{"id":253,"date":"2021-01-05T12:16:18","date_gmt":"2021-01-05T11:16:18","guid":{"rendered":"http:\/\/hebergement.universite-paris-saclay.fr\/upgeo\/?page_id=253"},"modified":"2022-02-19T00:14:34","modified_gmt":"2022-02-18T23:14:34","slug":"task-2-mathematical-model-for-the-quasi-static-thermo-hydro-mechanics-thm-via-upscaling-task-co-leaders-andro-mikelic-ludovic-goudenege-and-benjamin-brigaud","status":"publish","type":"page","link":"https:\/\/hebergement.universite-paris-saclay.fr\/upgeo\/?page_id=253&lang=en","title":{"rendered":"Task 2. Mathematical model for the quasi-static Thermo-Hydro-Mechanics (THM) via upscaling"},"content":{"rendered":"\n<p>There will be two main objectives of this task: (1) derive, using homogenization, the equations of quasi-static thermoporoelasticity and (2) develop, based on the geological data for the limestones and sandstones, a reliable high-fidelity numerical solver for the computation of the effective coefficients (permeability, Biot\u2019s coefficient, Gassmann tensor, thermal dispersivity and effective heat capacity). We will develop a model based on the fluid-structure thermodynamically compatible pore scale equations, corresponding to realistic rock mechanics parameters [1]. Then, we will homogenize the dimensionless equations with respect to the random microscopic geometry [2]. We expect to derive an analogous upscaled system for a random pore structure and we will develop its analysis, study its discretization in time and space and write a robust numerical solver [2]. Our objective will be to develop a flexible solver that will provide, for given statistically homogeneous geometrical structure, computations of the permeability, Biot\u2019s coefficient, Gassman\u2019s tensor and the thermal diffusivity. Finally, we will implement it as a plug-in for Eclipse, PumaFlow, Tough2 and DuMuX \/Dune software packages, which will be used in task 1 and 3.<\/p>\n\n\n\n<p>[1]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; C. J. van Duijn, A. Mikeli\u0107, M. F. Wheeler, and T. Wick, \u201cThermoporoelasticity via homogenization: Modeling and formal two-scale expansions,\u201d <em>Int. J. Eng. Sci.<\/em>, vol. 138, pp. 1\u201325, May 2019, doi: 10.1016\/j.ijengsci.2019.02.005.<\/p>\n\n\n\n<p>[2]&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; C. J. van Duijn, A. Mikeli\u0107, and T. Wick, \u201cMathematical theory and simulations of thermoporoelasticity,\u201d <em>Comput. Methods Appl. Mech. Eng.<\/em>, vol. 366, p. 113048, Jul. 2020, doi: 10.1016\/j.cma.2020.113048.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>There will be two main objectives of this task: (1) derive, using homogenization, the equations of quasi-static thermoporoelasticity and (2) develop, based on the geological data for the limestones and sandstones, a reliable high-fidelity numerical solver for the computation of the effective coefficients (permeability, Biot\u2019s coefficient, Gassmann tensor, thermal dispersivity and effective heat capacity). We [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":246,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-253","page","type-page","status-publish","hentry","post-preview"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Task 2. Mathematical model for the quasi-static Thermo-Hydro-Mechanics (THM) via upscaling - UPGEO<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hebergement.universite-paris-saclay.fr\/upgeo\/?page_id=253&lang=en\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Task 2. 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