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.
Guan et al. (Mon,) studied this question.