Image-based effective medium approximation for fast permeability evaluation of porous media core samples

An image-based effective medium approximation (EMA) is developed so as to permit very fast transport properties evaluations of 3D porous media. From an image-based porous network (IBPN) built upon digital image processing of 3D binary images, we focus on throat's local geometrical properties at the pore scale, for being the most sensible structural units which build up the local pressure. This approach is a 3D image-based extension of the critical point approach proposed in 2D fractures. We show, from analyzing various core rock samples available in the literature, that the asymptotic assumptions associated with the preeminence of critical points in throats are indeed geometrically relevant. We then describe how the image-based EMA evaluated from the conductances computed from the discrete IBPN can be reliably evaluated. The proposed method is evaluated upon the estimation of core sample permeability from binarized image obtained using X-ray tomography. Since it combines digital image treatments with statistical data post-processing without the need of computational fluid dynamics (CFD) computation, it is extremely cost efficient. The results are compared with a micro-scale Stokes flow computation in various rock samples. The sensitivity to the pore discretization also is discussed and illustrated.