All Title Author
Keywords Abstract

Chaotic Vibration Analysis of the Bottom Rotating Drill String

DOI: 10.1155/2014/429164

Full-Text   Cite this paper   Add to My Lib


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. 1. Introduction In oil and gas drilling engineering, the well is created by drilling a hole 5 to 50 inches (127.0?mm to 914.4?mm) in diameter into the earth with a drilling rig that rotates a drill string with a bit attached. In the process, severe drill string vibration is a major contributor to downhole tool failure. It may also cause hole damage and increase the need for more frequent rig repair. Typically, the drilling string vibration can be divided into three types or modes: lateral, longitudinal, and torsional. The destructive nature of each type of vibration is different. Lateral and longitudinal vibrations of the drill string have been undertaken extensive research since it proposed from mid-1960s, The main reason that caused the fatigue failure of the bottomhole assembly (BHA) [2] was considered to be the vibration of the drill string. Many studies of the drill string focused on the determination of natural frequencies [3, 4], bending stress calculation [5, 6], stability analysis [7], lateral displacement prediction [8], and so forth. Spanos et al. [9] established the finite element model of drill string lateral vibration and analyzed nonlinear random vibration. Chunjie and Tie [10] obtained the natural frequency of drill string longitudinal vibration from a finite element model. Vibrations of all three types (lateral, longitudinal, and torsional) may occur during rotary drilling and are coupled. Single vibration model cannot well describe the dynamics of BHA; furthermore, to establish a precise bottom hole kinetic theory model is difficult to achieve because of the underground complex situation. Additionally, the process of drill bit break rocks is a nonlinear process which is


[1]  R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: the TISEAN package,” Chaos, vol. 9, no. 2, pp. 413–435, 1999.
[2]  W. C. Chin, Wave Propagation in Petroleum Engineering: Modern Applications to Drillstring Vibrations, Measurement-While-Drilling, Swab-Surge, and Geophysics, Gulf Publication, Houston, Tex, USA, 1994.
[3]  S. L. Chen and M. Géradin, “An improved transfer matrix technique as applied to BHA lateral vibration analysis,” Journal of Sound and Vibration, vol. 185, no. 1, pp. 93–106, 1995.
[4]  A. P. Christoforou and A. S. Yigit, “Dynamic modelling of rotating drillstrings with borehole interactions,” Journal of Sound and Vibration, vol. 206, no. 2, pp. 243–260, 1997.
[5]  R. D. Graham, M. A. Frost III, and J. C. Wilhoit Jr., “Analysis of the motion of deep-water drill strings—part 1: forced lateral motion,” Journal of Engineering for Industry, vol. 87, no. 2, pp. 137–144, 1965.
[6]  R. Plunkett, “Static bending stresses in catenaries and drill strings,” Journal of Engineering for Industry, vol. 89, no. 1, pp. 31–36, 1967.
[7]  M. A. Vaz and M. H. Patel, “Analysis of drill strings in vertical and deviated holes using the Galerkin technique,” Engineering Structures, vol. 17, no. 6, pp. 437–442, 1995.
[8]  A. S. Yigit and A. P. Christoforou, “Coupled torsional and bending vibrations of drillstrings subject to impact with friction,” Journal of Sound and Vibration, vol. 215, no. 1, pp. 167–181, 1998.
[9]  P. D. Spanos, A. M. Chevallier, and N. P. Politis, “Nonlinear stochastic drill-string vibrations,” Journal of Vibration and Acoustics, vol. 124, no. 4, pp. 512–518, 2002.
[10]  H. Chunjie and Y. Tie, “The research on axial vibration of drill string with Delphi,” in Proceedings of the International Conference on Computational Intelligence and Natural Computing (CINC '09), pp. 478–481, Wuhan, China, June 2009.
[11]  T. Richard, E. Detournay, M. Fear, B. Miller, R. Clayton, and O. Matthews, “Influence of bit-rock interaction on stick-slip vibrations of PDC bits,” in Proceedings of the 2002 SPE Annual Technical Conference and Exhibition, MS77616, pp. 2407–2418, San Antonio, Tex, USA, September 2002.
[12]  K. Mongkolcheep, A. Palazzolo, A. Ruimi, and R. Tucker, “A modal approach for chaotic vibrations of a drillstring,” in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (DETC '09), pp. 1305–1314, San Diego, Calif, USA, August 2009.
[13]  A. D. Craig, R. Goodship, and D. R. Shearer, “High frequency downhole dynamic measurements provide greater understanding of drilling vibration in performance motor assemblies,” in Proceedings of the 2010 IADC/SPE Drilling Conference and Exhibition, pp. 377–386, New Orleans, La, USA, February 2010.
[14]  L. W. Ledgerwood III, O. J. Hoffmann, J. R. Jain, C. El Hakam, C. Herbig, and R. W. Spencer, “Downhole vibration measurement, monitoring and modeling reveal stick-slip as a primary cause of PDC bit damage in today's applications,” in Proceedings of the 2010 SPE Annual Technical Conference and Exhibition, pp. 2652–2661, Florence, Italy, September 2010.
[15]  P. D. Welch, “The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Transactions on Audio Electroacoustics, vol. 15, no. 62, pp. 70–73, 1967.
[16]  A. M. Fraser and H. L. Swinney, “Independent coordinates for strange attractors from mutual information,” Physical Review A, vol. 33, no. 2, pp. 1134–1140, 1986.
[17]  L. Cao, “Practical method for determining the minimum embedding dimension of a scalar time series,” Physica D, vol. 110, no. 1-2, pp. 43–50, 1997.
[18]  M. B. Kennel, R. Brown, and H. D. I. Abarbanel, “Determining embedding dimension for phase-space reconstruction using a geometrical construction,” Physical Review A, vol. 45, no. 6, pp. 3403–3411, 1992.
[19]  P. Grassberger and I. Procaccia, “Measuring the strangeness of strange attractors,” Physica D, vol. 9, no. 1-2, pp. 189–208, 1983.
[20]  P. Grassberger and I. Procaccia, “Estimation of the Kolmogorov entropy from a chaotic signal,” Physical Review A, vol. 28, no. 4, pp. 2591–2593, 1983.
[21]  A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D, vol. 16, no. 3, pp. 285–317, 1985.
[22]  M. T. Rosenstein, J. J. Collins, and C. J. de Luca, “A practical method for calculating largest Lyapunov exponents from small data sets,” Physica D, vol. 65, no. 1-2, pp. 117–134, 1993.
[23]  H. Kantz, “A robust method to estimate the maximal Lyapunov exponent of a time series,” Physics Letters A, vol. 185, no. 1, pp. 77–87, 1994.


comments powered by Disqus