Abstract
Drillstring–borehole interaction can produce severely damaging vibrations. An example is stick–slip vibration, which negatively affects drilling performance, tool integrity and completion time, and costs. Attempts to mitigate stick–slip vibration typically use passive means and/or change the operation parameters, such as weight on bit and rotational speed. Automating the latter approach, by means of feedback control, holds the promise of quicker and more effective mitigation. The present work presents three separate fractional-order controllers for mitigating drillstring slip–stick vibrations. For the sake of illustration, the drillstring is represented by a torsional vibration lumped parameter model with four degrees of freedom, including parameter uncertainty. The robustness of these fractional-order controllers is compared with traditional proportional-integral-derivative controllers under variation of the weight on bit and the drill bit’s desired rotary speed. The results confirm the proposed controllers effectiveness and feasibility, with rapid time response and less overshoot than conventional proportional-integral-derivative controllers.
Highlights
The drillstring system plays a vital role in the oil and gas extraction industry by transferring torque and weight on bit (WOB) from the rotary table on the surface to the bit in the borehole
The main contribution of the present work is the design of two novel fractional-order proportional-integral (FOPI) and fractional-order proportional-derivative (FOPD) controllers, and to implement them with a newly developed FOPID controller for stick–slip vibration mitigation
The main focus of this work was to demonstrate the effectiveness of fractional-order controllers to suppress the stick–slip vibration of a drillstring system and to track the desired velocity under parameter variations
Summary
The drillstring system plays a vital role in the oil and gas extraction industry by transferring torque and weight on bit (WOB) from the rotary table on the surface to the bit in the borehole. The main contribution of the present work is the design of two novel fractional-order proportional-integral (FOPI) and fractional-order proportional-derivative (FOPD) controllers, and to implement them with a newly developed FOPID controller for stick–slip vibration mitigation. Specific fractional-order controller topics covered include: (i) the development of mathematical models for FOPI and FOPD, which represent generalized forms of a conventional proportional derivative (PI), and a conventional proportional derivative (PD) controller as discussed by Lin et al.[1]; (ii) a study of the dynamic performance of the three fractionalorder controllers under variation of the WOB and reference velocity; and (iii) a comparison of fractional order vs conventional PID controllers. The drillstring is a complex system including an electric motor that rotates the rotary table, coupled with drill pipes and drill collars, and the drill bit.
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