Oilwell Drillstring Research Articles

Stick–slip vibrations in oil well drillstring: A review

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.

Effects of axial impact load on the dynamics of an oilwell drillstring

This article studies the dynamics of oilwell drillstring under large and small axial impact loads. For the case of large impact load, the drillstring is regarded as a continuous bar under the impact load of a falling mass, and the energy conservation method is implemented. A sensitivity analysis is conducted to investigate the effect of cross-sectional area of the drill string on the impact stress. Results show that the design of drillstring with different cross-sectional areas is not a suitable method. In order to understand the effect of high-frequency small axial impact (applied from percussion tools or downhole generators) on the drillstring vibration, a mechanical model in which the drillstring is regarded as a 2-degree-of-freedom system under a harmonic force is developed. Sensitivity analysis on the effects of impact generator placement and impact frequency on drillstring dynamics are conducted. Results show that the impact generator should be installed near the drill bit and that high frequency is recommended to be used.

Effects of Drill String Length on Stick–Slip Oscillation of the Oilwell Drill String

It has been demonstrated by numerous field data that the stick–slip phenomenon tends to appear in deep wells. However, the explanation for this phenomenon has scarcely been studied. Based on a torsional pendulum model, the relationship between stick–slip oscillation and drill string (DS) length is studied in this work. Firstly, the drill bit (DB) dynamics are obtained by solving the kinetic motion of the DB. Secondly, case studies with different DS lengths are conducted by referring to the actual drilling parameters. Thirdly, results and discussions related to the case studies are carried out, including obtaining the DB dynamics, DB dynamics for different DS lengths, determination of the critical length, and plausible interpretation for the occurrence of stick–slip oscillation. Results show that two types of oscillation are obtained, e.g., oscillations with or without stick–slip phenomenon. In the cases of stick–slip, the state trajectories possess stable limit cycles. In the cases of no stick–slip, the state trajectories possess a spiral that denotes the DB motion tends to a stable phase (uniform motion).

Numerical simulation of dynamic buckling response considering lateral vibration behaviors in drillstring

Mechanical behavior of oilwell drillstring coming at the motions of penetrating rock is associated with drilling safety and wellbore quality. A poor performance can be attended by elastic stability loss in a slender drillstring exerting undesired buckling and vibration phenomena in the working process. Devoting to investigating the dynamic buckling behavior is an efficient way to avoid fatigue failure of the drillstring components and enhance drilling rate. A dynamic analysis of the buckling behavior of the entire column considering violent lateral vibrations is presented as a result available. Analytical equations of the drilling system are integrated numerically with finite element method. A virtual contact element implemented between the drillstring and the borehole, in conjunction with Hertzian contact assumption, gives the direct access to calculate the contact force and positions. Lateral deflection, critical length and the effects of drilling parameters and stabilizer on the buckling deformation are captured to experience the realistic buckling response of a typical drillstring in a vertical well. Simulation results indicate that spiral pitch and wave numbers of a nonlinear spiral shape prevailing in the lower zone of drillstring are deeply associated with the cutting force at the bit. Improving a drillstring behavior performance in a real oilfield is observed that this model can assist in evaluating the properties of the working security and buckling resistance with complex boundary conditions.

Semi-analytical model of the axial movements of an oil-well drillstring in deviated wellbores

The lumped element model of the axial movement in a drillstring that was developed in Ref. [1], is extended to apply for deviated wellbores. This extension involves taking into account the Coulomb friction forces that are present in the curved boreholes. The Coulomb friction forces are proportional to the normal forces, which are dependent on the distributed mass of the drillstring and the curvature of the hole. We consider a constant rotation speed and since the Coulomb friction forces are opposing the movements, the axial friction components are proportional to the axial velocities divided by the constant rotation speed. We outline a methodology for predicting when the Coulomb friction forces are dominating the viscous friction forces in deviated wellbores. As in Ref. [1], the model is simply a convolution of the topside movement and a semi-analytical expression. The model is therefore suitable for a real-time implementation and the model is also an asset for finding reasonable physical approximations and to benchmark other models.

