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This paper presents a novel approach to modeling heat transfer in hydrocarbon-producing wells, aiming to simulate Annular Pressure Buildup (APB) in offshore wells. The proposed framework enhances traditional models by incorporating previously overlooked terms in pseudo-steady-state simulators. A Laplace transformation-based formulation of the governing differential equations is developed and solved to achieve better simulation results for shorter timespans. Two actual oilproducing wellbores are used for model validation. The first wellbore, a vertical well with the first annulus partially filled with N2, assesses the new formulation's performance compared to the traditional pseudosteady-state formulation. Additionally, a convergence test is conducted in this well to verify the level of additional computational complexity associated with the new formulation. Simulation results show that slower annuli heating leads to a slower APB, resulting in an 8 MPa difference in predicted pressurization. The second case, from a well undergoing an Extended Well Test, provides field data to simulate wellbore heating due to heat transfer from the production stream. A comparison of the new formulation with the field data demonstrates improved temperature representation within the first few days of production, with an average deviation of 4 K in predicted wellhead-produced fluid temperature.

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