Geoscience Reference
In-Depth Information
5.5.1
Fluid effects
In general, oil or gas fill will reduce the P velocity significantly compared with the
brine case, and for gas the effect is often fully developed at saturations of a few
percent
(fig. 5.18(a))
.
With increasing gas saturation beyond this point, the lowering
of density becomes important and the seismic velocity starts to increase again. The
density decreases linearly as gas saturation increases. The combined effect on acoustic
impedance is illustrated in
fig. 5.18(b)
.
The impedance of gas sands drops sharply from
the brine case for gas saturations of a few percent, and then decreases almost linearly as
gas saturation increases. Thus, low gas saturations may give reflections bright enough
to be confused with commercially significant accumulations. The effect of oil is more
linear over the entire saturation range, with little effect at low oil saturation but an often
strong effect at high saturations. S velocity is only slightly affected by differences in
fluid fill, via the effect on density; the S velocity is slightly higher for the oil and gas
cases.
The effect of fluid fill on P and S velocities can be calculated using Gassmann's
(1951)
equations. They are applicable at seismic frequencies to rocks with intergranular
porosity and fairly uniform grain size, and describe how the bulk and shear modulus
of a rock are related to the fluid fill.
The bulk modulus is a measure of resistance to change in volume under applied stress,
and the shear modulus is a measure of resistance to change in shape. P and S velocities
are related to the bulk modulus
K
, shear modulus
µ
and density
ρ
by the equations:
K
4
3
+
V
p
=
ρ
and
µ
ρ
.
V
s
=
Gassmann's equations assert that the bulk modulus (
K
sat
) of the rock saturated with a
fluid of bulk modulus
K
fl
is given by
K
sat
K
ma
−
K
d
K
ma
−
K
fl
K
fl
)
,
where
K
ma
is the bulk modulus of the matrix material,
K
d
is the bulk modulus of the
dry rock frame, and
K
sat
=
K
d
+
φ
(
K
ma
−
φ
is the porosity. The analogous relation for the shear modulus is
given by Gassmann as
µ
sat
=
µ
d
.
This means that the shear modulus is the same irrespective of fluid fill. This is intuitively
reasonable, as all fluids have zero shear modulus and are equally unable to help to resist
changes in shape of the rock under an applied stress.
