Advertisement

A Review of the Alpha Functions of Cubic Equations of State for Different Research Systems

  • Wenying Zhao
  • Li Xia
  • Xiaoyan Sun
  • Shuguang XiangEmail author
Article
  • 46 Downloads

Abstract

Alpha functions affect the predictive accuracy of cubic equations of state for the thermodynamic properties. The alpha functions usually aimed at predicting the specific compounds. This article reviewed various alpha functions for the prediction of five kinds of compounds—non-polar and weakly polar compounds, polar compounds, heavy hydrocarbons, reservoir fluids and natural gases, and water. Most alpha functions in polynomial and exponential forms can predict the thermodynamic properties of non-polar and weakly polar compounds. The alpha functions for the polar compounds usually have more coefficients or terms of variables in forms. Some alpha functions for heavy hydrocarbons are similar in forms to that for the simple fluid, some are generalized with the re-defined acentric factor, and the others are modified by introducing the triple temperature and normal boiling temperature into the functions. For the complex reservoir fluids and natural gases, the alpha functions are set as the characteristic constants of pseudo-components—pseudo-three phase temperature, pseudo-normal boiling temperature, pseudo-critical temperature, and pseudo-molecular weights—as the variables. The alpha functions for water are modified by adding more terms of reduced temperature into the functions to improve the predictive accuracy of vapor pressure. According to the properties of each kind of compounds, the universal alpha functions should be proposed for the simple fluid, and the specific alpha functions should be dedicatedly explored for the complex fluid and water.

Keywords

Alpha functions Cubic equations of state Non-polar and polar compounds Reservoir fluids Research progress 

Abbreviations

CPA

Cubic-plus-association

EoS

Equation of state

IML

Iwai–Margerum–Lu

LLE

Liquid–liquid equilibrium

NM

Nasrifar–Moshfeghian

PR

Peng–Robinson

PT

Patel–Teja

PTV

Patel–Teja–Valderrama

RK

Redlich–Kwong

SAFT

Statistical associate fluid theory

SRK

Soave–Redlich–Kwong

SRW

Schwartzentruber–Renon–Watanasiri

TRR

Translated Peng–Robinson

UNIFAC

Universal functional-group activity coefficients

VDW

Van der Waals

VDW-711

Translated VDW EOS

VLE

Vapor–liquid equilibrium

VTPR

Volume-translated Peng–Robinson

A, B, L, M, N, X, Y, a, b, c, d, f, k, l, m, n, p, q, x

Parameters of alpha functions

a

Van der Waals attractive parameter/specific parameter

Cf

A function of temperature and pressure

csw

Concentration of brine

T

Temperature

T*

A function of Tb and Tc or a function of characteristic energy

Tpt

Triple phase temperature

Trw

Reduced temperature of water

Greek Symbols

α

Alpha function

β

A function of Tbr and Tr

γ

A function of ω and Tr

ω

Acentric factor

ω

Re-defined acentric factor

Γ

Parameter of alpha function

χ

Parameter of alpha function

Subscripts

b

Normal boiling point property

c

Critical property

pt

Triple property

r

Reduced by critical parameter

Superscripts

(0)

Reference fluid property (ω = 0)

(1)

Reference fluid property (ω = 1)

Notes

Acknowledgments

This research was supported by the National Natural Science Foundation of China (No. 21476119) and Major Science and Technology Innovation Projects of Shandong Province (No. 2018CXGC1102).

