A control oriented guided tour in oilwell drilling vibration modeling

In tunnel excavation that integrates Resonant Sonic Head Drilling (RSHD) machine, one of the important stability problem to deal with is represented by the necessity to assign axial vibration amplitude induced by the RSHD to a resonant vibration mode. In general, a control law depends on system variables which are partially available for measurements. In drilling operation, the drillstring variables at the tip boundary aren't easy, if not impossible, to be measured. The sonic drillstring infinite dimension dynamics, derived in this paper, will play an important role in PDE (Partial Derivative Equation) observer design for the drill bit motion. The well-posedness problem is addressed, and the designed PDE-observer stability is detailed using the resolvent method. The wave peak amplitude is determined from the resonant drillstring mode shape, and the system's stability is analyzed around a practical frequency mode.

show abstract

“…So u ∈ H 2 (0, L ) verifies (18), (20) and we recover u, w 1 = u (0) , z 1 = u (L ) and v ∈ H 1 (0 , L ) and thus by (21) , we obtain w…”

Section: Well-posednessmentioning

confidence: 85%

“…Thus, this phenomena has intensively studied in the literature. One may refer to Saldivar et al [18] and Zhao [21] and references therein.…”

Section: Mathematical Modelmentioning

confidence: 99%

Reconstructed drill-bit motion for sonic drillstring dynamics

Ammari

Béji

2019

European Journal of Control

View full text Add to dashboard Cite

show abstract

“…The book [38] (chap. 2) and the survey [40] provide overviews of these techniques, which are, basically, of four kinds. To better motivate the model used in the sequel, a brief overview of the existing modeling tools is proposed but the reader can refer to [40] and the original papers to get a better understanding of how the models are constructed.…”

Section: Model Descriptionmentioning

confidence: 99%

“…There is a viscous damping at x = 0, and consequently a mismatch between the applied torque at the top and the angular speed. The topside boundary condition for the axial part is built on the same scheme and the following , [40].…”

Section: B Distributed Parameter Models (Dpm)mentioning

confidence: 99%

Practical Stability Analysis of a Drilling Pipe Under Friction With a PI-Controller

Barreau

Gouaisbaut

Seuret

2021

IEEE Trans. Contr. Syst. Technol.

View full text Add to dashboard Cite

This paper deals with the stability analysis of a drilling pipe controlled by a PI controller. The model is a coupled ODE / PDE and is consequently of infinite dimension. Using recent advances in time-delay systems, we derive a new Lyapunov functional based on a state extension made up of projections of the Riemann coordinates. First, we will provide an exponential stability result expressed using the LMI framework. This result is dedicated to a linear version of the torsional dynamic. On a second hand, the influence of the nonlinear friction force, which may generate the well-known stick-slip phenomenon, is analyzed through a new stability theorem. Numerical simulations show the effectiveness of the method and that the stick-slip oscillations cannot be weaken using a PI controller.

show abstract

“…In recent years there have been many attempts to model the drill-string behaviour with focus on the vibrations and control. Saldivar et al [7] reviewed the existing drilling models and classified them into a few categories such as distributed parameter, coupled Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) and lumped parameter ones. The latest category has an advantage of describing the system dynamics in a simple way, thereby simplifying the analysis for the controller design.…”

Section: Introductionmentioning

confidence: 99%

Suppression of drill-string stick–slip vibration by sliding mode control: Numerical and experimental studies

Vaziri¹,

Kapitaniak²,

Wiercigroch³

2018

Eur. J. Appl. Math

View full text Add to dashboard Cite

We investigate experimentally and numerically suppression of drill-string torsional vibration while drilling by using a sliding mode control. The experiments are conducted on the novel experimental drill-string dynamics rig developed at the University of Aberdeen (Wiercigroch, M., 2010, Modelling and Analysis of BHA and Drill-string Vibrations) and using commercial Polycrystalline Diamond Compact (PDC) drill-bits and rock-samples. A mathematical model of the experimental setup, which takes into account the dynamics of the drill-string and the driving motor, is constructed. Physical parameters of the experimental rig are identified in order to calibrate the mathematical model and consequently to ensure robust predictions and a close agreement between experimental and numerical results for stick–slip vibration is shown. Then, a sliding mode control method is employed to suppress stick–slip vibration. A special attention is paid to prove the Lyapunov stability of the controller in presence of model parameter uncertainties by defining a robust Lyapunov function. Again experimental and numerical results for the control cases are in a close agreement. Stick–slip vibration is eliminated and a significant reduction in vibration amplitude has been observed when using the sliding controller.

show abstract

A control oriented guided tour in oilwell drilling vibration modeling

Cited by 60 publications

References 40 publications

Reconstructed drill-bit motion for sonic drillstring dynamics

Reconstructed drill-bit motion for sonic drillstring dynamics

Practical Stability Analysis of a Drilling Pipe Under Friction With a PI-Controller

Suppression of drill-string stick–slip vibration by sliding mode control: Numerical and experimental studies

Contact Info

Product

Resources

About