Stick–slip vibrations in oil well drillstring: A review:

Liping Tang; Baolin Guo; Xiaohua Zhu; Changshuai Shi; Yunlai Zhou

doi:10.1177/1461348419853658

Stick–slip vibrations in oil well drillstring: A review:

Tang, Liping; Guo, Baolin; Zhu, Xiaohua; Shi, Changshuai; Zhou, Yunlai 2019-06-04 00:00:00 A survey of the literature related to theoretical and experimental studies on stick–slip vibration in oilwell drillstring is carried out in this study. It aims to explain key concepts and present the existing methods for studying this phenomenon. After briefly describing the stick–slip vibration related problems, theoretical models for such phenomenon are discussed including both coupled and uncoupled models. Discussion for experimental investigations including both laboratory and field tests are hereinafter addressed. This study aims to summarize the literature related to the stick–slip vibration, and help researchers in understanding and suppressing such phenomenon. Keywords Stick–slip vibration, drillstring, bottom-hole assembly, degree of freedom, structural coupling Introduction The drillstring exhibits severe stick–slip vibration induced by the contact between the drill bit and the formation. Stick–slip vibration of drillstring appears as periodic alternations of stick and slip phases. During the stick phase, the bit keeps stationary for a time interval and the torque on bit (TOB) increases to a value of breaking this state. During the slip phase, the bit releases all of a sudden and accelerates to an angular velocity several times as the 2,3 velocity of rotary table. Stick–slip vibration not only reduces the tool life, but also increases the non-productive time that increases the development expense. In addition, this vibration may cause lateral and axial vibrations, causing equipment failure and the rate of penetration (ROP) reduction. The investigation on stick–slip vibration in drillstring dated back to the publication of Belokobyl’skii and Prokopov where the friction induced vibration was analyzed and the self-excited drillstirng vibration concept was introduced. Dareing indicated the possibility of eliminating drillstring vibration by controlling the rotary speed and explored the self-excited vibration induced by motion of the bit. Dawson et al. discussed the drillstring vibration as a stick–slip phenomenon. The stick–slip phenomenon has undergone numerous outputs in the past decades; however, most of the publications are ﬁeld observations and methods for mitigating this motion, including both passive and active methods. Due to the variation of drilling conditions and drilling technologies advances, the stick–slip vibration plays an increasingly essential role. For instance, with the petroleum industry development, more and more deep and ultra-deep wells are considered for conduction. This study reviewed the literatures on slick–slip vibrations for oilwell drillstring, thus providing reference for the engineers and scientists working on this area. School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, China Department of Civil and Environmental Engineering, National University of Singapore, Singapore, Singapore Corresponding author: Xiaohua Zhu, School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China. Email: zxhth113@163.com Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www. creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage). 886 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Stick–slip vibration with uncoupled models The investigations reviewed in the following section are the mathematical methods for modeling stick–slip vibra- tions. The contributions are arranged under single degree of freedom (SDOF) lumped parameter models, multiple-DOF (MDOF) vibration models, and continuous system models. SDOF Lumped pendulum vibration models Halsey et al. studied the stick–slip vibration of drillstring through treating the bottom-hole assembly (BHA) as a lumped ﬂywheel. For given conditions, the SDOF model could not predict the formation of stick–slip motion. Kyllingstad and Halsey revealed an increase in mean torque with increasing the rotary speed, however, the related explanation was not provided. The damping effect was not considered in the model. Lin and Wang worked extensively on the lumped parameter model considering the damping effect. To better understand the cause of stick–slip phenomenon, Brett presented a model to show that torsional drillstring vibration can be initiated by variation of bit characteristics. The model regarded the drillstring as a lumped mass-spring system (Figure 1), and uses two coupled differential equations to describe the stick–slip motion. The results indicated that stick–slip vibration could be eliminated by controlling rotary table torque instead of rotary table velocity, which was not veriﬁed with ﬁeld-test. Rudat and Dashevskiy modeled the drillstring as a mechanical oscillator with rotational SDOF (Figure 2). The model was used to determine optimal parameters by predicting the intensity of downhole stick–slip vibration. However, only the steady state responses were presented. By using a SDOF model similar to the one shown in Figure 2, Qiu et al. studied the stick–slip vibration of drillstring. In the model, the bit-rock contact was modeled as random friction, and the stick motion and slip motion were treated separately. For the purpose of verifying the model, Monte Carlo simulation was conducted. Even simple lumped mass model with actual drilling parameters can reproduce complex nonlinear drilling dynamics processes. Cunha-Lima et al. developed a simpliﬁed SDOF model to study the torsional stability of the drillstring, for better understanding the causes of stick–slip phenomenon and the way to mitigate it. Based on 16–18 this model, a similar mechanical model was developed by Tang et al. to study the effect of drilling parameters on stick–slip vibration (Figure 3). Results showed that the rotary table velocity, the friction coefﬁcients, and viscous damping have signiﬁcant effect on both the occurrence of stick–slip vibration and its dynamics. 19,20 Another type of SDOF model used to investigate the stick–slip is the block-on-belt model, shown in Figure 4. Van de Vrande et al. developed a SDOF block on belt model to study the stick–slip motion of Figure 1. Lumped mass spring model of the drillstring. Tang et al. 887 drillstring. Periodic stick–slip vibration can be found by applying the smoothing procedure and simple shooting method with an ordinary differential equation (ODE) solver. MDOF vibration models Compared to SDOF, MDOF models can catch more details of the drilling system. Consequently, many inves- tigations focused on stick–slip vibrations by using MDOF vibration models. Abdulgalil and Siguerdidjane Figure 2. Mechanical SDOF model of the drillstring. Figure 3. Analytical model of the drillstring system. Figure 4. The block-on-belt model. 888 Journal of Low Frequency Noise, Vibration and Active Control 39(4) developed a simple dual DOF (DDOF) model (Figure 5) of stick–slip vibration by regarding the drilling system as a torsional pendulum. The assumption in this model is not always true, because the friction behavior can change easily due to the drilling condition variations. Canudas-de-Wit et al. developed a similar open-loop plant model (Figure 6) as used by Rudat and Dashevskiy with different boundary condition, where the assumption that rotary speed is constant. The friction-induced limit cycles were studied and the weight on bit (WOB) was used as a control parameter to extinguish limit cycles. Based on this type of DDOF model, Navarro-Lopez and Sua´ rez reproduced the stick–slip motion in various operating conditions. Bayliss et al. investigated the mitigation of stick–slip phe- nomenon in the drilling system via an online-identiﬁcation-based adaptive design; Karkoub et al. used genetic algorithms (GAs) to optimize stick–slip responses. Silveira and Wiercigroch evaluated the bit-rock interaction and developed a three DOF (TDOF) torsional pendulum model to investigate the drillstring stick–slip behavior. Patil and Teodoriu developed a TDOF stick– slip model (Figure 7) and studied the effects of inﬂuencing parameters such as rotary table velocity and WOB on stick–slip vibration, where the nonlinear friction forces represented the bit-rock interaction. 29–31 Navarro-Lopez et al. discussed a more generic discontinuous torsional model of four DOF (FDOF) (rotary table, drill-pipes, drill-collars, and drill bit), shown in Figure 8. Based on this model, a sliding motion leads to self-excited vibrations and bit stick phenomena at the BHA were analyzed. The key drilling parameters were determined by investigating Hopf bifurcations. Figure 5. Drilling rotary model by Abdulgalil and Siguerdidjane. Figure 6. The DDOF model by Canudas-de-Wit et al. Tang et al. 889 Kreuzer and Steidl developed a high dimensional drillstring model consisted of 51 elements, one element represents the rotary table, one element represents the BHA, and 49 elements model the string with self-excited stick–slip vibration. The ﬁnite element (FE) method was used to model drillstring; however, most of the reported investigations concentrated on investigating the BHA. In order to understand the severe torsional and axial vibrations excited by stick–slip vibration, Khulief et al. used Lagrangian method and FE method to derive the motion equation of the rotating drilling system. The drillstring model included both drill-pipes and drill-collars to study the dynamics of the drilling system in the existence of stick–slip vibrations. Kapitaniak et al. developed a detailed MDOF model of a drilling system using FE method to calibrate a TDOF mathematical model, in particular when stick–slip vibration occurs. Distributed vibration models A high dimensional or inﬁnite model can describe typical features when modeling an engineering system. But these models are computationally expensive. Palmov et al. studied the stick–slip vibration of drillstring basing on a distributed vibration in torsion, considering the BHA to be a rigid body. Based on this model, studies have tried to 36,37 interpret the instability initiation that results in stick–slip phenomenon of drillstring. Challamel proposed the direct method of Lyapunov to study the stability conditions of a distributed drillstring model. The stability of a drillstring relatively forms the bit-rock contact depending on the rock crushing process. Simulations illustrated that the bit converges towards stick–slip vibration with a typical limit cycle. Results also showed that the stick–slip Figure 7. The TDOF torsional pendulum model by Patil and Teodoriu. Figure 8. The FDOF lumped pendulum model describing the stick–slip vibration of a drillstring. 890 Journal of Low Frequency Noise, Vibration and Active Control 39(4) vibration behaves for polycrystalline diamond composite (PDC) bit with small variation of axial velocity and justiﬁes the use of an uncoupled torsional model. However, bit-rock interaction experiments with single cutters may not reveal the intrinsic velocity weakening effect. Further investigation in this ﬁeld was done by Saldivar 38,39 29–31 et al. In the study, a friction model similar to the one by Navarro-Lopez et al. was presented. D’Alembert transformation and Laplace transform were used to analyze and simulate the drillstring behavior. By investigating the occurrence of stick–slip vibration, some approaches for mitigating stick–slip vibration were put forward by manipulating BHA characteristics. Kreuzer and Steidl presented the wave equation for the torsional dynamics of the actual drillstring. Two principles were revealed: (a) existing a range of the drillstring rotation angular velocity where the stick–slip motion of the drillstring takes place, and (b) the process of stick–slip vibrations and their forms are independent of the initial conditions. Almost all the previous investigations focused only on stick–slip vibrations in the torsional direction. Ritto et al. thought that only one contact point at the bit-rock interaction in vertical wells exists. In horizontal drilling, nevertheless, there is stick–slip in the axial direction because of frictional force. Under this circumstance, they proposed a stochastic model taking into account the friction force between the drillstring and the borehole. Combining FE method with Monte Carlo method into the bar model, stick–slip behavior in the axial direction was obtained. For such bit-rock interaction model, the stochastic friction forces and the parameters selection are sources of uncertainties. In a latest work by Ritto, identiﬁcation of factors of the bit-rock contact model was investigated. In order to control stick–slip vibration through startup trajectory design, Aarsnes et al. presented a distributed model of drillstring to replicate the stick–slip vibration caused by transition of static and dynamic frictions. This work was followed by a distributed axial-torsional drillstring model to investigate the appearance and global characteristics of self-excited vibrations caused by the regenerative effect of bit-rock interaction. The investigation showed the effect of bit rotation rate on the excitation of multiple axial and torsional modes of the drillstring. In addition, a stability map of the slick–slip vibration was presented. Stick–slip vibration coupling models The vibrations in the drilling system are usually divided into three fundamental types: axial, transverse, and torsional modes, with different patterns of manifestation. Bit bounce, whirling and stick–slip are extreme states of the axial, transverse and torsional vibrations, respectively. The causes of these vibrations include the inter- action between the drillstring and borehole, bit-rock interaction, unbalance of curvature of the drillstring, and variation of the drilling parameters. These motions are usually complex and are coupled together or occur simultaneously. A number of publications studied the coupled vibration of drillstring, including lateral–torsion- al, lateral–axial, and axial–torsional coupled models. The coupled models related to stick–slip vibration are to be reviewed in this section. Stick–slip and bit bounce coupling models 46 47 Based on the simpliﬁed lumped model by Christoforou and Yigit, Yigit and Christoforou simulated the inﬂuences of operating conditions on bit bounce and stick–slip. It indicated that conditions at the interface of bit and rock are major factors of bit dynamics. Noted for the presented model, a number of parameters that should be determined by experimental measurement were included. The stick–slip vibration modeling typically considers only the torsional vibration of drillstring regarding the 36 48–50 interaction between the bit and rock as Coulomb friction referred to velocity weakening. Richard et al. proposed a DDOF discrete model (shown in Figure 9) considering the axial and torsional vibrations of the drilling system to study the self-excited stick–slip phenomenon. Coupling between the two vibration modes was realized by using a bit-rock contact principle where the friction and crushing processes were considered, which differed from the classical method used to reveal the stick–slip vibration. The dynamic responses can be obtained by the surface conditions of the drill bit and bit-rock contact principles, in conjunction with the motion equations for the torsional and axial vibrations. The model was restricted to an idealized drag bit that includes many identical radial blades distributed uniformly along axis of revolution of the drill bit (see Figure 10). For the developed model, a delay was introduced into the cutting process, leading to the occurrence of self- excited vibration that degenerates into stick–slip or bit bouncing for some conditions. In this model, the WOB was considered as a constant and this can be realized by adjusting the hook load, which means the axial displacement of the drillstring must be controlled at the surface to match the bit movement. The drill bit, however, encounters Tang et al. 891 48–50 Figure 9. Mechanical model of the drilling system. 48–50 Figure 10. Drill bit model developed by Richard et al. severe axial vibration and thus is difﬁcult to realize the proposed condition. The model neglected the dynamics of the delay-based effect on the assumption of a timescale separation between the axial and torsional dynamics. 49,50 51 Based on the model by Richard et al., Germay et al. identiﬁed the mechanisms of axial and torsional vibrations and their parametric dependence. The investigation of decoupling axial and torsional dynamics pro- vided an interpretation for the occurrence for most dynamic regimes. Germay et al. expanded on the model of Richard et al. by using continuous system model (also called distributed model) rather than a DDOF lumped model. The drillstring dynamic responses were studied using the FE method and some new features in the stick– slip vibration were detected. However, this model is always unstable according to a recently linear stability analysis by Nandakumar and Wiercigroch. In order to identify the exact origins and interplay of stick–slip and bit bounce, they proposed fully coupled DDOF model with a viscous damping and a state-dependent time delay. 54–56 Many other studies presented the coupled stick–slip phenomenon and bit bounce with a basic model by 49,50 57 Richard et al. Kamel and Yigit studied coupled axial and torsional behaviors of a drillstring through utilizing a DDOF lumped pendulum model where Lagrangian approach was used to estimate the equivalent system parameters and a new cutting and interaction model was used to describe the bit-rock contact. It was shown that the stick–slip motion and bit bounce could be minimized by proper choice of the operational param- eters. Kovalyshen considers the resonance between the cutting force and natural vibration modes as the reasons of drillstring vibration, and carried out a stability analysis of coupled vibrations of a drilling assembly. 892 Journal of Low Frequency Noise, Vibration and Active Control 39(4) 60,61 Figure 11. Free body diagram of the BHA with the axial acting forces. It demonstrated that the driving mechanism of the axial vibration mode is the regenerative effect, while the driving mechanism of the torsional vibration is the crushing process of the bit and the bit/rock contact. Based on this study, a root cause of stick–slip coupled with bit bounce was revealed. Alamo and Weber obtained a mathematical model to investigate the torsional vibration, considering the longitudinal vibration. For the stick–slip vibration model, the top rotates have a constant rotary speed and the bottom end are subjected to a cutting force which represents the bit-rock interaction. Finite difference was used to discretize the space domain and Runge-Kutta method was employed to obtain the time response. Results showed that the coupled model could describe the stick–slip vibration depending strongly on the rotary table velocity. Sampaio et al. considered the geometrical nonlinearity in modeling the coupling of axial and torsional vibra- tions. By using FE method and taking into account the large rotations and nonlinear strain displacements, linear and nonlinear models were compared. It showed that the linear and nonlinear models differ comparatively after the ﬁrst period of stick–slip. Based on the mechanical model proposed by Christoforou and Yigit considering the axial and torsional 60,61 behaviors of drillstring, Divenyi et al. developed a DDOF lumped parameters model (see Figure 11) to study the coupled axial and torsional motions where the coupled vibration was regarded as being induced by the bit- rock contact and the axial force was regarded as the catalyst of generating a resistive torque. The analyzed results show that the model is able to predict a full range of dynamic responses including the stick–slip vibration and bit bounce and to understand the drillstring dynamics and critical behaviors of the system by using different scenarios related to parameter changes. However, a number of parameters should be determined by experimental measure- ment. Particularly, measuring the parameters is challenging. For the complex drilling process, the parameters in the model changed easily. More ﬁeld data used to verify and optimize the model are needed. Basing on a DDOF model with coupling torsional and axial vibration, Vasconcellos and Savi conducted a parametric analysis of the transitions between different motion phases and the non-smooth dynamic responses of stick–slip and bit bounce. Sarker et al. applied a bond graph model of the drilling system to predict axial and torsional vibration, and coupling between the two vibrations due to bit/rock contact. Ertas et al. used transfer matrices to solve small torsional vibrations around a baseline solution in the frequency domain, accounting for well path, tool joints, viscous damping, surface boundary condition, bit features, and special vibration mitigation tool. Sairaﬁ et al. established a coupled stick–slip and bit bounce model with the driving system and hoisting system. Results demonstrated that controlling only torsional vibration is not effective in suppressing bit bounce phenomena and an axial controller should be implemented as well. Earlier studies for drillstring dynamic model lacked two essential features: the axial stiffness of the drillstring and friction from along the drillstring. Besselink et al. investigated the mechanisms leading to stick–slip using a model that includes axial motion, torsional motion, and a rate independent bit-rock contact law. It showed that the axial stick–slip phenomenon is dependent on the rotational bit speed and that the generation of torsional stick–slip phenomenon is driven by the axial motions, which means that mitigation of axial vibrations may also suppress torsional vibration. Besselink et al. furthered the work of mitigation of stick–slip vibration by using feedback control strategies. Previous works postulates that self-excited vibrations occur because of the coupling between the drillstring and 68 69 the regenerative effect in the bit-rock contact law. To prove this, Aarsnes and Aamo studied a graphical condition for stability of drillstring based on the Nyquist stability criterion. Tang et al. 893 Figure 12. The simplified drillstring model with equivalent lumped parameters. Stick–slip and whirl models coupling A time domain dynamical model allows the prediction of drillstring dynamics related to torsional and lateral vibrations. By using FE approach, Schmalhorst and Baumgart developed a nonlinear drillstring model taking into account arbitrarily shaped assemblies during drilling of curved boreholes. In the model, restitution forces act on the drillstring and contact velocity-dependent friction forces were introduced. The torsional and lateral DOF were coupled and the whirl and stick–slip phenomena combined with normal drilling conditions were solved numerically. Abbassian and Dunayevsky studied the stability of bit dynamics through a coupled torsional– lateral vibration model. 