Geomechanical Response of the Shale in the Colorado Group Near a Cased Wellbore Due to Heating
Authors: Wong R.C.K. , Samieh A.M. 
Published: March 2010

Abstract
Steam-stimulation is a viable in situ thermal recovery technique for heavy oil and oil sand reservoirs. This thermal recovery process introduces many complex geomechanical problems in oil sand and overburden formations. This paper addresses the geomechanical response of Colorado shale near a cased wellbore due to heating. The temperature, pore pressure, and stress response in Colorado shale near a cased wellbore due to heating are analyzed using a coupled thermal-mechanical-hydraulic solution. The possibility of failure or fracturing of the shale due to heating is assessed.

Introduction
Steam-stimulation processes are currently the most viable techniques for oil recovery from oil sand reservoirs. These thermal recovery processes cause many complex geomechanical effects in the oil sand layer and the geologic overburden strata due to elevated temperatures and pressures involved in the steam injection.
The study in this paper focuses on the effect of heating on shale near a cased well. Analytical solutions developed by Booker and Savvidou(1) are used to analyze the distributions of induced pore pressure, temperature, and stress near a heated wellbore. These results will be used to investigate the potential occurrence of any tensile fracture in the heated shale. Conclusions will be drawn, along with the limitations of the analysis, and recommendations made for further studies.

Problem Description
Figure 1 defines the problem. Steam is injected into a cased well such that the inside temperature is elevated to a constant level. Heat is continually conducted from the well to its metal casing, cement annulus, and the shale in the formation. Heating of shale causes thermal expansion of the shale structural matrix and pore fluid. Expansion of the structural matrix induces total stress changes. Expansion of the pore fluid increases the pore pressure, thereby generating pore pressure gradients and the potential for pore fluid flow. Hence, the heating process results in a thermalhydraulic-mechanical coupled process. Calculation of the changes in temperature, pore pressure, and stress changes near the heated well will require solution to this complex coupled problem.
FIGURE 1: Problem description. (Available in full paper)

Analytical Technique
Equilibrium Equation and Constitutive Law
For a saturated thermo-elastic geological medium, the equilibrium equations are:
Equation (1.a) (Available In Full Paper)
Equation (1.b) (Available In Full Paper)
Equation (1.c) (Available In Full Paper)
where σxx, σyy,..... σyz are the increase of total stress components (compressive stresses and strains are considered to be positive).
In the present study, the stiffness of the solids and pore fluid are assumed to be infinite in comparison to the shale skeleton stiffness. Thus, volume changes are due to changes in temperature and effective stresses. For an isotropic thermo-linear elastic material, the stress-strain relations are given by:
Equation (2.a) (Available In Full Paper)
Equation (2.b) (Available In Full Paper)
Equation (2.c) (Available In Full Paper)
Equation (2.d) (Available In Full Paper)
Equation (2.e) (Available In Full Paper)
Equation (2.f) (Available In Full Paper)
where the primed symbols represent effective stresses, E and ν are the drained Young's modulus and Poisson's ratio, G is the shear modulus, Ψ is the increase in temperature, and a' is the drained coefficient of volumetric thermal expansion of the geologic me