Friction factor for rough fractures: Roughness and flow inertia effects

The friction factor is one of the key parameters for evaluating fluid flow characteristics and pressure head loss in fractures, and accurate prediction is crucial for a deeper understanding of fracture flow processes. Traditional studies often consider roughness effects only in the inertial friction factor, overlooking its impact on the viscous friction factor. To address this limitation, this study introduces the equivalent permeability and non-Darcy coefficient of rough fractures and fits the Forchheimer equation using 78 experimental data points, proposing a model that simultaneously considers both non-Darcy effects and roughness effects on viscous and inertial friction factors. Flow simulations of two-dimensional real fractures yielded 3500 friction factor data points, which were further used to construct three artificial intelligence (AI) models: Random Forest, Support Vector Machine, and K-Nearest Neighbors. Sensitivity analysis and comparison with simulation data showed that the proposed model outperforms existing models in prediction trends, with its prediction range more accurately covering the majority of data. In contrast to traditional friction factor models that either only consider inertial effects or simultaneously account for both inertial and roughness effects, the proposed model provides more accurate predictions. Additionally, the three AI models demonstrate superior fitting performance in prediction trends and prediction ranges, better capturing the simulation data. These findings provide important theoretical and methodological support for further research on pressure head loss in fracture flow.