The permeability of coal seams directly determines the disaster prevention effect of water injection. It is of great significance to realize the accurate fractal expression of coal structure and construct a fractal permeability model for elucidating the dynamic evolution law of the permeability of coal during and after water injection. Therefore, a rough Menger sponge is used as the physical model to characterize the structure of the coal in this paper. Combined with the structure fractal dimension calculated by the increasing fractal construction method, a new fractal permeability model is established to describe the seepage process of water injection. The influence of the tortuosity and roughness of the pore surfaces on the seepage characteristics is discussed, and the theoretical permeability is compared with the results of NMR experiments and existing models. The volume fractal dimension obtained by calculation is between 2.74 and 2.77, which decreases with increasing confining pressure and increases with increasing pore water pressure. The research shows that the fractal dimensions of the pore structure and volume can quantitatively describe the specific surface area of porous medium and are directly proportional to the specific surface area. With the increase in the structure fractal dimension, the fluid flow resistance increases, and the theoretical permeability decreases. The results of the permeability comparison show that the variation law of the theoretical permeability is consistent with that of the liquid permeability and that the theoretical result is closer to the measured value because the tortuosity and roughness of the seepage channel surfaces is further considered in the model. The theoretical model provides reliable theoretical support for further perfecting seepage theory of porous media and improving the effect of coal seam water injection.

中文翻译：

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基于Menger Sponge递增分形构造方法的煤渗透率分形模型

煤层的渗透性直接决定注水的防灾效果。实现煤结构的精确分形表达，构建分形渗透率模型，对于阐明煤在注水过程中和注水后渗透率的动态演化规律具有重要意义。因此，本文采用粗糙的门格尔海绵作为物理模型来表征煤的结构。结合递增分形构造法计算的结构分形维数，建立了一种新的分形渗透率模型来描述注水渗流过程。讨论了孔隙表面的曲折度和粗糙度对渗流特性的影响，并将理论渗透率与核磁共振实验结果和现有模型进行了比较。计算得到的体积分形维数在2.74~2.77之间，随着围压的增加而减小，随着孔隙水压力的增加而增加。研究表明，孔隙结构和体积的分形维数可以定量描述多孔介质的比表面积，并且与比表面积成正比。随着结构分形维数的增大，流体流动阻力增大，理论渗透率减小。渗透率对比结果表明，理论渗透率的变化规律与液体渗透率的变化规律一致，由于模型进一步考虑了渗流通道表面的曲折和粗糙度，理论结果更接近实测值。 . 该理论模型为进一步完善多孔介质渗流理论、提高煤层注水效果提供了可靠的理论支持。