Maintaining wellbore stability is a critical problem when drilling for petroleum production in shale that tend to swell and deteriorate in the presence of the water phase of a drilling fluid. Linear and non-linear chemo-poroelastic models based on non-equilibrium thermodynamics have been developed to consider hydration swelling of water-absorbing rocks in wellbore stability analysis. In this paper, a finite element method is developed for both linear and non-linear models. The model is first verified through comparisons with the analytical results for the case of poro-thermoelasticity and chemo-poroelasticity. Thereafter, the finite element results for the linear chemo-poroelastic model are compared to those obtained using the non-linear theory. Results show that for mud properties within the range of interest, the linear model provides good results for the purpose of assessing shale instability.
The physico-chemical interactions between the mud and the formation significantly influence the resulting stress and pore pressure fields in swelling shale. It is thus necessary to consider their influence when conducting a rigorous wellbore stability analysis, particularly when drilling in high-temperature and high-pressure (HPHT) environments. The effect of chemo-mechanical process on shale deterioration and borehole instability under isothermal conditions has been extensively studied [1- 5]. It has been found that hydraulic fluid transport is often several times lower than the fluid transport induced by chemical and thermal gradients. Certain phenomena related to thermal processes in shale and other rocks have also been investigated using porothermoelastic theory [6, 7]. The significance of thermal stress and pore pressure around a wellbore and their impact on borehole stability has been shown in Wang and Papamichos  and Li et al. . Ghassemi and Diek  indicated that under certain condition, thermo-osmosis also might become several times larger than hydraulic flow in shales. Based on non-equilibrium thermodynamics, Heidug and Wong  developed a fully coupled Biotlike model to consider hydration swelling of waterabsorbing rocks. This model is more advantageous than traditional chemical potential theories because it can consider the solute transfer between the water phase of the drilling mud and the pore fluid. On the other hand, because of its coupled and non-linear nature, a numerical solution is needed making cumbersome for implementation in wellbore stability models. Ghassemi and Diek  developed a linear chemo-poroelasticity theory for swelling shales in which the chemical potential is expressed as a linear function of the solute mass fraction. The theory is able to capture the important phenomena observed in the laboratory and the filed, and allows analytical treatment of the field equations for a wellbore problem. Thereafter, Ghassemi et al.  presented a coupled chemo-poro-thermoelastic linear model that accounts for both the temperature and chemical potentials based on the work by Ghassemi and Diek . This is of particular need when drilling in HTHP shale formations. However, the linear model is suitable for stability analysis within the elastic range of rock response, and when using simple initial and boundary conditions. In addition, the results obtained from the linear models have not been quantitatively compared to those from the non-linear model of Heidug and Wong .