Study on Buckling Mechanical Behavior of Variable Cross-Section Tubing in Ultra-High-Temperature and High-Pressure Gas Wells

Buckling of variable-diameter tubing strings in ultra-high-temperature and high-pressure (UHTHP) deviated wells presents challenges that cannot be addressed by existing uniform-tubing models. This study develops a segmented Euler–Bernoulli buckling model that accounts for stiffness discontinuities at diameter transitions, temperature–pressure-coupled effective axial force, and wellbore-constraint effects. The model is developed for packer-constrained variable-diameter production tubing under UHTHP gas-production conditions. A global transfer matrix formulation is introduced to derive buckling characteristic conditions and critical loads. Results show that reduced stiffness at diameter transitions facilitates localized buckling and promotes the shift from sinusoidal to helical modes as the effective axial force increases. Variations in tubing or casing inner diameter significantly alter buckling-zone lengths and induce abrupt changes in dogleg severity. The proposed model provides a practical analytical framework for predicting the buckling behavior of variable-diameter tubing strings in UHTHP wells and offers guidance for tubing design and well integrity assessment.