Multifractal Analysis in Characterizing Adsorption Pore Heterogeneity of Middle- and High-Rank Coal Reservoirs

Nanopore heterogeneity has a significant effect on adsorption, desorption, and diffusion processes of coalbed methane. The adsorption pore size distribution heterogeneity was calculated by combining N₂ with CO₂ adsorption data, and factors affecting multifractal and single-fractal dimensions were studied. The results indicate that pore size distribution of micropores (with pore diameters smaller than 2 nm) and meso-macro-pores (with pore diameters between 2 and 100 nm) in coal samples exhibit typical multifractal behavior. The overall heterogeneity of micropores in high-rank coal samples is higher than that in the middle-rank coal samples. The low-probability measure areas control the overall heterogeneity of pores with diameters of 0.40-1.50 nm. The high-probability measure area heterogeneity and spectral width ratio have a higher linear correlation with coal rank and pore structure parameters than those of low-probability measure areas. Heterogeneity of high-probability measure areas and overall pore size distribution are controlled by pores with diameters of 0.72-0.94 nm. Multifractal parameters of meso-macro-pores have no clear relationship with coal rank. The pore volume of 2-10 nm diameter shows a good linear correlation with heterogeneity of low-probability measure areas, and pores of this diameter range are the key interval that affected pore size distribution heterogeneity. The single-fractal dimension obtained using the Frenkel-Halsey-Hill (FHH) model shows a positive linear correlation with heterogeneity of the low-probability measure areas. It indicates that this parameter can effectively characterize the pore size distribution heterogeneity of low-probability measure areas in meso-macro-pores.