| Abstract |
Rocks in geothermal systems are porous, compressible, and elastic. The presence of a moving fluid in the porous rock modifies its mechanical response. Its elasticity is evidenced by the compression that results from the decline of the fluid pressure, which can shorten the pore volume. This reduction of the pore volume can be the principal source of fluid released from storage. Poroelasticity explains how the fluid inside the pores bears a portion of the total load supported by the porous rock. The skeleton supports the remaining part of the load. The skeleton is treated as an elastic solid with a laminar flow of pore fluid coupled to the framework by equilibrium and continuity conditions. This paper introduces an original tensorial formulation of Biot’s isothermal theory of linear porous rocks and of its extension to thermoporoelastic processes. By defining a total stress tensor in four dimensions and three basic poroelastic coefficients, it is possible to deduce a system of equations coupling two tensors, one for the bulk rock and one for the fluid. The inclusion of the fourth dimension is necessary to extend the theory of solid linear elasticity to thermoporoelastic rocks, taking into account the effect of both, the fluid phase and the temperature. In linear thermo-poroelasticity, we need five poroelastic modules to describe the relations between strains and stresses. Introducing three volumetric thermal dilation coefficients, one for the fluid and two for the skeleton, a complete set of parameters for geothermal poroelastic rocks are obtained. This formulation makes more comprehensible the linear theory. The Finite Element Method is very convenient to solve the resulting equations. To illustrate the practical use of this tensor four-dimensional formulation three applications are outlined: a) Full deduction of the classical Biot’s theory coupled to thermal stresses; b) deformation of an aquifer under cold isothermal conditions and c) simulation of the same aquifer when its temperature changes to a geothermal state. |