Influence of fractal dimensions of fissures on characteristic parameters of non-Darcy seepage of coal gas in peripore coal bodies

The fractal dimension of fractures surrounding the borehole in coal can effectively reflect the geometrical characteristics of the fracture network, which impacts the non-Darcy gas seepage characteristics in fractured coal around the borehole. To investigate these characteristics, five types of coal samples with one to four through-going fractures were prepared, representing distinct geometrical features. The fractal dimension of the fracture network around the borehole was employed to quantitatively characterize its geometry, and a self-designed radial gas seepage system was utilized to conduct laterally confined radial seepage tests on fractured coal around the borehole, simulating the gas seepage process. The nonlinear characteristics and mechanisms of radial gas seepage in fractured coal around the borehole were analyzed using the Forchheimer equation. The results indicated: ① The fractured coal around the borehole exhibits robust fractal characteristics, with two-dimensional fractal dimensions (D2) ranging from 1.321 to 1.442 and three-dimensional fractal dimensions (D3) ranging from 2.321 to 2.442. Variations in the fractal dimension comprehensively reflect differences in fundamental geometric indices such as surface fracture rate (Rsc), number of fracture intersections (Nj), number of fracture segments (Nseg), total fracture length (Lsum), average fracture length (Lav), and average fracture width (e). ② Radial gas seepage in fractured coal around the borehole is influenced by three effects: local roughness, internal fluid friction, and tortuous flow. Under the same pressure gradient, a higher fractal dimension of the fracture network results in a lower flow rate through the network. ③ The seepage velocity of fractured coal around the borehole increases with the pressure gradient, gradually deviating from linearity. Greater seepage velocities lead to more pronounced nonlinearity. A higher fractal dimension of the fracture network limits the maximum achievable seepage velocity. ④ As the fractal dimension of the fracture network increases, the permeability of fractured coal around the borehole decreases, following the relationship 1011k = 4.6D32−23.9D3 + 31.9. Simultaneously, the β factor for non-Darcy flow increases. Moreover, the β factor decreases as permeability (k) increases.In summary, observing the fractal dimension of the fracture network around the borehole in gas pre-drainage operations along coal seams can provide crucial insights into the permeability of fractured coal, guiding the design of borehole layout parameters.