Image-based effective medium approximation for fast permeability evaluation of porous media core samples
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ORIGINAL PAPER
Image-based effective medium approximation for fast permeability evaluation of porous media core samples Jacques Franc1 · Romain Guibert1
´ · Pierre Horgue1 · Gerald Debenest1 · Franck Plouraboue´ 1
Received: 9 December 2019 / Accepted: 24 July 2020 © Springer Nature Switzerland AG 2020
Abstract 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. Keywords Porous media · Effective properties · Image-based method · Effective medium approximation · Permeability
1 Introduction Image-based pore-scale modeling has progressed significantly during the past decades, due to improvements in X-ray imaging sources and equipments, in image analysis processing, and computational fluid dynamics (CFD) efficiency.
Romain Guibert
[email protected] Jacques Franc [email protected] Pierre Horgue [email protected] G´erald Debenest [email protected] Franck Plourabou´e [email protected] 1
Institut de M´ecanique des Fluides de Toulouse, IMFT, Universit´e de Toulouse, CNRS, Toulouse, France
In the following, CFD methods refer to 3D discretization of Navier-Stokes equations up to pore scale. This also obviously includes all Stokes solvers (being the relevant low Reynolds limit of Navier-stokes ones) with any discrete formulation (e.g., finite volumes, finite elements, finite differences, immersed boundaries methods, and lattice Boltzmann method) defined either on structured or unstructured meshes. Obviously pore network models (PNM) do not pertain to CFD methods, since their definition and applications are much narrow. Nevertheless, the reliability of digital rock physics (DRP) predictions compared with real experiment measurements remains a challenging issue which needs to consider crucially important parameters such as typical pore-scale size, imag
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