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Viscosity Prediction for Petroleum Fluids Using Free Volume Theory and PC-SAFT

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Abstract

In this study, free volume theory (FVT) in combination with perturbed-chain statistical associating fluid theory is implemented for viscosity prediction of petroleum reservoir fluids containing ill-defined components such as cuts and plus fractions. FVT has three adjustable parameters for each component to calculate viscosity. These three parameters for petroleum cuts (especially plus fractions) are not available. In this work, these parameters are determined for different petroleum fractions. A model as a function of molecular weight and specific gravity is developed using 22 real reservoir fluid samples with API grades in the range of 22 to 45. Afterward, the proposed model accuracy in comparison with the accuracy of De la Porte et al. with reference to experimental data is presented. The presented model is used for six real samples in an evaluation step, and the results are compared with available experimental data and the method of De la Porte et al. Finally, the method of Lohrenz et al. and the method of Pedersen et al. as two common industrial methods for viscosity calculation are compared with the proposed approach. The absolute average deviation was 9.7 % for free volume theory method, 15.4 % for Lohrenz et al., and 22.16 for Pedersen et al.

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Abbreviations

A res :

Residual Helmholtz free energy

\( \tilde{a}^{res} \) :

Reduced residual Helmholtz free energy

\( \tilde{a}^{hc} \) :

Hard chain contribution to reduced Helmholtz free energy

\( \tilde{a}^{disp} \) :

Dispersion contribution to reduced Helmholtz free energy

\( AD\%_{FVT} = 100.\left| {\frac{{\upmu^{exp} -\upmu^{FVT} }}{{\upmu^{exp} }}} \right| \) :

Absolute deviation percent of calculated viscosity by FVT model

\( AD\%_{LBC} = 100.\left| {\frac{{\upmu^{exp} -\upmu^{LBC} }}{{\upmu^{exp} }}} \right| \) :

Absolute deviation percent of calculated viscosity by LBC method

B :

Characteristic of free volume overlap

EOS :

Equation of state

VS :

Volume shift

E :

Necessary energy to form a free space available for a molecule to diffuse

E 0 :

Barrier energy for molecule to diffuse

\( F_{c} \) :

Correction factor

fv :

Volume fraction

K:

Boltzmann constant

L :

Average characteristic molecular quadratic length

MW :

Molecular weight

\( M_{w} \) :

Molecular weight

MW_plus fraction:

Molecular weight of plus fraction

m :

Segment length

N :

Avogadro number

N A :

Avogadro number

N t :

Total mole in the cell

N L :

Liquid mole number in the cell

N G :

Gas mole number in the cell

\( OF\left( {a,b,c} \right) = \frac{1}{n}.\sum \left| {\frac{{\upmu^{exp} -\upmu^{calc} }}{{\upmu^{exp} }}} \right| \) :

Objective function for viscosity

Pc :

Critical pressure

Pbubble :

Bubble point pressure

R:

Universal gas constant

SP.GR:

Specific gravity

S_plus fraction:

Specific gravity of plus fraction

T:

Temperature (K)

Tc :

Critical temperature

Vc :

Critical volume

V l :

Liquid volume

V g :

Gas volume

x:

Liquid composition

xi :

Mole fraction of species i

y :

Gas composition

Zhc :

Hard chain contribution of compressibility factor

Zdisp :

Dispersion contribution of compressibility factor

Z g :

Gas compressibility factor

Z l :

Liquid compressibility factor

ε:

Depth of potential

η:

Viscosity

\( \upeta_{0} \) :

Dilute gas viscosity

\( \Delta\upeta \) :

Dense state viscosity

η:

