Nonlinear Modeling and Multidirectional Mitigation of Coupled Axial–Lateral–Torsional Drillstring Vibrations in Deep-Well Drilling

In deep–well drilling, the high slenderness ratio of the drillstring intensifies the coupling among axial, lateral, and torsional vibrations, making the drilling system susceptible to detrimental vibration modes such as stick–slip, whirl, and bit bounce. Most existing downhole vibration–mitigation tools are designed primarily to attenuate vibration in a single direction, and their placement relies largely on field experience; consequently, they are inadequate for controlling multidirectional coupled vibrations in deep wells. In this study, a nonlinear dynamic model for the coupled axial–lateral–torsional vibrations of a full–ength drillstring was developed based on the variational principle and the finite element method. The model incorporates nonlinear drillstring–borehole contact, dynamic bit–rock interaction, and multiphysics coupling among the temperature, pressure, and stress fields. The resulting nonlinear equations of motion were solved using a coupled numerical scheme that combines a modified Newton–Raphson iteration with a modified generalized–α time–integration method. An axial force–torque conversion method and a variable–stiffness matrix replacement method were developed to incorporate the multidirectional vibration–damping tool into the drillstring dynamic model. The vibration responses of drillstrings equipped with 8.5-, 12.25-, and 16-in. drill bits were investigated for different damper locations and drillstring configurations. The results indicate that decreasing the damper-to-bit distance generally improves the mitigation of lateral whirl and torsional stick–slip. The optimal damper-to-bit distances were 75, 50, and 50 m for the 8.5-, 12.25-, and 16-in. drill bits, respectively. For the horizontal section, the optimal installation location was between the stabilizer and the drill collar. The model was validated against field–measured triaxial vibration data from a well on the Yang 101 platform, yielding a peak-response prediction accuracy greater than 85% and an overall agreement greater than 90%. A field trial conducted over the 3300–4100 m interval of the Shiniulan Formation in Well Yang 101X2, Sichuan–Chongqing region, showed that the pre–run simulations identified a sweet-spot window within 50 m of the bit. The detrimental lateral, axial, and torsional vibrations of the drillstring were reduced by 47%, 62%, and 61%, respectively. The rate of penetration increased by 48% relative to that in offset wells in the same area, and more than 80% of the bit cutters remained intact. These results establish a closed–loop optimization workflow integrating pre–run simulation and downhole deployment and provide a theoretical and engineering basis for vibration prediction, drilling–parameter optimization, and vibration–damping tool design in deep oil and gas drilling operations.