Adaptive economic model predictive control with safety constraints for an Electric Submersible Pump Lifted Well

Abstract

We propose an economic adaptive predictive controller based on an output modifier adaptation (EMPC-MA) for controlling an electric submersible pump (ESP) lifted oil well. The modifiers constantly adapted the linear MPC model to handle the plant’s nonlinear behavior. A gradient-based approach approximates the economic function rendering an easy-to-solve quadratic programming (QP) problem. Furthermore, a zone control strategy prioritizes operation within time-varying safety constraints. To handle feasibility issues, artificial and slack variables are used in the terminal constraints. The controller is analyzed coupled with an Extended Kalman Filter based on a static model (SEKF) for estimation purposes since we assume that only a linear dynamic model and a rigorous static model are available for optimization and control purposes, which is the standard in the industry. Thus, the proposed approach does not need to linearize the model at each time step. Finally, the EMPC-MA + SEKF is compared to controllers without safety constraints and adaptation. Results reveal that some form of adaptation is necessary to handle nonlinearities and that pump safety conflicts with profit maximization. Moreover, the proposed controller always tends toward the economic optimal even when disturbances, noise, and parametric uncertainties are present.