Numerical analysis of drill string whirl for vertical well based on rolling model and small-strain shell element

Whirl is a kind of serious lateral vibration. Accurate numerical simulation of whirl for drill string is important for drilling engineering. In this study, a new finite element (FE) model using shell element is established, which can accurately describe the whirl and realize the visualization of motion. Rolling model of drill string in the borehole is proposed. Kinematic contact with clearance, Coulomb friction model and initial imperfection are considered in this model. The explicit dynamic method is selected to solve the convergence difficulty caused by complex contact between shell elements. Compared with the experiment results, the accuracy and reliability of the model are verified. Meanwhile, the effects of rotation speed, friction coefficient, weight-on-bit (WOB) and clearance between the drill string and the borehole wall on the whirl of vertical wells are also studied in the numerical simulation. The rotation speed and friction coefficient have an obvious positive effect on the random motion and backward whirl of drill string: The continuous increase of rotation speed or friction coefficient can cause backward whirl, after that, velocity, acceleration of drill string, contact force and friction will increase signifi-cantly. When the rotating speed increases from 400 rpm to 800 rpm, the whirling speed increases by 160%, the average friction and contact force increase by 290%, which is much higher than the increase of 100% of the rotating speed. Instead, WOB has little influence on the drilling parameters mentioned-above and the variations of average friction and contact force for different WOB does not exceed 10%. In addition, properly increasing the distance between the drill string and the borehole wall will make backward whirl easily occur. However, when the clearance is large enough, there will be no contact and the drill string will make irregular non-contact for-ward whirl. What's more, forward whirl has a positive impact on eccentric wear, and backward whirl reduces WOB transmission and increases risk of sticking. Therefore, drill string whirl should be reasonably utilized or its harm should be reduced in practical drilling engineering.