Thermoporoelasticity via homogenization I. Modeling and formal two-scale expansions

Abstract : In this paper we derive a macroscopic model for thermoporoelasticity from the pore scale linearized fluid-structure and energy equations. We consider the continuum mechanics thermody-namically compatible pore scale equations corresponding to realistic rock mechanics parameters. They are upscaled using two-scale asymptotic expansions. For the upscaled equations a Lya-punov functional (a generalization of Biot's free energy) is constructed and the well-posedness * C.J.v.D. acknowledges support of the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program " Investissements d'Avenir " (ANR-11-IDEX-1 of the model is discussed. Possible applications to large time numerical simulations are pointed out.
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Cornelis van Duijn, Andro Mikelic, Mary Wheeler, Thomas Wick. Thermoporoelasticity via homogenization I. Modeling and formal two-scale expansions. International Journal of Engineering Science, Elsevier, 2019, 138, ⟨10.1016/j.ijengsci.2019.02.005⟩. ⟨hal-01650194⟩

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