Effect of fluid slippage on eddy growth and non-Darcian flow in rock fractures

Fluid flow in rock fractures is usually theoretically and numerically investigated on the premise of no-slip boundary condition (BC). However, fluid slippage at rock surface is naturally present in some circumstances that might lead to a violation of no-slip BC. How and to what extent slip BC affects non-Darcian fracture flow remains poorly constrained. This study systematically investigated the slippery flow behaviors in rock fractures under sequentially-increasing pressure gradients. Two competing mechanisms impacting the apparent permeability (k) due to fluid slippage were revealed: k was not only enhanced by fluid slippage at fracture walls but also was reduced by the accelerated eddy growth due to enhanced velocity field. The increment in k caused by slip velocity initially dominated over the decrement caused by eddy growth during this competing process, but this dominant situation could reverse given a sufficiently large pressure gradient with fully-developed eddies. Moreover, the slippery fluid flow behavior was tested to be very sensitive to the slip length based on our sensitivity analysis. Therefore, a reasonable estimation of the slip length would be crucial to accurately determine the effects of fluid slippage. This study deepens our understanding of fluid flow in rock fractures when slip BC is present, and might provide theoretical guidance for organic pollution remediation, oil recovery, and geological carbon sequestration in fractured reservoirs.