Shale pore structure is an important factor in shale adsorption and percolation. To better characterize the pore structure of shales, this paper selects 24 shale core samples for high-pressure mercury intrusion (HPMI) test, and fractal theory and multifractal theory are applied to analyze the pore structures of shale nanopores. The fractal dimensions using different fractal models and the multifractal parameters are calculated from mercury intrusion capillary pressure (MICP). The correlations between fractal/multifractal parameters and shale nanopore structures are analyzed. The study reveals that the fractal dimension calculated from 3D capillary model can be used as an index for evaluating complex of shale nanopores. The fractal dimension increases with the increase of displacement pressure and homogeneity coefficient and decreases with the increase of the permeability and pore-throat radius. The multifractal analysis shows that shale nanopores have multifractal characteristics, and multifractal parameters can reflect the size, concentration, and asymmetry of pore size distribution (PSD). The PSD of shales are similar when they have similar multifractal parameters ($\mathrm{\Delta }\alpha ,\mathrm{\Delta }f,{\alpha }_0,{\alpha }_1,{\alpha }_2$). The information dimension $D_1$ and correlation dimension $D_2$ are positively correlated to the sizes of shale nanopores, and with the decreasing information dimension $D_1$, the pore size distributes more contributed. Besides, the information dimension $D_1$ has a strong and negative correlation with the fractal dimension derived from 3D capillary model.

页岩孔隙结构是页岩吸附和渗滤的重要因素。为了更好地表征页岩的孔隙结构，本文选择了24个页岩岩心样品进行高压压汞试验，并采用分形理论和多重分形理论对页岩纳米孔的孔隙结构进行了分析。使用不同的分形模型和多重分形参数的分形维数由压汞毛细管压力（MICP）计算得出。分形/多重分形参数与页岩纳米孔结构之间的相关性进行了分析。研究表明，从3D毛细管模型计算得到的分形维数可作为评估页岩纳米孔复合物的指标。分形维数随位移压力和均质系数的增加而增加，随渗透率和孔喉半径的增加而减小。多重分形分析表明，页岩纳米孔具有多重分形特征，多重分形参数可以反映孔径分布（PSD）的大小，浓度和不对称性。当页岩的PSD具有相似的多重分形参数时，它们的PSD是相似的（$\mathrm{\Delta }\alpha ，\mathrm{\Delta }F，{\alpha }_0，{\alpha }_{\mathrm{1个}}，{\alpha }_{\mathrm{2个}}$）。信息维度$d_{\mathrm{1个}}$ 和相关维度 $d_{\mathrm{2个}}$ 与页岩纳米孔的大小呈正相关，且与信息维的减小呈正相关 $d_{\mathrm{1个}}$，孔径分布贡献更大。此外，信息维度$d_{\mathrm{1个}}$ 与从3D毛细血管模型得出的分形维数具有强而负的相关性。