Geology Reference
In-Depth Information
Batzle and Wang (1992)
equations or locally derived
data and mixing rules
fl
pfl
fl
fl
fl
Mineral tables
and mixing rules
Mineral
K
0
Porosity Dry rock frame
K
d
Fluid
K
fl
fl
Pore space stiffness
K
Saturated bulk modulus
K
sat
+
+
fl
Shear modulus
(Fluid independent)
µ
fl
K=GPa, V=km/s,
=g/cc
fl
Figure 8.18
Practical equations for the application of Gassmann's relations to log data.
An implication of
Fig. 8.18
is that the dry rock
parameters that are inverted from the various inputs
are also those used in the fluid substitution step. This
data-driven approach is appropriate only for clean
blocky sands of moderate to high porosity and with
good quality log data. In practice, there is a QC step to
evaluate the dry rock moduli before proceeding.
There are a number of reasons why the dry rock
moduli may be in error such as inconsistencies in
the various log curves, either in terms of depth regis-
tration or the fact that they do not all investigate the
same volume of rock. It is recommended therefore
that the fluid substitution step is conditioned by a dry
rock model. Following Simm (
2007
) it is proposed
that the dry rock model is conditioned in
(1) Moduli calculation
4
3
μ:
V
s
2
V
p
2
μ ¼
ρ
b
K
sat
¼
ρ
b
(2) Dry rock inversion
K
0
K
fl
K
0
1
ϕ
K
ϕ
¼
K
0
K
d
¼
+
K
0
:
1
1
K
sat
K
fl
K
ϕ
(3) Dry rock modelling
1
vs nor-
malised modulus space (Mavko and Mukerji,
1995
;
Avseth et al.,
2005
) and the use of this plot will be
explained in the following sections. A practical work-
flow for Gassmann is presented below. For clarity, the
fluid substitution step has been divided into three
steps (labelled 4, 5 and 6), namely density substitu-
tion, shear velocity substitution and compressional
velocity substitution; the equation for fluid substitu-
tion of the compressional velocity is taken from
Downton and Gunderson (
2005
).
ϕ
162
0
f
