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<p>Stick–slip vibration in ultra-deep drill strings is highly nonlinear under high-temperature and high-pressure downhole conditions, but thermo-hydro-mechanical (THM) coupling remains insufficiently represented in existing models. This study develops a THM-coupled axial–torsional distributed-parameter model that accounts for temperature-dependent material properties, temperature- and pressure-dependent drilling-fluid damping, and thermo-mechanical damage at the bit-rock interface. A thermo-mechanical time-delayed bit-rock interaction (T-BRI) model is introduced, and the governing equations are solved using a velocity-Verlet symplectic scheme. As the well depth increases from 1200 to 6200&#xa0;m, the response shifts from low-order periodic oscillations to multi-frequency nonlinear vibrations, with stronger axial–torsional modal interaction. At 6200&#xa0;m, THM coupling reduces drilling-fluid viscosity by 48.8%, weakens system damping, and removes the transient stable interval of approximately 700–800&#xa0;s under the investigated condition. The T-BRI model captures the nonlinear competition between rock thermal softening and bit thermal degradation. A relatively stable operating window occurs at 400–600 °C, whereas severe thermal degradation above 700 °C intensifies system instability. These results support temperature-dependent parameter selection for mitigating stick–slip vibration in ultra-deep drilling.</p> Graphical abstract <p></p>

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Nonlinear dynamics analysis and hierarchical parameter optimization of ultra-deep drill string stick–slip vibrations under full THM coupling

  • 期刊论文

  • 发表日期：

    2026年7月31日

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  • Zhen Yuan,
  • Liang Guo,
  • Long Jiang,
  • Yuangang Wu,
  • Xiuwen Zhao,
  • Benjie Li

摘要

Stick–slip vibration in ultra-deep drill strings is highly nonlinear under high-temperature and high-pressure downhole conditions, but thermo-hydro-mechanical (THM) coupling remains insufficiently represented in existing models. This study develops a THM-coupled axial–torsional distributed-parameter model that accounts for temperature-dependent material properties, temperature- and pressure-dependent drilling-fluid damping, and thermo-mechanical damage at the bit-rock interface. A thermo-mechanical time-delayed bit-rock interaction (T-BRI) model is introduced, and the governing equations are solved using a velocity-Verlet symplectic scheme. As the well depth increases from 1200 to 6200 m, the response shifts from low-order periodic oscillations to multi-frequency nonlinear vibrations, with stronger axial–torsional modal interaction. At 6200 m, THM coupling reduces drilling-fluid viscosity by 48.8%, weakens system damping, and removes the transient stable interval of approximately 700–800 s under the investigated condition. The T-BRI model captures the nonlinear competition between rock thermal softening and bit thermal degradation. A relatively stable operating window occurs at 400–600 °C, whereas severe thermal degradation above 700 °C intensifies system instability. These results support temperature-dependent parameter selection for mitigating stick–slip vibration in ultra-deep drilling.

Graphical abstract