Build-Up Rate Prediction for Point-the-Bit Rotary Steerable System Based on 3D Dynamic Finite Element Method

Point-the-bit rotary steerable systems (RSSs) achieve trajectory build-up through the coupled action of internal steering offset, bit attitude change, bottom hole assembly (BHA) flexure, and nonlinear wellbore interaction. Unlike conventional rigid or quasi-static BUR models, this study developed a 3D dynamic finite element model for point-the-bit RSS. The drill string was discretized using Euler–Bernoulli beam elements, with an equivalent “hinge-deflection angle” constraint introduced at the steering unit. Relative angle loading was imposed using the penalty function method, with nonlinear boundary conditions (bit–formation interaction and borehole friction) coupled into the model. Based on the established model, the effects of deflection angle, weight on bit (WOB), and rotary speed were systematically quantified. The results show that when the deflection angle increases from 0.5° to 1.5°, the average BUR rises from 1.452°/30 m to 4.251°/30 m; when the WOB increases from 60 kN to 100 kN, the average BUR increases from 2.281°/30 m to 2.814°/30 m. Within the range of 50–90 r/min, rotary speed has a limited effect on the average BUR, but it can alter the characteristics of transient fluctuations. This approach provides a robust theoretical basis for BUR evaluation, parameter optimization, and control strategy design for rotary steerable tools.