Estimating Additional Resistivity by Permeability in Brine Saturated Sandstones

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.