A multi-domain physics-informed neural network for rapid prediction of wellbore temperature during drilling

Wellbore temperature is a key physical parameter that affects drilling fluid performance and downhole tool reliability. Accurate prediction and control of wellbore temperature are essential for safe drilling operations. Conventional prediction methods usually rely on numerical discretization, which makes them computationally expensive and difficult to deploy for real-time prediction. To address this limitation, this study incorporates the governing heat transfer equations, interface constraints, initial conditions, and boundary conditions into a physics-informed neural network (PINN) framework and develops a multi-domain PINN model consisting of a shared wellbore network and a shared near-well solid network. The model enables subsecond prediction of the wellbore temperature field under complex heat transfer conditions. For a case well in Sichuan, the average inference time after training is 265 ms per case, corresponding to a speedup factor of approximately 1496 relative to the conventional numerical model. The mean relative error between the predicted and measured temperatures is 3.28%, which is lower than the 3.62% error obtained from the conventional numerical simulation. These results suggest that the proposed multi-domain PINN model markedly improves computational efficiency while maintaining satisfactory engineering prediction accuracy. The effects of drilling fluid flow rate, drilling fluid density, and inlet temperature are further analyzed to identify the dominant controlling factors. The results show that flow rate mainly controls the bottomhole temperature response, whereas inlet temperature primarily governs the overall temperature level along the wellbore. This study provides an efficient and reliable approach for rapid wellbore temperature prediction, intelligent optimization of drilling parameters, and safety assessment of downhole tools.