Increased tubinghead temperature with increased rate may induce pressure increase in the annuli for the trapped fluid. Managing annular-pressure buildup (APB) for sustaining well deliverability is particularly crucial in subsea wells, where intervention is complicated. Ordinarily, a multistring casing design accommodates anomalous pressure rise from the standpoint of well integrity. However, management of day-to-day operations presents challenges when APB occurs. This study presents mechanistic models for understanding and mitigating APB during production. By preserving mass, momentum, and energy in the wellbore, we developed two approaches involving semisteady-state and transient formulations. The intrinsic idea is to mimic the physical process with minimal input parameters to estimate pressure buildup in the annuli. Our model formulation handles the mechanisms of fluid expansion and fluid influx/efflux quite rigorously. This approach appears to be quite sufficient because we account for most of the cases of APB encountered.