# Casing Wear Prediction Model Based on Drill String Whirling Motion in Extended-Reach Drilling

## Abstract

Casing wear has become an increasingly urgent research topic alongside advancements in extended-reach drilling (ERD) engineering. The drill string in an ERD operation is likely to undergo whirling motion, which is known to impact casing wear prediction accuracy; there have not yet been long-term studies on the related mechanisms, however. In this study, we develop a new prediction model called circumferential casing wear model (CCWD) based on the energy principle and the geometric properties, which accounts for the effects of drill string whirling motion on casing wear. Besides, composite casing wear models considering with the CCWD and casing wear groove model (CWGD) are also discussed. The results via case study to find that the proposed CCWD model of whirling motion can contribute to the accuracy of casing wear prediction. If the whirling motion is ignored, a large prediction error could occurred when only CWGD model is used. In the sensitivity analysis, the worn casing depth may increase alongside increases in whirling motion angular velocity, rotary table angular velocity, sliding and rolling friction coefficient, outer tool joint radius, and drill string weight. Slight variations in whirling motion angular velocity and rolling friction coefficient can cause substantial casing wear. Thus whirling motion must be strictly controlled during the drilling process to prevent engineering failure. To this effect, the model presented in this paper has both theoretical and practical applications for enhancing the accuracy of casing wear prediction to develop oil and gas reservoirs in ERD.

## Keywords

Casing wear Whirling motion Drill string Prediction model Composite wear## List of symbols

*a*Apparent radius (m)

*A*Worn casing area (m\(^{2}\))

- \(A_n\)
Worn casing area cumulated from 1 to

*n*th step length (m\(^{2}\))- \(A_{n+1}\)
Worn casing area cumulated from 1 to \((n+1)\)th step length (m\(^{2}\))

- \(d_\mathrm{ct}\)
Total worn casing depth (m)

- \(d_\mathrm{w}\)
Worn casing depth (m)

- \(d_\mathrm{wc}\)
Worn casing depth by eccentricity (m)

- \(d_\mathrm{wr} \)
Worn casing depth by whirling motion (m)

- EI
Bending stiffness (N m\(^{2}\))

- \(f_\mathrm{r} \)
Rolling friction force (N)

- \(f_\mathrm{s} \)
Sliding friction force (N)

- \(f_\mathrm{w} \)
Casing wear factor (dimensionless)

*F*Actual axial force (N)

- \(F_\mathrm{c} \)
Critical axial force (N)

- \(H_\mathrm{b} \)
Casing Brinell hardness (N/m\(^{2}\))

- \(L_\mathrm{s} \)
Sliding distance (m)

- \(L_\mathrm{r} \)
Rolling distance (m)

- \(N_\mathrm{d} \)
Total contact force (N)

- \(N_\mathrm{o} \)
Static contact force (N)

- \(N_\mathrm{c} \)
Centrifugal force (N)

*q*Drill string weight per length (N/m)

- \(R_\mathrm{ci} \)
Inner radius of the casing (m)

- \({R}^{\prime }_\mathrm{ci} \)
Modified inner radius of the casing (m)

- \(R_\mathrm{tj} \)
Outer radius of the tool joint (m)

- ROP
Rate of penetration (m/h)

*t*Time of sliding (s)

*v*Relative sliding velocity (m/s)

*W*Total dissipated energy (J)

- \(W_\mathrm{s} \)
Dissipated energy by sliding (J)

- \(W_\mathrm{r} \)
Dissipated energy by rolling (J)

## Greek

- \(\alpha \)
Inclination angle of a wellbore (degrees)

- \(\Delta A_n \)
Worn casing area of the

*n*th step length (m\(^{2}\))- \(\overline{\Delta d_\mathrm{wn} } \)
Modified worn casing depth with unit step length (m)

- \(\delta _\mathrm{r} \)
Rolling friction coefficient (dimensionless)

- \(\varepsilon \)
Eccentricity of whirling motion (m)

- \(\theta \)
Phase angle (degrees)

- \(\kappa \)
Wear efficiency (dimensionless)

- \(\mu _\mathrm{s} \)
Sliding friction coefficient (dimensionless)

- \(\Omega \)
Whirling motion angular velocity (rad/s)

- \(\omega \)
Angular velocity of the rotary table (rad/s)

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## Notes

### Acknowledgements

The authors gratefully acknowledge the financial support from the Natural Science Foundation of China (Grant numbers: U1762214, 51521063). This research is also supported by other projects (Grant Numbers: 2017ZX05009-003 and 2016YFC0303303).

