Theoretical and Simulation Study on the Collapse Strength of a Curved Casing in Horizontal Wells

Abstract

In horizontal wells or directional wells, a casing bends to be in accordance with the wellbore curvature of the wells. The collapse strength of a curved casing correspondingly decreases, which may cause well failure if neglected. Herein, a curved casing is taken as a bending beam under uniform load according to material mechanics. The differential equation of the deflection is established. The relationships among axial stress, hoop stress, radial stress of casing, and wellbore dogleg is obtained based on Lame theory. The equation of collapse strength of the curved casing is deduced using distortion-energy theory. To verify the theoretical result, a finite-element model of the casing is established with ANSYS software. The collapse strengths of casing in four cases are analyzed using theoretical and finite-element method. Results show that the theoretical results well match the numerical ones. The collapse strength of the casing decreases nonlinearly with increased curvature. For the casing with outer diameter (OD) of 139.7 mm and thickness of 10.54 mm, collapse strength decreases from 104.74 MPa to 99.30 MPa with increased wellbore curvature from 2°/30 m to 12°/30 m. The relative reduction in collapse strength increases nonlinearly with increased wellbore curvature. OD has a greater influence on the relative reduction than thickness. The maximum value of relative reduction is 6.099% when OD is 139.7 mm but only 4.039% when OD is 114.3 mm. These results provide a reference for casing selection in production or other cases.