Lyapunov-based zone economic MPC for safe and efficient drilling under variable measurement delays

During drilling, downhole measurements are often affected by time-varying measurement delays and intermittent data loss. The driller cannot adjust manipulated variables such as surface Weight on Bit (WOB_s), surface Revolutions per Minute (RPM_s), and mud pump flow rate continuously. This prevents the drilling system from operating at its optimum state in real-time, ultimately diminishing both safety and efficiency. To address these challenges, we develop an integrated coupled model of the drilling process, characterizing the relationship between Rate of Penetration (ROP) and Bottom Hole Pressure (BHP). Based on this model, we propose a novel Model Predictive Control (MPC) algorithm, the Lyapunov-based Zone Economic Model Predictive Control (LZEMPC) algorithm. This algorithm can manage BHP and optimize ROP concurrently, even under time-varying measurement delays and data loss. We use field data to conduct simulation experiments. The results demonstrate that the LZEMPC algorithm successfully maintains BHP within the formation pressure window while significantly improving drilling efficiency. In comparison to traditional methods, the LZEMPC approach effectively manages both safety and efficiency, providing a promising solution for real-time drilling optimization in challenging environments.