scholarly journals Component-based Modeling and Simulation of Nonlinear Drill-string Dynamics

2021 ◽  
pp. 1-12
Author(s):  
Njaal Kjaernes Tengesdal ◽  
Christian Holden ◽  
Eilif Pedersen
Keyword(s):  
Case Studies ◽  
Equations Of Motion ◽  
Graph Model ◽  
String Model ◽  
Drill String ◽  
Qualitative Behavior ◽  
Longitudinal Motion ◽  
Rotary Drilling ◽  
Assumed Mode Method ◽  
Finite Set

Abstract In this paper, we present a dynamic model for a generic drill-string. The model is developed with the intention for component-based simulation with coupling to external subsystems. The performance of the drill-string is vital in terms of efficient wellbore excavation for increased hydrocarbon extraction. Drill-string vibrations limit the performance of rotary drilling; the phenomenon is well-known and still a subject of interest in academia and in industry. In this work, we have developed a nonlinear flexible drill-string model based on Lagrangian dynamics, to simulate the performance during vibrations. The model incorporates dynamics governed by lateral bending, longitudinal motion and torsional deformation. The elastic property of the string is modeled by the assumed mode method, representing the elastic deformation, with a finite set of modal coordinates. By developing a bond graph model from the equations of motion, we can ensure correct causality of the model towards interacting subsystems. The model is analyzed through extensive simulations in case studies, comparing the qualitative behavior of the model with state-of-the art models. The flexible drill-string model presented in this paper can aid in developing system simulation case studies and parameter identification for offshore drilling operations.

scholarly journals Component-Based Modeling and Simulation of Nonlinear Drill-String Dynamics

2019 ◽  
Author(s):  
Njål Tengesdal ◽  
Christian Holden ◽  
Eilif Pedersen
Keyword(s):  
Case Studies ◽  
Equations Of Motion ◽  
Graph Model ◽  
String Model ◽  
Drill String ◽  
Qualitative Behavior ◽  
Longitudinal Motion ◽  
Rotary Drilling ◽  
String Vibrations ◽  
Finite Set

Abstract In this paper, we present a dynamic model for a generic drill-string. The model is developed with the intention for component-based simulation with coupling to external subsystems. The performance of the drill-string is vital in terms of efficient wellbore excavation for increased hydrocarbon extraction. Drill-string vibrations limit the performance of rotary drilling; the phenomenon is well-known and still a subject of interest in academia and in industry. In this work, we have developed a nonlinear flexible drill-string model based on Lagrangian dynamics, to simulate the performance during vibrations. The model incorporates dynamics governed by lateral bending, longitudinal motion and torsional deformation. The elastic property of the string is modeled with mode shape functions representing the elastic deformation, with a finite set of modal coordinates. By developing a bond graph model from the equations of motion, we can ensure correct causality of the model towards interacting subsystems. The model is analyzed through extensive simulations in case studies, comparing the qualitative behavior of the model with state-of-the art models. The flexible drill-string model presented in this paper will aid in developing simulation case studies and parameter identification for offshore drilling operations.

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.

Nonlinear Dynamic Study on Effects of Rub-Impact Caused by Oil-Rupture in a Multi-Shafts Turbine With a Squeeze Film Damper

2014 ◽  
Author(s):  
T. N. Shiau ◽  
C. R. Wang ◽  
D. S. Liu ◽  
W. C. Hsu ◽  
T. H. Young
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Rotor System ◽  
Squeeze Film ◽  
Speed Ratio ◽  
Frequency Spectra ◽  
Squeeze Film Damper ◽  
Assumed Mode Method ◽  
Nonlinear Dynamic Behavior

An investigation is carried out the analysis of nonlinear dynamic behavior on effects of rub-impact caused by oil-rupture in a multi-shafts turbine system with a squeeze film damper. Main components of a multi-shafts turbine system includes an outer shaft, an inner shaft, an impeller shaft, ball bearings and a squeeze film damper. In the squeeze film damper, oil forces can be derived from the short bearing approximation and cavitated film assumption. The system equations of motion are formulated by the global assumed mode method (GAMM) and Lagrange’s approach. The nonlinear behavior of a multi-shafts turbine system which includes the trajectories in time domain, frequency spectra, Poincaré maps, and bifurcation diagrams are investigated. Numerical results show that large vibration amplitude is observed in steady state at rotating speed ratio adjacent to the first natural frequency when there is no squeeze film damper. The nonlinear dynamic behavior of a multi-shafts turbine system goes in its way into aperiodic motion due to oil-rupture and it is unlike the usual way (1T = >2T = >4T = >8T etc) as compared to one shaft rotor system. The typical routes of bifurcation to aperiodic motion are observed in a multi-shafts turbine rotor system and they suddenly turn into aperiodic motion from the periodic motion without any transition. Consequently, the increasing of geometric or oil parameters such as clearance or lubricant viscosity will improve the performance of SFD bearing.

