| Abstract |
This paper introduces a new thermo-poroelastic model in terms of analytic equations, to describe the rock deformation produced by fluid injection/extraction in geothermal reservoirs, using radial coordinates. The model is fully coupled in isothermal poroelastic conditions, but is thermally uncoupled if local thermal non-equilibrium (LTNE) is considered. The uncoupled model describes the flow of fluid and conductive-convective heat in linearly deformable porous rocks according to linear Biot’s theory. The fluid flow can be of Darcy’s type or non-Darcian. There are thirteen unknowns in this model: fluid pressure, variation of the fluid content in the pores, radial displacement of the solid skeleton, radial and tangential strains and stresses, porosity, deformation velocity of the solid, fluid velocity and rock and fluid temperatures, respectively. Except the temperatures, all the unknowns are explicit functions of radius and time f (r, t). Considering LTNE, there is an effective volumetric heat transfer qsf [W/m3 ] between the solid skeleton and the liquid. The porosity is estimated as a function of fluid pressure and temperature. The radial deformation of the solid rock ur is an irrotational vector field, as a consequence, the variation of the fluid content ζf, becomes proportional to the pore pressure pf , which is calculated using the classical Theis model. In these conditions, the diffusion equation of ζf is integrated to obtain the solid radial displacement ur (r, t) in analytical form. The system of simultaneous equations with all its unknowns is immediately solved in cylindrical coordinates. Once the fluid velocity is obtained, the fluid temperature can be computed using a new analytical solution of the diffusion-convection equation. This radial thermoporoelastic model is didactic, useful and simple to use. It allows to explore different conditions for both the fluid and the geomechanical parameters, as well as different boundary and initial conditions; therefore, it can be used as a benchmark to test fully numerical models. Graphical results are shown to illustrate practical cases with extraction and injection of fluid into a reservoir using real data. This work is a current research in progress. |