Modification of the Infinite-Dimensional Neutral-Type Time-Delay Dynamic Model for the Coupled Axial–Torsional Vibrations in Drill Strings With a Drag Bit

2020 ◽  
Vol 15 (8) ◽  
Author(s):  
Shabnam Tashakori ◽  
Gholamreza Vossoughi ◽  
Hassan Zohoor ◽  
Ehsan Azadi Yazdi
Keyword(s):  
Time Delay ◽  
Dynamic Model ◽  
System Analysis ◽  
Dynamic Models ◽  
Neutral Type ◽  
Oscillatory Behavior ◽  
Drill String ◽  
Torsional Vibrations ◽  
Delay Model ◽  
Rock Interaction

Abstract Drill strings are subjected to complex coupled dynamics. Therefore, accurate dynamic modeling, which can represent the physical behavior of real drill strings, is of great importance for system analysis and control. The most widely used dynamic models for such systems are the lumped element models, which neglect the system distributed feature. In this paper, a dynamic model called neutral-type time delay model is modified to investigate the coupled axial–torsional vibrations in drill strings. This model is derived directly from the distributed parameter model by employing the d'Alembert method. Coupling of axial and torsional vibration modes occurs in the bit–rock interface. For the first time, the neutral-type time delay model is combined with a bit–rock interaction model that regards cutting process in addition to frictional contact. Moreover, mistakes made in some of the related previous studies are corrected. The resulting equations of motion are in terms of neutral-type delay differential equations with two constant delays, related to the oscillatory behavior of the system, and a state-dependent delay, induced by the bit–rock interaction. Illustrative simulation results are presented for a representative drill string, which demonstrates intense axial and torsional vibrations that may lead to system failure without a controller.

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.

Drilling Control System Using an Equivalent Input Disturbance-Based Control With a Neutral-Type Axial-Torsional Coupled Dynamics Model

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Chong Ke ◽  
Xingyong Song
Keyword(s):  
Coupling Effect ◽  
Neutral Type ◽  
Drill String ◽  
Hole Drilling ◽  
Type Model ◽  
Drilling Process ◽  
Rock Interaction ◽  
Input Disturbance ◽  
Torsional Coupling ◽  
Equivalent Input Disturbance

Abstract This paper proposed an equivalent input disturbance (EID)-based approach to control the vertical down-hole drilling process. To describe a drill string which is typically long with large axial-to-radius ratio, a neutral-type model is used to accurately capture dynamics of this type of slender string structure. The axial-torsional coupling effect due to drill bit/rock interaction is also included in the model. A new controller is then designed based on the coupled neutral model, and the coupling effect is specifically addressed in the design. To address the uncertainty of the bit/rock interaction, the EID method is used. A new Lyapunov–Krasovskii functional is proposed for the control design. To this end, a series of numerical simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

scholarly journals Parameter Estimation for Dynamic Model of the Financial System

2015 ◽  
Vol 63 (6) ◽  
pp. 2051-2055
Author(s):  
Veronika Novotná ◽  
Vladěna Štěpánková
Keyword(s):  
Time Delay ◽  
Dynamic Model ◽  
Dynamic Models ◽  
Financial System ◽  
Point Of View ◽  
Investment Demand ◽  
History Of ◽  
New Perspective ◽  
The Interest Rate

Economy can be considered a large, open system which is influenced by fluctuations, both internal and external. Based on non-linear dynamics theory, the dynamic models of a financial system try to provide a new perspective by explaining the complicated behaviour of the system not as a result of external influences or random behaviour, but as a result of the behaviour and trends of the system’s internal structures. The present article analyses a chaotic financial system from the point of view of determining the time delay of the model variables – the interest rate, investment demand, and price index. The theory is briefly explained in the first chapters of the paper and serves as a basis for formulating the relations. This article aims to determine the appropriate length of time delay variables in a dynamic model of the financial system in order to express the real economic situation and respect the effect of the history of factors under consideration. The determination of the delay length is carried out for the time series representing Euro area. The methodology for the determination of the time delay is illustrated by a concrete example.

scholarly journals Dynamic Model of Land Use Change in Landslide Hazard Zones in Tanah Datar District, West Sumatra

2019 ◽  
Vol 3 (1) ◽  
pp. 67-74
Author(s):  
Indang Dewata
Keyword(s):  
Land Use ◽  
Land Use Change ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
System Analysis ◽  
Dynamic Models ◽  
Forest Area ◽  
Land Resource ◽  
Change Policy ◽  
Policy Direction

