The document discusses estimating seismic velocities and attenuations of CO2 saturated sandstones through laboratory experiments. Core rock samples are injected with CO2 and seismic P and S waves are shot through the samples to determine how velocities and attenuation change with different CO2 concentrations and effective stress regimes. The experiments aim to understand these relationships at a small scale so they can be applied to understanding larger field conditions. Key parameters like bulk modulus, density, pore pressure, and effective stress are also discussed in relation to how they impact seismic wave propagation through rocks.

1.
Estimating
Seismic
Velocities
and
Attenuations
of
CO2
Saturated
Sandstones
Team
Name:
CO2
Team
Members:
Amarpaul
Bassi,
Li
Lam,
Sofya
Niyazova,
Julie
Truong
Geophysical
Solution
November
25,
2011

2. 2
Introduction
Often,
it
is
more
practical
to
determine
relationships
between
physical
parameters
on
a
laboratory
scale.
Compared
to
field
conditions,
laboratory
experiments
not
only
can
have
the
environmental
variables
be
carefully
controlled
but
the
costs
also
provide
an
additional
appealing
factor.
Once
a
relationship
is
formed,
it
can
be
applied
to
the
larger
scale
in
the
field
with
some
alterations
in
the
model.
In
this
case,
the
relationship
between
seismic
velocities
and
pore
pressure
are
experimentally
determined
by
mimicking
field
conditions
in
the
laboratory
with
differently
saturated
sandstone
cores
under
a
range
of
stress
settings.
Relevant
Geophysical
Parameters
The
geophysical
properties
that
we
concentrate
on
in
our
study
are
velocities
of
seismic
waves
and
attenuation
in
a
rock
material.
When
carbon
dioxide
(CO2)
is
injected
into
rocks,
the
characteristics
change
as
a
result
of
a
change
in
compressibility.
This
in
turn
affects
how
compressional
and
shear
seismic
waves
propagate
through
the
rock
(Wang
and
Nur,
1989).
The
Gassmann
equation
demonstrates
how
the
bulk
modulus
of
the
saturated
rock
is
related
to
the
bulk
modulus
of
the
rock
properties
and
the
pore
fluid
(Wang
and
Nur,
1989).
It
is
also
worthy
to
note
the
seismic
velocities
and
how
they
relate
the
bulk
modulus,
shear
modulus
and
density,
!! =
! + 4
3 !
!
!! =
!
!
From
the
formulas,
it
can
be
seen
that
Vp
will
decrease
with
an
increase
in
CO2
injection.
When
the
pore
pressure
is
increased,
the
pores
are
kept
open
and
cancel
some
of
the
effects
of
confining
pressure.
As
a
result,
density
increases.
So
Vp
and
Vs
will
have
lower
magnitudes
when
pore
pressure
is
high
(Wang
and
Nur,
1989).
Shear
wave
velocity
decreases
but
in
a
lower
magnitude
compared
to
Vp.
As
well,
dissolution
of
CO2
in
the
original
fluid
increases
density,
resulting
in
decreased
Vp
and
Vs.
Attenuation
is
the
decrease
in
energy
of
the
seismic
wave
as
it
propagates
through
the
rock
(Prasad
et
al,
2004).
The
fluids
in
the
pore
spaces
cause
attenuation
and
dispersion
of
body
waves
(Muller
et
al,
2010).
As
a
wave
propagates
through
a
medium,
it
produces
a
pressure
gradient,
which
causes
the
fluid
to
move.
As
the
fluid
passes
by
the
solid
particles,
friction
results
and
energy
is
lost.
Survey
Technique
for
Acquiring
Data
The
main
survey
technique
that
we
use
in
our
study
is
propagation
of
seismic
waves
through
a
core
rock
sample.
The
laboratory
experiment
is
set
up
to
determine
the
relationship
between
the
velocities
and
attenuation
of
seismic
waves
and
CO2
concentration
in
the
reservoir
rock.
The
experiment
technique
Vp
=
compressional
wave
velocity
Vs
=shear
wave
velocity
K
=
bulk
modulus
(incompressibility)
μ
=
shear
modulus
(rigidity)
ρ
=
density

