Computation of permeability with Fast Fourier Transform from 3-D digital images of porous microstructures

Abstract

Purpose – The purpose of this paper is to present a fully automated numerical tool for computing the effective permeability of porous media from digital images which come from the modern imagery technique. Design/methodology/approach – The permeability is obtained by the homogenization process applied to a periodic rigid solid in which the fluid flow is described by the Stokes equations. The unit cell problem is solved by using the Fast Fourier Transform (FFT) algorithm, well adapted for the microstructures defined by voxels. Findings – Various 3-D examples are considered to show the capacity of the method. First, the case of flow through regular arrays of aligned cylinders or spheres are considered as benchmark problems. Next, the method is applied to some more complex and realistic porous solids obtained with assemblies of overlapping spherical pores having identical or different radii, regularly or randomly distributed within the unit cell. Originality/value – The use of FFT allows the resolution of high-dimension problems and open various possibilities for computing the permeability of porous microstructures coming from X-ray microtomography.