The importance of local thermal non-equilibrium in the modeling of a fractured hot dry rock reservoir

International audienceThermal recovery from a HDR reservoir, viewed as a deformable fractured medium, is investigated with a focus on the assumption of local thermal non-equilibrium. The numerical model is used to investigate the coupled thermo-hydro-mechanical behavior of the Fenton Hill site. The time profile of the outlet fluid temperature displays a double-step pattern, a feature which is interpreted as characteristic of established local thermal non-equilibrium

A thermo‐hydro‐mechanical coupled model in local thermal non‐equilibrium for fractured HDR reservoir with double porosity

International audienceThe constitutive thermo-hydro-mechanical equations of fractured media are embodied in the theory of mixtures applied to three-phase poroelastic media. The solid skeleton contains two distinct cavities filled with the same fluid. Each of the three phases is endowed with its own temperature. The constitutive relations governing the thermomechanical behavior, generalized diffusion and transfer are structured by, and satisfy, the dissipation inequality. The cavities exchange both mass and energy. Mass exchanges are driven by the jump in scaled chemical potential, and energy exchanges by the jump in coldness. The finite element approximation uses the displacement vector, the two fluid pressures and the three temperatures as primary variables. It is used to analyze a generic hot dry rock geothermal reservoir. Three parameters of the model are calibrated from the thermal outputs of Fenton Hill and Rosemanowes HDR reservoirs. The calibrated model is next applied to simulate circulation tests at the Fenton Hill HDR reservoir. The finer thermo-hydro-mechanical response provided by the dual porosity model with respect to a single porosity model is highlighted in a parameter analysis. Emphasis is put on the influence of the fracture spacing, on the effective stress response and on the permeation of the fluid into the porous blocks. The dual porosity model yields a thermally induced effective stress that is less tensile compared with the single porosity response. This effect becomes significant for large fracture spacings. In agreement with field data, fluid loss is observed to be high initially and to decrease with time

Enhanced Geothermal Reservoirs with two Fluid Cavities and Unequal Solid and Fluid Temperatures

International audienceThermo-hydro-mechanical (THM) constitutive equations and generalized diffusion and transfer constitutive relations are developed in a comprehensive, coupled and unified framework, assuming a deformable rock formation. Particular attention is laid on both mass and energy exchanges between the cavities which are controlled by the out-of-balances of the chemical potentials and by the out-of-balances of the coldnesses, respectively. Emphasis is laid a) on the mass exchanges between the pore system and the fracture network, which are endowed each with their own pressure, and mainly; b) on the energy exchanges between the rock, the pore network and the fracture network, which are endowed each with their own temperature. Thermo-hydro-mechanical (THM) constitutive equations and generalized diffusion and transfer constitutive relations are developed in a comprehensive, coupled and unified framework, assuming a deformable rock formation. Particular attention is laid on both mass and energy exchanges between the cavities which are controlled by the out-of-balances of the chemical potentials and by the out-of-balances of the coldnesses, respectively. The model is applied to simulate circulation tests using a domestic finite element code. The parameters are calibrated from the thermal outputs of the Fenton Hill and Rosemanowes reservoirs. At variance with a double porosity model with Local Thermal Equilibrium (LTE), the Local thermal Non Equilibrium model (LTNE) displays the characteristic two step time profile that is reported for these two reservoirs. In agreement with field data, fluid loss is observed to be high initially and decreases with time. A sensitivity analysis is performed to determine the influences of the internal length scales, namely fracture spacing and crack aperture, in the complete framework of the dual porosity (2 pressures 2P) and local thermal non equilibrium (3 temperatures 3T) . The fine description of the effective stress, pore and fracture pressures, and solid, pore and fracture temperatures of the most general format (2P-3T) is essentially unchanged when the model is specialized to (2P-2T) with equal pore and solid temperatures. At variance, the quality of the description is degraded for the (1P-2T) model that omits the permeability contribution of the pores, and for the (1P-1T) standard single porosity LTE model. The progressive transition is quantified during circulation tests at the Fenton Hill HDR

Borehole stability analysis in a thermoporoelastic dual-porosity medium

International audienceThe problem of diffusion and mass transfer in dual porous media is considered in a threephase framework. The solid phase is assumed to contain two distinct cavities filled with fluid. The porous mixture is composed of two overlapping media: the porous blocks and the fissure network. The fluid can transfer between the cavities due to fluid pressure difference. In addition, hydraulic and thermal diffusions take place through the mixture. A global understanding of mass transfer, diffusion and deformation is provided. The governing equations associated with these phenomena are presented for a mixture in thermal equilibrium. The finite element approximation of the governing equations is formulated and applied to the stability analysis of a vertical borehole. A parametric analysis is carried out to evaluate the influence of mass transfer on the pressure profiles of the fluids around the borehole. Permeable and a semipermeable boundary conditions are compared to predict the potential for failure of the wellbore under drained and partially undrained conditions