Effects of the Synchronous Variation of the Static and the Kinetic Friction Coefficients on Stick–Slip Vibration of Drillstring

Stick–slip vibration (SSV) in oilwell drillstring presents one of the primary reasons of drilling performance deterioration as it reduces rate of penetration, aggravates tool failures, reduces wellbore quality, and increases drilling cost. Although a number of research works have focused on this subject, there is not a commonly accepted explanation of its cause yet. In our previous work, influences of the difference between the static and the kinetic friction coefficients (DBSKFC) on SSV have been investigated, wherein the kinetic friction coefficient is constant, while the static friction coefficient is variable. Then, what we are interested in is how the SSV behaves if the DBSKFC is a constant, while the two friction coefficients change synchronously. In this paper, a linearized lumped parameter model is presented to try to answer this question. By establishing the dynamic model of the drill bit and referring to a group of parameters normally used in drilling field, the drill bit dynamics with different friction coefficient combinations are obtained and the effects of friction coefficients on SSV are discussed.

Semi-analytical model of the axial movements of an oil-well drillstring in vertical wellbores

A lumped element model for the axial movement of an oil-well drillstring is presented. In this paper, the model is restricted to vertical holes, where damping is due to skin friction from time dependent Newtonian annular Couette-Poiseuille flow. The drillstring is constructed of pipes with different diameters and the diameter of the hole varies as a function of depth. Under these assumptions, the axial movement anywhere in the drillstring is basically a convolution between the axial movement on the top and a semi-analytical function that is derived in this paper. Expressions are given for transfer functions for downhole movements and pressures (surge and swab).In a vertical drilling situation, the motion is clearly underdamped, even when the hole is tight. The semi-analytical model illuminates various factors that are shown to be important for describing downhole pressure and motion. In particular the effect of added mass, the steady state viscous forces, the Basset viscous forces and the distribution of pipe sizes in the hole. The latter have non-neglectable impacts on where the resonant frequencies are located, how much they are amplified and what happens to the downhole pressure.Together with statistical power spectra of ocean wave patterns and the response amplitude operators for a floating structure, this model illustrates design concerns related to heave motion and how fast one can run the drillstring into the hole. Moreover, because of the computational simplicity of computing the convolution, the model is well suited for a real-time implementation.

Effects of weight on bit on torsional stick-slip vibration of oilwell drill string

The stick-slip phenomenon is a type of dysfunction detrimental to the drilling operation. Field application shows that stick-slip phenomenon is inclined to appear when using a large Weight on bit (WOB). In this paper, effects of the WOB on the stick-slip vibration are investigated. Based on a lumped torsional pendulum model of the drilling system, equation of motion of the drill bit is obtained. By using parameters commonly used in field applications, the bit dynamics are analyzed and the stick-slip vibrations are discussed. During the stick-slip motions, the negative damping effect occurs in the transition from the stick phase to the slip phase. With the increasing WOB, the bit behavior may change from the stable motion to the stick-slip vibration once the WOB reaches the critical value. In case of stick-slip vibration, the phase trajectory ultimately converges to a limit cycle which represents periodical bit motion. With increases in the WOB, the limit cycle enlarges. For cases without stick-slip vibrations, the drill bit vibrates damply and finally converges to a state of uniform motion. The results presented in this paper can be applied to interpret some of the field phenomena related to WOB.

Stabilization of torsional vibration in oilwell drillstring system

Stick-slip oscillations also known as torsional vibrations appearing in oilwell drilling systems are a source of economic losses, borehole disruption, pipes disconnection, and prolonged drilling time. The torsional dynamics is modeled by a damped wave equation. An important stability issue is to find a control law that reject perturbations due to torsional vibrations. Hence, the primary aim of this paper is to prove the well-posedness of the damped wave equation. In the next step, using the Riemann invariants, the damped wave equation is transformed into 2 × 2 first-order transport equations. The backstepping techniques combined with kernel equations and the Lyapunov theory are used to prove the local exponential stability of the transformed system, consequently the torsional dynamic. Simulation results are presented to illustrate the effectiveness of the control law.

