Experimental and numerical study on the Izbash equation coefficients in rough single fractures

The Izbash equation has been widely used in the subsurface applications. However, the Izbash equation is still empirical, and its coefficients (scaling factor λ and power exponent M) have not been systematically characterized and quantified. In this study, laboratory experiments and numerical simulations of fluid flow across a wide range of hydraulic gradients (J = 0–4) in horizontal rough fractures were conducted to comprehensively characterize and quantify the influence of fracture geometric attributes and fluid inertial effects on λ and M. The results showed that λ increased with fracture relative roughness (RSD). The fluid inertial effect (quantified by the non-Darcy effect factor E and Re) had a two-stage influence on λ. When the fluid flow was laminar, λ increased with E. However, when the fluid flow regime starts to transition from laminar flow to turbulent flow, λ decreased with increasing E. M is positively correlated with RSD and the fluid inertia effect E. We found that the transition of flow regime from laminar to turbulent flow depended on whether the recirculation zones are fully developed. The fully developed recirculation zones determine the distortions of the velocity field and flow field, which induced the turbulent flow. The quantitative models of λ and M were obtained based on numerical simulations, which quantified the coupling influence of the fracture geometric property and fluid inertial effect. The validity of quantitative models was verified by laboratory experiments. Our work provided a new understanding of the Izbash coefficients and laid a foundation for theoretical background exploration of the Izbash equation.