Mathematical Modeling of Electrokinetic Transport and Enhanced Oil Recovery In Porous Geo-Media - Electrokinetics for Petroleum and Environmental Engineers - page 204

Where, the viscous coupling is considered through the off-diagonal
coefficients for the water and the oil phases ( k

and ) respectively.
Equation 5.69 is analogous to the basic equation used in pressure driven
two-phase flow (eq. 5.67), where k e replaces K , and the electrical gradient
is the driving force. Analogous to the pressure driven two-phase flow, the
generalized off-diagonal relative EO permeability coefficients are used to
capture the contribution of the viscous coupling.

k

er wo , er ow ,

5.8.4 Evaluation of EO Transport Coefficients

Reliable prediction of the flow patterns necessitates accurate representa-
tion and determination of the relative permeability coefficients under the
applied electrical gradient. In this section, relative EO permeability coeffi-
cients are evaluated for a specific case of two-phase fluid flow in water-wet
porous media, where the second fluid phase is oil. It is postulated that the
viscous drag on the oil phase, exerted by the electro-osmotic flow of the
water phase is responsible for the transport of oil in the absence of a pres-
sure gradient.
The EO transport of non-conductive liquids (e.g., oil) using conductive
liquids (e.g., water) in capillaries, known as EO viscous pumps has been
investigated for MEMS devices and microfluidic technologies (Santiago,
2001; Brask et al., 2002; Yao and Santiago, 2003; Gao et al., 2005, 2007; Liu
et al., 2009). EO pumps are fabricated mostly of porous glass or fused silica
with deprotonated silanol groups on the surface and are based on the EO
flow of an electrolyte to generate pressure differentials under a DC electric
field (Santiago, 2001; Brask et al., 2002). The performance of EO pumps
has been reported to depend on the porosity, tortuosity, and pore size of
the porous matrix, pH and ionic concentration of the electrolyte (Santiago,
2001; Brask et al., 2002). The basic premise of EO pumps is that the EO
flow of the conducting fluid exerts a drag force on the non-conducting
fluid to generate two-phase flow. This is analogous to the postulated pro-
cess in electrically enhanced oil recovery in water wet porous medium.
In EKEOR applications, a similar viscous drag phenomenon leads to oil
transport under an applied electric field (Amba et al., 1964; Amba et al.,
1965; Chilingar et al., 1968, 1970; Wittle et al., 2006a,b, 2008 a,b,c, 2011;
Haroun et al., 2009; Hill et al., 2010; Ghazanfari et al., 2012a, 2012b, 2013a;
Al Shalabi et al., 2012).
We discuss here the experimental and analytical approaches on evalu-
ation of relative EO permeability coefficients. In order to evaluate the
relative permeability coefficients as a function of water saturation, the
porous medium is assumed to be water wet. So, we refer to water as the