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The Viscosity Surfaces of Propane in the Form of Multilayer Feed Forward Neural Networks

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Abstract

The present work focuses on the development of a viscosity equation η=η(ρ,T) for propane through a multilayer feedforward neural network (MLFN) technique. Having been successfully applied to a variety of fluids so far, the proposed technique can be regarded as a general approach to viscosity modeling. The MLFN viscosity equation has been based on the available experimental data for propane: validation on the 969 primary data shows an average absolute deviation (AAD) of 0.29% in the temperature, pressure, and density range of applicability, i.e., 90 to 630 K, 0 to 60 MPa, and 0 to 730 kg⋅m−3. This result is very promising, especially when compared with experimental data uncertainty. The minimum amount of required data for setting up the MLFN has been investigated, to explore the minimum cost of the model. Comparisons with other viscosity models are presented regarding amount of input data, claimed accuracy, and range of applicability, with the aim of providing a guideline when viscosity has to be calculated for engineering purposes. A high accuracy equation of state for the conversion of variables from experimental P,T to operative ρ,T has to be provided. To overcome this requirement, two viscosity explicit equations in the form η=η(P,T) are also developed, for the liquid and for the vapor phases. The respective AADs are 0.58 and 0.22%, comparable with those of the former η=η(ρ,T) equation. Finally, the trend of the experimental viscosity second virial coefficient is reproduced and compared with that obtained from the MLFN.

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Reference

  1. A. S. Teja and P. A. Thurner, Chem. Eng. Commun. 49:79(1986).

    Google Scholar 

  2. B. Willman and A. S. Teja, Chem. Eng. J. 37:65(1988).

    Google Scholar 

  3. K. J. Okeson and R. L. Rowley, Int. J. Thermophys. 12:119(1991).

    Google Scholar 

  4. G. Scalabrin and M. Grigiante, presented at 13th Symp. Thermophys. Properties, Boulder, Colorado (1997).

  5. G. Cristofoli, M. Grigiante, and G. Scalabrin, High Temp.-High Press. 33:83(2001).

    Google Scholar 

  6. G. Scalabrin, G. Cristofoli, and M. Grigiante, Int. J. Energy Research 26:1(2002).

    Google Scholar 

  7. M. O. McLinden, S. A. Klein, E. W. Lemmon, and A. P. Peskin, NIST Standard Reference Database 23, Version 6.0, (REFPROP) (1998).

  8. E. Vogel, Int. J. Thermophys. 16:1335(1995).

    Google Scholar 

  9. E. Vogel, C. Küchenmeister, E. Bich, and A. Laesecke, J. Phys. Chem. Ref. Data 27:947(1998).

    Google Scholar 

  10. G. Scalabrin, C. Corbetti, and G. Cristofoli, Int. J. Thermophys. 22:1383(2001).

    Google Scholar 

  11. G. Cristofoli, L. Piazza, and G. Scalabrin, Fluid Phase Equilib. 199:223(2002).

    Google Scholar 

  12. G. Scalabrin, L. Piazza, and V. Vesovic, High Temp.-High Press. 34:457(2002).

    Google Scholar 

  13. G. Scalabrin and G. Cristofoli, Int. J. Refrig. 26:302(2003).

    Google Scholar 

  14. J. Millat, J. H. Dymond, and C. A. Nieto de Castro, Transport Properties of Fluids (Cambridge Univ. Press, United Kingdom, 1996).

    Google Scholar 

  15. G. A. Olchowy and J. V. Sengers, Phys. Rev. Lett. 61:15(1988).

    Google Scholar 

  16. J. Luettmer-Strathmann, J. Sengers, and G. Olchowy, J. Chem. Phys. 103:7482(1995).

    Google Scholar 

  17. B. A. Younglove and J. F. Ely, J. Phys. Chem. Ref. Data 16:577(1987).

    Google Scholar 

  18. G. Cybenko, Mathematics of Control, Signals, and Systems 2:303(1989).

    Google Scholar 

  19. K. Hornik, M. Stinchcombe, and H. White, Neural Networks 2:359(1989).

    Google Scholar 

  20. V. Kurkova, Neural Networks 5:501(1992).

    Google Scholar 

  21. A. Laesecke, R. Krauss, K. Stephan, and W. Wagner, J. Phys. Chem. Ref. Data 19:1089(1990).

    Google Scholar 

  22. K. E. Starling, B. E. Eakin, and R. T. Ellington, AIChE J. 6:438(1960).

    Google Scholar 

  23. E. T. S. Huang, G. W. Swift, and F. Kurata, AIChE J. 12:932(1966).

    Google Scholar 

  24. J. G. Giddings, J. T. F. Kao, and R. Kobayashi, J. Chem. Phys. 45:578(1966).

    Google Scholar 

  25. L. T. Carmichael, V. M. Berry, and B. H. Sage, J. Chem. Eng. Data 9:411(1964).

    Google Scholar 

  26. H. J. Strumpf, A. F. Collings, and C. J. Pings, J. Chem. Phys. 60:3109(1974).

    Google Scholar 

  27. D. E. Diller, J. Chem. Eng. Data 27:240(1982).

    Google Scholar 

  28. J. Wilhelm and E. Vogel, J. Chem. Eng. Data 46:1467(2001).

    Google Scholar 

  29. R. Wobser and F. Mueller, Kolloid-Beih. 52:165(1941).

    Google Scholar 

  30. E. Bich and E. Vogel, in Transport Properties of Fluids, J. Millat, J. H. Dymond, and C. A. Nieto de Castro, eds. (Cambridge Univ. Press, United Kingdom, 1996), pp. 72-82.

