Torsional Stick–Slip Modeling and Mitigation in Horizontal Wells Considering Non-Newtonian Drilling Fluid Damping and BHA Configuration

Stick–slip vibration leads to accelerated wear of drilling tools and downhole tool failures, particularly in long horizontal sections. Existing drill-string dynamics models and control or digital-twin frameworks have significantly improved our understanding and mitigation of stick–slip, but most of them adopt simplified Newtonian or linear viscous damping and low-degree-of-freedom representations of the drill-string–fluid–BHA system, which can under-represent the influence of non-Newtonian oil-based drilling fluids and detailed BHA design in long horizontal wells. In this study, an n-degree-of-freedom torsional stick–slip vibration model for horizontal wells is developed that explicitly incorporates Herschel–Bulkley non-Newtonian rheological damping of the drilling fluid, distributed friction between the horizontal section and drill string, and bit–rock interaction. The model is implemented in a computational program and calibrated and validated against stick–slip field measurements from four shale-gas horizontal wells in the Luzhou area, showing good agreement in stick–slip frequency and peak angular velocity. Using the Stick–Slip Index (SSI) as a quantitative metric, the influences of rotary table speed, weight on bit (WOB), and bottom-hole assembly (BHA) configuration on stick–slip vibration in a representative case well are systematically analyzed. The results indicate that increasing rotary speed from 64 to 144 r/min progressively reduces stick–slip severity and eliminates it at 144 r/min, reducing WOB from 150 to 60 kN weakens and eventually removes stick–slip at the expense of penetration rate, drill collar length has a non-monotonic impact on SSI with potential high-frequency vibrations at longer lengths, and increasing heavy-weight drill pipe (HWDP) length from 47 to 107 m consistently intensifies stick–slip. Based on these simulations, SSI-based stick–slip severity charts are constructed to provide quantitative guidance for drilling parameter optimization and BHA configuration in field operations.