Failure of drill-strings is very costly in terms of money and time and occurs more frequently than oil companies would like to see. There are many reasons for drill-string failure, such as vibration, fatigue, and buckling. This paper addresses the problem of suppression of stick-slip oscillations in oil well drill-strings using proportional integral derivative (PID) and lead-lag controllers in conjunction with genetic algorithms. Simulation results are presented to validate the proposed control schemes.
The drilling process is affected by the dynamically induced vibrations caused by design imperfections as well as material elasticity. Because of these vibrations, premature wear and damage of drilling equipment may occur. Vibrations can decrease the rate of penetration (ROP), and thereby increase the cost of the well(1,2,3). Moreover, vibrations can interfere with measurement-while-drilling (MWD) tools or even cause their damage. Another major problem caused by vibrations is the induced wellbore instabilities which can worsen the condition of the well(4,5).
The literature on drill-strings can be classified in three groups: drill-string modelling, drill-string control, and drill-string technology. In this paper, we will focus on drill-string dynamics and control. There have been a significant number of research publications on drill-string dynamics and a representative few are considered here. Many different models for drill-strings are available in the literature, which may include one or more of the following phenomena: bit-bounce, stick-slip, forward and backward whirl, axial, lateral, and torsional vibrations; see, for example, Christoforou et al.(6), Jansen and van den Steen(7,8), and Leine et al.(9). Stick-slip is a major cause of torsional vibrations and many researchers have tried to minimize its effect on the behaviour of the drill-strings using active damping techniques(10,11,12). These techniques reduce the torque fluctuations and torsional drill-string vibrations affecting in this manner the stick-slip conditions. The underlying concept is to reduce the amplitude of the downhole rotational vibrations using torque feedback. The feedback is used by the rotational drive, which slows down the rotary rate when the torque increases and speeds it up when the torque decreases(8,13,14).