Geoscience Reference
In-Depth Information
512 μm
93 μm
181 μm
256 μm
3000 μm (This work)
850 μm
1
1 + Re
Model
425 μm
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0.01
0.1
1
10
0.1
1
10
Reynolds number, Re
Reynolds number, Re
(a)
(b)
Figure 2.14
Influence of the Reynolds number.
a)
Influence of the Reynolds number upon the relative coupling coefficient
C
/
C
0
(
C
is the
measured apparent streaming potential coupling coefficient and
C
0
is determined in the viscous laminar flow regime for Re << 1 where Re
denotes the Reynolds number).
b)
Influence of the Reynolds number upon the relative permeability
k
/
k
0
(
k
denotes themeasured apparent
permeability using Darcy
'
slaw,while
k
0
is determined in the viscous laminar flow regime for Re << 1) (Data from Bolève et al., 2007).
References
we found four types of waves (2 compressional P-waves
and 2 shear (S-)waves). Alternatively, this theory can be
simplified (at low frequencies) to recover the classical Biot
theory for a poroelastic material saturated with a Newto-
nian fluid. In this case, there are two compressional
P-waves and one shear (S-)wave mode (the fluid is not
able to sustain shear stresses). In all these cases, we deter-
mined the source current density associated with the
effective charge per unit volume and the Darcy velocity.
A comparison between the model and the experimen-
tal data showed that our model was able to explain both
the streaming potential coupling coefficient at low fre-
quencies and its dependency with salinity and frequency
up to 100 kHz. We also discussed the effect of the
Reynolds number upon the streaming potential coupling
coefficient, which corresponds to an alternative way to
see the transition between the laminar viscous and
laminar inertial flow regimes.
InChapter 4, wewill showhow to solve themacroscopic
equations (valid at the scale of the representative elemen-
tary volume) developed in this chapter, and we will
develop inverse algorithms to determine key properties
of the subsurface such as facies boundaries and material
properties.
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