Geology Reference
In-Depth Information
Table 8.2.
Mineral slowness values and coefficient values for
Eq. (8.9)
(after Raiga-Clemenceau et al.,
1988
).
Table 8.3.
Typical values for Archie coefficients 'a' and 'm'
(from Hacikoylu et al,
2006
).
Matrix
T
ma
(
μ
s/ft)
x
Lithology
a
m
Silica
55.5
1.6
Consolidated sandstone
0.81
2
Calcite
47.6
1.76
Unconsolidated sandstone
0.62
2.15
Dolomite
43.5
2
Average sands
1.45
1.54
Shaly sands
1.65
1.33
Clean granular rock
1.00
2.05
-
3
6
Clay volume
5.5
0-10%
5
10-20%
20-30%
30-40%
2500
4.5
4
2250
c=
0.05
0.15
0.25
0.35
3.5
3
2000
2.5
2
0
0.1
0.2
0.3
0.4
1750
Porosity
Wet sands
Gas sands
Castagna's
sandline
Figure 8.7
Han
'
s(
1986
) relations showing constant clay lines, with
a subset of Han
'
s(
1986
) data (after Avseth
et al
.,
2005
).
1500
the Gassmann (
1951
) fluid substitution equation.
Therefore, the time average equation should only be
used with brine as the fluid. Substituting to another
fluid would require the use of the Gassmann formu-
lation. The Raymer
1250
2500
3000
3500
4000
4500
V
p
(m/s)
Gardner equation on the
other hand is broadly consistent with Gassmann, sug-
gesting that any pore fluid may be used with this
model (Spikes and Dvorkin,
2005
).
-
Hunt
-
Figure 8.8
Comparison of a North Sea shaley sandstone dataset
and Castagna's sandline, an empirical V
p
-V
s
relation based on sands
from Gulf of Mexico and onshore United States.
Avseth et al.(
2005
) describe how if the relations
are re-written slightly the equations can be used to
determine a series of parallel lines on the porosity
8.2.2.3 Han's relations
The work of Han (
1986
) and Han et al.(
1986
) identi-
fied relationships between porosity, compressional
velocity and clay content in laboratory experiments
on well consolidated sandstones. It was realised that
the effect of increasing clay content is to effectively
soften the rock and reduce the compressional velocity.
The key relationships from the high pressure
(40 MPa) measurements are:
-
velocity crossplot, representing the effect of changing
clay content (
Fig. 8.7
).
8.2.2.4 Greenberg-Castagna relations
Given the high fidelity of modern shear logging
tools, the ideal shear velocity input to rock physics
analysis should be based on a log measurement. It is
often the case, particularly with old wells, however,
that there is no shear log and the shear velocity needs
to be predicted. Fortunately there is usually a strong
lithology dependent, but largely pressure independ-
ent, positive
V
p
¼
5
:
59
6
:
93
ϕ
2
:
18C
ð
8
:
12
Þ
V
s
¼
3
:
52
4
:
91
ϕ
1
:
89C,
ð
8
:
13
Þ
where V
p
is in km/s, C is clay volume fraction and
is
ϕ
155
porosity.
correlation between compressional
