vol. 14, iss. 1, pp. 135–144. https://doi.org/10.1002/aic.690140124.
  8. Abudour, A. M., Mohammad, S. A., Robinson Jr, R. L., & Gasem, A. M. (2013). Volume-translated Peng-Robinson equation of state for liquid densities of diverse binary mixtures. Fluid Phase Equilibria, vol. 349, pp. 37–55. https://doi.org/10.1016/j.fluid.2013.04.002.
  9. Aungier, R. H. (1995). A fast, accurate real gas equation of state for fluid dynamic analysis applications. Journal of Fluids Engineering, vol. 117, iss. 2, pp. 277–281. https://doi.org/10.1115/1.2817141.
  10. Wilson, G. M. (1966). Calculation of enthalpy data from a modified Redlich-Kwong equation of state. Advances in Cryogenic Engineering, vol. 11, pp. 392–400. https://doi.org/10.1007/978-1-4757-0522-5_43.
  11. King, C. J., Foss, A. S., Grens, E. A., Lynn, S., & Rudd, D. F. (1973). Chemical process design and engineering. Chemical Engineering Education, vol. 7, iss. 2, pp. 72–74.
  12. ANSYS FLUENT 12.0 User’s Guide https://www.afs.enea.it/project/neptunius/docs/fluent/html/ug/main_pre.htm.
  13. Bezverkhy, P. P., Martynets, V. G., & Matizen, E. V. (2009). Equation of state for 4He, including a regular and a scalar part. Low Temperature Physics, vol. 35, iss. 10, pp. 947–955. https://doi.org/10.1063/1.3253391.
  14. Rykov, S. V. & Bagautdinova, A. Sh. (2009). Chislennyy analiz krossovernogo uravneniya sostoyaniya [Numerical analysis of the crossover equation of state]. Nauchnyy zhurnal NIU ITMO. Seriya: Kholodilnaya tekhnika i konditsionirovaniye Scientific Journal NRU ITMO. Series: Refrigeration and Air Conditioning, no. 1, pp. 1–24 (in Russian).
  15. Lee, B. I. & Kesler, M. G. (1975). A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE Journal, vol. 21, iss. 3, pp. 510–527. https://doi.org/10.1002/aic.690210313.
  16. 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. https://doi.org/10.1063/1.555991.
  17. Zhu, Y., Jiang, Y., Liang, S., Guo, C., Guo, Y., & Cai, H. (2020). One-dimensional computation method of supercritical CO2 labyrinth seal. Applied Sciences, vol. 10, iss. 17, paper 5771. https://doi.org/10.3390/app10175771.
  18. Gilgen, R., Kleinrahm, R., & Wagner, W. (1992). Supplementary measurements of the (pressure, density, temperature) relation of carbon dioxide in the homogeneous region at temperatures from 220 K to 360 K and pressures up to 13 MPa. The Journal of Chemical Thermodynamics, vol. 24, iss. 12, pp. 1243–1250. https://doi.org/10.1016/S0021-9614(05)80264-2.
  19. Anwar, S. & Carroll, J. J. (2016). Carbon dioxide thermodynamic properties handbook: Covering temperatures from -20 °C to 250 °C and pressures up to 1000 bar. John Wiley & Sons, 608 p. https://doi.org/10.1002/9781119083948.
  20. Yamada, T. & Gunn, R. D. (1973). Saturated liquid molar volumes. Rackett equation. Journal of Chemical and Engineering Data, vol. 18, iss. 2, pp. 234–236. https://doi.org/10.1021/je60057a006.

 

Received 07 September 2021

Published 30 December 2021