Case Studies for the Successful Deployment of Wells Augmented Stuck Pipe Indicator in Wells Real Time Centre

2021 ◽  
Author(s):  
Meor M. Meor Hashim ◽  
M. Hazwan Yusoff ◽  
M. Faris Arriffin ◽  
Azlan Mohamad ◽  
Tengku Ezharuddin Tengku Bidin ◽  
...  
Keyword(s):  
Real Time ◽  
Case Studies ◽  
Drilling Fluid ◽  
Drill String ◽  
Drilling Operation ◽  
Cost Impact ◽  
Drilling Parameters ◽  
The Impact ◽  
Productive Time ◽  
Specific Challenge

Abstract The restriction or inability of the drill string to reciprocate or rotate while in the borehole is commonly known as a stuck pipe. This event is typically accompanied by constraints in drilling fluid flow, except for differential sticking. The stuck pipe can manifest based on three different mechanisms, i.e. pack-off, differential sticking, and wellbore geometry. Despite its infrequent occurrence, non-productive time (NPT) events have a massive cost impact. Nevertheless, stuck pipe incidents can be evaded with proper identification of its unique symptoms which allows an early intervention and remediation action. Over the decades, multiple analytical studies have been attempted to predict stuck pipe occurrences. The latest venture into this drilling operational challenge now utilizes Machine Learning (ML) algorithms in forecasting stuck pipe risk. An ML solution namely, Wells Augmented Stuck Pipe Indicator (WASP), is developed to tackle this specific challenge. The solution leverages on real-time drilling database and supplementary engineering design information to estimate proxy drilling parameters which provide active and impartial pattern recognition of prospective stuck pipe events. The solution is built to assist Wells Real Time Centre (WRTC) personnel in proactively providing a holistic perspective in anticipating potential anomalies and recommending remedial countermeasures before incidents happen. Several case studies are outlined to exhibit the impact of WASP in real-time drilling operation monitoring and intervention where WASP is capable to identify stuck pipe symptoms a few hours earlier and provide warnings for stuck pipe avoidance. The presented case studies were run on various live wells where restrictions are predicted stands ahead of the incidents. Warnings and alarms were generated, allowing further analysis by the personnel to verify and assess the situation before delivering a precautionary procedure to the rig site. The implementation of the WASP will reduce analysis time and provide timely prescriptive action in the proactive real-time drilling operation monitoring and intervention hub, subsequently creating value through cost containment and operational efficiency.

Squeal Analysis of a Disc Brake Considering Damping between a Disc and a Pad Lining

2012 ◽  
Vol 157-158 ◽  
pp. 1000-1003
Author(s):  
Ke Wei Zhou ◽  
Cheol Kim ◽  
Min Ok Yun ◽  
Ju Young Kim
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Element Model ◽  
Disc Brake ◽  
Vibration Modes ◽  
Assumed Mode Method ◽  
Frictional Damping ◽  
System Components ◽  
Mode Method ◽  
Assumed Mode

The improved equations of motion for a friction-engaged brake system have been newly derived on the basis of the assumed mode method and frictional damping. The equations of motion with a finite element model were constructed by a set of vibration modes found from FE modal analysis on all system components. Consequently, the modal information of system components are combined with equations of motion derived from the analytical model. Numerical analysis showed the mode which was unstable in an undamped case became stable in a damped case.

Nonlinear Dynamic Modeling of Elastic Beam Fixed on a Moving Cart and Carrying Lumped Tip Mass Subjected to External Periodic Force

2009 ◽  
Author(s):  
Fadi A. Ghaith
Keyword(s):  
Linear Model ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Open Loop ◽  
Beam Deflection ◽  
Mode Shapes ◽  
Euler Beam ◽  
Periodic Force ◽  
Assumed Mode Method ◽  
Tip Mass

In the present work, a Bernoulli – Euler beam fixed on a moving cart and carrying lumped tip mass subjected to external periodic force is considered. Such a model could describe the motion of structures like forklift vehicles or ladder cars that carry heavy loads and military airplane wings with storage loads on their span. The nonlinear equations of motion which describe the global motion as well as the vibration motion were derived using Lagrangian approach under the inextensibility condition. In order to investigate the influence of the axial movement of the cart on the response of the system, unconstrained modal analysis has been carried out, and accurate mode shapes of the beam deflection were obtained. The assumed mode method was utilized for approximating the beam elastic deformation based on the single unconstrained mode shapes. Numerical simulation has been carried out to estimate the open-loop response of the nonlinear beam-mass-cart model as well as for the simplified linear model under the influence of the periodic excitation force. Also a comparison study between the responses of the linear and nonlinear models was established. It was shown that the maximum values of the beam tip deflection estimated from the nonlinear model are lower than the corresponding values obtained via the linear model, which reveals the importance of considering nonlinear hardening term in formulating the equations of motion for such system in order to come with more accurate and reliable model.

scholarly journals Stick-slip and Torsional Friction Factors in Inclined Wellbores

2018 ◽  
Vol 148 ◽  
pp. 16002 ◽  
Author(s):  
Ulf Jakob F. Aarsnes ◽  
Roman J. Shor
Keyword(s):  
High Frequency ◽  
String Model ◽  
Drill String ◽  
Distributed Model ◽  
Dynamic Friction ◽  
Stick Slip ◽  
Rock Interaction ◽  
Interaction Field ◽  
Friction Factors ◽  
Start Ups

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.

