A nonlinear dynamic model for characterizing downhole motions of drill-string in a deviated well

- A new model is developed to characterize the motions of drillstring.
- The stick-slip, the deformation, and the fluid damping effects are considered
- Recognize the movement behavior of drill-string in different inclinations.
- Point out the main reason for causing drillstring wear out and key seating.

In this article, a nonlinear dynamic model with four degree-of-freedom (DOF) was established to characterize the behavior of drill-string in a deviated well. It should be noted that the stick-slip phenomenon, the lateral and torsional deformations of the drill-string, meanwhile, the fluid damping effects were taken into account. The space-state analysis method was employed to obtain a reduced-order model which could be solved by the Runge-Kutta numerical method. Effects of different inclinations (α) on nonlinear motions were illustrated qualitatively. These investigations revealed that the contact area between drill-string and hole wall is increased due to the gravity in the horizontal section (α=90∘), thus leading to the increase of friction torque. Drill-string creeps along the hole wall towards its rotational direction range in a 30° fan-shaped region, which is located at the low-side of borehole. When the torque is built up to a certain level that is enough to overcome the friction torque, drill-string will suddenly tumble and go to the next irregular cycle. The local friction contact is reflected as the stick-slip ring and tumbling at low-side of borehole, which is one of the main reasons for causing drill-string wear out and key seating. With the decrease of the inclination, the stick-slip and tumbling motions are weakened gradually even transferred into pure rotational motion in wellbore eventually. Phase portrait projection of the rotor's lateral motion was introduced to identify different motion states such as creeping, stick-slip and tumbling. The study provides a theoretical understanding of the nonlinear motion of the drill-string in non-vertical well. It can help us rediscover the key seating and can be used to better understand the downhole working conditions so as to guide field drilling.