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a)
c)
UNCEMENTED SAND
CEMENTED SAND
6000
6000
4000
4000
2000
2000
0
0
Wet sand
Gas sand
0
0
0.1
0.2
0.3
0.4
0.1
0.2
0.3
0.4
Porosity
Porosity
b)
d)
1
1
0.8
0.8
K ф /K 0
K ф /K 0
0.6
0.6
0.5
0.4
0.3
0.2
0.1
0.5
0.4
0.3
0.2
0.1
0.4
0.4
0.2
0.2
0
0
0
0.1
0.2
0.3
0.4
0
0.1
0.2
0.3
0.4
Porosity
Porosity
Figure 8.19 Fluid substitution and stiffness in sandstones. Two sands with 30% porosity are shown, soft uncemented sands in (a) and (b) and
stiffer cemented sands in (c) and (d). For the same porosity softer sands show greater fluid substitution effects in terms of compressional velocity.
the basis for the relative volume of sand and shale.
Shale properties are variable and therefore not shown
in Table 8.4 , but in any particular case it will usually
be straightforward to read off shale values from wire-
line logs for shales within or adjacent to the interval of
interest. In the absence of other information it is often
assumed that the sand mineral is quartz. However,
there may be some uncertainty in the effective mineral
modulus if feldspar is present (Smith, 2011 ). Ideally
the type of feldspar needs to be known, given the range
of modulus values for different types of feldspar.
Sometimes, detailed lithology logs will be available,
where logs have been inverted for volume fractions
of a range of minerals. Mineralogical reports can be
useful if there are exotic minerals present with prop-
erties very different from those of quartz and shale.
Another potential issue for the interpreter in para-
meterising Gassmann
et al.( 2001 ) has shown that dry clay densities can
vary between 2.2 g/cc to 2.84 g/cc and the bulk moduli
(K) can vary between 10 GPa and 70 GPa, while the
shear modulus is roughly equal to 0.47K. Often, espe-
cially in exploration settings, the types of clays are
unknown.
Single effective mineral densities are calculated as
the arithmetic average of the constituent minerals,
weighted by volume fraction. To calculate the effect-
ive bulk modulus (K 0 ), the moduli of the constituent
minerals must be combined according to a mixing
scheme. There are several possibilities as discussed in
Section 8.2.1 , of which the Voigt
Hill (VRH)
average (Hill, 1952 ) and the Hashin-Shtrikman ( 1963 )
are the most commonly used.
-
Reuss
-
8.2.4.2 Fluid parameters
If there is more than one fluid present, the properties
of a fluid mixture need to be calculated. Similar to
mineral mixing, the density of a fluid mixture is
s equation is the uncertainty in
the modulus of dry clay. The parameters of dry clays
vary dramatically ( Fig. 8.20 and Table 8.5 ). Wang
'
164
 
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