Structural coal has low permeability and high gas content. The increase of mining depth seriously restricts the safe mining of deep mines. Hydraulic flushing is the main means of gas extraction. The shape of the hydraulic flushing hole is an important basis to determine the pumping radius, which is widely regarded as a cylinder. However, due to the differences in the stress level, water force, friction and external moisture, the pore morphology, and permeability evolution need to be further studied. At present, the hole shape for hydraulic punching is equivalent to a cylinder in drilling design and evaluation, which is one of the important bases to determine the effective extraction radius. However, the hole shape is affected by many factors, so the scientific equivalent to a cylinder remains to be discussed. The BR-PKN equation describing the hole shape is established by introducing and combining the Bergmark–Roos equation and PKN model, and the hole’s shape is shown by MATLAB. To verify its accuracy, YZD18.5 is used as an onsite logging tool for data acquisition and analysis, and the hole section is drawn. The BR-PKN equation and permeability evolution model are simulated by COMSOL Multiphysics, and the permeability evolution law of conventional cylinder with hydraulic flushing is compared and analyzed. The results show that 1) the shape of the hydraulic punch hole is ellipsoid with three different axes, and its horizontal section is approximately an ellipse; 2) within the influence range of quasi-ellipsoid holes, the permeability changes in the long and short axis of quasi-ellipsoid holes are similar. The permeability evolution curve of the coal first increases, then decreases, and finally, flattens with the increase of distance from borehole, and the permeability of the coal body increases with the extension of extraction time); 3) the permeability of the equivalent ellipsoid pore decreases with the increase in coal water content. The effective radius in the long and short axes of the minimum cross section of the quasi-ellipsoid hole is 0.89 and 0.95 times the effective extraction radius of the equivalent cylinder, which provides a basis for a drilling layout.

The shape of the hydraulic flushing hole is an important basis to determine the effective pumping radius. In the design and evaluation of the drilling hole, it is usually equivalent to a cylinder. However, the formation of the shape of the hole is affected by the gravity of coal and rock bulk, the friction of coal and rock, water force, stress, and other factors, so the scientific nature that is equivalent to a cylinder remains to be discussed. In this paper, based on the analysis of the whole process of hydraulic flushing and the formation of the pore shape, gravity, friction, water force, and ground stress of coal and rock bulk are selected as important factors affecting the pore shape, and the parallel Bergmark-Roos equation and PKN model are introduced to establish the BR-PKN equation of the pore shape of hydraulic flushing. MATLAB is used to reproduce the shape of the hydraulic flushing hole, which is a kind of ellipsoid with three different axes. In order to verify the accuracy of the hole shape, the YZD18.5 video imaging logging tool for mine lateral resistivity is used to collect and analyze the shape data of the hydraulic flushing hole, and the hole section is drawn, which is basically consistent with the theoretical derivation of the hydraulic flushing hole shape. COMSOL is used to simulate the hydraulic flushing equivalent of the ellipsoid hole compared with the cylinder hole under the same coal output and extraction time of 90 days. The extraction radius, desorption surface area, and effective extraction volume are 0.95, 0.79, and 1.14 times, respectively, providing a basis for the optimal design of hydraulic flushing.