Numerical stress analysis for the multi-casing structure inside a wellbore in the formation using the boundary element method

A multi-casing structure in drilling engineering can be considered as an inhomogeneous body consisting of many different materials. The mechanical behavior of the inhomogeneous body in an infinite domain is very com- plicated. In this paper, a detailed expression about the fictitious stress method of the boundary element method （BEM） is demonstrated for the inhomogeneous body. Then the fictitious stress method is deployed to investigate the stresses for the multi-casing structure under non-uniform loading conditions and an irregular wellbore. Three examples of the multi-casing structure in the borehole imply the high effectiveness of BEM for complex geometries related to the borehole in an infinite formation. The effects of casing eccentricity and the interfacial gap on the stress field are discussed. The eccentric casing takes the potential yield when the eccentric orientation is along the direction of Sh. Under different eccentric orientations, the yon Mises stress in the casing increases with increasing degree of eccentricity. The radial stress in the multi-casing structure is always continuous along the radius, but the circumferential stress is discontinuous at the interface. The radial stress decreases and the circumferential stress increases with the increasing of the interfacial gap between the adjacent materials.