Modeling of Torsional Vibrations Dynamic in Drill-String by Using PI-Observer

Torsional vibrations, appeared in drill string of oil well, are one of the major cause of drilling failures, in most of cases the penetration rate reduction and drilling costs expansion. The driller’s intervention is basically based on parameters manipulation to mitigate torsional vibrations, precisely variation of the angular velocity of the Top drive. The weight on bit variation is also proven to be practically effective in the reduction of such vibration but with a considerable time delay. In this paper, we modeled the nonlinear dynamic of the down hole using a PI Observer, thus, we estimate the downhole angular speed and perceive the torsional vibrations as soon as they appear so that the time delay is minimized. The obtained model is useful to design robust controller to mitigate the torsional vibrations in real-time.