3. 3
consists
of
injecting
CO2
into
the
core
sample,
shooting
P-­‐
and
S-­‐
waves
through
the
sample
and
detecting
the
changes
in
velocities
and
attenuation
of
the
waves.
Changes
in
seismic
velocities
and
the
degree
of
attenuation
are
dependent
upon
the
effective
stress
regime
of
the
rock
and
the
chemistry
of
the
fluid.
The
effective
stress
regime
is
the
result
of
total
regional
stress
minus
pore
pressure
of
the
rock,
Effective
stress
=
Total
regional
stress
–
Pore
pressure
The
effective
stress
regime
of
the
core
sample
is
changed
once
it
is
brought
to
the
surface.
The
total
regional
stress
can
be
approximated
by
the
rock
column
above
the
core
sample
and
simulated
in
the
laboratory
environment
via
a
rock
compressor.
The
pore
pressure
is
dependent
upon
the
degree
of
saturation
with
original
fluids,
the
amount
of
injected
CO2,
and
with
the
fluid
type
in
the
rock.
The
degree
of
saturation
with
original
fluids
is
easily
simulated
in
the
laboratory
environment
by
drying
and
soaking
the
core
sample
in
water.
The
injected
CO2
fills
in
the
free
pore
space
resulting
in
the
build
up
of
the
pore
pressure.
After
a
critical
pore
pressure
is
reached,
it
starts
dissolving
into
the
fluid
thus
changing
the
original
fluid
type.
The
concentration
of
CO2
is
manifested
through
the
amount
of
the
gas
injected
leading
to
a
pore
pressure
build
up.
Thus
the
pore
pressure
is
proportionally
related
to
the
amount
of
injected
CO2,
and
the
relationship
can
be
mathematically
derived.
The
amount
of
CO2
dissolved
in
the
fluid
is
also
a
function
of
the
amount
of
the
injected
CO2
and
the
relationship
can
also
be
mathematically
derived.
The
experimental
injection
of
CO2
changes
the
pore
pressure
and
the
fluid
type,
thus
affecting
the
velocities
and
the
degree
of
attenuation
of
seismic
waves.
Due
to
the
limiting
size
of
the
core,
the
experiment
is
limited
to
high
frequency
seismic
waves
with
a
short
wavelength
in
order
to
be
able
to
resolve
the
parameters
in
question.
Those
types
of
waves
are
created
by
a
seismic
transducer.
The
transmitter
is
placed
at
one
end
of
the
core
and
the
receivers
are
placed
at
the
opposite
end,
which
record
the
velocities
of
P-­‐
and
S-­‐waves
and
their
corresponding
attenuation.
Based
on
the
results,
the
relationship
between
the
velocities
and
attenuation
of
seismic
waves
and
CO2
concentration
in
core
sample
is
determined.
Detailed
Experimental
Description
The
experiment
is
applied
to
a
homogeneous,
1
meter
in
length
sandstone
core.
Being
porous,
sandstone
is
a
very
suitable
rock
type
for
a
sequestration
reservoir.
The
CO2
is
injected
at
a
gas
phase.
The
degree
of
saturation
with
original
fluids
affects
the
amount
of
CO2
to
be
injected.
To
minimize
the
complexity
involving
varying
levels
of
saturation,
three
limiting
cases
of
saturation
levels
will
be
studied.
Water
is
taken
as
an
original
fluid.

