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An analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks

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  • Xu, Peng
  • Yu, Boming
  • Qiu, Shuxia
  • Cai, Jianchao

Abstract

In this paper, an analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks is presented. A dual-domain model is applied to simulate the heterogeneous porous media embedded with a constructal tree network based on the fractal distribution of pore space and tortuosity nature of flow paths. The analytical expressions for seepage velocity, pressure drop, local and global permeability of the network and binary system are derived, and the transport properties for the optimal branching structure are discussed. Notable is that the global permeability (Kn) of the network and the volume fraction (fn) occupied by the network exhibit linear scaling law with the fractal dimension (Dp) of channel diameter bylogKn∼0.46Dp and logfn∼1.03Dp, respectively. Our analytical results are in good agreement with the available numerical results for steady-state soil vapor extraction and indicate that the fractal dimension for pore space has significant effect on the permeable properties of the media. The proposed dual-domain model may capture the characteristics of heterogeneous porous media and help understanding the transport mechanisms of the radial flow in the media.

Suggested Citation

  • Xu, Peng & Yu, Boming & Qiu, Shuxia & Cai, Jianchao, 2008. "An analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6471-6483.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:26:p:6471-6483
    DOI: 10.1016/j.physa.2008.08.021
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    Cited by:

    1. Agson-Gani, Putra H. & Zueter, Ahmad F. & Xu, Minghan & Ghoreishi-Madiseh, Seyed Ali & Kurnia, Jundika C. & Sasmito, Agus P., 2022. "Thermal and hydraulic analysis of a novel double-pipe geothermal heat exchanger with a controlled fractured zone at the well bottom," Applied Energy, Elsevier, vol. 310(C).
    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.

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