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Thermoporoelasticity via homogenization: modeling and formal two-scale expansions. (English) Zbl 1425.74396

Summary: 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 thermodynamically compatible pore scale equations corresponding to realistic rock mechanics parameters. They are upscaled using two-scale asymptotic expansions. For the upscaled equations a Lyapunov functional (a generalization of Biot’s free energy) is constructed and the well-posedness of the model is discussed. Possible applications to large time numerical simulations are pointed out.

MSC:

74Q05 Homogenization in equilibrium problems of solid mechanics
74F05 Thermal effects in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
80A20 Heat and mass transfer, heat flow (MSC2010)

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References:

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