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Determining rock resistivity for saturation estimation in reservoirs is challenging due to the complex nature of pores in the rock. This paper aims to establish a computational relationship between formation factors ( F ) and permeability ( K ) by combining theoretical and experimental data. Firstly, the relationship between the permeability of the curved capillary model and formation factors, as well as the relationship between the permeability of the complex curved capillary model and formation factors, are deduced. Theoretical analysis proved that the formation factors( F ) have a power relationship with permeability( K ) and porosity ( φ ), and confirms the existence of additional resistivity ( R x ). To validate the the theoretical study, we conducted model analysis using open experimental data from thirty-five sandstone cores with different porosity and permeability from the tight gas sandstone in the Western U.S. Basins, which measured resistivity data in saline at 20ppm, 40ppm, and 80ppm, respectively. We confirmed the existences of additional resistivity ( R x ) by fitting the relationship between the rock resistivity of saturated formation water ( R o ) and the formation water resistivity ( R w ). We then fitted the formation resistivity change factor ( F d ) with permeability ( K ), the formation resistivity change factor ( F d ) with porosity ( φ ), the additional resistivity ( R x ) with permeability ( K ), and the additional resistivity ( R x ) with porosity ( φ ). Both changeable formation resistivity change factor ( F d ) and additional resistivity ( R x ) showed a strong linear relationship with permeability ( K ) in logarithmic coordinates. We also verified the existence of a suitable equation using available experimental data by changing formation parameters and permeability. The study shows that the fitting equations may be utilized to determine changeable formation resistivity change factor ( F d ), additional resistivity ( R x ), and the rock resistivity of saturated formation water ( R o ) with varying permeability. The predicted rock resistivity of saturated formation water ( R o ) strongly correlates with the one measured in the laboratory, providing better precision for future reservoir evaluation in saturation estimations.

The conductive paths formed by fractures and cave in complex reservoirs differ from those formed by pores and throats in clastic rocks. In this paper, a new formation model based on fractured and caved reservoirs is established, and the electrical characteristics of rocks are analyzed with different pore structures using resistance law to understand their effects on rock resistivity. The ratio of fracture width to cave radius (C e value) and fracture dip are employed to depict pore structure in this model. Our research shows that the electrical characteristics of rocks in fractured and caved reservoirs are strongly affected by pore structure and porous fluid distribution. Although the rock electrical properties associated with simple pore structure agree well with Archie formulae, the relationships between F and or between I and S w , in more complicated pore structures, are nonlinear in double logarithmic coordinates. The parameters in Archie formulae are not constant and they depend on porosity and fluid saturation. Our calculations suggest that the inclined fracture may lead to resistivity anisotropy in the formation. The bigger dip the inclining fracture has, the more anisotropy the formation resistivity has. All of these studies own practical sense for the evaluation of oil saturation using resistivity logging data.

Many cases have indicated that the conductivity and permeability of porous media may decrease to zero at a nonzero percolation porosity instead of zero porosity. However, there is still a lack of a theoretical basis for the percolation mechanisms of the conductivity and permeability. In this paper, the analytical percolation expressions of both conductivity and permeability are derived based on fractal theory by introducing the critical porosity. The percolation models of the conductivity and permeability were found to be closely related to the critical porosity and microstructural parameters. The simulation results demonstrated that the existence of the critical could lead to the non-Archie phenomenon. Meanwhile, the increasing critical porosity could significantly decrease the permeability and the conductivity at low porosity. Besides, the complex microstructure could result in more stagnant pores and a higher critical porosity. This study proves the importance of the critical porosity in accurately evaluating the conductivity and permeability, and reveals the percolation mechanisms of the conductivity and permeability in complex reservoirs. By comparing the predicted conductivity and permeability with the available experimental data, the validity of the proposed percolation models is verified.