scholarly journals Nonlinear Model and Qualitative Analysis for Coupled Axial/Torsional Vibrations of Drill String

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Fushen Ren ◽  
Baojin Wang ◽  
Suli Chen ◽  
Zhigang Yao ◽  
Baojun Bai
Keyword(s):  
Nonlinear Dynamics ◽  
Qualitative Analysis ◽  
Axial Stress ◽  
Drill String ◽  
Torsional Vibrations ◽  
Flexible Shell ◽  
Coupling Vibration ◽  
Axial Excitation ◽  
Key Factor ◽  
Analysis Of Dynamics

A nonlinear dynamics model and qualitative analysis are presented to study the key effective factors for coupled axial/torsional vibrations of a drill string, which is described as a simplified, equivalent, flexible shell under axial rotation. Here, after dimensionless processing, the mathematical models are obtained accounting for the coupling of axial and torsional vibrations using the nonlinear dynamics qualitative method, in which excitation loads and boundary conditions of the drill string are simplified to a rotating, flexible shell. The analysis of dynamics responses is performed by means of the Runge-Kutta-Fehlberg method, in which the rules that govern the changing of the torsional and axial excitation are revealed, and suggestions for engineering applications are also given. The simulation analysis shows that when the drill string is in a lower-speed rotation zone, the torsional excitation is the key factor in the coupling vibration, and increasing the torsional stress of the drill string more easily leads to the coupling vibration; however, when the drill string is in a higher-speed rotating zone, the axial excitation is a key factor in the coupling vibration, and the axial stress in a particular interval more easily leads to the coupling vibration of the drill string.

Nonlinear Modeling and Qualitative Analysis of Coupled Vibrations in a Drill String

2018 ◽  
Vol 28 (10) ◽  
pp. 1850119
Author(s):  
Fushen Ren ◽  
Baojin Wang ◽  
Suli Chen
Keyword(s):  
Qualitative Analysis ◽  
Nonlinear Modeling ◽  
Coupled Model ◽  
Axial Rotation ◽  
Drill String ◽  
Coupled Vibration ◽  
Lateral Vibrations ◽  
Axial Excitation ◽  
Torsional Excitation ◽  
Runge Kutta

A coupled model for axial/torsional/lateral vibrations of the drill string is presented, in which the nonlinear dynamics and qualitative analysis method are employed to find out the key factors and sensitive zone for coupled vibration. The drill string is simplified as an equivalent shell under axial rotation. After dimensionless processing, the mathematical model for coupled axial/torsional/lateral vibrations of the drill string is obtained. The Runge–Kutta–Fehlberg method is employed for the numerical simulation, and the rules that govern the changing of the torsional and axial excitation are revealed. And the stability domains of the explicit Runge–Kutta method are analyzed. Furthermore, the suggestions for field applications are also presented. It is demonstrated by simulation results that the lateral/axial/torsional vibrations exist simultaneously and couple with each other. The system will obtain a stable period motion with an axial excitation zone before the coupled vibration in the three directions, and continue to increase the axial excitation to cause the coupled vibration easily. The torsional excitation of the drill string mainly contributes to the coupled vibration in the three directions when in a specific rotation speed zone. The system is more likely to obtain a periodic motion through adjusting the torsional excitation out of this zone.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

A Semi-Analytical Study of Stick-Slip Oscillations in Drilling Systems

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
B. Besselink ◽  
N. van de Wouw ◽  
H. Nijmeijer
Keyword(s):  
Dynamic Analysis ◽  
Limit Cycle ◽  
Analytical Approach ◽  
String Model ◽  
Drill String ◽  
Axial Stiffness ◽  
Torsional Vibrations ◽  
Stick Slip ◽  
Rock Interaction ◽  
Stiffness And Damping