## References

- 1.Bradley, W.B.; Fontenot, J.E.: The prediction and control of casing wear. J. Pet. Technol.
**27**(2), 233–245 (1975)CrossRefGoogle Scholar - 2.Williamson, J.S.: Casing wear: the effect of contact pressure. J. Pet. Technol.
**33**(12), 2382–2388 (1981)CrossRefGoogle Scholar - 3.Best, B.: Casing wear caused by tooljoint hardfacing. SPE Drill. Eng.
**1**(1), 62–70 (1986)CrossRefGoogle Scholar - 4.White, J.P.; Dawson, R.: Casing wear: laboratory measurements and field predictions. SPE Drill. Eng.
**2**(1), 56–62 (1987)CrossRefGoogle Scholar - 5.Song, J.S.; Bowen, J.; Klementich, F.: The internal pressure capacity of crescent-shaped wear casing. SPE-23902-MS (1992)Google Scholar
- 6.Hall, R.W.; Garkasi, A.; Deskins, G.; Vozniak, J.: Recent Advances in Casing Wear Technology. In: IADC/SPE Drilling Conference, Dallas, Texas (1994)Google Scholar
- 7.Hall, R.W.; Malloy, K.P.: Contact pressure threshold: an important new aspect of casing wear. In: SPE Production Operations Symposium, Oklahoma City (2005)Google Scholar
- 8.Gao, D.L.; Sun, L.Z.; Lian, J.H.: Prediction of casing wear in extended-reach drilling. Pet. Sci.
**7**(4), 494–501 (2010)CrossRefGoogle Scholar - 9.Gao, D.L.; Sun, L.Z.: New method for predicting casing wear in horizontal drilling. Pet. Sci. Technol.
**30**(9), 883–892 (2012)CrossRefGoogle Scholar - 10.Sun, L.Z.; Gao, D.L.; Zhu, K.L.: Models & tests of casing wear in drilling for oil and gas. J. Nat. Gas Sci. Eng.
**4**, 44–47 (2012)CrossRefGoogle Scholar - 11.Wolf, S.F.; Zacksenhouse, M.; Arian, A.: Field measurements of downhole drillstring vibrations. SPE-14330-MS (1985)Google Scholar
- 12.Burgess, T.M.; Mcdaniel, G.L.; Das, P.K.: Improving BHA tool reliability with drillstring vibration models: field experience and limitations. SPE-16109-MS (1987)Google Scholar
- 13.Vandiver, K.J.; Nicholson, J.W.; Shyu, R.J.: Case studies of the bending vibration and whirling motion of drill collars. Spe Drill. Eng.
**5**(4), 282–290 (1990)CrossRefGoogle Scholar - 14.Jansen, J.D.: Non-linear rotor dynamics as applied to oilwell drillstring vibrations. J. Sound Vib.
**147**(1), 115–135 (1991)CrossRefGoogle Scholar - 15.Jansen, J.D.: Whirl and chaotic motion of stabilized drill collars. Spe Drill. Eng.
**7**(2), 107–114 (1992)CrossRefGoogle Scholar - 16.Gao, D.L.; Gao, B.K.; Geng, R.P.: Analysis of drillstring whirling. Oil Drill. Prod. Technol.
**18**(6), 9–13 (1996)Google Scholar - 17.Li, Z.F.; Wang, Z.Y.; Yang, X.J.; Tian, X.M.: Swirling analysis of drilling strings and anti-whirl stabilizers design. Oil Drill. Prod. Technol.
**30**(3), 124–127 (2008)Google Scholar - 18.Tan, L.C.; Gao, D.L.; Zhou, J.H.: Casing wear prediction with considering initial internal casing eccentricity. Arab. J. Sci. Eng. (2017). https://doi.org/10.1007/s13369-017-2890-7
- 19.Tan, L.C.; Gao, D.L.; Zhou, J.H.: A prediction model of casing wear in extended-reach drilling with buckled drillstring. J. Appl. Mech.
**85**(2), 1–12 (2018)Google Scholar - 20.Gao, B.K.; Gao, D.L.: Rolling friction of whirling drillstring. J. China Univ. Pet.
**22**(2), 26–28 (1998)MathSciNetGoogle Scholar - 21.Huq, M.Z.; Celis, J.P.: Expressing wear rate in sliding contacts based on dissipated energy. Wear
**252**(5–6), 375–383 (2002)CrossRefGoogle Scholar - 22.Yu, L.; Zhang, L.B.; Fan, J.C.; Shi, D.: The research on calculation method of casing wear caused by drill-pipe revolution. Drill. Prod. Technol.
**27**(4), 66–69 (2004)Google Scholar - 23.Tan, C.J.; Gao, D.L.; Tang, H.X.; Wei, C.J.: Method of casing wear prediction for Liuhua mega extended-reach wells in south china sea. Oil Drill. Prod. Technol.
**28**(1), 13–14 (2006)Google Scholar