Stability analysis of coupled torsional vibration and pressure in oilwell drillstring system

ABSTRACTTo address security issues in oilwell drillstring system, the drilling operation handling which is in generally not autonomous but ensured by an operator may be drill bit destructive or fatal for the machine. To control of stick-slip phenomenon, the drillstring control at the right speed taking only the drillstring vibration is not sufficient as the mud dynamics and the pressure change around the drill pipes cannot be neglected. A coupled torsional vibration and pressure model is presented, and the well-posedness problem is addressed. As a Partial Differential Equation-Ordinary Differential Equation (PDE-ODE) coupled system, and in order to maintain a non destructive downhole pressure, we investigate the control stability with and without the damping term in the wave PDE. In terms of, the torsional variable, the downhole pressure, and the annulus pressure, the coupled system equilibrium is shown to be exponentially stable.

Dynamic model for longitudinal and torsional motions of a horizontal oilwell drillstring with wellbore stick-slip friction

Horizontal oilwell drillstring failures are very costly. Vibration causes excessive wear and tear on the bottom hole assembly and reduces the life of the drill bit, and has motivated extensive research on these types of drillstring vibrations. Two key factors in simulation of motions of horizontal drillstrings are to have a model capturing coupling among various types of vibration, and an accurate but efficient treatment of the wellbore friction. In this paper, a bond graph dynamic model of a horizontal oilwell drillstring has been developed that predicts longitudinal motion, torsional motion, and coupling between longitudinal and torsional motion excited by bit-rock interaction. A lumped segment modeling approach of vertical drillstring dynamics has been extended to include dynamic wellbore friction in the ‘build’ and ‘horizontal’ sections of the drillstring. The model incorporates torsional viscous damping, longitudinal hydrodynamic damping, and buoyancy effect due to drilling fluid; an extended bit-rock interaction model that allows the drillstring to advance at the rate of penetration, a downhole mud motor, and top drive ac motor dynamics. The friction coefficient between drillstring and wellbore has been tuned with the aid of field data from a horizontal oilfield in Canada. The model predicts the expected coupling between weight on bit, bit speed, and bit-rock interaction conditions; and their effect on longitudinal and torsional motions. Finally, an experiment was conducted with a downhole axial vibration tool (“Agitator®”). A force excitation source, which simulates the Agitator® tool, in the longitudinal direction has been implemented in the horizontal section of the virtual drillstring. Simulations show a better weight transfer to the bit, with a low frequency and high amplitude force excitation giving best performance.

On the formation of limit cycle of the friction-induced stick-slip vibration in oilwell drillstring

Abstract In this paper, the stick-slip vibration in oilwell drillstring is studied. The drilling system is modelled as a lumped-parameter torsional pendulum and the interaction between the drill bit and the rock is treated as Coulomb friction. Equation of motion of the drill bit is established and the dynamic responses of the drill bit are obtained. A drilling system with the drillstring length 3000 m is analysed, in which the system parameters are selected by reference to the actual drilling situation. After the slip vibrations in the initial stage, final state of the drill bit is a stable stick-slip vibration of which the limit cycle is a closed loop. In order to find the stability of the limit cycle corresponds to the periodically stick-slip vibration, different initial conditions for the drill bit are studied. Results show that the drill bit will lead to a periodic motion and the phase trajectories ultimately converge to the same limit cycle corresponds to stable stick-slip vibration.

An intuitive and efficient approach to integrated modelling and control of three-dimensional vibration in long shafts

A nonlinear three-dimensional bond graph-based shaft model is presented, in which axial, torsional, and lateral vibrations can be predicted along with contact with external objects. Rigid lumped segments with six degrees of freedom are connected by axial, torsional, shear, and bending springs to approximate continuous system response. Parasitic springs and dampers enforce boundary conditions, contact forces are generated with stiff springs, and sliding friction forces during contact are incorporated using coordinate transformations and dynamic Coulomb friction. The model is easily reconfigurable for different boundary conditions, and the bond graph formalism facilitates the inclusion of (semi-)active control submodels such as electromechanical actuators or dampers. Simulations of a rotating 80-metre oilwell drillstring show realistic axial, torsional and lateral vibration. Active lateral vibration control is implemented, with a proportional controller acting on strain gauge output to attenuate vibration and reduce wellbore contact.

