Geology Reference
In-Depth Information
Such problems are commonly remedied by apply-
ing cut-offs, i.e. fluid substitution is done only if the
porosity is greater than a particular value and V
sh
less
than a certain value. This may be justified on the basis
that at low porosities and high shale volume, the rock
is unlikely to be of reservoir quality, but the solution
is inelegant, giving rise to saw-tooth effects in the
substituted logs where the porosity and V
sh
logs vary
around the cut-off values.
It might be argued that the main issue with the
results shown in
Fig. 8.58
is that the Gassmann
implementation should have been parameterised
using total porosity. The problem with a total por-
osity scheme, however, is the uncertainty over the
modulus of dry clay (
section 8.2.4
). Total porosity
was calculated for the dataset shown in
Fig 8.58
using densities of 2.6g/cc and 2.65g/cc for clay and
quartz respectively and it was assumed that V
cl
¼
V
cl
Phi
t
S
wt
ρ
V
p
σ
0
1
0.5
0
1
0 1.95
2.95 2000
4000 0
0.5
0.7
V
sh
. In addition, the water saturation was calculated
in terms of the total porosity
(
Eq. (8.31)
). Two
separate Gassmann calculations were performed on
the data using dry clay moduli of 36 GPa and 10
GPa. The dry rock and fluid substitution results are
shown in
Figs. 8.59
and
8.60
, respectively. It is
evident that the stiffness of the shaley sands, and
consequently the effect of fluid substitution in shaley
sands, depends to a large extent on the moduli of
dry clay. The lower value of dry clay modulus
appears to give a more reasonable result than the
higher dry clay value.
Another approach to avoiding unreasonable
results in shaley sands, particularly in the case where
effective porosity has been used as an input, is the
model-based approach described in
Section 8.2.3.
Figure 8.61a
shows how a trend can be drawn
through the mineral point and the sand data of
Fig. 8.59
. The shape of the curve can be adjusted to
reflect the key factors in porosity reduction (i.e.
sorting vs cementation). The fluid substitution result
is shown in
Fig. 8.61b
. It is very similar to the total
porosity case with low values of dry clay (
Fig. 8.60
,
red curves) and intuitively reasonable given that the
clean sands show the largest velocity change and the
shaley sands show much smaller effects. There is no
single answer, of course, as a range of dry rock
trends could have been fit to the data. The model-
based approach is a practical solution for deriving
reasonable results in exploration settings where log
data and petrophysical interpretations may not be
optimal, and time is short.
Figure 8.60
Fluid substitution in shaley sands - total porosity
approach. Fluid substitution to gas using dry clay moduli of 37.5
GPa (black curves) and 10 GPa (red curves). Depth marker spacing is
10 m (after Simm,
2007
).
8.5.2 Laminated sands
It is possible to apply the model-based fluid substitu-
tion approach described in the previous section to
laminated sand and shale zones and get reasonable
results, but conceptually laminated zones require a
different approach. Given that the laminae in these
reservoirs are below logging and seismic resolution
the fluid substitution problem can be simply
approached from the viewpoint of mixing between
shale, wet sand and hydrocarbon (pay) sand end
members (Katahara,
2004
). The technique is based
on the fact that using the Backus (
1962
) average
formulation for the effective parameters of sequences
of thin layers, bulk density and compliance (i.e.
inverse of
modulus) vary linearly with shale
content (Katahara,
2004
). Thus for a laminated sand/
shale sequence:
Μ
or
μ
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