4. 4
Table
1:
Three
limiting
cases
of
saturation
levels
Case
1
Case
2
Case
3
0%
saturation.
The
core
is
completely
dry.
The
injected
CO2
fills
in
the
free
pore
space.
100%
saturation.
The
core
is
completely
soaked
in
water.
The
injected
CO2
dissolves
into
the
water.
50%
saturation†
.
The
core
is
half
soaked.
Initially,
the
injected
CO2
fill
in
the
free
pore
space
and
after
the
critical
pressure
is
reached,
starts
dissolving
into
the
water.
†
The
difference
in
weight
between
the
dry
and
fully
saturated
core
sample
is
the
amount
of
water
soaked
up.
50%
saturation
is
obtained
by
letting
the
core
sit
and
evaporate
water
until
half
of
the
initially
soaked
water
remains,
indicated
by
the
mean
weight
between
the
dry
and
fully
soaked
sample.
The
total
regional
stress
is
approximated
by
the
rock
column
above
the
location
from
where
the
core
sample
is
retrieved,
and
is
simulated
by
Grigg’s
Rig
–
Uniaxial
Compression.
The
core
sample
is
placed
into
a
rigid
walled
cylinder
and
a
press
of
a
specific
weight,
which
is
equivalent
to
the
total
regional
stress,
is
mounted
on
top.
A
range
of
total
regional
stresses
is
simulated
for
each
of
the
three
cases.
By
doing
this,
the
approximately
computed
total
regional
stress
and
the
thickness
of
the
reservoir
unit
are
accounted
for.
For
illustration,
the
range
total
regional
stresses
is
denoted
(MPa1,
MPa2,...,MPan)
and
the
table
below
summarizes
the
experiment
runs.
Table
2:
Experimental
runs
where,
Vp
=
velocity
of
P-­‐wave;
Vs
=
velocity
of
S-­‐wave;
Ap
=
attenuation
of
P-­‐wave;
As
=
attenuation
of
S-­‐wave
Total
regional
stress
Case
1
-­‐
0%
saturation
Case
2
-­‐
100%
saturation
Case
3
-­‐
50%
saturation
Run
at
MPa1
Measure
Vp,
Vs,
Ap,
As
Measure
Vp,
Vs,
Ap,
As
Measure
Vp,
Vs,
Ap,
As
Run
at
MPa2
Measure
Vp,
Vs,
Ap,
As
Measure
Vp,
Vs,
Ap,
As
Measure
Vp,
Vs,
Ap,
As
...
Measure
Vp,
Vs,
Ap,
As
Measure
Vp,
Vs,
Ap,
As
Measure
Vp,
Vs,
Ap,
As
Run
at
MPan
Measure
Vp,
Vs,
Ap,
As
Measure
Vp,
Vs,
Ap,
As
Measure
Vp,
Vs,
Ap,
As
For
every
case,
each
run
of
total
regional
stress
CO2
is
injected
in
fixed
incremental
amounts
and
the
corresponding
pore
pressure
is
measured.
After
each
injection,
P-­‐
and
S-­‐waves
are
shot
through
the
core
and
their
velocities
(Vp
and
Vs)
and
corresponding
attenuations
(Ap
and
As)
are
recorded.
The
waves
are
created
via
a
seismic
transducer.
The
transmitter
is
placed
at
one
end
of
the
core
and
the
receivers
are
placed
at
the
opposite
end.
For
identification
of
any
dependency
of
the
seismic
waves
on
their
wavelength,
the
P-­‐
and
S-­‐waves
are
shot
at
a
range
of
frequencies
(f1,
f2,
...
,fn).
According
to
the
wave
theory
the
relationship
between
the
wavelength
and
frequency
is:
! =
!
!
Where
!
is
wavelength,
!
is
frequency,
and
!
is
the
velocity
of
propagation
through
the
core.
Since
the
wave
velocity
(!)
is
being
measured,
then
by
varying
frequencies,
different
wavelengths
are
produced.

