Skip to main content
SpringerLink
Log in

Modeling of the Interfacial Behavior of \(\hbox {CO}_{2}\) + \(\hbox {H}_{2}\)O and \(\hbox {H}_{2}\)S + \(\hbox {H}_{2}\)O with CPA EOS and Gradient Theory

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

In this work, the combination of the gradient theory and cubic plus association equation of state has been applied to describing the interfacial density profiles and surface tensions of \(\hbox {CO}_{2}\) + \(\hbox {H}_{2}\)O and \(\hbox {H}_{2}\)S + \(\hbox {H}_{2}\)O systems. The ranges of temperature and pressure are (297.9–469.4) K and (1–691.4) bar, respectively. Different cross-association schemes are applied to the phase equilibrium of \(\hbox {CO}_{2}\) + \(\hbox {H}_{2}\)O and \(\hbox {H}_{2}\)S + \(\hbox {H}_{2}\)O systems and the experimental cross-association energies have been used for the model resulting in more accurate phase equilibrium calculations. Moreover, two forms of influence parameter in terms of bulk densities of phase and temperature are used for the present model. Firstly, the coefficients of influence parameters are regressed based on the surface tensions of pure components (carbon dioxide, hydrogen sulfide and water). The binary interaction parameter of the cross-influence parameter is set equal to zero making this model predictive. Subsequently, the interfacial density profiles of the components have been determined. The predictions of the bulk-density-dependent influence parameter are in good agreement with the experimental surface tensions (overall AAD of 14.75 % and 8.87 % for temperature and bulk-density-dependent influence parameters, respectively).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Abbreviations

T :

Temperature (K)

a :

Attractive parameter in CPA EOS (J\(\cdot \hbox {m}^{3}\cdot \hbox {mol}^{-2}\))

\(A'_{r}, \ B'_{r}\) :

Adjustable parameters of the density-dependent influence parameter

\(a_{0}\) :

Adjustable parameter of the CPA EOS

\(A_{r}, \ B_{r}\) :

Adjustable parameters of the temperature-dependent influence parameter

\(AAD \%\) :

Absolute average deviation

b :

Covolume parameter in CPA EOS (\(\hbox {m}^{3}\cdot \hbox {mol}^{-1}\))

\(c_{1}\) :

Adjustable parameter of the CPA EOS

\(f_{0}\) :

Helmholtz free energy density (J\(\cdot \hbox {m}^{-3}\))

g :

Simplified radial distribution function

\(k_{ij}\) :

Binary interaction parameter for the attractive parameter in the CPA EOS

\(l_{ij}\) :

Symmetric parameter

P :

Pressure (Pa)

R :

Ideal gas constant [J\(\cdot \hbox {mol}^{-1}\cdot \hbox {K}^{-1}\))

\(x_{i}\) :

Mole fraction of each component i in the liquid phase

\(X_{A_{i}}\) :

The pure-component i mole fraction (not bonded at site A)

\(y_{i}\) :

Mole fraction of each component i in the vapor phase

Z :

Compressibility factor

z :

Position in the interface (nm)

\(\beta ^{assoc}\) :

The association volume of pure fluid

\(\beta ^{cross}\) :

The cross-association volume

\(\chi \) :

Influence parameter (J\(\cdot \hbox {m}^{5}\cdot \hbox {mol}^{-2}\))

\(\Delta ^{A_{i} E_{j}}\) :

The cross-association strength

\(\Delta ^{dp_{i} da_{i}}\) :

The association strength of pure fluid

\(\mu \) :

Chemical potential (J\(\cdot \hbox {mol}^{-1}\))

\(\Omega \) :

Grand thermodynamic potential (J\(\cdot \hbox {m}^{-3}\))

\(\rho \) :

Molar density (mol\(\cdot \hbox {m}^{-3}\))

\(\sigma \) :

Surface tension (mN\(\cdot \hbox {m}^{-1}\))

\(\varepsilon ^{assoc}\) :

The association energy (J\(\cdot \hbox {mol}^{-1}\))

\(\varepsilon ^{cross}\) :

The cross-association energy (J\(\cdot \hbox {mol}^{-1}\))

B :

Bulk

c :

Critical condition

s :

Surface

assoc :

Association

calc :

Calculated result

exp :

Experimental

L :

Liquid

phys :

Physical

ref :

Reference variable

V :