Elastodynamic and finite element vibration analysis of a drillstring with a downhole vibration generator tool and a shock sub

Applying high-frequency axial oscillation into an oilwell drillstring in the “bottom-hole assembly” (BHA) has the potential to enhance drilling efficiency in extended reach wells. Downhole vibration generator tools such as agitators reduce the drillstring–wellbore friction and enhance the rate of penetration. However, introducing controlled vibrations into the drillstring can result in undesired vibration waves propagating along the drillstring, leading to inefficient drilling and catastrophic fatigue failure of the BHA components, “measurement-while-drilling” tools, and mud motors. A dynamic model of the entire drillstring, including vibration generators and shock subs, is required to study the effect of vibration generators on the complex nonlinear coupled axial-lateral dynamics of a drillstring inside a wellbore, to study the effect of vibration tools on the developed cutting force at the bit, and to facilitate simulation-based design of shock subs. A dynamic finite element model (FEM) and an analytical elastodynamic model, both including the vibration generator tool and a shock sub, have been developed. The “Bypassing PDEs” method was implemented on the Lagrangian of the system to develop the analytical equations. A multi-mode expanded Galerkin’s approximation, in conjunction with a multi-span BHA and Hertzian contact assumption, allowed analysis of multiple BHA contact points and, thus, more realistic estimates of drilling rotary speeds that can cause excessive vibration. The models also include torque, mud damping, spatially varying axial force, geometric nonlinearity, and axial stiffening. While the analytical model has fast running time and symbolic solution, the FEM model enables easy reconfiguration and future extensions of model geometry, interactions, and modified BHA configurations. There is agreement between the analytical and FEM simulation results for the vibration suppression ability of the shock sub, dynamic amplification of the vibrating tool force, critical rotary speeds, axial force along the drillstring, axial and lateral displacements, and the contact locations and severity.

Vibration Analysis of a Drillstring in Vibration-Assisted Rotary Drilling: Finite Element Modeling With Analytical Validation

Introducing sources of axial vibration into an oilwell drillstring has the potential to improve the drilling efficiency. Vibration generator tools, such as drillstring agitators, are under development or in current use to excite the bottom-hole assembly (BHA) axially in order to increase power and weight at the bit, improve the rate of penetration (ROP), reduce drillstring-wellbore friction, and accelerate the cutting removal process. Enhanced drilling under the effect of intentional imposed vibration is called “vibration-assisted rotary drilling” or VARD. While potentially enhancing the drilling process, VARD tools can also excite many unwanted vibration modes of the drillstring. These unwanted vibrations can cause fatigue damage and failure of BHA components such as “measurement while drilling” (MWD) tools, bit and mud motors, and consequently, inefficient drilling. This motivates a study of the complex dynamic behavior of an axially excited drillstring. Transverse vibration is the most destructive type of drillstring vibration, and the coupling between transverse and axial vibration of a drillstring subjected to an applied VARD force is of great interest to the experts in the field. In this study, the coupled axial-transverse vibration behavior of the entire drillstring under the effect of a VARD tool is investigated. A dynamic finite element method (FEM) model of the vertical drillstring assuming a multispan BHA is generated and validated with a coupled nonlinear axial-transverse elastodynamic mathematical model. The effects of mud damping, driving torque, multispan contact and spatially varying axial load are included. Geometry, axial stiffening and Hertzian contact forces are sources of nonlinearity in the model. A mesh sensitivity analysis is conducted to reduce computational time. The accuracy of the retained modes in the analytical equations is verified by extracting the total effective mass derived by the FEM model. There is agreement between the FEM and analytical models for coupled-transverse and axial vibration velocities, displacements, resonance frequencies and contact locations and behavior. While the analytical model has fast running time and symbolic solution, the FEM model enables easy reconfiguration of the drillstring for different boundary conditions, inclusion of additional elements such as shock subs, and changing the number and locations of stabilizers.

