Skip to main content
SpringerLink
Log in

Calculation of Filtration Characteristics of Porous Media by Their Digitized Images with the Use of Lattice Boltzmann Equations

  • KINETIC THEORY OF TRANSFER PROCESSES
  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

We have investigated the features of using STR and MTR models of lattice Boltzmann equations for calculating the filtration characteristics of porous media with the use of their digital images. The results of calculations performed on the basis of these models were compared with the results of analytical calculations made with the use of stationary Navier–Stokes equations and continuity equations. Calculations of the laminar flow in a pipe with the use of the MTR model had a much higher accuracy as compared to analogous calculations by the SRT model and showed independence of the relaxation parameter. It has been established that for fluid flow in pore channels the MRT model and the Navier–Stokes equations give comparable results, whereas in using the SRT model the numerical solution depends on the relaxation parameter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. J. Blunt, B. Bijeljic, H. Dong, O. Gharbi, S. Iglauer, P. Mostaghimi, A. Paluszny, and C. Pentland, Pore-scale imaging and modeling, Adv. Water Resour., 51, 197–216 (2013).

    Article  Google Scholar 

  2. M. Andrew, B. Bijeljic, and M. J. Blunt, Pore-scale contact angle measurements at reservoir conditions using X-ray tomography, Adv. Water Resour., 68, 24–31 (2014).

    Article  Google Scholar 

  3. N. Watanabe, T. Ishibashi, Y. Ohsaki, Y. Tsuchiya, T. Tamagawa, N. Hirano, H. Okabe, and N. Tsuchiya, X-ray CT based numerical analysis of fracture flow for core samples under various confining pressures, Eng. Geol., 123, 338–346 (2011).

    Article  Google Scholar 

  4. L. Farber, S. G. Tardo, and J. N. Michaels, Use of X-ray tomography to study the porosity and morphology of granules, Powder Technol., 132, 57– 63 (2003).

    Article  Google Scholar 

  5. P. Mostaghimi, M. J. Blunt, and B. Bijeljic, Computations of absolute permeability on micro-CT images, Math. Geosci., 45, 103–125 (2013).

    Article  MathSciNet  Google Scholar 

  6. J. Dvorkin, M. Armbruster, C. Baldwin, Q. Fang, N. Derzhi, C. Gomez, B. Nur, A. Nur, and Y. Mu, The future of rock physics: Computational methods vs. lab testing, First Break, 26, 63–68 (2008).

    Google Scholar 

  7. T. R. Zakirov, A. A. Galeev, É. A. Korolev, I. S. Nuriev, and E. O. Statsenko, Investigation of the filtration and volume properties of Ashal′chinsk-deposit sandstones using X-ray computer tomograph, Neft. Khoz., No. 8, 36–40 (2015).

  8. T. R. Zakirov, A. A. Galeev, A. A. Konovalov, and E. O. Statsenko, X-ray CT based analysis of the "representative threedimensional element" of the filtration and capacity properties of Ashal′chinsk sandstones, Neft. Khoz., No. 10, 54–57 (2015).

  9. T. R. Zakirov, A. A. Galeev, É. A. Korolev, and E. O. Statsenko, Investigation of the porosity and absolute permeability coefficients of a carbonate collector using X-ray computed microtomography, Neft. Khoz., No. 6, 56–69 (2016).

  10. T. R. Zakirov, A. A. Galeev, E. A. Korolev, and E. O. Statsenko, Flow properties of sandstone and carbonate rocks by X-ray computed tomography, Curr. Sci., 110, Issue 11, 2142–2147 (2016).

    Article  Google Scholar 

  11. S. Chen and G. Doolen, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30, 329–364 (1998).

    Article  MathSciNet  Google Scholar 

  12. G. V. Krivovichev, On stability of lattice Boltzmann finite-difference schemes, Vych. Metody Programmir., 14, 1–8 (2013).

    Google Scholar 

  13. C. Pan, L. S. Luo, and C. T. Miller, An evaluation of lattice Boltzmann schemes for porous medium flow simulation, Comput. Fluids, 35, 898–909 (2006).

    Article  MATH  Google Scholar 

  14. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press (2001).

  15. E. Aslan, I. Taymaz, and A. C. Benim, Investigation of the lattice Boltzmann SRT and MRT stability for lid driven cavity flow, Int. J. Mater., Mech. Manufactur., 2, No. 4, 317–324 (2014).

    Google Scholar 

  16. X. Niu, T. Munekata, Sh. Hyodoa, and K. Suga, An investigation of water-gas transport processes in the gas-diffusion-layer of a PEM fuel cell by a multiphase multiple-relaxation-time lattice Boltzmann model, J. Power Source, 172, 542–552 (2007).

    Article  Google Scholar 

  17. P. L. Bhatnagar, E. P. Gross, and M. A. Krook, Model for collision processes in gases. I. Small-amplitude processes in charged and neutral one-component systems, Phys. Rev., 94, 511–525 (1954).

    Article  MATH  Google Scholar 

  18. P. Lallemand and L. Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev., 61, No. 6, 6546–6562 (2000).

    MathSciNet  Google Scholar 

  19. Q. Zou and X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids, 9, 1591–1598 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  20. O. M. Belotserkovskii, Numerical Simulation in Continuum Mechanics [in Russian], Fiz. Mat. Lit., Moscow (1994).

    MATH  Google Scholar 

  21. P. Roache, Computational Fluid Dynamics [Russian translation], Mir, Moscow (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan Federal University, 18 Kremlevskaya Str., Kazan, 420008, Russia

    T. R. Zakirov, A. A. Galeev, E. O. Statsenko & L. I. Khaidarova

  2. Institute of Mechanics and Mechanical Engineering, Kazan, science center of the Russian Academy of Sciences, 2/31 Lobachevskii Str., Kazan, 420111, Russia

    T. R. Zakirov

Authors
  1. T. R. Zakirov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Galeev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. O. Statsenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. I. Khaidarova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. R. Zakirov.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 91, No. 4, pp. 1128–1138, July–August, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zakirov, T.R., Galeev, A.A., Statsenko, E.O. et al. Calculation of Filtration Characteristics of Porous Media by Their Digitized Images with the Use of Lattice Boltzmann Equations. J Eng Phys Thermophy 91, 1069–1078 (2018). https://doi.org/10.1007/s10891-018-1833-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-018-1833-9

Keywords

Search

Navigation