Multifractal Characterization of Pore Heterogeneity and Water Distribution in Medium- and High-Rank Coals via Nuclear Magnetic Resonance

Abstract

Comprehensive assessment of pore structure and multiphase water distribution is critical to the flow and transport process in coalbed methane (CBM) reservoirs. In this study, nuclear magnetic resonance (NMR) and multifractal analysis were integrated to quantify the multiscale heterogeneity of nine medium- and high-rank coals under water-saturated and dry conditions. By applying the box-counting method to transverse relaxation time (T2) spectra, multifractal parameters were derived to characterize pore heterogeneity and residual water distribution. The influencing factors of pore heterogeneity were also discussed. The results show that pore structures in high-rank coals (HCs) exhibit a broader multifractal spectrum and stronger rightward spectrum than those of medium-rank coals, reflecting micropore-dominated heterogeneity and the complexity induced by aromatization in HCs. The vitrinite content enhances micropore development, increasing the heterogeneity and complexity of pore structure and residual water distribution. Inertinite content shows opposite trends compared to vitrinite content for the effect on pore structure and water distribution. Volatile yield reflects coal metamorphism and thermal maturity, which inversely correlates with pore heterogeneity and complexity. Residual water mainly distributes to adsorption pores and pore throats, shortening T2 relaxation (bound water effect) and reducing spectral asymmetry. The equivalence of the multifractal dimension and singularity spectrum validates their joint utility in characterizing pore structure. Minerals enhance pore connectivity but suppress complexity, while moisture and ash contents show negligible impacts. These findings provide a theoretical reference for CBM exploration, especially in optimizing fluid transportation and CBM production strategies and identifying CBM sweet spots.

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