A torque estimator-based control strategy for oil-well drill-string torsional vibrations active damping including an auto-tuning algorithm

Considerable compliance of the lengthy oil-well drill string combined with low tool inertia and stick–slip friction between the tool and the rock bed causes notable undesired torsional vibrations of the drill-string electrical drive. In order to attenuate the torsional vibrations and, thus, improve both the quality and the productivity of the drilling process, an automatically tuned active damping control strategy based on drill-string torque estimation is proposed in the paper. The core of the strategy includes a proportional-integral (PI) controller extended with estimator-based drill-string torque feedback loop. Furthermore, an appropriate algorithm that prevents drill-string back-spinning caused by the limited braking power of the power converter is presented. Finally, an auto-tuning algorithm is proposed, which is built around an adaptive Kalman filter-based estimator of drill-string drive natural frequencies. The drill-string control strategy is verified experimentally using a drill string hardware-in-the-loop setup under the laboratory conditions, as well as on an actual oil-drilling rig.

Stability analysis of helical rod based on exact Cosserat model

Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler's angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov's stability of the helical equilibrium is discussed in static category. Euler's critical values of axial force and torque are obtained. Lyapunov's and Euler's stability conditions in the space domain are the necessary conditions of Lyapunov's stability of the helical rod in the time domain.

An alternative characterization of bit-sticking phenomena in a multi-degree-of-freedom controlled drillstring

A piecewise-smooth model of three degrees of freedom, which exhibits friction-induced stick-slip oscillations, is considered. This model corresponds to a simplified torsional lumped-parameter model of an oilwell drillstring. An alternative method to characterize the stick-slip motion and other bit-sticking problems in such a drilling system is proposed. This method is based on the study of the relationships between the different types of system equilibria and the existing sliding motion when the bit velocity is zero. It is shown that such a sliding motion plays a key role in the presence of nondesired bit oscillations and transitions. Furthermore, a proportional-integral-type controller is designed in order to drive the rotary velocities to a desired value. The ranges of the controller and the system parameters which lead to a closed-loop system without bit-sticking phenomena are identified.

Avoiding harmful oscillations in a drillstring through dynamical analysis

Complexity of oilwell drillstrings makes unfeasible the direct application of control methodologies to suppress non-desired oscillations existing in these systems. A reasonable alternative is to develop operation recommendations and parameter selection methods to guide the driller to avoid such oscillations. In this paper, by using dynamical analysis tools, operation recommendations and the detection of safe drilling parameters in a conventional oilwell drillstring are presented. To this end, a more generic lumped-parameter model than those considered until now is proposed. Particularly, this model takes into account the fact that the drillstring length increases as drilling operation makes progress. The analysis of a sliding motion giving rise to self-excited bit stick–slip oscillations and bit sticking phenomena at the bottom-hole assembly is performed. Finally, the identification of key drilling parameters ranges for which non-desired torsional oscillations are present is carried out by studying Hopf bifurcations in the vicinity of the system equilibrium point when rotary velocities are greater than zero.

Stick-slip Whirl Interaction in Drillstring Dynamics

Abstract This paper attempts to explain the complicated behavior of oilwell drillstring motion when both torsional stick-slip and lateral whirl vibration are involved. It is demonstrated that the observed phenomena in experimental drillstring data could be due to the fluid forces of the drilling mud. A Stick-slip Whirl Model is presented which consists of a submodel for the whirling motion and a submodel for the stick-slip motion, both as simple as possible. The Stick-slip Whirl Model is a simplification of a drillstring confined in a borehole wall with drilling mud. The model is as simple as possible to expose only the basic phenomena but is discontinuous. Bifurcation diagrams of this discontinuous model for varying rotation speeds reveal discontinuous bifurcations. The disappearance of stick-slip vibration when whirl vibration appears is explained by bifurcation theory. The numerical results are compared with the experimental data from a full-scale drilling rig.