Analysis of nonlinear vibration of lateral-torsional coupling for drill string in deviated well

To clarify the motion characteristic of the drill string in deviated well, the nonlinear dynamic model of lateral-torsional coupling for drill string system is established by the Lagrange equation. This model incorporates the contact between the drill string and borehole wall, torque dissipation, and borehole trajectory effects. Additionally, the contact behavior using linear elastic contact model is simulated. Meanwhile, the torque transfer law in the drill string system is described by a discrete torque-drag model. Finally, numerical simulations are employed to determine the dynamic properties of the drill string system. The results reveal that friction losses in drill string systems are increased with higher well inclination angles. The motion of BHA along the x direction is predominantly concentrated near the wellhole center at inclination angle of 65 degrees, while in the y direction it primarily focuses on the low side of the wellhole. An increase in inclination angle leads to a more prominent occurrence of stick-slip motion in the drill string. When inclination angle more than 25 degrees, there is a slightly higher collision frequency observed between the BHA and the low side of the borehole wall compared to that with the upper side. When increasing the WOB (weight on bit) to 160 kN, stick-slip motion becomes more pronounced within the drill string. Through parametric dynamics analysis of the drill string system, the rotary speed can be controlled in range from 40 to 70 r/min, and the WOB should be restricted in range from 20 to 40 kN in well depth 5000 m.