Ensuring Well Stability in the Arctic: An Analytical Method for Estimating the Permafrost Thaw Radius

Thermal interaction between oil and gas wells and permafrost rocks leads to their thawing which can cause infrastructure deformation, greenhouse gas emissions, and landscape degradation. This paper presents a simplified engineering method for estimating the thaw radius around a cylindrical well with a constant wall temperature. Based on the Stefan condition and a quasi-steady-state temperature distribution in the thawed zone, an analytical formula (Equation 9) is derived. This formula explicitly relates the thaw radius to the well radius, thermal conductivity of the thawed soil, ice content, and latent heat of fusion, wall temperature, and time. The method accounts for the heterogeneity of the geological profile by identifying intervals with average thermophysical properties. Calculations for typical permafrost conditions (loam, ice content of 0.3, initial temperature - 2 °C, wall temperature - 5 °C) show that the thaw radius reaches 4.3 m after three years and exceeds 14 m after ten years at a wall temperature of 6 °C. Ice content slows down thawing, while high thermal conductivity accelerates it. The proposed formula has been verified by comparison with a finite-difference numerical model and the Kutasov–Eppelbaum method; the discrepancy does not exceed 15 %, which is acceptable for conservative engineering estimates. The method is suitable for rapid calculations to account for depth-dependent variations in permafrost properties. The results contribute to sustainable infrastructure design in permafrost regions by enabling quantitative assessment of safe well spacing, selection of operational regimes, and well thermal protection methods.