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Article

Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

by
Qiang Wang
,
Yongquan Hu
,
Jinzhou Zhao
*,
Lan Ren
,
Chaoneng Zhao
and
Jin Zhao
State Key Laboratory of Oil-Gas Reservoir Geology & Exploitation, Southwest Petroleum University, Chengdu 610500, China
*
Author to whom correspondence should be addressed.
Energies 2019, 12(17), 3381; https://doi.org/10.3390/en12173381
Submission received: 4 August 2019 / Revised: 21 August 2019 / Accepted: 27 August 2019 / Published: 2 September 2019
(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)
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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.
Keywords: fractal; slippage effect; Knudsen diffusion; surface diffusion; apparent permeability fractal; slippage effect; Knudsen diffusion; surface diffusion; apparent permeability
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MDPI and ACS Style

Wang, Q.; Hu, Y.; Zhao, J.; Ren, L.; Zhao, C.; Zhao, J. Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory. Energies 2019, 12, 3381. https://doi.org/10.3390/en12173381

AMA Style

Wang Q, Hu Y, Zhao J, Ren L, Zhao C, Zhao J. Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory. Energies. 2019; 12(17):3381. https://doi.org/10.3390/en12173381

Chicago/Turabian Style

Wang, Qiang, Yongquan Hu, Jinzhou Zhao, Lan Ren, Chaoneng Zhao, and Jin Zhao. 2019. "Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory" Energies 12, no. 17: 3381. https://doi.org/10.3390/en12173381

APA Style

Wang, Q., Hu, Y., Zhao, J., Ren, L., Zhao, C., & Zhao, J. (2019). Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory. Energies, 12(17), 3381. https://doi.org/10.3390/en12173381

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