Three-scale analysis of the permeability of a natural shale

C. A. Davy and P. M. Adler
Phys. Rev. E 96, 063116 – Published 26 December 2017

Abstract

The macroscopic permeability of a natural shale is determined by using structural measurements on three different scales. Transmission electron microscopy yields two-dimensional (2D) images with pixels smaller than 1 nm; these images are used to reconstruct 3D nanostructures. Three-dimensional focused ion beam–scanning electron microscopy (5.95- to 8.48-nm voxel size) provides 3D mesoscale pores of limited relative volume (1.71–5.9%). Micro-computed tomography (700-nm voxel size) provides information on the mineralogy of the shale, including the pores on this scale which do not percolate; synthetic 3D media are derived on the macroscopic scale by a training image technique. Permeability of the nanoscale, of the mesoscale structures and of their superposition is determined by solving the Stokes equation and this enables us to estimate the permeabilities of the 700-nm voxels located within the clay matrix. Finally, the Darcy equation is solved on synthetic 3D macroscale media to obtain the macroscopic permeability which is found in good agreement with experimental results obtained on the centimetric scale.

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  • Received 7 May 2017

DOI:https://doi.org/10.1103/PhysRevE.96.063116

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

C. A. Davy*

  • Laboratoire de Mécanique de Lille (LML), FRE CNRS 3723 and Ecole Centrale de Lille, CS 20048, F-59651 Villeneuve d'Ascq Cedex, France

P. M. Adler

  • UPMC METIS. Boîte 105, 4 place Jussieu, 75252 Paris cedex 05, France

  • *catherine.davy@centralelille.fr
  • pierre.adler@upmc.fr

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Vol. 96, Iss. 6 — December 2017

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