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Transport in Porous Media

, Volume 106, Issue 2, pp 285–301 | Cite as

A Lattice Boltzmann Model for Simulating Gas Flow in Kerogen Pores

  • Junjie Ren
  • Ping Guo
  • Zhaoli GuoEmail author
  • Zhouhua Wang
Article

Abstract

Nanoscale phenomena in kerogen pores could result in complicated non-Darcy effects in shale gas production, and so classical simulation approaches based on Darcy’s law may not be appropriate for simulating shale gas flow in shale. In general, understanding the shale gas transport mechanisms in a kerogen pore is the first and most important step for accurately simulating shale gas flow in shale. In this work, we present a novel lattice Boltzmann (LB) model, which can take account of the effects of surface diffusion, gas slippage, and adsorbed layer, to study shale gas flow in a kerogen pore under real gas conditions. With the Langmuir isothermal adsorption equation and the bounce-back/specular-reflection boundary condition, the gas–solid and gas–gas molecular interactions at the solid surface are incorporated into the LB model. Furthermore, the effects of surface diffusion and gas slippage on the free-gas velocity profile and mass flux in a kerogen pore are studied via the LB model. It is found that the free-gas velocity profile appears as a parabolic profile in a kerogen pore and the free-gas velocity at the center of the kerogen pore is apparently higher than that near the wall. In particular, we find that both surface diffusion and gas slippage can enhance the mass flux. Compared with gas slippage, surface diffusion is a more important factor on the shale gas transport in small pores, while it can be negligible in large pores.

Keywords

Shale gas Lattice Boltzmann model Surface diffusion Gas slippage Kerogen pore 

Notes

Acknowledgments

We gratefully acknowledge the referees for their detailed and constructive comments. P.G. and Z.H.W would like to acknowledge the support by the National Natural Science Foundation of China (51204141). Z.L.G. would like to acknowledge the support by the National Natural Science Foundation of China (51125024) and the National Basic Research Programme of China (2011CB707305).

