An Analytical Solution to Stress State of Casing-Cement Sheath-Formation System with the Consideration of its Initial Loaded State and Wellbore Temperature Variation

Stress state analysis to casing-cement sheathformation system (CCSFS) is the foundation of the wellbore integrity design and examination. Many elastic mechanic models have been established to calculate the stresses and displacements of CCFS, but all analytical models and most finite element models took no account of the initial loaded state, and ignored the initial stresses and displacements on cement sheath and formation, and regarded the given outer casing diameter and the measured wellbore diameter as the initial inner and outer diameters of cement sheath respectively. Now, a few finite element models have taken the initial stress of cement sheath into account, but ignored the initial strains of cement sheath and formation. To accurately solve the stresses of CCSFS and better direct the wellbore integrity design and examination, a new analytical model to solve the stresses of CCSFS with vertical wellbore and isotropic horizontal in-situ stress has been derived according to elastic mechanic theory, which can take the initial loaded state and temperature variation into account. Combining with an instance analysis, the stress distribution rules influenced by its initial loaded state and inner casing pressure have been discussed. Research showed that whether considering the initial loaded state can cause significant differences on the stress values and their variation trends of CCSFS. Especially, the tangential stress in casing unit and the radial stress in cement sheath have the maximum differences. Taking the initial loaded state into account is fully necessary and conducive to wellbore integrity design and examination. Keywords-wellbore integrity; cement sheath; initial loaded state; stress; analytical model