Numerical investigation of macroscopic permeability of biporous solids with elliptic vugs

In this paper, we aim to determine the effective permeability of biporous solids containing fractures in a computational homogenization framework. Precisely, at the local scale, we use the Brinkman law for the porous solids and the Stokes equations within fractures. The resolution of the Brinkman/Stokes coupled equations is performed with the fast Fourier transform iterative scheme on periodic unit cells. The role of the dimensions and orientation of the cracks is investigated. The simulation results are also compared with an analytical formulation based on Mori–Tanaka estimates. The findings indicate that, depending on the considered flow direction, the dimensions and orientation of cracks strongly affect the effective permeability of fractured porous media. Besides, we also determine the macroscopic permeability for a population of fractures with regular and random orientations, dimensions and shapes. The results are then given and discussed. Graphic Abstract