A Boundary Element Method for Thermo-poroelasticity with Applications in Rock Mechanics

Coupled thermal and poromechanical processes play an important role in many geomechanics problems, such as borehole stability analysis and studies of initiation and propagation of hydraulic fractures. Thermal effects, as well as hydraulic effects, can greatly change the stresses and pore pressure fields around an underground opening. This is due to the fact that thermal loading induces a volumetric deformation because of thermal expansion/contraction of both the pore fluid and the rock solid. Volumetric expansion can result in significant pressurization of the pore fluid. In order to take into account the influence of temperature gradients on pore pressure and stresses, it is necessary to use a non-isothermal poroelastic theory, or thermo-poroelasticity. Many problems formulated within the framework of thermo-poroelasticity are not amenable to analytical treatment and need to be solved numerically. The boundary element method (BEM) has proven suitable for the poroelastic and thermoelastic problems. In this thesis, a two-dimensional transient indirect BEM is developed to solve coupled thermoporoelastic problems. The indirect BEM has two sub-formulations, namely, the displacement discontinuity (DD) method and the fictitious stress (FS) method. The DD method has shown to be particularly suitable for crack-shaped problems (Crouch and Starfield, 1983). A combine FS-DD model is developed to take advantage of the strengths of both FS and DD methods. The boundary integral equations, fundamental solutions, and the numerical implementations for the development of this model are described. The model is tested using some poroelastic and thermo-poroelastic examples. The numerical predictions show good agreement with analytical solutions or previously published results. The results indicate that the transient formulation of the indirect BEM (FS-DD) model is an accurate and suitable means for solving problems in thermo-poroelasticity. In addition to verification of the numerical techniques, the model is applied to borehole stability and fracture problems in high temperature underground environments. Drilling-induced stress and pore pressure distributions around a borehole are analyzed. Effects of thermal loading and pore pressure loading are considered. The results indicate that cooling the borehole wall will induce a pore pressure reduction and additional tensile stresses in the formation. Therefore, the potential for tensile fracture at the wall and inside the rock increases. The influence of excavation geometry on borehole stability under combined poro-thermo-mechanical loading is also considered. It is found that an elliptical borehole will be more likely to fail in tension due to the pressure of the mud column and cooling. The examples also indicate that cooling increases crack opening and stress intensity, leading to crack growth. Fracturing is more likely to occur in the cooled zone. In general, cooling at the borehole wall can lead to fracturing and instability; cooling the crack surface can cause the crack to open up and further propagate. Pore pressure effects in these problems are far less important than thermal effects according to the study. However, thermal effects tend to develop slowly and can be neglected in hydraulic fracture propagation