Advertisement

Mathematical Model and Experimental Investigation of Bit-Bounce in Horizontal Oil Well Drillstring

  • Baojin Wang
  • Fushen RenEmail author
  • Zhigang Yao
  • Tiancheng Fang
Research Article - Mechanical Engineering
  • 19 Downloads

Abstract

The bit-bounce is detrimental to the service life of drillstring and bit. This study highlights the influence of axial excitation and torsional excitation on the bit-bounce in horizontal well. Because of the complicated surroundings of downhole, Hamilton principle, a kind of energy method, is employed in this paper to derive the motion equation of the drillstring, which is discreted through finite element method. The impact–friction between the drillstring and borehole wall, and bit–rock and fluid–structure interaction are also modeled in this paper. The research results show that both axial excitation and torsional excitation greatly affect the dynamic behavior of the drillstring. Both the amplitude and the intensity of bit-bounce reduce with the development of the axial excitation and torsional excitation. And the test results are in agreement with the numerical simulation. The results of both have been mutually verified.

Keywords

Coupled vibrations Hamilton principle Drillstring Qualitative analysis Horizontal well 

List of Symbols

θx

Angular displacement along x direction

θy

Angular displacement along y direction

θz

Angular displacement along z direction

u

Displacement along x direction

v

Displacement along y direction

w

Displacement along z direction

U

Strain energy

T

Kinetic energy

W

Work done by the external forces

Fg

Work done by gravity

Fif

Work done by impact–friction

Ff

Work done by fluid–structure interaction

WBR

Work done by bit–rock interaction

n

Number of elements

le

Length of element

ξ

Local coordinate

qe

Displacement vector of element

\({\dot{\mathbf{q}}}_{{\mathbf{e}}}\)

The first derivative with time

\({\mathbf{N}}_{{\mathbf{u}}}^{\prime }\)

The first derivation of shape function with ξ

δue

Variation of the displacement ue

r

Radial displacement of drillstring

rgap

Gap between the drillstring and borehole wall

Re

External radius of drillstring

Rh

Radius of borehole wall

kim

Impact factor

\(\varPsi_{\text{im}} \left( r \right)\)

Determination coefficient of the drillstring

μ

Coefficient of kinetic friction between drillstring and borehole wall

Fn

Contact force in normal direction

xn

Coordinate at node n

Tc

Cutting torque

Wc

Cutting weight

a

Radius of bit

ɛ

Intrinsic specific energy

ζ

A number characterizing the orientation of the cutting force

σ

Maximum contact load

d

Instantaneous cutting depth

Bn

Number of blades of bit

Nu

Shape function of u

\({\mathbf{N}}_{{\theta_{x} }}\)

Shape function of θx

Fin

Normal component of hydrodynamic forces

Fit

Tangential component of hydrodynamic forces

FA

Lateral non-viscous hydrodynamic force

FN

Frictional viscous hydrodynamic force

Mf

Mass per unit length

pi

Pressure of internal flow

pe

Pressure of external flow

Ui

Flow speed of internal flow

Uex

Flow speed of external flow

ρf

Density of drilling mud

FL

Viscous force

fz

Viscous force

Cf

Viscosity damping coefficient

Df

Hydraulic diameter

ppump

Output pressure of pump

r

Angular velocity vector

I

Cross-sectional moment of inertia matrix

I1

Polar moment of inertia

I2

Cross-sectional moment of inertia

V

Volume of drillstring

\({\varvec{\upvarepsilon}}\)

Strain tensor

\({\varvec{\upsigma}}\)

Stress tensor

\({\mathbf{F}}_{{{\mathbf{LIN}}}}\)

Vector of linear force

\({\mathbf{F}}_{{{\mathbf{NL}}}}\)

Vector of nonlinear force

\(\varTheta_{1}\)

Additional damping factor

\(\varTheta_{2}\)

Additional damping factor

\(\varOmega_{x}\)

Driving angular speed

V0

Initial axial speed

Δt

Time step

α

Integral coefficient

β

Integral coefficient

Notes

Acknowledgements

The authors would like to acknowledge financial support by Natural Science Foundation of China, Project 11372071, Natural Science Foundation of Heilongjiang Province, Project LH2019A003, and Fundamental Research Funds for Provincial Undergraduate Universities of Heilongjiang Province, Project 2019QNL-13.

