Stick-slip Oscillations Research Articles

Stochastic modeling for hysteretic bit–rock interaction of a drill string under torsional vibrations

This paper aims at constructing a stochastic model for the hysteretic behavior of the nonlinear bit–rock interaction of a drill string under torsional vibrations. The proposed model takes into account the fluctuations of the stick–slip oscillations observed during the drilling process. These fluctuations are modeled by introducing a stochastic process associated with the variations of the torque on bit, which is a function of the bit speed. The parameters of the stochastic model are calibrated with field data. The response of the proposed stochastic model, considering the random bit–rock interaction, is analyzed, and statistics related to the stability of the drill string are estimated.

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).

Axial and torsional self-excited vibrations of a distributed drill-string

We consider a distributed axial-torsional drill-string model with a rate-independent bit-rock interaction law to study the occurrence and non-local characteristics of axial and torsional self-excited vibrations as caused by the regenerative effect. A first contribution of the paper is the derivation of a non-dimensional version of the full non-linear distributed drill-string–bit-rock interaction model and showing how it relates to the minimal set of characteristic quantities. Using this model the study shows how multiple axial modes of the drill-string are excited, or attenuated, depending on the bit rotation rate. This indicates that a lumped drill-string model approximation is insufficient for the general case. Then, a comprehensive simulation study is performed to create a stability map for the occurrence of stick-slip oscillations. In particular, the significance of the axial topside boundary condition, i.e., constant velocity vs. constant hook-load, is evaluated. A central finding is that increasing the axial loop gain (determined by the bit-rock parameters) tends to both increase the area of stable torsional dynamics and increase the rate of penetration for a constant imposed weight on bit. This also corresponds to a more severe axial instability.

Verifying Safety and Persistence in Hybrid Systems Using Flowpipes and Continuous Invariants

We describe a method for verifying the temporal property of persistence in non-linear hybrid systems. Given some system and an initial set of states, the method establishes that system trajectories always eventually evolve into some specified target subset of the states of one of the discrete modes of the system, and always remain within this target region. The method also computes a time-bound within which the target region is always reached. The approach combines flowpipe computation with deductive reasoning about invariants and is more general than each technique alone. We illustrate the method with a case study showing that potentially destructive stick-slip oscillations of an oil-well drill eventually die away for a certain choice of drill control parameters. The case study demonstrates how just using flowpipes or just reasoning about invariants alone can be insufficient and shows the richness of systems that one can handle with the proposed method, since the systems features modes with non-polynomial ODEs. We also propose an alternative method for proving persistence that relies solely on flowpipe computation.

The effects of grooved rubber blocks on stick–slip and wear behaviours

This work presents an experimental and theoretical combined study of the effects of the elastic rubber blocks with different surface modifications on the friction-induced stick–slip oscillation and wear of a brake pad sample in sliding contact with an automobile brake disc. The experiments are conducted on the customized experimental setup in a pad-on-disc configuration. The experimental results show that (1) the friction system with the plain rubber block still exhibits visible stick–slip oscillation, but the intensity of the stick–slip oscillation is reduced to a certain degree compared with the Original friction system (without rubber block); (2) the grooved rubber blocks display a better ability to reduce the stick–slip oscillation compared with the plain rubber block; (3) the rubber blocks with a vertical groove (perpendicular to the relative velocity) or a horizontal groove (parallel to the relative velocity) or a diagonal groove (45° inclined to the relative velocity) on their surfaces can suppress the stick–slip oscillation more effectively with various degrees of success. The experimental results also reveal the varying effects of the different rubber blocks on wear. To explain the experimental phenomenon reasonably, a theoretical analysis is conducted to investigate the effects of different rubber blocks on both stick–slip oscillation and wear using ABAQUS. Furthermore, the analysis of the contact pressure on the pad interfaces and the deformation of the rubber blocks are studied to provide a possible explanation of the experimental results.

Avoiding stick slip vibrations in drilling through startup trajectory design

A distributed model of a drill string with a collars section is presented with Coulomb friction as a distributed source term. This model is capable of replicating stick slip oscillations as caused by the reduction in friction from static to dynamic. We design a feed-forward startup trajectory for initiating rotation of the drill string that effectively avoids the stick slip limit cycle. The trajectory design is performed using the differential flatness of the bit angular velocity, and by treating the reduction from static to dynamic friction as an estimated disturbance to be canceled, thus conforming to the canonical 3-DOF controller design for tracking and disturbance rejection. A simulation study illustrates the feasibility of the approach.

