Nonlinear Dynamics Analysis and Hierarchical Parameter Optimization of Ultra-Deep Drill String Stick-Slip Vibrations under Full THM Coupling

Addressing the stick-slip vibration challenges of ultra-high-aspect-ratio drill strings in ultra-deep wells under extreme conditions, this study establishes a fully coupled thermo-hydro-mechanical (THM) nonlinear dynamical model. The model incorporates temperature-dependent material constitutive relations and nonlinear fluid damping, while proposing a novel Thermo-mechanical and Time-delayed Bit-Rock Interaction (T-BRI) model accounting for bit thermal equilibrium and rock thermal damage. The Velocity Verlet symplectic algorithm is adopted to solve the model, revealing a "scale effect" in the dynamical response as well depth increases, characterized by limit cycle proliferation and topological degeneration. Thermo-hydraulic coupling analysis indicates that high-temperature-induced "thermal thinning" of drilling fluid causes significant damping attenuation, leading to a sharp shrinkage of the operational safety window. Further multi-dimensional stability analysis demonstrates that localized thermal accumulation at the bit induces stick-slip oscillations in previously stable regimes; however, an optimization window dominated by rock thermal softening is identified in the medium-temperature range (400–600 °C). Finally, a hierarchical parameter optimization strategy based on thermal state feedback is proposed, which suggests that active downhole thermal management serves as a fundamental and effective approach to suppressing stick-slip vibrations in ultra-deep drilling.