References

  1. 1.
    C. Coquelet, A. Chapoy, D. Richon, Int. J. Thermophys. 25, 133 (2004)Google Scholar
  2. 2.
    P.M. Mathias, T.W. Copeman, Fluid Phase Equilibria 13, 91 (1983)Google Scholar
  3. 3.
    C.H. Twu, in Proceedings of the International Symposium on Thermodynamics in Chemical Engineering and Industry (1988)Google Scholar
  4. 4.
    D.B. Robinson, D.-Y. Peng, The Characterization of the Heptanes and Heavier Fractions for the GPA Peng-Robinson Programs (Gas Processors Association, Tulsa, 1978)Google Scholar
  5. 5.
    K.A.M. Gasem, W. Gao, Z. Pan, R.L. Robinson, Fluid Phase Equilibria 181, 113 (2001)Google Scholar
  6. 6.
    A. Haghtalab, M.J. Kamali, S.H. Mazloumi, P. Mahmoodi, Fluid Phase Equilibria 293, 209 (2010)Google Scholar
  7. 7.
    S. Law, J. Lielmezs, Thermochim. Acta 84, 71 (1985)Google Scholar
  8. 8.
    P. Hosseinifar, S. Jamshidi, Fluid Phase Equilibria 408, 58 (2016)Google Scholar
  9. 9.
    D.Y. Peng, in ACS Symposium Series (1980)Google Scholar
  10. 10.
    X. Li, D. Yang, Ind. Eng. Chem. Res. 52, 13829 (2013)Google Scholar
  11. 11.
    J.H. Van der Waals, On the Continuity of the Gaseous and Liquid State (Leiden University, Holland, 1873)zbMATHGoogle Scholar
  12. 12.
    O. Redlich, J.N.S. Kwong, Chem. Rev. 44, 233 (1949)Google Scholar
  13. 13.
    G.M. Wilson, Adv. Cryog. Eng. 9, 168 (1964)Google Scholar
  14. 14.
    G. Soave, Chem. Eng. Sci. 27, 1197 (1972)Google Scholar
  15. 15.
    R. Stryjek, J.H. Vera, Can. J. Chem. Eng. 64, 323 (1986)Google Scholar
  16. 16.
    R. Stryjek, J.H. Vera, Can. J. Chem. Eng. 64, 820 (1986)Google Scholar
  17. 17.
    I. Androulakis, N. Kalospiros, D. Tassios, Fluid Phase Equilibria 45, 135 (1989)Google Scholar
  18. 18.
    M. Mohsen-Nia, J. Petrol. Sci. Eng. 113, 97 (2014)Google Scholar
  19. 19.
    A. Kumar, R. Okuno, Ind. Eng. Chem. Res. 53, 440 (2014)Google Scholar
  20. 20.
    A. Kumar, R. Okuno, in Society of Petroleum Engineering Technical Conference and Exhibition, San Antonio, Texas, Texas (2012)Google Scholar
  21. 21.
    A. Kumar, R. Okuno, Fluid Phase Equilibria 335, 46 (2012)Google Scholar
  22. 22.
    G. Heyen, in Proceedings of the 2nd World Congress of Chemical Engineering, Frankfurt (1980)Google Scholar
  23. 23.
    C.H. Twu, D. Bluck, J.R. Cunningham, J.E. Coon, Fluid Phase Equilibria 69, 33 (1991)Google Scholar
  24. 24.
    C.H. Twu, J.E. Coon, J.R. Cunningham, Fluid Phase Equilibria 104, 83 (1995)Google Scholar
  25. 25.
    M. Aznar, A. Silva-Telles, J.O. Valderrama, Chem. Eng. Commun. 190, 1411 (2003)Google Scholar
  26. 26.
    Y. Le Guennec, S. Lasala, R. Privat, J.N. Jaubert, Fluid Phase Equilibria 427, 513 (2016)Google Scholar
  27. 27.
    P. Mahmoodi, M. Sedigh, J. Supercrit. Fluid. 120, 191 (2017)Google Scholar
  28. 28.
    P. Mathias, H.C. Klotz, Chem. Eng. Prog. 90, 67 (1994)Google Scholar
  29. 29.
    C. Colina, J. Santos, C. Olivera-Fuentes, High Temp-high Press 29, 525 (1997)Google Scholar
  30. 30.
    R.M. Gibbons, A.P. Laughton, J. Chem. Soc. Faraday Trans. 2 80, 1019 (1984)Google Scholar
  31. 31.
    N.C. Patel, Int. J. Thermophys. 17, 673 (1996)ADSGoogle Scholar
  32. 32.
    M.M. Abbott, J.M. Prausnitz, Fluid Phase Equilibria 37, 29 (1987)Google Scholar
  33. 33.
    S.I. Sandler, J. Supercrit. Fluid 55, 496 (2010)Google Scholar
  34. 34.
    F. Yang, Q. Liu, Y. Duan, Z. Yang, Chem. Eng. Sci. 192, 565 (2018)Google Scholar
  35. 35.
