| Abstract |
Rocks in geothermal systems are porous, compressible, and elastic. Presence of a moving fluid in the porous rock modifies its mechanical response. Rock 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 water inside the pores bears a portion of the total load supported by the porous rock. The remaining part of the load is supported by the rock-skeleton, constituted of solid volume and pores, which is treated as an elastic solid with a laminar flow of pore fluid coupled to the framework by equilibrium and continuity conditions. A rock mechanics model is a group of equations capable of predicting the porous medium deformation under different internal and external forces of mechanic and thermal origin. This paper introduces an original tensorial formulation of both, the Biot’s classic theory (1941) and its extension to non-isothermal processes, including the deduction of experimental thermo-poroelastic parameters supporting that theory. 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 and solid phase and the temperature changes. 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 is obtained. Introduction of Gibbs free enthalpy as a thermodynamic potential allows include easily thermal tensions. This tensor four-dimensional formulation is equivalent to the simple vector formulation in seven dimensions, and makes more comprehensible and clear the linear thermopoelastic theory, rendering the resulting equations more convenient to be solved using the Finite Element Method. To illustrate the practical use of this tensor formulation some applications are outlined: a) full deduction of the classical Biot’s theory coupled to thermal stresses, b) how tension changes produce fluid pressure changes, c) how any change in fluid pressure or in temperature or in fluid mass can produce a change in the volume of the porous rock, d) how the increase of pore pressure and temperature induces a dilation of the rock. High sensitivity of some petro-physical parameters to any temperature change is shown, and some cases of deformation in overexploited aquifers are also presented. |