References

  1. Adesida, A., Akkutlu, I.Y., Resasco, D.E., Rai, C.S.: Characterization of Barnett shale pore size distribution using DFT analysis and Monte Carlo simulations. Paper SPE 147397. Paper presented at the SPE annual technical conference and exhibition held in Denver, Colorado, 30 Oct–2 Nov 2011Google Scholar
  2. Aidun, C.K., Clausen, J.R.: Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42(1), 439–472 (2010)CrossRefGoogle Scholar
  3. Akkutlu, I.Y., Fathi, E.: Multiscale gas transport in shales with local Kerogen heterogeneities. SPE J. 17(04), 1002–1011 (2012)CrossRefGoogle Scholar
  4. Ambrose, R.J., Hartman, R.C., Diaz-Campos, M., Akkutlu, I.Y., Sondergeld, C.H.: Shale gas-in-place calculations Part I: New pore-scale considerations. SPE J. 17(1), 219–229 (2012)CrossRefGoogle Scholar
  5. Ansumali, S., Karlin, I.V.: Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev. E 66(2), 026311 (2002)CrossRefGoogle Scholar
  6. Cao, B.Y., Chen, M., Guo, Z.Y.: Effect of surface roughness on gas flow in microchannels by molecular dynamics simulation. Int. J. Eng. Sci. 44(13), 927–937 (2006)CrossRefGoogle Scholar
  7. Cercignani, C.: The Boltzmann Equation and its Applications. Springer, New York (1988)CrossRefGoogle Scholar
  8. Cercignani, C.: Mathematical methods in kinetic theory. Plenum Press, New York (1990)CrossRefGoogle Scholar
  9. Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases. Cambridge University Press, Cambridge (1970)Google Scholar
  10. Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30(1), 329–364 (1998)CrossRefGoogle Scholar
  11. Dempsey, J.R.: Computer routine treats gas viscosity as a variable. Oil Gas J. 63, 141–143 (1965)Google Scholar
  12. Fathi, E., Akkutlu, I.Y.: Mass transport of adsorbed-phase in stochastic porous medium with fluctuating porosity field and nonlinear gas adsorption kinetics. Transp. Porous Med. 91(1), 5–33 (2012)CrossRefGoogle Scholar
  13. Fathi, E., Akkutlu, I.Y.: Lattice Boltzmann method for simulation of shale gas transport in kerogen. SPE J. 18(1), 27–37 (2013)CrossRefGoogle Scholar
  14. Fathi, E., Tinni, A., Akkutlu, I.Y.: Correction to Klinkenberg slip theory for gas flow in nano-capillaries. Int. J. Coal. Geol. 103, 51–59 (2012)CrossRefGoogle Scholar
  15. Freeman, C.M., Moridis, G.J., Blasingame, T.A.: A numerical study of microscale flow behavior in tight gas and shale gas reservoir systems. Transp. Porous Med. 90(1), 253–268 (2011)CrossRefGoogle Scholar
  16. Guo, Z.L., Shi, B.C., Zhao, T.S., Zheng, C.G.: Discrete effects on boundary conditions for the lattice Boltzmann equation in simulating microscale gas flows. Phys. Rev. E 76(5), 056704 (2007)CrossRefGoogle Scholar
  17. Guo, Z.L., Zhao, T.S., Shi, Y.: Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows. J. Appl. Phys. 99(7), 074903 (2006)CrossRefGoogle Scholar
  18. Guo, Z.L., Zheng, C.G., Shi, B.C.: Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow. Phys. Rev. E 77(3), 036707 (2008)CrossRefGoogle Scholar
  19. Hartman, R.C., Ambrose, R.J., Akkutlu, I.Y., Clarkson, C.R.: Shale gas-in-place calculations. Part II-Multicomponent gas adsorption effects. Paper SPE 144097. Paper presented at the North American unconventional gas conference and exhibition held in The Woodlands, Texas, 14–16 June 2011Google Scholar
  20. He, X., Luo, L.S.: Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 56(6), 6811–6817 (1997)CrossRefGoogle Scholar
  21. Kang, S.M., Fathi, E., Ambrose, R.J., Akkutlu, I.Y., Sigal, R.F.: Carbon dioxide storage capacity of organic-rich shales. SPE J. 16(4), 842–855 (2011)CrossRefGoogle Scholar
  22. Langmuir, I.: The constitution and fundamental properties of solids and liquids. Part I. Solids. J. Am. Chem. Soc. 38(11), 2221–2295 (1916)CrossRefGoogle Scholar
  23. Luo, L.S.: Unified theory of lattice Boltzmann models for nonideal gases. Phys. Rev. Lett. 81(8), 1618–1621 (1998)CrossRefGoogle Scholar
  24. Markvoort, A.J., Hilbers, P.A.J., Nedea, S.V.: Molecular dynamics study of the influence of wall–gas interactions on heat flow in nanochannels. Phys. Rev. E 71(6), 066702 (2005)CrossRefGoogle Scholar
  25. Ozkan, E., Raghavan, R., Apaydin, O.G.: Modeling of fluid transfer from shale matrix to fracture network. Paper SPE 134830. Paper presented at the SPE annual technical conference and exhibition held in Florence, Italy, 19–22 Sept 2010Google Scholar
  26. Reese, J.M., Gallis, M.A., Lockerby, D.A.: New directions in fluid dynamics: non-equilibrium aerodynamic and microsystem flows. Philos. Trans. R. Soc. Lond. A 361(1813), 2967–2988 (2003)CrossRefGoogle Scholar
  27. Shan, X., Chen, H.: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E. 47, 1815–1819 (1993)CrossRefGoogle Scholar
  28. Shan, X., He, X.: Discretization of the velocity space in the solution of the Boltzmann equation. Phys. Rev. Lett. 80(1), 65–68 (1998)CrossRefGoogle Scholar
  29. Shen, C., Tian, D.B., Xie, C., Fan, J.: Examination of the LBM in simulation of microchannel flow in transitional regime. Microscale Thermophys. Eng. 8(4), 423–432 (2004)CrossRefGoogle Scholar
  30. Shi, Y., Zhao, T.S., Guo, Z.L.: Lattice Boltzmann simulation of dense gas flows in microchannels. Phys. Rev. E 76(1), 016707 (2007)CrossRefGoogle Scholar
  31. Succi, S.: The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, Oxford (2001)Google Scholar
  32. Succi, S.: Mesoscopic modeling of slip motion at fluid–solid interfaces with heterogeneous catalysis. Phys. Rev. Lett. 89(6), 064502 (2002)CrossRefGoogle Scholar
  33. Verhaeghe, F., Luo, L.S., Blanpain, B.: Lattice Boltzmann modeling of microchannel flow in slip flow regime. J. Comput. Phys. 228(1), 147–157 (2009)CrossRefGoogle Scholar
  34. Zhang, X.L., Xiao, L.Z., Shan, X.W., Guo, L.: Lattice Boltzmann simulation of shale gas transport in organic nano-pores. Sci. Rep. 4, 4843 (2014)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Junjie Ren
    • 1
  • Ping Guo
    • 1
  • Zhaoli Guo
    • 2
    Email author
  • Zhouhua Wang
    • 1
  1. 1.State Key Laboratory of Oil and Gas Reservoir Geology and ExploitationSouthwest Petroleum UniversityChengduPeople’s Republic of China
  2. 2.State Key Laboratory of Coal CombustionHuazhong University of Science and TechnologyWuhanPeople’s Republic of China

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