During drilling circulation, the wellbore temperature field changes in response to drilling-fluid rheology, borehole geometry, drillstring eccentricity, and cuttings concentration. Conventional wellbore temperature models use fixed heat-transfer parameters and therefore cannot accurately represent real-time heat-transfer conditions. To address this limitation, a transient temperature model was developed. Bottomhole annular-fluid temperatures generated by OLGA were used as synthetic observations for MHE calibration. An MHE-based calibration method was developed to estimate the equivalent heat-transfer correction factor. The temperature model was first benchmarked against the Kabir analytical model and the commercial simulator OLGA. The estimated correction factor was then used by the mechanistic model to update the wellbore temperature field. The results showed that, under different initial values of the correction factor and assumed measurement-noise standard deviations, the equivalent heat-transfer correction factor converged to a steady-state value of approximately 0.941. Additional sensitivity tests showed generally stable calibration performance under moderate parameter settings, whereas stronger observation noise reduced calibration stability and accuracy. Under varying operating conditions, the calibrated bottomhole temperature yielded a mean absolute error of 0.033–0.332 °C, representing a reduction of 45.97–98.73% relative to the corresponding uncalibrated results. When the observation delay was extended to 2400 s (d = 8), the MAE was still reduced by 26.50–68.20% across different operating stages. These numerical results show that the proposed method can use bottomhole temperature observations to dynamically compensate for equivalent heat-transfer model mismatch under the investigated simulation conditions. The method reduces model-prediction errors and improves bottomhole temperature prediction under the tested varying operating conditions. The proposed method has potential applications in wellbore temperature prediction and high-temperature risk assessment for deep-well drilling.

Gas influx during managed pressure drilling alters the annular hydrostatic and frictional pressures as the gas migrates and expands, complicating bottom-hole pressure (BHP) regulation. Control-oriented two-phase-flow models that neglect dynamic gas temperature may inaccurately predict gas expansion and pressure response. This study develops a thermally coupled four-state model and a feedback-linearization-based model predictive control (FL-MPC) strategy for gas migration before the gas reaches the wellhead. The model incorporates the local annular-liquid temperature, interfacial heat transfer, pressure–volume work, and the adopted gas equation of state. The wellhead-pressure-to-BHP channel has a relative degree of two, while the feedback-linearization gain and coordinate transformation remain regular over the investigated trajectory. On the zero-output manifold at 508 bar, the gas-volume derivative remained positive at all 1201 sampled states, with a minimum internal growth coefficient of 2.71 × 10⁻⁴ s⁻¹. In a separate 2500-step OLGA validation case, thermal coupling reduced the gas-temperature RMSE from 6.354 to 0.730 K and the BHP RMSE from 2.199 to 2.091 bar. At the 508 bar setpoint, FL-MPC entered the settling band at step 104, compared with steps 123 and 162 for NMPC and PID, respectively, and achieved an RMSE of 0.814 bar. Its average computation time was 0.195 ms per step, compared with 22.65 ms for NMPC. Robustness tests under small parameter, initial-state, and measurement perturbations maintained BHP tracking and satisfied the actuator constraints.