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Coupling effect of power-law fluid properties and scaled fractal characteristics on flow through fractured media

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  • Zhu, Jianting

Abstract

Non-Newtonian fluid flow through fractured media widely exists in both natural and man-made materials, where fractures have been shown to have self-similar and fractal characteristics. In this study, a new analytical approach is developed to calculate the flowrate of a power-law fluid through fractal fractures, in which fracture trace length follows a fractal distribution and the aperture and trace length are related by a scaled power-law function. The average fracture flowrate in the fractal fractures is obtained through integrating flows in all fractures. The interplay of the power-law properties and fractal characteristic parameters on the flow through the fractal fractures is quantified and discussed. The results demonstrate that the average flowrate decreases with the fractal dimension of fracture length and scaling exponent. The increase in the trace length range ratio leads to the increased flowrate. The power-law index plays a significant role in the flowrate through fractal fractures coupling with the effect of pressure head gradient. The increase in pressure head gradient amplifies the effect of power-law fluid index on the flowrate in fractal fractures.

Suggested Citation

  • Zhu, Jianting, 2020. "Coupling effect of power-law fluid properties and scaled fractal characteristics on flow through fractured media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    • Handle: RePEc:eee:phsmap:v:559:y:2020:i:c:s0378437120305628
    DOI: 10.1016/j.physa.2020.125073
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    References listed on IDEAS

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    1. Xiao-Hua Tan & Xiao-Ping Li & Lie-Hui Zhang & Jian-Yi Liu & Jianchao Cai, 2015. "Analysis of transient flow and starting pressure gradient of power-law fluid in fractal porous media," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(04), pages 1-15.
    2. Zhu, Jianting, 2018. "Effective aperture and orientation of fractal fracture network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 27-37.
    3. Xiao-Hua Tan & Jian-Yi Liu & Jia-Hui Zhao & Xiao-Ping Li & Guang-Dong Zhang & Chuan Tang, 2014. "A Pressure Transient Model for Power-Law Fluids in Porous Media Embedded with a Tree-Shaped Fractal Network," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, February.
    4. Xu, Peng & Yu, Boming & Feng, Yongjin & Liu, Yanjun, 2006. "Analysis of permeability for the fractal-like tree network by parallel and series models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 884-894.
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