72–74 Whirling and parametric resonances of drillstring have been investigated. In these investigations, the rotary table velocity was regarded as a constant and the torsional vibration was not included. Based on this, Yigit and Christoforou considered the coupling between the lateral and torsional motions of drillstring and assumed the excitation at the bit to be related to the bit rotation. The motion equations for coupled torsional and lateral motions were established through a simpliﬁed model shown in Figure 12. Apart from the strong coupling and nonlinear features included in the model, a consistent model was utilized to characterize the impacts of drill collars with the borehole. Results showed that there is signiﬁcant energy transfer between the torsional and lateral motions at certain frequencies and that adjusting the surface torque is more efﬁcient in eliminating the stick–slip vibrations. In another work of them, the rotary drive system was also included in the mechanical model. Based on the results obtained from theoretical analysis, a linear quadratic regulator controller was designed to mitigate the stick–slip and whirl motions. Drillstring vibration is highly nonlinear and the mechanical model can only be established by a group of nonlinear differential equations. The linear control approaches are not accurate for controlling the coupled lateral and torsional vibrations. Based on the mechanical model presented by Yigit and Christoforou, Al-Hiddabi et al. developed an inversion control design method based on nonlinear differential equations to control the torsional and lateral vibrations. In order to interpret the complex drillstring motions where stick–slip vibration and lateral whirl are involved, Leine et al. developed a simpliﬁed lumped stick–slip whirl model of the drilling system. The model exposes only the basic phenomena but was discontinuous. For this model, discontinuous bifurcations are obtained, providing explanation for the disappearance of stick–slip phenomenon when whirl motion appears. However, the experi- mental results were obtained by averaging the torque on bit over several revolutions and may not hold at a more relevant time scale. Melakhessou et al. proposed a FDOF mathematical model to investigate the stick–slipt and whirl vibrations, with lateral movement, rotation of the section, bending around thetangential orientation, and torsional displace- ment of the drillstring were included. Field cases showed that stick–slip and whirl can be eliminated when a roller reamer is introduced. Sowers et al. developed a conceptual model coupling stick–slip and whirl in order to understand the mechanism of roller reamers improving drilling performance by decoupling or suppressing 894 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Figure 13. A schematic depicts the drillstring model. drillstring vibrations. Vlajic et al. presented a distributed parameter model (Figure 13) to describe the coupled bending and torsional vibrations while the interaction forces between the drillstring and the wellbore were taken into account. Both the whirl and stick–slip phenomena were investigated numerically and the results were com- pared with the experimental results. Butlin and Langley claimed that drillstring dynamical models contain three features (1) efﬁcient so as to conduct parametric investigation, (2) simple so as to reveal the underlying mechanisms, and (3) retain enough details to associate real conditions. By using a reduced order model that takes into account the nonlinear inter- action laws and solving by time domain integration, results from cases studies demonstrated the occurrences of a number of phenomena, including stick–slip vibration and whirl. Apart from the mathematical models, ﬁeld tests 2,81,83–85 on the stick–slip and whirl were also carried out by many researchers. Fully coupled vibration models 86–88 Tucker and Wang proposed a torsional rectiﬁcation mechanism to study stick–slip and compared it with existing soft-torque devices via several mathematical models. It shows that the approach proposed can eliminate many of the volatilities suffered by the existing suppression approach used to control stick–slip vibration. Baumgart derived a fully coupled mathematical model for the drilling process and solved it as an initial value problem. For the nonlinear differential equations of motion for the drillstring, the axial, lateral and tor- sional motion of the drillstring as well as the ﬂow rate, the mud pressure, and buckling were included. WOB and torque on bit were obtained from characteristic curves, which are functions of the penetration rate, and the angular bit velocity. Results showed the self-induced characteristics of the stick–slip and bit bounce phenomenon. However, discussions on the lateral vibration results were not included. 4,46 Christoforou and Yigit claimed that bit-rock and drillstring-borehole interactions as well as the geometric and dynamic nonlinearities give rise to the coupling of the drillstring vibrations. They presented a fully coupled model for the three basic modes of vibration of actively controlled drillstring with the mutual dependence of these vibrations. The model was similar to the one presented in Figure 15. It showed that torsional vibration due to bit motion excites axial and lateral motions leading to bit bounce and impacts with the borehole. An active control strategy was proposed to control the stick–slip vibration of the drilling system. Khulief and Al-Naser developed a 12-DOF FE model for drillstring with the coupling vibration and gyro- scopic effects were considered. The reduced order model was obtained by modal transformation, and the modal features and lateral dynamics of the drillstring at the drill bit were presented. Khulief et al. presented a dynamic drillstring model accounting for the axial-bending vibration and the torsional-bending vibration. The gyroscopic effect, the gravitational force, and the drillstring-borehole impact were considered, wherein the force–displace- ment principle was applied to describe the impact force and the energy balance relations were used to determine the viscous damping. Tang et al. 895 Figure 14. General scheme of the dynamical model. By using Timoshenko beam theory, Ritto et al. established a numerical model to investigate the effect of the drilling ﬂuid on the dynamics of the drillstring (Figure 14). A simpliﬁed ﬂuid–structure interaction model account- ing for the mudﬂow in and out of the drillstring was used. Other factors such as rotation and hanging force at the top, bit-rock interaction, shock and rubbing on the drillstring, weight of the drillstring, and ﬁnite strains that couple axial, lateral, and torsional vibrations were taken into account. However, the effect of ﬂuid ﬂow was not considered. Liu et al. developed an eight-DOF discrete model of the drillstring to study its nonlinear vibrations, consid- ering the axial, lateral, and torsional dynamics, shown in Figure 15. In the model, time-delay aspects, nonlinear- ities because of dry friction, loss of contact, and collisions were considered. Based on this model, numerical analyses were conducted for various drilling conditions. Results revealed that the drillstring behaviors can be self-excited due to stick–slip friction and time-delay effects and that the whirl motion of the drillstring alternates periodically between the stick and slip phases. Liu et al. analyzed the stability of the drilling system in terms of stability volumes in the space of rotate speed, cutting depth, and cutting coefﬁcient. The stability volume provides a guide for choosing parameters for rotary drilling operations. Based on the state and delayed-state feedback, a control strategy was presented and the effectiveness of this approach to mitigate stick–slip vibrations was studied. These two works were extended with developing a 32 segments model, and stability analysis of the degenerated one-segment model shows a stable region for the drilling operations. For reproducing all major types of drillstring vibrations, Kapitaniak et al. constructed an experimental rig where the commercial drill bits and rock samples were utilized. A mathematical model of the drillstring was presented by using low dimensional ODE model based on torsional pendulum. Various dynamical phenomena of the drillstring, such as stick–slip vibration, whirl, bit bounce, and buckling, were obtained. In a recent work by Moraes and Savi, a FDOF nonsmooth model with including axial-torsional-lateral coupling was developed to study the drillstring vibration, considering bit rock, wellbore interactions, eccentricity of drillstring, and hydro- dynamic force. By carrying out parametric studies, characteristics of stick–slip, bit bounce, and whirl motions were obtained. Experimental investigations Finnie and Bailey conducted experimental tests to study the axial load, torque at the top of a drilling system. Fritz did tests to investigate the dynamics of a vibratory rotor that paved the way for drillstring dynamics testing. For the drilling industry, comprehensive experimental facilities have been developed to characterize the bit 896 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Figure 15. Schematic of the discrete drilling system model. performance. These facilities have improved the understanding of the interaction between the drill bit and rock formation, resulting in high performance drilling tool and proper operation. The investigations reviewed in the following section focuses on the experimental studies of stick–slip vibrations in drillstring. Laboratory studies In order to identify the vibration effects on bit performance, Chen et al. designed a number of laboratory facilities and ﬁeld tests. Results showed that roller cone bit may encounter stick–slip phenomenon under some drilling conditions and stick–slip motion does not adversely inﬂuence the penetration rate. Melakhessou et al. developed a FDOF model to study the interaction between the drillstring and the wellbore during the drilling process. The nonlinear equations for describing the model were solved numerically. For ver- iﬁcation, experimental setup was used including two opto-electronic devices, as shown in Figure 16. The dynamic features obtained from model analysis were compared with the experimental results. It showed that the simulation results agreed with experimental observations when stick–slip vibrations occur. For better understanding the causes of stick–slip vibration, Mihajlovic et al. developed an experimental drillstring setup and torsional oscillation with and without stick–slip were observed in steady state (see Figure 17). A Lyapunov-based stability study and numerical and experimental bifurcation analyses were conducted. A comparison between theoretical and experimental bifurcation diagrams was carried out to know the predictive quality of the theoretical model. It showed that the friction characteristics were linked to the existence of torsional vibration with and without stick–slip. However, axial vibrations were not considered and coupled motions with considering stick–slip vibration have not been conducted. Khulief and Al-Sulaiman designed a drilling test apparatus (Figure 18) that can reproduce the drillstring dynamics for different excitation mechanisms. The test apparatus includes a motor that can generate different Tang et al. 897 79,101 Figure 16. Scheme of the experimental setup. Figure 17. Experimental drillstring setup. speeds, a brake was used to produce stick–slip conditions, and a shaker was used to apply WOB. The experimental results were employed to input and tune some parameters applied in the elastodynamic FE model. Theoretical analysis by Canudas-de-Wit et al. revealed that the stick–slip could be effectively controlled by applying an adaptation law (referred to as D-OSKILL) without requiring variations in the top drive and drill- string. Lu et al. developed a laboratory setup to generate stick–slip phenomenon (Figure 19). For the experi- ments, the rotational speed and WOB applied onto the drillstring are 20 rad/s and 180 N, respectively. Results showed that the WOB is returned to the nominal values when the stick–slip is suppressed, which agrees with the simulation results. Experimental results also showed that ROP reduces when the D-ODKILL is used but the stick–slip vibrations are signiﬁcantly minimized. Forster studied the mitigation of stick–slip vibration by introducing axial excitations into the drillstring. For this purpose, laboratory tests were conducted at the National Oilwell Varco Downhole Ltd. on small-scale vibration test apparatus designed to reproduce the stick–slip phenomenon and test different stick–slip reduction methods (Figure 20). For this setup, the tool performances with and without axial excitation can be tested. The axial excitation frequencies and axial load amplitudes of the typical axial excitation tools have been reproduced during the tests. It demonstrated that the axial excitations signiﬁcantly mitigate the stick–slip vibration. In order to facilitate the studies of the drilling system dynamics, Liao et al. constructs a laboratory-scale drillstring setup to investigate the working conditions experienced by a drillstring, as shown in Figure 21. A variable speed motor was used to drive and two encoders were used to measure two discs. An unbalanced 898 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Figure 18. Photograph of the laboratory test rig. Figure 19. Laboratory setup to generate stick–slip phenomenon. Tang et al. 899 Figure 20. In-house built vibration test rig. Figure 21. Laboratory scale arrangement of a rotary drilling system. mass, which represents the drill bit, was attached to the bottom disc. Results showed that impact and stick–slip motions are observed at a low speed and that whirl is observed at a high speed. The experimental studies are beneﬁcial to the reduced-order models in capturing the stick–slip vibration. Patil and Teodoriu reviewed comparatively the laboratory experiments of torsional vibrations and presented the experimental setup of drillstring at Clausthal University of Technology (as shown in Figure 22). Results from the theoretical analyses on stick–slip showed that the primary driving mechanism of stick–slip is not the self-excited axial vibrations, and not the velocity weakening effect but the crushing action of the drill bit and the interaction between the bit and rock. In order to verify this conclusion, Kovalyshen presented the results of the ongoing experiments of stick–slip vibrations. Figure 23 shows the small-scale drill rig. It shows that the experimental results agree with the theoretical analyses. 900 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Figure 22. Experimental setup of the rotational drilling system at Clausthal University of Technology. Figure 23. The small-scale drill rig. Halsey et al. studied the stick–slip vibration by conducting a comparison between theoretical analysis and experimental results based on a full-scale laboratory experimental rig. Raymond et al. constructed a setup to obtain root understanding of BHA dynamics, but the tests are limited to the axial motions only. Detournay 110,111 et al. developed a phenomenological model to investigate the cutting bit dynamics, WOB, torque, angular velocity, bit design, and cutter number are included, and experiments with a small drilling machine were Tang et al. 901 112 113 conducted to verify this model. Esmaeili et al. constructed a full-scale drillstring rig, which actually drills into the rock sample. The laboratory apparatus consists of a steel frame, top drive, draw work, weights, measurement sensors, drill bit, drillstring, and a control unit. It has the ability of exerting 80 kg WOB on a bit of 2–3 inches. The relationships between drilling parameters with the ROP and drillstring vibration were obtained. Lines et al. conducted laboratory tests to gain insight into the downhole data and characterize the stick–slip vibration of the rotary steerable system. Based on a simple test-rig for analyzing drilling dynsmic, Real et al. explained the stick–slip cycles. As can be seen from the works related to laboratory tests of stick–slip vibration, there are differences among the test rigs. In fact, the performance of a test rig depends to some extent on the concentration of the theoretical model. Due to the complex behavior of stick–slip phenomenon, a small change on the rig (for example boundary condition of the drillstring) may lead to totally different results. For most of the reported stick–slip phenomena, they were regarded as torsional vibrations. In a work by Wang et al., the axial stick–slip motion of drillstring was reported. They built an experimental apparatus to investigate the toolface behavior in slide drilling. Results indicated that axial stick–slip vibration appears in the case of toolface disorientation due to friction. Field testing Dufeyte and Henneuse presented the investigation of bit and drillstring dynamics when the stick–slip vibration occurs based on 3500 hours ﬁeld measurements. It showed that varying certain parameters such as rotary table velocity, WOB, and mud viscous might mitigate stick–slip. Fear et al. described the failure nature and depen- dence on operating conditions of bit encountered with stick–slip vibrations. In order to verify the laboratory studies of the inﬂuences of stick–slip and whirl on the drilling performance, Chen et al. carried out ﬁeld tests in soft to medium formation in an inclined well with its slope angle 20 .It shows that the maximum bit velocity during stick–slip is twice more than the rotary table velocity. Results indicated that (1) stick–slip can be eradicated via using an advanced PDC bit stabilization techniques, (2) stabi- lizer added to the BHA does not remove the stick–slip vibration, and (3) the stick–slip propensity for a PDC bit is associated with the relationship between torque and rotary speed. Selnes et al. reported the ﬁeld cases of using an anti-stall tool to reduce friction-induced stick–slip phenom- enon. Yaveri et al. performed a case study on 16 offshore wells to understand the drilling dynamics. The reasons for the stick–slip and whirl occurrence and the corresponding intensity were evaluated, which can give solutions to reduce both drillstring vibration and drilling cost. The real-time downhole measurement can monitor the occurrence and severity of stick–slip phenomenon. However, due to the low frequency of the measurement data and increasing complexity of BHA, the information does not necessarily reveal the root cause of drilling dysfunction. Combining the engineering experiences with a progressive drilling dynamical model, Wu et al. studied the primary causes of stick–slip phenomenon in a number of ﬁeld cases. In a drilling application in Brazil, stick–slip vibration was regarded as the root cause of premature reamer. Based on this, an abrasion resistant cutter was implemented on the reamer and the BHA was optimized to mitigate stick–slip. Asymmetric vibration damping tool offers beneﬁts in minimizing downhole vibration and therefore maximiz- ing ROP. However, application of this tool has the potential to cause eccentric wear to BHA, which can cause a reduction in downhole tool life and drilling efﬁciency. In order to reduce eccentric wear and maximize drilling performance, works with respect to placement of the damping tool within drilling while underreaming operations were carried out on full-scale drilling rigs. Discussion on experimental results Regarding to the experimental setups, which use a break to recreate the velocity weakening effect or lumped torsional masses connected with strings to represent the drillstring, they recreate certain simpliﬁed equations that sometimes used to describe stick–slip and some details of the drilling system cannot be caught. As a result, the ability of such experiments (not use the actual ﬁeld scale drillstring) to study causes and attenuation of drillstring stick–slip vibration is extremely limited. The phenomenon of drillstring stick–slip is a limit cycle caused by instability in the torsional dynamics of a drillstring. This instability is also often referred to as a self-excited vibration. To explain the occurrence of this 71,122 instability, a velocity weakening effect (essentially a Stribeck-like effect) in the torque has been proposed, resulting in a classical approach to study stick–slip. It demonstrated that the velocity weakening effect is related to 902 Journal of Low Frequency Noise, Vibration and Active Control 39(4) 12,123 the mud pressure, strength of the bottom of the hole, wear state of the bit, and bit geometry. Experimental works (single cutter experiments) showed that PDC cutter does not exhibit any inherent velocity weakening effect, 124 107 seemingly discrediting much of the previous work. Moreover, experiments of Kovalyshen did not ﬁnd any evident velocity weakening effect. Consequently, we may question whether the velocity weakening effect is the root cause of stick–slip, a companion of this phenomenon, or irrelevant to it, is still not clear. Based on the machine tool chattering analysis, Elsayed and Raymond conducted experiments to simulate chatter (self-excited vibration) in actual ﬁeld conditions. Results showed that chatter takes place when using PDC bit even in soft formation and that the chatter severity correlates to the lack of stability in the system. Richard et al. developed a coupled torsional-axial model of the drilling system to study the relationship between the bit 51,52 geometry and the velocity weakening effect. This model was further extended by Germay et al. However, observations obtained from this model are not in line with ﬁeld results, so the instability presented by Richard 50 51,52 et al. and Germay et al. is probably different from the observation in the ﬁeld. The cause or mechanism of stick–slip vibration, having resulted in much contention, still needs to be investigated. Numerical simulations In general, the drillstring for oilwell drilling is a complex system and its dynamics are related to many factors. Up to now, most of the existing publications try to reveal a single vibration mode or the coupling of single modes. However, revealing all types of vibrations of drillstring in a theoretical model or ﬁnite element (FE) model is difﬁcult. In a work by Khulief and Al-Naser, a FE model of the drillstring by which related dynamic effects including stick–slip can be obtained was presented. In the model, gyroscopic effect, torsional-bending inertia coupling, inertia-axial stiffening coupling and gravity were taken into account. Ghasemloonia investigated the dynamic behavior of the entire drillstring under the action of a vibration-assisted rotary drilling tool, using a dynamic FE model of the vertical drillstring. In the model, the effects of mud damping, driving torque, multispan contact, and varying axial load were included. Kapitaniak et al. used ABAQUS software to investigate the stick–slip vibration, whirling, bit bounce, and helical buckling of the drillstring. The FE models were calibrated via new experimental rig for reproducing major types of drillstring vibrations. Results showed that just a low- dimensional model is enough to predict the behavior of a drillstring in certain conﬁguration. Based on numerical simulation, Zhao et al. revealed that the axial stick–slip movement of the drillstring can lead to abnormal ﬂuctuation of downhole pressure. Sarker et al. used a nonlinear 3D multibody model to study the stick–slip and whirl, and a dynamic FE model of an enclosed shaft under axially compressive load moving inside the borehole was established to verify the theoretical model. By combining with experimental results obtained at Memorial 128 129 University of Newfoundland, they also simulated the case of using an axially vibrating tool. Tang et al. investigated the effect of high-frequency torsional impacts on mitigation of stick–slip phenomenon, and the ABAQUS program was used to simulate the torque on drill bit. Results indicated that the stick–slip vibration can be mitigated by using high-frequency torsional impacts. In order to know the axial load transfer and drill- string dynamics during the slide drilling, Wang et al. used a second-order ﬁnite difference method to solve a uniﬁed mechanical model of the drillstring. Parameter simulation results showed that impacts applied on the drillstring can mitigate the stick–slip vibration and make the movement of the drillstring smoother. When looked into more detail, publications related to numerical simulations on the stick–slip of drillstring are comparatively scarce and most of the references are related to analytical methods or experimental tests. Conclusions This study summarized the researches on stick–slip vibrations in drillstring including mechanical models and experimental investigations. For theoretical modeling, lumped pendulum models (SDOF and MDOF models) were typically used to study the drillstring dynamics. The modeling of stick–slip phenomenon in vertical drillstring might conform to the real conditions. For the directional wells, however, works should continue to clarify whether simple lumped pendulum models are ﬁt to describe stick–slip, and how well these models characterize the real drillstring systems. Distributed system is capable of describing typical features of a complex drilling system. For a contributed model considering both damping and nonlinear frictional characteristics, however, obtaining the analytical solutions is difﬁcult. Consequently, the areas of semi-analytical techniques need more research efforts. Laboratory investigations were conducted together with the theoretical analysis and ﬁeld studies to replicate the stick–slip vibration and demonstrate the reliability of published data. Stick–slip vibration root cause and bit performance were studied and the effects of dynamic parameters were quantiﬁed. There were also many other Tang et al. 903 parameters that are important for the occurrence of stick–slip and have been scantily studied through experi- ments, such as bit-rock interaction and rock lithology. Due to large length-to-diameter ratio of the deep drillstring, stick–slip phenomenon is more inclined to appear in these wells. Managing the problems of stick–slip vibration in drillstring is a long-term task. As drill bit tech- nology has evolved to a mature stage, it important to design more efﬁcient downhole tools and develop efﬁcient control approaches to mitigate stick–slip. In general, many improvements have been achieved in studying the stick–slip vibrations. However, progresses have been much slower than expected and many challenges remain. There are still many problems or drilling accidents generated by stick–slip, such as drillstring twist off, low ROP, poor wellbore trajectory, et al. With the increase in the well depth and complexity of drilling technology, advanced and deep-going works are worthy to be done. For example, stick–slip phenomenon of the drillstring in directional or horizontal wells or ocean drilling, the effects of system parameters on stick–slip phenomenon of drill- 132 133,134 string, and the methods for controlling this type of vibration. Declaration of conflicting interests The author(s) declared no potential conﬂicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following ﬁnancial support for the research, authorship, and/ or publication of this article: This work is supported by the China Postdoctoral Science Foundation (Grant no. 43XB3793XB), National Natural Foundation of China (Grant no. 51674214) and Scientiﬁc Innovation Group for Youths of Sichuan Province (Grant no. 2019JDTD0017). ORCID iDs Liping Tang https://orcid.org/0000-0003-0981-2120 Xiaohua Zhu https://orcid.org/0000-0002-0507-3773 Yunlai Zhou https://orcid.org/0000-0002-2347-647X References 1. Khulief YA, Al-Sulaiman FA and Bashmal S. Vibration analysis of drillstrings with self-excited stick slip oscillations. J Sound Vib 2007; 299: 540–558. 