Efficient drilling of geothermal wells hinges on a thorough comprehension of temperature distribution along the wellbore, vital for preventing tool failures and reducing non-productive time (NPT). This involves ascertaining the requisite mud cooling at the surface and optimizing circulation flow rates to extract heat effectively. While extensive theoretical work exists in temperature profiling, practical implementations have been limited. This paper introduces a field-deployable model addressing these challenges through the implementation of a Physics-Informed Machine Learning (PIML) method. This innovative approach distinguishes itself by integrating a physics-based model with real-time data, resulting in a notable enhancement in temperature prediction accuracy. The refined predictions facilitate precise determination of required wellbore cooling and mud flow rates, consequently aiding in extending the lifespan of downhole tools during drilling operations. The physics-based temperature model is developed, considering critical factors such as heat transfer in both axial and radial directions, as well as friction between the fluid and casings/ drill pipes. This construction harnesses the 3D finite difference method (FDM). A dynamic simulation framework seamlessly integrates essential data for development and simulation assimilation, encompassing wellbore survey data, bottom hole assembly (BHA) data, mud properties, and additional contextual information. Real-time data, continuously streamed every second from the drilling rig, undergoes discrete event simulation (DES). Subsequently, this data undergoes processing utilizing an FDM-based engine, generating a dynamic temperature profile of the fluid every five-minute interval at a minimum, if not quicker due to state change. The assimilation of the FDM model is accomplished through the calibration of the geothermal gradient using Ensemble Kalman Filter (EnKF). Observed data, including inlet mud temperature (utilized as FDM input) and outlet mud temperature (compared to FDM output), is incorporated into the assimilation process. This comprehensive approach ensures an accurate representation of downhole temperature dynamics, facilitating proactive measures for enhanced downhole tools functionality and drilling optimization. After constructing the model, validation was conducted using the Utah FORGE dataset to showcase the predictive capability of the FDM model in estimating outlet mud temperature over specific time intervals through assimilation. The assimilated temperature history simulated closely mirrored the actual field data. This algorithm not only showcased proficiency in the temperature prediction but also introduced an innovative approach for calibrating and identifying other input parameters, such as fluid properties in response to potential temperature variations and geothermal gradient. Essentially, the proposed technique leverages the FDM model in inverse, serving as a soft sensor. This approach provides valuable insights for control, planning, and understanding by elucidating parameters that are typically challenging to determine.

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