Abstract
This article presents the analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, occluded macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for the pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its size is characterized by the macro-porosity. Confrontations are made with numerical solutions in order to investigate the applicability of the analytical pressure and velocity solutions to microstructures of finite size.
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Bouchelaghem, F. Analytical Determination of Flow Patterns in a Double Porosity Medium Containing Ellipsoidal Occluded Macro-Voids. Transp Porous Med 85, 97–115 (2010). https://doi.org/10.1007/s11242-010-9548-1
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DOI: https://doi.org/10.1007/s11242-010-9548-1