A theoretical study of the critical external pressure for casing collapse

• A new casing collapse model while considering the elastic and plastic regions is proposed.
• The effects of wall thickness variation, ovality and non-uniform external pressure are considered.
• The effects of axial force, bending moment and torque are included.

A new theoretical casing collapse model is proposed on the basis of a refined reduced modulus calculation method. The reduced modulus of considers the co-existence of the elastic and plastic regions on the casing cross section. The collapse pressure for an ideal circular casing is expressed as a weighted harmonic sum of the critical elastic pressure and casing yielding pressure. Three kinds of casing imperfections including the wall thickness variation, ovality and non-uniform external pressure on casing collapse are further considered to amend the ideal casing collapse model. The equivalent wall thickness due to wall thickness variation is introduced, and the critical elastic pressure and yielding pressure under the effects of initial ovality and non-uniform external pressure are obtained. On this basis, the collapse pressure for an oval casing with thickness variation under non-uniform external pressure is obtained with superposition principle. The effects of axial force, bending moment and torque on collapse pressure are included with the reduced yielding point. All the above factors are integrated into a unified casing collapse model. At last, the comparison between the new model and API specification is further discussed. The results indicate that the new model gives a more sophisticated description of casing collapse problem. Introducing the casing imperfections improves the consistency between the theoretical and experimental results at the transition between elastic and plastic ranges. The non-uniform external pressure plays the most important role in the casing collapse problem. The existence of non-uniform external pressure, axial force, bending moment and torque also reduces the critical casing collapse pressure a lot.