An Elasto-Plastic Semi-Analytical Solution of Wellbore Stability for Enhanced Geothermal Systems

Abstract

In recent times, the dependency on renewable energy is increasing due to environmental problems, and one of the sources of renewable energy is in the form of geothermal energy. In the Geothermal energy system, the heat energy is extracted from the underground geothermal reservoir through wellbores. The creation of wellbores are very expensive. Therefore, for continuous and economical energy production, the stability of the wellbore is important. In the present study, a semi-analytical solution is developed for wellbore stability by introducing a new thermo-elastoplastic constitutive model. The thermo-elastoplastic model is formulated by adopting a temperature-based yield criteria from Parisio et al., (2019) study. The proposed constitutive model follows stability, convexity, and normality, making it possible to obtain a unique solution to a boundary value problem. Non-associative flow rule is adopted to satisfy the material normality requirement. The proposed model is validated by using the experimental triaxial test results on Comiso limestone at different temperatures. Further, a semi-analytical solution is formulated for the wellbore stability using the developed simple elastoplastic constitutive model. The semi-analytical solution is validated by comparing it with the results obtained from the equivalent Drucker-Preager perfect-plasticity model by FE (Finite element)˗analysis. The results are in good agreement with each other. Hence the solution is used to obtain the response of stresses and deformation around the wellbore with varying depth and radial distance. At last, a parametric study is conducted in order to assess the effect of parameters on the results. Out-of-plane stress, in-plane stress, dilation parameter, and temperature up to 400°C do not have any significant effect on the radial stress as the wellbore opening. Stress and deformation response is highly impacted by the internal wellbore pressure. The dilation parameter affects the deformation and vertical stress response of the wellbore. It is observed that the temperatures above 500°C, the radius of the plastic zone increases drastically. The wellbore stability solution and its constitutive model can be adopted for the enhanced geothermal system wellbore stability analyses during construction.