Geoscience Reference
In-Depth Information
At first sight these equations are not very useful, because to calculate the saturated
moduli we need to know the moduli for the dry rock frame. It may be possible to
measure dry rock properties directly in the laboratory, or predict them from porosity
and mineralogy using various theoretical models. However, laboratory measurements
are not often available, and the theoretical predictions are quite sensitive to the shape
of the pores, which may not be known. This problem can be side-stepped if all we want
to do is to calculate the moduli for some particular fluid fill (e.g. gas or oil) when we
know the saturated moduli for some other fluid fill (e.g. brine). If we have a well with
wireline log data, then the initial saturated moduli can be calculated from the P and S
sonic and density logs. Sometimes, however, the log data will be of doubtful quality. A
useful check is possible because the Gassmann calculation proceeds via calculation of
the parameters for the dry rock frame, and these can be compared with what is generally
expected for the particular rock type. The workflow to do this is as follows.
(1) Calculate the shear modulus from the measured shear velocity and density. If there
is no shear velocity log, it can be predicted from other log data by methods described
below:
µ
=
V
s
ρ.
(2) Calculate the saturated bulk modulus from
3
.
(3) Derive the dry bulk modulus from
4
K
sat
=
V
p
ρ
−
K
sat
φ
K
ma
K
fl
+
1
−
φ
−
K
ma
K
d
=
.
φ
K
ma
K
fl
K
sat
+
K
ma
−
1
−
φ
(4) For QC purposes, calculate the dry rock Poisson ratio from
3
K
d
−
2
µ
2
6
K
d
.
The dry bulk modulus and Poisson's ratio can be compared with expected values
for particular types of rock, as explained shortly. It may be necessary to edit the
data to make sure that the values remain within a reasonable range.
(5) When the values in step (4) are acceptable, calculate the fluid moduli for the new
case. Here and in step (3) above we need to be able to estimate the moduli of mixtures
of fluids, i.e. hydrocarbons and brine. The moduli for the individual constituents can
be obtained by methods to be considered below, and combined using the equation
1
K
fl
=
σ
=
d
µ
+
S
w
K
w
+
1
−
S
w
K
h
,
where
S
w
is the water saturation (decimal fraction),
K
h
is the bulk modulus of the
hydrocarbon and
K
w
is that of brine. This formula shows why even a small amount