Packing fraction density

References

  1. A. Allal, M. Moha-Ouchane, C. Boned, Phys. Chem. Liq. 39, 1–30 (2001)

    Article  Google Scholar 

  2. A. Allal, C. Boned, A. Baylaucq, Phys. Rev. E Stat. Nonlinear Soft Matter. Phys. 64, 101–110 (2001)

    Article  Google Scholar 

  3. J.H. Dymond, M.A. Awan, Int. J. Thermophys. 10, 941–951 (1989)

    Article  ADS  Google Scholar 

  4. M. Assael, J. Dymond, M. Papadaki, P. Patterson, Fluid Phase Equilib. 75, 245–255 (1992)

    Article  Google Scholar 

  5. S.E. Quiñones-Cisneros, C.K. Zéberg-Mikkelsen, E.H. Stenby, Fluid Phase Equilib. 169, 249–276 (2000)

    Article  Google Scholar 

  6. S.E. Quiñones-Cisneros, C.K. Zéberg-Mikkelsen, E.H. Stenby, Fluid Phase Equilib. 178, 1–16 (2001)

    Article  Google Scholar 

  7. S.E. Quiñones-Cisneros, U.K. Deiters, J. Phys. Chem. B 110, 12820–12834 (2006)

    Article  Google Scholar 

  8. T. Goel, C.N. Patra, T. Mukherjee, C. Chakravarty, J. Chem. Phys. 129, 164–174 (2008)

    Google Scholar 

  9. G. Galliero, C. Boned, J. Fernández, J. Chem. Phys. 134, 64–74 (2011)

    Article  Google Scholar 

  10. L.T. Novak, Int. J. Chem. Reactor Eng. 9, 1–20 (2011)

    Google Scholar 

  11. A.S. de Wijn, V. Vesovic, G. Jackson, J.M. Trusler, J. Chem. Phys. 128, 204–214 (2008)

    Google Scholar 

  12. R. Srivastava, D.K. Dwivedee, K.N. Khanna, J. Mol. Liq. 139, 29–34 (2008)

    Article  Google Scholar 

  13. G. Galliéro, C. Boned, A. Baylaucq, Ind. Eng. Chem. Res. 44, 6963–6972 (2005)

    Article  Google Scholar 

  14. G. Galliero, C. Boned, Phys. Rev. E Stat. Phys. Plasmas Fluids 79, 102–120 (2009)

    Google Scholar 

  15. M.S. Zabaloy, J.M. Machado, E.A. Macedo, Int. J. Thermophys. 22, 829–858 (2001)

    Article  Google Scholar 

  16. M.S. Zabaloy, V.R. Vasquez, E.A. Macedo, J. Supercrit. Fluids 36, 106–117 (2005)

    Article  Google Scholar 

  17. A. Allal, C. Boned, P. Daugé, Phys. Chem. Liq. 39, 607–624 (2001)

    Article  Google Scholar 

  18. A. Baylaucq, M. Comuñas, C. Boned, A. Allal, J. Fernández, Fluid Phase Equilib. 199, 249–263 (2002)

    Article  Google Scholar 

  19. C.K. Zéberg-Mikkelsen, A. Baylaucq, M. Barrouhou, C. Boned, Phys. Chem. Chem. Phys. 5, 1547–1551 (2003)

    Article  Google Scholar 

  20. M. Comuñas, A. Baylaucq, F. Plantier, C. Boned, J. Fernández, Fluid Phase Equilib. 222, 331–338 (2004)

    Article  Google Scholar 

  21. P. Reghem, A. Baylaucq, M. Comunas, J. Fernández, C. Boned, Fluid Phase Equilib. 236, 229–236 (2005)

    Article  Google Scholar 

  22. D.l. Porte, in Sensitivities to Component Characterizations of Heavy Oil Viscosity in Numerical Reservoir Simulation of Steam-Injection Processes (Chemical Engineering Department, Imperial College, London, 2012)

  23. E. Behzadfar, S.G. Hatzikiriakos, Fuel 116, 578–587 (2014)

    Article  Google Scholar 

  24. M. Almasi, J. Chem. Eng. Data 60, 714–720 (2015)

    Article  Google Scholar 

  25. J.J. De la Porte, C.A. Kossack, Fuel 136, 156–164 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  27. D.-Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15, 59–64 (1976)

