Geology Reference
In-Depth Information
Seismic
Figure 8.16
An overview of the
applicability of the Gassmann model at
different frequencies.
Sonic
Ultrasonic
0.1MHz
0
100Hz
1kHz
10kHz
1MHz
500Hz
100kHz
Low frequency
?
High frequency
High porosity/permeability rocks
with low viscosity fluids
Gassmann
Biot-Gassmann
Low/moderate porosity/permeability
sands with high viscosity fluids
Biot-Gassmann
+
Squirt flow
Gassmann
?
Sandstones and carbonates
with moderate to high porosity
Gassmann OK
Considered that sonic log responses in these logs are
essentially low frequency and Gassmann is applicable
At logged frequencies:
Velocities may be dispersive
Patchy saturation may characterise low saturation gas
scenarios
At seismic frequencies:
Potential for uncertainty in fluid and mineral moduli
Common Gassmann pitfall of exaggerated fluid
substitution effect
Gassmann needs to be adjusted to achieve intuitive result
Tight sand
Gassmann application
requires care
Shaley sands and
laminated sands
Rocks with fractures or
dual porosity systems
Other models required
Figure 8.17
Various practical rock physics scenarios and the applicability of Gassmann's equation.
et al.,
2001
) but recent work suggests that the rele-
vanceofGassmannmaydependonthenatureofthe
pore types and distributions (e.g. Xu and Payne,
2009
). There is also a potential issue in the inter-
action between fluid and carbonate matrix. For
example, Baechle et al.(
2007
) have described how
the introduction of brine into a dry carbonate may
soften or harden the rock. Certainly, if fractures or
dual porosity systems are present then Gassmann
will be inappropriate for the purposes of modelling
fluid substitution effects.
Figure 8.18
presents a series of equations that
enable the practical
s
relations with log data. It describes how the saturated
bulk modulus is defined by four components, namely
mineral, fluid, porosity and the dry rock frame. The
stiffness characteristics of the rock introduced in
Chap-
ter 5
, an important element in the magnitude of fluid
substitution effects on compressional velocity, are con-
trolled essentially by a combination of the mineral,
porosity and the dry rock frame modulus, referred to
as the pore space stiffness (Mavko and Mukerji,
1995
).
implementation of Gassmann
'
161
