Modeling of fluid diffusion in layers with double porosity using homogenization

Abstract eng:
The paper deals with the perfusion in hierarchically arranged double porous media constituted by transversely periodic layers. In each layer the reference periodic cell is composed of several compartments comprising the matrix, featured by permeability decreasing with the scale parameter, and several disconnected channels where the permeability is scale independent. Homogenization of the steady Darcy flow in such medium is performed by the method of periodic unfolding. The limit model involves the homogenized permeabilities associated with the channels and the transmission and drainage coefficients associated with the mass redistribution between the microstructural compartments. Due to the layered organization of the medium, the diffusion problem in 3D heterogeneous body can be replaced by a finite number of 2D problems describing the homogenized fluid redistribution in each homogenized layer. For such decomposition, coupling conditions governing the fluid exchange between the layers can be derived. This model is intended for simulations of the blood perfusion in the brain tissue.

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