Cross-Geometry Flow-Field Prediction in Irregular Wellbores Using Parameterized Physics-Informed Neural Networks

Irregular borehole enlargement alters annular flow structures and can create low-velocity regions that impair hole cleaning. However, conventional computational fluid dynamics (CFD) requires repeated geometric reconstruction and numerical simulations for each wellbore configuration, while existing physics-informed models have limited capability for cross-geometry extrapolation. This study develops transfer-learning-based parameterized physics-informed neural networks (TLP-PINNs) for the rapid three-dimensional prediction of Herschel–Bulkley drilling-fluid flow in locally enlarged irregular wellbores. A Gaussian enlargement ratio is introduced as an explicit geometric input, while mass and momentum conservation equations, boundary conditions, adaptive loss weighting, extrapolation-distance-driven physics-point allocation, and partial-layer transfer learning are integrated into a unified framework. The source model generally maintains good in-range interpolation accuracy for the velocity field within the 10–50% enlargement range, although the pressure error shows greater case-to-case variability for unseen intermediate geometries. For the unseen 80% enlargement case, transfer learning reduces the relative RMSEs of axial velocity, velocity magnitude, and pressure from 14.0%, 13.5%, and 3.5% to 9.42%, 9.50%, and 1.34%, respectively, with corresponding Rp2 of 0.9668, 0.9663, and 0.9992. The transferred model also accurately captures the low-velocity zone within the enlarged section and the associated redistribution of the local pressure gradient, while reducing neural-network training time by 51.2% relative to full-domain retraining. These results demonstrate a practical cross-geometry framework for the rapid hydraulic assessment of irregular wellbores and provide detailed flow-field information for subsequent analyses of hole cleaning and particle transport.