Rotary drilling systems are known to exhibit torsional stick-slip vibrations, which decrease drilling efficiency and accelerate the wear of drag bits. The mechanisms leading to these torsional vibrations are analyzed using a model that includes both axial and torsional drill string dynamics, which are coupled via a rate-independent bit-rock interaction law. Earlier work following this approach featured a model that lacked two essential aspects, namely, the axial flexibility of the drill string and dissipation due to friction along the bottom hole assembly. In the current paper, axial stiffness and damping are included, and a more realistic model is obtained. In the dynamic analysis of the drill string model, the separation in time scales between the fast axial dynamics and slow torsional dynamics is exploited. Therefore, the fast axial dynamics, which exhibits a stick-slip limit cycle, is analyzed individually. In the dynamic analysis of a drill string model without axial stiffness and damping, an analytical approach can be taken to obtain an approximation of this limit cycle. Due to the additional complexity of the model caused by the inclusion of axial stiffness and damping, this approach cannot be pursued in this work. Therefore, a semi-analytical approach is developed to calculate the exact axial limit cycle. In this approach, parametrized parts of the axial limit cycle are computed analytically. In order to connect these parts, numerical optimization is used to find the unknown parameters. This semi-analytical approach allows for a fast and accurate computation of the axial limit cycles, leading to insight in the phenomena leading to torsional vibrations. The effect of the (fast) axial limit cycle on the (relatively slow) torsional dynamics is driven by the bit-rock interaction and can thus be obtained by averaging the cutting and wearflat forces acting on the drill bit over one axial limit cycle. Using these results, it is shown that the cutting forces generate an apparent velocity-weakening effect in the torsional dynamics, whereas the wearflat forces yield a velocity-strengthening effect. For a realistic bit geometry, the velocity-weakening effect is dominant, leading to the onset of torsional vibrations.

Torsional Vibrations and Nonlinear Dynamic Characteristics of Drill Strings and Stick-Slip Reduction Mechanism

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Jialin Tian ◽  
Genyin Li ◽  
Liming Dai ◽  
Lin Yang ◽  
Hongzhi He ◽  
...  
Keyword(s):  
Torsional Vibration ◽  
Nonlinear Dynamic ◽  
Drill String ◽  
Drilling Process ◽  
Drill Bit ◽  
Torsional Vibrations ◽  
Reduction Mechanism ◽  
Nonlinear Dynamic Model ◽  
Stick Slip ◽  
Research Results

Torsional stick–slip vibrations easily occur when the drill bit encounters a hard or a hard-soft staggered formation during drilling process. Moreover, serious stick–slip vibrations of the drill string is the main factor leading to low drilling efficiency or even causing the downhole tools failure. Therefore, establishing the stick–slip theoretical model, which is more consistent with the actual field conditions, is the key point for new drilling technology. Based on this, a new torsional vibration tool is proposed in this paper, then the multidegree-of-freedom torsional vibrations model and nonlinear dynamic model of the drill string are established. Combined with the actual working conditions in the drilling process, the stick–slip reduction mechanism of the drill string is studied. The research results show that the higher rotational speed of the top drive, smaller viscous damping of the drill bit, and smaller WOB (weight on bit) will prevent the stick–slip vibration to happen. Moreover, the new torsional vibration tool has excellent stick–slip reduction effect. The research results and the model established in this paper can provide important references for reducing the stick–slip vibrations of the drill string and improving the rock-breaking efficiency.

Algebraic Criteria for Qualitative Analysis of Nonlinear Dynamics in Biochemistry

2008 ◽  
Author(s):  
Kiriakos Kiriakidis ◽  
George Nakos
Keyword(s):  
Nonlinear Dynamics ◽  
Asymptotic Stability ◽  
Convex Hull ◽  
Qualitative Analysis ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Biochemical Reaction ◽  
Aggregate Modeling ◽  
Linear Differential Inclusions ◽  
Linear Differential

Aggregate modeling can approximate the convex hull of local matrices to nonlinear dynamics for any given accuracy. The authors use aggregate models to extend sufficient conditions for asymptotic stability of linear differential inclusions to nonlinear dynamics. An example illustrates the applicability of the proposed criteria to the analysis of nonlinear biochemical reaction chains.