2. Wu X and Agnihotri M. Decoupling stick-slip and whirl to achieve breakthrough in drilling performance. In: Proceedings of the IADC/SPE drilling conference and exhibition, New Orleans, LA, 2-4 February 2010. 3. Warren TM and Oster JH. Torsional resonance of drill collars with PDC bits in hard rock. In: Proceedings of the SPE annual technical conference and exhibition, New Orleans, LA, 27-30 September 1998. 4. Christoforou AP and Yigit AS. Active control of stick slip vibrations: the role of fully coupled dynamics. In: Proceedings of the SPE Middle East oil show, Bahrain, 17-20 March 2001. 5. Belokobyl’skii SV and Prokopov VK. Friction induced self-excited vibration of drill rig with exponential drag law. Soviet Appl Mech 1982; 18: 98–101. 6. Dareing DW. Rotary speed, drill collars control drillstring bounce. Oil Gas J 1983; 81: 63–68. 7. Dawson R, Lin YQ and Spanos PD. Drill-string stick slip oscillations. In: Proceedings of the 1987 SEM Spring conference on experimental mechanics, Houston, TX, 14-19 June 1987. 8. Zhu X, Tang L and Yang Q. A literature review of approaches for stick-slip vibration suppression in oilwell drillstring. Adv Mech Eng 2014; 6: 967952. 9. Halsey GW, Kyllingstad A and Kylling A. Torque feedback used to cure slip-stick motion. In: Proceedings of the SPE 63st annual technical conference and exhibition, Houston, TX, 2-5 October 1988. 10. Kyllingstad A and Halsey GW. A study of slip/stick motion of the bit. SPE Drill Eng 1988; 3: 369–373. 11. Lin YQ and Wang Y.H. Stick slip vibration of drill strings. J Manuf Sci Eng 1991; 113: 38–43. 12. Brett JF. The genesis of torsional drillstring vibrations. SPE Drill Eng 1992; 7: 168–174. 13. Rudat J and Dashevskiy D. 2011. Development of an innovative model based stick slip control system. In: Proceedings of the SPE/IADC drilling conference, Amsterdam, Netherlands, 1-3 March 2011. 14. Qiu H, Yang J and Butt S. Investigation on bit stick-slip vibration with random friction coefﬁcients. J Petrol Sci Eng 2018; 164: 127–139. 15. Cunha-Lima LC, Aguiar RR, Ritto TG, et al. Analysis of the torsional stability of a simpliﬁed drillstring. In: Proceedings of the XVII international symposium on dynamic problems of mechanics, Natal, Brazil, 2015. 16. Tang L and Zhu X. Effects of the difference between the static and the kinetic friction coefﬁcients on a drill string vibration linear approach. Arab J Sci Eng 2015; 40: 3723–3729. 904 Journal of Low Frequency Noise, Vibration and Active Control 39(4) 17. Tang L, Zhu X, Shi C, et al. Investigation of the damping effect on stick-slip vibration of oil and gas drilling system. J Vib Eng Technol 2016; 4: 79–88. 18. Tang L, Zhu X, Qian X, et al. Effects of weight on bit on torsional stick-slip vibration of oilwell drill string. J Mech Sci Technol 2017; 31: 4589–4597. 19. Leine RI, Campen DH, Kraker AD, et al. Stick slip vibrations induced by alternate friction models. Nonlinear Dyn 1998; 16: 41–54. 20. Nosrati A and Farshidianfar A. 2009. Analytical approximations for stick-slip vibration amplitudes based on a discre- tization method. In: Congress on sound and vibration, Krakow, Poland, 5-9 July 2009. 21. Van de Vrande BL, Van Campen DH and De Kraker A. An approximate analysis of dry friction induced stick slip vibrations by a smoothing procedure. Nonlinear Dyn 1999; 19: 157–169. 22. Abdulgalil F and Siguerdidjane H. 2004. Nonlinear friction compensation design for suppressing stick slip oscillations in oil well drillstrings. In: Proceedings of the 5th Asian control conference, Melbourne, Australia, 20-23 July 2004. 23. Canudas-de-Wit C, Rubio FR and Corchero MA. DOSKIL: a new mechanism for controlling stick-slip oscillations in oil well drillstrings. IEEE Trans Contr Syst Technol 2008; 16: 1177–1191. 24. Navarro-Lopez EM and Suarez R. 2004. Practical approach to modeling and controlling stick-slip oscillations in oilwell drillstrings. In: IEEE international conference on control applications, Taipei, China, 2-4 September 2004. 25. Bayliss MT, Panchal N and Whidborne JF. 2012. Rotary steerable directional drilling stick-slip mitigation control. In: Proceedings of the IFAC workshop on automatic control in offshore oil and gas production, Trondheim, Norway, 31 May-1 June 2012. 26. Karkoub M, Magid YA and Balachandran B. Drill string torsional vibration suppression using GA optimized control- lers. J Can Petrol Technol 2009; 48: 32–38. 27. Silveira M and Wiercigroch M. Low dimensional models for stick-slip vibration of drillstrings. J Phys Conference Series 2009; 181: 1–8. 28. Patil PA and Teodoriu C. 2013 Model development of torsional drillstring an investigating parametrically the stick-slips inﬂuencing factors. J Energy Resour Technol135: 013103 29. Navarro-Lopez EM and Corte´ s D. Avoiding harmful oscillations in a drillstring through dynamical analysis. J Sound Vib 2007; 307: 152–171. 30. Navarro-Lopez EM and Corte´ s D. Sliding-mode control of a multi-DOF oilwell drillstring with stick-slip oscillations. In: Proceedings of the American control conference, New York, NY, 11-13 July 2007. 31. Navarro-Lopez EM and Castro EL. Non-desired transitions and sliding mode control of a muti-DOF mechanical system with stick slip oscillations. Chaos Soliton Fract 2009; 41: 2035–2044. 32. Kreuzer E and Steidl M. Model order reduction of a drill string model with self-excited stick slip vibrations. Proc Appl Math Mech 2009; 9: 295–296. 33. Khulief YA and Al-Sulaiman FA. Laboratory investigation of drillstring vibrations. J Mech Eng Sci 2009; 223: 2249–2262. 34. Kapitaniak M, Hamaneh VV, Cha´ vez JP, et al. Unveiling complexity of drillstring vibrations: experiments and modeling. Int J Mech Sci 2015; 102: 324–337. 35. Palmov VA, Brommundt E and Belyaev AK. Stability analysis of drillstring rotation. Dyn Stabil Syst 1995; 10: 99–110. 36. Challamel N. Rock destruction effect on the stability of a drilling structure. J Sound Vib 2000; 233: 235–254. 37. Challamel N, Sellami H and Chenevez E. 2000. A stick-slip analysis based on rock/bit interaction: theoretical and experi- mental contribution. In: Proceedings of the SPE/IADC drilling conference, New Orleans, USA, 23-25 February 2000. 38. Saldivar B and Mondie´ S. Drilling vibration reduction via attractive ellipsoid method. J Franklin I 2013; 350: 485–502. 39. Saldivar B, Mondie´ S, Loiseau JJ, et al. Stick-slip oscillations in oilwell drillstrings: distributed parameter and neutral type retarded model approaches. In: Proceedings of the 18th IFAC World Congress, Milano, Italy, 28 August-2 September 2011. 40. Kreuzer E and Steidl M. Controlling torsional vibrations of drill strings via decomposition of traveling waves. Arch Appl Mech 2012; 82: 515–531. 41. Ritto TG, Escalante MR, Sampaio R, et al. Drillstring horizontal dynamics with uncertainty on the frictional force. J Sound Vib 2013; 332: 145–153. 42. Ritto TG. Bayesian approach to identify the bit rock interaction parameters of a drill string dynamical model. J Braz Soc Mech Sci Eng 2015; 37: 1173–1182. 43. Aarsnes UJF, Meglio FD and Shor RJ. Avoiding stick slip vibrations in drilling through startup trajectory design. J Process Contr 2018; 70: 24–35. 44. Aarsnes UJF and Wouw N. Axial and torsional self-excited vibrations of a distributed drill-string. J Sound Vib 2019; 444: 127–151. 45. Ghasemloonia A, Rideout DG and Butt SD. Vibration analysis of a drillstring in vibration-assisted rotary drilling: ﬁnite element modeling with analytical validation. J Energy Resour Technol 2013; 135: 032902 46. Christoforou AP and Yigit AS. Fully coupled vibrations of actively controlled drillstrings. J Sound Vib 2003; 267: 1029–1045. Tang et al. 905 47. Yigit AS and Christoforou AP. Stick slip and bit bounce interaction in oil well drillstring. J Energy Resour Technol 2006; 128: 268–274. 48. Richard T, Detournay E, Fear MJ, et al. Inﬂuence of bit-rock interaction on stick-slip vibrations of PDC bits. In: Proceedings of the SPE annual technical conference and exhibition, San Antonio, 29 September-2 October 2002. 49. Richard T, Germay C and Detournay E. Self-excited stick slip oscillations of drill bits. CR Mecanique 2004; 332: 619–626. 50. Richard T, Germay C and Detournay E. A simpliﬁed model to explore the root cause of stick slip vibrations in drilling systems with drag bits. J Sound Vib 2007; 305: 432–456. 51. Germay C, Deno€el V and Detournay E. Multiple mode analysis of the self-excited vibrations of rotary drilling systems. J Sound Vib 2009; 325: 362–381. 52. Germay C, Wouw NV, Nijmeijer H, et al. Nonlinear drillstring dynamics analysis. SIAM J Appl Dyn Syst 2009; 8: 527–553. 53. Nandakumar K and Wiercigroch M. Stability analysis of a state dependent delayed, coupled two DOF model of drill- string vibration. J Sound Vib 2013; 332: 2575–2592. 54. Kovalyshen Y. Understanding root cause of stick-slip vibrations in deep drilling with drag bits. Int J Nonlin Mech 2014; 67: 331–341. 55. Depouhon A and Detournay E. Instability regimes and self-excited vibrations in deep drilling system. J Sound Vib 2014; 333: 2019–2039. 56. Depouhon A and Detournay E. Stick-slip instabilities in rotary drilling system. In: Proceedings of the 49th US Rock mechanics/geomechanics symposium, San Francisco, CA, 28 June-1 July 2015. 57. Kamel JM and Yigit AS. Modeling and analysis of stick-slip and bit bounce in oil well drillstrings equipped with drag bits. J Sound Vib 2014; 333: 6885–6899. 58. Alamo FC and Weber HI. Stick-slip analysis in drill string. In: Proceedings of the 18th international congress of mechanical engineering, Ouro Preto, Brazil, 2005. 59. Sampaio R, Piovan MT and Lozano GV. Stick slip patterns in coupled extensional and torsional vibrations of drill- strings. Mecanica Computacional XXIV 2005; 24: 861–877. 60. Divenyi S, Savi MA, Wiercigroch M, et al. Modelling of stick-slip and bit bounce in drill-string dynamics via smoothen functions. In: Proceedings of VI national congress of mechanical engineering, Paraiba, Brazil, 2010. 61. Divenyi S, Savi MA, Wiercigroch M, et al. Drill string vibration analysis using non-smooth dynamics approach. Nonlinear Dyn 2012; 70: 1017–1035. 62. Vasconcellos MN and Savi MA. 2010. Analysis of oil well drilling dynamics from non-smooth models. In: Proceedings of the Mecanica computational, Santa Fe, Argentina, XXIX, 8807–8817. 63. Sarker MM, Rideout DG and Butt SD. 2012. Dynamic model of an oilwell drillstring with stick slip and bit bounce interaction. In: Proceedings of the international conference on bond graph modeling, Genoa, Italy, 8-11 July 2012. 64. Ertas D, Bailey JR, Wang L, et al. Drillstring mechanics model for surveillance, root cause analysis, and mitigation of torsional and axial vibrations. SPE Drill Complet 2014; 29: 405–417. 65. Sairaﬁ FA, Ajmi KE, Yigit AS, et al., 2016. Modeling and control of stick-slip and bit bounce in oil well drill strings. In: Proceedings of the SPE/IADC drilling technology conference and exhibition, Abu Dhabi, UAE, 26-28 January 2016. 66. Besselink B, Van de Wouw N and Nijmeijer H. A semi-analytical study of stick slip oscillations in drilling systems. ASME J Comput Nonlinear Dyn 2011; 6: 1–9. 67. Besselink B, Vromen T, Kremers N, et al. Analysis and control of stick-slip oscillations in drilling system. IEEE T Contr Syst Technol 2015; 2015: 1–12. 68. Insperger T, Ste´ pa´ n G and Turi J. State-dependent delay in regenerative turning processes. Nonlinear Dyn 2006; 47: 275–283. 69. Aarsnes UJF and Aamo OM. Linear stability analysis of self-excited vibrations in drilling using an inﬁnite dimensional model. J Sound Vib 2016; 360: 239–259. 70. Schmalhorst B and Baumgart A. Combined simulation of whirl and stick-slip phenomenon using a nonlinear ﬁnite element model. In: Proceedings of the energy week conference and exhibition, Houston, TX, 28-30 January 1997. 71. Abbassian F and Dunayevsky VA. Application of stability approach to torsional and lateral bit dynamics. SPE Drill Complet 1998; 13: 99–107. 72. Vandiver JK, Nicholson JW and Shyu RJ. Case studies of the bending vibration and whirling motion of drill collars. SPE Drill Eng 1990; 5: 282–290. 73. Berlioz A, Der Hogopian J, Dufour R, et al. Dynamic behavior of a drill string experimental investigation of lateral instabilities. J Vib Acoust 1996; 118: 292–298. 74. Gulyayev VI and Shevchuk LV. Drill string bit whirl simulation with the use of frictional and nonholonomic models. J Vib Acoust 2015; 138: 011021. 75. Yigit AS and Christoforou AP. Coupled torsional and bending vibrations of drillstrings subject to impact with friction. J Sound Vib 1998; 215: 167–181. 76. Yigit AS and Christoforou AP. Coupled torsional and bending vibrations of actively controlled drillstrings. J.Sound Vib 2000; 234: 67–83. 906 Journal of Low Frequency Noise, Vibration and Active Control 39(4) 77. Al-Hiddabi SA, Samanta B and Seibi A. Non-linear control of torsional and bending vibrations of oilwell drillstrings. J Sound Vib 2003; 265: 401–415. 78. Leine RI, Campen DH and Keulfjes WJG. Stick slip whirl interaction in drillstring dynamics. J Vib Acoust 2002; 124: 209–220. 79. Melakhessou H, Berlioz A and Ferraris G. A nonlinear well drillstring interaction model. J Vib Acoust 2003; 125: 46–52. 80. Sowers SF, Dupriest FE, Bailey JR, et al. Roller reamers improve drilling performance in wells limited by bit and bottomhole assembly vibrations. In: Proceedings of the SPE/IADC drilling conference and exhibition, Amsterdam, Netherlands, 17-19 March 2009. 81. Vlajic N, Liao CM, Karki H, et al. Stick-slip and whirl motions of drill strings: numerical and experimental studies. In: Proceedings of the ASME 2011 international design engineering technical conferences and computers and information in engineering conference, Washington, DC, 2011, 28-31 August 2011. 82. Butlin T and Langley RS. An efﬁcient model of drillstring dynamics. J Sound Vib 2015; 356: 100–123. 83. Leseultre A, Lamine E and Jonsson A. An instrumented bit: a necessary step to the intelligent BHA. In: Proceedings of the SPE/IADC drilling conference, Dallas, TX, 1998, 3-6 March 1998. 84. Yaveri M, Damani K and Kalbhor H. 2010. Solutions to the down hole vibrations during drilling. In: Proceedings of the 34th annual SPE international conference and exhibition, Calabar, Nigeria. 85. Stroud D, Bird N, Norton P, et al. Roller reamer fulcrum in point the bit rotary steerable system reduces stick slip and backward whirl. In: Proceedings of the IADC/SPE drilling conference and exhibition, San Diego, CA, 2012, 6- 8 March 2012. 86. Tucker RW and Wang C. On the effective control of torsional vibrations in drilling systems. J Sound Vib 1999; 224: 101–122. 87. Tucker RW and Wang C. An integrated model for drillstring dynamics. J Sound Vib 1999; 224: 123–165. 88. Tucker RW and Wang C. Torsional vibration control and cosserat dynamics of a drill rig assembly. Meccanica 2003; 38: 143–159. 89. Baumgart A. Stick slip and bit bounce of deep hole drillstrings. J Energy Resour Technol 2000; 122: 78–82. 90. Khulief YA and Al-Naser H. Finite element dynamic analysis of drillstrings. Finite Elem Anal Des 2005; 41: 1270–1288. 91. Khulief YA, Al-Sulaiman FA and Bashmal S. Vibration analysis of drillstrings with string-borehole interaction. J Mech Eng Sci 2008; 222: 2099–2110. 92. Ritto TG, Sampaio R and Soize C. Drill-string dynamics coupled with the drilling ﬂuid dynamics. In: Proceedings of the XIII international symposium on dynamic problems of mechanics, Angra dos Reis, Brazil, 2009, 2-6 March 2009. 93. Liu X, Vlajic N, Long X, et al. Nonlinear motions of a ﬂexible rotor with a drill bit: stick-slip and delay effects. Nonlinear Dyn 2013; 72: 61–77. 94. Liu X, Vlajic N, Long X, et al. Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control. Nonlinear Dyn 2014; 78: 1891–1906. 95. Liu X, Vlajic N, Long X, et al. State-dependent delay inﬂuenced drill-string oscillations and stability analysis. J Vib Acoust 2014; 136: 051008. 96. Moraes LPP and Savi MA. Drill-string vibration analysis considering an axial-torsional-lateral nonsmooth model. J Sound Vib 2019; 438: 220–237. 97. Finnie I and Bailey JJ. An experimental study of drill string vibration. J Eng Industry 1960; 82: 129–135. 98. Fritz RJ. The effects of an annular ﬂuid on the vibrations of a long rotor, part 2-test. J Basic Eng 1970; 92: 923–929. 99. Aarrestad TV and Kyllingstad A. An experimental and theoretical study of a coupling mechanism between longitudinal and torsional drillstring vibration at the bit. SPE Drill Eng 1988; 3: 12–18. 100. Chen SL, Blackwood K and Lamine E. Field investigation of the effects of stick-slip, lateral and whirl vibrations on roller cone bit performance. SPE Drill Complet 2002; 17: 15–20. 101. Patil PA and Teodoriu C. A comparative review of modelling and controlling torsional vibrations and experimentation using latoratory setups. J Petrol Sci Eng 2013; 112: 227–238. 102. Mihajlovic N, Wouw N, Hendriks MPM, et al. Friction-induced vibrations in an experimental drill-string system for various friction situations. In: Proceedings of the ENOC-2005, Eindhoven, Netherlands, 7-12 August 2005. 103. Mihajlovic N, Wouw N, Hendriks MPM, et al. Friction induced limit cycling in ﬂexible rotor systems, an experimental drillstring setup. Nonlinear Dyn 2006; 46: 273–291. 104. Lu H, Dumon J and Canudas-de-Wit C. Experimental study of the D-OSKILL mechanism for controlling the stick-slip oscillations in a drilling laboratory testbed. In: Proceedings of the IEEE multi-conference on systems and control, Saint Petersburg, Russia, 8-10 July 2009. 105. Forster I. Axial excitation as a means of stick slip mitigation- small scale rig testing and full scale ﬁeld testing. In: Proceedings of the SPE/IADC drilling conference, Amsterdam, Netherlands, 1-3 March 2011. 106. Liao CM, Balachandran B, Karkoub M, et al. Drillstring dynamics: reduced order models and experimental studies. J Vib Acoust 2011; 133: 041008. 107. Kovalyshen Y. Experiments on stick-slip vibrations in drilling with drag bits. In: Proceedings of the 48th US Rock mechanics/geomechanics symposium, Minneapolis, MN, 1-4 June 2014. Tang et al. 907 108. Halsey GW, Kyllingstad A, Aarrestad TV, et al. Drillstring torsional vibrations: comparison between theory and exper- iment on a full-scale research drilling rig. In: Proceedings of the SPE 61st annual technical conference and exhibition, New Orleans, LO, 5-8 October 1986. 109. Raymond DW, Elsayed MA, Polsky Y, et al. Laboratory simulation of drill bit dynamics using a model-based servohy- draulic controller. J Energy Resour Technol 2008; 130: 043103. 110. Detournay E and Defourny P. A phenomenological model for the drilling action of drag bits. Int J Rock Mech Min Sci Geomech Abstr 1992; 29: 13–23. 111. Detournay E, Richard T and Shepherd M. Drilling response of drag bits: theory and experiment. Int J Rock Mech Min Sci 2008; 45: 1347–1360. 112. Richard T, Dagrain F, Poyol E, et al. Rock strength determination from scratch tests. Eng Geol 2012; 147–148: 91–100. 113. Esmaeili A, ElahifaR B and Fruhwirth RK. Experimental evaluation of real-time mechanical formation classiﬁcation using drill string vibration measurements. In: Proceedings of the SPE annual technical conference and exhibition, Texas, USA, 8-10 October 2012. 114. Lines LA, Stroud DRH and Coveney VA. 2013. Torsional resonance – an understanding based on ﬁeld and laboratory tests with latest generation point the bit rotary steerable system. In: Proceedings of the IADC/SPE drilling conference and exhibition, Amsterdam, Netherlands, 5-7 March 2013. 115. Real FF, Lobo DM, Ritto TG, et al. Experimental analysis of stick-slip in drilling dynamics in a laboratory test-rig. J Petrol Sci Eng 2018; 170: 755–762. 116. Wang X, Ni H and Wang R. Experimental study on toolface disorientation and correction during slide drilling. J Petrol Sci Eng 2019; 173: 853–860. 117. Dufeyte MP and Henneuse H. Detection and monitoring of the slip-stick motion: ﬁeld experiments. In: Proceedings of the SPE/IADC drilling conference, Amsterdam, Netherlands, 11-14 March 1991. 118. Fear MJ, Abbassian F, Parﬁtt SHL, et al. The destruction of PDC bits by severe slip-stick vibration. In: Proceedings of the IADC/SPE drilling conference, Amsterdam, Netherlands, 4-6 March 1997. 119. Selnes KS, Clemmensen C and Reimers N. Drilling difﬁcult formations efﬁciently with the use of an antistall tool. SPE Drill. Complet 2009; 24: 531–536. 120. Wu X, Karuppiah V, Nagaraj M, et al. Identifying the root cause of drilling vibration and stick slip enables ﬁt for purpose solutions. In: Proceedings of the IADC/SPE drilling conference and exhibition, San Diego, CA, 6-8 March 2012. 121. Kabbara A, McCarthy J and Burnett T. 2012. Understanding how the placement of an asymmetric vibration damping tool within drilling while underreaming assemblies can inﬂuence performance and reliability. In: Proceedings of the SPE drilling conference and exhibition, San Diego, CA, 6-8 March 2012. 122. Jansen JD and Steen L. Active damping of self-excited torsional vibrations in oil well drillstrings. J Sound Vib 1995; 179: 647–668. 123. Jain JR, Ledgerwood LW, Hoffmann OJ, et al. Mitigation of torsional stick slip vibrations in oil well drilling through PDC bit design: putting theories to the test. In: Proceedings of the SPE annual technical conference and exhibition, Denver, CO, 30 October-2 November 2011. 124. Nishimatsu Y. The mechanics of rock cutting. Int J Rock Mech Min Sci 1972; 9: 261–270. 125. Elsayed MA and Raymond DW. Measurement and analysis of chatter in a compliant model of a drillstring equipped with a PDC bit. In: Proceedings of the American Society of Mechanical Engineers’ energy technology conference and exhibition, New Orleans, LA, 14-17 February 2000. 126. Zhao D, Hovda S and Sangesland S. Abnormal down hole pressure variation by axial stick-slip of drillstring. J Petrol Sci Eng 2016; 145: 194–204. 127. Sarker M, Rideout DG and Butt SD. Dynamic model for 3D motions of a horizontal oilwell BHA with wellbore stick-slip whirl interaction. J Petrol Sci Eng 2017; 157: 482–506. 128. Sarker M, Rideout DG and Butt SD. Dynamic model for longitudinal and torsional motions of a horizontal oilwell drillstring with wellbore stick-slip friction. J Petrol Sci Eng 2017; 150: 272–287. 129. Tang L, Zhu X and Shi C. Effects of high-frequency torsional impacts on mitigation of stick-slip vibration in drilling system. J Vib Eng Technol 2017; 5: 111–122. 130. Wang P, Ni H, Wang X, et al. Modelling the load transfer and tool surface for friction reduction drilling by vibrating drill-string. J Petrol Sci Eng 2018; 164: 333–343. 131. Dao NH, Menand S and Isbell M. Mitigating and understanding stick-slip in unconventional wells. In: Proceedings of the SPE/IADC international drilling conference and exhibition, Hague, The Netherlands, 5-7 March 2019. 132. Christian ED. Identifying the optimum zone for reducing drill string vibrations. In: Proceedings of the SPE annual technical conference and exhibition, San Antonio, USA, 9-11 October 2017. 133. Tang L and Zhu X. On the development of high-frequency torsional impact drilling techniques for hard formation drilling. Adv Mech Eng 2018; 10: 1–15. 134. Monteiro HLS and Trindade MA. Performance analysis of proportional-integral feedback control for the reduction of stick-slip-induced torsional vibrations in oil well drillstrings. J Sound Vib 2017; 398: 28–38. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Journal of Low Frequency Noise, Vibration and Active Control" SAGE http://www.deepdyve.com/lp/sage/stick-slip-vibrations-in-oil-well-drillstring-a-review-HCFlwmL3Y3

