Multiscale decomposed roughness disturbance on non-Darcy flow characteristics in a single fracture

Fractures with different multiscale roughnesses are widely encountered in subsurface engineering, and their impact on non-Darcy flow is critical for predicting fluid transport. Although numerous studies have examined fluid through multiscale fractures, the specific effects of wavelet decomposed roughness wavelengths (L) and amplitudes (Δ) remains poorly understood. Here, a decomposed roughness model was introduced using multiscale wavelet decomposition to construct fracture geometries with controlled L and Δ. Relative velocity (Vr) field was employed to emphasize decomposed roughness disturbance and classify it into enhanced and reduced velocity region (EVE/RVR). The disturbance intensity (γ) used to quantify disturbance. Sensitive analysis indicates that L exhibits a noteworthy role on the deviation of Darcy flow. Hydraulic parameters eh, β, and Rec scale with L via power-law relationships. Specifically, β exhibits periodic oscillations as L increases, which was modeled by adding a sinusoidal term. It observed that γ increases with Re due to stronger viscous and inertial effects. However, at Re = 100–1000, γ decreases as EVR expands and RVR contracts. The γ variation with L using a logistic oscillation modulation function. Inertial effects and roughness also lead to recirculation zones (RZs). The recirculation zone area ratio (θ) is as follows: θ = A1Re/(A2 + Re), indicating transitions from scale to inertial dominated stage. The relationship between γ and Rec transitions from a inertial dominated regime at small scales to a scale dominated regime at larger scales. This work offers new insight into multiscale roughness disturbance on the initial deviation of Darcy flow.