Nanopore Size Distribution Heterogeneity of Organic-Rich Shale Reservoirs Using Multifractal Analysis and Its Influence on Porosity–Permeability Variation

The shale nanopore size (diameter [less than] 100 nm) distribution heterogeneity (SNDH) is one of the important factors affecting gas production. However, quantitative analysis of the SNDH and the applicability of single and multifractal models need to be further studied. Here, based on low-temperature liquid nitrogen and carbon dioxide tests of organic-rich shale in Qinshui Basin, multifractal dimension variation of micropores ([less than] 2 nm) and mesopores (2–100 nm) are studied, and the multifractal factors that affect the distribution of nanopores are determined. Additionally, the differences between single fractal and multifractal results are compared. Based on this, dynamic variation of porosity and permeability under the constraints of the nanopore structure is discussed from the perspective of multifractal variation. The results of this study are as follows: (1) The pore size distribution of micropores and meso–macropores in shale samples exhibit typical multifractal behavior. The overall distribution heterogeneity of meso–macropores is mainly affected by the distribution of pores in the low-value area of pore volume (LAPV), while the overall distribution heterogeneity of micropores is affected by the distribution of the high-value area of the pore volume. The multifractal parameters and influencing factors of micropores and meso–macropores are clearly different. (2) The single fractal dimension D2 calculated using the Frenkel–Halsey–Hill model has a negative correlation with the multifractal parameters, implying that the distribution heterogeneity of the LAPV gradually decreases with the increase of the D2 value, indicating that the physical meaning of the two models is obviously different. (3) The pore distribution heterogeneity affects permeability variation and diffusion process of shale reservoir. With the increase of the multifractal dimension of meso–macropores, the damaging effect of stress on permeability is stronger. The more heterogeneous the micropore size distribution, the smaller is the ″modification effect″ of stress on the diffusion coefficient.