Study of the Pore Structure Effect on Seepage in Coal Reservoirs Based on Multifractal Analysis

Coalbed methane is vital for the transition toward low-carbon energy systems, yet its recovery efficiency is critically limited by inaccurate classification of movable water during drainage and depressurization due to the complex pore–fracture system. To understand the influence of the pore–fracture structure on water flow law in coal reservoirs, this study constructed the relationship based on the memory effect of multiscale complex pore–fracture structures on seepage. Nuclear magnetic resonance (NMR) measurements were performed on water-saturated coal samples both before and after centrifugation, enabling the experimental identification of absolute irreducible water, partial movable water, and absolute movable water and yielding dual cutoffs. The complexity of the pore–fracture structure of the samples was quantified by multifractal analysis of the NMR test results. A fractional derivative model was developed to determine dual cutoffs, T2c1 and T2c2, based on the memory effect and validated against experimental data. Compared to empirical models, the proposed fractional derivative model improves R2 fitting accuracy by 4.2% for T2c1 and 9.7% for T2c2, demonstrating its superior capability in translating structural complexity into physically meaningful cutoff determination. This work provides a mechanism-based approach for water typing, presenting a reliable foundation for drainage and depressurization in coalbed methane reservoir.