    Google Scholar 

  31. J. Kestin, S. T. Ro, and W. A. Wakeham, Trans. Faraday Soc. 67:2308(1971).

    Google Scholar 

  32. B. H. Sage and W. N. Lacey, Ind. Eng. Chem. 30:829(1938).

    Google Scholar 

  33. L. B. Bicher, Jr. and D. L. Katz, Ind. Eng. Chem. 35:754(1943).

    Google Scholar 

  34. G. W. Swift, J. Lohrenz, and F. Kurata, AIChE J. 6:415(1960).

    Google Scholar 

  35. J. D. Baron, J. G. Roof, and F. W. Wells, J. Chem. Eng. Data 4:283(1959).

    Google Scholar 

  36. W. R. Van Wijk, J. H. van der Veen, H. C. Brinkman, and W. A. Seeder, Physica 7:45(1940).

    Google Scholar 

  37. A. S. Smith and G. G. Brown, Ind. Eng. Chem. 35:705(1943).

    Google Scholar 

  38. G. W. Swift, A. J. Christy, and F. Kurata, AIChE J. 5:98(1959).

    Google Scholar 

  39. S. E. Babb, Jr. and G. J. Scott, J. Chem. Phys. 40:3666(1964).

    Google Scholar 

  40. G. I. Galkov and S. F. Gerf, Zh. Tekh. Fiz. 11:613(1941).

    Google Scholar 

  41. M. R. Lipkin, J. A. Davison, and S. S. Kurtz, Jr., Ind. Eng. Chem. 34:976(1942).

    Google Scholar 

  42. Y. Abe, J. Kestin, H. E. Khalifa, and W. A. Wakeham, Physica A 93:155(1978).

    Google Scholar 

  43. Y. Abe, J. Kestin, H. E. Khalifa, and W. A. Wakeham, Ber. Bunsenges. Phys. Chem. 83:271(1979).

    Google Scholar 

  44. M. Trautz and K. G. Sorg, Ann. Phys. 10:81(1931).

    Google Scholar 

  45. J. Kestin, H. E. Khalifa, and W. A. Wakeham, J. Chem. Phys. 66:1132(1977).

    Google Scholar 

  46. A. Klemenc and W. Remi, Monatsh. Chem. 44:307(1923).

    Google Scholar 

  47. M. Trautz and F. Kurz, Ann. Phys. 9:981(1931).

    Google Scholar 

  48. E. W. Comings, B. J. Mayland, and R. S. Egly, Univ. Illinois Eng. Exptl. Sta. Bull. 354:1(1944).

    Google Scholar 

  49. T. Titani, Bull. Chem. Soc. Japan 5:98(1930).

    Google Scholar 

  50. K. Nagaoka, Y. Yamashita, Y. Tanaka, H. Kubota, and T. Makita, J. Chem. Eng. Japan 19:263(1986).

    Google Scholar 

  51. M. Diaz Pena and J. A. R. Cheda, Anal. Quim. (Esp.) 71:34(1975).

    Google Scholar 

  52. J. D. Lambert, K. J. Cotton, M. W. Pailthorpe, A. M. Robinson, J. Scrivins, W. R. F. Vale, and R. M. Young, Proc. Roy. Soc. London Ser. A231:280(1955).

    Google Scholar 

  53. H. Adzumi, Bull. Chem. Soc. Japan 12:199(1937).

    Google Scholar 

  54. S. F. Gerf and G. I. Galkov, Zh. Tekh. Fiz. 10:725(1940).

    Google Scholar 

  55. H. Senftleben and H. Gladish, Z. Phys. 125:653(1949).

    Google Scholar 

  56. D. G. Friend and J. C. Rainwater, Chem. Phys. Lett. 107:590(1984).

    Google Scholar 

  57. J. C. Rainwater and D. G. Friend, Phys. Rev. A 36:4062(1987).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  60. H. Miyamoto and K. Watanabe, Int. J. Thermophys. 21:1045(2000).

    Google Scholar 

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Authors and Affiliations

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

    G. Scalabrin & G. Cristofoli

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  1. G. Scalabrin
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  2. G. Cristofoli
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Correspondence to G. Scalabrin.

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Scalabrin, G., Cristofoli, G. The Viscosity Surfaces of Propane in the Form of Multilayer Feed Forward Neural Networks. International Journal of Thermophysics 24, 1241–1263 (2003). https://doi.org/10.1023/A:1026194916689

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