A semi-analytical method for the stress distribution around a borehole with multiple casings and cement sheaths

Abstract

In this paper, a semi-analytical method is developed to predict the stress distribution around a cased borehole with multiple casings and cement sheaths. The stress field formulations of a borehole system with multiple casings and multiple cement sheaths with undetermined coefficients are first derived using the elasticity theory. Then the undetermined coefficients in the stress field formulations are determined based on the stress boundary conditions and finite element method (FEM). Especially, the junction of casing and cement sheath, and the junction of cement sheath and formation are all set to be unwelded in the developed method, which can express the real conditions more effectively. And the developed method overcomes the limitation that the stress field simulated by the FEM is discontinuous. In addition, the developed method has the simple formula expressions, which make it is more convenient and accurate for the practical applications. Numerical results of the developed method show that it can predict the stress distribution around a borehole system with multiple casings and multiple cement sheaths effectively.