Geology Reference
In-Depth Information
Relatively steep trend -
diagenesis
1
Han et al (1986) data
<5% V sh
5-10% V sh
30-50% V sh
0.8
North Sea Forties Fmn
0.6
0.5
0.4
0.3
0.2
10-30% V sh
0.4
Low angle
trend - sorting
0.1
0.2
0
0
0.1
0.2
0.3
0.4
Porosity
Figure 8.28 Normalised bulk modulus crossplot for selected sandstone data showing typical trends and ranges of values (after Simm, 2007 )
where
V sh
0-0.05
0.05-0.1
0.1-0.15
0.15-0.2
0.2-0.3
>0.3
0.3
0 : 5
b+ b 2
¼
4ac
y
0.2
2a
¼
a
S
1
1
K 0
K fl
S+ M
K 0
0.1
¼ ϕ
b
S
M
K fl
1
0
M
K 0
c
¼ ϕ
S
0
0.1
0.2
0.3
0.4
Porosity
31
ð
σ d
Þ
S
¼
Figure 8.29 Dry rock Poisson's ratio as a function of porosity and
clay content in consolidated sandstones (data from Han, 1986 ).
1+
σ
d
V p 2
M
¼
ρ:
ð
8
:
35
Þ
parameters such as porosity are included in the V s
prediction it can be used effectively to establish a con-
sistency of the inputs to Gassmann
Once K d is derived then the shear velocity can be
calculated:
s equation. It can
work well in sandstone settings where there is a fairly
narrow range of dry rock Poisson
'
r ,
μ
ρ
V s ¼
ð
8
:
36
Þ
sratio.However,in
practice there may be limitations to the technique as it
requires total porosity and can be difficult to stabilise,
particularly for the prediction of shear velocity in shales.
'
where
ð
σ
Þ
3K d 1
2
d
μ ¼
:
ð
8
:
37
Þ
21+
ð
σ d
Þ
8.2.5.3 A simple model for porosity change
In the context of trying to understand seismic ampli-
tudes by modelling fluid effects using Gassmann, the
question often arises: what would the effect of a
Hilterman ( 1990 ) used this technique with log data and
modelled the dry rock Poisson
s ratio as a function of
volume of shale ( Fig. 8.31 ). Owing to the fact that
'
171
 
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