Geoscience Reference
In-Depth Information
data are exceptionally good in terms of quality. It is
indeed difficult to get very good data in unsaturated con-
ditions because of the drift of the electrodes (see discus-
sions in Revil & Linde, 2011, and Jougnot & Linde, 2013,
for the drift associated with saturation effects and Petiau
& Dupis, 1980, and Petiau, 2000, for other sources of
noises). They measured a coupling coefficient at satura-
tion of
C
=
in these two papers. We analyzed the streaming potential
coupling coefficient data of Samples E3 and E39 (dolo-
mitic limestones; see properties in Table 3.2). In both
cases, the second Archie
s exponent (saturation expo-
nent) was independently determined using resistivity
measurements. The van Genuchten parameters were
found to be roughly the same using the capillary pressure
curves and the relative streaming potential coupling coef-
ficient data.
'
3.3 mVm
−
1
−
for a pore water conductivity
σ
w
= 0.044 S m
−
1
. The second Archie
of
s exponent (sat-
uration exponent) was measured and found equal to
n
=1.87. The van Genuchten exponent was measured
and was found equal to
n
v
=3.88 (by fitting the capillary
pressure curve). This yields
m
v
= 0.74. A comparison
between the data of Mboh et al. (2012) and
Equation (3.220) is shown in Figure 3.11. The best fit
of the data yields
m
v
=0.69 ± 0.05, very close to the value
determined from the capillary pressure curve (see
Figure 3.11). As mentioned by Mboh et al. (2012), this
implies that the values of the relative coupling coefficient
contains information regarding the van Genuchten para-
meters, as suggested by Linde et al. (2007) and Revil
et al. (2007).
In Figures 3.12 and 3.13, we reanalyzed the data pre-
sented in Revil and Cerepi (2004) and Revil et al. (2007),
correcting a few mistakes in the unit conversions found
'
3.6 Conclusions
We have extended the seismoelectric theory to unsatu-
rated and two-phase flow conditions assuming that
the rheology of the two immiscible fluids is viscous
Newtonian. We developed the equations under three
levels of models: (1) the full extension of the Biot theory
to two-phase flow conditions, (2) a simple extension of
the classical Biot theory assuming that the second (non-
wetting) phase is infinitely compressible and connected
to a reservoir at constant pressure (e.g., the atmosphere
for vadose zone processes), and (3) a simple extension of
the acoustic approximation discussed in Chapters 1 and 2.
We have also showed that
the theory agrees with
Sample M, sand
Experimental data (sand)
Model
Experimental data (sand)
Model
1
7
s
e
-1/
m
v
-1
1-
m
v
p
e
=
4500Pa,
s
r
= 0.12,
m
v
=
0.63
C
r
=
s
w
-(n+1)
1-(1-
s
e
1/
m
v
)
m
v
2
s
e
p
c
=
p
e
0.8
6
s
r
= 0.09 ± 0.01
m
v
=
0.692 ± 0.004 (
R =
0.9996)
0.6
5
0.4
4
0.2
3
0
2
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
Water saturation,
s
w
(—)
Water saturation,
s
w
(—)
Figure 3.11
Comparison between experimental data and the prediction of the model developed by Revil et al. (2007) with the van
Genuchtenmodel (see also Linde et al., 2007). The experimental data are fromMboh et al. (2012) (Sample M, sand). Left panel: relative
streaming potential coupling coefficient versus saturation. We used the measured value of the saturation exponent (second Archie
'
s
exponent)
n
=1.87. Right panel: capillary pressure curve (nonwetting fluid: air).
