Geoscience Reference
In-Depth Information
a brine-filled reservoir drilled with water-based mud, Gassmann substitution is used
to predict the effect of oil or gas saturation, and these values are then compared with
the observed logs in oil zones drilled with a water-based mud or brine zones drilled
with an oil-based mud to see whether invasion is causing problems. This only works if
the reservoir properties (porosity, clay content) are similar for the various zones to be
compared; it is unfortunately quite common for hydrocarbon fill to influence diagenesis
and so porosity.
5.5.2
P-wave velocity and porosity
Porosity exerts a strong influence on P velocity. A relationship that is often used to
describe the effect in brine-filled sands is the Wyllie time-average equation (Wyllie
1
1
−
φ
V
ma
,
where
V
is the velocity in a rock of matrix velocity
V
ma
and porosity
V
=
V
fl
+
containing
fluid of velocity
V
fl
. Despite the similarity to the equation for calculating densities, it is
important to note that the Wyllie equation has no proper physical basis and is essentially
an empirical result. It is in effect an upper bound for velocity at any given porosity.
Velocities are affected by the degree of consolidation and the geometry of the pores.
The equation is applicable for consolidated sands in which small cracks and flat pores
have been closed, and predicts a strong effect of porosity on velocity
(fig. 5.21)
.
φ
5.5.3
P-wave velocity and clay content
The presence of clay has a significant effect on the properties of a sandstone. The
details depend on how the clay is distributed in the rock. There is a conflict between
the effects on the matrix (softening it and so reducing velocity) and the effect on the
porosity (stiffening it and increasing velocity). Experiments by Marion
et al
.
(1992)
showed that introducing clay into an experimental sand led to an increase in velocity
due to the change in porosity. On the other hand,
fig. 5.22
shows that a large velocity
reduction is caused by a small amount of clay, at a given porosity. This plot was created
effects are observed in actual examples.
5.5.4
P-wave velocity and density
In cases where a sonic log is available but density is not (or vice versa), it is useful to be
able to predict one from the other. Some general lithology-specific empirical relations
