Study of multifractal characteristics and gas migration law in gas-bearing coal microstructure using nuclear magnetic resonance

Understanding the adsorption and desorption characteristics of methane in coal-based porous media is critical for advancing coalbed methane resource development. In the context of the later stages of coalbed methane extraction, this study employs a nuclear magnetic resonance experimental system to investigate the adsorption and desorption behaviors of methane in coal under varying adsorption pressures. The structural characteristics of coal and the corresponding T2 spectrum curves of methane adsorption and desorption were obtained under different pressures. Multifractal analysis of the T2 spectra was conducted to derive the generalized fractal dimension spectrum and the multifractal singularity spectrum, characterizing the methane distribution across different spatial scales. This analysis enabled the quantitative evaluation of the multifractal characteristics of methane distribution and the dynamic response of various parameters during adsorption and desorption processes. The results indicate that methane adsorption in coal is primarily governed by micropores and small pores smaller than 0.1 μm, which account for over 90% of the total adsorption capacity. The adsorption behavior follows the Langmuir model. In contrast, in medium and large pores (> 0.1 μm), methane exists predominantly in a free state, and adsorption capacity increases linearly with pressure. Multifractal analysis further reveals that increasing adsorption pressure reduces the uniformity of methane distribution (Δα decreases by 17.48%–28.03%), and the dense adsorption layer within micropores and small pores significantly inhibits gas migration from larger pores. Thus, elucidating the mechanisms behind the low desorption efficiency during the late stage of coalbed methane production offers a theoretical foundation for enhancing coalbed methane recovery.