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References (136)

E. Kreuzer, M. Steidl (2009)
Model Order Reduction of a Drill‐String‐Model with Self‐Excited Stick‐Slip Vibrations
PAMM, 9
M. Bayliss, Neilkunal Panchal, J. Whidborne (2012)
Rotary Steerable Directional Drilling Stick/Slip Mitigation Control
IFAC Proceedings Volumes, 45
Shilin Chen, K. Blackwood, E. Lamine (2002)
Field Investigation of the Effects of Stick-Slip, Lateral, and Whirl Vibrations on Roller-Cone Bit Performance
Spe Drilling & Completion, 17
Knut Selnes, Carl Clemmensen, N. Reimers (2009)
Drilling Difficult Formations Efficiently With the Use of an Antistall Tool
Distributed Computing
W. Tucker, C. Wang (1999)
On the Effective Control of Torsional Vibrations in Drilling Systems
Journal of Sound and Vibration, 224
R. Leine, van Campen, W.J.G. Keultjes (2002)
Stick-Slip Whirl Interaction in Drillstring Dynamics
Journal of Vibration and Acoustics, 124
(2015)
Analysis of the torsional stability of a simplified drillstring
K. Nandakumar, M. Wiercigroch (2013)
Stability analysis of a state dependent delayed, coupled two DOF model of drill-stringvibration
Journal of Sound and Vibration, 332
T. Ritto, R. Sampaio, Christian Soize (2009)
Drill-string dynamics coupled with the drilling fluid dynamics
T. Richard, E. Detournay, M. Fear, Brian Miller, R. Clayton, Oliver Matthews (2002)
Influence Of Bit-Rock Interaction On Stick-Slip Vibrations Of PDC Bits
A. Christoforou, A. Yigit (2001)
Active Control of Stick-Slip Vibrations: The Role of Fully Coupled Dynamics
SPE middle east oil show
A. Yigit, A. Christoforou (1998)
Coupled torsional and bending vibrations of drillstrings subject to impact with friction
Journal of Sound and Vibration, 215
A. Depouhon, E. Detournay (2014)
Instability regimes and self-excited vibrations in deep drilling systems
Journal of Sound and Vibration, 333
Eva Navarro-Lópeza, Domingo Cortésb (2007)
Avoiding harmful oscillations in a drillstring through dynamical analysis
Journal of Sound and Vibration, 307
J. Brett (1992)
The genesis of torsional drillstring vibrations
Spe Drilling Engineering, 7
Elsayed, D. Raymond (1999)
Measurement and analysis of chatter in a compliant model of a drillstring equipped with a PDC bit
M. Kapitaniak, Vahid Hamaneh, J. Chávez, K. Nandakumar, M. Wiercigroch (2015)
Unveiling complexity of drill–string vibrations: Experiments and modelling
International Journal of Mechanical Sciences, 101
Y. Kovalyshen (2014)
Experiments on Stick-Slip Vibrations in Drilling with Drag Bits
J. Thomsen, A. Fidlin (2003)
Analytical approximations for stick-slip vibration amplitudes
International Journal of Non-linear Mechanics, 38
A. Baumgart (2000)
Stick-Slip and Bit-Bounce of Deep-Hole Drillstrings
Journal of Energy Resources Technology-transactions of The Asme, 122
I. Forster (2011)
Axial Excitation as a Means of Stick Slip Mitigation - Small Scale Rig Testing and Full Scale Field Testing
Distributed Computing
Fredy Alamo, H. Weber (2005)
STICK-SLIP ANALYSIS IN DRILL STRINGS
van Vrande, van Campen, De Kraker (1999)
An Approximate Analysis of Dry-Friction-Induced Stick-Slip Vibrations by a Smoothing Procedure
Nonlinear Dynamics, 19
N. Challamel (2000)
ROCK DESTRUCTION EFFECT ON THE STABILITY OF A DRILLING STRUCTURE
Journal of Sound and Vibration, 233
J. Rudat, D. Dashevskiy (2011)
Development of an Innovative Model-Based Stick/Slip Control System
Distributed Computing
Finite element dynamic analysis of drillstrings. Finite
Alan Kabbara, J. Mccarthy, T. Burnett, I. Forster (2012)
Understanding How the Placement of an Asymmetric Vibration Damping Tool Within Drilling While Underreaming Assemblies Can Influence Performance and Reliability
Distributed Computing
U. Aarsnes, F. Meglio, R. Shor (2018)
Avoiding stick slip vibrations in drilling through startup trajectory design
Journal of Process Control
B. Besselink, van Wouw, H. Nijmeijer (2011)
A Semi-Analytical Study of Stick-Slip Oscillations in Drilling Systems
Journal of Computational and Nonlinear Dynamics, 6
E. Navarro-López, E. Licéaga-Castro (2009)
Non-desired transitions and sliding-mode control of a multi-DOF mechanical system with stick-slip oscillations
Chaos Solitons & Fractals, 41
R. Sampaio, M. Piovan, G. Lozano (2005)
STICK-SLIP PATTERNS IN COUPLED EXTENSIONAL/TORSIONAL VIBRATIONS OF DRILL-STRINGS
J. Jain, L. Ledgerwood, O. Hoffmann, T. Schwefe, Danielle Fuselier (2011)
Mitigation of Torsional Stick-Slip Vibrations in Oil Well Drilling through PDC Bit Design: Putting Theories to the Test
G. Halsey, A. Kyllingstad, A. Kylling (1988)
Torque Feedback Used to Cure Slip-Stick Motion
Software - Practice and Experience
(2017)
Effects of high-frequency torsional impacts on mitigation of stick-slip vibration in drilling system
M. Sarker, D. Rideout, S. Butt (2017)
Dynamic model for longitudinal and torsional motions of a horizontal oilwell drillstring with wellbore stick-slip friction
Journal of Petroleum Science and Engineering, 150
D. Raymond, M. Elsayed, Y. Polsky, S. Kuszmaul (2008)
Laboratory Simulation of Drill Bit Dynamics Using a Model-Based Servohydraulic Controller
Journal of Energy Resources Technology-transactions of The Asme, 130
E. Kreuzer, M. Steidl (2012)
Controlling torsional vibrations of drill strings via decomposition of traveling waves
Archive of Applied Mechanics, 82
Hayat Melakhessou, A. Berlioz, G. Ferraris (2003)
A Nonlinear Well-Drillstring Interaction Model
Journal of Vibration and Acoustics, 125
Nenad Mihajlovic, van Wouw, M. Hendriks, H. Nijmeijer (2005)
Friction-induced Vibrations in an Experimental Drill-string System for Various Friction Situations
T. Butlin, R. Langley (2015)
An efficient model of drillstring dynamics
Journal of Sound and Vibration, 356
Xianping Wu, Venki Karuppiah, M. Nagaraj, U. Partin, Marcia Machado, Mariana Franco, H. Duvvuru (2012)
Identifying the Root Cause of Drilling Vibration and Stick-Slip Enables Fit-for-Purpose Solutions
Distributed Computing
Xianbo Liu, N. Vlajic, X. Long, G. Meng, B. Balachandran (2014)
State-Dependent Delay Influenced Drill-String Oscillations and Stability Analysis
Journal of Vibration and Acoustics, 136
T. Insperger, G. Stépán, J. Turi (2006)
State-dependent delay in regenerative turning processes
Nonlinear Dynamics, 47
(2016)
Investigation of the damping effect on stick-slip vibration of oil and gas drilling system
T. Ritto, M. Escalante, R. Sampaio, M. Rosales (2013)
Drill-string horizontal dynamics with uncertainty on the frictional force
Journal of Sound and Vibration, 332
U. Aarsnes, N. Wouw (2019)
Axial and torsional self-excited vibrations of a distributed drill-string
Journal of Sound and Vibration
Deniz Ertas, J. Bailey, Lei Wang, P. Pastusek (2014)
Drillstring Mechanics Model for Surveillance, Root Cause Analysis, and Mitigation of Torsional Vibrations
Spe Drilling & Completion, 29
A. Kyllingstad, G. Halsey (1988)
A study of slip/stick motion of the bit
Spe Drilling Engineering, 3
Deniz Ertas, J. Bailey, Lei Wang, P. Pastusek (2013)
Drillstring Mechanics Model for Surveillance, Root Cause Analysis, and Mitigation of Torsional and Axial Vibrations
Distributed Computing
Marcos Silveira, M. Wiercigroch (2009)
Low dimensional models for stick-slip vibration of drill-strings
, 181
Y. Khulief, F. Al-Sulaiman (2009)
Laboratory investigation of drillstring vibrations
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 223
V. Palmov, E. Brommundt, A. Belyaev (1995)
Stability analysis of drillstring rotation
Dynamics and Stability of Systems, 10
Y. Khulief, F. Al-Sulaiman, S. Bashmal (2008)
Vibration analysis of drillstrings with string—borehole interaction
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 222
Y. Kovalyshen (2014)
Understanding root cause of stick–slip vibrations in deep drilling with drag bits
International Journal of Non-linear Mechanics, 67
S. Al-Hiddabi, B. Samanta, A. Seibi (2003)
Non-linear control of torsional and bending vibrations of oilwell drillstrings
Journal of Sound and Vibration, 265
E. Navarro-López, D. Cortés (2007)
Sliding-mode control of a multi-DOF oilwell drillstring with stick-slip oscillations
2007 American Control Conference
T. Ritto (2015)
Bayesian approach to identify the bit–rock interaction parameters of a drill-string dynamical model
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 37
F. Abdulgalil, H. Siguerdidjane (2004)
Nonlinear Friction Compensation Design for Suppressing Stick Slip Oscillations in Oil Well Drillstrings
IFAC Proceedings Volumes, 37
E. Detournay, P. Defourny (1992)
A phenomenological model for the drilling action of drag bits
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 29
E. Navarro-López, Rodolfo Suárez (2004)
Practical approach to modelling and controlling stick-slip oscillations in oilwell drillstrings
Proceedings of the 2004 IEEE International Conference on Control Applications, 2004., 2
I. Finnie, J. Bailey (1960)
An Experimental Study of Drill-String Vibration
Journal of Engineering for Industry, 82
Liping Tang, Xiaohua Zhu (2018)
On the development of high-frequency torsional impact drilling techniques for hard formation drilling
Advances in Mechanical Engineering, 10
C. Germay, V. Denoël, E. Detournay (2009)
Multiple mode analysis of the self-excited vibrations of rotary drilling systems
Journal of Sound and Vibration, 325
Ahmad Ghasemloonia, D. Rideout, S. Butt (2013)
Vibration Analysis of a Drillstring in Vibration-Assisted Rotary Drilling: Finite Element Modeling With Analytical Validation
Journal of Energy Resources Technology-transactions of The Asme, 135
P. Patil, C. Teodoriu (2013)
Model Development of Torsional Drillstring and Investigating Parametrically the Stick-Slips Influencing Factors
Journal of Energy Resources Technology-transactions of The Asme, 135
M-P. Dufeyte, H. Henneuse (1991)
Detection and Monitoring of the Slip-Stick Motion: Field Experiments
Distributed Computing
Xianbo Liu, N. Vlajic, X. Long, G. Meng, B. Balachandran (2013)
Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects
Nonlinear Dynamics, 72
Nenad Mihajlovic, van Wouw, M. Hendriks, H. Nijmeijer (2006)
Friction-induced limit cycling in flexible rotor systems: An experimental drill-string set-up
Nonlinear Dynamics, 46
T. Richard, C. Germay, E. Detournay (2007)
A simplified model to explore the root cause of stick–slip vibrations in drilling systems with drag bits
Journal of Sound and Vibration, 305
B. Schmalhorst, A. Baumgart (1997)
Combined simulation of whirl and stick-slip phenomena using a nonlinear finite element model
Hugo Monteiro, M. Trindade (2017)
Performance analysis of proportional-integral feedback control for the reduction of stick-slip-induced torsional vibrations in oil well drillstrings
Journal of Sound and Vibration, 398
G. Halsey, Å. Kyllingstad, T. Aarrestad, D. Lysne (1986)
Drillstring Torsional Vibrations: Comparison Between Theory and Experiment on a Full-Scale Research Drilling Rig
Software - Practice and Experience
M. Fear, F. Abbassian, S. Parfitt, A. McClean (1997)
The Destruction of PDC Bits by Severe Slip-Stick Vibration
Distributed Computing
Belem Saldivar, S. Mondié, J. Loiseau, V. Răsvan (2011)
Stick-slip Oscillations in Oillwell Drilstrings: Distributed Parameter and Neutral Type Retarded Model Approaches
IFAC Proceedings Volumes, 44
A. Berlioz, J. Hagopian, R. Dufour, E. Draoui (1996)
Dynamic Behavior of a Drill-String: Experimental Investigation of Lateral Instabilities
Journal of Vibration and Acoustics, 118
E. Detournay, T. Richard, M. Shepherd (2008)
Drilling response of drag bits: Theory and experiment
International Journal of Rock Mechanics and Mining Sciences, 45
Jasem Kamel, A. Yigit (2014)
Modeling and analysis of stick-slip and bit bounce in oil well drillstrings equipped with drag bits
Journal of Sound and Vibration, 333
Luciano Moraes, M. Savi (2019)
Drill-string vibration analysis considering an axial-torsional-lateral nonsmooth model
Journal of Sound and Vibration
Chien-Min Liao, B. Balachandran, M. Karkoub, Y. Abdel-Magid (2011)
Drill-String Dynamics: Reduced-Order Models and Experimental Studies
Journal of Vibration and Acoustics, 133
R. Leine, van Campen, De Kraker, van Steen (1998)
Stick-Slip Vibrations Induced by Alternate Friction Models
Nonlinear Dynamics, 16
Y. Nishimatsu (1972)
The mechanics of rock cutting
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 9
Yao-Qun Lin, Yu-hwa Wang (1991)
Stick-Slip Vibration of Drill Strings
Journal of Engineering for Industry, 113
H. Qiu, Jianming Yang, S. Butt (2018)
Investigation on bit stick-slip vibration with random friction coefficients
Journal of Petroleum Science and Engineering, 164
N. Vlajic, Chien-Min Liao, H. Karki, B. Balachandran (2011)
Stick-Slip and Whirl Motions of Drill Strings: Numerical and Experimental Studies
V. Dunayevsky, F. Abbassian (1998)
Application of Stability Approach to Bit Dynamics
Spe Drilling & Completion, 13
T. Richard, C. Germay, E. Detournay (2004)
Self-excited stick–slip oscillations of drill bits
Comptes Rendus Mecanique, 332
Xue-ying Wang, H. Ni, Ruihe Wang (2019)
Experimental study on toolface disorientation and correction during slide drilling
Journal of Petroleum Science and Engineering
R. Tucker, C. Wang (2003)
Torsional Vibration Control and Cosserat Dynamics of a Drill-Rig Assembly
Meccanica, 38
D. Zhao, S. Hovda, S. Sangesland (2016)
Abnormal down hole pressure variation by axial stick-slip of drillstring
Journal of Petroleum Science and Engineering, 145
N. Challamel, H. Sellami, E. Chenevez, L. Gossuin (2000)
A Stick-slip Analysis Based on Rock/Bit Interaction: Theoretical and Experimental Contribution
Distributed Computing
J. Jansen, L. Steen (1995)
Active damping of self-excited torsional vibrations in oil well drillstrings
Journal of Sound and Vibration, 179
Alexandre Depouhon, E. Detournay (2015)
Stick-Slip Instabilities in Rotary Drilling Systems
A. Esmaeili, B. Elahifar, R. Fruhwirth, G. Thonhauser (2012)
Experimental Evaluation of Real-Time Mechanical Formation Classification using Drill String Vibration Measurements
C. Canudas-de-Wit, F. Rubio, M. Corchero (2008)
D-OSKIL: A New Mechanism for Controlling Stick-Slip Oscillations in Oil Well Drillstrings
IEEE Transactions on Control Systems Technology, 16
D. Dareing (1983)
Rotary speed, drill collars control drillstring bounce
Oil & Gas Journal
Peng Wang, H. Ni, Xue-ying Wang, Ruihe Wang (2018)
Modelling the load transfer and tool surface for friction reduction drilling by vibrating drill-string
Journal of Petroleum Science and Engineering, 164
V. Gulyayev, L. Shevchuk (2016)
Drill String Bit Whirl Simulation With the Use of Frictional and Nonholonomic Models
Journal of Vibration and Acoustics, 138
W. Tucker, C. Wang (1999)
An Integrated Model for Drill-String Dynamics
Journal of Sound and Vibration, 224
Y. Khulief, F. Al-Sulaiman, S. Bashmal (2007)
Vibration analysis of drillstrings with self-excited stick–slip oscillations
Journal of Sound and Vibration, 299
C. Germay, N. Wouw, H. Nijmeijer, R. Sepulchre (2009)
Nonlinear Drillstring Dynamics Analysis
SIAM J. Appl. Dyn. Syst., 8
Etaje Christian (2017)
Identifying the Optimum Zone for Reducing Drill String Vibrations
Steven Sowers, F. Dupriest, J. Bailey, Lei Wang (2009)
Use of Roller Reamers Improves Drilling Performance in Wells Limited by Bit and Bottomhole Assembly Vibrations
Distributed Computing
U. Aarsnes, O. Aamo (2016)
Linear stability analysis of self-excited vibrations in drilling using an infinite dimensional model
Journal of Sound and Vibration, 360
(2010)
Analysis of oil well drilling dynamics from non-smooth models
Application of stability approach to torsional and lateral bit dynamics
F. Real, D. Lobo, T. Ritto, F. Pinto (2018)
Experimental analysis of stick-slip in drilling dynamics in a laboratory test-rig
Journal of Petroleum Science and Engineering
R. Fritz (1970)
The Effects of an Annular Fluid on the Vibrations of a Long Rotor, Part 1—Theory
Journal of Basic Engineering, 92
Y. Khulief, H. Al-Naser (2005)
Finite element dynamic analysis of drillstrings
Finite Elements in Analysis and Design, 41
P. Patil, C. Teodoriu (2013)
A comparative review of modelling and controlling torsional vibrations and experimentation using laboratory setups
Journal of Petroleum Science and Engineering, 112
T. Warren, J. Oster (1998)
Torsional resonance of drill collars with PDC bits in hard rock
Software - Practice and Experience, 51
Haochuan Lu, J. Dumon, C. Canudas-de-Wit (2009)
Experimental study of the D-OSKIL mechanism for controlling the stick-slip oscillations in a drilling laboratory testbed
2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC)
A. Yigit, A. Christoforou (2000)
COUPLED TORSIONAL AND BENDING VIBRATIONS OF ACTIVELY CONTROLLED DRILLSTRINGS
Journal of Sound and Vibration, 234
M. Sarker, G. Rideout (2012)
Dynamic Model of an Oilwell Drillstring with Stick-Slip and Bit-Bounce Interaction
T. Aarrestad, Å. Kyllingstad (1988)
An experimental and theoretical study of a coupling mechanism between longitudinal and torsional drillstring vibrations at the bit
Spe Drilling Engineering, 3
Xianbo Liu, N. Vlajic, X. Long, G. Meng, B. Balachandran (2014)
Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control
Nonlinear Dynamics, 78
A. Yigit, A. Christoforou (2006)
Stick-Slip and Bit-Bounce Interaction in Oil-Well Drillstrings
Journal of Energy Resources Technology-transactions of The Asme, 128
(1982)
Friction-induced self-excited vibrations of drill rig with exponential drag law
Soviet Applied Mechanics, 18
M. Karkoub, Y. Abdel-Magid, B. Balachandran (2009)
Drill-String Torsional Vibration Suppression Using GA Optimized Controllers
Journal of Canadian Petroleum Technology, 48
A. Christoforou, A. Yigit (2003)
Fully coupled vibrations of actively controlled drillstrings
Journal of Sound and Vibration, 267
D. Stroud, Neil Bird, Peter Norton, M. Kennedy, Malcolm Greener (2012)
Roller Reamer Fulcrum in Point-The-Bit Rotary Steerable System reduces Stick-Slip and Backward Whirl
Distributed Computing
L. Lines, D. Stroud, V. Coveney (2013)
Torsional Resonance - An Understanding Based on Field and Laboratory Tests with Latest Generation Point-the-Bit Rotary Steerable System.
Distributed Computing
N. Dao, S. Menand, M. Isbell (2019)
Mitigating and Understanding Stick-Slip in Unconventional Wells
Day 2 Wed, March 06, 2019
Belem Saldivar, S. Mondié (2013)
Drilling vibration reduction via attractive ellipsoid method
J. Frankl. Inst., 350
M. Sarker, D. Rideout, S. Butt (2017)
Dynamic model for 3D motions of a horizontal oilwell BHA with wellbore stick-slip whirl interaction
Journal of Petroleum Science and Engineering, 157
Kim Vandiver, James Nicholson, R. Shyu (1990)
Case studies of the bending vibration and whirling motion of drill collars
Spe Drilling Engineering, 5
Xianping Wu, L. Paez, U. Partin, Mukul Agnihotri (2010)
Decoupling Stick/Slip and Whirl To Achieve Breakthrough in Drilling Performance
Distributed Computing
Xiaohua Zhu, Liping Tang, Qiming Yang (2014)
A Literature Review of Approaches for Stick-Slip Vibration Suppression in Oilwell Drillstring
Advances in Mechanical Engineering, 6
Mokhtar Yaveri, K. Damani, Harshad Kalbhor (2010)
Solutions to the Down Hole Vibrations During Drilling
Liping Tang, Xiaohua Zhu, X. Qian, C. Shi (2017)
Effects of weight on bit on torsional stick-slip vibration of oilwell drill string
Journal of Mechanical Science and Technology, 31
F. Sairafi, K. Ajmi, A. Yigit, A. Christoforou (2016)
Modeling and Control of Stick Slip and Bit Bounce in Oil Well Drill Strings
A. Leseultre, E. Lamine, A. Jonsson (1998)
An Instrumented Bit: A Necessary Step to the Intelligent BHA
Distributed Computing
Liping Tang, Xiaohua Zhu (2015)
Effects of the Difference Between the Static and the Kinetic Friction Coefficients on a Drill String Vibration Linear Approach
Arabian Journal for Science and Engineering, 40
Analysis and control of stick-slip oscillations in drilling system
Sandor Divenyi, M. Savi, M. Wiercigroch, E. Pavlovskaia (2012)
Drill-string vibration analysis using non-smooth dynamics approach
Nonlinear Dynamics, 70
M. Savi, E. Pavlovskaia (2010)
MODELLING OF STICK-SLIP AND BIT-BOUNCE IN DRILL-STRING DYNAMICS VIA SMOOTHEN FUNCTIONS
T. Richard, F. Dagrain, E. Poyol, E. Detournay (2012)
Rock strength determination from scratch tests
Engineering Geology, 147

