Drilling geothermal and high-pressure, high-temperature (HPHT) wells can present significant challenges to drilling automation and well control due to extreme formation temperatures and elevated pressures. Proactive management of both downhole pressure and temperature is crucial to maintaining wellbore integrity, ensuring the functionality of downhole tools, and preventing well loss. Despite separate advancements in managed pressure drilling (MPD) and managed temperature drilling (MTD), integrated managed pressure and temperature drilling (MPD-MTD) has not yet been addressed. This paper introduces an integrated MPD-MTD control framework based on improved reduced drift-flux model (RDFM) that incorporates temperature dynamics, interface mass transfer, and a new lumped pressure dynamics model to describe geothermal and HPHT drilling. The proposed MPD-MTD control strategy utilizes MPD choke adjustments, flow rate modulation, and mud cooling to simultaneously regulate downhole pressure and temperature. System identification techniques are adopted to develop a reduced-order model that captures the key thermal-pressure dynamics. This reduced model simplifies the thermal-hydraulic interactions, allowing for efficient and yet accurate controller design. Based on this reduced-order model, a multi-input-multi-output (MIMO) controller was developed to simultaneously control both the bottomhole pressure and temperature. Simulations were conducted to demonstrate the utility of the developed MIMO controller. Various drilling scenarios and control actuations were evaluated, showing that the proposed integrated MPD-MTD under the MIMO control framework outperforms the decoupled MPD and MTD control strategies with respect to the stabilization time, overshot, and robustness for both downhole temperature and pressure.

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