Study on Methane Diffusion Characteristics and Lost Methane Estimation Model for Coals with Different Structures Based on Tortuosity

Coal seam methane content is a key predictive indicator for coal and gas outbursts, but its accuracy is compromised by methane diffusion behavior arising from pore structure differences among coals with different structural types. Existing models fail to accurately estimate the lost methane amount for coals with different structures, leading to unreliable outburst prediction. In this work, four coal samples with different degrees of destruction were selected. Both low-temperature liquid nitrogen adsorption experiments and methane desorption tests under various adsorption equilibrium pressures were carried out. The applicability of the unipore, bidisperse, and time-dependent diffusion models was compared. Based on tortuosity, the relationship between pore structure and methane diffusion capacity was quantitatively analyzed, the actual methane diffusion distance was obtained, and then a lost methane estimation model accounting for tortuosity (τ-STDM) was established. The results show that with increasing degree of coal destruction, the proportions of micropores and small pores increase while the macropore proportion decreases, and both total pore volume and total specific surface area increase. The desorption ratio and the effective diffusion coefficient D e both increase, and D e exhibits a linear increase with pressure. The time-dependent diffusion model achieves the highest fitting accuracy and accurately describes the dynamic process of methane release from rapid initial escape to slow later-stage release. Methane diffusion behavior is closely related to diffusion distance: the higher the degree of coal destruction, the shorter the actual diffusion distance, and thus the stronger the diffusion capacity. The proposed τ-STDM model yields a maximum lost methane estimation error of only 7.82%, which is significantly better than the 35.85% error of the √t model. The τ-STDM model is easy to apply and suitable for coals with different structures. This study provides a theoretical basis for accurate methane content determination in composite coal seams.