Method Selection for Analyzing the Mesopore Structure of Shale—Using a Combination of Multifractal Theory and Low-Pressure Gas Adsorption

Nitrogen adsorption experiments have been extensively applied to shale pore structure research and evaluation. The pore structure can be quantitatively characterized in accordance with the nitrogen adsorption–desorption isotherm using various calculation models, whereas the results obtained using different models can more effectively indicate the pore characteristics of shale remains unclear. Further, there has not been any unified process in the optimization of calculation models for pore size distribution (PSD). In this study, the Barret–Joyner–Halenda adsorption (BJH-AD) and BJH desorption (BJH-DE) models were used with Longmaxi Formation shale as an example. Subsequently, the density functional theory (DFT) calculations were conducted on different shale lithofacies samples. Next, the pore structure parameters and heterogeneity obtained using different models were compared, and the consistency parameters of different models were obtained in accordance with Cronbach’s alpha. The results indicated that the pore structure parameters obtained using the BJH-AD model were underestimated since the macroscopic thermodynamic theory was not applicable to this study. The DFT model showed multiple peaks in the range of 1–10 nm, whereas the BJH-DE model had a significant artificial peak in the range of 3.8 nm due to the tensile strength effect, thus suggesting that the DFT model is more capable of characterizing the pores with a pore size 10 nm lower than the BJH model. The PSD curves generated using the three models exhibited multifractal characteristics, whereas the results of the heterogeneity achieved using different models were different. Moreover, the consistency of the results of different models can be studied in depth by combining Cronbach’s alpha with various heterogeneity parameters. The DFT model exhibited high consistency in pore structure parameters and pore heterogeneity, thus suggesting that the DFT method of N 2 is the optimal physical adsorption data analysis method in the shale mesoporous range. Accordingly, the nitrogen adsorption curve, the hysteresis loop shape, multifractal parameters, and Cronbach’s alpha were integrated to generate a working flow chart of the nitrogen adsorption model for N 2 -adsorption-model optimization.