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

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 ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. We also examine the impact of various matrix structural parameters on conductivity. It is found that increasing the length of mother channel ([Formula: see text], length ratio ([Formula: see text], the number of branching layers ([Formula: see text], and tortuosity fractal dimension ([Formula: see text] leads to a decrease in conductivity, whereas increasing the diameter of mother channel ([Formula: see text], diameter ratio ([Formula: see text], the cross-sectional porosity ([Formula: see text], [Formula: see text], and the channel bifurcation number ([Formula: see text] 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.