Permeability of Microcracked Porous Solids: Modeling from Homogenization to Percolation

Abstract

This paper establishes a comprehensive modeling for permeability of porous solids incorporating cracks with clustering extent ranging from nonoverlapping to percolation. The geometry of cracks is characterized through the crack density, orientation, connectivity, and fractal dimension of crack networks. The interaction direct derivative (IDD) model from effective medium theory is developed to predict the permeability of solids with nonoverlapping cracks and further extended by a two-step scheme to account for cracks with local clustering. The continuum percolation theory is adopted to build the permeability scaling law for crack networks approaching percolation. The comprehensive model thus established was validated against numerical simulations for crack networks with different geometry characteristics. The obtained results show that (1) the classical IDD model can predict satisfactorily the permeability for nonoverlapping cracks and the crack opening has nearly no impact on overall permeability, (2) the extended IDD model considers successfully the local clustering of cracks, the prediction range is greatly enhanced for overall permeability, and the impact of crack opening is still limited, and (3) as crack networks approachi percolation, the overall permeability observes a scaling law highlighting the importance of crack connectivity, and the impact of crack opening assumes a power law with the exponent related to the fractal dimension of crack networks.