Parametric solutions of coupled Thermo-Hydro-Mechanical problems in real time with Proper Generalized Decomposition

Proper Generalized Decomposition (PGD) is a Model Order Reduction (MOR) technique used in this study to solve parametric transient Thermo-Hydro-Mechanical (THM) problems in porous media, with focus on deep geological repositories. PGD enables computing real-time solutions for THM parametric problems, which are critical in applications like enhanced oil recovery, geothermal energy, and nuclear waste disposal. This study offers two key contributions. First, it describes the separated discrete operators required by PGD to account for material and geometrical parameters in transient THM problems. Second, it explores the effectiveness of PGD through three repository model problems: (1) parametrized by rock material properties (elastic modulus, thermal and hydraulic conductivity), (2) geometrically parametrized by canister spacing, and (3) a combined four-parameter model demonstrating PGD’s ability to handle multiparameter problems. The results show that PGD applied for THM processes in porous media provides efficient, real-time solutions for complex problems, significantly enhancing computational performance to allow its incorporation in multiquery and real-time scenarios.