A Toolface Prediction Model Considering Nonlinear Wellbore Friction for Directional Coring Drilling Tool

In directional coring drilling, toolface adjustment is performed during drilling interruption by rotating the drill string through the top drive. Because the bottom-hole toolface angle cannot be transmitted to the surface in real time, a dynamic prediction model is required to guide toolface control. Existing flexible drill string models, however, generally neglect the nonlinear wellbore friction caused by stick–slip motion, reducing prediction accuracy. To address this issue, a distributed-parameter torsional dynamic model is established and discretized into a multi-degree-of-freedom system. A friction-state-based prediction–correction iterative algorithm is proposed to resolve the strong coupling between wellbore friction and system dynamics. At each time step, the sticking or slipping state is identified from the predicted motion, and the wellbore friction torque is iteratively updated until the friction state and dynamic equilibrium simultaneously converge, enabling accurate prediction of the drill bit toolface angle. Simulation results show that the proposed model captures the key dynamic characteristics of toolface adjustment. Under typical operating conditions, the drill bit start-up delay is 3.53 s, the peak angular velocity reaches 1.73°/s, and the peak transmitted torque is 2.28 kN·m. After the top drive stops, the drill bit continues rotating because of inertia, resulting in a 2.12° toolface overshoot and an angular lag rate of 21.2%. In addition, the effects of weight on bit, top-drive speed, and equivalent damping on toolface adjustment are quantified, providing guidance for parameter optimization. The proposed method provides a theoretical basis for toolface prediction and control in intelligent directional coring drilling.