Although the microstructure of matrix has a significant impact on coal thermal–hydrological–mechanical interaction, this effect has not been included in the permeability analysis of the coal bed methane (CBM) extraction. Previous studies have typically investigated the relationship between coal porosity and permeability through classical cubic permeability model, neglecting the contribution of the coal seam microstructure to permeability. In this paper, we proposed a new fractal model by defining the permeability of the coal as a function of temperature and effective stress, and characterized the permeability by two microstructural parameters of coal with a thermal variable: (1) fractal dimension of the fracture; (2) maximum fracture length; (3) coal seam temperature. And this fractal model is applied to couple the gas flow, thermal conduction and deformation of the coal. The results show that the fractal permeability model is more effective in characterizing the thermal conduction and seepage processes in coal seam than the classical cubic permeability model. Compared with the cubic-law permeability model, the permeability changes about 19.62% with the different fractal dimension, and about 95.01% with the different maximum fracture length. As the fractal dimension increases from 1.25894 to 1.25926, the gas pressure decreases by 185,117.5 Pa. Furthermore, permeability decreases with the increase of coal seam temperature, and different coal parameters have various contributions to the structural parameters. However, the classical cubic permeability model cannot capture these conclusions.

尽管基体的微观结构对煤的热－水－力学相互作用有重大影响，但煤层气（CBM）提取的渗透率分析中并未包括这种影响。以前的研究通常通过经典立方渗透率模型研究了煤孔隙度与渗透率之间的关系，而忽略了煤层微观结构对渗透率的贡献。在本文中，我们通过定义煤的渗透率随温度和有效应力的变化，提出了一种新的分形模型，并通过具有热变量的煤的两个微观结构参数来表征渗透率：（1）裂缝的分形维数；（2）最大断裂长度；（3）煤层温度。然后将此分形模型用于耦合气流，煤的热传导和变形。结果表明，分形渗透率模型比典型的三次渗透率模型更能有效地描述煤层的热传导和渗流过程。与立方定律渗透率模型相比，不同分形维数的渗透率变化约19.62％，最大断裂长度不同时渗透率变化约95.01％。随着分形维数从1.25894增加到1.25926，气体压力降低185,117.5 Pa。此外，渗透率随着煤层温度的升高而降低，不同的煤参数对结构参数有不同的贡献。但是，经典的三次渗透率模型无法捕获这些结论。结果表明，分形渗透率模型比典型的三次渗透率模型更能有效地描述煤层的热传导和渗流过程。与立方定律渗透率模型相比，不同分形维数的渗透率变化约19.62％，最大断裂长度不同时渗透率变化约95.01％。随着分形维数从1.25894增加到1.25926，气体压力降低185,117.5 Pa。此外，渗透率随着煤层温度的升高而降低，不同的煤参数对结构参数有不同的贡献。但是，经典的三次渗透率模型无法捕获这些结论。结果表明，分形渗透率模型比典型的三次渗透率模型更能有效地描述煤层的热传导和渗流过程。与立方定律渗透率模型相比，不同分形维数的渗透率变化约19.62％，最大断裂长度不同时渗透率变化约95.01％。随着分形维数从1.25894增加到1.25926，气体压力降低185,117.5 Pa。此外，渗透率随着煤层温度的升高而降低，不同的煤参数对结构参数有不同的贡献。但是，经典的三次渗透率模型无法捕获这些结论。