Abstract: Under prolonged internal and external dynamic disturbances coupled with water erosion, rock fractures are often partially filled with porous media, leaving unfilled apertures of finite opening within the fracture. To elucidate the fluid exchange mechanism between the porous infill and the adjacent open space, a theoretical seepage model is developed. Analytical solutions for the streamwise flow distribution within the unfilled aperture are derived for low-Reynolds-number conditions, while a predictive expression incorporating an inertial correction coefficient is proposed for high-Reynolds-number regimes. A corresponding numerical model is established to systematically investigate the fluid interaction between the porous region and the unfilled aperture. The numerical results validate the theoretical model across both low and high Reynolds numbers. The proposed partially filled fracture model effectively captures the exchange process between seepage flow in the porous medium and free flow in the unfilled aperture. The flow rate in the unfilled aperture increases rapidly near the inlet and then gradually levels off along the fracture. After inertial and permeability corrections are applied to the interfacial exchange coefficient, the derived streamwise flow-rate expression remains applicable under high-permeability and high-Reynolds-number conditions, with the theoretical predictions matching the numerical simulations to within 95.6% accuracy. An increase in the Reynolds number significantly alters the internal flow field, shifting the primary interaction zone downstream and transforming the pressure-drop-versus-flow-rate relationship from linear to nonlinear, accompanied by local pressure reversal and flow recirculation. The aperture size of the unfilled gap directly influences both the steady-state flow-rate peak and its downstream growth trend: a larger aperture yields a higher peak flow rate, which progressively approaches the total flow rate of the partially filled fracture. Under low-Reynolds-number conditions, the extent of the main interaction zone first increases and then decreases with increasing aperture, whereas under high-Reynolds-number conditions it exhibits a hyperbolic decay. The permeability of the filling matrix also exerts a substantial effect: higher permeability raises the steady-state flow peak while shrinking the interaction zone. Beyond a critical permeability K_c, the proposed analytical expression for the unfilled-aperture flow distribution ceases to be valid; however, when the matrix permeability is below10⁻¹¹m², the applicability of the expression becomes independent of the Reynolds number.