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

International audienceAccessing 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

Thermal recovery from a fractured medium in local thermal non‐equilibrium

International audienceThermal recovery from a hot dry rock (HDR) reservoir viewed as a deformable fractured medium is investigated with a focus on the assumption of local thermal non-equilibrium (LTNE). Hydraulic diffusion, thermal diffusion, forced convection and deformation are considered in a two-phase framework, the solid phase being made by impermeable solid blocks separated by saturated fractures. The finite element approximation of the constitutive and field equations is formulated and applied to obtain the response of a generic HDR reservoir to circulation tests. 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 or fluid velocity. The thermally induced effective 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

Thermo-hydro-mechanical study of deformable porous media with double porosity in local thermal non-equilibrium

Un modèle constitutif complètement couplé est présenté pour l'analyse rigoureuse de la déformation, de l'écoulement de fluides et de transfert de chaleur dans les milieux poreux saturés à double porosité soumis à des chargements thermo-hydro-mécaniques, y compris ceux induisant un non-équilibre thermique local. La phase solide contient deux cavités distinctes: le bloc poreux et le réseau des fissures. Les équations de champs sont obtenues à partir des équations de conservation de la masse, du mouvement et de l'énergie et sont résolues par une approche par élément finis. Le modèle est utilisé pour deux types d'applications: la stabilité d'un puits de forage stimulée thermiquement pour la récupération de pétrole et l'extraction de chaleur dans un réservoir géothermique fracturé. Les différences substantielles, particulièrement de la contrainte effective, soulignent l'influence majeure de la double porosité et du non-équilibre thermique pour prédire le comportement des milieux fracturés.A fully coupled constitutive model is presented for a rigorous analysis of deformation, hydraulic and heat flows in saturated dual porosity media subject to thermo-hydro-mechanical loadings including those able to cause local thermal non-equilibrium. The solid phase is assumed to contain two distinct cavities: the porous blocks and the fissure network. The governing equations are derived based on the equations of conservation of mass, momentum and energy. Solution to the governing equations is obtained numerically using the finite element approach. The capabilities of the model address two energy applications: the stability of a borehole in a thermally enhanced oil recovery context and the heat extraction of enhanced geothermal systems. Substantial differences, particularly in the effective stress response, highlight the major influence of the dual porosity model and the importance of the local thermal non-equilibrium assumption to predict the behaviour of fractured media

Rachel Gelet

Gelet Rachel. Rachel Gelet. In: Diplômées, n°231, 2009. Les femmes officiers dans les armées françaises. pp. 262-263

Rachel Gelet

Gelet Rachel. Rachel Gelet. In: Diplômées, n°234, 2010. Echos des recherches en cours. pp. 137-138

Thermo-hydro-mécanique des milieux poreux déformables avec double porosité et non-équilibre thermique local

A fully coupled constitutive model is presented for a rigorous analysis of deformation, hydraulic and heat flows in saturated dual porosity media subject to thermo-hydro-mechanical loadings including those able to cause local thermal non-equilibrium. The solid phase is assumed to contain two distinct cavities: the porous blocks and the fissure network. The governing equations are derived based on the equations of conservation of mass, momentum and energy. Solution to the governing equations is obtained numerically using the finite element approach. The capabilities of the model address two energy applications: the stability of a borehole in a thermally enhanced oil recovery context and the heat extraction of enhanced geothermal systems. Substantial differences, particularly in the effective stress response, highlight the major influence of the dual porosity model and the importance of the local thermal non-equilibrium assumption to predict the behaviour of fractured media.Un modèle constitutif complètement couplé est présenté pour l'analyse rigoureuse de la déformation, de l'écoulement de fluides et de transfert de chaleur dans les milieux poreux saturés à double porosité soumis à des chargements thermo-hydro-mécaniques, y compris ceux induisant un non-équilibre thermique local. La phase solide contient deux cavités distinctes: le bloc poreux et le réseau des fissures. Les équations de champs sont obtenues à partir des équations de conservation de la masse, du mouvement et de l'énergie et sont résolues par une approche par élément finis. Le modèle est utilisé pour deux types d'applications: la stabilité d'un puits de forage stimulée thermiquement pour la récupération de pétrole et l'extraction de chaleur dans un réservoir géothermique fracturé. Les différences substantielles, particulièrement de la contrainte effective, soulignent l'influence majeure de la double porosité et du non-équilibre thermique pour prédire le comportement des milieux fracturés