The Effect of Roughness on the Nonlinear Flow in a Single Fracture with Sudden Aperture Change

Abstract

Abstract Abrupt changes in aperture (sudden expansion and contraction) are commonly seen in naturally occurred or artificial single fractures. The relevant research mainly focuses on the changes in fluid properties caused by the sudden expansion of the aperture in smooth parallel fractures. To investigate the effects of roughness on the nonlinear flow properties in a single rough fracture with abruptly aperture change (SF-AC), the flow characteristics of the fractures under different Reynolds numbers Re (50~2000) are simulated by the turbulence k-ε steady-state modulus with the Naiver-Stokes equation. The results show that, in a rough SF-AC, the growth of the eddy and the flow path deflection of the mainstream zone are more obvious than those in a smooth SF-AC, and the discrepancies between the rough and smooth SF-ACs become even more obvious when the relative roughness and/or Re values become greater. The increase of the fracture roughness leads to the generation of more local eddies on the rough SF-ACs and enhances the flow path deflection in the sudden expansion fracture. The number of eddies increases with Re, and the size of eddy area increases linearly with Re at first. When Re reaches a value of 300-500, the growth rate of the eddy size slows down and then stabilizes. Groundwater flow in a rough SF-AC follows a clearly visible nonlinear (or non-Darcy) flow law other than the linear Darcy’s law. The Forchheimer equation fits the hydraulic gradient-velocity (J-v) better than the linear Darcy’s law. The corresponding critical Re value at which the nonlinear flow starts to dominate in a rough SF-AC is around 300~500.