Dynamic Calibration of Wellbore Circulation Temperature Model Using the Unscented Kalman Filter

Summary Deep and ultra-deep wells are characterized by extreme temperature and pressure conditions, which significantly complicate wellbore flow and heat transfer processes. Precise determination of the convective heat transfer coefficient (CHTC) is essential for reliably forecasting wellbore temperature profiles. However, the CHTC assumed in the traditional wellbore temperature prediction model is a fixed value, ignoring the influence of changes in flow conditions (such as flow type on the CHTC), making it difficult to achieve fine prediction and update of the wellbore temperature profile. In this paper, we construct a CHTC calibration and wellbore temperature dynamic update model based on the unscented Kalman filter (UKF) algorithm. Mathematical models of different heat transfer control bodies are constructed based on the energy conservation equation. The governing equations are discretized using the finite difference method, and the Gauss-Seidel iteration is used to solve them collectively to obtain the wellbore temperature distribution. Field-measured data of three real wells are used to validate the proposed model, and the mean relative errors (MREs) of the bottomhole temperature (BHT) and outlet temperature (OLT) are less than 5%. Furthermore, based on the actual measurement while drilling (MWD) data, the UKF algorithm is used to correct the CHTC profile in the annulus, and the wellbore temperature profiles are dynamically updated in real time. The validation results indicate that the dynamic calibration model achieves a MRE of 0.21% and a mean absolute error (MAE) of 0.34°C in BHT prediction. The wellbore temperature dynamic update model proposed in this paper provides a novel method for accurate prediction of wellbore temperature.