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A FRACTAL ELECTRICAL CONDUCTIVITY MODEL FOR WATER-SATURATED TREE-LIKE BRANCHING NETWORK

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

E-mail Address: xiaoboqi2006@126.com

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YIDAN ZHANG

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

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HUAN ZHOU

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

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SHAOFU LI

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

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YANBIN WANG

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

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, and

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

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https://doi.org/10.1142/S0218348X23500755Cited by:16 (Source: Crossref)

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 ( $α$ , $β$ , $N$ , $m$ , $d_{0}$ , $l_{0}$ , $D_{d}$ , $D_{l})$ in tree-like branching network on the resistance, conductivity and formation factor. The results show that the total resistance $R$ is proportional to $l_{0}$ , $α$ , and inversely proportional to $d_{0}$ , $β$ . 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.

Keywords:

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