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.

翻译：本研究探讨了含库仑摩擦接触的断裂多孔介质中混合维热-水-力(THM)模型，该类模型在深层地热系统水力压裂及CO2封存诱发地震风险评估等应用中具有重要作用。我们首先将基于热力学第一、二定律推导的热力学一致THM模型[16]扩展至混合维框架。考虑两种能量方程形式：基于能量守恒或熵平衡方程，假定不存在热-孔隙-弹性耗散。研究重点在于针对两类方程形式及一般单相流体热力学模型，设计保持能量估计的时空离散格式。该目标通过基于强制通量的非等温流有限体积离散与非保守对流项定制离散方法实现，并与采用面常量拉格朗日乘子表征表面牵引力的接触-力学模型混合有限元离散相结合，从而保持接触项的耗散特性。通过二维算例比较两种THM模型离散格式的收敛性、精度和鲁棒性，涵盖对流主导热力学机制的离散裂缝网络模型，以及弱可压缩液体或高可压缩气体热力学模型。