Influence of recirculation zones on viscous and inertial permeabilities in rough single fractures

Recirculation zones (RZs) in rock fractures have been widely observed by experiments and numerical simulations. While previous studies focused on the effects of RZs on flow regimes and solute transport, limited attention has been given to their evolution across a wide range of flow velocities and the associated impacts on fracture permeability. In this study, numerical simulations were conducted to investigate the evolution of RZs over a wide range of Reynolds numbers (Re) and their effects on the viscous (kv) and inertial (ki) permeabilities of single fractures. A three-stage evolution of RZ across a wide Re range was detected: Stage I (rapid growth): During the initial formation of RZs, their volume (Sv′) increases rapidly with Re; Stage II (slow growth): As Re increases, Sv′ continues to grow, but dSv′/dRe gradually decreases. Stage III (fully developed): At higher Re, Sv′ becomes insensitive to further increases in Re, with dSv′/dRe ≈ 0. During the transition from Stage I to Stage II, the expanding Sv′ compresses the main flow channel (MFC), reducing its nonlinearity. This leads to a decrease in viscous permeability (kv) and an increase in inertial permeability (ki) as Re increases. In Stage III, RZs become fully developed and independent of Re, resulting in stable kv and ki as RZs and MFCs reach a highly differentiated and stable configuration. A critical Re (Rec,stable) was defined to capture the stable kv and ki, referred to as kvglobal and kiglobal, respectively, encapsulating the overall evolution of hydraulic conductivity in rock fractures. Additionally, quantitative models for kvglobal and kiglobal were derived and validated.