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A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach

Author

Listed:
  • Gang Lei

    (College Petroleum of Engineering & Geoscience, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Nai Cao

    (College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China)

  • Di Liu

    (School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 100083, China)

  • Huijie Wang

    (College of Engineering, Peking University, Beijing 100871, China)

Abstract

Prediction of the non-linear flow in porous media is still a major scientific and engineering challenge, despite major technological advances in both theoretical and computational thermodynamics in the past two decades. Specifically, essential controls on non-linear flow in porous media are not yet definitive. The principal aim of this paper is to develop a meaningful and reasonable quantitative model that manifests the most important fundamental controls on low velocity non-linear flow. By coupling a new derivative with fractional order, referred to conformable derivative, Swartzendruber equation and modified Hertzian contact theory as well as fractal geometry theory, a flow velocity model for porous media is proposed to improve the modeling of Non-linear flow in porous media. Predictions using the proposed model agree well with available experimental data. Salient results presented here include (1) the flow velocity decreases as effective stress increases; (2) rock types of “softer” mechanical properties may exhibit lower flow velocity; (3) flow velocity increases with the rougher pore surfaces and rock elastic modulus. In general, the proposed model illustrates mechanisms that affect non-linear flow behavior in porous media.

Suggested Citation

  • Gang Lei & Nai Cao & Di Liu & Huijie Wang, 2018. "A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach," Energies, MDPI, vol. 11(11), pages 1-11, November.
  • Handle: RePEc:gam:jeners:v:11:y:2018:i:11:p:2986-:d:179851
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    Citations

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    Cited by:

    1. Penghui Su & Zhaohui Xia & Ping Wang & Wei Ding & Yunpeng Hu & Wenqi Zhang & Yujie Peng, 2019. "Fractal and Multifractal Analysis of Pore Size Distribution in Low Permeability Reservoirs Based on Mercury Intrusion Porosimetry," Energies, MDPI, vol. 12(7), pages 1-15, April.
    2. Jianchao Cai & Zhien Zhang & Qinjun Kang & Harpreet Singh, 2019. "Recent Advances in Flow and Transport Properties of Unconventional Reservoirs," Energies, MDPI, vol. 12(10), pages 1-5, May.
    3. Lijun Gao & Yunze Li & Huijuan Xu & Xin Zhang & Man Yuan & Xianwen Ning, 2019. "Numerical Investigation on Heat-Transfer and Hydromechanical Performance inside Contaminant-Insensitive Sublimators under a Vacuum Environment for Spacecraft Applications," Energies, MDPI, vol. 12(23), pages 1-21, November.

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