scholarly journals Modelling of drill string nonlinear dynamics with a drilling fluid flow

2018 ◽  
Vol 97 (1) ◽  
pp. 91-100
Author(s):  
Askar K. Kudaibergenov ◽  
◽  
L. A. Khajiyeva ◽  
Keyword(s):  
Nonlinear Dynamics ◽  
Fluid Flow ◽  
Drilling Fluid ◽  
Drill String

Measurement and Evaluation of Shaft Torsional Vibrations Using Shaft Instantaneous Angular Velocity

2018 ◽  
Author(s):  
Jindrich Liska ◽  
Jan Jakl ◽  
Sven Kunkel
Keyword(s):  
Angular Velocity ◽  
Electrical Power ◽  
Sampling Rate ◽  
Direct Consequence ◽  
Optical Probe ◽  
Torsional Vibrations ◽  
Black And White ◽  
Direct Compensation ◽  
Key Factor ◽  
Measurement And Evaluation

Online evaluation of possible failures of a turbine is a key factor for a successful long-term turbine operation. Fluctuations of generator air-gap torque, caused for example by non-stationary conditions of electrical power grid, influence shaft torsional vibrations as well as rotating blades vibrations. Symptoms of shaft torsional vibrations are not measurable by normally used relative shaft vibrations sensors, so special measurement must be used. The direct consequence of shaft torsional vibrations is local acceleration or deceleration of shaft circumference when it is measured by a stationary sensor. This article deals with a measurement method using an optical probe measuring the passage of black and white stripes of a zebra tape which is stuck on the rotor. The shaft torsional vibrations manifest themselves as a phase modulation of the optical probe output signal, so the sampling rate influence the achievable resolution of the calculated shaft vibrations. The presented method for the calculation of the shaft torsional vibrations is based on the evaluation of shaft instantaneous angular velocity. The advantage of this method is a direct compensation of possible non-regular geometry of the zebra tape. The analysis of shaft torsional vibrations evaluation using this method is supplemented by two case studies from the authors’ current work.

scholarly journals Drillstring Failure: Analytical and Experimental Approach

2019 ◽  
Vol 300 ◽  
pp. 04004
Author(s):  
Edris Hassan ◽  
Jamil Abdo ◽  
Jan Kwak ◽  
Abdullah Al Shabibi
Keyword(s):  
Torsional Vibration ◽  
Oil And Gas ◽  
Drill Pipe ◽  
Oil And Gas Industry ◽  
Drill String ◽  
Design Parameters ◽  
Experimental Investigations ◽  
Torsional Vibrations ◽  
Stick Slip ◽  
The Impact

Drilling is one of the costliest activities in oil and gas industry due to the complexity of interactions with downhole rock formation. Under such conditions, the uncertainty of drillstring behaviour increase and hence it becomes difficult to predict the causes, occurrences, and types of failures. Lateral and torsional vibrations often cause failure of Bottom Hole Assembly (BHA), drillstring failure, drill bit and wall borehole damages. In this work, a model is presented to determine the impact of lateral and torsional vibrations on a drillstring during the drilling operation. The model aims to mimic real drillstring behaviour inside a wellbore with regards to its dynamic movements due to multiple real situations such as eccentricity of collars, drill pipe sections, and stick-slip phenomena occurring due to the interaction of the bit and the drillstring with the well formation. The work aims to develop a basis for determining critical operating speeds and design parameters to provide safe drilling procedures and reduce drill string fatigue failure. Lagrangian approach is used in this study to attain drillstring lateral and torsional vibration coupling equations. The nonlinear equations are solved numerically to obtain the response of the system. In this work, we also present a brief description of an in-house constructed experimental setup. The setup has the capability to imitate the downhole lateral and torsional vibration modes. Parameters from the experimental investigations are incorporated for validation of the mathematical models and for prediction of the drillstring fatigue life. Such investigations are essential for oil and gas industries as they provide solutions and recommendations about operational speed, lateral and torsional amplitudes measurements and corrections, and the conditions for avoiding occurrence of natural frequencies of the system.

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