Abstract
Abstract
Oilwell drilling is often accompanied by self-excited stick-slip vibrations. This type of motion may also excite severe axial and lateral vibrations in the bottom hole assembly, causing damage to the equipment. This paper presents a fully coupled model for axial, bending and torsional vibrations, and an active control strategy for stick-slip vibrations. The proposed model includes the mutual dependence of these vibrations, as well as their related effects such as, bit/formation and drillstring/borehole wall interactions. The control strategy is based on optimal state feedback control designed to control the drillstring rotational motion. Simulation results are in close qualitative agreement with field observations regarding stick-slip vibrations. It is shown that the proposed control is effective in suppressing stick-slip vibrations once they are initiated. It is also demonstrated, that axial vibrations help in reducing stick-slip vibrations and the control effort. However, care must be taken in selecting a set of operating parameters to avoid transient instabilities in the axial and lateral motions.
Introduction
It is well known that stick-slip vibrations are detrimental to the service life of oilwell drillstrings and down-hole equipment. Large cyclic stresses induced by this type of motion can lead to fatigue problems. In addition, the high bit speed level in the slip phase can excite severe axial and lateral vibrations in the bottom hole assembly, which may cause bit bounce, excessive bit wear and reduction in the penetration rate. Stick-slip vibrations are self-excited, and generally disappear as the rotary table speed is increased beyond a threshold value. However, increasing the rotary speed may cause lateral problems such as backward and forward whirling, impacts with the borehole wall and parametric instabilities. Therefore, it is desirable to extend the range of safe drilling speeds. In order to achieve this, a proper understanding of the coupled dynamics of drillstrings is necessary. For this reason drillstring vibrations and ways to control them have received a lot of attention in recent years [1–8].
The control methods include operational guidelines to avoid, eliminate or reduce torsional vibrations as well as active control methods using feedback. Although most proposed control methods have been shown to be successful in controlling torsional vibrations, the effects of this control on bending vibrations have not been studied. In order to design and implement an effective control system, a coupled model is essential for identifying the critical speeds as well as predicting the behavior of the whole system [9]. Recently, the authors proposed a model that considers the full coupling between torsional and lateral vibrations of actively controlled drillstrings [10]. The proposed model was demonstrated to be quite realistic with respect to stick-slip vibrations, which were effectively eliminated through an optimal state feedback control scheme. In the current paper, this model is extended to include the effects of axial motion. The Weight-on-Bit (WOB) and Torque-on-Bit (TOB) expressions are more realistic since they are directly related to the axial and torsional motions. Simulation results show that axial vibrations have a positive effect in reducing stick-slip vibrations and the control effort. However, control of torsional vibrations may have negative effects in increasing axial and lateral vibrations. Therefore, care must be taken in selecting the operating parameters.
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