Geoscience Reference
In-Depth Information
Table 2.3
Material properties used in the seismoelectric
forward model.
In such a case, we can neglect the time required by the
EM disturbances to diffuse between the reservoir and
the receivers (see Revil et al., 2003, for a discussion of
the diffusion time associated with the diffusion of low-
frequency EM disturbances).
Using the constitutive equation derived in Chapter 1,
we can model the problem by solving only the quasistatic
Poisson-type problem:
Parameter
Value
Units
Reference
ρ
s
2650
kg m
−
3
Mavko et al. (1998)
kg m
−
3
ρ
w
1000
Mavko et al. (1998)
kg m
−
3
ρ
o
900
Karaoulis et al. (2012)
K
s
36.5
GPa
Mavko et al. (1998)
K
fr
18.2
GPa
Mavko et al. (1998)
G
13.8
GPa
Mavko et al. (1998)
∇
σ
∇
ψ
=
∇
J
S
,
2 214
K
w
2.25
GPa
Jardani et al. (2010)
K
o
1.50
GPa
Charoenwongsa et al. (2010)
J
S
=
Q
0
Q
0
2
V
w
=
−
i
ω
V
k
ω
∇
p
−
ω
ρ
f
u
,
2 215
η
w
1×10
-
3
Pa s
Jardani et al. (2010)
50 × 10
−
3
η
o
Pa s
Light motor oil
where
ψ
is the electrostatic potential (
E
=
−∇
ψ
in the
quasistatic limit of the Maxwell equations),
is the elec-
trical conductivity of the porous medium,
J
S
is the source
current density of the electrokinetic kind,
σ
s
ω
=
ρ
+
ω
2
2
f
k
ω
,
ρ
ρ
2 212
ρ
f
is the fluid
density, and
Q
0
2
V
is the effective excess charge (of the dif-
fuse layer) per unit pore volume (in Cm
−
3
). For saturated
rocks,
Q
0
θ
ω
=
α
+
ω
ρ
f
k
ω
,
2 213
where
k
ω
is not the dynamic permeability of the porous
material,
V
can be directly computed from the low-
frequency permeability
k
0
through the semiempirical
formula shown in Figure 1.9.
ρ
f
is an effective fluid density,
λ
is the Lamé
coefficient, and
corresponds to the apparent mass
density of the solid phase at a given frequency
ρ
s
ω
ω
. Typical
material properties can be found in Table 2.3.
2.3 Experimental approach and data
2.2.3 Description of the electrokinetic
coupling
As explained in Chapter 1, the electrokinetic coupling at
work in the seismoelectric response is the result of the
relative displacement of the pore water with respect to
the solid phase. The drag of a fraction of the charge density
contained in the pore water is responsible for a net source
current density in a framework attached to the solid phase
(Pride, 1994; Revil et al., 1999a; Leroy & Revil, 2004). The
model developed by Pride (1994) is an extension of the
classical streaming potential theory and takes the form
of the Biot
2.3.1 Measuring key properties
2.3.1.1 Measuring the cation exchange capacity
and the specific surface area
Seismoelectric phenomena are related to the properties
of the interface between the mineral phase and the pore
water phase. Two of the most important parameters
characterizing this interface are the cation exchange
capacity (CEC) and the specific surface area. The CEC
can be measured by the titration of the mineral surface
with a cation that has a strong affinity for the active sites
populating this surface (e.g., copper ammonium, cobalt).
Knowing the amount of sorbed charge and the mass of
the grains, we directly measure the charge per unit mass
of solid grains, which is defined as the CEC (expressed
therefore in the International System of Unit in Coulomb
kg
−
1
or C kg
−
1
). Key references include Chapman (1965),
Worthington (1973), Gillman (1979), Thomas (1982),
and Gillman and Sumpter (1986).
The specific surface area of a material can be obtained
using the so-called Brunauer
Frenkel equations coupled to the Maxwell
equations via the source current density. However, this
formulation has a drawback: it required knowledge of
the zeta potential, a microscopic potential of the electrical
double layer at the pore water/solid interface.
In the following text, we also consider the resulting EM
disturbances in the quasistatic limit of the Maxwell equa-
tions, like the works on self-potential signals by Suski
et al. (2006) and Jardani et al. (2007). This assumption
is valid because the target is assumed to be close enough
(less than a kilometer) from the receivers (such as anten-
nas, nonpolarizing electrodes, and magnetometers).
-
Teller (BET)
method (Brunauer et al., 1938). A dry sample is used
and its surface is covered by a monolayer of nitrogen
-
Emmett
-
