Application of fractal theory to predict the coal permeability of multi-scale pores and fractures

Finding out the contributions of pores and fissures at different scales in coal to permeability can lay a foundation for studying the flow regularity of fluid in coal seam. In this paper, coal samples from Changping mine and Pingdingshan No.6 mine were taken as research objects, and mathematical models for calculating the permeability of micron-scale pores and micron-scale fractures were constructed by the method of Scanning Electron Microscope (SEM). A mathematical model for calculating the permeability of nano-scale seepage pores and nano-scale diffusion pores was constructed by the method of mercury injection and fractal dimension. According to the parameters of perimeter, area, length, average width, volume and specific surface area of pores and fractures at different scales measured by SEM and mercury injection, the permeability of pores and fractures at different scales was calculated by the established mathematical model, and the calculated results were compared with the measured values. The results show that, the measured permeability varied linearly with the calculated total permeability, by introducing the effective porosity, the model for calculating permeability of pores and fractures at different scales using SEM and mercury intrusion method compensates for a single calculation method. The nano-scale diffusion pores accounted for the highest proportion (between 71.21% and 90.66%) of the total effective porosity, while they had little influence on permeability and contributed less than 0.1% to the permeability. The micron-scale seepage pores and fractures accounted for the smallest proportion in terms of effective porosity, ranging from 3.24% to 14.78%, while contributing the most (more than 70%) to the overall permeability. With the increase of permeability, the contributions of micron-scale seepage pores and fractures in the coal samples to effective porosity and permeability increased; however, contributions of nano-scale diffusion pores to effective porosity and permeability both decreased.