Environmental Engineering Reference
In-Depth Information
Where, S
f
is the total internal pore surface area (m
2
). The specific con-
ductivity of the sample in this model is given as:
L t
−
2
t
−
2
(5.50)
=
s
+
S
s
ee
f
s
where,
s
f
and
s
S
are the specific conductivity of the fluid in the capil-
laries (Ω
-1
m
-1
) and the specific surface conductivity respectively. The coef-
icient
L
ev
( =
L
ev
) is given as:
LL
t
−
2
(5.51)
==−
ex
/
m
ev
ve
where,
e
is the dielectric constant of the fluid (Farads per meter),
m
is
the viscosity of the fluid (Pascal seconds) and
x
is the zeta potential at
the slipping plane in DDL (volts). The
L
vv
coefficient is given by Darcy's
law as:
K
L
=
(5.52)
vv
m
where, K is the intrinsic permeability (m
2
). Substituting the coefficients
in equation 5.48, Ishido and Mizutani (1981) derived the following equa-
tion for the coupled flow:
(
)
∇+
⎧
I
t
−
2
t
−
2
E t
−
2
P
=−
s
+
S
s
ex
/
m
∇
f
s
⎪
⎪
(5.53)
⎨
)
∇−
⎜
E
k
⎞
⎟
∇
(
q t
=
−
2
ex
/
m
P
m
Saunders et al., (2006) defined the coupling term as:
ex
m
f
===
(5.54)
LLL
F
ev
ve
s
s
f
is the forma-
tion factor,
s
r
is the conductivity of the soil/rock fluid system, and
s
f
is
the conductivity of the pore fluid. For single phase steady state flow, when
the electrical current caused by advection is balanced by electrical cur-
rent caused by conduction, the streaming potential coupling coefficient is
defined as (Saunders et al., 2006, 2008):
where,
e
is fluid permittivity,
x
is zeta potential, and
F
=
r
ex
ms
∇
∇
E
P
L
f
(5.55)
C
=
==
s
r
f
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