Comparison of Transformer and Long Short-Term Memory-Based Nonlinear Model Predictive Control for Automatic Managed Pressure Drilling

Abstract Managed Pressure Drilling (MPD) is an advanced drilling technique that enhances safety and efficiency by maintaining precise control over bottomhole pressure. Nonlinear Model Predictive Control (NMPC) has proven effective in MPD due to its ability to handle constraints and nonlinearities. However, NMPC performance depends on the accuracy of the underlying system model. Traditionally, low-fidelity first-principle models have been used for MPD control system design, but recent advances in data-driven modeling offer alternatives. This study presents a comparative analysis of two predictive controllers using Machine Learning (ML)-based NMPC frameworks—Long Short-Term Memory (LSTM) networks and Transformer-based self-attention mechanisms—for automatic MPD. The machine learning models were trained using the input-output data collected from the simulated model of the MPD. The ability of the trained models in making predictions of bottomhole pressure was tested using the validation dataset. The r2 score of the LSTM model on the validation dataset is 0.8747 and that of the transformer model is 0.8639 while the RMSE value is 116820 for the LSTM model and 113130 for the transformer model. The RMSE values are considered low given that bottomhole pressures in the system are of the order of 10 million (~107 Pa). These trained models were employed as the prediction models in the NMPC formulation. The ML-based NMPC were evaluated on their ability to track bottomhole pressure setpoints during normal drilling operation and to reject bottomhole pressure disturbances which can be caused by measurement error or plant model mismatch. The LSTM-based NMPC demonstrated slightly better setpoint tracking and faster disturbance rejection as a result of its shorter rise time. For the servo simulation, the Integral Absolute Error (IAE) was 3.2544×107 for LSTM-based NMPC and 3.9345×107 for Transformer-based NMPC. Under regulatory conditions involving disturbances in bottomhole pressure measurements, the LSTM-based controller had an IAE of 6.15×106, compared to 9.5733×106 for the Transformer-based NMPC. In terms of computational efficiency, transformer-based NMPC with an average computational time of 0.5862s outperformed LSTM-NMPC with 2.1768s for setpoint tracking over a simulation time of 750s. Overall, while LSTM-based NMPC exhibited slightly better control accuracy performance, Transformer-based NMPC exhibits better potential for applications in a real-time automatic MPD operation given its very low computational time.