The pore structure of low-rank coal reservoirs was highly complex. It was the basis for predicting the gas occurrence and outburst disasters. Different scale pores have different effects on adsorption–desorption, diffusion, and seepage in coalbed methane. To study the pore structure distribution characteristics, which are in different scales of low-rank coal with different metamorphism grade, the pore structure parameters of low-rank coal were obtained by using the mercury injection, N₂ adsorption, and CO₂ adsorption. These three methods were used to test the pore volume and specific surface area of low-rank coal in their test ranges. Then, the fractal dimension method was used to calculate the fractal characteristics of the pore structure of full aperture section to quantify the complexity of the pore structure. The experimental results showed that the pore volume and specific surface area of low-rank coal were mainly controlled by microporous. The pore fractal characteristics were obvious. With the influence of coalification process, as the degree of coal metamorphism increases, fluctuations in the comprehensive fractal dimension, specific surface area, and pore volume of the pore size range occur within the range of R_max = 0.50% to 0.65%.

The distribution characteristics of adsorbed CH₄ across pores of various sizes underpin coal mine gas disaster prevention, resource assessment, and efficient coalbed methane (CBM) extraction. Utilizing Grand Canonical Monte Carlo (GCMC) simulations as a theoretical framework, this study establishes a mathematical model linking microscopic pore structure to macroscopic CH₄ adsorption thermodynamics in coal. Results reveal that micropores (0.38–1.5 nm) dominate pore structures in coal. For micropores (0.419–1.466 nm), CH₄ adsorption follows the Dubinin-Astakhov (DA) equation. The adsorption parameters change significantly as pore diameter increases, indicating that micropore size distribution predominantly governs CH₄ adsorption in coal. For larger pores (1.619–4.040 nm), Langmuir equation analysis reveals no significant changes in CH₄ adsorption parameters with increasing pore size, suggesting that the CH₄ adsorption behavior in pore structures larger than 1.5 nm is relatively consistent and does not vary substantially with respect to pore size. The accuracy of the mathematical model improves with coal rank, reducing prediction errors from 35.371% to 11.044%. Decomposed CH₄ adsorption isotherms reveal that while CH₄ adsorption capacity increases with equilibrium pressure for all pores, smaller pores achieve saturation at lower pressures. The proportion of total adsorption attributed to smaller pores peaks before declining with further pressure increases.

CH₄ flow dynamics in coal, governed primarily by adsorption, desorption, and seepage processes, are critical for determining gas extraction efficiency. Coal seam deformation under varying stress conditions further significantly impacts CH₄ flow. Utilizing a self-developed coal solid-gas coupling test apparatus, this study conducted simultaneous measurements of CH₄ flow and coal deformation under different axial-to-radial stress ratios. The temporal relationship between CH₄ flow and coal deformation was analyzed, establishing a quantitative correlation between the two. The influence of stress on both phenomena was examined. A model incorporating residual strain was developed to evaluate coal strain throughout the entire CH₄ flow process. Results demonstrated that both CH₄ flow and coal deformation exhibit Langmuir-like relationships with time. Similarly, a Langmuir-like relationship was observed between the amount of CH₄ adsorbed and coal deformation during adsorption. Within the experimental stress range, an increase in the axial-to-radial stress ratio inhibited CH₄ flow, consequently reducing coal deformation. Volumetric strain exhibited greater sensitivity to changes in the stress ratio compared to radial or axial strain. Residual strain was identified in coal during both CH₄ adsorption and desorption, with its prominence inversely related to the axial-to-radial stress ratio. The model, accounting for residual strain alongside isothermal flow and deformation characteristics, accurately represented the temporal evolution of coal deformation during CH₄ flow. This research provides a theoretical foundation for enhancing the efficacy of gas extraction.

Modeling the pre-extraction of coalbed methane presents a significant mathematical challenge due to the complex interplay of multiple physical fields. This paper presents a robust mathematical model based on a thermo-hydro-mechanical damage (THMD) framework to describe this process. The model is formulated as a system of coupled, non-linear partial differential equations (PDEs) that integrate governing equations for heat transfer, fluid seepage, and solid mechanics with a damage evolution law derived from continuum damage mechanics. A key contribution of this work is the integration of this multi-physics model, solved numerically using the Finite Element Method (FEM), with a statistical modeling approach using Response Surface Methodology (RSM) and Analysis of Variance (ANOVA). This integrated framework allows for a systematic analysis of the model’s parameter space and a rigorous quantification of sensitivities. The ANOVA results reveal that the model’s damage output is most sensitive to the borehole diameter (F = 2531.51), while the effective extraction radius is predominantly governed by the initial permeability (F = 4219.59). This work demonstrates the power of combining a PDE-based multi-physics model with statistical metamodeling to provide deep, quantitative insights for optimizing gas extraction strategies in deep, low-permeability coal seams.