Abstract: This paper analyzes the buckling characteristics of drilling string in curved wells under the influence of torque. The buckling differential equation and the buckling critical load calculation model of drilling string in a curved wellbore are derived. The finite element models of drilling string in buildup and drop-off sections are established for ϕ127.0 mm drilling pipes in a ϕ215.9 mm wellbore, and the buckling characteristics of drilling strings with and without torque are compared and analyzed. The results show that the sinusoidal buckling configuration of drilling string is not related to torque. It is only decided by the axial load on drilling string. Torque has great influence on spiral buckling configuration. The relative error between the critical buckling loads of drilling strings obtained by numerical simulation under different build-up rates and analytical solution is within 15%, which proves the reliability of numerical simulation. When torque is applied in curved wellbore, the helical angular displacement increases, and the corresponding critical sinusoidal and helical buckling loads decrease. Sinusoidal buckling of drilling string does not change much, and torque has more influence on spiral buckling deformation. In the buildup section, sinusoidal and spiral buckling start at the top of the drilling string, while the bottom of the drilling string maintains a balanced state. In the drop-off section, when the torque is not considered, the initial sinusoidal buckling and spiral buckling first appear at the lower part of the drilling string. When the torque is considered, the initial sinusoidal buckling appears at the upper part of the drilling string, while the initial spiral buckling appears at both the upper and lower parts of the drilling string. Compared with the buildup section, the critical axial loads of drilling string buckling in the drop-off section are very small, which indicates that the possibility of buckling in the buildup section is relatively small, while that in the drop-off section is much easer to occur. The results are expected to provide a reference for the design, buckling control, and strength check of drilling strings in horizontal and extended reach wells.

Key words: curved hole, buckling, torque, numerical simulation, analytical solution