Inverse Problem Theory to Estimate Thermo-Poroelastic Parameters: An Analytical/ Experimental Approach

Behnoud far, P. (Amirkabir university of Technology) | Gholilou, A. (Curtin University) | Al-Ajmi, A. M. (Sultan Qaboos University) | Salimi, H. (Curtin University)


ABSTRACT: Induced stresses are one of the main factors affecting wellbore instability and associated problems in drilling operations. These stresses are significantly impacted by pore pressure variation and thermal stresses in the fields. Heat and fluid transfer capability of rock and thermal expansion coefficient are important parameters in the study of stresses using a thermo-poroelastic model. In this study, the field equations governing the problem have been derived based on the thermo-poroelastic theory and solved analytically. Afterward, the couple of 50 mm synthetics sand-cement samples are applied in laboratory experiments. The in situ stresses and wellbore pressure are applied on the sample in a true triaxial stress cell (TTSC). In the laboratory tests, the temperatures are controlled and cooled oil is injected into the sample. The strains are measured and calculated based on experiment and model. In the next step, a genetic algorithm has been applied to solve an inverse problem and get a match between experimental data and the modeling results. Ultimately, the important properties for the interactions of fluid and rock can be estimated. With this approach, the required thermal and flow parameters are estimated with good accuracy without using time consuming and costly tests.


Wellbore stability has an important role during drilling. The formations around wellbore experience new stress conditions due to the removal of drilled rocks (Fjaer, Horsrud et al. 2008, Al-Ajmi and Zimmerman 2009). Any point below ground carries different stresses, namely vertical stress due to the overburden or weight of overlaying formations, horizontal stresses from tectonic movements and pore pressures (Amadei 1984).

The assumed rock formation behavior is a significant factor in modeling the stresses around a borehole. In this regard, Mclean and Addis (Mclean and Addis 1990) pointed out that a poro-elasto-plastic model can give more realistic results than a linear elastic model. In addition, Bradford and Cook (1994) suggested using an elasto-plastic model for stress modeling and they have applied their recommendation in wellbore stability analysis for vertical well with isotropic in situ stresses. Furthermore, Chemo-poro-elastic model is used to determine the stresses around the wellbore in shale formations(Ma, Chen et al.).