Static Formation Temperature Inversion in Ultra-Deep Wells Based on an IGWO-RBF Surrogate Model

In ultra-deep well drilling, directly measuring the static formation temperature (SFT) is highly time-consuming, as it requires extended shut-in periods for the wellbore to reach full thermal equilibrium, making it impractical for routine engineering operations. To overcome this challenge, this paper establishes a wellbore–formation transient temperature model (WFTM) and proposes an SFT inversion method based on the Improved Grey Wolf Optimizer (IGWO) and Radial Basis Function (RBF) neural network. The RBF network serves as a surrogate model to replace the WFTM during iterative optimization, avoiding the prohibitive computational cost of repeated WFTM evaluations and enabling rapid prediction of the transient wellbore temperature field. Meanwhile, the IGWO algorithm uses the measured bottomhole circulating temperature (BHCT) as a constraint to optimize the geothermal gradient in SFT inversion. Multi-well validation shows that the RBF surrogate predicts BHCT with relative errors consistently below 1%, demonstrating its effectiveness as a substitute for the WFTM. Compared with the direct iterative approach (IGWO-WFTM), the IGWO-RBF method yields slightly lower SFT inversion accuracy, but this deviation remains within engineering tolerances, and the computational time is reduced by approximately 18 times. Requiring only surface temperature and routinely measured BHCT, the proposed approach offers a practical and efficient pathway for real-time assessment of formation temperature during ultra-deep oil well drilling.