Micro-pore structures are an essential factor for the electrical properties of porous rock. Theoretical electrical conductivity models considering pore structure can highly improve the accuracy of reservoir estimation. In this study, a pore structure characterization method based on a multi-fractal theory using capillary pressure is developed. Next, a theoretical electrical conductivity equation is derived based on the new pore structure characterization method. Furthermore, a distinct interrelationship between fractal dimensions of capillary pressure curves ($D_v$) and of resistivity index curves (${\mathrm{D}}_t$ and ${\mathrm{D}}_r$) is obtained. The experimental data of 7 sandstone samples verify that the fitting result by the new pore structure characterization method is highly identical to the experimental capillary pressure curves, and the accuracy of the improved rock resistivity model is higher than the Archie model. In addition, capillary pressure curves can be directly converted to resistivity index curves according to the relationship model between fractal dimensions of capillary pressure curves ($D_v$) and resistivity index curves (${\mathrm{D}}_t$ and ${\mathrm{D}}_r$). This study provides new ideas to improve the accuracy of pore structure characterization and oil saturation calculation; it has good application prospects and guiding significance in reservoir evaluation and rock physical characteristics research.

Estimation of oil saturation in low-resistivity-contrast reservoirs using resistivity-log analysis is an inherently challenging process. However, nuclear magnetic resonance (NMR) logging is less sensitive to formation-water salinity and rock matrix variations when predicting fluid properties. Integrating a greater volume of well logging data to effectively address the issue of reservoir parameter calculation represents the trend of big data development. This feature allows NMR logging to have significant advantages over conventional resistivity-based methods in evaluating low-resistivity-contrast reservoirs. The proposed method of estimating oil saturation integrates both NMR and resistivity logging data through two key steps. First, the oil saturation of the invaded zone is estimated using an NMR-based oil saturation model, which has been validated through experimental NMR data obtained from oil-bearing rock samples. Second, the oil saturation of the uninvaded zone is derived by inverting a resistivity-based oil saturation model. Based on analyses of the experimental data and thin sections, the primary reason for low resistivity-contrast in the study area is attributed to the presence of montmorillonite and illite–montmorillonite mixed-layer minerals. The application results demonstrate that the oil saturation calculated using this new method aligns well with both experimental measurements and production test data. Compared to the Archie model that is normally applied in resistivity-contrast reservoirs, the proposed method shows improved accuracy, indicating its effectiveness for such reservoir evaluations.

The pore structure of sandstone reservoir, primarily influenced by depositional parameters and diagenetic features, is crucial for petroleum engineering and petrophysics. Core analysis shows that samples from different sedimentary micro-facies can be grouped into distinct areas on a cross-plot of porosity versus permeability, and submerged distributary channels facies have the best pore structure, followed by river mouth bars facies, distal bar/blanket sand facies, and bay facies. In order to quantitatively characterize the influence of sedimentary microfacies and diagenesis on pore structure, seepage factor f (slope of the line through (\(\phi\), \({\text{Log}}_{10}\left(K\right)\)) and (\({\phi }_{max}\), \({\text{Log}}_{10}\left({K}_{max}\right)\)) on porosity–permeability cross-plot) and diagenetic indictor C_d (relative value of f value to the center of the f range) are introduced to quantitatively characterize the effects of sedimentary micro-facies and diagenesis on pore structure, respectively. Results show that the smaller the f value, the more favorable the sedimentary micro-facies are to reservoir pore structure. And within a specific distribution range centered on f, the larger the C_d value, the more favorable the diagenesis is to reservoir pore structure. Application results are consistent with petrographic features from core analysis, which indicates that the method is effective. This method provides a quantitative characterization method of the mapping relationship between macroscopic geological and microscopic pore structure, and can be effectively applied to reservoir analysis and pore structure characterization.

Resistivity is a key parameter in shale reservoir characterization. Diverse micro-pore types and complex conduction mechanisms in shale result in poor accuracy when applying existed conductivity models. Establishing a high-precision conductivity response model requires comprehensive consideration of the pore structure and clay-bound water conduction. The primary novelty of this work lies in replacing macroscopic empirical fitting parameters with a mechanistic, multi-dimensional fractal framework. We develop a novel conductivity response characterization model that explicitly couples multi-dimensional fractal pore structure theory with clay-bound water conduction. Experimental data verification demonstrates the new model’s superior characterization accuracy. Results indicate three distinct zones in the shale conductivity-pore water conductivity relationship: a nonlinear zone, a transition zone, and a linear zone. A higher cation exchange rate on clay surfaces leads to an increase in the nonlinear characteristics of the conductivity for both the shale and the pore water in low-salinity regions. An increase in the values of the conduction path fractal dimension, pore morphology fractal dimension, and pore fractal dimension all contribute to reduced shale conductivity. While sharing clay-induced conductivity terms with conventional dual-water and shale volume models, the new model offers advantages in operational simplicity and parameter accessibility. This research provides a physically rigorous and highly accessible approach for conductivity-based reservoir parameter calculation, offering new technical perspectives for complex shale oil/gas evaluation.