Experimental and numerical study for the inertial dependence of non-Darcy coefficient in rough single fractures

Abstract This study experimentally and numerically investigated the influence of the inertial effect of fluid flow on the non-Darcy coefficient (β). The results showed that the non-Darcy coefficient (β), apparent permeability (ka), and hydraulic aperture (eh) decreased with the increase of Reynolds number (Re), which indicated that the non-Darcy coefficient depended on the geometric properties of a single fracture and the fluid inertial effect. The quantification model of the non-Darcy coefficient was improved. Under the guidance of fluid inertial effect, the β performed a positive power-law relationship with eh; under the coupling effect of fluid inertial effect and fracture geometric properties, the β behaved negative power-law relationship with eh, which was similar to the non-Darcy coefficient quantitative model that ignored the fluid inertial effect in the previous study. Therefore, the geometric properties were the dominant ones for fracture flow when it was affected by the coupling effect of geometric properties and inertial effects. Then, the quantitative model of the non-Darcy coefficient was improved. Based on the improved non-Darcy coefficient quantitative model, a new critical Reynolds number prediction model (CRN model) was constructed. Compared with other CRN models, the new CRN model considering the coupling effect of fluid and media properties could more accurately predict the critical Reynolds number (Rec) in rough single fractures, which further proved the existence and importance of the inertial dependence of the non-Darcy coefficient.