Geoscience Reference
In-Depth Information
5.5.6
Dry rock moduli
As we saw above, dry rock moduli are calculated as a step in performing Gassmann fluid
substitution. Comparing them with expected values is a useful check on the accuracy
of the input data.
Dry rock moduli vary systematically with porosity. Murphy et al . (1993) derived the
following empirical relations for clean sands from laboratory measurements:
2 )
K d =
38
.
18(1
3
.
39
φ +
1
.
95
φ
2 )
µ =
42
.
65(1
3
.
48
φ +
2
.
19
φ
,
where
is the fractional porosity and the moduli are in GPa.
A different approach, though leading to a similar outcome, is the critical poros-
ity model (Nur et al ., 1998) . In this model, dry rock elastic moduli vary linearly
from the mineral value at zero porosity to zero at the critical porosity, where the
rock begins to behave as though it were a suspension (fig. 5.25) . The value of the
critical porosity depends on grain sorting and angularity, but for sands is usually
in the range 35-40%. The predictions can be unreliable at high porosities, as the
critical value is approached. Figures 5.26 and 5.27 show some examples of plots
of elastic moduli against porosity for real rocks. There are variations in the moduli
of real sandstones due to the presence of clay and microcracks. Many points plot
well below the model predictions, which are only really applicable to consolidated
sands. Dry rock Poisson's ratios are generally in the range 0.1-0.25 for sandstones
(fig. 5.28) .
For carbonates, the picture is more complicated. Chalks are amenable to the same
general approach as sandstones, but in most carbonates the moduli are strongly affected
by pore shape. Marion & Jizba (1997) give some examples.
φ
The Critical Porosity Model
Mineral modulus
Mineral modulus
φ
µ dry
=
µ 0
1
φ
c
φ
K dry
=
K
1
modulus
modulus
0
φ
c
Critical porosity
Critical porosity
0
0
φ c
porosity
porosity
Fig. 5.25
The concept of critical porosity.
 
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