5. 5
Since
the
core
is
1
meter
in
length,
the
maximum
wavelength
limit
is
the
length
of
the
core.
Therefore,
in
order
to
obtain
proper
measurements
the
last
frequency
(fn)
is
such
that
produces
the
maximum
wavelength
of
1
meter.
The
initial
frequency
(f1)
is
set
at
experimenter’s
discrepancy.
The
CO2
is
injected
and
the
measurements
are
taken
until
the
pore
pressure
equates
the
total
regional
stress.
Below
is
the
table
of
the
experiment
measurements
for
Case
1.
The
incremental
CO2
injection
is
denoted
as
Xg:
Table
3:
Experimental
measurements
for
case
1
for
a
range
of
total
regional
stresses
Case
1
-­‐
0%
saturation:
Run
at
total
regional
stress
of
MPan
CO2
injection
Pore
Pressure
f1
f2
…
fn
1
Xg
CO2
PpX
Vs1,
Vp1,
Ap1,
As1
Vs2,
Vp2,
Ap2,
As2
Vs…,
Vp…,
Ap…,
As…
Vsn,
Vpn,
Apn,
Asn
2
2Xg
CO2
Pp2X
Vs1,
Vp1,
Ap1,
As1
Vs2,
Vp2,
Ap2,
As2
Vs…,
Vp…,
Ap…,
As…
Vsn,
Vpn,
Apn,
Asn
3
3Xg
CO2
Pp3X
Vs1,
Vp1,
Ap1,
As1
Vs2,
Vp2,
Ap2,
As2
Vs…,
Vp…,
Ap…,
As…
Vsn,
Vpn,
Apn,
Asn
…
…
…
…
…
…
…
n
nX
g
CO2
PpnX
=
MPa1
Vs1,
Vp1,
Ap1,
As1
Vs2,
Vp2,
Ap2,
As2
Vs…,
Vp…,
Ap…,
As…
Vsn,
Vpn,
Apn,
Asn
The
same
data
parameters
are
collected
for
a
range
of
different
total
regional
stresses
for
each
case.
The
above
experiment
measurements
are
also
repeated
for
other
two
cases:
100%
saturation
and
50%
saturation.
However,
based
on
the
fact
that
S-­‐waves
do
not
propagate
through
fluids,
for
Case
2
-­‐
100%
saturation,
only
P-­‐wave
velocity
and
P-­‐waves
attenuation
are
measured.
Once
the
experimental
data
is
collected
the
scatter
plots
for
each
of
the
three
cases
are
graphed
and
the
relationships
are
mathematically
derived
though
best
fitted
curves.
For
Case
2
-­‐
100%
saturation,
only
Vp
and
Ap
are
measured.
The
relationships
are:
1) Vp
and
Vs
versus
Pp
at
a
specific
frequency.
2) Ap
and
As
versus
Pp
at
a
specific
frequency.
3) Vp
and
Vs
versus
f
at
a
specific
Total
regional
stress.
4) Ap
and
As
versus
f
at
a
specific
Total
regional
stress.
1) Vp
and
Vs
versus
Pp
at
a
specific
frequency
2) Ap
and
As
versus
Pp
at
a
specific
frequency

