Buckling of tubular strings in curved wells

A general theory for buckling of tubular strings is given. The theory is based on basic differential equations for force and moment balance and on the minimum energy principle. Two buckling modes are discussed, particularly: sinusoidal buckling and helical buckling. The derivation of the critical force for sinusoidal buckling confirms earlier works. This theory, however, predicts a critical force for helical buckling that is 2.5% higher than formulas available in the literature. In contrast to most literature in the field, the theory presented here is not restricted to straight wells but also applies to curved wells. Included in the paper are also numerical results on contact forces, compression and pitch length for super-critical forces. Finally, the validity of the theory and the derived results is discussed. It is concluded that most of the simplifying assumptions upon which the theory is based, are well satisfied in real cases. However, the assumption of a perfectly straight string geometry may represent a limitation when applying the theory to coiled tubing with a high residual bending.