Nonlinear stochastic drillstrings vibrations: parametric study for stick-slip suppression

Unstable vibrations caused by the transition between static and kinetic frictions produces stick-slip motions which is one of the primary causes of poor drilling efficiency and mechanism failure in the drilling process. Coupled lateral and torsional drill string dynamics are explored numerically and experimentally within this article. A reduced order model able to capture the non-linear responses, observed during dry-friction whirling, is presented along with scaled experimental apparatus tests. To reduce stick-slip oscillations, the control strategies are mostly focused on the angular velocity of the upper part of the drill string, the torque on bit and the torque of friction. These parameters are investigated, and the simulation results are seen to be in good agreement with experimental observations.

Stochastic torsional stability of an oil drill-string

The aim of this paper is to investigate the influence of uncertainties on the torsional vibration of drill-strings, in order to find out which uncertainty affects most significantly the torsional stability. The unstable torsional behavior is commonly associated to polycrystalline diamond compact bits, and manifests itself in the form of stick-slip oscillations. The stick-slip is a severe type of self-excited vibration characterized by large fluctuations in the rotation of the bit. It not only increases the bit wear, but also can cause drill-string failures. The analysis were done using a mathematical model of the drill-string based on classical torsion theory discretized by means of the finite element method. The bit-rock torque was included in the model as a nonlinear boundary condition at the bottom end of the drill-string. The values of the model parameters are typical values of a real drilling situation, which are subject to a high degree of uncertainty, what justifies a stochastic analysis. We have built probability distributions for the uncertain parameters and used Monte Carlo method to obtain the stochastic stability maps.

Fractional-order stability analysis of earthquake dynamics

Fractional calculus is suitable for systems with memory and for fractal systems. Earthquakes have both properties. It is fair to claim that a fractional model is very efficient for earthquake modeling. Our study is focused on the effects of the fractional-order derivative on the 'train model' of Burridge–Knopoff. We note that these effects introduce additional degrees of freedom. Contrary to the integer model in which the fault remains seismologically active, the fractional derivative causes the transition from stick–slip oscillation to a stable equilibrium state. It is shown that the motion along the fault could be suppressed or reduced to an aseismic creeping when the fractional-order decreases. In the fractional model, we establish that the magnitude of the earthquake strongly depends on the fractional-order derivative. The stability of the stationary state is studied using fractional stability theory and the obtained results exhibit the powerful dependance of this stability on the fractional-order derivative. Chaos in the fractional-order system is controlled using a simple feedback controller. Furthermore, the finite-time stability of the fractional earthquake controller is investigated and sufficient conditions for the finite-time stability are presented. It appears that the estimated time of finite stability grows with the increment of the order of the fractional derivative. Moreover, the numerical simulations perfomed through the improved Adams–Bashforth–Moulton predictor–corrector scheme yield results that corroborate the theoretical predictions.

Active control of stick-slip torsional vibrations in drill-strings

This paper presents active vibration control to reduce the stick-slip oscillations in drill-strings. A simplified two degrees-of-freedom drill-string torsional model is considered. The nonlinear interaction between the rock and the bit is included in the model, where its parameters are fitted with field data from a 5 km drill-string system. Different proportional-derivative (PD)-control strategies are employed and compared, including the one that takes into account the weight-on-bit (axial force) and the bit speed. Optimization problems are proposed to obtain the values of the gain coefficients, and a torsional stability map is constructed for different weight-on-bit values and top-drive speeds. It is noted that the information of the dynamics at the bottom increases the performance of the PD-controller significantly in terms of the torsional vibration suppression, for the system analyzed.

Lubrication pressure and fractional viscous damping effects on the spring-block model of earthquakes

We examine the dynamical behaviours of the “single mass-spring” model for earthquakes considering lubrication pressure effects on pre-existing faults and viscous fractional damping. The lubrication pressure supports a part of the load, thereby reducing the normal stress and the associated friction across the gap. During the co-seismic phase, all of the strain accumulated during the inter-seismic duration does not recover; a fraction of this strain remains as a result of viscous relaxation. Viscous damping friction makes it possible to study rocks at depth possessing visco-elastic behaviours. At increasing depths, rock deformation gradually transitions from brittle to ductile. The fractional derivative is based on the properties of rocks, including information about previous deformation events (i.e., the so-called memory effect). Increasing the fractional derivative can extend or delay the transition from stick-slip oscillation to a stable equilibrium state and even suppress it. For the single block model, the interactions of the introduced lubrication pressure and viscous damping are found to give rise to oscillation death, which corresponds to aseismic fault behaviour. Our result shows that the earthquake occurrence increases with increases in both the damping coefficient and the lubrication pressure. We have also revealed that the accumulation of large stresses can be controlled via artificial lubrication.

