Capillary-Controlled Multistage Imbibition in Heterogeneous Porous Media: Insights from Nuclear Magnetic Resonance-Guided Pressure Inversion

Abstract Microscale characterization of spontaneous imbibition mechanisms is essential for improving the underground hydrogen storage efficiency and coal seam gas recovery. In this study, low-field nuclear magnetic resonance technology was employed to investigate dynamic water transport during coal imbibition through thermodynamic and temporal analyses of T2 spectra evolution. A coupled adsorption-kinetic and multistage seepage model was developed to describe the imbibition process. Anomalous imbibition coefficient behaviors were revealed, with pore structure impacts and engineering applications being systematically discussed. The results show that imbibition kinetics are governed by a dynamic capillary-viscous equilibrium, while water adsorption follows dual-process pseudo-first-order kinetics. The imbibition curves exhibit either two-stage (piston diffusion) or three-stage (single-tube piston diffusion) patterns, characterized by distinct temporal exponents (n). Specifically, the process involves preferential flow through dominant pathways (n = 1), pressure-driven piston-like even filling of accessible pores (n = 0.5), and diffusion-based saturation of micropores (n = 0.2). The capillary pressure can be derived from the intercept of the piston-like stage. Anomalous high imbibition coefficients (R > 1) are attributed to pore connectivity. From an engineering perspective, low-pressure injection at controlled critical rates is recommended for coals exhibiting three-stage imbibition to prevent water channeling, while preemptive modification of capillary properties is necessary for two-stage coals to mitigate water-blocking effects.