Abstract Although the impact of matrix microstructures on the evolution of coal permeability is significant, this impact has not been included in the analysis of coupled multiple processes during the extraction of coal seam gas. Previous studies normally investigate the relation between microstructures and coal porosity or permeability through imaging characterization techniques. In this study, we developed a fractal permeability model that defines coal permeability as a function of effective stress. In this model, coal microstructure is characterized by three fractal parameters: (1) fractal dimension of pore size; (2) fractal dimension of throat tortuosity; and (3) maximum pore size. These fractal dimensions may evolve with the effective stress through porosity. We applied this fractal permeability model to fully couple coal deformation and gas flow. Model results illustrate the significant differences between the fractal approach and the classical cubic model between permeability and porosity. When the porosity remains unchanged, the permeability calculated by the classical cubic model remains as a constant. However, the fractal permeability changes due to different microstructural parameters. These results show that the macroscopic permeability of coal is directly proportional to the fractal dimension and the maximum pore size, and is inversely proportional to the fractal dimension of the throat tortuosity. These characteristics cannot be captured by the classical cubic porosity-permeability model.

中文翻译：

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煤变形与气流全耦合的分形方法

摘要 尽管基体微观结构对煤渗透率演化的影响是显着的，但在煤层气提取过程中多过程耦合的分析中并未包括这种影响。以前的研究通常通过成像表征技术研究微观结构与煤孔隙度或渗透率之间的关系。在这项研究中，我们开发了一个分形渗透率模型，该模型将煤渗透率定义为有效应力的函数。在该模型中，煤的微观结构由三个分形参数表征：（1）孔径的分形维数；(2)喉道曲折的分形维数；(3) 最大孔径。这些分形维数可能会随着有效应力通过孔隙度而演变。我们应用这种分形渗透率模型来完全耦合煤变形和气流。模型结果说明了分形方法与经典三次模型在渗透率和孔隙度之间的显着差异。当孔隙度保持不变时，经典三次模型计算的渗透率保持不变。然而，分形渗透率因不同的微观结构参数而变化。这些结果表明，煤的宏观渗透率与分形维数和最大孔径成正比，与喉道曲折度的分形维数成反比。经典的立方孔隙度-渗透率模型无法捕捉到这些特征。模型结果说明了分形方法与经典三次模型在渗透率和孔隙度之间的显着差异。当孔隙度保持不变时，经典三次模型计算的渗透率保持不变。然而，分形渗透率因不同的微观结构参数而变化。这些结果表明，煤的宏观渗透率与分形维数和最大孔径成正比，与喉道曲折度的分形维数成反比。经典的立方孔隙度-渗透率模型无法捕捉到这些特征。模型结果说明了分形方法与经典三次模型在渗透率和孔隙度之间的显着差异。当孔隙度保持不变时，经典三次模型计算的渗透率保持不变。然而，分形渗透率因不同的微观结构参数而变化。这些结果表明，煤的宏观渗透率与分形维数和最大孔径成正比，与喉道曲折度的分形维数成反比。经典的立方孔隙度-渗透率模型无法捕捉到这些特征。由于不同的微观结构参数，分形渗透率会发生变化。这些结果表明，煤的宏观渗透率与分形维数和最大孔径成正比，与喉道曲折度的分形维数成反比。经典的立方孔隙度-渗透率模型无法捕捉到这些特征。由于不同的微观结构参数，分形渗透率会发生变化。这些结果表明，煤的宏观渗透率与分形维数和最大孔径成正比，与喉道曲折度的分形维数成反比。经典的立方孔隙度-渗透率模型无法捕捉到这些特征。