Prediction of Annular Pressure Under Wellhead Uplift Load in Deepwater Subsea Wells

To address the large deviation in annular trapped pressure prediction during testing and production stages of deepwater high-temperature and high-pressure wells, conventional models neglect the elastic uplift effect of the wellhead. This study overcomes the limitations of the plane strain model and establishes a three-dimensional thermos–hydro–mechanical coupled annular pressure prediction model based on the longitudinal stiffness constraint of the subsea wellhead. The deepwater wellbore–formation system is treated as a composite elastic structure. A generalized plane strain assumption is introduced to define the elastic boundary conditions and longitudinal segmentation characteristics of the wellhead. Based on generalized Hooke’s law, the three-dimensional stress–strain constitutive equation of casing is modified. A displacement model incorporating axial–radial coupling is derived, and an equivalent longitudinal stiffness coefficient of the wellhead is introduced. A coupled axial force equilibrium equation and a three-dimensional annular volume compatibility equation are established. Considering multi-annulus coupling, a volume compatibility matrix equation is formulated, and a successive approximation iterative algorithm with a relaxation factor is developed. Using a deepwater high-temperature, high-pressure gas well in the South China Sea as a case study, the effects of wellhead stiffness, free section length, and annular temperature rise on annular pressure are investigated via a single-variable method and compared with traditional rigid models. Results show that the subsea wellhead exhibits elastic uplift behavior. Its longitudinal stiffness has a reverse S-shaped nonlinear influence on annular pressure. Increasing the free section length significantly reduces annular pressure. The proposed model predicts values 17–21% lower than traditional rigid models, providing a more realistic representation of annular pressure evolution. The findings offer theoretical support and engineering guidance for deepwater well integrity design and annular pressure risk management.