The current studies primarily analyze the heterogeneity and complexity of mesopore structures based on low-temperature nitrogen (N₂) adsorption curves and the Frenkel–Halsey–Hill (FHH) fractal model. However, these studies ignore the fact that the low-temperature N₂ desorption curve can also reflect the desorption performance of the mesopore structure. In this research, novel fractal indicators for characterizing the adsorption–desorption performance of mesopores based on the fractal dimension from the N₂ adsorption curves and N₂ desorption curves are proposed. The novel fractal indicators I₁ and I₂ are applied to evaluate the adsorption–desorption performance of mesopores with pore size 2–5 nm and pore size 5–50 nm, respectively. The fractal indicator I₁ shows an increasing trend with coalification, reflecting that the gas adsorption performance of 2–5 nm mesopores is enhanced with coalification. The fractal indicator I₂ exhibits a trend of first increasing and then decreasing with coalification, indicating the gas desorption performance of mesopores with pore size 5–50 nm decreases first and then increases. The proposed indicators provide novel analytical parameters for further understanding the gas adsorption–desorption mechanism of porous coal-based or carbon-based materials.

To analyze the transformed effect of three-dimensional (3D) fracture in coal by CO₂ phase transition fracturing (CO₂-PTF), the CO₂-PTF experiment under a fracturing pressure of 185 MPa was carried out. Computed Tomography (CT) scanning and fractal theory were used to analyze the 3D fracture structure parameters. The fractal evolution characteristics of the 3D fractures in coal induced by CO₂-PTF were analyzed. The results indicate that the CO₂ phase transition fracturing coal has the fracture generation effect and fracture expansion-transformation effect, causing the maximum fracture length, fracture number, fracture volume and fracture surface area to be increased by 71.25%, 161.94%, 3970.88% and 1330.03%. The fractal dimension (D_N) for fracture number increases from 2.3523 to 2.3668, and the fractal dimension (D_V) for fracture volume increases from 2.8440 to 2.9040. The early dynamic high-pressure gas jet stage of CO₂-PTF coal influences the fracture generation effect and promotes the generation of 3D fractures with a length greater than 140 μm. The subsequent quasi-static high-pressure gas stage influences the fracture expansion-transformation effect, which promotes the expansion transformation of 3D fractures with a length of less than 140 μm. The 140 μm is the critical value for the fracture expansion-transformation effect and fracture generation effect. Five indicators are proposed to evaluate the 3D fracture evolution in coal caused by CO₂-PTF, which can provide theoretical and methodological references for the study of fracture evolution characteristics of other unconventional natural gas reservoirs and their reservoir stimulation.