THEORETICAL AND NUMERICAL ANALYSES OF PERMEABILITY OF POROUS MEDIUM WITH CRACKING INCLUSIONS

Cracked porous material is considered as a two phase composite with a porous matrix and cracking inclusions. An interaction direct derivative (IDD) solution is derived to analyze the permeability of this composite through classic micromechanics theory. Based on the repeating unit cell concept, a simple model with periodic microstructures is suggested to represent cracking geometry in order to study the impact of geometrical characteristics including cracking length, density, orientation, average spacing and connectivity. The finite element analysis is further developed to calculate its overall permeability, which is compared with the IDD explicit results. IDD solution employs the single parameter, cracking density, to capture the impact of cracking on permeability with good applicability and accuracy as cracking degree is not too high. Numerical simulation also shows that: IDD solution tends to deviate from numerical results and underestimate the interaction of cracks as the cracking density is further increasing and cracks approach more closer between one another. During this approaching course, the relationship between cracking density and overall permeability can be described by logarithm law. Once cracks are connected together eventually, the overall permeability would be mutated, and the strong near-field interaction of connectivity should be taken into account to estimate the overall permeability.