Laplace-Based Analytical Modeling of Transient Wellbore-Formation Heat Transfer during Drilling Fluid Circulation

Summary To address the low efficiency and mesh dependence of numerical simulations for predicting the transient wellbore/formation temperature field during drilling fluid circulation, we develop an unsteady coupled analytical model based on Laplace transforms and Duhamel’s theorem. A 1D unsteady energy equation is formulated for the circulating fluid in the drillpipe and annulus, while the surrounding formation is described by a 2D radial transient conduction model. The two domains are coupled through interface boundary conditions, yielding closed-form solutions for both wellbore and formation temperatures. Model predictions are validated against finite element simulations and field temperature measurements, showing agreement while reducing computation time by two to four orders of magnitude. Parametric analyses indicate that circulation time and formation thermal properties largely control the extent of formation thermal disturbance, whereas flow rate, inlet temperature, and fluid heat capacity primarily govern the wellbore temperature profile. The results reveal a trade-off: Increasing flow rate or fluid heat capacity can not only improve wellbore cooling but can elevate thermal stress risk at the well wall. The proposed model enables rapid thermal assessment and supports operational optimization for safer and more energy-efficient circulation design.