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ISSN: 0263-0923
eISSN: 2048-4046
DOI: 10.1177/1461348419853658
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Abstract

A survey of the literature related to theoretical and experimental studies on stick–slip vibration in oilwell drillstring is carried out in this study. It aims to explain key concepts and present the existing methods for studying this phenomenon. After briefly describing the stick–slip vibration related problems, theoretical models for such phenomenon are discussed including both coupled and uncoupled models. Discussion for experimental investigations including both laboratory and field tests are hereinafter addressed. This study aims to summarize the literature related to the stick–slip vibration, and help researchers in understanding and suppressing such phenomenon. Keywords Stick–slip vibration, drillstring, bottom-hole assembly, degree of freedom, structural coupling Introduction The drillstring exhibits severe stick–slip vibration induced by the contact between the drill bit and the formation. Stick–slip vibration of drillstring appears as periodic alternations of stick and slip phases. During the stick phase, the bit keeps stationary for a time interval and the torque on bit (TOB) increases to a value of breaking this state. During the slip phase, the bit releases all of a sudden and accelerates to an angular velocity several times as the 2,3 velocity of rotary table. Stick–slip vibration not only reduces the tool life, but also increases the non-productive time that increases the development expense. In addition, this vibration may cause lateral and axial vibrations, causing equipment failure and the rate of penetration (ROP) reduction. The investigation on stick–slip vibration in drillstring dated back to the publication of Belokobyl’skii and Prokopov where the friction induced vibration was analyzed and the self-excited drillstirng vibration concept was introduced. Dareing indicated the possibility of eliminating drillstring vibration by controlling the rotary speed and explored the self-excited vibration induced by motion of the bit. Dawson et al. discussed the drillstring vibration as a stick–slip phenomenon. The stick–slip phenomenon has undergone numerous outputs in the past decades; however, most of the publications are ﬁeld observations and methods for mitigating this motion, including both passive and active methods. Due to the variation of drilling conditions and drilling technologies advances, the stick–slip vibration plays an increasingly essential role. For instance, with the petroleum industry development, more and more deep and ultra-deep wells are considered for conduction. This study reviewed the literatures on slick–slip vibrations for oilwell drillstring, thus providing reference for the engineers and scientists working on this area. School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, China Department of Civil and Environmental Engineering, National University of Singapore, Singapore, Singapore Corresponding author: Xiaohua Zhu, School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China. Email: zxhth113@163.com Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www. creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage). 886 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Stick–slip vibration with uncoupled models The investigations reviewed in the following section are the mathematical methods for modeling stick–slip vibra- tions. The contributions are arranged under single degree of freedom (SDOF) lumped parameter models, multiple-DOF (MDOF) vibration models, and continuous system models. SDOF Lumped pendulum vibration models Halsey et al. studied the stick–slip vibration of drillstring through treating the bottom-hole assembly (BHA) as a lumped ﬂywheel. For given conditions, the SDOF model could not predict the formation of stick–slip motion. Kyllingstad and Halsey revealed an increase in mean torque with increasing the rotary speed, however, the related explanation was not provided. The damping effect was not considered in the model. Lin and Wang worked extensively on the lumped parameter model considering the damping effect. To better understand the cause of stick–slip phenomenon, Brett presented a model to show that torsional drillstring vibration can be initiated by variation of bit characteristics. The model regarded the drillstring as a lumped mass-spring system (Figure 1), and uses two coupled differential equations to describe the stick–slip motion. The results indicated that stick–slip vibration could be eliminated by controlling rotary table torque instead of rotary table velocity, which was not veriﬁed with ﬁeld-test. Rudat and Dashevskiy modeled the drillstring as a mechanical oscillator with rotational SDOF (Figure 2). The model was used to determine optimal parameters by predicting the intensity of downhole stick–slip vibration. However, only the steady state responses were presented. By using a SDOF model similar to the one shown in Figure 2, Qiu et al. studied the stick–slip vibration of drillstring. In the model, the bit-rock contact was modeled as random friction, and the stick motion and slip motion were treated separately. For the purpose of verifying the model, Monte Carlo simulation was conducted. Even simple lumped mass model with actual drilling parameters can reproduce complex nonlinear drilling dynamics processes. Cunha-Lima et al. developed a simpliﬁed SDOF model to study the torsional stability of the drillstring, for better understanding the causes of stick–slip phenomenon and the way to mitigate it. Based on 16–18 this model, a similar mechanical model was developed by Tang et al. to study the effect of drilling parameters on stick–slip vibration (Figure 3). Results showed that the rotary table velocity, the friction coefﬁcients, and viscous damping have signiﬁcant effect on both the occurrence of stick–slip vibration and its dynamics. 19,20 Another type of SDOF model used to investigate the stick–slip is the block-on-belt model, shown in Figure 4. Van de Vrande et al. developed a SDOF block on belt model to study the stick–slip motion of Figure 1. Lumped mass spring model of the drillstring. Tang et al. 887 drillstring. Periodic stick–slip vibration can be found by applying the smoothing procedure and simple shooting method with an ordinary differential equation (ODE) solver. MDOF vibration models Compared to SDOF, MDOF models can catch more details of the drilling system. Consequently, many inves- tigations focused on stick–slip vibrations by using MDOF vibration models. Abdulgalil and Siguerdidjane Figure 2. Mechanical SDOF model of the drillstring. Figure 3. Analytical model of the drillstring system. Figure 4. The block-on-belt model. 888 Journal of Low Frequency Noise, Vibration and Active Control 39(4) developed a simple dual DOF (DDOF) model (Figure 5) of stick–slip vibration by regarding the drilling system as a torsional pendulum. The assumption in this model is not always true, because the friction behavior can change easily due to the drilling condition variations. Canudas-de-Wit et al. developed a similar open-loop plant model (Figure 6) as used by Rudat and Dashevskiy with different boundary condition, where the assumption that rotary speed is constant. The friction-induced limit cycles were studied and the weight on bit (WOB) was used as a control parameter to extinguish limit cycles. Based on this type of DDOF model, Navarro-Lopez and Sua´ rez reproduced the stick–slip motion in various operating conditions. Bayliss et al. investigated the mitigation of stick–slip phe- nomenon in the drilling system via an online-identiﬁcation-based adaptive design; Karkoub et al. used genetic algorithms (GAs) to optimize stick–slip responses. Silveira and Wiercigroch evaluated the bit-rock interaction and developed a three DOF (TDOF) torsional pendulum model to investigate the drillstring stick–slip behavior. Patil and Teodoriu developed a TDOF stick– slip model (Figure 7) and studied the effects of inﬂuencing parameters such as rotary table velocity and WOB on stick–slip vibration, where the nonlinear friction forces represented the bit-rock interaction. 29–31 Navarro-Lopez et al. discussed a more generic discontinuous torsional model of four DOF (FDOF) (rotary table, drill-pipes, drill-collars, and drill bit), shown in Figure 8. Based on this model, a sliding motion leads to self-excited vibrations and bit stick phenomena at the BHA were analyzed. The key drilling parameters were determined by investigating Hopf bifurcations. Figure 5. Drilling rotary model by Abdulgalil and Siguerdidjane. Figure 6. The DDOF model by Canudas-de-Wit et al. Tang et al. 889 Kreuzer and Steidl developed a high dimensional drillstring model consisted of 51 elements, one element represents the rotary table, one element represents the BHA, and 49 elements model the string with self-excited stick–slip vibration. The ﬁnite element (FE) method was used to model drillstring; however, most of the reported investigations concentrated on investigating the BHA. In order to understand the severe torsional and axial vibrations excited by stick–slip vibration, Khulief et al. used Lagrangian method and FE method to derive the motion equation of the rotating drilling system. The drillstring model included both drill-pipes and drill-collars to study the dynamics of the drilling system in the existence of stick–slip vibrations. Kapitaniak et al. developed a detailed MDOF model of a drilling system using FE method to calibrate a TDOF mathematical model, in particular when stick–slip vibration occurs. Distributed vibration models A high dimensional or inﬁnite model can describe typical features when modeling an engineering system. But these models are computationally expensive. Palmov et al. studied the stick–slip vibration of drillstring basing on a distributed vibration in torsion, considering the BHA to be a rigid body. Based on this model, studies have tried to 36,37 interpret the instability initiation that results in stick–slip phenomenon of drillstring. Challamel proposed the direct method of Lyapunov to study the stability conditions of a distributed drillstring model. The stability of a drillstring relatively forms the bit-rock contact depending on the rock crushing process. Simulations illustrated that the bit converges towards stick–slip vibration with a typical limit cycle. Results also showed that the stick–slip Figure 7. The TDOF torsional pendulum model by Patil and Teodoriu. Figure 8. The FDOF lumped pendulum model describing the stick–slip vibration of a drillstring. 890 Journal of Low Frequency Noise, Vibration and Active Control 39(4) vibration behaves for polycrystalline diamond composite (PDC) bit with small variation of axial velocity and justiﬁes the use of an uncoupled torsional model. However, bit-rock interaction experiments with single cutters may not reveal the intrinsic velocity weakening effect. Further investigation in this ﬁeld was done by Saldivar 38,39 29–31 et al. In the study, a friction model similar to the one by Navarro-Lopez et al. was presented. D’Alembert transformation and Laplace transform were used to analyze and simulate the drillstring behavior. By investigating the occurrence of stick–slip vibration, some approaches for mitigating stick–slip vibration were put forward by manipulating BHA characteristics. Kreuzer and Steidl presented the wave equation for the torsional dynamics of the actual drillstring. Two principles were revealed: (a) existing a range of the drillstring rotation angular velocity where the stick–slip motion of the drillstring takes place, and (b) the process of stick–slip vibrations and their forms are independent of the initial conditions. Almost all the previous investigations focused only on stick–slip vibrations in the torsional direction. Ritto et al. thought that only one contact point at the bit-rock interaction in vertical wells exists. In horizontal drilling, nevertheless, there is stick–slip in the axial direction because of frictional force. Under this circumstance, they proposed a stochastic model taking into account the friction force between the drillstring and the borehole. Combining FE method with Monte Carlo method into the bar model, stick–slip behavior in the axial direction was obtained. For such bit-rock interaction model, the stochastic friction forces and the parameters selection are sources of uncertainties. In a latest work by Ritto, identiﬁcation of factors of the bit-rock contact model was investigated. In order to control stick–slip vibration through startup trajectory design, Aarsnes et al. presented a distributed model of drillstring to replicate the stick–slip vibration caused by transition of static and dynamic frictions. This work was followed by a distributed axial-torsional drillstring model to investigate the appearance and global characteristics of self-excited vibrations caused by the regenerative effect of bit-rock interaction. The investigation showed the effect of bit rotation rate on the excitation of multiple axial and torsional modes of the drillstring. In addition, a stability map of the slick–slip vibration was presented. Stick–slip vibration coupling models The vibrations in the drilling system are usually divided into three fundamental types: axial, transverse, and torsional modes, with different patterns of manifestation. Bit bounce, whirling and stick–slip are extreme states of the axial, transverse and torsional vibrations, respectively. The causes of these vibrations include the inter- action between the drillstring and borehole, bit-rock interaction, unbalance of curvature of the drillstring, and variation of the drilling parameters. These motions are usually complex and are coupled together or occur simultaneously. A number of publications studied the coupled vibration of drillstring, including lateral–torsion- al, lateral–axial, and axial–torsional coupled models. The coupled models related to stick–slip vibration are to be reviewed in this section. Stick–slip and bit bounce coupling models 46 47 Based on the simpliﬁed lumped model by Christoforou and Yigit, Yigit and Christoforou simulated the inﬂuences of operating conditions on bit bounce and stick–slip. It indicated that conditions at the interface of bit and rock are major factors of bit dynamics. Noted for the presented model, a number of parameters that should be determined by experimental measurement were included. The stick–slip vibration modeling typically considers only the torsional vibration of drillstring regarding the 36 48–50 interaction between the bit and rock as Coulomb friction referred to velocity weakening. Richard et al. proposed a DDOF discrete model (shown in Figure 9) considering the axial and torsional vibrations of the drilling system to study the self-excited stick–slip phenomenon. Coupling between the two vibration modes was realized by using a bit-rock contact principle where the friction and crushing processes were considered, which differed from the classical method used to reveal the stick–slip vibration. The dynamic responses can be obtained by the surface conditions of the drill bit and bit-rock contact principles, in conjunction with the motion equations for the torsional and axial vibrations. The model was restricted to an idealized drag bit that includes many identical radial blades distributed uniformly along axis of revolution of the drill bit (see Figure 10). For the developed model, a delay was introduced into the cutting process, leading to the occurrence of self- excited vibration that degenerates into stick–slip or bit bouncing for some conditions. In this model, the WOB was considered as a constant and this can be realized by adjusting the hook load, which means the axial displacement of the drillstring must be controlled at the surface to match the bit movement. The drill bit, however, encounters Tang et al. 891 48–50 Figure 9. Mechanical model of the drilling system. 48–50 Figure 10. Drill bit model developed by Richard et al. severe axial vibration and thus is difﬁcult to realize the proposed condition. The model neglected the dynamics of the delay-based effect on the assumption of a timescale separation between the axial and torsional dynamics. 49,50 51 Based on the model by Richard et al., Germay et al. identiﬁed the mechanisms of axial and torsional vibrations and their parametric dependence. The investigation of decoupling axial and torsional dynamics pro- vided an interpretation for the occurrence for most dynamic regimes. Germay et al. expanded on the model of Richard et al. by using continuous system model (also called distributed model) rather than a DDOF lumped model. The drillstring dynamic responses were studied using the FE method and some new features in the stick– slip vibration were detected. However, this model is always unstable according to a recently linear stability analysis by Nandakumar and Wiercigroch. In order to identify the exact origins and interplay of stick–slip and bit bounce, they proposed fully coupled DDOF model with a viscous damping and a state-dependent time delay. 54–56 Many other studies presented the coupled stick–slip phenomenon and bit bounce with a basic model by 49,50 57 Richard et al. Kamel and Yigit studied coupled axial and torsional behaviors of a drillstring through utilizing a DDOF lumped pendulum model where Lagrangian approach was used to estimate the equivalent system parameters and a new cutting and interaction model was used to describe the bit-rock contact. It was shown that the stick–slip motion and bit bounce could be minimized by proper choice of the operational param- eters. Kovalyshen considers the resonance between the cutting force and natural vibration modes as the reasons of drillstring vibration, and carried out a stability analysis of coupled vibrations of a drilling assembly. 