A NEW FRACTAL MODEL OF COAL PERMEABILITY BASED ON THE INCREASING FRACTAL CONSTRUCTION METHOD OF THE MENGER SPONGE

Abstract

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.