Geology Reference
In-Depth Information
Saturated elastic moduli are then calculated using
Gassmann
components (assuming the silt is suspended in the
clay) to derive the effective solid moduli (Avseth
et al.,
2005
).
The
s(
1951
) equation. These models effectively
address the issues of effective pressure on unconsoli-
dated grain packs and the effect of cement in
stiffening the rock. When fit to log data it is possible
to infer whether the sand is unconsolidated or
cemented. Not only is this useful for seismic litho
facies characterisation but it may also be useful in
sanding assessment for reservoir production.
There are two commonly used contact models, the
'
model
assumes that the porosity reduces owing to the uni-
form deposition of cement on the surface of the sand
grains. Only a small amount of cement deposited at
grain contacts is required to significantly increase the
stiffness of the rock. The mathematical solution for
this scenario was determined by Dvorkin et al.(
1994
).
The model inputs are solid phase and cement phase
bulk and shear moduli, and coordination number
(representing the radius of contact of the cement
layer). In the Oseberg samples clay cement gave
slightly lower velocities than quartz cement. There is
no effective pressure dependency built into the model.
Figure 8.34
illustrates examples of friable and
cemented sand trends in data from the North Sea
and Gulf of Mexico. The similarity of the trends in
the two basins is striking. However, it should be
remembered that there a large number of variables
(i.e. sorting, shaliness, effective pressure, and amount
of cement) that may give rise to similar values of
velocity for a given porosity. The friable sand and
cemented sand models are not necessarily mutually
exclusive. For example, a combination of the friable
and cemented sand models can potentially describe
the situation where a sorting trend has a constant
value of cement (i.e the constant cement model
(Avseth,
2000
; Avseth et al.,
2005
)(
Fig. 8.35
). It is
recommended that the reader consults Avseth et al.
(
2005
) for a thorough discussion of a variety of
models describing specific sand/shale scenarios,
including models to describe the dispersed clay and
laminated shale effects described in
Chapter 5.
'
cemented sand
'
or
'
contact cement
'
'
'
'
'
model.
These two models were derived by Dvorkin and Nur
(
1996
) from a study of two sets of laboratory data on
sandstones from the North Sea, one from the Oseberg
Field and one from the Troll Field. Thin-section
images showed slight quartz cementation of the
grains in the Oseberg samples, whereas cementation
was absent in the Troll samples.
With the
friable sand
model and the
cemented sand
'
model, a high porosity dry rock end member is
determined for a random pack of identical spherical
grains at critical porosity. Hertz
'
friable sand
'
or
'
uncemented sand
-
Mindlin theory
(Mindlin,
1949
)
-
Shtrikman bound then interpolates between this
point and the mineral moduli at zero porosity. This
interpolation represents the deterioration in poros-
ity due to decrease in sorting. The model inputs
are the solid phase bulk andshearmoduli,critical
porosity, effective pressure and the average number
of contacts per grain (the
is used. The
lower Hashin
).
Empirical models relate the coordination number to
porosity. The
'
coordination number
'
model can be effectively
used to derive a constant clay model for sandy
shales by substituting a much larger critical porosity
(60%
'
friable sand
'
-
70%) and a Reuss mix of clay and silt
a)
b)
Figure 8.34
Modulus versus porosity
crossplots for North Sea (grey) and Gulf
Coast (black) wells; (a) porosity vs M (ρV
2
p
),
2
s
10
(b) porosity vs G (ρV
). The curves are
from the theoretical contact cement
model (upper branch) and uncemented
model (lower branch), after Dvorkin
30
8
et al
.,
2002
.
20
6
4
10
2
0.1
0.2
0.3
0.4
0.1
0.2
0.3
0.4
175
Porosity
Porosity