892 Journal of Low Frequency Noise, Vibration and Active Control 39(4) 60,61 Figure 11. Free body diagram of the BHA with the axial acting forces. It demonstrated that the driving mechanism of the axial vibration mode is the regenerative effect, while the driving mechanism of the torsional vibration is the crushing process of the bit and the bit/rock contact. Based on this study, a root cause of stick–slip coupled with bit bounce was revealed. Alamo and Weber obtained a mathematical model to investigate the torsional vibration, considering the longitudinal vibration. For the stick–slip vibration model, the top rotates have a constant rotary speed and the bottom end are subjected to a cutting force which represents the bit-rock interaction. Finite difference was used to discretize the space domain and Runge-Kutta method was employed to obtain the time response. Results showed that the coupled model could describe the stick–slip vibration depending strongly on the rotary table velocity. Sampaio et al. considered the geometrical nonlinearity in modeling the coupling of axial and torsional vibra- tions. By using FE method and taking into account the large rotations and nonlinear strain displacements, linear and nonlinear models were compared. It showed that the linear and nonlinear models differ comparatively after the ﬁrst period of stick–slip. Based on the mechanical model proposed by Christoforou and Yigit considering the axial and torsional 60,61 behaviors of drillstring, Divenyi et al. developed a DDOF lumped parameters model (see Figure 11) to study the coupled axial and torsional motions where the coupled vibration was regarded as being induced by the bit- rock contact and the axial force was regarded as the catalyst of generating a resistive torque. The analyzed results show that the model is able to predict a full range of dynamic responses including the stick–slip vibration and bit bounce and to understand the drillstring dynamics and critical behaviors of the system by using different scenarios related to parameter changes. However, a number of parameters should be determined by experimental measure- ment. Particularly, measuring the parameters is challenging. For the complex drilling process, the parameters in the model changed easily. More ﬁeld data used to verify and optimize the model are needed. Basing on a DDOF model with coupling torsional and axial vibration, Vasconcellos and Savi conducted a parametric analysis of the transitions between different motion phases and the non-smooth dynamic responses of stick–slip and bit bounce. Sarker et al. applied a bond graph model of the drilling system to predict axial and torsional vibration, and coupling between the two vibrations due to bit/rock contact. Ertas et al. used transfer matrices to solve small torsional vibrations around a baseline solution in the frequency domain, accounting for well path, tool joints, viscous damping, surface boundary condition, bit features, and special vibration mitigation tool. Sairaﬁ et al. established a coupled stick–slip and bit bounce model with the driving system and hoisting system. Results demonstrated that controlling only torsional vibration is not effective in suppressing bit bounce phenomena and an axial controller should be implemented as well. Earlier studies for drillstring dynamic model lacked two essential features: the axial stiffness of the drillstring and friction from along the drillstring. Besselink et al. investigated the mechanisms leading to stick–slip using a model that includes axial motion, torsional motion, and a rate independent bit-rock contact law. It showed that the axial stick–slip phenomenon is dependent on the rotational bit speed and that the generation of torsional stick–slip phenomenon is driven by the axial motions, which means that mitigation of axial vibrations may also suppress torsional vibration. Besselink et al. furthered the work of mitigation of stick–slip vibration by using feedback control strategies. Previous works postulates that self-excited vibrations occur because of the coupling between the drillstring and 68 69 the regenerative effect in the bit-rock contact law. To prove this, Aarsnes and Aamo studied a graphical condition for stability of drillstring based on the Nyquist stability criterion. Tang et al. 893 Figure 12. The simplified drillstring model with equivalent lumped parameters. Stick–slip and whirl models coupling A time domain dynamical model allows the prediction of drillstring dynamics related to torsional and lateral vibrations. By using FE approach, Schmalhorst and Baumgart developed a nonlinear drillstring model taking into account arbitrarily shaped assemblies during drilling of curved boreholes. In the model, restitution forces act on the drillstring and contact velocity-dependent friction forces were introduced. The torsional and lateral DOF were coupled and the whirl and stick–slip phenomena combined with normal drilling conditions were solved numerically. Abbassian and Dunayevsky studied the stability of bit dynamics through a coupled torsional– lateral vibration model. 72–74 Whirling and parametric resonances of drillstring have been investigated. In these investigations, the rotary table velocity was regarded as a constant and the torsional vibration was not included. Based on this, Yigit and Christoforou considered the coupling between the lateral and torsional motions of drillstring and assumed the excitation at the bit to be related to the bit rotation. The motion equations for coupled torsional and lateral motions were established through a simpliﬁed model shown in Figure 12. Apart from the strong coupling and nonlinear features included in the model, a consistent model was utilized to characterize the impacts of drill collars with the borehole. Results showed that there is signiﬁcant energy transfer between the torsional and lateral motions at certain frequencies and that adjusting the surface torque is more efﬁcient in eliminating the stick–slip vibrations. In another work of them, the rotary drive system was also included in the mechanical model. Based on the results obtained from theoretical analysis, a linear quadratic regulator controller was designed to mitigate the stick–slip and whirl motions. Drillstring vibration is highly nonlinear and the mechanical model can only be established by a group of nonlinear differential equations. The linear control approaches are not accurate for controlling the coupled lateral and torsional vibrations. Based on the mechanical model presented by Yigit and Christoforou, Al-Hiddabi et al. developed an inversion control design method based on nonlinear differential equations to control the torsional and lateral vibrations. In order to interpret the complex drillstring motions where stick–slip vibration and lateral whirl are involved, Leine et al. developed a simpliﬁed lumped stick–slip whirl model of the drilling system. The model exposes only the basic phenomena but was discontinuous. For this model, discontinuous bifurcations are obtained, providing explanation for the disappearance of stick–slip phenomenon when whirl motion appears. However, the experi- mental results were obtained by averaging the torque on bit over several revolutions and may not hold at a more relevant time scale. Melakhessou et al. proposed a FDOF mathematical model to investigate the stick–slipt and whirl vibrations, with lateral movement, rotation of the section, bending around thetangential orientation, and torsional displace- ment of the drillstring were included. Field cases showed that stick–slip and whirl can be eliminated when a roller reamer is introduced. Sowers et al. developed a conceptual model coupling stick–slip and whirl in order to understand the mechanism of roller reamers improving drilling performance by decoupling or suppressing 894 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Figure 13. A schematic depicts the drillstring model. drillstring vibrations. Vlajic et al. presented a distributed parameter model (Figure 13) to describe the coupled bending and torsional vibrations while the interaction forces between the drillstring and the wellbore were taken into account. Both the whirl and stick–slip phenomena were investigated numerically and the results were com- pared with the experimental results. Butlin and Langley claimed that drillstring dynamical models contain three features (1) efﬁcient so as to conduct parametric investigation, (2) simple so as to reveal the underlying mechanisms, and (3) retain enough details to associate real conditions. By using a reduced order model that takes into account the nonlinear inter- action laws and solving by time domain integration, results from cases studies demonstrated the occurrences of a number of phenomena, including stick–slip vibration and whirl. Apart from the mathematical models, ﬁeld tests 2,81,83–85 on the stick–slip and whirl were also carried out by many researchers. Fully coupled vibration models 86–88 Tucker and Wang proposed a torsional rectiﬁcation mechanism to study stick–slip and compared it with existing soft-torque devices via several mathematical models. It shows that the approach proposed can eliminate many of the volatilities suffered by the existing suppression approach used to control stick–slip vibration. Baumgart derived a fully coupled mathematical model for the drilling process and solved it as an initial value problem. For the nonlinear differential equations of motion for the drillstring, the axial, lateral and tor- sional motion of the drillstring as well as the ﬂow rate, the mud pressure, and buckling were included. WOB and torque on bit were obtained from characteristic curves, which are functions of the penetration rate, and the angular bit velocity. Results showed the self-induced characteristics of the stick–slip and bit bounce phenomenon. However, discussions on the lateral vibration results were not included. 4,46 Christoforou and Yigit claimed that bit-rock and drillstring-borehole interactions as well as the geometric and dynamic nonlinearities give rise to the coupling of the drillstring vibrations. They presented a fully coupled model for the three basic modes of vibration of actively controlled drillstring with the mutual dependence of these vibrations. The model was similar to the one presented in Figure 15. It showed that torsional vibration due to bit motion excites axial and lateral motions leading to bit bounce and impacts with the borehole. An active control strategy was proposed to control the stick–slip vibration of the drilling system. Khulief and Al-Naser developed a 12-DOF FE model for drillstring with the coupling vibration and gyro- scopic effects were considered. The reduced order model was obtained by modal transformation, and the modal features and lateral dynamics of the drillstring at the drill bit were presented. Khulief et al. presented a dynamic drillstring model accounting for the axial-bending vibration and the torsional-bending vibration. The gyroscopic effect, the gravitational force, and the drillstring-borehole impact were considered, wherein the force–displace- ment principle was applied to describe the impact force and the energy balance relations were used to determine the viscous damping. Tang et al. 895 Figure 14. General scheme of the dynamical model. By using Timoshenko beam theory, Ritto et al. established a numerical model to investigate the effect of the drilling ﬂuid on the dynamics of the drillstring (Figure 14). A simpliﬁed ﬂuid–structure interaction model account- ing for the mudﬂow in and out of the drillstring was used. Other factors such as rotation and hanging force at the top, bit-rock interaction, shock and rubbing on the drillstring, weight of the drillstring, and ﬁnite strains that couple axial, lateral, and torsional vibrations were taken into account. However, the effect of ﬂuid ﬂow was not considered. Liu et al. developed an eight-DOF discrete model of the drillstring to study its nonlinear vibrations, consid- ering the axial, lateral, and torsional dynamics, shown in Figure 15. In the model, time-delay aspects, nonlinear- ities because of dry friction, loss of contact, and collisions were considered. Based on this model, numerical analyses were conducted for various drilling conditions. Results revealed that the drillstring behaviors can be self-excited due to stick–slip friction and time-delay effects and that the whirl motion of the drillstring alternates periodically between the stick and slip phases. Liu et al. analyzed the stability of the drilling system in terms of stability volumes in the space of rotate speed, cutting depth, and cutting coefﬁcient. The stability volume provides a guide for choosing parameters for rotary drilling operations. Based on the state and delayed-state feedback, a control strategy was presented and the effectiveness of this approach to mitigate stick–slip vibrations was studied. These two works were extended with developing a 32 segments model, and stability analysis of the degenerated one-segment model shows a stable region for the drilling operations. For reproducing all major types of drillstring vibrations, Kapitaniak et al. constructed an experimental rig where the commercial drill bits and rock samples were utilized. A mathematical model of the drillstring was presented by using low dimensional ODE model based on torsional pendulum. Various dynamical phenomena of the drillstring, such as stick–slip vibration, whirl, bit bounce, and buckling, were obtained. In a recent work by Moraes and Savi, a FDOF nonsmooth model with including axial-torsional-lateral coupling was developed to study the drillstring vibration, considering bit rock, wellbore interactions, eccentricity of drillstring, and hydro- dynamic force. By carrying out parametric studies, characteristics of stick–slip, bit bounce, and whirl motions were obtained. Experimental investigations Finnie and Bailey conducted experimental tests to study the axial load, torque at the top of a drilling system. Fritz did tests to investigate the dynamics of a vibratory rotor that paved the way for drillstring dynamics testing. For the drilling industry, comprehensive experimental facilities have been developed to characterize the bit 896 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Figure 15. Schematic of the discrete drilling system model. performance. These facilities have improved the understanding of the interaction between the drill bit and rock formation, resulting in high performance drilling tool and proper operation. The investigations reviewed in the following section focuses on the experimental studies of stick–slip vibrations in drillstring. Laboratory studies In order to identify the vibration effects on bit performance, Chen et al. designed a number of laboratory facilities and ﬁeld tests. Results showed that roller cone bit may encounter stick–slip phenomenon under some drilling conditions and stick–slip motion does not adversely inﬂuence the penetration rate. Melakhessou et al. developed a FDOF model to study the interaction between the drillstring and the wellbore during the drilling process. The nonlinear equations for describing the model were solved numerically. For ver- iﬁcation, experimental setup was used including two opto-electronic devices, as shown in Figure 16. The dynamic features obtained from model analysis were compared with the experimental results. It showed that the simulation results agreed with experimental observations when stick–slip vibrations occur. For better understanding the causes of stick–slip vibration, Mihajlovic et al. developed an experimental drillstring setup and torsional oscillation with and without stick–slip were observed in steady state (see Figure 17). A Lyapunov-based stability study and numerical and experimental bifurcation analyses were conducted. A comparison between theoretical and experimental bifurcation diagrams was carried out to know the predictive quality of the theoretical model. It showed that the friction characteristics were linked to the existence of torsional vibration with and without stick–slip. However, axial vibrations were not considered and coupled motions with considering stick–slip vibration have not been conducted. Khulief and Al-Sulaiman designed a drilling test apparatus (Figure 18) that can reproduce the drillstring dynamics for different excitation mechanisms. The test apparatus includes a motor that can generate different Tang et al. 897 79,101 Figure 16. Scheme of the experimental setup. Figure 17. Experimental drillstring setup. speeds, a brake was used to produce stick–slip conditions, and a shaker was used to apply WOB. The experimental results were employed to input and tune some parameters applied in the elastodynamic FE model. Theoretical analysis by Canudas-de-Wit et al. revealed that the stick–slip could be effectively controlled by applying an adaptation law (referred to as D-OSKILL) without requiring variations in the top drive and drill- string. Lu et al. developed a laboratory setup to generate stick–slip phenomenon (Figure 19). For the experi- ments, the rotational speed and WOB applied onto the drillstring are 20 rad/s and 180 N, respectively. Results showed that the WOB is returned to the nominal values when the stick–slip is suppressed, which agrees with the simulation results. Experimental results also showed that ROP reduces when the D-ODKILL is used but the stick–slip vibrations are signiﬁcantly minimized. Forster studied the mitigation of stick–slip vibration by introducing axial excitations into the drillstring. For this purpose, laboratory tests were conducted at the National Oilwell Varco Downhole Ltd. on small-scale vibration test apparatus designed to reproduce the stick–slip phenomenon and test different stick–slip reduction methods (Figure 20). For this setup, the tool performances with and without axial excitation can be tested. The axial excitation frequencies and axial load amplitudes of the typical axial excitation tools have been reproduced during the tests. It demonstrated that the axial excitations signiﬁcantly mitigate the stick–slip vibration. In order to facilitate the studies of the drilling system dynamics, Liao et al. constructs a laboratory-scale drillstring setup to investigate the working conditions experienced by a drillstring, as shown in Figure 21. A variable speed motor was used to drive and two encoders were used to measure two discs. An unbalanced 898 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Figure 18. Photograph of the laboratory test rig. Figure 19. Laboratory setup to generate stick–slip phenomenon. Tang et al. 899 Figure 20. In-house built vibration test rig. Figure 21. Laboratory scale arrangement of a rotary drilling system. mass, which represents the drill bit, was attached to the bottom disc. Results showed that impact and stick–slip motions are observed at a low speed and that whirl is observed at a high speed. The experimental studies are beneﬁcial to the reduced-order models in capturing the stick–slip vibration. Patil and Teodoriu reviewed comparatively the laboratory experiments of torsional vibrations and presented the experimental setup of drillstring at Clausthal University of Technology (as shown in Figure 22). Results from the theoretical analyses on stick–slip showed that the primary driving mechanism of stick–slip is not the self-excited axial vibrations, and not the velocity weakening effect but the crushing action of the drill bit and the interaction between the bit and rock. In order to verify this conclusion, Kovalyshen presented the results of the ongoing experiments of stick–slip vibrations. Figure 23 shows the small-scale drill rig. It shows that the experimental results agree with the theoretical analyses. 