Geology Reference
In-Depth Information
Bulk density (g/cc)
40
1.8 2.0 2.2 2.4 2.6 2.8 3.0
4.5
30000
25000
30
Dolomite
4.4
1
4.3
20000
20
Limestone
3
5
4.2
Rock salt
15000
2, 4
Anhydrite
10
4.1
12000
10000
Time-average
(Sandstone)
4.0
0
3.9
8000
0
0.2
0.4
0.6
0.8
1
Sandstone
7000
Porosity
3.8
Shal
e
6000
ρ
=0.23V
0.25
Figure 8.2
Bounds on bulk modulus of a brine-filled sandstone,
after Nur et al.(
1998
). In this case the constituents are quartz and
brine. The curves shown are (1) Voigt average, (2) Reuss average, (3)
upper Hashin-Shtrikman, (4) lower Hashin-Shtrikman and (5)
modified Voigt bound.
3.7
5000
3980
3.6
0.2
0.3
0.4
0.5
Logarithm of bulk density (g/cc)
brine filled sandstones, given the fact that their form
roughly coincides with sorting and diagenetic trends
(
Chapter 5
) it is possible to generate predictive rock
physics models based on modification of the bounds.
Avseth et al.(
2005
) describe modifications to the
Hashin
Figure 8.3
Velocity-density relationships in rocks of different
lithology (re-drawn after Gardner et al.,
1974
.)
physical justification they can be very useful. Pre-
sented below are some of the most commonly used.
Shtrikman bounds in order to mimic the
effect of cementing and sorting trends.
Theoretical bounds are commonly used in predict-
ing the effective moduli of mineral or fluid mixtures.
For example, a common approach to calculating the
effective mineral and fluid moduli for input to Gass-
mann
-
Gardner
'
s relations
-
compressional velocity and
density.
Wyllie
'
s equation
-
compressional velocity and
porosity.
Han
'
s relations
-
compressional velocity, porosity
and clay content.
s equation is to use the average of the Voigt and
Reuss bounds (called the Voigt
'
Greenberg
-
Castagna
-
compressional and shear
Hill average
(Hill,
1952
)) for mineral mixing and the Reuss aver-
age for fluid mixing. A Reuss average effectively
assumes that the fractions (or saturations) of different
fluids is the same in each pore within the rock (i.e a
homogenous fluid mix). Alternative approaches to
fluid mixing may be required in flushed or swept
reservoir settings (see
Section 8.4.4
).
-
Reuss
-
velocity.
Faust
'
s relation
-
resistivity and compressional
velocity.
8.2.2.1 Gardner's relations
In many rocks, compressional velocity and bulk dens-
ity have a positive relationship, so that as velocity
increases so does density (
Fig. 8.3
).
Gardner et al.(
1974
) developed a series of (brine-
saturated) lithology dependent relations of the form:
8.2.2 Empirical models
Empirical rock physics models are derived from fits
made to experimental results. Numerous models have
been published. These are often simple regression-
type relationships involving two or three parameters.
Experience has shown that despite often having little
dV
f
p
,
ρ
b
¼
ð
8
:
5
Þ
where
ρ
b
is bulk density in g/cc, V
p
is the P wave velocity
in km/s, and d and f are constants. The various lithology
dependent coefficients are shown in
Table 8.1
.
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