Vibration Control of the Rotating Flexible-Shaft/Multi-Flexible-Disk System With the Eddy-Current Damper

2002 ◽  
Vol 124 (4) ◽  
pp. 519-526 ◽  
Author(s):  
Rong-Fong Fung ◽  
Jung-Hung Sun ◽  
Shih-Ming Hsu
Keyword(s):  
Eddy Current ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Bilinear System ◽  
Optimal Feedback Control ◽  
Disk System ◽  
Control Laws ◽  
Assumed Mode Method ◽  
Eddy Current Damper ◽  
Flexible Disk

In this paper, the rotating flexible-Timoshenko-shaft/flexible-disk coupling system is formulated by applying the assumed-mode method into the kinetic and strain energies, and the virtual work done by the eddy-current damper. From Lagrange’s equations, the resulting discretized equations of motion can be simplified as a bilinear system (BLS). Introducing the control laws, including the quadratic, nonlinear and optimal feedback control laws, into the BLS, it is found that the eddy-current damper can be used to suppress flexible and shear vibrations simultaneously, and the system is globally asymptotically stable. Numerical results are provided to validate the theoretical analysis.

Vibratory Power Losses and Delivery to Rock During Rotary-Vibratory Drilling: Part I: Theory

1980 ◽  
Vol 102 (1) ◽  
pp. 102-109
Author(s):  
D. C. Ohanehi ◽  
L. D. Mitchell
Keyword(s):  
Dynamic Response ◽  
Theoretical Basis ◽  
Drilling Fluid ◽  
Blast Hole ◽  
Drill String ◽  
Power Delivery ◽  
Drilling Process ◽  
Power Losses ◽  
Rotary Drilling ◽  
Drilling Unit

This paper explores a possible theoretical basis for the failure of attempts to develop rotary-vibratory drilling units. With the critical needs in geothermal blast hole excavation and oil exploration, this nation cannot overlook the possibility of accelerating the drilling process by factors of 2 to 20 over the conventional rotary drilling rates. This paper develops the theory for the dynamic response of a vibrating drill string in a viscous drilling fluid with the energy lost to shear work. It develops the relations for power delivery to the rock as well as the total vibratory power to drive the system. Thus vibratory power losses can be computed by a difference. Part II of this paper applied this theory to a typical effort at developing a rotary-vibratory drilling unit. In the case studied, the power delivery was ineffective and at certain frequencies large losses resulted.

The steady flow due to a rotating sphere at low and moderate Reynolds numbers

1980 ◽  
Vol 101 (2) ◽  
pp. 257-279 ◽  
Author(s):  
S. C. R. Dennis ◽  
S. N. Singh ◽  
D. B. Ingham
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Finite Set ◽  
Flow Variables ◽  
Theoretical Results ◽  
Radial Variable ◽  
Good Agreement

The problem of determining the steady axially symmetrical motion induced by a sphere rotating with constant angular velocity about a diameter in an incompressible viscous fluid which is at rest at large distances from it is considered. The basic independent variables are the polar co-ordinates (r, θ) in a plane through the axis of rotation and with origin at the centre of the sphere. The equations of motion are reduced to three sets of nonlinear second-order ordinary differential equations in the radial variable by expanding the flow variables as series of orthogonal Gegenbauer functions with argument μ = cosθ. Numerical solutions of the finite set of equations obtained by truncating the series after a given number of terms are obtained. The calculations are carried out for Reynolds numbers in the range R = 1 to R = 100, and the results are compared with various other theoretical results and with experimental observations.The torque exerted by the fluid on the sphere is found to be in good agreement with theory at low Reynolds numbers and appears to tend towards the results of steady boundary-layer theory for increasing Reynolds number. There is excellent agreement with experimental results over the range considered. A region of inflow to the sphere near the poles is balanced by a region of outflow near the equator and as the Reynolds number increases the inflow region increases and the region of outflow becomes narrower. The radial velocity increases with Reynolds number at the equator, indicating the formation of a radial jet over the narrowing region of outflow. There is no evidence of any separation of the flow from the surface of the sphere near the equator over the range of Reynolds numbers considered.

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