900 Journal of Low Frequency Noise, Vibration and Active Control 39(4) Figure 22. Experimental setup of the rotational drilling system at Clausthal University of Technology. Figure 23. The small-scale drill rig. Halsey et al. studied the stick–slip vibration by conducting a comparison between theoretical analysis and experimental results based on a full-scale laboratory experimental rig. Raymond et al. constructed a setup to obtain root understanding of BHA dynamics, but the tests are limited to the axial motions only. Detournay 110,111 et al. developed a phenomenological model to investigate the cutting bit dynamics, WOB, torque, angular velocity, bit design, and cutter number are included, and experiments with a small drilling machine were Tang et al. 901 112 113 conducted to verify this model. Esmaeili et al. constructed a full-scale drillstring rig, which actually drills into the rock sample. The laboratory apparatus consists of a steel frame, top drive, draw work, weights, measurement sensors, drill bit, drillstring, and a control unit. It has the ability of exerting 80 kg WOB on a bit of 2–3 inches. The relationships between drilling parameters with the ROP and drillstring vibration were obtained. Lines et al. conducted laboratory tests to gain insight into the downhole data and characterize the stick–slip vibration of the rotary steerable system. Based on a simple test-rig for analyzing drilling dynsmic, Real et al. explained the stick–slip cycles. As can be seen from the works related to laboratory tests of stick–slip vibration, there are differences among the test rigs. In fact, the performance of a test rig depends to some extent on the concentration of the theoretical model. Due to the complex behavior of stick–slip phenomenon, a small change on the rig (for example boundary condition of the drillstring) may lead to totally different results. For most of the reported stick–slip phenomena, they were regarded as torsional vibrations. In a work by Wang et al., the axial stick–slip motion of drillstring was reported. They built an experimental apparatus to investigate the toolface behavior in slide drilling. Results indicated that axial stick–slip vibration appears in the case of toolface disorientation due to friction. Field testing Dufeyte and Henneuse presented the investigation of bit and drillstring dynamics when the stick–slip vibration occurs based on 3500 hours ﬁeld measurements. It showed that varying certain parameters such as rotary table velocity, WOB, and mud viscous might mitigate stick–slip. Fear et al. described the failure nature and depen- dence on operating conditions of bit encountered with stick–slip vibrations. In order to verify the laboratory studies of the inﬂuences of stick–slip and whirl on the drilling performance, Chen et al. carried out ﬁeld tests in soft to medium formation in an inclined well with its slope angle 20 .It shows that the maximum bit velocity during stick–slip is twice more than the rotary table velocity. Results indicated that (1) stick–slip can be eradicated via using an advanced PDC bit stabilization techniques, (2) stabi- lizer added to the BHA does not remove the stick–slip vibration, and (3) the stick–slip propensity for a PDC bit is associated with the relationship between torque and rotary speed. Selnes et al. reported the ﬁeld cases of using an anti-stall tool to reduce friction-induced stick–slip phenom- enon. Yaveri et al. performed a case study on 16 offshore wells to understand the drilling dynamics. The reasons for the stick–slip and whirl occurrence and the corresponding intensity were evaluated, which can give solutions to reduce both drillstring vibration and drilling cost. The real-time downhole measurement can monitor the occurrence and severity of stick–slip phenomenon. However, due to the low frequency of the measurement data and increasing complexity of BHA, the information does not necessarily reveal the root cause of drilling dysfunction. Combining the engineering experiences with a progressive drilling dynamical model, Wu et al. studied the primary causes of stick–slip phenomenon in a number of ﬁeld cases. In a drilling application in Brazil, stick–slip vibration was regarded as the root cause of premature reamer. Based on this, an abrasion resistant cutter was implemented on the reamer and the BHA was optimized to mitigate stick–slip. Asymmetric vibration damping tool offers beneﬁts in minimizing downhole vibration and therefore maximiz- ing ROP. However, application of this tool has the potential to cause eccentric wear to BHA, which can cause a reduction in downhole tool life and drilling efﬁciency. In order to reduce eccentric wear and maximize drilling performance, works with respect to placement of the damping tool within drilling while underreaming operations were carried out on full-scale drilling rigs. Discussion on experimental results Regarding to the experimental setups, which use a break to recreate the velocity weakening effect or lumped torsional masses connected with strings to represent the drillstring, they recreate certain simpliﬁed equations that sometimes used to describe stick–slip and some details of the drilling system cannot be caught. As a result, the ability of such experiments (not use the actual ﬁeld scale drillstring) to study causes and attenuation of drillstring stick–slip vibration is extremely limited. The phenomenon of drillstring stick–slip is a limit cycle caused by instability in the torsional dynamics of a drillstring. This instability is also often referred to as a self-excited vibration. To explain the occurrence of this 71,122 instability, a velocity weakening effect (essentially a Stribeck-like effect) in the torque has been proposed, resulting in a classical approach to study stick–slip. It demonstrated that the velocity weakening effect is related to 902 Journal of Low Frequency Noise, Vibration and Active Control 39(4) 12,123 the mud pressure, strength of the bottom of the hole, wear state of the bit, and bit geometry. Experimental works (single cutter experiments) showed that PDC cutter does not exhibit any inherent velocity weakening effect, 124 107 seemingly discrediting much of the previous work. Moreover, experiments of Kovalyshen did not ﬁnd any evident velocity weakening effect. Consequently, we may question whether the velocity weakening effect is the root cause of stick–slip, a companion of this phenomenon, or irrelevant to it, is still not clear. Based on the machine tool chattering analysis, Elsayed and Raymond conducted experiments to simulate chatter (self-excited vibration) in actual ﬁeld conditions. Results showed that chatter takes place when using PDC bit even in soft formation and that the chatter severity correlates to the lack of stability in the system. Richard et al. developed a coupled torsional-axial model of the drilling system to study the relationship between the bit 51,52 geometry and the velocity weakening effect. This model was further extended by Germay et al. However, observations obtained from this model are not in line with ﬁeld results, so the instability presented by Richard 50 51,52 et al. and Germay et al. is probably different from the observation in the ﬁeld. The cause or mechanism of stick–slip vibration, having resulted in much contention, still needs to be investigated. Numerical simulations In general, the drillstring for oilwell drilling is a complex system and its dynamics are related to many factors. Up to now, most of the existing publications try to reveal a single vibration mode or the coupling of single modes. However, revealing all types of vibrations of drillstring in a theoretical model or ﬁnite element (FE) model is difﬁcult. In a work by Khulief and Al-Naser, a FE model of the drillstring by which related dynamic effects including stick–slip can be obtained was presented. In the model, gyroscopic effect, torsional-bending inertia coupling, inertia-axial stiffening coupling and gravity were taken into account. Ghasemloonia investigated the dynamic behavior of the entire drillstring under the action of a vibration-assisted rotary drilling tool, using a dynamic FE model of the vertical drillstring. In the model, the effects of mud damping, driving torque, multispan contact, and varying axial load were included. Kapitaniak et al. used ABAQUS software to investigate the stick–slip vibration, whirling, bit bounce, and helical buckling of the drillstring. The FE models were calibrated via new experimental rig for reproducing major types of drillstring vibrations. Results showed that just a low- dimensional model is enough to predict the behavior of a drillstring in certain conﬁguration. Based on numerical simulation, Zhao et al. revealed that the axial stick–slip movement of the drillstring can lead to abnormal ﬂuctuation of downhole pressure. Sarker et al. used a nonlinear 3D multibody model to study the stick–slip and whirl, and a dynamic FE model of an enclosed shaft under axially compressive load moving inside the borehole was established to verify the theoretical model. By combining with experimental results obtained at Memorial 128 129 University of Newfoundland, they also simulated the case of using an axially vibrating tool. Tang et al. investigated the effect of high-frequency torsional impacts on mitigation of stick–slip phenomenon, and the ABAQUS program was used to simulate the torque on drill bit. Results indicated that the stick–slip vibration can be mitigated by using high-frequency torsional impacts. In order to know the axial load transfer and drill- string dynamics during the slide drilling, Wang et al. used a second-order ﬁnite difference method to solve a uniﬁed mechanical model of the drillstring. Parameter simulation results showed that impacts applied on the drillstring can mitigate the stick–slip vibration and make the movement of the drillstring smoother. When looked into more detail, publications related to numerical simulations on the stick–slip of drillstring are comparatively scarce and most of the references are related to analytical methods or experimental tests. Conclusions This study summarized the researches on stick–slip vibrations in drillstring including mechanical models and experimental investigations. For theoretical modeling, lumped pendulum models (SDOF and MDOF models) were typically used to study the drillstring dynamics. The modeling of stick–slip phenomenon in vertical drillstring might conform to the real conditions. For the directional wells, however, works should continue to clarify whether simple lumped pendulum models are ﬁt to describe stick–slip, and how well these models characterize the real drillstring systems. Distributed system is capable of describing typical features of a complex drilling system. For a contributed model considering both damping and nonlinear frictional characteristics, however, obtaining the analytical solutions is difﬁcult. Consequently, the areas of semi-analytical techniques need more research efforts. Laboratory investigations were conducted together with the theoretical analysis and ﬁeld studies to replicate the stick–slip vibration and demonstrate the reliability of published data. Stick–slip vibration root cause and bit performance were studied and the effects of dynamic parameters were quantiﬁed. There were also many other Tang et al. 903 parameters that are important for the occurrence of stick–slip and have been scantily studied through experi- ments, such as bit-rock interaction and rock lithology. Due to large length-to-diameter ratio of the deep drillstring, stick–slip phenomenon is more inclined to appear in these wells. Managing the problems of stick–slip vibration in drillstring is a long-term task. As drill bit tech- nology has evolved to a mature stage, it important to design more efﬁcient downhole tools and develop efﬁcient control approaches to mitigate stick–slip. In general, many improvements have been achieved in studying the stick–slip vibrations. However, progresses have been much slower than expected and many challenges remain. There are still many problems or drilling accidents generated by stick–slip, such as drillstring twist off, low ROP, poor wellbore trajectory, et al. With the increase in the well depth and complexity of drilling technology, advanced and deep-going works are worthy to be done. For example, stick–slip phenomenon of the drillstring in directional or horizontal wells or ocean drilling, the effects of system parameters on stick–slip phenomenon of drill- 132 133,134 string, and the methods for controlling this type of vibration. Declaration of conflicting interests The author(s) declared no potential conﬂicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following ﬁnancial support for the research, authorship, and/ or publication of this article: This work is supported by the China Postdoctoral Science Foundation (Grant no. 43XB3793XB), National Natural Foundation of China (Grant no. 51674214) and Scientiﬁc Innovation Group for Youths of Sichuan Province (Grant no. 2019JDTD0017). ORCID iDs Liping Tang https://orcid.org/0000-0003-0981-2120 Xiaohua Zhu https://orcid.org/0000-0002-0507-3773 Yunlai Zhou https://orcid.org/0000-0002-2347-647X References 1. Khulief YA, Al-Sulaiman FA and Bashmal S. Vibration analysis of drillstrings with self-excited stick slip oscillations. J Sound Vib 2007; 299: 540–558. 2. Wu X and Agnihotri M. Decoupling stick-slip and whirl to achieve breakthrough in drilling performance. In: Proceedings of the IADC/SPE drilling conference and exhibition, New Orleans, LA, 2-4 February 2010. 3. Warren TM and Oster JH. Torsional resonance of drill collars with PDC bits in hard rock. In: Proceedings of the SPE annual technical conference and exhibition, New Orleans, LA, 27-30 September 1998. 4. Christoforou AP and Yigit AS. Active control of stick slip vibrations: the role of fully coupled dynamics. In: Proceedings of the SPE Middle East oil show, Bahrain, 17-20 March 2001. 5. Belokobyl’skii SV and Prokopov VK. Friction induced self-excited vibration of drill rig with exponential drag law. Soviet Appl Mech 1982; 18: 98–101. 6. Dareing DW. Rotary speed, drill collars control drillstring bounce. Oil Gas J 1983; 81: 63–68. 7. Dawson R, Lin YQ and Spanos PD. Drill-string stick slip oscillations. In: Proceedings of the 1987 SEM Spring conference on experimental mechanics, Houston, TX, 14-19 June 1987. 8. Zhu X, Tang L and Yang Q. A literature review of approaches for stick-slip vibration suppression in oilwell drillstring. Adv Mech Eng 2014; 6: 967952. 9. Halsey GW, Kyllingstad A and Kylling A. Torque feedback used to cure slip-stick motion. In: Proceedings of the SPE 63st annual technical conference and exhibition, Houston, TX, 2-5 October 1988. 10. Kyllingstad A and Halsey GW. A study of slip/stick motion of the bit. SPE Drill Eng 1988; 3: 369–373. 11. Lin YQ and Wang Y.H. Stick slip vibration of drill strings. J Manuf Sci Eng 1991; 113: 38–43. 12. Brett JF. The genesis of torsional drillstring vibrations. SPE Drill Eng 1992; 7: 168–174. 13. Rudat J and Dashevskiy D. 2011. Development of an innovative model based stick slip control system. In: Proceedings of the SPE/IADC drilling conference, Amsterdam, Netherlands, 1-3 March 2011. 14. Qiu H, Yang J and Butt S. Investigation on bit stick-slip vibration with random friction coefﬁcients. J Petrol Sci Eng 2018; 164: 127–139. 15. Cunha-Lima LC, Aguiar RR, Ritto TG, et al. Analysis of the torsional stability of a simpliﬁed drillstring. In: Proceedings of the XVII international symposium on dynamic problems of mechanics, Natal, Brazil, 2015. 16. Tang L and Zhu X. Effects of the difference between the static and the kinetic friction coefﬁcients on a drill string vibration linear approach. Arab J Sci Eng 2015; 40: 3723–3729. 904 Journal of Low Frequency Noise, Vibration and Active Control 39(4) 17. Tang L, Zhu X, Shi C, et al. Investigation of the damping effect on stick-slip vibration of oil and gas drilling system. J Vib Eng Technol 2016; 4: 79–88. 18. Tang L, Zhu X, Qian X, et al. Effects of weight on bit on torsional stick-slip vibration of oilwell drill string. J Mech Sci Technol 2017; 31: 4589–4597. 19. Leine RI, Campen DH, Kraker AD, et al. Stick slip vibrations induced by alternate friction models. Nonlinear Dyn 1998; 16: 41–54. 20. Nosrati A and Farshidianfar A. 2009. Analytical approximations for stick-slip vibration amplitudes based on a discre- tization method. In: Congress on sound and vibration, Krakow, Poland, 5-9 July 2009. 21. Van de Vrande BL, Van Campen DH and De Kraker A. An approximate analysis of dry friction induced stick slip vibrations by a smoothing procedure. Nonlinear Dyn 1999; 19: 157–169. 22. Abdulgalil F and Siguerdidjane H. 2004. Nonlinear friction compensation design for suppressing stick slip oscillations in oil well drillstrings. In: Proceedings of the 5th Asian control conference, Melbourne, Australia, 20-23 July 2004. 23. Canudas-de-Wit C, Rubio FR and Corchero MA. DOSKIL: a new mechanism for controlling stick-slip oscillations in oil well drillstrings. IEEE Trans Contr Syst Technol 2008; 16: 1177–1191. 24. Navarro-Lopez EM and Suarez R. 2004. Practical approach to modeling and controlling stick-slip oscillations in oilwell drillstrings. In: IEEE international conference on control applications, Taipei, China, 2-4 September 2004. 25. Bayliss MT, Panchal N and Whidborne JF. 2012. Rotary steerable directional drilling stick-slip mitigation control. In: Proceedings of the IFAC workshop on automatic control in offshore oil and gas production, Trondheim, Norway, 31 May-1 June 2012. 26. Karkoub M, Magid YA and Balachandran B. Drill string torsional vibration suppression using GA optimized control- lers. J Can Petrol Technol 2009; 48: 32–38. 27. Silveira M and Wiercigroch M. Low dimensional models for stick-slip vibration of drillstrings. J Phys Conference Series 2009; 181: 1–8. 28. Patil PA and Teodoriu C. 2013 Model development of torsional drillstring an investigating parametrically the stick-slips inﬂuencing factors. J Energy Resour Technol135: 013103 29. Navarro-Lopez EM and Corte´ s D. Avoiding harmful oscillations in a drillstring through dynamical analysis. J Sound Vib 2007; 307: 152–171. 30. Navarro-Lopez EM and Corte´ s D. Sliding-mode control of a multi-DOF oilwell drillstring with stick-slip oscillations. In: Proceedings of the American control conference, New York, NY, 11-13 July 2007. 31. Navarro-Lopez EM and Castro EL. Non-desired transitions and sliding mode control of a muti-DOF mechanical system with stick slip oscillations. Chaos Soliton Fract 2009; 41: 2035–2044. 