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Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

Author

Listed:
  • Qiang Wang

    (State Key Laboratory of Oil-Gas Reservoir Geology & Exploitation, Southwest Petroleum University, Chengdu 610500, China)

  • Yongquan Hu

    (State Key Laboratory of Oil-Gas Reservoir Geology & Exploitation, Southwest Petroleum University, Chengdu 610500, China)

  • Jinzhou Zhao

    (State Key Laboratory of Oil-Gas Reservoir Geology & Exploitation, Southwest Petroleum University, Chengdu 610500, China)

  • Lan Ren

    (State Key Laboratory of Oil-Gas Reservoir Geology & Exploitation, Southwest Petroleum University, Chengdu 610500, China)

  • Chaoneng Zhao

    (State Key Laboratory of Oil-Gas Reservoir Geology & Exploitation, Southwest Petroleum University, Chengdu 610500, China)

  • Jin Zhao

    (State Key Laboratory of Oil-Gas Reservoir Geology & Exploitation, Southwest Petroleum University, Chengdu 610500, China)

Abstract

Based on fractal geometry theory, the Hagen–Poiseuille law, and the Langmuir adsorption law, this paper established a mathematical model of gas flow in nano-pores of shale, and deduced a new shale apparent permeability model. This model considers such flow mechanisms as pore size distribution, tortuosity, slippage effect, Knudsen diffusion, and surface extension of shale matrix. This model is closely related to the pore structure and size parameters of shale, and can better reflect the distribution characteristics of nano-pores in shale. The correctness of the model is verified by comparison with the classical experimental data. Finally, the influences of pressure, temperature, integral shape dimension of pore surface and tortuous fractal dimension on apparent permeability, slip flow, Knudsen diffusion and surface diffusion of shale gas transport mechanism on shale gas transport capacity are analyzed, and gas transport behaviors and rules in multi-scale shale pores are revealed. The proposed model is conducive to a more profound and clear understanding of the flow mechanism of shale gas nanopores.

Suggested Citation

  • Qiang Wang & Yongquan Hu & Jinzhou Zhao & Lan Ren & Chaoneng Zhao & Jin Zhao, 2019. "Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory," Energies, MDPI, vol. 12(17), pages 1-18, September.
    • Handle: RePEc:gam:jeners:v:12:y:2019:i:17:p:3381-:d:263273
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    Citations

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    Cited by:

    1. Xiaoqi Wang & Yanming Zhu & Yang Wang, 2020. "Fractal Characteristics of Micro- and Mesopores in the Longmaxi Shale," Energies, MDPI, vol. 13(6), pages 1-21, March.
    2. Mehrdad Massoudi, 2020. "Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications," Energies, MDPI, vol. 13(6), pages 1-4, March.
    3. Yongquan Hu & Qiang Wang & Jinzhou Zhao & Shouchang Xie & Hong Jiang, 2020. "A Novel Porous Media Permeability Model Based on Fractal Theory and Ideal Particle Pore-Space Geometry Assumption," Energies, MDPI, vol. 13(3), pages 1-17, January.

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