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Meccanica

Erschienen in:

21.05.2018

Stochastic torsional stability of an oil drill-string

verfasst von: B. F. Nogueira, T. G. Ritto

Erschienen in: Meccanica | Ausgabe 11-12/2018

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Abstract

The aim of this paper is to investigate the influence of uncertainties on the torsional vibration of drill-strings, in order to find out which uncertainty affects most significantly the torsional stability. The unstable torsional behavior is commonly associated to polycrystalline diamond compact bits, and manifests itself in the form of stick-slip oscillations. The stick-slip is a severe type of self-excited vibration characterized by large fluctuations in the rotation of the bit. It not only increases the bit wear, but also can cause drill-string failures. The analysis were done using a mathematical model of the drill-string based on classical torsion theory discretized by means of the finite element method. The bit-rock torque was included in the model as a nonlinear boundary condition at the bottom end of the drill-string. The values of the model parameters are typical values of a real drilling situation, which are subject to a high degree of uncertainty, what justifies a stochastic analysis. We have built probability distributions for the uncertain parameters and used Monte Carlo method to obtain the stochastic stability maps.

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Bit rate of penetration: the downward speed of the bit. The bit rate of penetration is a measure of how fast the rig is drilling the hole. Higher penetration rates imply quicker drilling progress and less time being spent in the process [12].

When one uses linear basis functions and chooses the elements such that $\rho (z)$, G(z), J(z) do not vary inside them, the finite element mass and stiffness matrices are given by [22]:

$$\begin{aligned} {\mathbf {M}}^{(e)} = \frac{\rho J \, l}{6} \left[ \begin{array}{cc} 2 &{} 1\\ 1 &{} 2 \end{array}\right] \phantom {aaaaaa} {\mathbf {K}}^{(e)} = \frac{GJ}{l} \left[ \begin{array}{cc} 1 &{} -1\\ -1 &{} 1 \end{array}\right] \end{aligned}$$

(3)

where l is the finite element length.

Hysteresis: is the history dependence of a physical system outputs. The system outputs depend not only on the present inputs, but also on the past inputs.

The vertical load per unit horizontal area is given by $(f_{Bit})_{z} = \frac{(F_{Bit})_{z}}{\pi (R_{Bit})^{2}}$, where $(F_{Bit})_{z}$ is the weight-on-bit, $R_{Bit}$ is the bit radius.

The sign function extracts the sign of its argument. For all $x \ne 0$ we define [27]: ${{{\mathrm{sgn}}}}(x) := \frac{x}{|x|}$. If $x=0$ we define ${{{\mathrm{sgn}}}}(x) := 0$.

Cutter wearflat: horizontal flat surface below the cutter.

The coefficient of variation function measures the dispersion of a random variable, ${{\mathrm{cv}}}:= {{{\mathrm{\upsigma }}}}/{{{\mathrm{\upmu }}}}$, where ${{\mathrm{\upmu }}}$ is the mean function and ${{\mathrm{\upsigma }}}^{2}$ is the variance function.

Halliburton (1997) Petroleum well construction. Wiley, Duncan

Aadnoy B, Cooper I, Miska S, Mitchell RF, Payne ML (2009) Advanced drilling and well technology. Society of Petroleum Engineers, Richardson

Germay C, Denöel V, Detournay E (2009) Multiple mode analysis of the self-excited vibrations of rotary drilling systems. J Sound Vib 325:362–381. https://doi.org/10.1016/j.jsv.2009.03.017 ADSCrossRef

Spanos PD, Chevallier AM, Politis NP (2002) Nonlinear stochastic drill-string vibrations. ASME J Vib Acoust 124(4):512–518. https://doi.org/10.1115/1.1502669 CrossRef

Kotsonis SJ, Spanos PD (1997) Chaotic and random whirling motion of drillstrings. ASME J Energy Resour Technol 119(4):217–222. https://doi.org/10.1115/1.2794993 CrossRef

Ritto TG, Soize C, Sampaio R (2009) Non-linear dynamics of a drill-string with uncertain model of the bit-rock interaction. Int J Non-Linear Mech 44(8):865–876. https://doi.org/10.1016/j.ijnonlinmec.2009.06.003 CrossRef

Ritto T, Soize C, Sampaio R (2010) Probabilistic model identification of the bit-rock interaction model uncertainties in nonlinear dynamics of a drill-string. Mech Res Commun 37(2010):584–589. https://doi.org/10.1016/j.mechrescom.2010.07.004 CrossRefMATH

Ritto TG, Soize C, Sampaio R (2010) Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model. Comput Mech 45:415–427. https://doi.org/10.1007/s00466-009-0462-8 CrossRefMATH

Ritto TG, Escalante MR, Sampaio R, Rosales MB (2013) Drill-string horizontal dynamics with uncertainty on the frictional force. J Sound Vib 332(1):145–153. https://doi.org/10.1016/j.jsv.2012.08.007 ISSN 0022-460XADSCrossRef

10.

Ritto TG, Sampaio R (2013) Measuring the efficiency of vertical drill-strings: a vibration perspective. Mech Res Commun 52:32–39. https://doi.org/10.1016/j.mechrescom.2013.06.003 ISSN 0093-6413CrossRef

11.

