A Comparative Study on the Calculation Accuracy of Numerical and Analytical Models for Wellbore Temperature in Ultra-Deep Wells

The accurate prediction of wellbore temperature during drilling is the key factor in the scientific evaluation of wellbore fluid flow safety and pressure control. Therefore, based on the principle of energy conservation between wellbore and formation in each area, the numerical and analytical models for wellbore-formation heat transfer were built. The fully implicit finite difference method and the analytical method were adopted to solve the mathematical models, respectively. Given the wellbore structure and drilling parameters of an ultra-deep well in Shunbei Oilfield, calculation accuracy of the above two models on the calculation results and the influencing factors were analyzed from the aspect of the heat transfer mechanism. The analysis showed that during drilling, the annular fluid temperature in the lower well section was lower than the original ground temperature, while the fluid temperature in the upper well section was higher than it. In the analytical model, a simplified dimensionless time function was used to represent the quasi-steady state heat exchange mode from distant formations to near well walls, and the comprehensive heat transfer coefficient was employed to characterize the total heat exchange between the formation and annulus, and between the annulus and the interior of the drill string. As a result, the wellbore-formation heat exchange was reduced, and thus the calculated fluid temperature in the annulus and drill string was lower than the result from numerical simulations. The results revealed that the calculated results of the heat transfer model were highly consistent with the downhole measurements, while the errors of the numerical solution and analytical solution were 1.46% and 6.94%, respectively, with a difference of 13.15 ℃. The research results provide a theoretical basis for an in-depth understanding of the wellbore-formation heat transfer mechanism and the accurate evaluation of the temperature field during drilling.