Chaotic Vibration Analysis of the Bottom Rotating Drill String

Drill string vibration is a widely studied topic. This paper developed a real-time measurement system near the drilling bit and extracted the lateral vibration, longitudinal vibration time series of bottom rotating drill string. In order to reconstruct the phase space, we estimated the delay time with mutual information and calculated the embedding dimension through Cao’s method. Finally, the chaotic characterization of the system is analyzed by calculating the correlation dimension and the largest Lyapunov exponent. The results show that such system can exhibit positive finite-time Lyapunov exponents and a clear convergence toward the correlation dimension, which is a strong indicator for the chaotic behavior of the system. It is expected that the new dynamics found in this paper could be of potential implication to the control methods of the drill string vibration.

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Development and Application of the Downhole Drilling String Shock-Absorption and Hydraulic Supercharging Device

Shock and Vibration ◽

10.1155/2016/2041671 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Yongwang Liu ◽

Zhichuan Guan ◽

Hongning Zhang ◽

Bo Zhang

Keyword(s):

Longitudinal Vibration ◽

Rock Breaking ◽

Drill String ◽

Field Application ◽

Drilling Speed ◽

Technical Design ◽

Fundamental Study ◽

String Vibration ◽

Drilling String ◽

Breaking Energy

It is a hot topic for deep/ultradeep wells to improve rock-breaking efficiency and drilling speed by available downhole energy. Based on different downhole energies and working conditions, specialized plunger pump is proposed to convert longitudinal vibration of drilling string into rock-breaking energy. Technical design is developed to generate high-pressure water jet. And then a simulation model is built to verify feasibility of the technical design. Through simulation, the influence law of key factors is obtained. On this basis, this device is tested in several wells. The result indicates this device can increase drilling speed as much as 136%. Meanwhile the harmful vibration can be absorbed. The energy from drilling string vibration is of high frequency and increases as well depth and formation anisotropy increase. By reducing adverse vibration, this device is able to increase the drilling speed and the service life also meets the demand of field application. The longest working time lasts for more than 130 hours. The performance of this device demonstrates great application prospect in deep/ultradeep resources exploration. To provide more equipment support for deep/ultradeep wells, more effort should be put into fundamental study on downhole drill string vibration and related equipment.

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The Chaotic Attractor of the Sediment Movement

Fractals ◽

10.1142/s0218348x98000237 ◽

1998 ◽

Vol 06 (02) ◽

pp. 191-196

Author(s):

Fengsu Chen ◽

Kongxian Xue ◽

Wenkang Cai

Keyword(s):

Phase Space ◽

Lyapunov Exponent ◽

Chaotic Attractor ◽

Yangtze River ◽

Correlation Dimension ◽

Chaotic Behavior ◽

Largest Lyapunov Exponent ◽

The Yangtze River ◽

Sediment Movement ◽

Reconstructed Phase Space

We consider the chaotic behavior of the sediment movement with the observed data of the Yangtze River in China and the method of the reconstructed phase space and we find that in the sediment movement there is an attractor. As far as the real example mentioned in this paper is concerned, the correlation dimension and the largest Lyapunov exponent are around 6.6 and 0.013 respectively. These results are crucially referential for estimating the mode of the sediment movement, designing the scheme of the sediment observation, and studying the predictability problem of the sediment.

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Chaotic dynamics of cardioventilatory coupling in humans: effects of ventilatory modes

AJP Regulatory Integrative and Comparative Physiology ◽

10.1152/ajpregu.90862.2008 ◽

2009 ◽

Vol 296 (4) ◽

pp. R1088-R1097 ◽

Cited By ~ 6

Author(s):

Laurence Mangin ◽

Christine Clerici ◽

Thomas Similowski ◽

Chi-Sang Poon

Keyword(s):

Time Series ◽

Correlation Dimension ◽

Chaotic Dynamics ◽

Chaotic Behavior ◽

Intrathoracic Pressure ◽

Ventilator Weaning ◽

Largest Lyapunov Exponent ◽

Ventilatory Mode ◽

Limit Value ◽

Noise Limit

Cardioventilatory coupling (CVC), a transient temporal alignment between the heartbeat and inspiratory activity, has been studied in animals and humans mainly during anesthesia. The origin of the coupling remains uncertain, whether or not ventilation is a main determinant in the CVC process and whether the coupling exhibits chaotic behavior. In this frame, we studied sedative-free, mechanically ventilated patients experiencing rapid sequential changes in breathing control during ventilator weaning during a switch from a machine-controlled assistance mode [assist-controlled ventilation (ACV)] to a patient-driven mode [inspiratory pressure support (IPS) and unsupported spontaneous breathing (USB)]. Time series were computed as R to start inspiration (RI) and R to the start of expiration (RE). Chaos was characterized with the noise titration method (noise limit), largest Lyapunov exponent (LLE) and correlation dimension (CD). All the RI and RE time series exhibit chaotic behavior. Specific coupling patterns were displayed in each ventilatory mode, and these patterns exhibited different linear and chaotic dynamics. When switching from ACV to IPS, partial inspiratory loading decreases the noise limit value, the LLE, and the correlation dimension of the RI and RE time series in parallel, whereas decreasing intrathoracic pressure from IPS to USB has the opposite effect. Coupling with expiration exhibits higher complexity than coupling with inspiration during mechanical ventilation either during ACV or IPS, probably due to active expiration. Only 33% of the cardiac time series (RR interval) exhibit complexity either during ACV, IPS, or USB making the contribution of the cardiac signal to the chaotic feature of the coupling minimal. We conclude that 1) CVC in unsedated humans exhibits a complex dynamic that can be chaotic, and 2) ventilatory mode has major effects on the linear and chaotic features of the coupling. Taken together these findings reinforce the role of ventilation in the CVC process.

