Production optimization of gas-lifted oil wells via extremum seeking control

Abstract

In this work, the design of on-line optimization algorithms are perceived, in particular, those based on Extremum Seek Control (ESC) for production optimization of gas-lifted oil wells due to its ability to overcome system’s uncertainties. The control scheme maintains the oil production around the optimum point of the Well Performance Curve (WPC). The gradient information of the WPC is not used a priori, in fact it is obtained via periodic perturbation injected or on-line curve fitting estimation. This work investigates the nonlinear Eikrem’s model for the gas-lifted oil well, providing a comprehensive literature study and a simplified model which captures the main behavior of the full model. This new second order model capturing the essential dynamics of the well known Eikrem’s model is proposed for which a nonlinear controller based on feedback linearization is employed in an inner loop to improve the internal transient and allow a better ESC performance in the outer loop. At first, it is assumed that the plant state is available for feedback and then, a state estimation based on realistic sensor readings is considered. The gas-lifted oil well dynamic model was scrutinized in order to allow a deep understanding of the process providing a suitable choice for the measured variables to estimate the system states. Additionally, other nonlinear controllers are taken into account and compared to the feedback linearization control scheme in order to provide alternatives to the inner control loop strategy. A new dither- free ESC algorithm is proposed to overcome the low frequency limitation of the classic periodic perturbation ESC schemes required for time scale separation. The effectiveness of the proposed scheme is supported by simulation results.