Mathematical Modeling of Electrokinetic Transport and Enhanced Oil Recovery In Porous Geo-Media - Electrokinetics for Petroleum and Environmental Engineers - page 195

1.8

Numeric C/C0; 35d; C0=0.05M; L=20cm
Test C/C0; 35 days; C0=0.15M; L=10cm
Numeric pH; 35d
Test pH; 35 days

1.6

1.4

1.2

1
0.8

15d C/C 0

0.6

35d pH

0.4

35d C/C 0

0.2

0

0 0.2 0.4

Distance from anode end, X/L

0.6 0.8 1

Figure 5.3 Variation of total lead (Pb) concentration and pH distribution as predicted by
Cao (1997) model and measured by experiment for a 35.day duration (After Pamukcu,
2009)

between the applied electrical and pressure (hydraulic) gradients (Ishido
and Mizutani, 1981, Morgan et al., 1989; Revil and Pezard, 1999; Revil et
al., 2007; Saunders et al., 2008; Jackson, 2010). The general relationship
between the fluxes of electric current ( I ) and fluid volume flow ( q ), and the
electric potential gradient (

E) and fluid pressure gradient ( P) are given

∇ ∇

as (Jackson, 2010):

I LELP
qLELP

=− ∇ − ∇

⎧
⎩

(5.48)

ee ev

=− ∇ − ∇

ve vv

Where, L ij are the phenomenological coefficients. The term L ee ∇ E rep-

resents Ohm's law, and the term L vv ∇ P represents Darcy's law. The terms

E and correspond to the coupling effect. In order to give
explicit expressions of L ij coefficients for a general porous medium, Ishido
and Mizutani (1981) used a capillary tube model with cross-sectional area
of A (m 2 ), overall length L (m) in the direction of general flow, the length
of a tortuous pore channel as Lf f , and the free cross-sectional area available
to flow as A f . The porosity (n), tortuosity (t), specific internal area S (m -1 ),
and the hydraulic radius h (m) of the model is defined as:

L ev ∇ P and L ve ∇

AL
AL

L
L

S
AL

AL
S

f f f f f f

n t S h nS

− 1

(5.49) = , = , = , = =

f