Vapor

References

  1. V. Shah, D. Broseta, G. Mouronval, F. Montel, Int. J. Greenh. Gas Control 2, 594–604 (2008)

    Article  Google Scholar 

  2. T. Lafitte, B. Mendiboure, M.M. Pineiro, D. Bessieres, C. Miqueu, J. Phys. Chem. B 114, 11110–11116 (2010)

    Article  Google Scholar 

  3. X.-S. Li, J.-M. Liu, D. Fu, Ind. Eng. Chem. Res. 47, 8911–8917 (2008)

    Article  Google Scholar 

  4. A. Georgiadis, G. Maitland, J.P.M. Trusler, A. Bismarck, J. Chem. Eng. Data 55, 4168–4175 (2010)

    Article  Google Scholar 

  5. L.M.C. Pereira, A. Chapoy, R. Burgass, M.B. Oliveira, J.A.P. Coutinho, B. Tohidi, J. Chem. Thermodyn. 93, 404–415 (2016)

    Article  Google Scholar 

  6. T. Akutsu, Y. Yamaji, H. Yamaguchi, M. Watanabe, R.L. Smith Jr., H. Inomata, Fluid Phase Equilib. 257, 163–168 (2007)

    Article  Google Scholar 

  7. P. Chiquet, J.-L. Daridon, D. Broseta, S. Thibeau, Energy Convers. Manag. 48, 736–744 (2007)

    Article  Google Scholar 

  8. B. Kvamme, T. Kuznetsova, A. Hebach, A. Oberhof, E. Lunde, Comput. Mater. Sci. 38, 506–513 (2007)

    Article  Google Scholar 

  9. S. Bachu, D.B. Bennion, J. Chem. Eng. Data 54, 765–775 (2009)

    Article  Google Scholar 

  10. B.-S. Chun, G.T. Wilkinson, Ind. Eng. Chem. Res. 34, 4371–4377 (1995)

    Article  Google Scholar 

  11. A. Hebach, A. Oberhof, N. Dahmen, A. Kögel, H. Ederer, E. Dinjus, J. Chem. Eng. Data 47, 1540–1546 (2002)

    Article  Google Scholar 

  12. G.G. Strathdee, R.M. Given, J. Phys. Chem. 80, 1714–1719 (1976)

    Article  Google Scholar 

  13. S. Khosharay, F. Varaminian, Korean J. Chem. Eng. 30, 724–732 (2013)

    Article  Google Scholar 

  14. S. Khosharay, M. Abolala, F. Varaminian, J. Mol. Liq. 198, 292–298 (2014)

    Article  Google Scholar 

  15. G. Niño-Amézquita, D. van Putten, S. Enders, Fluid Phase Equilib. 332, 40–47 (2012)

    Article  Google Scholar 

  16. A. Hernàndez, M. Cartes, A. Mejía, Fuel 229, 105–115 (2018)

    Article  Google Scholar 

  17. A. Hernández, Chem. Phys. 534, 110747 (2020)

    Article  Google Scholar 

  18. A. Hernández, S. Khosharay, Int. J. Thermophys. 41, 1–22 (2020)

    Article  Google Scholar 

  19. A. Hernández, D. Zabala, Int. J. Thermophys. 42, 1–21 (2021)

    Article  ADS  Google Scholar 

  20. A. Hernández, Int. J. Thermophys. 41, 1–18 (2020)

    Article  Google Scholar 

  21. A. Hernández, Int. J. Thermophys. 42, 1–27 (2021)

    Article  ADS  Google Scholar 

  22. A. Hernández, R. Tahery, Int. J. Thermophys. 42, 1–27 (2021)

    Article  ADS  Google Scholar 

  23. Y. Danten, T. Tassaing, M. Besnard, J. Phys. Chem. A 109, 3250–3256 (2005)

    Article  Google Scholar 

  24. B. Jönsson, G. Karlström, H. Wennerström, Chem. Phys. Lett. 30, 58–59 (1975)

    Article  ADS  Google Scholar 

  25. I. Tsivintzelis, G.M. Kontogeorgis, M.L. Michelsen, E.H. Stenby, Fluid Phase Equilib. 306, 38–56 (2011)

    Article  Google Scholar 

  26. I. Tsivintzelis, G.M. Kontogeorgis, M.L. Michelsen, E.H. Stenby, AIChE J. 56, 2965–2982 (2010)

    Article  Google Scholar 

  27. S. Khosharay, S. Tourang, F. Tajfar, Fluid Phase Equilib. 454, 99–110 (2017)

    Article  Google Scholar 

  28. S. Khosharay, M.S. Mazraeno, F. Varaminian, Int. J. Refrig. 36, 2223–2232 (2013)

    Article  Google Scholar 

  29. S. Khosharay, M.S. Mazraeno, F. Varaminian, A. Bagheri, Int. J. Refrig. 40, 347–361 (2014)

    Article  Google Scholar 

