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A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

Author

Listed:
  • X.-H. Tan

    (State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum University, Chengdu 610500, P. R. China)

  • C.-Y. Liu

    (State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum University, Chengdu 610500, P. R. China)

  • X.-P. Li

    (State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum University, Chengdu 610500, P. R. China)

  • H.-Q. Wang

    (#x2020;CNPC Southwest Oil and Gas Field Exploration and Development Research Institute 610041, P. R. China)

  • H. Deng

    (#x2020;CNPC Southwest Oil and Gas Field Exploration and Development Research Institute 610041, P. R. China)

Abstract

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster DcTσ become bigger with an increase of stress. However, the pore fractal dimension of solid cluster Dcfσ and capillary bundle Dpfσ remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

Suggested Citation

  • X.-H. Tan & C.-Y. Liu & X.-P. Li & H.-Q. Wang & H. Deng, 2018. "A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(02), pages 1-12, February.
    • Handle: RePEc:wsi:ijmpcx:v:29:y:2018:i:02:n:s0129183118500195
    DOI: 10.1142/S0129183118500195
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    Cited by:

    1. You, Xu-Tao & Liu, Jian-Yi & Jia, Chun-Sheng & Li, Jun & Liao, Xin-Yi & Zheng, Ai-Wei, 2019. "Production data analysis of shale gas using fractal model and fuzzy theory: Evaluating fracturing heterogeneity," Applied Energy, Elsevier, vol. 250(C), pages 1246-1259.
    2. Yilong Li & Hao Yang & Xiaoping Li & Mingqing Kui & Jiqiang Zhang, 2022. "Experiments on Water-Gas Flow Characteristics under Reservoir Condition in a Sandstone Gas Reservoir," Energies, MDPI, vol. 16(1), pages 1-17, December.

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