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 Ampere'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. (c) 2007 Elsevier Inc. All rights reserved.