A Thermo-Mechanical Analytical Model for Geothermal Wells in the Formation with Anisotropic In-Situ Stress

This work focuses on the theoretical investigation of the thermo-mechanical behaviors of a geothermal well in the formation with anisotropic in-situ stress. First of all, the complex problem of a geothermal well is divided into three simple subproblems: the uniform load subproblem, the cosine load subproblem and the temperature load subproblem. The uniform load subproblem and the temperature load subproblem are analytically solved using the displacement method in elasticity theory, while the cosine load subproblem is analytically solved using the stress function method in elasticity theory. The analytical results of subproblems are compared with the numerical results from finite element method to verify the obtained analytical solutions of subproblems. Then, a thermo-mechanical analytical model of a geothermal well, which includes the analytical formulations of displacement field and stress field, is proposed by superposing the analytical solutions of the above three subproblems. At last, the proposed analytical model is used to investigate thermo-mechanical behaviors of a geothermal well in the formation with anisotropic in-situ stress. Some important influence factors on the stress field of cement sheath of the geothermal well are analyzed and discussed comprehensively. Some valuable results are obtained, which also show that the proposed analytical model can effectively predict the thermo-mechanical behaviors of a geothermal well in the formation with anisotropic in-situ stress. This work is useful for the research on mechanical integrity design of a geothermal well and other related research in oil-gas well engineering.