Constitutive equations for ionic transport in porous shales

Abstract

[1] 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.

Electrokinetic coupling in unsaturated porous media

“…(in units of C m -3 ) is defined as the excess of charge per unit pore volume at full water saturation [9,10,11]. We neglect the charge density that is associated with the interface between the wetting and the non-wetting phases, since it is small in comparison with the charge density associated with the pore water-solid interface [9].…”

What is the significance of pore pressure in a saturated shale layer?

“…[20] As proposed by Derjaguin et al [1987], and formalized by different authors [e.g., Sherwood, 1994;Moyne and Murad, 2002;Revil and Leroy, 2004], fluid flow across a clay-rock is proportional to the gradient of the "hydrodynamic" or "partial" pressure p f = p N − p D , i.e., the bulk or equilibrium solution pressure. This suggests that the disjoining pressure has no direct impact on fluid flow.…”

Modeling Coupled Processes in Clay Formations for Radioactive Waste Disposal

“…In the literature, two kinds of modeling approaches for diffusive transport in clay materials are available (Revil and Leroy, 2004;Appelo et al, 2010;Bourg et al, 2003;Jougnot et al, 2009). One is based on the explicit consideration of coupling between diffusive and electro-chemical processes.…”

“…Modeling of diffusive transport in clay rocks (natural system) is complicated by the existence of heterogeneities at different scales and coupling between diffusive and electro-chemical processes (Revil and Leroy, 2004;Appelo et al, 2010;Bourg et al, 2003;Jougnot et al, 2009). At a local scale, different pore spaces co-exist within a representative elementary volume (REV), or a "point" within the context of continuum mechanics.…”