Numerical solution for stick-slip oscillator with geometric non-linearity

Linear spring mass framework controlled by moving belt friction have been subjected to various examinations. Dynamical attributes like amplitude and frequency of oscillations have been in a big way studied along by the whole of the different approach mechanisms for this model. Along by all of the dynamical characteristics, bifurcation structures also have been investigated. On the other hand, the corresponding self-excited SD oscillator has not instructed comparable attention. This complimentary presents the numerical investigation of the character of a self-excited SD oscillator resting on a belt moving with consistent speed and excited by dry friction. The moving belt friction is displayed as the Stirbeck friction (friction first decreases and then increase smoothly with interface speed) to figure the scientific model. It is demonstrated that the pure-slip oscillation phase influenced by system parameter α. The influence of different system parameters on the dynamical characteristics was alongside considered.

Complex dynamics of drill-strings: Theory and experiments

We investigate complex drill-string dynamics in a downhole drilling where strong nonlinear interactions between various types of vibration take place. First, we present a low dimensional model of the downhole drilling where a drill-bit cutting a rock formation has a strong coupling between torsional and axial oscillations. The model can be used to study drilling stability as an example results are given. Then we introduce a new experimental rig developed by the Centre for Applied Dynamics Research at the University of Aberdeen, capable of reproducing all major types of drill-string vibration. One of the most important features of this versatile experimental rig is the fact that commercial drill-bits, employed in the drilling industry, and real rock-samples are used. The rig operate in different configurations, which enables the experimental study of various phenomena, such as stick-slip oscillations, whirling and drill-bit bounce. It also allows to determine mechanical characteristics of the drill-bits, which are used to calibrate mathematical models.

Stick-slip and Torsional Friction Factors in Inclined Wellbores

Stick slip is usually considered a phenomenon of bit-rock interaction, but is also often observed in the field with the bit off bottom. In this paper we present a distributed model of a drill string with an along-string Coulomb stiction to investigate the effect of borehole inclination and borehole friction on the incidence of stick-slip. This model is validated with high frequency surface and downhole data and then used to estimate static and dynamic friction. A derivation of the torsional drill string model is shown and includes the along-string Coulomb stiction of the borehole acting on the string and the ‘velocity weakening’ between static and dynamic friction. The relative effects of these two frictions is investigated and the resulting drillstring behavior is presented. To isolate the effect of the along-string friction from the bit-rock interaction, field data from rotational start-ups after a connection (with bit off bottom) is considered. This high frequency surface and downhole data is then used to validate the surface and downhole behavior predicted by the model. The model is shown to have a good match with the surface and downhole behavior of two deviated wellbores for depths ranging from 1500 to 3000 meters. In particular, the model replicates the amplitude and period of the oscillations, in both the topside torque and the downhole RPM, as caused by the along-string stick slip. It is further shown that by using the surface behavior of the drill-string during rotational startup, an estimate of the static and dynamic friction factors along the wellbore can be obtained, even during stick-slip oscillations, if axial tension in the drillstring is considered. This presents a possible method to estimate friction factors in the field when off-bottom stick slip is encountered, and points in the direction of avoiding stick slip through the design of an appropriate torsional start-up procedure without the need of an explicit friction test.

Proportional-Derivative Control of Stick-Slip Oscillations in Drill-Strings

Stick-slip oscillation in drill-string is a universal phenomenon in oil and gas drilling. It could lead to the wear of drill bit, even cause catastrophic failure of drill-strings and measurement equipment. Therefore, it is crucial to study drilling parameters and develop appropriate control method to suppress such oscillation. This paper studies a discrete model of the drill-string system taking into account torsional degree-of-freedom, drill-string damping, and highly nonlinear friction of rock-bit interaction. In order to suppress the stick-slip oscillation, a new proportional-derivative controller, which can maintain drill bit’s rotation at a constant speed, is developed. Numerical results are given to demonstrate its efficacy and robustness.

