Three Dimensional Non-linear Anisotropic Thermo-Chemo-Poro-Elastoplastic Modelling of Borehole Stability in Chemically Active Rocks

Borehole stability problems are mostly encountered when drilling through chemically active formations such as shales. Shales are highly laminated rocks with transversely isotropic behaviour, and low permeability. Their mechanical behaviour is also characterized by non-linear active elastoplasticity. In this work, a systematic approach is taken towards modelling of coupling problems of thermal, chemical, hydraulic and mechanical interactions in shale formations.First, the governing equations of poroelasticity are extended to thermo-chemo-poroelasticity to investigate the change in pore pressure and stresses around the borehole due to physic-chemical interaction between drilling and pore fluid. The ion advection and thermal convection processes are taken into account in formulation of governing equations. They are taken into consideration in order to assess their effects on pore pressure and stresses around the borehole in a range of shale permeability. A new numerical algorithm is proposed using a special finite element technique (Characteristic Galerkin Technique) to stabilize the advection/convection solutions.Next, the irreversible strains are considered through different elastoplastic constitutive laws (Drucker-Prager and Modified Cam Clay). A new concept is introduced in which a post failure of shales can be explained by. This concept is embedded in both the Drucker-Prager and Modified Cam Clay yield locus to give them the capability of modelling the time dependent deterioration of shales mechanical properties.The developed model is then extended to three dimensional spaces to study the effect of overburden pressure on plastic deformation and therefore, stability of the borehole. This is particularly important to test the validity of plane strain assumption considered in borehole stability. Finally, a non-linear elastoplastic transversely isotropic behaviour of shale is considered to investigate the effect of stress dependency of mechanical parameters, in three dimensional stress spaces, on borehole stability.Form the results of this study it has been found that:The solute transfer between the drilling fluid and the shale formation is controlled primarily by permeability of the shale formations. For the range of shale formations studied, there exists a threshold permeability below which the solute transfer is dominated by diffusion process and above which by fluid in motion (fluid flow). When the salinity of drilling fluid is higher than that of pore fluid (Cm>Cs) the solute transfer from the fluid to the formation increases due to advection and that the solute transfer is faster for advection-dominated process than that for diffusion-dominated process only. Thus, chemical equilibrium can be reached sooner due to advection which makes the chemical osmosis disappear. When the diffusion dominates the solute transfer process, chemical osmosis can be sustained over a longer period of time. It was also found that the state of stresses around the wellbore can be significantly altered by the advection of solute. When advection is considered the tangential stress at the wellbore wall is likely to be tensile. Also the effective radial stress can be seen to decrease near the wellbore wall.Similar observation can be made for thermal convection compared to ion advection except that the effect of thermal convection on pore pressure is much smaller than ion advection in a range of shale permeability. Therefore, thermal convection can be neglected in the range of shale permeability.From the results it was also found that at early time, when the change in pore pressure induced by undrained response is not negligible, change in pore pressure is basically a function of three processes namely poroelastic undrained response, hydraulic flow and chemical osmosis. The definition of early time for undrained response depends on formation permeability. Lower formation permeability longer effect of undrained response can be seen.It was further revealed that when heating of a formation is considered, a plastic zone forms for all three boundary conditions of solute mass fraction (Cm = Cs, Cm>Cs and CmCs, however, the rock can gain strength against shear failure by preventing formation of a plastic zone or by maintain a stronger bonding between the shale plates.A new concept for the yield locus of chemically active rocks using experimental results was introduced. The concept was tested in the fame of the modified Cam Clay model to describe the post failure of the rocks. The results obtained using this concept indicates that it is not necessary for elastic stresses to reach the yield surface to cause plastic deformation. Plastic deformation can take place in constant elastic stresses due to change in size and shape of yield surface with change in solute concentration until failure occurs.Results also showed that the formation of plastic zone is not only a function of horizontal in-situ stresses but also vertical stress. As vertical in-situ stress deviates from the magnitudes of horizontal in-situ stresses the size of plastic zone increases. The formation of plastic zone mainly affects the tangential stresses around the wellbore. As a result of formation of plastic zone hoop stresses strongly relax on the wellbore wall which has a potential to lead the wellbore towards hydraulic fracturing.Moreover, the solid displacement shows non-linearity in elastic region. Consequently linear elastic theory is somehow restricted to predict the accurate behaviour. Using Cam Clay model the non-linear elasticity is taken into account. However, in order to realistically model the transversely isotropic behaviour of shale, an experimental correlation was extracted from the literature and used to model the non-linear elastic transversely isotropic case. The linear elastic transversely isotropic seemed to produce more conservative stresses around the borehole than the stress-dependent transversely isotropic case. Results also showed that elastic stresses remarkably relax in stress-dependent elastic case which is especially pronounced between 30° to 45° angle on the borehole wall. It is also evident from the results that the rock is more likely to experience formation of plastic zone in transversely isotropic case than that of stress-dependent transversely isotropic case