The 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.

SUMMARYThermal 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.

The 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.

No abstract

International audienceThis paper presents the formulation of finite element methods for the numerical modeling of a poro-elastic two-phase (aggregates/mixture phase) solid. The displacement and pressure fields are decomposed, following the EAS method, into a regular part and an enhanced part. This leads to discontinuous strain and pressure gradient fields allowing to capture the jump in mechanical and hydrical properties passing through the interface between the aggregates and the mixture phase. All these enhanced fields are treated in the context of the Embedded Finite Element Method through a local enhancement of the finite element interpolations as these jumps appear. The local character of these interpolations lead after a static condensation of the enhanced fields to a problem exhibiting the same structure as common poro-elastic finite element models, but incorporating now the mechanical and hydrical properties of a two-phase solid

No abstract

Granular soils subjected to seepage flow may suffer suffusion, i.e. a selective internal erosion. Extending the classical approach of poromechanics, we deduce a new form of the Clausius-Duhem inequality accounting for dissipation due to suffusion and we deduce restrictions on the constitutive laws of the soil. We suggest (i) a possible coupling between the seepage forces and the suffusion kinetics (ii) an extension of an existing elastoplastic model for the skeleton mechanical behaviour. Numerical integrations of the elastoplastic model are carried out under drained axisymmetric triaxial and oedometric conditions. As a result, we prove that the extended model is able to qualitatively reproduce the suffusion induced strains as well as the strength reduction experimentally observed. Predictions on the oedometric behaviour of suffusive soils are also provided.

Summary A general thermo‐hydro‐mechanical framework for the modelling of internal erosion is proposed based on the theory of mixtures applied to two‐phase porous media. The erodible soil is partitioned in two phases: one solid phase and one fluid phase. The solid phase is composed of nonerodible grains and erodible particles. The fluid phase is composed of water and fluidized particles. Within the fluid phase, species diffuse. Across phases, species transfer. The modelling of internal erosion is contributed directly by mass transfer from the solid phase towards the fluid phase. The constitutive relations governing the thermomechanical behaviour, generalised diffusion, and transfer are structured by the dissipation inequality. The particular case of soil suffusion is investigated with a focus on constitutive laws. A new constitutive law for suffusion is constructed based on thermodynamic conditions and experimental investigations. This erosion law is linearly related to the power of seepage flow and to the erosion resistance index. Owing to its simplicity, this law tackles the overall trend of the suffusion process and permits the formulation of an analytical solution. This new model is then applied to simulate laboratory experiments, by both analytical and numerical methods. The comparison shows that the newly developed model, which is theoretically consistent, can reproduce correctly the overall trend of the cumulated eroded mass when the permeability evolution is small. In addition, the results are provided for four different materials, two different specimen sizes, and various hydraulic loading paths to demonstrate the applicability of the new proposed law.