Quantitative Analysis of Multi-Angle Correlation Between Fractal Dimension of Anthracite Surface and Its Coal Quality Indicators in Different Regions

The nanoporous structure of coal is crucial for the occurrence and development of coalbed methane (CBM). This study, leveraging the combined characterization of atomic force microscopy (AFM) and Gwyddion software (v2.62), investigated six anthracite samples with varying degrees of metamorphism (Ro = 2.11–3.36%). It revealed the intrinsic relationships between their nanoporous structures, surface morphologies, fractal characteristics, and coalification processes. The research found that as Ro increases, the surface relief of coal decreases significantly, with pore structures evolving from being macropore-dominated to micropore-enriched, and the surface tending towards smoothness. Surface roughness parameters (Ra, Rq) exhibit a negative correlation with Ro. Quantitative data indicate that area porosity, pore count, and shape factor positively correlate with metamorphic grade, while mean pore diameter negatively correlates with it. The fractal dimensions calculated using the variance partition method, cube-counting method, triangular prism measurement method, and power spectrum method all show nonlinear correlations with Ro, moisture (Mad), ash content (Aad), and volatile matter (Vdaf). Among these, the fractal dimension obtained by the triangular prism measurement method has the highest correlation with Ro, Aad, and Vdaf, while the variance partition method shows the highest correlation with Mad. This study clarifies the regulatory mechanisms of coalification on the evolution of nanoporous structures and surface properties, providing a crucial theoretical foundation for the precise evaluation and efficient exploitation strategies of CBM reservoirs.