    E. Neau, O. Hernández-Garduza, J. Escandell, C. Nicolas, I. Raspo, Fluid Phase Equilibria 276, 87 (2009)Google Scholar
  36. 36.
    P. Mahmoodi, M. Sedigh, Fluid Phase Equilibria 436, 69 (2017)Google Scholar
  37. 37.
    P. Mahmoodi, M. Sedigh, J. Supercrit. Fluid 112, 22 (2016)Google Scholar
  38. 38.
    Y. Le Guennec, R. Privat, J.-N. Jaubert, Fluid Phase Equilibria 429, 301 (2016)Google Scholar
  39. 39.
    A. Pina-Martinez, Y. Le Guennec, R. Privat, J.-N. Jaubert, P.M. Mathias, J. Chem. Eng. Data 63, 3980 (2018)Google Scholar
  40. 40.
    I.H. Bell, M. Satyro, E.W. Lemmon, J. Chem. Eng. Data (2018) (Ahead of Print)Google Scholar
  41. 41.
    J.M. Prausnitz, R.N. Lichtenthaler, E.G. de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria (Prentice-Hall PTR, Upper Saddle River, 1999)Google Scholar
  42. 42.
    N.M. Alsaifi, G.N. Patey, P. Englezos, Chem. Eng. Res. Des. 92, 2936 (2014)Google Scholar
  43. 43.
    I. Tsivintzelis, G.M. Kontogeorgis, C. Panayiotou, J. Phys. Chem. B 121, 2153 (2017)Google Scholar
  44. 44.
    W. Gao, R.L. Robinson, K.A.M. Gasem, Fluid Phase Equilibria 179, 207 (2001)Google Scholar
  45. 45.
    G.N. Nji, W.Y. Svrcek, H. Yarranton, M.A. Satyro, Energy Fuels 23, 366 (2009)Google Scholar
  46. 46.
    P.C.N. Mak, J. Lielmezs, Thermochim. Acta 197, 131 (1992)Google Scholar
  47. 47.
    J. Lielmezs, P.C.N. Mak, Thermochim. Acta 196, 415 (1992)Google Scholar
  48. 48.
    L.-S. Wang, J. Gmehling, AIChE J. 45, 1125 (1999)Google Scholar
  49. 49.
    A.M. Palma, A.J. Queimada, J.A.P. Coutinho, Ind. Eng. Chem. Res. 56, 15163 (2017)Google Scholar
  50. 50.
    M.S. Graboski, T.E. Daubert, Ind. Eng. Chem. Process Des. Dev. 17, 448 (1978)Google Scholar
  51. 51.
    M.S. Graboski, T.E. Daubert, Ind. Eng. Chem. Process Des. Dev. 17, 443 (1978)Google Scholar
  52. 52.
    H. Li, D. Yang, Energy Fuel 25, 1 (2011)Google Scholar
  53. 53.
    A.F. Young, F.L.P. Pessoa, V.R.R. Ahón, Ind. Eng. Chem. Res. 55, 6506 (2016)Google Scholar
  54. 54.
    R. Stryjek, J.H. Vera, in ACS Symposium Series, Washington (1986)Google Scholar
  55. 55.
    P. Wang, Z. Li, S. Xiang, Petrochem. Technol. 33, 951 (2004)Google Scholar
  56. 56.
    L.A. Forero G, J.A. Velásquez J, Fluid Phase Equilibria 342, 8 (2013)Google Scholar
  57. 57.
    L.-B. Wen, C.-Y. Xin, S.-C. Yang, Appl. Energy 87, 115 (2010)Google Scholar
  58. 58.
    L.A. Forero G, J.A. Velásquez J, Fluid Phase Equilibria 364, 75 (2014)Google Scholar
  59. 59.
    P.M. Mathias, Ind. Eng. Chem. Process Des. Dev. 22, 385 (1983)Google Scholar
  60. 60.
    P.M. Mathias, Ind. Eng. Chem. Res. 42, 7037 (2003)Google Scholar
  61. 61.
    Z. Jin, Y. Yang, K. Liu, H. Lu, Chin. J. Chem. Eng. 1, 145 (1993)Google Scholar
  62. 62.
    M.S. Zabaloy, J.H. Vera, Ind. Eng. Chem. Res. 37, 1591 (1998)Google Scholar
  63. 63.
    K. Fotouh, K. Shukla, Chem. Eng. Commun. 159, 209 (1997)Google Scholar
  64. 64.
    J.C. Tsai, Y.P. Chen, Fluid Phase Equilibria 145, 193 (1998)Google Scholar
  65. 65.
    P. Wang, Z. Li, S. Xiang, Shiyou Huagong 33, 951 (2004)Google Scholar
  66. 66.
    M.H. Joshipura, S.P. Dabke, N. Subrahmanyam, Indian Chem. Eng. 52, 116 (2010)Google Scholar
  67. 67.
    G. Soave, Chem. Eng. Sci. 39, 357 (1984)Google Scholar
  68. 68.
    G.A. Melhem, R. Saini, B.M. Goodwin, Fluid Phase Equilibria 47, 189 (1989)Google Scholar
  69. 69.
    J. Schwartzentruber, H. Renon, S. Watanasiri, Chem. Eng. 97, 118 (1990)Google Scholar
