Pore space of tight sandstone samples exhibits fractal characteristics. Nuclear magnetic resonance is an effective method for pore size characterization. This paper focuses on fractal characteristics of pore size from nuclear magnetic resonance (NMR) of tight sandstone samples. The relationship between the fractal dimension from NMR with pore structure and water saturation is parameterized by analyzing experimental data. Based on it, a pore structure characterization and classification method for water-saturated tight sandstone and a water saturation prediction method in a gas-bearing sandstone reservoir have been proposed. To verify the models, the fractal dimension from NMR of 19 tight sandstone samples selected from the gas-bearing tight sandstone reservoir of Shahejie Formation in Nanpu Sag and that of 16 of them under different water saturation states are analyzed. The application result of new methods in the gas-bearing tight sandstone reservoir of Shahejie Formation in Nanpu Sag shows consistency with experimental data. This paper has facilitated the development of the NMR application by providing a non-electrical logging idea in reservoir quality evaluation and water saturation prediction. It provides a valuable scientific resource for reservoir engineering and petrophysics of unconventional reservoir types, such as tight sandstone, low porosity, and low permeability sandstone, shale, and carbonate rock reservoirs.

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.

The nuclear magnetic resonance (NMR) estimate of permeability is a fundamental method that has numerous applications in reservoir engineering and petrophysics. To improve the accuracy of the NMR-based permeability model, many variables are introduced into NMR-based permeability prediction models due to geometric complexity and pore structure heterogeneity. In this paper, two pore structure characterization methods are investigated based on the Kozeny-Carman model and equivalent component model. Furthermore, an NMR-based permeability model accounting for the effect of pore structure is developed based on the analysis of the relationship between two pore structure parameters, and it is applied to practically predict permeability. Results indicate that the new model-calculated permeability has good agreement with experimental data; moreover, the adaptability of the new NMR-based permeability prediction model is highly improved through reducing undetermined variables, and key parameters can be measured directly using NMR. The new model provides a valuable scientific resource and assists in the evaluation of hydrocarbon-bearing reservoirs with complex pore structure, such as tight sandstone, shale, and carbonate rock.