References

  1. 1.
    Albdiry, M.T.; Almensory, M.F.: Failure analysis of drillstring in petroleum industry: a review. Eng. Fail. Anal. 65, 74–85 (2016).  https://doi.org/10.1016/j.engfailanal.2016.03.014 Google Scholar
  2. 2.
    Xu, S.; Liu, Y.Z.; Zhou, L.U.; Yan, Y.M.: Failure analysis of the 18CrNi3Mo steel for drilling bit. J. Fail. Anal. Prev. 14(2), 183–190 (2014).  https://doi.org/10.1007/s11668-014-9802-x Google Scholar
  3. 3.
    Jacek, K.: Adaptive control of drillstring torsional oscillations. IFAC-Papers Online 50(1), 13360–13365 (2017).  https://doi.org/10.1016/j.ifacol.2017.08.2252 Google Scholar
  4. 4.
    Kamell, J.M.; Yigit, A.S.: Modeling and analysis of stick-slip and bit bounce in oil well drillstrings equipped with drag bits. J. Sound Vib. 333(25), 6885–6899 (2014).  https://doi.org/10.1016/j.jsv.2014.08.001 Google Scholar
  5. 5.
    Yigit, M.; Al-Ansary, A.; Khalid, M.: Active control of drillstring vibrations by mode localization. J. Struct. Control 4(1), 47–63 (1997).  https://doi.org/10.1002/stc.4300040107 Google Scholar
  6. 6.
    Vaziri, V.; Kapitaniak, M.; Wiercigroch, M.: Suppression of drill-string stick–slip vibration by sliding mode control: numerical and experimental studies. Eur. J. Appl. Math. 29(5), 805–825 (2018).  https://doi.org/10.1017/S0956792518000232 MathSciNetzbMATHGoogle Scholar
  7. 7.
    Rappold, K.: Drillstring vibration measurements detect bit stick-slip. Oil Gas J. 91(9), 66–70 (1993)Google Scholar
  8. 8.
    Wu, W.B.; Jiang, G.S.; Huang, S.G.: Vertical dynamic response of pile embedded in layered transversely isotropic soil. Math. Probl. Eng. 2014, 1–12 (2014).  https://doi.org/10.1155/2014/126916 MathSciNetzbMATHGoogle Scholar
  9. 9.
    Wilson, J.K.; Heisig, G.: Nonlinear drillstring-dynamics modeling of induced vibrations in unconventional horizontals. SPE Drill. Complet. 32(3), 243–256 (2015).  https://doi.org/10.2118/173049-PA Google Scholar
  10. 10.
    Sampaio, R.; Piovan, M.T.; Lozano, G.V.: Coupled axial/torsional vibrations of drill-strings by means of nonlinear model. Mech. Res. Commun. 34(5–6), 497–502 (2007).  https://doi.org/10.1016/j.mechrescom.2007.03.005 zbMATHGoogle Scholar
  11. 11.
    Gupta, S.K.; Wahi, P.: Tuned dynamics stabilizes an idealized regenerative axial-torsional model of rotary drilling. J. Sound Vib. 412, 457–473 (2018).  https://doi.org/10.1016/j.jsv.2017.08.044 Google Scholar
  12. 12.
    Gupta, S.K.; Wahi, P.: Global axial–torsional dynamics during rotary drilling. J. Sound Vib. 375, 332–352 (2016).  https://doi.org/10.1016/j.jsv.2016.04.021 Google Scholar
  13. 13.
    Bakhtiari-Nejad, F.; Hosseinzadeh, A.: Nonlinear dynamic stability analysis of the coupled axial-torsional motion of the rotary drilling considering the effect of axial rigid-body dynamics. Int. J. Non-linear Mech. 88, 85–96 (2017).  https://doi.org/10.1016/j.ijnonlinmec.2016.10.011 Google Scholar
  14. 14.
    Zhu, Q.T.; Zou, Z.M.; Huang, B.; Ma, H.; Xia, J.X.: Downhole vibration causing a drill collar failure and solutions. Nat. Gas Ind. B 4(2), 73–80 (2017)Google Scholar
  15. 15.
    Dong, G.J.; Chen, P.: 3D numerical simulation and experiment validation of dynamic damage characteristics of anisotropic shale for percussive-rotary drilling with a full-scale PDC bit. Energies 11(6), 1326 (2018).  https://doi.org/10.3390/en11061326 MathSciNetGoogle Scholar
  16. 16.