    Article  Google Scholar 

  28. W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, Ind. Eng. Chem. Res. 29, 1709–1721 (1990)

    Article  Google Scholar 

  29. W.G. Chapman, G. Jackson, K.E. Gubbins, Mol. Phys. 65, 1057–1079 (1988)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  31. S.H. Huang, M. Radosz, Ind. Eng. Chem. Res. 30, 1994–2005 (1991)

    Article  Google Scholar 

  32. J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40, 1244–1260 (2001)

    Article  Google Scholar 

  33. M. Assareh, C. Ghotbi, M. Tavakkoli, G. Bashiri, Fluid Phase Equilib. 408, 273–283 (2016)

    Article  Google Scholar 

  34. F. Varzandeh, E.H. Stenby, W. Yan, Fluid Phase Equilib. 433, 97–111 (2017)

    Article  Google Scholar 

  35. S.P. Tan, H. Adidharma, B.F. Towler, M. Radosz, Ind. Eng. Chem. Res. 44, 8409–8418 (2005)

    Article  Google Scholar 

  36. S.P. Tan, H. Adidharma, B.F. Towler, M. Radosz, Ind. Eng. Chem. Res. 45, 2116–2122 (2006)

    Article  Google Scholar 

  37. W.A. Burgess, D. Tapriyal, I.K. Gamwo, B.D. Morreale, M.A. McHugh, R.M. Enick, Ind. Eng. Chem. Res. 51, 16721–16733 (2012)

    Article  Google Scholar 

  38. F. Llovell, R.M. Marcos, L.F. Vega, J. Phys. Chem. B 117, 8159–8171 (2013)

    Article  Google Scholar 

  39. S.E. Quiñones-Cisneros, C.K. Zéberg-Mikkelsen, E.H. Stenby, Chem. Eng. Sci. 56, 7007–7015 (2001)

    Article  Google Scholar 

  40. S.E. Quiñones-Cisneros, C.K. Zéberg-Mikkelsen, J. Fernández, J. García, AIChE J. 52, 1600–1610 (2006)

    Article  Google Scholar 

  41. S. Quiñones-Cisneros, C. Zéberg-Mikkelsen, A. Baylaucq, C. Boned, Int. J. Thermophys. 25, 1353–1366 (2004)

    Article  ADS  Google Scholar 

  42. K.A.G. Schmidt, S.E. Quiñones-Cisneros, B. Kvamme, Energy Fuels 19, 1303–1313 (2005)

    Article  Google Scholar 

  43. R. Bagherinia, M. Assareh, F. Feyzi, Fluid Phase Equilib. 425, 21–30 (2016)

    Article  Google Scholar 

  44. Y.H. Dehaghani, M. Assareh, F. Feyzi, Fluid Phase Equilib. 1, 14 (2017)

    Google Scholar 

  45. J. Lohrenz, B.G. Bray, C.R. Clark, J. Pet. Technol. 231, 1117–1127 (1964)

    Google Scholar 

  46. K.S. Pedersen, A. Fredenslund, P.L. Christensen, P. Thomassen, Chem. Eng. Sci. 39, 1011–1016 (1984)

    Article  Google Scholar 

  47. M.R. Riazi, T.E. Daubert, Ind. Eng. Chem. Res. 26, 755–759 (1987)

    Article  Google Scholar 

  48. B.I. Lee, M.G. Kesler, AIChE J. 21, 510–527 (1975)

    Article  Google Scholar 

  49. C.H. Whitson, in Topics on Phase Behavior and Flow of Petroleum Reservoir Fluids (Norwegian Institute of Technology, Department of Petroleum and Chemical Engineering, University of Trondheim, 1983)

