Flow Study in a Double Porosity Medium Containing Ellipsoidal Occluded Macro-voids

摘要

This paper presents an analytical study of permeability evolution in a dual length-scale porous medium: at the smallest or microscopic scale, connected inter-layer and inter-particular voids are present within the clay matrix, while at the upper or mesoscopic scale, non-connected inter-aggregate pores are present. By assuming ellipsoidal shapes for the macro-voids and low concentrations in macro-voids, analytical expressions are derived for the effective permeability tensor at the macroscopic scale, based on the analysis of fluid flow at pore level. The permeability tensor is obtained solely from the study of fluid flow in the clay matrix performed in Part I, without the need of solving Stokes’ equations in the inter-aggregate void space. The analytical permeability depends on the macro-porosity and the eccentricity ratio, and its evolution with both parameters is investigated over the range of validity of the analytical solution, that is, for porosity values lower than 10% and eccentricity ratios allowing non-connectedness of the macro-voids. Comparisons are also made with existing correlations between permeability and porosity. The analytical expressions obtained are applied to permeability predictions in pure bentonite clay, saturated and mechanically compacted under high pressures, and soaked by pollutant solutions.