Permeability is an important indicator of coalbed methane production. Previous classical theoretical permeability models under unconstrained boundary conditions have difficulty matching experimental results. Consideration of the actual cleat geometry can explain the non-equilibrium evolution of permeability to some extent, but the matrix swelling strain ignores the impact of damage effects. In this study, cleat damage is considered and the damage ratio is calculated. Damage as a function of strain can be solved iteratively by post-processing calculations using COMSOL Livelink with MATLAB software for correcting the permeability equation. Unlike conventional permeability models, this modified permeability model incorporates damage effects. Damage effects and matrix adsorption swelling are interactive and coupled processes. The main parameters controlling the matrix swelling strain are Young's modulus, Heterogeneous coefficient, gas injection pressure, Langmuir strain constant, and Poisson's ratio. Based on these parameters, eight working conditions are designed to compare the models without and with damage effects, and the numerical solutions of the two models are also compared with experimental data. The results show that the cleat damage model is valid better in coal permeability prediction than conventional models without damage effect. This is because the cleat damage inhibits fracture aperture rebound, which has a crucial influence on the evolution of permeability. Through this study, it is shown that the experimentally tested permeability results can indeed be explained by the impact of damage deformation on the cleat aperture.

渗透率是煤层气产量的重要指标。以往在无约束边界条件下的经典理论渗透率模型难以匹配实验结果。考虑实际割理几何形状可以在一定程度上解释渗透率的非平衡演化，但基质膨胀应变忽略了损伤效应的影响。在这项研究中，考虑了防滑钉的损坏并计算了损坏率。作为应变函数的损伤可以通过使用 COMSOL Livelink 和 MATLAB 软件进行后处理计算来迭代求解，以修正渗透率方程。与传统的渗透率模型不同，这种修改后的渗透率模型包含了损伤效应。损伤效应和基质吸附膨胀是相互作用和耦合的过程。杨氏模量、非均质系数、注气压力、朗缪尔应变常数和泊松比。在这些参数的基础上，设计了8个工况，比较了没有和有损伤影响的模型，并将两种模型的数值解与实验数据进行了比较。结果表明，割理损伤模型在煤渗透率预测中的有效性优于没有损伤效应的常规模型。这是因为割理损伤抑制了裂缝孔径回弹，这对渗透率的演变具有至关重要的影响。通过这项研究，表明实验测试的渗透率结果确实可以用损伤变形对割理孔径的影响来解释。