  In this study, we explore mixed-dimensional Thermo-Hydro-Mechanical (THM)
models in fractured porous media accounting for Coulomb frictional contact at
matrix fracture interfaces. The simulation of such models plays an important
role in many applications such as hydraulic stimulation in deep geothermal
systems and assessing induced seismic risks in CO2 storage. We first extend to
the mixed-dimensional framework the thermodynamically consistent THM models
derived in [16] based on first and second principles of thermodynamics. Two
formulations of the energy equation will be considered based either on energy
conservation or on the entropy balance, assuming a vanishing
thermo-poro-elastic dissipation. Our focus is on space time discretisations
preserving energy estimates for both types of formulations and for a general
single phase fluid thermodynamical model. This is achieved by a Finite Volume
discretisation of the non-isothermal flow based on coercive fluxes and a
tailored discretisation of the non-conservative convective terms. It is
combined with a mixed Finite Element formulation of the contact-mechanical
model with face-wise constant Lagrange multipliers accounting for the surface
tractions, which preserves the dissipative properties of the contact terms. The
discretisations of both THM formulations are investigated and compared in terms
of convergence, accuracy and robustness on 2D test cases. It includes a
Discrete Fracture Matrix model with a convection dominated thermal regime, and
either a weakly compressible liquid or a highly compressible gas
thermodynamical model.
