*3.1. Validation*

To validate the proposed transient heat transfer model, we compared the calculated temperature with the data from Yang et al.'s paper [18]. The necessary input parameters used are the same as those of Yang et al.'s work, as presented in Table 1. The model well has a total depth of 4900 m and 124 ◦C at the bottom-hole depth, a relatively deep high-temperature well in an operational manner. In the high-temperature well, thermal disturbance in the formation can be distinctively identified because heat exchange between the cold drilling fluid and formation remarkably occurs. The circulation time is 24 h, and the circulation rate is 18 L/s (approximately 285 gallons/min), which is the typical range of a drilling operational condition. Considering the high formation pressure in the deep well, we use slightly heavy mud with 1.2 kg/m<sup>3</sup> of mud density. We assume zero casing thickness with the negligible thermal resistance of the casing.

**Table 1.** Parameters of drilling operation and formation.


This work describes thermal disturbance in the radial direction. We validated our radial temperature estimation at the drilling hole, the annulus, and the wellbore wall (Figure 4). Though there is a slight difference in the lower depth near the bottom hole, the overall temperature distributions in all three cases are consistent with the reference data.

**Figure 4.** Comparison of calculated temperature with reference data.
