Open AccessConstitutive equations for ionic transport in porous shales
Author(s) -
Revil A.,
Leroy P.
Publication year - 2004
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/2003jb002755
Subject(s) - constitutive equation , oil shale , thermodynamics , porosity , porous medium , ionic bonding , materials science , mineralogy , mechanics , physics , chemistry , geology , geotechnical engineering , ion , quantum mechanics , finite element method , paleontology
The constitutive coupled equations describing ionic transport in a porous shale are obtained at the scale of a representative elementary volume by volume averaging the local Nernst‐Planck and Stokes equations. The final relationships check the Onsager reciprocity to the first order of perturbation of the state variables with respect to the thermostatic state. This state is characterized by a modified version of the Donnan equilibrium model, which accounts for the partition of the counterions between the Stern and diffuse Gouy‐Chapman layers. After upscaling the local equations the material properties entering the macroscopic constitutive equations are explicitly related to the porosity of the shale, its cation exchange capacity, and some textural properties such as the electrical cementation exponent entering Archie's law. This new model is then applied to predict the salt filtering and electrodiffusion efficiencies of a shale layer.