  30. S. Khosharay, F. Varaminian, Int. J. Refrig. 47, 26–35 (2014)

    Article  Google Scholar 

  31. S. Khosharay, J. Nat. Gas Sci. Eng. 23, 474–480 (2015)

    Article  Google Scholar 

  32. S. Khosharay, N. Rezakhani, Period. Polytech. Chem. Eng. 60, 282–289 (2016)

    Article  Google Scholar 

  33. G.M. Kontogeorgis, E.C. Voutsas, I.V. Yakoumis, D.P. Tassios, Ind. Eng. Chem. Res. 35, 4310–4318 (1996)

    Article  Google Scholar 

  34. G.M. Kontogeorgis, I.V. Yakoumis, H. Meijer, E. Hendriks, T. Moorwood, Fluid Phase Equilib. 158, 201–209 (1999)

    Article  Google Scholar 

  35. M.B. Oliveira, I.M. Marrucho, J.A.P. Coutinho, A.J. Queimada, Fluid Phase Equilib. 267, 83–91 (2008)

    Article  Google Scholar 

  36. M.B. Oliveira, A.J. Queimada, G.M. Kontogeorgis, J.A.P. Coutinho, J. Supercrit. Fluids 55, 876–892 (2011)

    Article  Google Scholar 

  37. G. Soave, Chem. Eng. Sci. 27, 1197–1203 (1972)

    Article  Google Scholar 

  38. M.S. Wertheim, J. Stat. Phys. 35, 19–34 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  39. M.S. Wertheim, J. Stat. Phys. 35, 35–47 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  40. M.S. Wertheim, J. Stat. Phys. 42, 459–476 (1986)

    Article  ADS  Google Scholar 

  41. M.S. Wertheim, J. Stat. Phys. 42, 477–492 (1986)

    Article  ADS  Google Scholar 

  42. S.H. Huang, M. Radosz, Ind. Eng. Chem. Res. 29, 2284–2294 (1990)

    Article  Google Scholar 

  43. A.J. Queimada, C. Miqueu, I.M. Marrucho, G.M. Kontogeorgis, J.A.P. Coutinho, Fluid Phase Equilib. 228, 479–485 (2005)

    Article  Google Scholar 

  44. G.T. Dee, B.B. Sauer, J. Colloid Interface Sci. 152, 85–103 (1992)

    Article  ADS  Google Scholar 

  45. H. Kahl, S. Enders, Fluid Phase Equilib. 172, 27–42 (2000)

    Article  Google Scholar 

  46. C. Miqueu, B. Mendiboure, A. Graciaa, J. Lachaise, Fluid Phase Equilib. 207, 225–246 (2003)

    Article  Google Scholar 

  47. R.C. Reid, J.M. Prausnitz, T.K. Sherwood, The Properties of Liquids and Gases (McGraw-Hill, New York, 1977)

    Google Scholar 

  48. NIST Chemistry Webbook. http://www.webbook.nist.gov/chemistry/fluid/. Accessed 26 April 2020

  49. E.A. Müller, A. Mejía, J. Phys. Chem. Lett. 5, 1267–1271 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

A.H. acknowledges the economic support given by the UCSC.

Author information

Authors and Affiliations

  1. School of Chemical, Petroleum and Gas, Semnan University, Semnan, Iran

    Fatemeh Biglar

  2. Departamento de Ingeniería Industrial, Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile

    Ariel Hernández

  3. Iranian Institute of Research & Development in Chemical Industries (IRDCI)-ACECR, Tehran, Iran

    Shahin Khosharay

Authors
  1. Fatemeh Biglar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ariel Hernández
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shahin Khosharay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ariel Hernández.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Biglar, F., Hernández, A. & Khosharay, S. Modeling of the Interfacial Behavior of \(\hbox {CO}_{2}\) + \(\hbox {H}_{2}\)O and \(\hbox {H}_{2}\)S + \(\hbox {H}_{2}\)O with CPA EOS and Gradient Theory. Int J Thermophys 42, 108 (2021). https://doi.org/10.1007/s10765-021-02853-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10765-021-02853-6

Keywords

Search

Navigation