Fractal and multifractal characteristics of shale nanopores

Abstract

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 (Δα,Δf,α0,α1,α2). The information dimension D1 and correlation dimension D2 are positively correlated to the sizes of shale nanopores, and with the decreasing information dimension D1, the pore size distributes more contributed. Besides, the information dimension D1 has a strong and negative correlation with the fractal dimension derived from 3D capillary model.