Population growth has an impact on land resource needs, pressure on land use will have an impact on environmental degradation. As an effort to reduce pressure, policy efforts in land use are needed. This study aims to develop dynamic models in land use and develop land use policy direction.The method used in dynamic modeling uses system analysis and land change policy direction using ISM analysis. In dynamic modeling, land use change uses three scenarios, namely: optimistic scenario, muder scenario, and pessimistic scenario. In determining the direction of the policy involving all stakeholders as many as 15 experts. The results of dynamic model analysis show that forest area changes from time to time of 1.6 percent per year. Changes in forest areas will have an impact on increasing environmental disasters. As an effort to save the environment, there is a need for law enforcement and strict sanctions against perpetrators of forest area destruction

Statistical Determination of Bit-Rock Interaction and Drill String Mechanics for Automatic Drilling Optimization

2020 ◽  
Author(s):  
Adrian Ambrus ◽  
Benoît Daireaux ◽  
Liv A. Carlsen ◽  
Rodica G. Mihai ◽  
Mohsen Karimi Balov ◽  
...  
Keyword(s):  
Transfer Function ◽  
Dynamic Models ◽  
Drill String ◽  
Model Parameters ◽  
Drilling Process ◽  
Transfer Function Model ◽  
Transient Effects ◽  
Model Approximation ◽  
Function Model ◽  
Rock Interaction

Abstract The ability to predict the response of a drill bit to the topside axial and rotational velocities of the drill-string is a prerequisite for any system aimed at automatically controlling the drilling parameters to optimize the rate of penetration and the overall quality of the well construction process. When drilling with a Polycrystalline Diamond Compact (PDC) bit, even the steady-state response can exhibit complex behavior, characterized by the presence of (at least) three different regimes whose range and parameters depend upon the bit characteristics and the mechanical properties of the formations being drilled. Transient effects significantly complicate the situation, especially when vibrations (axial, rotational or lateral) disturb the drilling process. Often, the root cause of these vibrations lies in the bit-rock interaction itself, while the drill string, through its elasticity and interaction with the borehole wall, may amplify or attenuate these vibrations. Therefore, continuous calibration of the drill string and bit-rock parameters from available surface and downhole measurements is critical for any automated control system relying on dynamic models of the drilling process. We present a calibration procedure whose goal is two-fold: first, to identify the time-varying parameters involved in the bit-rock interaction, and second, to provide a low-order, transfer function model approximation of the drill string axial and rotational dynamics. Our approach is based on particle filter techniques and a refined instrumental variable method for transfer function model estimation, and allows for real-time estimation of the various model parameters. We illustrate its behavior against recorded drilling data, where the proposed methods are shown to capture the different dynamics in place. We explain, in addition, how the calibrated drill string and bit-rock interaction models can be integrated in a framework to identify drilling parameter regions prone to axial or rotational vibrations.

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

2019 ◽  
Vol 25 (10) ◽  
pp. 1663-1672 ◽  
Author(s):  
Fabio F. Real ◽  
Anas Batou ◽  
Thiago G. Ritto ◽  
Christophe Desceliers
Keyword(s):  
Stochastic Model ◽  
Drill String ◽  
Hysteretic Behavior ◽  
Drilling Process ◽  
Torsional Vibrations ◽  
Stick Slip ◽  
Rock Interaction ◽  
Proposed Model ◽  
The Stability ◽  
Torque On Bit

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.

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.

scholarly journals A Time Delay Model for Solar and Stellar Dynamos

2006 ◽  
Vol 652 (1) ◽  
pp. 696-708 ◽  
Author(s):  
A. L. Wilmot‐Smith ◽  
D. Nandy ◽  
G. Hornig ◽  
P. C. H. Martens
Keyword(s):  
Time Delay ◽  
Delay Model

A variable reabsorption time-delay model for pharmacokinetics of drugs

1987 ◽  
Vol 12 (2) ◽  
pp. 129-133 ◽  
Author(s):  
C. Labat ◽  
K. Mansour ◽  
M. F. Malmary ◽  
M. Terrissol ◽  
J. Oustrin
Keyword(s):  
Time Delay ◽  
Delay Model

Evaluation of GPS Ionospheric Time-Delay Model

1987 ◽  
Vol AES-23 (3) ◽  
pp. 332-338 ◽  
Author(s):  
W.A. Feess ◽  
S.G. Stephens
Keyword(s):  
Time Delay ◽  
Delay Model
Sign in / Sign up

Export Citation Format

Share Document