A new theoretical model for the nonlinear flow in a rough rock fracture under shear

Shear deformations significantly affect the nonlinearity of fluid flow in rock fractures. To estimate this nonlinear flow using the Izbash equation, it is necessary to determine the Izbash coefficients. However, their parametric expressions are rarely mentioned, particularly when the shear-flow process is involved. This study proposed an improved Izbash equation-based model by incorporating the Darcy–Weisbach equation, along with a friction factor. The proposed model considers two asymptotic cases. At low Re regime, the fluid flow regime is dominated by the viscous effect, and the proposed model can be approximated to the cubic law. When Re reaches a certain threshold (Res), the fluid flow transitions into a fully turbulent flow regime where the inertia force dominates the fluid behaviours. Consequently, the proposed model is equivalent to the quadratic term of the Forchheimer equation. The proposed model is verified with the experimental results conducted on 5 rough fracture surfaces with normal stress from 0.5 to 3 MPa. Good correlations between the experimental and analytical curves illustrated that the proposed model of strong theoretical foundation yielded good prediction signified by the Normalised Objective Function (NOF) and an average error (σ¯ave) within 0.18 and 15 %, respectively.