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Although the slippery boundary condition (BC) has been validated to enhance fracture permeability ( k ), the coupling effects of heterogeneous slippery BC and inertia on k remain less understood. We used computational fluid dynamics to investigate the competing roles of slippery BC and inertial forces in controlling k evolution with increasing pressure gradient by designing six cases with different slip length scenarios for a two-dimensional natural fracture. Our results suggest that pronounced inertial effects were directly related to and demonstrated by the growth of recirculation zone (RZ); this caused flow regimes transitioning from Darcy to non-Darcy and significantly reduced k , with an identical tailing slope for six cases, regardless of the variability in slip lengths. Moreover, the slippery BC dominantly determine the magnitude of k with orders depending on the slip length. Lastly, our study reveals that the specific k evolution path for the case with a varying slip length was significantly different from other cases with a homogeneous one, thus encouraging more efforts in determining the slip length for natural fractures via experiments.

Effects of Slip Length and Inertia on the Permeability of Fracture with Slippery Boundary Condition