    Vijayan, K.; Vlajic, N.; Friswell, M.I.: Drillstring–borehole interaction: backward whirl instabilities and axial loading. Meccanica 52(11–12), 2945–2957 (2017).  https://doi.org/10.1007/s11012-017-0623-3 MathSciNetGoogle Scholar
  17. 17.
    Zhu, X.Z.; He, Y.D.; Chen, L.; Yuan, H.Q.: Nonlinear dynamics analysis of a drillstring-bit-wellbore system for horizontal oil well. Adv. Sci. Lett. 16(1), 13–19 (2012).  https://doi.org/10.1166/asl.2012.3275 Google Scholar
  18. 18.
    Westermann, H.; Gorelik, I.; Rudat, J.; Moritz, C.; Neubauer, M.; Wallaschek, J.; Hohn, O.: A new test rig for experimental studies of drillstring vibrations. SPE Drill. Complet. 30(2), 119–128 (2015).  https://doi.org/10.2118/176019-PA Google Scholar
  19. 19.
    Adam, W.: Improvements in root-cause analysis of drillstring vibration. J. Petrol. Technol. 68(12), 64–65 (2016).  https://doi.org/10.2118/1216-0064-JPT Google Scholar
  20. 20.
    Sarker, M.; Rideout, D.G.; Butt, S.D.: Dynamic model for 3D motions of a horizontal oilwell BHA with wellbore stick-slip whirl interaction. J. Petrol. Sci. Eng. 157, 482–506 (2017).  https://doi.org/10.1016/j.petrol.2017.07.025 Google Scholar
  21. 21.
    Reckmann, H.; Herbig, C.; Jain, J.; Queslati, H.; Hohl, A.: Investigation of lateral and torsional vibrations of drillstrings based on simulations, laboratory modal analysis and field tests. Oil Gas Eur. Mag. 40(1), 18–20 (2014)Google Scholar
  22. 22.
    Elliott, A.: Simulation of fully-coupled BHA dynamics using multibody dynamics. Oil Gas Eur. Mag. 41(1), 28–30 (2015)Google Scholar
  23. 23.
    Wilson, J.K.; Heisig, G.: Nonlinear drillstring- dynamics modeling of induced vibrations in unconventional horizontals. SPE Drill. Complet. 30(3), 243–256 (2015).  https://doi.org/10.2118/173049-PA Google Scholar
  24. 24.
    Belem, S.; Sabine, M.; Jean, J.L.; Vladimir, R.: Suppressing axial-torsional coupled vibrations in drillstrings. J. Control Eng. Appl. Inform. 15(1), 3–10 (2013)Google Scholar
  25. 25.
    Ghasemloonia, A.; Rideout, D.G.; Butt, S.D.: Vibration analysis of a drillstring in vibration assisted rotary drilling: finite element modeling with analytical validation. J. Energy Res. Technol. 135(3), 1–18 (2013).  https://doi.org/10.1115/1.4023333 Google Scholar
  26. 26.
    Rideout, D.G.; Ghasemloonia, A.; Farid, A.; Butt, S.D.: An intuitive and efficient approach to integrated modelling and control of three-dimensional vibration in long shafts. Int. J. Simul. Process Model. 10(2), 163–178 (2015).  https://doi.org/10.1504/IJSPM.2015.070468 Google Scholar
  27. 27.
    Baumgart, A.: Stick-slip and bit-bounce of deep-hole drillstrings. J. Energy Res. Technol. 122(2), 78–82 (2000).  https://doi.org/10.1115/1.483168 Google Scholar
  28. 28.
    Yaveri, M.; Damani, K.; Kalbhor, H.: Solutions to the downhole vibrations during drilling. In: 34th Annual SPE International Conference and Exhibition. Nigeria (2010)Google Scholar
  29. 29.
    Kapitaniak, M.; Vaziri, V.; Páez Chávez, J.; et al.: Experimental studies of forward and backward whirls of drill-string. Mech. Syst. Signal Process. 2018(100), 454–465 (2018).  https://doi.org/10.1016/j.ymssp.2017.07.014 Google Scholar
  30. 30.
    Reckmann, H.; Jogi, P.; Kpetehoto, F.T.; Chandrasekaran, S.; Macpherson, J.D.: MWD failure rates due to drilling dynamics. In: IADC/SPE Drilling Conference and Exhibition. Louisiana (2010)Google Scholar