6. 6
3) Vp
and
Vs
versus
f
at
a
specific
Total
regional
stress
4) Ap
and
As
versus
Pp
at
a
specific
Total
regional
stress
Figure
1:
The
illustration
graphs
for
each
relationship
are
presented.
Determination
of
the
first
two
relationships
is
the
main
goal
of
the
experiment,
whereas
the
last
two
relationships
are
important
supplementary
information
needed
for
calibration
of
obtained
velocities
and
attenuations.
By
knowing
the
relationship
between
the
seismic
wave
velocities,
attenuation
and
the
pore
pressure,
one
might
use
this
knowledge
to
calculate
the
concentration
of
CO2
present
in
the
core.
Case
Study
Support
Geological
formations
that
are
subjected
to
saturation
of
CO2
will
cause
changes
in
seismic
velocities
and
attenuation,
which
is
reflected
in
changes
of
seismic-­‐wave
scattering
and
propagation.
Siggins
(2006)
uses
three
different
sandstones,
two
synthetic
and
one
field
sample,
to
test
the
effects
of
confining
and
pore
pressures
on
the
sandstones
that
mimic
in-­‐situ
reservoir
pressures.
The
three
different
sandstones
include:
(1)
a
synthetic
sandstone
with
calcite
intergranular
cement,
(2)
a
synthetic
sandstone
with
silica
intergranular
cement,
and
(3)
a
core
sample
from
the
Otway
Basin
Waare
Formation.
Initially,
the
three
sandstones
were
tested
at
“room-­‐dried”
conditions,
using
confining
pressures
in
increments
of
5MPa
and
up
to
65
MPa.
The
sandstones
were
then
flooded
with
CO2,
first
a
gas
phase
at
a
pressure
of
6
Mpa
and
temperature
of
22
°C,
then
with
a
liquid
phase
at
pressures
from
7
Mpa
to
17
Mpa
and
a
temperature
of
22
°C.
Both
P-­‐
and
S-­‐waves
were
recorded
at
each
effective
pressure
increment
(where,
Peffective
=
Pconfining
–
Pore
Pressure)
and
velocity
versus
effective
pressure
responses
were
calculated
from
the
experimental
data
for
both
P-­‐
and
S-­‐waves.
Attenuations
(Q-­‐1
)
were
calculated
from
the
waveform
data.
Theoretical
calculations
of
velocity
as
a
function
of
effective
pressure
for
each
of
the
sandstone
samples
were
determined.
When
compared
to
the
initial
dry,
unsaturated
state
of
the
sandstone
samples,
both
P-­‐
and
S-­‐wave
velocities
decreased
by
approximately
8%
in
both
of
the
synthetic
sandstones
when
liquid
CO2
was
injected.
However,
the
Waare
sample
only
showed
a
relative
decrease
in
S-­‐wave
velocities.
On
the
other
hand,
attenuation
in
all
of
the
sandstones
increased
after
saturation
of
liquid
CO2.
The
experimental
graphs
are
below
(Figure
2).

7. 7
The
experiment
presented
by
Siggins
(2006)
is
similar
to
ours;
however
his
variable
is
effective
stress.
The
case
study
can
be
applied
to
our
geophysical
solution
by
demonstrating
that
seismic
velocities
and
their
associated
attenuations
are
quantifiable,
especially
if
we
want
to
be
able
to
determine
the
changes
in
CO2
concentrations
of
a
reservoir
within
a
laboratory
environment.
Laboratory
experiments
are
a
key
component
to
up
scaling
projects
that
can
be
used
in
the
field
environment.

8. 8
Figure
2:
Velocity
vs.
effective
pressure
response
for
both
dry
and
liquid
saturated
CO2
conditions.
Attenuations
(Q-­‐1)
are
also
presented.
The
theoretical
Gassmann
predictions
for
the
liquid
CO2
saturated
state
for
both
P-­‐
and
S-­‐waves
are
included
as
solid
curves
(modified
after
Siggins,
2006).
Gassmann predictions was particularly g
pressures. In the case of the silica-cemented
wasexcellentateffectivepressuresof20 MP
material required effective pressures of 27
agreement
and theory
discrepanci
to varying
aspect-ratio
and intergr
the rock st
of the calci
in the CIP
some water
Sass, 1999)
formation
pore space.
not take the
space into c
Waarre Fo
discrepancy
experiment
this sandst
had been
so significa
relief is to
attenuation
that of th
– is evide
Microstruc
have comp
integrity of
Fig. 4. Comparison of the velocity versus effective pressure response
for CIPS synthetic sandstone in the room-dried state with the CO2
saturated state. CO2
is in the gaseous phase at a temperature of 22°C
and a pore pressure of 6 MPa.
Fig. 5. Veloci
pressure resp
sandstones f
saturated) an
conditions. C
attenuations
presented. In
the liquid sta
of 22°C and
17 MPa. The
predictions f
saturated sta
waves are in
64

9. 9
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Anthony
F.,
2006,
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