Abstract: During the perforation operations in ultra-deep wells,the huge shock wave generated by the detonation of perforating charges can cause severe vibration of the pipe string,potentially leading to string damage.To address this issue,Hamilton's principle is used to develop a longitudinal-transversal-torsional coupling nonlinear dynamic model of the pipe string system,considering the influence of factors such as string-casing wall contact and high temperature and high pressure environment in ultra-deep wells.By integrating the detonation pressure field with the dynamic model,accurate predictions of string vibration under detonation state can be obtained.The research findings are used to study how explosive perforation affects the longitudinal-transversal-torsional coupling vibrations of the pipe string in ultra-deep wells under high temperature and high pressure conditions.The results show that appropriate arrangement of dampers below the packer (20~25 m) can effectively reduce the load on pipe string,suppress the vibration of the string,and prevent adverse collisions between the pipe string and casing and thus protect the dampers from damaging.When a single damper is insufficient for perforation conditions,a dual-damper arrangement can effectively suppress pipe string vibration,reduce the load to pipe string,and extend the service life of the pipe string tools.These findings are of significant importance for reducing the risks of perforation strings.

Key words: perforation string, impact vibration model, ultra-deep well, detonation pressure field, dynamic response, damping arrangement, stress propagation