Electrokinetic coupling in unsaturated porous media

• Published in: Journal of colloid and interface science Vol. 313; no. 1; pp. 315 - 327
• Main Authors: Revil, A., Linde, N., Cerepi, A., Jougnot, D., Matthäi, S., Finsterle, S.
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.09.2007; Elsevier
• Subjects: Capillary pressure; Capillarypressure; Chemistry; Clay; Colloidal state and disperse state; CURRENT DENSITY; DOLOMITE; DRAINAGE; Earth Sciences; ELECTRIC CONDUCTIVITY; Electro-osmosis; ELECTRODYNAMICS; Environmental Sciences; Exact sciences and technology; General and physical chemistry; Geophysics; Global Changes; NernstPlanck equation; Nernst–Planck equation; PERMEABILITY; Physics; POROUS MATERIALS; Porous media; SATURATION; Sciences of the Universe; Stokes equation; Streaming potential; Surface physical chemistry; WATER; WATER SATURATION; Porous media; Clay; Electro-osmosis; Streaming potential; Nernst–Planck equation; Stokes equation; Saturation; Capillary pressure; Electrokinetics; Osmosis; Potential; Porous material; Nernst-Planck equation
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1016/j.jcis.2007.03.037

We consider a charged porous material that is saturated by two fluid phases that are immiscible and continuous on the scale of a representative elementary volume. The wetting phase for the grains is water and the nonwetting phase is assumed to be an electrically insulating viscous fluid. We use a volume-averaging approach to derive the linear constitutive equations for the electrical current density as well as the seepage velocities of the wetting and nonwetting phases on the scale of a representative elementary volume. These macroscopic constitutive equations are obtained by volume-averaging Ampère's law together with the Nernst–Planck equation and the Stokes equations. The material properties entering the macroscopic constitutive equations are explicitly described as functions of the saturation of the water phase, the electrical formation factor, and parameters that describe the capillary pressure function, the relative permeability functions, and the variation of electrical conductivity with saturation. New equations are derived for the streaming potential and electro-osmosis coupling coefficients. A primary drainage and imbibition experiment is simulated numerically to demonstrate that the relative streaming potential coupling coefficient depends not only on the water saturation, but also on the material properties of the sample, as well as the saturation history. We also compare the predicted streaming potential coupling coefficients with experimental data from four dolomite core samples. Measurements on these samples include electrical conductivity, capillary pressure, the streaming potential coupling coefficient at various levels of saturation, and the permeability at saturation of the rock samples. We found very good agreement between these experimental data and the model predictions. Resistivity, capillary pressure curve, and relative streaming potential coupling coefficient versus saturation of water in a porous medium.