Drilling of a borehole in fluid saturated rocks exerts significant influence on its surrounding reservoir. As have been observed extensively, stresses, pressure and/or thermal loadings on the borehole wall will lead to great change of stress field in the rock. As a result, stabilities of the borehole wall and pre-existing fractures will be at risks. In this paper, a mixed boundary element model (BEM) is developed to solve these problems within the framework of thermo-poroelasticity. The model is applied to borehole stability and fracture problems in high temperature subsurface environments. Instability of borehole wall in naturally fractured rocks can be simulated and predicted by studying the potential of crack initiation and growth. This model provides a flexible tool to deal with two-dimensional transient thermal-poroelastic problems.
1. INTRODUCTION
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 poromechanical effects, can greatly change the stresses and pore pressure fields around an underground opening. This is due to the fact that thermal loading induces volumetric deformation because of thermal expansion/contraction of both the pore fluid and the rock solid. A 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. However, 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 [e.g., 1, 2]. The advantage of the method is that it reduces the problem dimensionality by one thereby reducing the computational efforts significantly. In this paper, a two-dimensional transient indirect BEM is developed to solve coupled thermo-poroelastic problems.
The indirect BEM has two sub-formulations, namely, displacement discontinuity (DD) method and fictitious stress (FS) method. The DD method is particularly suitable for crack-shaped problem. A mixed FS-DD model is developed to take advantage of the strengths of both FS and DD methods. The model is applied to some thermo-poroelastic problems in borehole stability and hydraulic fracturing.
2. THERMO-POROELASTICITY
Thermo-poroelasticity is developed on the basis of poroelasticity and thermoelasticity. It couples the time-dependent processes of fluid diffusion and heat diffusion to mechanical behavior. Constitutive equations for this theory were first introduced by Palciauskas and Domenico [3] by extending the classic Biot's poroelastic theory [4] for the non-isothermal case. This theory was later established by other investigators, e.g., McTigue [5], and Coussy [6].
The governing equations for thermo-poroelasticity can be found in the works of McTigue [5] which consist of constitutive equations, transport laws and balance laws.
From the governing equations, the field equations can be derived for temperature, displacement, and pore pressure:
Navier Equation:
(available in full paper)
Diffusion equation for pore pressure p:
(available in full paper)
Diffusion equation for temperature T:
(available in full paper)
