Nonlinear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading

• Nonlinear flow in rough fractures under confining pressure up to 30 MPa was demonstrated.
• The ascending–descending variation of critical Reynolds number with confining pressure was illustrated.
• A power-law function between B and eh and a new CRN model were proposed.

This study experimentally investigated the nonlinear flow characteristics at low Reynolds number through rough-walled fractures subjected to a wide range of confining pressures (1.0–30.0 MPa). Both mated granite and unmated sandstone fractures were adopted for water flow tests and the experimental results were well fitted with the Forchheimer equation. The coefficients of viscous and inertial pressure drops experience an enlargement of 2–5 orders of magnitude with the increasing confining pressure. The critical Reynolds number Rec was successfully estimated based on the Forchheimer equation by taking α percentage (usually 10%) of the nonlinear effect as the critical point between the linear and nonlinear flow. The obtained Rec versus confining pressure curves generally display a nonlinear weakening stage (I) in the early stage of confining pressure loading, which is followed by a nonlinear enhancement stage (II) as the confining pressure further increases. A zoning map of fluid flow regimes based on Rec in the full range of the confining pressures (1.0–30.0 MPa) was presented. For the first time, an empirical relationship between the nonlinear coefficient B and the hydraulic aperture eh in rock fractures under varying confining pressure was developed based on the laboratory observations. A critical Reynolds number equation was then proposed to quantify the onset of nonlinear flow through rough-walled fractures with varying eh.