Pavone DR, Desplans JP (1994) Application of high sampling rate downhole measurements for analysis and cure of stick-slip in drilling. Soc Pet Eng 25–28. https://doi.org/10.2118/28324-MS

12.

Cochener J (2010) Quantifying drilling efficiency. U.S. Energy Information Administration. https://www.eia.gov/workingpapers/pdf/

13.

Abbassian F, Dunayevsky V (1998) Application of stability approach to torsional and lateral bit dynamics. Soc Pet Eng 13:99–107. https://doi.org/10.2118/30478-PA

14.

Franca LFFMP (2004) Perfuração Percussiva-Rotativa Auto-Excitada em Rochas Duras. Ph.D. Thesis, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, Brazil

15.

Christoforou AP, Yigit AS (2003) Fully coupled vibrations of actively controlled drill-strings. J Sound Vib 267:1029–1045. https://doi.org/10.1016/S0022-460X(03)00359-6 ADSCrossRef

16.

Germay C, van de Wouw N, Nijmeijer H, Sepulchre R (2009) Nonlinear drill-string dynamics analysis. J Appl Dyn Syst 8(2):527–553. https://doi.org/10.1137/060675848 MathSciNetCrossRefMATH

17.

Liu X, Vlajic N, Long X, Meng G, Balachandran B (2013) Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects. Nonlinear Dyn 72:61–77. https://doi.org/10.1007/s11071-012-0690-x MathSciNetCrossRef

18.

Percy JG (2004) Análise de Incertezas em Vibrações Laterais e de Torção Acopladas em Colunas de Perfuração. M.Sc. Dissertation, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, Brazil

19.

Tucker RW, Wang C (2003) Torsional vibration control and cosserat dynamics of a drill-rig assembly. Meccanica 38:145–161. https://doi.org/10.1023/A:1022035821763 CrossRefMATH

20.

Ritto TG, Aguiar RR, Hbaieb S (2017) Validation of a drill string dynamical model and torsional stability. Meccanica. https://doi.org/10.1007/s11012-017-0628-y

21.

Meirovitch L (1967) Anaytical methods in vibrations, 1st edn. Prentice Hall, Upper SaddleMATH

22.

Pilkey WD (2005) Formulas for stress, strain, and structural matrices, 2nd edn. Wiley, HobokenMATH

23.

Wojewoda J, Stefański A, Wiercigroch M, Kapitaniak T (2008) Hysteretic effects of dry friction: modelling and experimental studies. Philos Trans R Soc A 366(1866). https://doi.org/10.1098/rsta.2007.2125

24.

Woodhouse J, Putelat T, McKay A (2015) Are there reliable constitutive laws for dynamic friction? Philos Trans R Soc A 373(2051). https://doi.org/10.1098/rsta.2014.0401

25.

Khulief YA, al Sulaiman FA, Bashmal S (2007) Vibration analysis of drillstrings with self excited stick-slip oscillations. J Sound Vib 299:540–558. https://doi.org/10.1016/j.jsv.2006.06.065 ADSCrossRef

26.

Leine RI, van Campen DH, Keultjes WJG (2002) Stick-slip whirl interaction in drill-string dynamics. J Vib Acoust 124(2). https://doi.org/10.1115/1.1452745

27.

Wikipedia (2016) Wikipedia, the free encyclopedia. http://en.wikipedia.org

28.

Brett J (1992) The genesis of bit-induced torsional drillstring vibrations. Soc Pet Eng 7:168–174. https://doi.org/10.2118/21943-PA

29.

Lima LC, Aguiar R, Ritto T, Hbaieb S (2005) Analysis of the torsional stability of a simplified drillstring. In: 17th international symposium on dynamic problems of mechanics

30.

Nogueira BF (2016) Stochastic stability analysis of torsional and lateral vibrations of an oil drill-string. M.Sc. Dissertation, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, Brazil

31.

Meirovitch L (2001) Fundamentals of vibrations. McGraw-Hill, New York

32.

Depouhon A (2007) Stability of TAZ apparatus: a drilling equivalent. M.Sc. Dissertation, University of Minnesota. http://hdl.handle.net/2268/129456

33.

Papoulis A (1991) Probability, random variables and stochastic processes, 3rd edn. McGraw-Hill, New YorkMATH

34.

Kapur JN, Kesavan HK (1992) Entropy optimization principles with applications. Academic Press, San DiegoCrossRef

35.

Bourgoyne AT Jr, Millheim KK, Chenevert ME, Young FS Jr (1986) Applied drilling engineering. Society of Petroleum Engineers, Richardson

36.

Ogunnaike BA (2009) Random phenomena fundamentals and engineering applications of probability and statistics. CRC Press, Boca RatonCrossRef

37.

Gaffney ES (1976) Measurements of dynamic friction between rock and steel. Technical report, systems, science and software

38.

Walsri C (2009) Compressive strength of sandstone under true triaxial stress states. M.Sc. dissertation, Suranaree University of Technology, Nakhon Ratchasima, Isan, Thailand

Titel: Stochastic torsional stability of an oil drill-string
verfasst von: B. F. Nogueira
T. G. Ritto
Publikationsdatum: 21.05.2018
Verlag: Springer Netherlands
Erschienen in: Meccanica / Ausgabe 11-12/2018
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-018-0859-6

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