Development of analytical solution for thermo-mechanical stresses of multi-layered hollow cylinder for the application of underground hydrogen storage

Abstract

Hydrogen fuel has been playing an important role nowadays, it is considered as clean fuel and the hydrogen element is highly abundant. Storage of hydrogen in geological formations has been widely applied particularly for large-scale energy storage that required to meet high energy demand. There are different types of underground hydrogen storage methods, one of the most popular and reliable method is to store the hydrogen in depleted oil and gas wells. The structure of the depleted oil and gas well usually constructed by several layers of different materials such as formations, cement and casing. To ensure the well integrity is maintained, a reliable analytical solution to estimate the development of stress under pressure and thermal loading is required. In this paper, a more effective method to estimate the thermo-mechanical stresses of multi-layered hollow cylinder well is developed. The analytical solution is established by considering the well as generalized plane strain problem. The derivation of the equations and the algorithm to obtain results for four layered gas well were demonstrated. In general, the results obtained from the proposed analytical solution are well in agreement with the numerical results. The variations of results obtained from analytical solution and numerical solution are only less than 0.1%.