Skip to main content
SpringerLink
Log in

An Extended Equation of State Modeling Method II. Mixtures

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

This work is the extension of previous work dedicated to pure fluids. The same method is extended to the representation of thermodynamic properties of a mixture through a fundamental equation of state in terms of the Helmholtz energy. The proposed technique exploits the extended corresponding-states concept of distorting the independent variables of a dedicated equation of state for a reference fluid using suitable scale factor functions to adapt the equation to experimental data of a target system. An existing equation of state for the target mixture is used instead of an equation for the reference fluid, completely avoiding the need for a reference fluid. In particular, a Soave–Redlich–Kwong cubic equation with van der Waals mixing rules is chosen. The scale factors, which are functions of temperature, density, and mole fraction of the target mixture, are expressed in the form of a multilayer feedforward neural network, whose coefficients are regressed by minimizing a suitable objective function involving different kinds of mixture thermodynamic data. As a preliminary test, the model is applied to five binary and two ternary haloalkane mixtures, using data generated from existing dedicated equations of state for the selected mixtures. The results show that the method is robust and straightforward for the effective development of a mixture- specific equation of state directly from experimental data.

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

Similar content being viewed by others

References

  1. R. Tillner-Roth, Die Thermodynamischen Eigenschaften von R152a, R134a und Ihren Gemischen, DKV Forschungsberichte, Nr. 41 (Deutsches Kälte- und Klimatechnischer Verein (DKV), Stuttgart, 1993).

  2. Tillner-Roth R. (1998) Fundamental Equations of State. Shaker Verlag, Aachen

    Google Scholar 

  3. E. W. Lemmon and R. T Jacobsen, in Thermodynamic Properties of Mixtures of Refrigerants R-32, R-125, R-134a and R-152a. Proc. IEA Annex 18, IEA, Toronto, Canada (1996).

  4. Tillner-Roth R., Friend D.G. (1998). J. Phys. Chem. Ref. Data 27:63

    ADS  Google Scholar 

  5. R. Tillner-Roth, J. Li, A. Yokozeki, H. Sato, and K. Watanabe, Thermodynamic Properties of Pure and Blended Hydrofluorocarbon (HFC) Refrigerants (Japan Society of Refrigerating and Air Conditioning Engineers, Tokyo, 1998).

  6. Lemmon E.W., Tillner-Roth R. (1999). Fluid Phase Equilib. 165:1

    Article  Google Scholar 

  7. Lemmon E.W., Jacobsen R.T. (1999). Int. J. Thermophys. 20:825

    Article  Google Scholar 

  8. Leach J.W., Chappelear P.S., Leland T.W. (1968). AIChE J. 14:568

    Article  Google Scholar 

  9. Leland T.W., Chappelear P.S. (1968). Ind. Eng. Chem. 60:15

    Article  Google Scholar 

  10. Mollerup J. (1980). Fluid Phase Equilib. 4:11

    Article  Google Scholar 

  11. Ely J.F. (1990). Adv. Cryog. Eng. 35:1511

    Google Scholar 

  12. Huber M.L., Ely J.F. (1994). Int. J. Refrig. 17:18

    Article  MATH  Google Scholar 

  13. J. F. Ely and I. M. Marrucho, in Equations of State for Fluids and Fluid Mixtures. Part I, J. V. Sengers, R. F. Kayser, C. J. Peters, and H. J. White Jr., eds. (Elsevier, Amsterdam, 2000), pp. 289–320.

  14. Clarke W.P., Jacobsen R.T., Lemmon E.W., Penoncello S.G., Beyerlein S.W. (1994). Int. J Thermophys. 15:1289

    Article  Google Scholar 

  15. Nowarski A., Friend D.G. (1998). Int. J. Thermophys. 19:1133

    Article  Google Scholar 

  16. Piazza L., Scalabrin G., Marchi P., Richon D. (2006). Int. J. Refrig. 29:1182

    Article  Google Scholar 

  17. Scalabrin G., Marchi P., Bettio L., Richon D. (2006). Int. J. Refrig. 29:1195

    Article  Google Scholar 

  18. G. Scalabrin, L. Bettio, P. Marchi, L. Piazza, and D. Richon, Int. J. Thermophys. (in press).

  19. Redlich O., Kwong J.N.S. (1949). Chem. Rev. 44:233

    Article  Google Scholar 

  20. Soave G. (1972). Chem. Eng. Sci. 27:1197

    Article  Google Scholar 

  21. Kůrková V. (1992). Neural Networks 5:501

    Article  Google Scholar 

  22. Péneloux A., Rauzy E., Fréze R. (1982). Fluid Phase Equilib. 8:7

    Article  Google Scholar 

  23. Span R. (2000) Multiparameter Equations of State. Springer Verlag, Berlin

    Google Scholar 

  24. Scalabrin G., Piazza L., Cristofoli G. (2002). Int. J. Thermophys. 23:57

    Article  Google Scholar 

  25. Scalabrin G., Piazza L., Richon D. (2002). Fluid Phase Equilib. 199:33

    Article  Google Scholar 

  26. Scalabrin G., Cristofoli G., Richon D. (2002). Fluid Phase Equilib. 199:265

    Article  Google Scholar 

  27. Scalabrin G., Cristofoli G., Richon D. (2002). Fluid Phase Equilib. 199:281

    Article  Google Scholar 

  28. Scalabrin G., Marchi P., Stringari P., Richon D. (2006). Fluid Phase Equilib. 242:72

    Article  Google Scholar 

  29. Scalabrin G., Marchi P., Stringari P., Richon D. (2006). Fluid Phase Equilib. 242:79

    Article  Google Scholar 

  30. Tillner-Roth R., Yokozeki A. (1997). J. Phys. Chem. Ref. Data 26:1273

    ADS  Google Scholar 

  31. Outcalt S.L., McLinden M.O. (1995). Int. J. Thermophys. 16:79

    Article  Google Scholar 

  32. Tillner-Roth R., Baehr H.D. (1994). J. Phys. Chem. Ref. Data 23:657

    Article  ADS  Google Scholar 

  33. Outcalt S.L., McLinden M.O. (1997). Int. J. Thermophys. 18:1445

    Google Scholar 

  34. Rumelhart D.E., McClelland J.L. (1986) Parallel Distributed Processing: Exploration in the Microstructure of Cognition. MIT Press, Cambridge, Massachusetts

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica Tecnica, Università di Padova, via Venezia 1, I-35131, Padova, Italy

    G. Scalabrin, P. Marchi & P. Stringari

  2. Centre Energétique et Procédés, Ecole Nationale Supérieure des Mines de Paris CEP/ TEP, 35 rue Saint Honoré, 77305, Fontainebleau, France

    D. Richon

Authors
  1. G. Scalabrin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Marchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Stringari
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Richon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Richon.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Scalabrin, G., Marchi, P., Stringari, P. et al. An Extended Equation of State Modeling Method II. Mixtures. Int J Thermophys 27, 1319–1353 (2006). https://doi.org/10.1007/s10765-006-0112-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10765-006-0112-8

Keywords

Search

Navigation