Characterizing the Relationship Between Non‐Darcy Effect and Hydraulic Aperture in Rough Single Fractures

Hydraulic aperture (eh) which is independent of inertial effect has been widely used as an important parameter to study the geometric properties of single fractures in previous studies. However, the inertial effect dependence of hydraulic aperture was gradually revealed in recent studies. Therefore, hydraulic aperture could provide a new method to characterize the non‐Darcy effect. In this study, 2D numerical simulations based on Navier‐Stokes equation were carried out to explore the feasibility of characterizing non‐Darcy effect based on hydraulic aperture. The results showed that the onset of flow regimes transition from Darcy to non‐Darcy could be well characterized by the hydraulic aperture. Before the non‐Darcy flow appeared, the initial hydraulic aperture (eh0) maintained constant regardless of the inertial effect (quantified by non‐Darcy effect factor E), once the non‐Darcy effect emerged, the hydraulic aperture decreased with the increase of inertial effect. The increased volume of low‐velocity zone in the rough single fractures was considered as the mechanism of non‐Darcy effect. And the existence of critical relative roughness (Rc) was found and it would affect the critical non‐Darcy effect factor (Ed) or critical Reynolds number (Rec) by affecting the development of low velocity region and preferential flow paths. From the overall trend, the hydraulic aperture decreased with the increase of E, and it fluctuated due to the development of recirculation zones (RZs). Moreover, the predictive model of non‐Darcy effect factor (E) based on hydraulic aperture was obtained and the validity of the model was preliminarily verified. Key Points The onset and development of non‐Darcy effect could be well characterized by the reduction of hydraulic aperture The mechanism of non‐Darcy effect is closely related to the low‐velocity regions and preferential flow paths The magnitude of fluid inertial effect in a rough single fracture could be predicted based on the hydraulic aperture