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

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...

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Bibliographic Details
Published in:Transport in porous media 2018-08, Vol.124 (1), p.137-158
Main Authors: Brun, Mats K., Berre, Inga, Nordbotten, Jan M., Radu, Florin A.
Format: Article
Language:English
Subjects:
Civil Engineering
Classical and Continuum Physics
Computational fluid dynamics
Conservation equations
Coordinates
Deformation effects
Derivation
Earth and Environmental Science
Earth Sciences
Elastic deformation
Elastic systems
Energy conservation
Fluid flow
Fluid-structure interaction
Geotechnical Engineering & Applied Earth Sciences
Heat transfer
Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Mathematical models
Porous materials
Static deformation
Thermoelasticity
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Summary: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.
ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-018-1056-8