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A Fractal Electrical Conductivity Model For Water-Saturated Tree-Like Branching Network

Author

Listed:
  • HUAIZHI ZHU

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • BOQI XIAO

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China†Hubei Provincial Key Laboratory of Chemical Equipment Intensification and Intrinsic Safety, School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China‡Hubei Provincial Engineering Technology Research, Center of Green Chemical Equipment, School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • YIDAN ZHANG

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • HUAN ZHOU

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • SHAOFU LI

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • YANBIN WANG

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

  • GONGBO LONG

    (School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China†Hubei Provincial Key Laboratory of Chemical Equipment Intensification and Intrinsic Safety, School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China‡Hubei Provincial Engineering Technology Research, Center of Green Chemical Equipment, School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, P. R. China)

Abstract

Electrical conductivity is an important physical property of porous media, and has great significance to rock physics and reservoir engineering. In this work, a conductivity model including pore water conductivity and surface conductivity is derived for water-saturated tree-like branching network. In addition, combined with Archie’s law, a general analytical formula for the formation factor is presented. Through the numerical simulation of the analytical formula above, we discuss the impact of some structural parameters (α, β, N, m, d0, l0, Dd, Dl) in tree-like branching network on the resistance, conductivity and formation factor. The results show that the total resistance R is proportional to l0, α, and inversely proportional to d0, β. The relation between conductivity and porosity in this model is contrasted with previous models and experimental data, and the results show considerable consistency at lower porosity. It is worth noting that when α = 0, the conductivity and porosity curve of this model overlap exactly with those plotted by the parallel model. The fractal conductance model proposed in this work reveals the operation of the current in the tree-like branching network more comprehensively.

Suggested Citation

  • Huaizhi Zhu & Boqi Xiao & Yidan Zhang & Huan Zhou & Shaofu Li & Yanbin Wang & Gongbo Long, 2023. "A Fractal Electrical Conductivity Model For Water-Saturated Tree-Like Branching Network," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-12.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:07:n:s0218348x23500755
    DOI: 10.1142/S0218348X23500755
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