  31. 31.
    Hsu, F.; Wilhoit, J.; James, C. Lateral vibration of drill pipe including wall reaction. In: Conference on Drilling and Rock Mechanics. Texas (1965)Google Scholar
  32. 32.
    Ghasemloonia, A.; Rideout, D.G.; Butt, S.D.: Analysis of multi-mode nonlinear coupled axial-transverse drillstring vibration in vibration assisted rotary drilling. J. Pet. Sci. Eng. 116, 36–49 (2014).  https://doi.org/10.1016/j.petrol.2014.02.014 Google Scholar
  33. 33.
    Khulief, Y.A.; Al-Sulaiman, F.A.; Bashmal, S.: Vibration analysis of drillstrings with string–borehole interaction. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 222(11), 2099–2110 (2008).  https://doi.org/10.1243/09544062JMES968 Google Scholar
  34. 34.
    Khulief, Y.A.: Spatial formulation of elastic multibody systems with impulsive constraints. Multibody Syst. Dyn. 4(4), 383–406 (2000).  https://doi.org/10.1023/A:1009801322539 zbMATHGoogle Scholar
  35. 35.
    Yevhen, K.: Understanding root cause of stick–slip vibrations in deep drilling with drag bits. Int. J. Non-Linear Mech. 67, 331–341 (2014).  https://doi.org/10.1016/j.ijnonlinmec.2014.10.019 Google Scholar
  36. 36.
    Jasem, M.K.; Yigit, A.S.: Modeling and analysis of stick-slip and bit bounce in oil well drillstrings equipped with drag bits. J. Sound Vib. 333(25), 6885–6899 (2014).  https://doi.org/10.1016/j.jsv.2014.08.001 Google Scholar
  37. 37.
    Zamanian, M.; Khadem, S.E.; Ghazavi, M.R.: Stick-slip oscillations of drag bits by considering damping of drilling mud and active damping system. J. Petrol. Sci. Eng. 59(3–4), 289–299 (2007).  https://doi.org/10.1016/j.petrol.2007.04.008 Google Scholar
  38. 38.
    Cassel, K.W.: Variational Methods with Applications in Science and Engineering. Cambridge University Press, Cambridge (2013)zbMATHGoogle Scholar
  39. 39.
    Wu, W.B.; Jiang, G.S.; Huang, S.G.: Vertical dynamic response of pile embedded in layered transversely isotropic soil. Math. Probl. Eng. 2014, 1–12 (2014).  https://doi.org/10.1155/2014/126916 MathSciNetzbMATHGoogle Scholar
  40. 40.
    Khulief, Y.A.; Al-Sulaiman, F.A.; Bashmal, S.: Vibration analysis of drillstrings with self-excited stick–slip oscillations. J. Sound Vib. 299(3), 540–558 (2007).  https://doi.org/10.1016/j.jsv.2006.06.065 Google Scholar
  41. 41.
    Richard, T.; Germay, C.; Detournay, E.: A simplified model to explore the root cause of stick-slip vibrations in drilling systems with drag bits. J. Sound Vib. 305(3), 432–456 (2007).  https://doi.org/10.1016/j.jsv.2007.04.015 Google Scholar
  42. 42.
    Ritto, T.G.; Soize, C.; Sampaio, R.: Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model. Comput. Mech. 45(5), 415–427 (2010).  https://doi.org/10.1007/s00466-009-0462-8 zbMATHGoogle Scholar
  43. 43.
    Logan, D.L.: A First Course in the Finite Element Method (forth edition), United States (2007)Google Scholar
  44. 44.
    Timothy, S.: Numerical Analysis, United States (2012)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.Department Mechanical Science and EngineeringNortheast Petroleum UniversityDaqingChina
  2. 2.Department of Petroleum EngineeringMissouri University of Science and TechnologyRollaUSA
  3. 3.Beijing Industrial Technician CollegeBeijingChina
  4. 4.School of Civil Engineering and ArchitectureNortheast Petroleum UniversityDaqingChina

Personalised recommendations