Research Journal of Recent Sciences ________________________________________________ ISSN 2277-2502Vol. 2(6), 78-82, June (2013) Res.J.Recent Sci. International Science Congress Association 78 Design of a Controller for Suppressing the Stick-slip Oscillations in Oil well DrillstringAzadi Sassan and Bake HalimberdiDepartment of Electrical and Computer Engineering, Semnan University, IRANAvailable online at: www.isca.in Received 22nd January 2013, revised 23rd February 2013, accepted 10th March 2013 AbstractIn oil well drilling operations, one of the important problems to deal with is represented by the necessity of suppressing harmful stick-slip self-excited oscillations. This oscillation is a source of failures which reduce rate of penetration (ROP) and increase drilling operation costs. Stick-slip leads to excessive bit wear, premature tool failures and a poor rate of penetration. In this paper we propose to use the weight on the bit (WoB) force as an additional control variable to compensate stick-slip oscillations. We use changes of torque applied to drillstring for adaptation of oB. Torque and WoBare both measurable and bit speed and bit torque is not necessary. Simulations applying this method show that the stick-slip oscillations can be eliminated without requiring a re-design of the velocity rotary-table control. Keywords: Oil well drilling, weight on bit (oB), stick-slip, Dynamic model. Introduction There has for the past 50 years been conducted extensive research on the subject of torsional vibrations on drill strings used by the oil industry. These torsional vibrations are an important cause for deteriorated drill string performance. They can lead to premature failure of bits, motors and other expensive components used in drilling operations. One of the main reasons for torsional vibrations is the stick-slip phenomenon. The phenomenon is characterized by stick-phases, where the rotation comes to a complete stop, and slip-phases where the angular velocity of the bit increase up to three times its nominal value. This undesirable motion of the bit will not only lead to unwanted wear, but also significantly reduce the rate of penetration (ROP), which is an important consideration financially associated with drilling operations. Many ways of reducing these vibrations have been proposed, both from practical and theoretical viewpoints. Historically, the experience of drillers has revealed that the manipulation of different drilling parameters (increasing the rotary speed, decreasing the weight-on-bit (oB), modifying the drilling mud characteristics, introducing an additional friction at the bit, etc). However, this strategy depends too much on the personal skills of each drilling technician to be really effective. More effective control methodologies have appeared in the literature in order to compensate drillstring stick-slip vibrations. In 1998, a H-control method to suppress stick-slip oscillations on a contemplated system has been proposed. H-control has been a widely used solution in controlling vibration problems, such as in cutting processes where it is used to suppress machine tool chatter. Another method to suppress stick-slip oscillations is to use the weight on bit as an additional control variable. This method, called Drilling OScillation KILler (D-OSKIL), was introduced in4,5. In this method when the stick-slip oscillations occur, the drillstring pulled upward to reduce WOB. In bit-velocity varying WOB is introduced. Dynamic Modeling of a DrillstringDrillstring systems are used by the oil industry to extract gas and oil from earth surface. With rotating the bit connected to end of drillstring, by rotary table or top drive a hole is made on the surface of the earth crushing the rock formation. The drillstring consists of the BHA and drill pipes screwed end to end to each other to form a long pipe. The BHA comprises the cutting device, regarded as bit, stabilizers (at least two spaced apart) which prevent the drillstring from underbalacing, and a series of pipe sections which are relatively heavy known as drill collars. Drillstrings usually include at the top of the BHA a section of heavy-weight drill pipe. While the length of the BHA remains constant, the total length of the drill pipes increases as the borehole depth does so and can reach several kilometers. Multiple kind of models have been used in literature to describe drillstring systems. However, lumped parameters models have been shown to be valid enough to properly describe the stick-slip oscillation phenomena and easy enough to make the study not too complex3-7. The model used here (figure 2) is a two-degree-of-freedom model with two inertial masses and , locally damped by cand c. The inertias are coupled with each other by an elastic shaft of stiffness k and damping c. The variables and stand for the rotary and the bit angle. The rotary torque control signal used to regulate the rotary angular velocity j  . The represents the total fiction (fb) and viscosity torque over the drill bit. Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 2(6), 78-82, June (2013) Res. J. Recent Sci. International Science Congress Association 79 The model equations are the following: ( ) ( ) )(T-TkcJbrmbrbrrrjjjjjj      (1)       (2) and, sgn( j j j    + = (3) j j j    + = (4) And we use the equations (5), (6) and (7) to describe the friction torque over the drill bit. sgn())sgn(obififif  (5)  (6)      (7) Where is the system state vector, j m  is the velocity-depending dry friction coefficient at the bit, sb, cbare the static and Coulomb friction coefficients associated with the inertia with 0 cbsb 1, is a positive constant, sbis the static friction torque associated with and sb= obsb, is the bit radius, obis the WOB, which is directly related with the hook-on-load applied at the surface, eb) is the applied external torque that must overcome the static friction torque Tsbto make the bit move, and � specifies a small enough neighborhood of = b j  The resulting friction model is represented in Figure 2, and it is compared with a classical dry friction model with an exponential-decaying law at the sliding phase. The dry friction torque fbfor � b j  varies between sband cb= obcb. Assuming =u as control input, a PID control action is added to the model at the top end of the drillstring in order to maintain the top velocity constant. Then: yKKtKtuirdrp+-W+-W=)()()(jj  (8) With W the reference velocity, )), and �0, �0, �0 and �0. Control u is saturated to some value umax � 0, u| umaxAccording to field experience, the increase of W and the decrease of the ob can make stick-slip disappear. The model parameters used for the simulations are extracted from: =.518kgm, J=0.0318kgm, c=0.18Nms/rad, c=0.0001Nms/rad, c=0.03Nms/rad, k=0.073Nm/rad, Tcb=5Nm, sb=8Nm, Tcr=0.5Nm, D=10-6, 9.0 = b g , umax=20, K=3, =10, K=4. Figure 4 presents the block diagram of drilling system and closed loop speed control. In figure 1 and figure 5, a comparison between stick- slip oscillations measured in the field (Figure obtained from) and the ones produced by simulating the closed-loop system in Matlab/Simulink can be seen. Inertias, stiffness and damping coefficients correspond to a reduced-scale model extracted from. Although these values do not correspond with real parameters, they can be used to describe the behavior of the drillstring. Designing the Stick-Slip Compensator From simulation studies and figure 5 we can say that approximately when bit sticking the torque on surface () is decreasing and when bit slipping torque is increasing. If we increase the ob when slipping, the maximum speed of bit is reduced and duration of slipping will be longer. And if we decrease the ob when bit sticking the duration of sticking is reduced. It is concluded that the manipulation of the obcan be a solution for stick-slip oscillations. The variation of the ob is proposed as follows: obob (9) for avoiding from unwanted conditions and lowering the ROP, obmust be saturated to maximum %20 of nominal ob greater than ob0 and %20 of nominal ob lower than ob0. ob-variation low (9) can be applied to model. Simulation ResultsBlock diagram of drilling system with compensator is presented in figure 6 and result of simulation is presented in figure 7. In this simulation the compensator is turned on at t= 55s. in this case, although stick-slip cycles are suppressed. Oscillating behavior of bit speed may not desirable after turning on the compensator. The compensator makes little change in ob to eliminate the oscillation. After compensation, ob force recovers its nominal drilling value. ConclusionA model describing the torsional behavior of a generic vertical oilwell drillstring has been presented and a model by manipulating ob for suppressing stick-slip oscillations has been proposed. Then make some simulations in Matlab\Simulink with applying the compensator. The control strategy achieves two main goals: i. the velocity at the top end of the drillstring is maintained to a reference value, ii. the bit velocity tracks the surface velocity with a reduction of the BHA sticking. Research Journal of Recent Sciences ______ _ Vol. 2(6), 78-82, June (2013) International Science Congress Association Drillstrings modeling oriented to the description of mechanical vibrations and the control of them are open research problems. In order to have more realist ic models, the consideration of drillstring length, lateral and axial dynamics and the influence of Stick- slip oscillations measured in the field (Figure obtained from _ ________________________________ ______________ International Science Congress Association Drillstrings modeling oriented to the description of mechanical vibrations and the control of them are open research problems. ic models, the consideration of drillstring length, lateral and axial dynamics and the influence of circulating drilling muds are needed. It is also necessary to make an analysis of the influence of the drillstring length, formation properties and bit char acteristics in model parameters which would lead to a robust performance analysis. Figure-1 slip oscillations measured in the field (Figure obtained from 4) Figure-2 Drilling Equipment ______________ _________ ISSN 2277-2502 Res. J. Recent Sci. 80 circulating drilling muds are needed. It is also necessary to make an analysis of the influence of the drillstring length, acteristics in model parameters which would lead to a robust performance analysis. Research Journal of Recent Sciences ______ _ Vol. 2(6), 78-82, June (2013) International Science Congress Association Mechanical model of drillstring and friction model Stick- slip oscillation in Bit speed produced by simulating the closed W ob r W Controller + - _ ________________________________ ______________ International Science Congress Association Figure-3 Mechanical model of drillstring and friction model Figure-4 Block diagram of drilling system Figure-5 slip oscillation in Bit speed produced by simulating the closed - loop system in Matlab/Simulink (Simulation with 10 rad/s and ob=1) W ob Drillstring Model Controller r j  b j  bfT Friction Model ______________ _________ ISSN 2277-2502 Res. J. Recent Sci. 81 loop system in Matlab/Simulink (Simulation with = Research Journal of Recent Sciences ______ _ Vol. 2(6), 78-82, June (2013) International Science Congress Association Block diagram of drilling system with compensator Simulation results of system with compensator (turned on at t=55s) References 1.Morten Krotoy Johannessen Torgeir Myrvold, Stick prevention of drill strings using nonlinear model reduction and nonlinear model predictive control, Thesis of master of science of Norwegian University of Science and Technology Department of Engineering Cybernetics, MAY (2010)2.A.F.A. S errarens, M.J.G. van de Molengraft, J.J. Kok and L. van den Steen, H- infinity control for suppressing stick slip in oil-well drillstrings, IEEE Control Systems (1998)3.E.M. Navarro- L´opez and R. Su´arez approach to modeling and controlling stick in oil-well drillstrings, in IEEE International Conference on Control Applications Taipei, Taiwan, 1454 rW Controller + - ob + _ ________________________________ ______________ International Science Congress Association Figure-6 Block diagram of drilling system with compensator Figure-7 Simulation results of system with compensator (turned on at t=55s) Myrvold, Stick -Slip prevention of drill strings using nonlinear model reduction Thesis of master of science of Norwegian University of Science and Technology Department of Engineering Cybernetics, MAY errarens, M.J.G. van de Molengraft, J.J. Kok and infinity control for suppressing stick - IEEE Control Systems , 19-30 L´opez and R. Su´arez -Cortez, Practical approach to modeling and controlling stick -slip oscillations IEEE International Conference on 1454 -1460(2004)4.Carlos Canudas-de- Wit, Francisco R. Rubio, "D new mechanism for controlling stick well drillstrings." IEEE Transactions on control systems technology, 16(6), (2008)5.Corchero M.A., Canudas-de - Stability of the D- OSKIL oscillation suppression mechanism for oil well drillstrings 45th IEEE Conference on Decision and Control Diego, California, 1315 December 6.E.M. Navarro- L´opez and D. Cort´es, Avoiding harmful oscillations in a drillstring through dynamical analysis, accepted in Journal of Sound and Vibration 7. Marcos Silveira and Marian Wiercigroch, Low dimensional models for stick- slip vibration of drill International Conference on Modern Practice in Stress and Vibration Analysis, Journal of Physics 181 (2009) Drillstring Model Controller r j  bj  bfT T m d/dt  - + Friction Model T=55s ______________ _________ ISSN 2277-2502 Res. J. Recent Sci. 82 Wit, Francisco R. Rubio, "D -OSKIL: A mechanism for controlling stick -slip oscillations in oil IEEE Transactions on control systems - Wit, C. and Rubio F.R., OSKIL oscillation suppression well drillstrings , Paper presented at the 45th IEEE Conference on Decision and Control , San December (2006) L´opez and D. Cort´es, Avoiding harmful oscillations in a drillstring through dynamical analysis, Journal of Sound and Vibration , (2006) Marcos Silveira and Marian Wiercigroch, Low dimensional slip vibration of drill -strings, 7th International Conference on Modern Practice in Stress and Vibration Analysis, Journal of Physics : Conference Series