Investigation of the ultimate residual strengthen of a worn casing by using the arc-length algorithm

The accurate prediction of the ultimate residual strength (URS) (including collapse, burst, and tensile strength) of worn casing is important in the design and safety assessment of casings for the oil and gas industry. Based on the true stress–strain constitutive relationship of P110 steel, this paper establishes a three-dimensional (3D) finite element model (FEM) to obtain the URS of worn casing by using the arc-length algorithm. The effects of worn defect length, wear percentage, drillstring diameter, and casing thickness on the URS are investigated. Moreover, three full-scale experiments on casings with different wear percentages are conducted to verify the accuracy and reliability of the 3D FEM and of the algorithm. The validation proves that the URS of worn casing can be predicted by the 3D FEM to a satisfactory degree of accuracy. The URS has an exponential relation with defect length, but a linear relation with wear percentage, drillstring diameter, and casing thickness. The effects of numerous factors on the URS are also studied. Regression analysis is conducted on the basis of 3D FEM predictions, and the corresponding design equations for worn casing are presented.