Geoscience Reference
In-Depth Information
Since the pore fluid pressure P at the ground surface is close to zero, the potential
dž
0 at
z
D
0 whereas the electric field has only vertical component. As is evident
from Eq. (
8.13
), the total current
j
D
r
‰ in the uniform medium is equal to zero
everywhere. This means that the magnetic field due to electrokinetic effect is absent
as well. In Chap.
10
we show that the significant variations of electric potential
can only be expected around the inhomogeneities of rock conductivity and of
streaming potential coefficient C.
8.1.3
Electrokinetic Effect in Anisotropical Media
However the magnetic effects can appear in a homogeneous but a macro-
anisotropical medium (Surkov
2000
). As one example, let us assume that the rock
has a plane-stratified structure in which the water-saturated layers are sandwiched
between the low-permeable layers. The underground fluid can filtrate along the
networks of clustered channels located inside the water-saturated layers but it
cannot flow across these layers. For simplicity, we suppose that all the layers are
parallel and make the same angle Ǜ with the vertical axis
z
.
The medium conductivity along the high-conducting water-saturated layers is
greater than that of the dry rock. So, the average rock conductivity can exhibit
anisotropic properties as well because of the higher conductivity along the layers as
compared to that across these layers. However, at first the average rock conductivity
is considered as a scalar constant value.
The origin of coordinate system x;y;
z
is situated at the ground surface while
the axes x
0
;y
0
;
z
0
of the auxiliary coordinate system fixed to the high-permeable
layers are shown in Fig.
8.4
. The components of electrokinetic current density in
the coordinate system x
0
;y
0
;
z
0
are given by
j
ek
x
0
D
C@
x
0
P; j
ek
y
0
D
C@
y
0
P; j
ek
z
0
D
0:
(8.14)
The same vector in the basic coordinate system x;y;
z
can be expressed through
pore pressure gradient in the following manner
j
ek
D
C
r
P;
(8.15)
where C denotes the tensor with the following components
0
1
10 0
0 sin
2
Ǜ sin 2Ǜ=2
0 sin 2Ǜ=2 cos
2
Ǜ
C
D
@
A
:
(8.16)
A cylindrical region with enhanced pore fluid pressure (see Fig.
8.4
) has
been studied by Surkov (
2000
) to examine the electrokinetic effect in the above
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