A new analytical model of wellbore collapse pressure based on stability theory

Abstract

In theory, the wellbore collapse for the petroleum drilling belongs to the limit point instability, and should be treated as the stability problem, but instead of the strength problem. For this purpose, a new analytical model was established to determine the collapse pressure based on the stability theory. Using the elastoplastic mechanics, the stress and displacement around the wellbore were solved, and the equilibrium path (i.e., the relation between the inner pressure and the radial displacement) was proposed. According to the equilibrium path, it can be found that the wellbore collapse occurs at the end of the plastic softening stage and the beginning of the residual stage. Additionally, a comprehensive numerical validation was performed based on the numerical methods, to examine the proposed analytical model. The stress and displacement around the wellbore by the proposed method agree well with those from the numerical method, with a deviation of less than 8.9%. Finally, the parametric analysis was performed to investigate the effects of the plastic hardening modulus, the plastic softening modulus, the yielding stress, the strength limit and the residual strength on the equilibrium path. The results show that the collapse pressure decreases as the plastic hardening modulus, the plastic softening modulus, the yield limit and the residual strength increasing. On the contrary, an increasing of the strength limit can increase the wellbore collapse pressure, which is different to the common understanding.