Seminar 15 June

This week’s seminar will be held by Mats Brun at 1pm.

Title: Upscaling and discretization of coupled geomechanics, flow and heat in a poro-elastic medium in the quasi-static situation

Abstract:
Motivated by geothermal energy storage in the subsurface, we undertake the formal derivation of Biot’s law for a poro-elastic medium completely saturated by a fluid, coupled with heat conduction laws for both the fluid and solid phase. We assume small displacements of the solid structure (i.e. linear strain), a fully connected void and grain space, that the fluid flow is incompressible, and that the fluid/solid interface coupling conditions may be linearized. We start with the microscale model, and apply the technique of homogenization in order to derive the upscaled model, in the case of periodically distributed pores. Assuming the homogenization ansatz holds true, we obtain a fully coupled system of equations on the macro-scale accounting for the effects of geomechanics, heat conduction, and fluid flow within a porous material.

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