In this chapter, we examine the coupled thermo-hydro-mechanical behavior of a fluid-saturated porous medium of infinite extent bounded internally by a fluid-filled cavity of cylindrical shape. The fluid within the cavity can be subjected, separately or simultaneously, to a temperature rise and a pressure pulse. We present analytical results for this radially symmetric thermo-poroelasticity problem.

Examples of the analytical treatment of the isothermal problem of a cylindrical cavity are given by Rice and Cleary (1976) and Detournay and Cheng (1988, 1993). Coupled thermo-hydro-mechanical problems of a cylindrical cavity subjected to either a constant temperature change or a constant heat flux were studied by McTigue (1990), Wang and Papamichos (1994, 1999) and Zhou et al. (1998). Zhou et al. (1998) account for thermodynamically coupled heat–water flow known as thermo-osmosis. The case of a rigid cylindrical heat source buried in clay was examined by Seneviratne et al. (1994). Wu et al. (2012) give an analytical solution to the problem of a cylindrical cavity (wellbore) subjected to a constant fluid pressure and temperature rise on the cavity wall, with non-hydrostatic stresses applied remotely.

The goal of this chapter is to present analytical results for the development of fluid pressure within a cylindrical cavity located in a fluid-saturated poroelastic medium when the cavity is subjected, separately, to either pressurization or a temperature rise. Computational results for the cylindrical cavity problem were obtained using the finite element program ABAQUS (Student Edition).

Thermo-Poroelasticity of a Geomaterial With a Fluid-Filled Cylindrical Cavity

Assume that a fluid-filled cylindrical cavity of very large length is embedded into a poroelastic geomaterial. The radius of the cylindrical cavity is a. We place the origin of the cylindrical coordinate system (r, ϕ, z) at the center of a circular cross-section of the cavity and direct the z-axis of the coordinate system along the axis of the cylinder (Fig. 6.1). For the sake of simplicity, we can assume that the displacement along the z-axis is zero, i.e., the axial strain ε zz is identically zero. Owing to the linearity of the problem, the effect of non-zero axial strain can be added to the resulting solution later using the superposition principle, as described in Chapter 5.