Exploration & Production - Oil and Gas review

Bit-sticking Phenomena in a Multidegree-of-freedom Controlled Drillstring

Figure 5: The Rotary Velocities Reach the Desired Rotary Velocity with a Linear Control

A

10 12

2 4 6 8

0 050 B

2,000 4,000 6,000 8,000 10,000 12,000

0 0 u* = 0 u = WobRbμsb

Time (seconds) u = WobRbμsb

100 150 u = K1

t .. . [Ω – φr

( 0 )] d + K2 (Ω – φr ) + K3 (φr – φb .

) + u*, u* = W ob

Rb μsb = Tsb u* = 0 u* = 0

Different controllers have been proposed to eliminate stick-slip oscillations.32,42,43,45–49

They aim to establish the values of Wob, u and Ω

that ensure a drillstring free of bit-sticking phenomena. These controllers lead to similar results. Consequently, here, and only as an example, a quite simple controller is presented. This controller is a proportional integral (PI)-type controller proposed in reference 31:

Ω

If a feedback control input was used for u, and given a (Wob, Ω), the ranges for the torque u in order to avoid bit-sticking phenomena could

be established in a more accurate way.

Can We Eliminate the Bit-sticking Phenomena? In this article, only the torque u will be considered as the control input that can modify the drillstring behaviour. A dynamic controller could also be considered for the Wob, as presented by Navarro López et al.27

(6) u* = 0

In Figure 5, the results of applying this control to the drillstring of three DOF are presented. As analysed in reference 31, the permanent stuck-bit situation is eliminated by including u* in u. Furthermore, the control goal of eliminating bit-sticking phenomena is also achieved for typical drilling rotary velocities Ω.

Conclusion 50 Time (seconds) A: Velocities; B: Weight of bit (Wob) = 74,386N, desired rotary velocities (Ω) = 12 radians per second.

The Role of a Dynamic Model in the Prevention of Bit-sticking Phenomena

By using a dynamic model for describing the behaviour of the key elements of a drillstring, and by applying dynamical systems analysis

tools, we can establish ranges of Wob, Ω and u that lead to safe drilling operations.

By means of a bifurcation analysis we can obtain graphics such as the

one shown in Figure 4. As long as we restrict to values of (Wob, u, Ω) for which the equilibrium of the system is stable, avoiding the curves corresponding to Hopf bifurcations and unstable and periodic orbits branches, we will avoid bit-sticking phenomena.

1. 2.

Spanos PD, et al., Oil and gas well drilling: A vibrations perspective, Shock and Vibration Digest, 2003;35(2):85–103.

Navarro-López EM, Notas Acerca del Modelado, Análisis y Control de las Vibraciones Mecánicas en una Sarta de Perforación, Drilling Monograph, Instituto Mexicano del Petróleo, IMP, June 2003.

3.

Challamel N, et al., A stick-slip analysis based on rock/bit interaction: Theoretical and experimental contribution, Proceedings of the IACD/SPE Drilling Conference, New Orleans, February 2000.

4. 5.

Dykstra MW, et al., Drillstring component mass imbalance: A major source of downhole vibrations, SPE Drilling and Completion, 1996;2(4):234–41.

Brett JF, The genesis of torsional drillstring vibrations, 100 150

can be very useful for controlling the old but still challenging problem of modelling, analysis and control of mechanical vibrations in drillstrings. n

Acknowledgements

I will be always grateful to Professor Rodolfo Suárez Cortez of the Instituto Mexicano del Petróleo (IMP) for having invited me to work on this topic in 2002, and for being such a supportive guide and incomparable human being. I am also thankful for the support of the Research Council UK (EP/E50048/1) and the EPSRC-funded project DYVERSE: A New Kind of Control for Hybrid Systems (EP/I001689/1).

SPE Drilling Engineering, 1992;168–74. 6. 7.

Henneuse H, Surface detection of vibrations and drilling optimization: Field experience, Proceedings of the IADC/SPE Drilling Conference, New Orleans, 1998;409–23.

Kriesels PC, et al., Cost savings through an integrated approach to drillstring vibration control, Proceedings of the SPE/IADC Middle East Drilling Technology Conference, Abu Dhabi, 1999.

8. 9.

Finnie I, Bailey JJ, An experimental study of drill-string vibration, J Eng Ind Trans ASME, 1960;129–35.

Cunningham RA, Analysis of downhole measurements of drill string forces and motions, J Eng Ind Trans ASME, 1968; 208–16.

10. Close DA, et al., Measurement of BHA vibration using MWD,

Proceedings of the IADC/SPE Drilling Conference, Dallas, Texas, 1988;659–68.

11. Jansen JD, Non-linear rotor dynamics as applied to oilwell drillstring vibrations, J Sound Vib, 1991;147(1):115–35.

12. van der Heijden GHM, Nonlinear Drillstring Dynamics. A Quest for the Origin of Chaotic Vibrations, PhD thesis, University of Utrecht, The Netherlands, October 1994.

13. Jansen JD, Whirl and chaotic motion of stabilized drill collars, SPE Drilling Engineering, 1992;107–14.

14. Jansen JD, Nonlinear Dynamics of Oilwell Drillstrings, PhD Thesis, Delft University, The Netherlands, 1993.

15. Théron A, et al., The effect of dynamical parameters on precession in rotary drilling, J Energ Resour Tech, 2001;123:181–6.

Bringing together control-engineering methods and dynamical systems analysis tools is pivotal to understand the complex phenomena that occur in a drillstring. The complexity of drilling mechanisms and practices makes the use of automated-type control mechanisms difficult. Consequently, the control device must be interpreted as an offline safe-parameter selection method to guide the driller in order to design the well-drilling profile. Novel perspectives in the modelling and control of complex dynamic systems, such as the paradigms of hybrid dynamic systems,50

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EXPLORATION & PRODUCTION – VOLUME 8 ISSUE 2

τ

τ

Control u (Nm)

Velocities (radians per second)

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