  50. W. Yan, F. Varzandeh, E.H. Stenby, Fluid Phase Equilib. 386, 96–124 (2015)

    Article  Google Scholar 

  51. X. Liang, W. Yan, K. Thomsen, G.M. Kontogeorgis, Fluid Phase Equilib. 375, 254–268 (2014)

    Article  Google Scholar 

  52. X. Liang, W. Yan, K. Thomsen, G.M. Kontogeorgis, Fluid Phase Equilib. 406, 147–155 (2015)

    Article  Google Scholar 

  53. I. Polishuk, Ind. Eng. Chem. Res. 53, 14127–14141 (2014)

    Article  Google Scholar 

  54. T.H. Chung, L.L. Lee, K.E. Starling, Ind. Eng. Chem. Fundam. 23, 8–13 (1984)

    Article  Google Scholar 

  55. T.H. Chung, M. Ajlan, L.L. Lee, K.E. Starling, Ind. Eng. Chem. Res. 27, 671–679 (1988)

    Article  Google Scholar 

  56. C. Wilke, J. Chem. Phys. 18, 517–519 (1950)

    Article  ADS  Google Scholar 

  57. L. Zipperer, F. Herning, Das Gas-und Wasserfach 4, 49–59 (1936)

    Google Scholar 

  58. C. Boned, C.K. Zéberg-Mikkelsen, A. Baylaucq, P. Daugé, Fluid Phase Equilib. 212, 143–164 (2003)

    Article  Google Scholar 

  59. X. Canet, P. Dauge, A. Baylaucq, C. Boned, C.K. Zéberg-Mikkelsen, S.E. Quiñones-Cisneros, E.H. Stenby, Int. J. Thermophys. 22, 1669–1689 (2001)

    Article  Google Scholar 

  60. A.M. Elsharkawy, S.A. Hassan, Y.S. Hashim, M.A. Fahim, Ind. Eng. Chem. Res. 42, 4132–4142 (2003)

    Article  Google Scholar 

  61. M. Al-Ajmi, P.C. Tybjerg, C.P. Rasmussen, J.A. Shaikh, in SPE Middle East Oil and Gas Show and Conference (Society of Petroleum Engineers, 2011)

  62. W.D. McCain, The Properties of Petroleum Fluids (PennWell Books, Houston, 1990)

    Google Scholar 

  63. K.S. Pedersen, P.L. Christensen, J.A. Shaikh, Phase Behavior of Petroleum Reservoir Fluids (CRC Press, Boca Raton, 2014)

    Book  Google Scholar 

  64. K.S. Pedersen, A. Fredenslund, P. Thomassen, Properties of Oils and Natural Gases (Gulf Pub Co, Houston, 1989)

    Google Scholar 

  65. M.A. Barrufet, K.R. Hall, A. Estrada-Baltazar, G.A. Iglesias-Silva, J. Chem. Eng. Data 44, 1310–1314 (1999)

    Article  Google Scholar 

  66. D. Ducoulombier, H. Zhou, C. Boned, J. Peyrelasse, H. Saint-Guirons, P. Xans, J. Phys. Chem. 90, 1692–1700 (1986)

    Article  Google Scholar 

  67. G.A. Iglesias-Silva, A. Estrada-Baltazar, K.R. Hall, M.A. Barrufet, J. Chem. Eng. Data 44, 1304–1309 (1999)

    Article  Google Scholar 

  68. A.J. Queimada, S. Quinones-Cisneros, I.M. Marrucho, J.A. Coutinho, E.H. Stenby, Int. J. Thermophys. 24, 1221–1239 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Thermodynamics Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran

    Younes Khoshnamvand & Mehdi Assareh

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  1. Younes Khoshnamvand
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  2. Mehdi Assareh
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Correspondence to Mehdi Assareh.

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Khoshnamvand, Y., Assareh, M. Viscosity Prediction for Petroleum Fluids Using Free Volume Theory and PC-SAFT. Int J Thermophys 39, 54 (2018). https://doi.org/10.1007/s10765-018-2377-0

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