An analytical thermo-poro-elasticity model for the mechanical responses of a wellbore and core during overcoring

To accurately measure in situ stresses using overcore techniques, the key is to find the relationship between the stresses and measured strains on the wellbore wall and on the core at two stages, i.e. before and after overcoring. For gas shales, where there exist large pressure and temperature changes, we developed an analytical model for the stage before overcoring to study the evolution of all field variables, i.e. temperature, pressure, stress, strain and displacement (TPSSD), when an inclined wellbore is drilled in an infinite and homogenous thermo-poro-elastic media (THM) subjected to three far-field principal stresses, whose axes may not coincide with the horizontal and vertical planes. In that paper we investigated the thermal and poro-elastic effects on the strain changes around and especially at the wellbore wall. As an extension of the previous work. In this paper, we describe an analytical model to give the mechanical responses of the wellbore and core for the stage after overcoring. Strain changes at the wellbore wall are examined in detail because these are measured by the overcore method. By using the analytical solutions presented at a specific time and the strains before overcoring as an initial state, the transient solutions for the evolution of temperature, pressure, stress, strain and displacement (TPSSD) are obtained so that for the two critical stages before and after overcoring a reasonable estimate of the in situ stresses can be obtained. As well as the strain changes, the temperature and pressure at the wellbore wall, which vary with time, are also required to find in situ stresses in the inverse model. Fortunately, their effects become progressively less important with time due to the small size of overcored sample. The critical time is calculated when the thermal and porous effects can be ignored. Two cases, i.e. constant and exponentially time-varying temperature boundary conditions, are investigated.