A physics-informed hybrid ML framework for pore pressure and fracture gradient prediction in carbonate reservoirs.

Accurate prediction of formation pore pressure and fracture gradient is essential for safe mud-weight selection and wellbore stability, especially in heterogeneous offshore carbonate reservoirs. Classical empirical methods (Eaton, Miller, and Zhang) often degrade in such settings, while purely data-driven models can be hard to justify when calibration data are sparse. This study presents a physics-informed hybrid framework that integrates classical model outputs with a new Adaptive Calibration Layer (ACL) and an uncertainty quantification module (UQM) within a gradient-boosted learning architecture. The ACL learns depth-dependent corrections from sparse MDT/XPT points while enforcing physical smoothness. The framework was evaluated on six wells from an Iranian offshore carbonate gas field. After calibration, classical models achieved R2 = 0.85-0.90 with RMSE = 0.7-1.1 MPa, whereas the hybrid model improved cross-well performance to R2 = 0.94, RMSE = 0.45 MPa, and MAE = 0.32 MPa (about 60% error reduction). The UQM reports depth-wise 95% confidence bounds, typically within ± 0.4 MPa, enabling risk-aware mud-weight planning. Overall, the method narrows uncertainty in the operational drilling window and improves pressure and fracture-gradient prediction in carbonate drilling.