Analytical Model of Shale Gas Permeability Based on the Pore Size Distribution from FE-SEM and Image Analysis

Shale matrix permeability is vital to the evaluation of shale petrophysical property. In this study, an analytical model that considers pore size distribution, tortuosity, adsorption, and slippage effects is developed, to calculate the permeability of shale samples. Specifically, field emission scanning electron microscope (FE-SEM), the ImageJ software, and the MATLAB programming and numeric computing environment are employed to experimentally characterize the pore structure and to fit and optimize the pore size distribution. The discrete pore size distributions of organic matter and inorganic matter pores for Longmaxi and Qiongzhusi shale samples are determined based on FE-SEM images. According to the sum of squares error (SSE), coefficient of determination (R2), root-mean-square error (RMSE), and outcome of the fit, the Gaussian 2 correlation function is optimized to fit the continuous pore size distribution. Finally, the permeabilities of five shale rock samples are calculated and compared with the measured results from the Longmaxi and Qiongzhusi Formations. The results illustrate that the multi-term Gaussian fit is more suitable for calculating the permeability of samples with multimodal pore size distributions than the multi-segment Gaussian fit. The calculated results from the pore size distribution are more accuracy than those from the representative mean pore radius. The influence of pore size distribution on permeability and how seepage mechanisms in different pore sizes work together to represent permeability changes at the core scale will be investigated in the future. The study provides a more reliable calculation of the shale matrix permeability compared to previous methods.