Perturbation finite element method for stress analysis of horizontal well casing during thermal production

The stress analysis of the horizontal well casing in petroleum recovery is a three dimensional problem which would require large amount of CPU time using a general finite element method (FEM) program. A more efficient method is developed using a combination of perturbation methods and finite element methods. The geometric and structural characteristics of the horizontal well are used to develop a group of general control elastic mechanical equations for the horizontal well using natural coordinates. Then the perturbation method is introduced to simplify the problem from three dimensional to two dimensional with a radius relative non dimensional parameter. Finally, the structure is separated into circumferential finite elements using new FEM equations. A software procedure is then developed and applied to analyze practical horizontal well stress conditions. The analysis method not only simplifies the problem but also reveals the variation mechanism of the shearing stress and the axial displacement of the horizontal well due by thermal effects, and explains why the ground part of the horizontal well is uplifted during thermal production.