<p>The migration and seepage mechanisms of supercritical CO₂ (SC-CO₂) in rock fracture structures represent significant scientific challenges that must be addressed to successfully implement CO₂ fracturing technology for enhancing oil and gas recovery and achieving effective CO₂ geologic storage. This study employed a single rough fracture model to systematically investigate the linear and nonlinear seepage behaviors of SC-CO₂ within coal fracture structures. In the linear seepage phase, a permeability formula applicable to a single rough fracture in coal was developed by incorporating the equivalent permeation opening coefficient. Subsequently, this formula was employed to clarify the relationship between permeability and the variations in roughness and opening size. For the nonlinear seepage phase, we derived calculation formulas for the inertia coefficient in the Forchheimer equation, filling a gap in previous studies where such formulas lacking. Though analyzing the relationship curves between the frictional drag coefficient and the Reynolds number, four distinct flow regime zones of SC-CO₂ within a single rough fracture in coal were identified. To develop an effective methodology for distinguishing the transition from linear to nonlinear flow regime of SC-CO₂, we established a critical Reynolds number criterion based on the non-Darcy effect factor. Furthermore, we elucidated how fracture roughness and opening size affect the critical Reynolds number. This study not only deepens our understanding of both linear and nonlinear seepage mechanisms of SC-CO₂ within coal fracture structures but also provides valuable theoretical guidance for reducing post-storage leakage risks in long-term CO₂ storage in coal seams, as well as enhancing coalbed methane recovery during CO₂ fracturing stimulation.</p>