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PREDICTING THE ELECTRICAL CONDUCTIVITY OF DUAL-POROSITY MEDIA WITH FRACTAL THEORY

HUAIZHI ZHU

https://orcid.org/0009-0002-0483-9535

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

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JUN GAO

https://orcid.org/0009-0002-7180-7234

School of Mechanical and Electrical Engineering, Wuhan Business University, Wuhan 430056, P. R. China

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BOQI XIAO

https://orcid.org/0000-0001-7243-1676

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

Corresponding author.

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YIDAN ZHANG

https://orcid.org/0009-0008-4840-4908

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

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YANBIN WANG

https://orcid.org/0009-0004-4701-2778

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

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PEILONG WANG

https://orcid.org/0009-0005-6839-2826

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

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BILIANG TU

https://orcid.org/0009-0009-1458-1604

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

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, and

GONGBO LONG

https://orcid.org/0000-0001-6815-7045

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/S0218348X23501311Cited by:7 (Source: Crossref)

Abstract

The microspatial structure of porous media affects the electrical properties of reservoir rocks significantly. In this work, a dual-porosity model is established to investigate the electrical properties of porous media, in which tree-like networks and capillary channels represent fractures and pores. By using fractal theory, we established an analytical equation for the conductivity of water-saturated dual-porosity media. The analytical equation, devoid of any empirical constants, expresses the electrical properties of the porous media as a function of some structural parameters ( $D_{g}$ $D_{g}$ , $D_{f}$ $D_{f}$ , $D_{τ}$ $D_{τ}$ , $α$ $α$ , $β$ $β$ , $m$ $m$ , $N$ $N$ , $𝜃$ $𝜃$ , $\partial$ $\partial$ , $Γ$ $Γ$ , $l_{0}$ $l_{0}$ , $d_{0})$ $d_{0})$ . We also examine the impact of various matrix structural parameters on conductivity. It is found that increasing the length of mother channel ( $l_{0})$ $l_{0})$ , length ratio ( $α)$ $α)$ , the number of branching layers ( $m)$ $m)$ , and tortuosity fractal dimension ( $D_{τ})$ $D_{τ})$ leads to a decrease in conductivity, whereas increasing the diameter of mother channel ( $d_{0})$ $d_{0})$ , diameter ratio ( $β)$ $β)$ , the cross-sectional porosity ( $φ_{g}$ $φ_{g}$ , $φ_{f})$ $φ_{f})$ , and the channel bifurcation number ( $N)$ $N)$ enhances conductivity. Furthermore, we validated this analytical model by comparing it with the experimental data available, and the results demonstrate good agreement. This research has proposed an advanced conductivity model that enables us to better understand the underlying physical mechanisms of the electrical properties in porous media.

Keywords:

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