32. Kreuzer E and Steidl M. Model order reduction of a drill string model with self-excited stick slip vibrations. Proc Appl Math Mech 2009; 9: 295–296. 33. Khulief YA and Al-Sulaiman FA. Laboratory investigation of drillstring vibrations. J Mech Eng Sci 2009; 223: 2249–2262. 34. Kapitaniak M, Hamaneh VV, Cha´ vez JP, et al. Unveiling complexity of drillstring vibrations: experiments and modeling. Int J Mech Sci 2015; 102: 324–337. 35. Palmov VA, Brommundt E and Belyaev AK. Stability analysis of drillstring rotation. Dyn Stabil Syst 1995; 10: 99–110. 36. Challamel N. Rock destruction effect on the stability of a drilling structure. J Sound Vib 2000; 233: 235–254. 37. Challamel N, Sellami H and Chenevez E. 2000. A stick-slip analysis based on rock/bit interaction: theoretical and experi- mental contribution. In: Proceedings of the SPE/IADC drilling conference, New Orleans, USA, 23-25 February 2000. 38. Saldivar B and Mondie´ S. Drilling vibration reduction via attractive ellipsoid method. J Franklin I 2013; 350: 485–502. 39. Saldivar B, Mondie´ S, Loiseau JJ, et al. Stick-slip oscillations in oilwell drillstrings: distributed parameter and neutral type retarded model approaches. In: Proceedings of the 18th IFAC World Congress, Milano, Italy, 28 August-2 September 2011. 40. Kreuzer E and Steidl M. Controlling torsional vibrations of drill strings via decomposition of traveling waves. Arch Appl Mech 2012; 82: 515–531. 41. Ritto TG, Escalante MR, Sampaio R, et al. Drillstring horizontal dynamics with uncertainty on the frictional force. J Sound Vib 2013; 332: 145–153. 42. Ritto TG. Bayesian approach to identify the bit rock interaction parameters of a drill string dynamical model. J Braz Soc Mech Sci Eng 2015; 37: 1173–1182. 43. Aarsnes UJF, Meglio FD and Shor RJ. Avoiding stick slip vibrations in drilling through startup trajectory design. J Process Contr 2018; 70: 24–35. 44. Aarsnes UJF and Wouw N. Axial and torsional self-excited vibrations of a distributed drill-string. J Sound Vib 2019; 444: 127–151. 45. Ghasemloonia A, Rideout DG and Butt SD. Vibration analysis of a drillstring in vibration-assisted rotary drilling: ﬁnite element modeling with analytical validation. J Energy Resour Technol 2013; 135: 032902 46. Christoforou AP and Yigit AS. Fully coupled vibrations of actively controlled drillstrings. J Sound Vib 2003; 267: 1029–1045. Tang et al. 905 47. Yigit AS and Christoforou AP. Stick slip and bit bounce interaction in oil well drillstring. J Energy Resour Technol 2006; 128: 268–274. 48. Richard T, Detournay E, Fear MJ, et al. Inﬂuence of bit-rock interaction on stick-slip vibrations of PDC bits. In: Proceedings of the SPE annual technical conference and exhibition, San Antonio, 29 September-2 October 2002. 49. Richard T, Germay C and Detournay E. Self-excited stick slip oscillations of drill bits. CR Mecanique 2004; 332: 619–626. 50. Richard T, Germay C and Detournay E. A simpliﬁed model to explore the root cause of stick slip vibrations in drilling systems with drag bits. J Sound Vib 2007; 305: 432–456. 51. Germay C, Deno€el V and Detournay E. Multiple mode analysis of the self-excited vibrations of rotary drilling systems. J Sound Vib 2009; 325: 362–381. 52. Germay C, Wouw NV, Nijmeijer H, et al. Nonlinear drillstring dynamics analysis. SIAM J Appl Dyn Syst 2009; 8: 527–553. 53. Nandakumar K and Wiercigroch M. Stability analysis of a state dependent delayed, coupled two DOF model of drill- string vibration. J Sound Vib 2013; 332: 2575–2592. 54. Kovalyshen Y. Understanding root cause of stick-slip vibrations in deep drilling with drag bits. Int J Nonlin Mech 2014; 67: 331–341. 55. Depouhon A and Detournay E. Instability regimes and self-excited vibrations in deep drilling system. J Sound Vib 2014; 333: 2019–2039. 56. Depouhon A and Detournay E. Stick-slip instabilities in rotary drilling system. In: Proceedings of the 49th US Rock mechanics/geomechanics symposium, San Francisco, CA, 28 June-1 July 2015. 57. Kamel JM and Yigit AS. Modeling and analysis of stick-slip and bit bounce in oil well drillstrings equipped with drag bits. J Sound Vib 2014; 333: 6885–6899. 58. Alamo FC and Weber HI. Stick-slip analysis in drill string. In: Proceedings of the 18th international congress of mechanical engineering, Ouro Preto, Brazil, 2005. 59. Sampaio R, Piovan MT and Lozano GV. Stick slip patterns in coupled extensional and torsional vibrations of drill- strings. Mecanica Computacional XXIV 2005; 24: 861–877. 60. Divenyi S, Savi MA, Wiercigroch M, et al. Modelling of stick-slip and bit bounce in drill-string dynamics via smoothen functions. In: Proceedings of VI national congress of mechanical engineering, Paraiba, Brazil, 2010. 61. Divenyi S, Savi MA, Wiercigroch M, et al. Drill string vibration analysis using non-smooth dynamics approach. Nonlinear Dyn 2012; 70: 1017–1035. 62. Vasconcellos MN and Savi MA. 2010. Analysis of oil well drilling dynamics from non-smooth models. In: Proceedings of the Mecanica computational, Santa Fe, Argentina, XXIX, 8807–8817. 63. Sarker MM, Rideout DG and Butt SD. 2012. Dynamic model of an oilwell drillstring with stick slip and bit bounce interaction. In: Proceedings of the international conference on bond graph modeling, Genoa, Italy, 8-11 July 2012. 64. Ertas D, Bailey JR, Wang L, et al. Drillstring mechanics model for surveillance, root cause analysis, and mitigation of torsional and axial vibrations. SPE Drill Complet 2014; 29: 405–417. 65. Sairaﬁ FA, Ajmi KE, Yigit AS, et al., 2016. Modeling and control of stick-slip and bit bounce in oil well drill strings. In: Proceedings of the SPE/IADC drilling technology conference and exhibition, Abu Dhabi, UAE, 26-28 January 2016. 66. Besselink B, Van de Wouw N and Nijmeijer H. A semi-analytical study of stick slip oscillations in drilling systems. ASME J Comput Nonlinear Dyn 2011; 6: 1–9. 67. Besselink B, Vromen T, Kremers N, et al. Analysis and control of stick-slip oscillations in drilling system. IEEE T Contr Syst Technol 2015; 2015: 1–12. 68. Insperger T, Ste´ pa´ n G and Turi J. State-dependent delay in regenerative turning processes. Nonlinear Dyn 2006; 47: 275–283. 69. Aarsnes UJF and Aamo OM. Linear stability analysis of self-excited vibrations in drilling using an inﬁnite dimensional model. J Sound Vib 2016; 360: 239–259. 70. Schmalhorst B and Baumgart A. Combined simulation of whirl and stick-slip phenomenon using a nonlinear ﬁnite element model. In: Proceedings of the energy week conference and exhibition, Houston, TX, 28-30 January 1997. 71. Abbassian F and Dunayevsky VA. Application of stability approach to torsional and lateral bit dynamics. SPE Drill Complet 1998; 13: 99–107. 72. Vandiver JK, Nicholson JW and Shyu RJ. Case studies of the bending vibration and whirling motion of drill collars. SPE Drill Eng 1990; 5: 282–290. 73. Berlioz A, Der Hogopian J, Dufour R, et al. Dynamic behavior of a drill string experimental investigation of lateral instabilities. J Vib Acoust 1996; 118: 292–298. 74. Gulyayev VI and Shevchuk LV. Drill string bit whirl simulation with the use of frictional and nonholonomic models. J Vib Acoust 2015; 138: 011021. 75. Yigit AS and Christoforou AP. Coupled torsional and bending vibrations of drillstrings subject to impact with friction. J Sound Vib 1998; 215: 167–181. 76. Yigit AS and Christoforou AP. Coupled torsional and bending vibrations of actively controlled drillstrings. J.Sound Vib 2000; 234: 67–83. 906 Journal of Low Frequency Noise, Vibration and Active Control 39(4) 77. Al-Hiddabi SA, Samanta B and Seibi A. Non-linear control of torsional and bending vibrations of oilwell drillstrings. J Sound Vib 2003; 265: 401–415. 78. Leine RI, Campen DH and Keulfjes WJG. Stick slip whirl interaction in drillstring dynamics. J Vib Acoust 2002; 124: 209–220. 79. Melakhessou H, Berlioz A and Ferraris G. A nonlinear well drillstring interaction model. J Vib Acoust 2003; 125: 46–52. 80. Sowers SF, Dupriest FE, Bailey JR, et al. Roller reamers improve drilling performance in wells limited by bit and bottomhole assembly vibrations. In: Proceedings of the SPE/IADC drilling conference and exhibition, Amsterdam, Netherlands, 17-19 March 2009. 81. Vlajic N, Liao CM, Karki H, et al. Stick-slip and whirl motions of drill strings: numerical and experimental studies. In: Proceedings of the ASME 2011 international design engineering technical conferences and computers and information in engineering conference, Washington, DC, 2011, 28-31 August 2011. 82. Butlin T and Langley RS. An efﬁcient model of drillstring dynamics. J Sound Vib 2015; 356: 100–123. 83. Leseultre A, Lamine E and Jonsson A. An instrumented bit: a necessary step to the intelligent BHA. In: Proceedings of the SPE/IADC drilling conference, Dallas, TX, 1998, 3-6 March 1998. 84. Yaveri M, Damani K and Kalbhor H. 2010. Solutions to the down hole vibrations during drilling. In: Proceedings of the 34th annual SPE international conference and exhibition, Calabar, Nigeria. 85. Stroud D, Bird N, Norton P, et al. Roller reamer fulcrum in point the bit rotary steerable system reduces stick slip and backward whirl. In: Proceedings of the IADC/SPE drilling conference and exhibition, San Diego, CA, 2012, 6- 8 March 2012. 86. Tucker RW and Wang C. On the effective control of torsional vibrations in drilling systems. J Sound Vib 1999; 224: 101–122. 87. Tucker RW and Wang C. An integrated model for drillstring dynamics. J Sound Vib 1999; 224: 123–165. 88. Tucker RW and Wang C. Torsional vibration control and cosserat dynamics of a drill rig assembly. Meccanica 2003; 38: 143–159. 89. Baumgart A. Stick slip and bit bounce of deep hole drillstrings. J Energy Resour Technol 2000; 122: 78–82. 90. Khulief YA and Al-Naser H. Finite element dynamic analysis of drillstrings. Finite Elem Anal Des 2005; 41: 1270–1288. 91. Khulief YA, Al-Sulaiman FA and Bashmal S. Vibration analysis of drillstrings with string-borehole interaction. J Mech Eng Sci 2008; 222: 2099–2110. 92. Ritto TG, Sampaio R and Soize C. Drill-string dynamics coupled with the drilling ﬂuid dynamics. In: Proceedings of the XIII international symposium on dynamic problems of mechanics, Angra dos Reis, Brazil, 2009, 2-6 March 2009. 93. Liu X, Vlajic N, Long X, et al. Nonlinear motions of a ﬂexible rotor with a drill bit: stick-slip and delay effects. Nonlinear Dyn 2013; 72: 61–77. 94. Liu X, Vlajic N, Long X, et al. Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control. Nonlinear Dyn 2014; 78: 1891–1906. 95. Liu X, Vlajic N, Long X, et al. State-dependent delay inﬂuenced drill-string oscillations and stability analysis. J Vib Acoust 2014; 136: 051008. 96. Moraes LPP and Savi MA. Drill-string vibration analysis considering an axial-torsional-lateral nonsmooth model. J Sound Vib 2019; 438: 220–237. 97. Finnie I and Bailey JJ. An experimental study of drill string vibration. J Eng Industry 1960; 82: 129–135. 98. Fritz RJ. The effects of an annular ﬂuid on the vibrations of a long rotor, part 2-test. J Basic Eng 1970; 92: 923–929. 99. Aarrestad TV and Kyllingstad A. An experimental and theoretical study of a coupling mechanism between longitudinal and torsional drillstring vibration at the bit. SPE Drill Eng 1988; 3: 12–18. 100. Chen SL, Blackwood K and Lamine E. Field investigation of the effects of stick-slip, lateral and whirl vibrations on roller cone bit performance. SPE Drill Complet 2002; 17: 15–20. 101. Patil PA and Teodoriu C. A comparative review of modelling and controlling torsional vibrations and experimentation using latoratory setups. J Petrol Sci Eng 2013; 112: 227–238. 102. Mihajlovic N, Wouw N, Hendriks MPM, et al. Friction-induced vibrations in an experimental drill-string system for various friction situations. In: Proceedings of the ENOC-2005, Eindhoven, Netherlands, 7-12 August 2005. 103. Mihajlovic N, Wouw N, Hendriks MPM, et al. Friction induced limit cycling in ﬂexible rotor systems, an experimental drillstring setup. Nonlinear Dyn 2006; 46: 273–291. 104. Lu H, Dumon J and Canudas-de-Wit C. Experimental study of the D-OSKILL mechanism for controlling the stick-slip oscillations in a drilling laboratory testbed. In: Proceedings of the IEEE multi-conference on systems and control, Saint Petersburg, Russia, 8-10 July 2009. 105. Forster I. Axial excitation as a means of stick slip mitigation- small scale rig testing and full scale ﬁeld testing. In: Proceedings of the SPE/IADC drilling conference, Amsterdam, Netherlands, 1-3 March 2011. 106. Liao CM, Balachandran B, Karkoub M, et al. Drillstring dynamics: reduced order models and experimental studies. J Vib Acoust 2011; 133: 041008. 107. Kovalyshen Y. Experiments on stick-slip vibrations in drilling with drag bits. In: Proceedings of the 48th US Rock mechanics/geomechanics symposium, Minneapolis, MN, 1-4 June 2014. Tang et al. 907 108. Halsey GW, Kyllingstad A, Aarrestad TV, et al. Drillstring torsional vibrations: comparison between theory and exper- iment on a full-scale research drilling rig. In: Proceedings of the SPE 61st annual technical conference and exhibition, New Orleans, LO, 5-8 October 1986. 109. Raymond DW, Elsayed MA, Polsky Y, et al. Laboratory simulation of drill bit dynamics using a model-based servohy- draulic controller. J Energy Resour Technol 2008; 130: 043103. 110. Detournay E and Defourny P. A phenomenological model for the drilling action of drag bits. Int J Rock Mech Min Sci Geomech Abstr 1992; 29: 13–23. 111. Detournay E, Richard T and Shepherd M. Drilling response of drag bits: theory and experiment. Int J Rock Mech Min Sci 2008; 45: 1347–1360. 112. Richard T, Dagrain F, Poyol E, et al. Rock strength determination from scratch tests. Eng Geol 2012; 147–148: 91–100. 113. Esmaeili A, ElahifaR B and Fruhwirth RK. Experimental evaluation of real-time mechanical formation classiﬁcation using drill string vibration measurements. In: Proceedings of the SPE annual technical conference and exhibition, Texas, USA, 8-10 October 2012. 114. Lines LA, Stroud DRH and Coveney VA. 2013. Torsional resonance – an understanding based on ﬁeld and laboratory tests with latest generation point the bit rotary steerable system. In: Proceedings of the IADC/SPE drilling conference and exhibition, Amsterdam, Netherlands, 5-7 March 2013. 115. Real FF, Lobo DM, Ritto TG, et al. Experimental analysis of stick-slip in drilling dynamics in a laboratory test-rig. J Petrol Sci Eng 2018; 170: 755–762. 116. Wang X, Ni H and Wang R. Experimental study on toolface disorientation and correction during slide drilling. J Petrol Sci Eng 2019; 173: 853–860. 117. Dufeyte MP and Henneuse H. Detection and monitoring of the slip-stick motion: ﬁeld experiments. In: Proceedings of the SPE/IADC drilling conference, Amsterdam, Netherlands, 11-14 March 1991. 118. Fear MJ, Abbassian F, Parﬁtt SHL, et al. The destruction of PDC bits by severe slip-stick vibration. In: Proceedings of the IADC/SPE drilling conference, Amsterdam, Netherlands, 4-6 March 1997. 119. Selnes KS, Clemmensen C and Reimers N. Drilling difﬁcult formations efﬁciently with the use of an antistall tool. SPE Drill. Complet 2009; 24: 531–536. 120. Wu X, Karuppiah V, Nagaraj M, et al. Identifying the root cause of drilling vibration and stick slip enables ﬁt for purpose solutions. In: Proceedings of the IADC/SPE drilling conference and exhibition, San Diego, CA, 6-8 March 2012. 121. Kabbara A, McCarthy J and Burnett T. 2012. Understanding how the placement of an asymmetric vibration damping tool within drilling while underreaming assemblies can inﬂuence performance and reliability. In: Proceedings of the SPE drilling conference and exhibition, San Diego, CA, 6-8 March 2012. 122. Jansen JD and Steen L. Active damping of self-excited torsional vibrations in oil well drillstrings. J Sound Vib 1995; 179: 647–668. 123. Jain JR, Ledgerwood LW, Hoffmann OJ, et al. Mitigation of torsional stick slip vibrations in oil well drilling through PDC bit design: putting theories to the test. In: Proceedings of the SPE annual technical conference and exhibition, Denver, CO, 30 October-2 November 2011. 124. Nishimatsu Y. The mechanics of rock cutting. Int J Rock Mech Min Sci 1972; 9: 261–270. 125. Elsayed MA and Raymond DW. Measurement and analysis of chatter in a compliant model of a drillstring equipped with a PDC bit. In: Proceedings of the American Society of Mechanical Engineers’ energy technology conference and exhibition, New Orleans, LA, 14-17 February 2000. 126. Zhao D, Hovda S and Sangesland S. Abnormal down hole pressure variation by axial stick-slip of drillstring. J Petrol Sci Eng 2016; 145: 194–204. 127. Sarker M, Rideout DG and Butt SD. Dynamic model for 3D motions of a horizontal oilwell BHA with wellbore stick-slip whirl interaction. J Petrol Sci Eng 2017; 157: 482–506. 128. Sarker M, Rideout DG and Butt SD. Dynamic model for longitudinal and torsional motions of a horizontal oilwell drillstring with wellbore stick-slip friction. J Petrol Sci Eng 2017; 150: 272–287. 129. Tang L, Zhu X and Shi C. Effects of high-frequency torsional impacts on mitigation of stick-slip vibration in drilling system. J Vib Eng Technol 2017; 5: 111–122. 130. Wang P, Ni H, Wang X, et al. Modelling the load transfer and tool surface for friction reduction drilling by vibrating drill-string. J Petrol Sci Eng 2018; 164: 333–343. 131. Dao NH, Menand S and Isbell M. Mitigating and understanding stick-slip in unconventional wells. In: Proceedings of the SPE/IADC international drilling conference and exhibition, Hague, The Netherlands, 5-7 March 2019. 132. Christian ED. Identifying the optimum zone for reducing drill string vibrations. In: Proceedings of the SPE annual technical conference and exhibition, San Antonio, USA, 9-11 October 2017. 133. Tang L and Zhu X. On the development of high-frequency torsional impact drilling techniques for hard formation drilling. Adv Mech Eng 2018; 10: 1–15. 134. Monteiro HLS and Trindade MA. Performance analysis of proportional-integral feedback control for the reduction of stick-slip-induced torsional vibrations in oil well drillstrings. J Sound Vib 2017; 398: 28–38.

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"Journal of Low Frequency Noise, Vibration and Active Control" – SAGE

Published: Jun 4, 2019

Keywords: Stick–slip vibration; drillstring; bottom-hole assembly; degree of freedom; structural coupling

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Stick–slip vibrations in oil well drillstring: A review:

Stick–slip vibrations in oil well drillstring: A review:

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Stick–slip vibrations in oil well drillstring: A review:

Stick–slip vibrations in oil well drillstring: A review:

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