Transient Temperature Modeling and Safe Logging Window Optimization for Ultra-Deep Buried-Hill Wells

High temperatures in ultra-deep buried-hill wells of the Bohai Bay Basin and rapid wellbore temperature recovery after circulation shutdown restrict the available operating time of logging tools. To quantitatively determine the safe logging window, a transient wellbore–formation heat transfer model was developed to simulate the complete circulation cooling and shut-in recovery process. Formation thermal heterogeneity was characterized using lithology, porosity, and shale volume fraction, and the governing equations were solved using a hybrid explicit–implicit finite volume method with refined radial grids near the wellbore and stage-dependent time stepping. The safe logging window was determined according to the allowable operating temperature of logging tools. Field validation in Well M15 yielded a mean absolute error and root mean square error of 0.75 °C and 0.87 °C, respectively, while the relative temperature prediction errors for another 12 wells were all below 5%. Benchmark tests demonstrated that the proposed method reduced computational time by approximately 69% compared with the uniform small-time-step scheme. Under the investigated conditions, increasing the circulation rate from 10 L/s to 30 L/s reduced the bottom-hole temperature from approximately 120 °C to 65 °C, whereas the cooling benefit gradually diminished at higher rates. The safe logging window exhibited clear dependence on measurement depth and tool temperature limits; at 5274.87 m in Well M15, the predicted windows were 3.32 h and 17.78 h for temperature limits of 150 °C and 170 °C, respectively. Sensitivity analysis indicated that the geothermal gradient was the dominant factor affecting the safe window, while thermal conductivity and bedding anisotropy also influenced the prediction results. The proposed model provides a quantitative basis for optimizing circulation cooling strategies and logging timing in ultra-deep buried-hill wells and offers an effective approach for safe logging window evaluation under high-temperature complex geological conditions.