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Dynamic Characteristics of Downhole Bit Load and Analysis of Conversion Efficiency of Drill String Vibration Energy

Energies ◽

10.3390/en14010229 ◽

2021 ◽

Vol 14 (1) ◽

pp. 229

Author(s):

Yuqiang Xu ◽

Hongning Zhang ◽

Zhichuan Guan

Keyword(s):

Energy Conversion ◽

Conversion Efficiency ◽

Rotation Rate ◽

Longitudinal Vibration ◽

Drill Pipe ◽

Energy Conversion Efficiency ◽

Elastic Stiffness ◽

Positive Influence ◽

Drill String ◽

String Vibration

The longitudinal vibration of the drill pipe contains considerable energy which can be used to improve the rock-breaking efficiency during drilling. It is very important to the development of drilling speed-up tools to have a comprehensive understanding of the energy conversion efficiency of downhole drill string vibration. In this paper, the characteristics of downhole bit load and longitudinal vibration of drill string under different conditions were studied in the experiment, and the analysis method of energy conversion efficiency from drill string vibration to spring potential energy was proposed. The experimental analysis showed that the fluctuation of the downhole bit load was reduced by 10%–90% after the spring was installed in the bottom hole assembly. The rotation rate and the spring elastic stiffness had a significant and positive influence on the fluctuation amplitude of the downhole bit load. Meanwhile, the longitudinal vibration amplitude and acceleration of the drill string peaked at the elastic stiffness of 1 kN/mm. The closer the spring position to the drill bit was, the more severe the longitudinal vibration of the drill string above the spring component was. The bit load and the rotation rate had a positive influence on the severity of longitudinal vibration. The analysis of energy conversion efficiency showed that the available mechanical energy range of the longitudinal vibration of the drill pipe was about 200–420 kW. The work power of the drill string vibration to the spring component increased sharply and then decreased with the increasing of elastic stiffness. The energy conversion efficiency came to the optimal value when the elastic stiffness was between 1 kN/mm and 2 kN/mm. Increasing the rotation rate, keeping the bit load below 134.5 kN and installing the spring component near the drill bit are beneficial for improving the energy conversion efficiency of drill string vibration. This paper reveals the main factors affecting the energy conversion efficiency of drill string vibration and their influencing laws, and determines the range of WOB, rotation speed, spring position and stiffness to obtain the best energy conversion efficiency.

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FINITE CORRELATION DIMENSION AND POSITIVE LYAPUNOV EXPONENTS FOR SURFACE WAVE DATA IN THE ADRIATIC SEA NEAR VENICE

Fractals ◽

10.1142/s0218348x95000060 ◽

1995 ◽

Vol 03 (01) ◽

pp. 55-78 ◽

Cited By ~ 2

Author(s):

L. BERGAMASCO ◽

M. SERIO ◽

A.R. OSBORNE ◽

L. CAVALERI

Keyword(s):

Surface Wave ◽

Lyapunov Exponents ◽

Correlation Dimension ◽

Adriatic Sea ◽

Chaotic Behavior ◽

Largest Lyapunov Exponent ◽

Northern Adriatic Sea ◽

Northern Adriatic ◽

Wave Data ◽

Surface Wave Data

We study wind-driven surface wave data taken on an offshore platform in 16 m of water, about 20 km from Venice in the Northern Adriatic Sea. The data are investigated for the effects of chaos and to this end they are subjected to a variety of time series analysis techniques from the field of dynamical systems theory. For certain data sets we find a finite value for the correlation dimension (~7) and a positive value for the largest Lyapunov exponent (~1.5×10−3 bit/sec). In spite of the fact that these results suggest the possibility of chaotic behavior in the data, the correct interpretation is that the data are essentially stochastic, and that the correlation dimensions and Lyapunov exponents result from the anomalous statistical behavior of certain near-Gaussian random processes whose properties we discuss.

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EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127408022640 ◽

2008 ◽

Vol 18 (12) ◽

pp. 3679-3687 ◽

Cited By ~ 6

Author(s):

AYDIN A. CECEN ◽

CAHIT ERKAL

Keyword(s):

Time Series ◽

Lyapunov Exponent ◽

Lyapunov Exponents ◽

Correlation Dimension ◽

Time Series Data ◽

Logistic Map ◽

Model Identification ◽

Series Data ◽

Largest Lyapunov Exponent ◽

The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

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Drill String Vibration: A Proxy for Identifying Lithologic Boundaries while Drilling

10.2973/odp.proc.sr.179.015.2002 ◽

2002 ◽

Cited By ~ 1

Author(s):

G. Meyers ◽

D. Goldberg ◽

J. Rector

Keyword(s):

Drill String ◽

String Vibration

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Research of Extracting Information about Reservoir Logging Signals Based on Chaos Characteristics

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.380-384.3742 ◽

2013 ◽

Vol 380-384 ◽

pp. 3742-3745

Author(s):

Chun Yan Nie ◽

Rui Li ◽

Wan Li Zhang

Keyword(s):

Lyapunov Exponent ◽

Correlation Dimension ◽

Approximate Entropy ◽

Water Layer ◽

Time Correlation ◽

Largest Lyapunov Exponent ◽

Characteristic Parameters ◽

Chaotic Characteristic ◽

Oil Water

The mechanism of logging signals generating was researched. In the same time, correlation dimension, largest Lyapunov exponent and approximate entropy of chaotic characteristics were extracted. On this basis, chaotic characteristic parameters were applied in processing, analysis and interpretation, try to find chaotic characteristics of different of reservoirs for example oil, water layer and the dry layer. The results showed that chaos characteristics in different reservoir is different, therefore, we can distinguish the different natures of reservoirs by extracting chaos characteristics.

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