Physics-Informed Fusion Neural Network for Real-Time Bottomhole Pressure Control in Managed Pressure Drilling

Managed pressure drilling (MPD) is the core technology for developing formations with high pressure and narrow density windows. It precisely maintains the bottomhole pressure (BHP) within the safe operating window defined by formation pore pressure and fracture pressure by actively regulating the wellbore pressure profile. If pressure control becomes unstable, it can easily trigger gas kicks or lost circulation, posing a severe threat to operational safety. However, existing model predictive control (MPC) schemes have significant limitations: pure data-driven models exhibit poor generalization under complex conditions, while control algorithms based on traditional mechanistic models struggle to meet the stringent real-time requirements of field control cycles due to high-complexity numerical iteration processes. To balance control precision and real-time performance, this paper proposes a physics-informed model predictive control framework (PINC-MPC). During the training phase, physical prior knowledge such as the law of mass conservation is embedded into the neural network as constraints to construct a physically consistent deep surrogate model, enabling it to characterize complex wellbore characteristics. In the control phase, this surrogate model replaces the time-consuming numerical solving process of the mechanistic model within the MPC loop, achieving near-real-time state prediction and rolling optimization while ensuring physical fidelity. Experimental results indicate that PINC-MPC demonstrates superior control performance. Its median single-step solving time is only 16.81 ms, achieving an 11.1-fold acceleration compared to the mechanistic model-based scheme (187.3 ms). In a 5000 s full-cycle closed-loop control experiment, the total time required for the former is only 1.68 s, while the latter reaches 18.73 s, representing an efficiency improvement of approximately 91%. In terms of control accuracy, the integrated absolute error (IAE), reflecting the total deviation of the control process, significantly decreased from 63.40 MPa·s for the industrial successive linearization MPC (SLMPC) to 12.90 MPa·s, an improvement of 79.7%. Especially in extreme dynamic conditions such as simulated pump shutdowns for pipe connections and sudden gas kicks, the framework demonstrates excellent predictive ability and response efficiency. It can proactively trigger compensation actions to keep BHP fluctuations within 0.30 MPa, significantly outperforming the traditional SLMPC method. The research results prove that PINC-MPC provides an efficient, precise, and robust nonlinear control strategy for MPD systems, offering important engineering reference value for enhancing the automation level of intelligent drilling systems.