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Numerical Application of a Stick-Slip Control and Experimental Analysis using a Test Rig
Last modified: 2017-11-26
Abstract
Part of the process of exploration and development of an oil field consists of the drilling operations for oil and gas wells. Particularly for deep water and ultra deep water wells, the operation requires the control of a very flexible structure which is subjected to complex boundary conditions such as the nonlinear interactions between drill bit and rock formation and between the drill string and borehole wall. Concerning this complexity, the stick-slip phenomenon is a major component related to the torsional vibration and it can excite both axial and lateral vibrations. That may cause premature failure of drill string components. Therefore, the reduction and avoidance of stick-slip oscillations are a very valuable practice in terms of savings and exploration time. With these intentions, this study has the main goal of confronting the torsional vibration problem using a real-time conventional controller, a model-based control and a combination of both strategies over a test rig setup model Fig.1.
The approach is obtained following steps such as: open-loop analysis of the
drilling system considering two major systems (DC-motor actuator and a drill-strings system setup); closed-loop analysis using four proposed control strategies. Design of a controller based on dynamical results of open-loop and closed-loop analysis; suppression of the torsional vibration considering the nonlinearity based on the friction model applied to rotary inertias of the test rig; evaluation of a non-stop control system while rotating; and, verification by numerical simulations. In this study, the theoretical basis behind the drilling system will be given, as well as numerical results providing a stable and satisfactory controlled reduced scale drilling system using the following strategies: Proportional and Integral Controller (PI); Proportional, Integral and Derivative Controller (PID); Model Predictive Controller (MPC); Proportional, Integral and Derivative and Model Predictive Controller (PID + MPC).
The state-space model of the electromechanical system is given by Eqs. 1 and 2., and the associated general block diagram and the elements of the closed-loop control system is shown in Fig. 2. %\ref{fig.4.1}.
This closed-loop control system compares the measured angular velocity $\dot{\theta}_{3}$ to the reference angular velocity $\Omega_{ref}$. The error signal $E(t) = \Omega_{ref} - \dot{\theta}_{3}$ is used by the controller to manipulate the system. Thus, the controller provides the supply voltage $U_{m}$ (control signal) to activate the DC motor. In its turn, the DC motor provides the motor Torque $T_{n}$ to act on the drilling system in order to provide rotary motion. Also, a severity instability analysis is performed for the four control strategies. So, the concept of \textbf{Stick-Slip Severity ($SSS$)} is considered in Eq. 3. The SSS is defined as a color map that plots the relation between Normal Force acting in the rotors and angular velocity to identify severe torsional vibration (stick-slip) according to a certain criterion.
The SSS is used to evaluate the instability criterion based on the difference between maximum and minimum downhole angular velocity divided by the reference angular velocity. Then, the map is generated iteratively by comparing the values of $SSS$. The determined criterion quantifies the response amplitude of the system while oscillating around the reference velocity, and then classifies the high amplitudes in the stick-slip regime. As a result of SSS for the four control strategies, the Fig. 3 illustrates a comparison between them. Moreover, simulations showing a 2D and 3D map of the controllers, using the SSS, are performed, as illustrated in Fig. 4 and Fig.5. Also, the dynamics of a real-scale model and of the test-rig model are performed and analyzed, as illustrated in Fig. 6.
The approach is obtained following steps such as: open-loop analysis of the
drilling system considering two major systems (DC-motor actuator and a drill-strings system setup); closed-loop analysis using four proposed control strategies. Design of a controller based on dynamical results of open-loop and closed-loop analysis; suppression of the torsional vibration considering the nonlinearity based on the friction model applied to rotary inertias of the test rig; evaluation of a non-stop control system while rotating; and, verification by numerical simulations. In this study, the theoretical basis behind the drilling system will be given, as well as numerical results providing a stable and satisfactory controlled reduced scale drilling system using the following strategies: Proportional and Integral Controller (PI); Proportional, Integral and Derivative Controller (PID); Model Predictive Controller (MPC); Proportional, Integral and Derivative and Model Predictive Controller (PID + MPC).
The state-space model of the electromechanical system is given by Eqs. 1 and 2., and the associated general block diagram and the elements of the closed-loop control system is shown in Fig. 2. %\ref{fig.4.1}.
This closed-loop control system compares the measured angular velocity $\dot{\theta}_{3}$ to the reference angular velocity $\Omega_{ref}$. The error signal $E(t) = \Omega_{ref} - \dot{\theta}_{3}$ is used by the controller to manipulate the system. Thus, the controller provides the supply voltage $U_{m}$ (control signal) to activate the DC motor. In its turn, the DC motor provides the motor Torque $T_{n}$ to act on the drilling system in order to provide rotary motion. Also, a severity instability analysis is performed for the four control strategies. So, the concept of \textbf{Stick-Slip Severity ($SSS$)} is considered in Eq. 3. The SSS is defined as a color map that plots the relation between Normal Force acting in the rotors and angular velocity to identify severe torsional vibration (stick-slip) according to a certain criterion.
The SSS is used to evaluate the instability criterion based on the difference between maximum and minimum downhole angular velocity divided by the reference angular velocity. Then, the map is generated iteratively by comparing the values of $SSS$. The determined criterion quantifies the response amplitude of the system while oscillating around the reference velocity, and then classifies the high amplitudes in the stick-slip regime. As a result of SSS for the four control strategies, the Fig. 3 illustrates a comparison between them. Moreover, simulations showing a 2D and 3D map of the controllers, using the SSS, are performed, as illustrated in Fig. 4 and Fig.5. Also, the dynamics of a real-scale model and of the test-rig model are performed and analyzed, as illustrated in Fig. 6.