An uncoupled radial thermoporoelastic model with local thermal non-equilibrium

Abstract

A new analytic model is introduced to describe rock deformation produced by fluid injection / extraction in geothermal reservoirs. This model is fully coupled under isothermal conditions and thermally uncoupled if local thermal non-equilibrium (LTNE) is considered. The model describes both fluid flow with conductive-convective heat transfer and rock deformation in cylindrical coordinates. There are 13 unknowns in the model: fluid pressure, fluid content variation, solid skeleton displacement, radial, tangential and volumetric strains, two stresses, porosity, solid deformation velocity, fluid velocity, rock and fluid temperatures. Considering LTNE, there is an effective heat transfer between the solid skeleton and the liquid. The porosity is estimated as a function of fluid pressure and temperature. The solid radial deformation is an irrotational vector field, thus the fluid content variation, is proportional to pore pressure, which is calculated using the classical Theis solution. Therefore, the solid radial displacement can be obtained in analytical form. Once the fluid velocity is computed, the fluid temperature is deduced from a new analytical solution of the diffusion-convection equation. This model is didactic, useful and simple. It allows to explore different options for both the fluid and the poroelastic parameters, with different boundary conditions. Graphic results illustrate practical cases with fluid extraction/injection into a reservoir using real data.