Abstract
Mean field homogenization schemes are formulated for the Stokes to Darcy upscaling of the permeability on the basis of generalized inhomogeneity problems in which flow is described by Brinkman equations. The average velocity and drag force concentrations for flow in a potentially composite inclusion are characterized in terms of a permeability contribution tensor and an equivalent permeability, which allow for the direct transposition to Stokes to Darcy upscaling of most homogenization schemes available in elasticity (self-consistent, differential, Mori–Tanaka, Maxwell, …). The unified framework extends existing effective medium and cell model permeability estimates. Its flexibility is illustrated on a panel of microstructures of porous media: granular or fibrous materials, materials with spanning cylindrical or crack-like pores, double porosity materials with disconnected or connected meso-porosity and compared with existing or newly produced full field simulation results.
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