The significance of local thermal non-equilibrium in simulations of enhanced geothermal recovery

Accessing the thermo-mechanical response of large deep hot dry rock (HDR) reservoirs during geothermal extraction remains a challenging task that can be comprehended with numerical tools. Of crucial im-portance to the economic viability of these HDR reservoirs is the knowledge of thermal output evolution, fluid excessive pressure and induced thermal stress, at various steps of the circulation tests. Thermal recovery from a HDR reservoir, viewed as a deformable fractured medium, is investigated with a focus on the assumption of lo-cal thermal non-equilibrium (LTNE). To this end, a fully coupled finite element formulation for a thermo-elastic fractured medium in LTNE is developed (Gelet et al. 2013). Hydraulic diffusion, thermal diffusion, forced con-vection and deformation are considered in a two-phase framework, the solid phase being made by impermeable solid blocks separated by saturated fractures. Each of the two phases is endowed with its own temperature. The resulting system of equations is used to address a generic HDR reservoir subjected to temperature and pressure gradients. A change of time profile of the outlet fluid temperature is observed as the fracture spacing increases, switching from a single-step pattern to a double-step pattern, a feature which is viewed as characteristic of established LTNE. A dimensionless number is proposed to delineate between local thermal equilibrium (LTE) and non-equilibrium. This number embodies local physical properties of the mixture, elements of the geometry of the reservoir and the production flow rate. All the above properties being fixed, the resulting fracture spacing threshold between LTNE and LTE is found to decrease with increasing porosity. The thermally induced effec-tive stress is tensile near the injection well, illustrating the thermal contraction of the rock, while the pressure contribution of the fracture fluid is negligible during the late period.