Characteristics and factors influencing the nonlinear seepage of paste material injected into a fractal-like tree fracture bifurcation network around coal seam boreholes

The sealing efficiency of pressure grouting in coal seam boreholes is pivotal for enhancing gas extraction and mitigating environmental risks. Therefore, this study integrated theoretical and modeling approaches to investigate the development of fractures around coal seam boreholes, elucidate the migration behavior of non-Newtonian sealing slurries within fracture networks, and analyze the effects of structural parameters of fractal-like tree fracture networks on paste material permeation. First, a fractal-like, tree-like fracture bifurcation network is introduced to describe the distribution of fractures around coal seam boreholes, and the spatial fractional constitutive equation of non-Newtonian fluid is used to solve the nonlocality of non-Newtonian fluid flow and the potential correlation of particles inside the fluid. Then, the seepage model of grouting sealing material in the fracture network around coal seam drilling is constructed, and the associated seepage characteristics are examined. The research reveals the direct influence of critical parameters such as the space fractional derivative order (alpha), fracture network opening ratio (beta), fracture network length ratio (gamma), maximum bifurcation series (m), fracture opening fractal dimension (De), tortuosity fractal dimension (DT), primary fracture length (l0), the maximum opening of fracture network (emax), and the number of fracture bifurcations per level (s) on the seepage characteristics of grouting materials. Specifically, it can be obtained by the theoretical model that the permeability of the fracture network is positively correlated with beta, s, De, and emax, while it is negatively correlated with alpha, gamma, m, DT, and l0. These findings provide a theoretical basis for understanding the seepage behavior of non-Newtonian fluids in engineering coal-rock fracture networks and developing efficient sealing materials for coal seams.