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Real-time solutions of parametric Thermo-Hydro-Mechanical problems with Proper Generalized Decomposition

par Moaven, Arash
Président du jury Berke, Peter
Promoteur Zlotnik, Sergio;Massart, Thierry,Jacques
Publication Non publié, 2023-07-04

Thèse de doctorat

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Résumé :

The Proper Generalized Decomposition (PGD) is a mathematical framework belonging to the Model Order Reduction (MOR) class of techniques. To the best of the author's knowledge, this methodology has not been applied to transient coupled Thermo-Hydro-Mechanical (THM) problems in porous media. THM models have been developed for various geo-environmental applications, such as enhanced oil recovery, geothermal energy extraction, and deep geological repositories. This thesis studies the application of the PGD technique to THM problems, drawing inspiration from the concept of deep geological repositories. The study demonstrates how the PGD methodology can be used to obtain real-time solutions to THM problems, using a simplified deep geological repository as an example.The developed generalized solutions provided by PGD are perfectly suited to be used in multi-query situations, such as parameter identification and calibration procedures, optimization, or uncertainty quantification. The extremely fast response obtained after the training phase opens the doors to real-time inversions, control situations, or simply increasing the accuracy of the inverse identification procedures by allowing a much larger number of evaluations of the objective function when compared to traditional discretization techniques.This work presents two main contributions. First, it provides a detailed description of the separated discrete operators that are required in the PGD methodology when material parameters, geometrical parameters, or a combination of both are considered. This is done in the context of transient coupled THM problems. Second, the study investigates several configurations related to the use of the PGD methodology in the context of coupled problems and transient problems.Two models of a simplified deep geological repository problem are presented to show the capabilities of the proposed methodology. The first one is parametrized by the physical properties of the host rock (elastic modulus, thermal conductivity, hydraulic conductivity). This would be useful, for example, in the solution of an inverse problem to characterize the actual properties of the rock. The second model addresses a geometrical parametrization that controls the distance between the canisters when the repository is set to a grid canister. This is intended for the development useful to study and design the repository and to determine, for example, an optimal distance avoiding temperature runouts.The study as a whole employs a combination of techniques (PGD with the modeling of coupled THM processes in porous media) to produce a range of solutions and an efficient solver that functions in real-time.