Trajectory-Integrated Kriging Prediction of Static Formation Temperature for Ultra-Deep Well Drilling

The accurate prediction of static formation temperature (SFT) is essential for ensuring safety and efficiency in ultra-deep well drilling operations. Excessive downhole temperatures (>150 °C) can degrade drilling fluids, damage temperature-sensitive tools, and pose serious operational risks. Conventional methods for SFT determination—including direct measurement, temperature recovery inversion, and artificial intelligence models—are often limited by post-drilling data dependency, insufficient spatial resolution, high computational costs, or a lack of adaptability to complex wellbore geometries. In this study, we propose a new pseudo-3D Kriging interpolation framework that explicitly incorporates real wellbore trajectories to improve the spatial accuracy and applicability of pre-drilling SFT predictions. By systematically optimizing key hyperparameters (θ = [10, 10], lob = [0.1, 0.1], upb = [20, 200]) and applying a grid resolution of 100 × 100, the model demonstrates high predictive fidelity. Validation using over 5.1 million temperature data points from 113 wells in the Shunbei Oilfield reveals a relative error consistently below 5% and spatial interpolation deviations within 5 °C. The proposed approach enables high-resolution, trajectory-integrated SFT forecasting before drilling with practical computational requirements, thereby supporting proactive thermal risk mitigation and significantly enhancing operational decision-making on ultra-deep wells.