## Upscaling of the Coupling of Hydromechanical and Thermal Processes in a Quasi-static Poroelastic Medium

##### Type

Journal article###### Peer reviewed

###### publishedVersion

##### Åpne

##### Dato

2018-08

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We undertake a formal derivation of a linear poro-thermo-elastic system within the
framework of quasi-static deformation. This work is based upon the well-known derivation
of the quasi-static poroelastic equations (also known as the Biot consolidation model) by
homogenization of the fluid-structure interaction at the microscale. We now include energy,
which is coupled to the fluid-structure model by using linear thermoelasticity, with the full
system transformed to a Lagrangian coordinate system. The resulting upscaled system is similar
to the linear poroelastic equations, but with an added conservation of energy equation,
fully coupled to the momentum and mass conservation equations. In the end, we obtain a
system of equations on the macroscale accounting for the effects of mechanical deformation,
heat transfer, and fluid flow within a fully saturated porous material, wherein the coefficients
can be explicitly defined in terms of the microstructure of the material. For the heat transfer
we consider two different scaling regimes, one where the Péclet number is small, and
another where it is unity.We also establish the symmetry and positivity for the homogenized
coefficients.

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##### Utgiver

Springer##### Samlinger

Copyright 2018 The Authors