Benchmarking of Industrial Stick-Slip Mitigation Controllers

The present paper evaluates how three different top-drive feedback controllers influence the occurrence of a stick-slip limit cycle in a rotating drill string. The considered controllers are: 1) The industry standard stiff, high-gain controller, 2) SoftTorque, and, 3) ZTorque. The evaluation is performed as a simulation study on a distributed model of a drill string with a collar section and Coulomb friction as a distributed source term. This model is capable of replicating stick-slip oscillations as caused by the reduction in friction from static to dynamic, and have been shown to yield a good match with field data. The simulation study is summarized as a map for each controller indicating the existence and amplitude of oscillations, parametrized in the key friction parameters.

Cluster synchronization of dry friction oscillators

Synchronization is a well known phenomenon in non-linear dynamics and is treated as correlation in time of at least two different processes. In scope of this article, we focus on complete and cluster synchronization in the systems of coupled dry friction oscillators, coupled by linear springs. The building block of the system is the classic stick-slip oscillator, which consists of mass, spring and belt-mass friction interface. The Stribeck friction itself is modelled using Stribeck friction model with exponential non-linearity. The oscillators in the systems are connected in nearest neighbour fashion, both in open and closed ring topology. We perform a numerical study of the properties of the dynamics of the systems in question, in two-parameter space (coupling coefficient vs. angular excitation frequency) and explore the possible configurations of cluster synchronization.

Suppression of Drill-String Stick-Slip Vibration

We investigate experimentally and numerically suppression of drill-string torsional vibration while drilling by using a sliding mode control. The experiments are conducted on the novel experimental drilling rig developed at the University of Aberdeen [1] and using PDC commercial drill-bits and real rock-samples. A mathematical model of the experimental setup which takes into account the dynamics of the drill-string and the driving motor, is proposed. Then a sliding mode control method is employed to suppress stick-slip oscillations. The experimental and numerical results considering a time delay of the actuator are in a close agreement. Stick-slip vibration is eliminated and significant reduction in vibration amplitude has been observed when using the controller.

Trajectory tracking control for rotary steerable systems using interval type-2 fuzzy logic and reinforcement learning

Rotary steerable system (RSS) is a directional drilling technique which has been applied in oil and gas exploration under complex environment for the requirements of fossil energy and geological prospecting. The nonlinearities and uncertainties which are caused by dynamical device, mechanical structure, extreme downhole environment and requirements of complex trajectory design in the actual drilling work increase the difficulties of accurate trajectory tracking. This paper proposes a model-based dual-loop feedback cooperative control method based on interval type-2 fuzzy logic control (IT2FLC) and actor-critic reinforcement learning (RL) algorithms with one-order digital low-pass filters (LPF) for three-dimensional trajectory tracking of RSS. In the proposed RSS trajectory tracking control architecture, an IT2FLC is utilized to deal with system nonlinearities and uncertainties, and an online iterative actor-critic RL controller structured by radial basis function neural networks (RBFNN) and adaptive dynamic programming (ADP) is exploited to eliminate the stick–slip oscillations relying on its approximate properties both in action function (actor) and value function (critic). The two control effects are fused to constitute cooperative controller to realize accurate trajectory tracking of RSS. The effectiveness of our controller is validated by simulations on designed function tests for angle building hole rate and complete downhole trajectory tracking, and by comparisons with other control methods.

Adaptive and Real-Time Optimal Control of Stick–Slip and Bit Wear in Autonomous Rotary Steerable Drilling

Deviated, horizontal, and multilateral wells are drilled to increase the contact area between the well path and the reservoir and as a result, the well productivity will be increased. Directional steering systems (DSS) are used to control the direction in nonvertical wells. Rotary steerable system (RSS) is the current state of the art of DSS. In this research, the problem of real-time control of autonomous RSS with unknown formation rock strength was presented. The aim of this study is to develop a real-time control scheme for real-time optimization of drilling parameters to (1) maximize the rate of penetration (ROP), (2) minimize the deviation from the planned well bore trajectory, (3) reduce the stick–slip oscillations, and (4) assess the degree of bit wear. Nonlinear model for the drilling operation was developed using energy balance equation, where rock specific energy (RSE) is used to calculate the minimum power required for a given ROP. A proposed mass spring system was used to represent the phenomena of stick–slip oscillation. The model parameters have been adaptively estimated at each control iteration to tackle any disturbances or variations in the formation properties. The bit wear is mathematically represented using Bourgoyne model. Detailed mathematical formulation and computer simulation were used for evaluation of the performance of the proposed technique based on real well field data. The obtained results showed excellent ability to accommodate the changes in the formation properties. In addition, the rates of bit wear and stick–slip oscillations have been optimized.