  70. 70.
    G.S. Almeida, M. Aznar, A.S. Telles, Cad. Eng. Quim. 8, 95 (1991)Google Scholar
  71. 71.
    M.A. Trebble, P.R. Bishnoi, Fluid Phase Equilibria 35, 1 (1987)Google Scholar
  72. 72.
    G.K. Folas, G.M. Kontogeorgis, M.L. Michelsen, E.H. Stenby, Ind. Eng. Chem. Res. 45, 1516 (2006)Google Scholar
  73. 73.
    Z. Chen, D. Yang, J. Chem. Eng. Data 62, 3488 (2017)Google Scholar
  74. 74.
    W. Sheng, B.C.Y. Lu, Fluid Phase Equilibria 56, 71 (1990)Google Scholar
  75. 75.
    K. Nasrifar, M. Moshfeghian, J. Petrol. Sci. Eng. 42, 223 (2004)Google Scholar
  76. 76.
    C.H. Twu, J.E. Coon, J.R. Cunningham, Fluid Phase Equilibria 96, 19 (1994)Google Scholar
  77. 77.
    K. Nasrifar, O. Bolland, Ind. Eng. Chem. Res. 43, 6901 (2004)Google Scholar
  78. 78.
    F. Esmaeilzadeh, M. Roshanfekr, Fluid Phase Equilib. 239, 83 (2006)Google Scholar
  79. 79.
    B. E. Garcia-Flores, D. N. Justo-Garcia, R. P. Stateva, F. Garca-Sanchez, Adv. Nat. Gas Technol. 359–384 (2012)Google Scholar
  80. 80.
    Y. Du, T.-M. Guo, Chem. Eng. Sci. 45, 893 (1990)Google Scholar
  81. 81.
    M. Bonyadi, F. Esmaeilzadeh, Fluid Phase Equilibria 273, 31 (2008)Google Scholar
  82. 82.
    H. Saffari, A. Zahedi, Chin. J. Chem. Eng. 21, 1155 (2013)Google Scholar
  83. 83.
    D. Hou, H. Deng, H. Zhang, K. Li, L. Sun, Y. Pan, J. Chem. 2015, 11 (2015)Google Scholar
  84. 84.
    S. Valiollahi, B. Kavianpour, S. Raeissi, M. Moshfeghian, J. Nat. Gas Sci. Eng. 34, 1137 (2016)Google Scholar
  85. 85.
    Z. Li, W. Jia, C. Li, J. Nat. Gas Sci. Eng. 36, 586 (2016)Google Scholar
  86. 86.
    I. Søreide, C.H. Whitson, Fluid Phase Equilibria 77, 217 (1992)Google Scholar
  87. 87.
    Y. Iwai, M.R. Margerum, B.C.Y. Lu, Fluid Phase Equilibria 42, 21 (1988)Google Scholar
  88. 88.
    P. Watson, M. Cascella, D. May, S. Salerno, D. Tassios, Fluid Phase Equilibria 27, 35 (1986)Google Scholar
  89. 89.
    J. Valderrama, J. Chem. Eng. Jpn. 23, 87 (1990)Google Scholar
  90. 90.
    N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37, 463 (1982)Google Scholar
  91. 91.
    G. Soave, Chem. Eng. Sci. 35, 1725 (1980)Google Scholar
  92. 92.
    J. Lielmezs, S.K. Howell, H.D. Campbell, Chem. Eng. Sci. 38, 1293 (1983)Google Scholar
  93. 93.
    E.E. Kalu, Q. Nguyen, X.P. Yang, J. Lielmezs, Thermochim. Acta 112, 215 (1987)Google Scholar
  94. 94.
    J.M. Yu, B.C.Y. Lu, Fluid Phase Equilibria 34, 1 (1987)Google Scholar
  95. 95.
    K. Nasrifar, M. Moshfeghian, Fluid Phase Equilibria 190, 73 (2001)Google Scholar
  96. 96.
    A. Vahid, H.R. Rahdar, F. Emami, F. Feyzi, in AIChE Annual Meeting, San Francisco, USA (2006)Google Scholar
  97. 97.
    D.-Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15, 59 (1976)Google Scholar
  98. 98.
    C.H. Twu, J.E. Coon, J.R. Cunningham, Fluid Phase Equilibria 105, 49 (1995)Google Scholar
  99. 99.
    C.H. Twu, J.E. Coon, J.R. Cunningham, Fluid Phase Equilibria 105, 61 (1995)Google Scholar
  100. 100.
    A. Haghtalab, P. Mahmoodi, S.H. Mazloumi, Can. J. Chem. Eng. 89, 1376 (2011)Google Scholar
  101. 101.
    V.N. Kabadi, R.P. Danner, Ind. Eng. Chem. Process Des. Dev. 24, 537 (1985)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Process System EngineeringQingdao University of Science & TechnologyQingdaoPeople’s Republic of China
  2. 2.College of Chemistry and Chemical EngineeringQilu Normal UniversityJinanPeople’s Republic of China

Personalised recommendations