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Evaluation of Absolute Permeability in Heterogeneous and Anisotropic Porous Media Using the Lattice Boltzmann Simulations

Lobachevskii Journal of Mathematics volume 42, pages 3048–3059 (2021)Cite this article

Abstract

This paper presents a systematical study of the effect of porosity, pore-level heterogeneity and anisotropy on the absolute permeability of digital images of porous media. The main goal is to develop an analytical formula that estimates permeability as a function of these three parameters at once. Permeability is assessed based on numerical simulations using the lattice Boltzmann equations. Digital models of porous media are generated by a combined method consisting of Monte-Carlo and quartet structure generation set (QSGS) algorithms. Increase in heterogeneity negatively affects permeability. With an increase in porosity, the effect of heterogeneity on flow properties decreases. There was a linear decrease in permeability during the transition between favorable and unfavorable anisotropy. The influence of anisotropy is most pronounced in samples with high porosity and monotonically reduces with decreasing porosity. Heterogeneity negatively influences on the sensitivity of flow properties to changes in anisotropy and independent on porosity.

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Funding

This study was supported by the Russian Science Foundation, project no. 19-77-00019.

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Authors and Affiliations

  1. Institute of Geology and Petroleum Technologies, Kazan Federal University, 420008, Kazan, Russia

    T. R. Zakirov, A. N. Kolchugin, A. A. Galeev & M. G. Khramchenkov

  2. Kazan Branch of Joint Supercomputer Center, Scientific Research Institute of System Analysis, Russian Academy of Sciences, 420111, Kazan, Russia

    M. G. Khramchenkov

Authors
  1. T. R. Zakirov
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  2. A. N. Kolchugin
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  3. A. A. Galeev
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  4. M. G. Khramchenkov
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Corresponding authors

Correspondence to T. R. Zakirov, A. N. Kolchugin, A. A. Galeev or M. G. Khramchenkov.

Additional information

(Submitted by A. M. Elizarov)

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Zakirov, T.R., Kolchugin, A.N., Galeev, A.A. et al. Evaluation of Absolute Permeability in Heterogeneous and Anisotropic Porous Media Using the Lattice Boltzmann Simulations. Lobachevskii J Math 42, 3048–3059 (2021). https://doi.org/10.1134/S1995080221120404

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  • DOI: https://doi.org/10.1134/S1995080221120404

Keywords:

  • absolute permeability
  • heterogeneity
  • anisotropy
  • porous media
  • tortuosity
  • Kozeny–Carman equation
  • lattice Boltzmann equations