Investigation on the nonlinear gas seepage mechanism in a series structure of heterogeneous coal surrounding a hydraulic fracturing-induced borehole

When hydraulic fracturing is applied, fractured zones with significantly different permeabilities form around the borehole, and gas flows both within and across these zones. The series-connected cross-zone seepage is influenced by the heterogeneity of the coal, resulting in a more complex gas migration mechanism. To reveal this mechanism, a nonlinear seepage model was established based on the permeability calculation formula for coal in series, the Forchheimer equation, and the ideal gas law. Using a multi-channel coal-rock matrix seepage system, series seepage experiments were conducted under both homogeneous and heterogeneous conditions. Results indicate: (1) For homogeneous coal in series, the pressure exhibits a convex upward trend, demonstrating a pressure maintenance effect under gas expansion. In contrast, the pressure in heterogeneous coal decreases stepwise, with each segment following a power-law decrease. (2) In heterogeneous series seepage, density and pressure trends are similar, while the apparent non-Darcy factor exhibits an opposite trend to pressure. Flow evolution is synergistically influenced by the interface effect and the non-Darcy characteristics of each substructure. At the interfaces, seepage instability is induced by the abrupt change in pore throat, amplifying nonlinear behavior. (3) In the heterogeneous fracturing-induced structure, the low-permeability zones become the critical medium controlling gas migration. Optimizing the fracturing process to generate a more homogeneous fracture network can weaken physical property interfaces, suppress seepage instability, and enhance gas migration. These findings refine non-Darcy gas seepage theory in heterogeneous structures and are significant for accurately predicting the gas drainage range after hydraulic fracturing and optimizing drainage design.