Laplace Transform-Based Modeling of Heat Transfer in Producing Wellbores

Abstract

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 oil-producing 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 pseudo-steady-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.