Geoscience Reference
In-Depth Information
To generate the porous medium, we use a random sim-
ulator to create a stochastic realization for the clay con-
tent and the model of Revil and Cathles (1999)to
determine the porosity and the permeability at satura-
tion. A multiphase flow simulator computes the satura-
tion profiles, which are used to compute the P-wave
velocity and resistivity distributions. The P-wave velocity
and the permeability of the water phase are shown in
Figure 6.7 for snapshot 3, while the electrical conductiv-
ity and the porosity are shown in Figure 6.8. P-wave
velocity does not depend much on the saturation. In this
example, the velocity distribution is set to be between
4050 and 4300 m s
−
1
, and the electrical conductivity dis-
tribution varies over an order of magnitude. The
influence of water saturation on resistivity is much
greater than its influence on P-wave velocity.
We use a Gaussian seismic source (magnitude 1.0 ×
10
4
Nm, delay time
t
s
=30 ms, dominant frequency
f
c
=
160 Hz). We then solve the poroacoustic equations
described in Chapter 1 (see extension to the partially sat-
urated case in Chapter 3) and the Poisson equation for
the electrical potential in the frequency domain, based
on the material properties provided in Table 6.2. Solve
for the confining pressure,
P
(
r
,
t
), of the solid phase
and pore fluid pressure
p
(
r
,
t
). Finally, we compute the
electrical potential by solving the Poisson equation
coupled to the poroacoustic problem for the frequency
range 8 to 800 Hz. This choice of frequencies is valid
P-wave velocity (m s
-1
)
2340
4320
4300
2360
4280
2380
4260
2400
4240
4220
2420
4200
2440
4180
50
100
150
200
Offset (m)
(a)
Permeability (m
2
)
2340
−14
2360
−14.5
2380
−15
2400
−15.5
2420
2440
−16
50
100
150
200
(b)
Offset (m)
Figure 6.7
Sketch of the distribution of the P-wave velocity and permeability of the pore water phase at snapshot 3. Note that
the saturation front is characterized by a sharp contrast in permeability.
a)
Velocity distribution for the compressional wave.
b)
Distribution of the permeability. (
See insert for color representation of the figure
.)
