Analytical solutions for an extended overcore stress measurement method based on a thermo-poro-elastic analysis

A theoretical generalized plane-strain thermo-poro-elastic (THM) wellbore model is developed for application to the conventional overcore stress measurement method, under the situations when the thermal effect cannot be decoupled from the measured strains on the borehole walls. The THM theory developed by Coussy is used to describe the effects of both the pore pressure and the temperature on the stress and strain distributions around an inclined wellbore, which is assumed to be drilled instantly and subjected to initial stresses with arbitrary directions. The Laplace transformation is used to obtain the temperature, pressure, displacement, strain and stresses in the three-dimensional state around the wellbore. As special cases, the solutions of the above field variables are also provided for the poro-elastic (HM), thermo-elastic (TM) and pure elastic (CM) cases. Based on the THM solutions obtained, the stresses at the borehole wall, which vary with time, provide a bridge to find the in situ stresses from the measured strains at the wellbore surface. In this THM overcore stress measurement method, the temperature and the pressure (if a fluid is present) at the wellbore wall are another two parameters that need to be measured for stress inversion.