International Journal of Geosciences, 2012, 3, 908-917
http://dx.doi.org/10.4236/ijg.2012.325093 Published Online October 2012 (http://www.SciRP.org/journal/ijg)
Effects of CO2 Injection on the Seismic Velocity of
Sandstone Saturated with Saline Water
Marte Gutierrez, Daisuke Katsuki, Abdulhadi Almrabat
Civil and Environmental Engineering Colorado School of Mines, St. Golden, USA
Received August 16, 2012; accepted September 15, 2012; accepted October 14, 2012
ABSTRACT
Geological sequestration (GS) of carbon dioxide (CO2) is considered as one of the most promising technologies to re-
duce the amount of anthropogenic CO2 emission in the atmosphere. To ensure success of CO2 GS, monitoring is essen-
tial on ascertaining movement, volumes and locations of injected CO2 in the sequestration reservoir. One technique is to
use time-lapsed seismic survey mapping to provide spatial distribution of seismic wave velocity as an indicator of CO2
migration and volumes in a storage reservoir with time. To examine the use of time-lapsed seismic survey mapping as a
monitoring tool for CO2 sequestration, this paper presents mathematical and experimental studies of the effects of su-
percritical CO2 injection on the seismic velocity of sandstone initially saturated with saline water. The mathematical
model is based on poroelasticity theory, particularly the application of the Biot-Gassmann substitution theory in the
modeling of the acoustic velocity of porous rocks containing two-phase immiscible pore fluids. The experimental study
uses a high pressure and high temperature triaxial cell to clarify the seismic response of a sample of Berea sandstone to
supercritical CO2 injection under deep saline aquifer conditions. Measured ultrasonic wave velocity changes during CO2
injection in the sandstone sample show the effects of pore fluid distribution in the seismic velocity of porous rocks. CO2
injection was shown to decrease the P-wave velocity with increasing CO2 saturation whereas the S-wave velocity was
almost constant. The results confirm that the Biot-Gassmann theory can be used to model the changes in the acoustic
P-wave velocity of sandstone containing different mixtures of supercritical CO2 and saline water provided the distribu-
tion of the two fluids in the sandstone pore space is accounted for in the calculation of the pore fluid bulk modulus. The
empirical relation of Brie et al. for the bulk modulus of mixtures of two-phase immiscible fluids, in combination with
the Biot-Gassmann theory, was found to satisfactorily represent the pore-fluid dependent acoustic P-wave velocity of
sandstone.
Keywords: Biot-Gassmann Theory; CO2 Geological Sequestration; Poroelasticity; Porous Rocks; Two-Phase Fluid
Flow; Seismic Velocity
1. Introduction
There has been increasing evidence that anthropogenic
release of carbon dioxide (CO2) in the atmosphere has
been one of the main causes of changes in global weather
patterns. One major solution to reduce the further release
of CO2 in the atmosphere from human activities is geo-
logical sequestration (GS) whereby carbon dioxide (CO2)
is injected and permanently stored in underground geo-
logical formations. The estimated volume of potential
sequestration reservoirs is abundant [1,2]. Depleted oil
and gas reservoirs and abandoned mines are important
candidates for CO2 storage. Deep saline aquifers are also
very promising because of their huge estimated capaci-
ties and high connectivity of pore spaces [3].
CO2 injected in geological formations is trapped due to
different mechanisms, including stratigraphic and struc-
tural trapping, residual CO2 trapping, solubility trapping,
and mineral trapping [1]. A large part of injected CO2 is
initially trapped due to the structural and stratigraphic
trapping mechanisms. The volume ratio of CO2 trapped
due to solubility and mineral trapping mechanisms is
expected to increase with time. Along with this change,
site integrity is expected to increase as the formation gets
mineralized by geochemical interactions between CO2
and the host rock.
To be economically feasible, CO2 needs to displace in
situ saline water efficiently. Injection of CO2 is carried
out in the form of a supercritical fluid as a result of high
in situ fluid pressure and temperature. This is advanta-
geous in terms of injectivity because supercritical CO2
(referred to as scCO2 in this paper) is less viscous than
liquid CO2 and denser than CO2 vapor. However, CO2
injection pressures, which must be greater than in situ
pore pressures, can cause adverse effects in the reservoir,
C
opyright © 2012 SciRes. IJG

M. GUTIERREZ ET AL. 909
such as induced seismic activity, deterioration of the
capping and sealing properties of the cap rock layers,
opening of fractures, and shear failure of faults resulting
in leakage of CO2 in water aquifers or to the atmosphere
[4]. Thus, one of the main technical issues in CO2 geo-
logical sequestration is the prediction of the flow, trans-
port and prolonged stability of CO2 in deep saline forma-
tions. Development of field monitoring techniques for
CO2 migration is also essential for the safe and reliable
operations of CO2 sequestration. Field monitoring is cru-
cial to determine injected CO2 movement, volumes and
locations in the sequestration reservoir. Direct monitor-
ing techniques use observation wells and tracers to ob-
serve CO2 migration in reservoirs. However, drilling ob-
servation wells is expensive, time consuming, provides
only limited data which may not fully represent in situ
conditions, and has the risk of deteriorating the sealing
capacity of the cap rock [1].
Indirect geophysical methods such as seismic and elec-
tric resistivity surveys can be used for economical, large-
scale field underground fluid monitoring. Time-lapsed
seismic survey mapping can provide spatial distribution
of seismic wave velocity which can be correlated with
CO2 migration and volumes in a storage reservoir with
time. The acoustic velocity response of rock media filled
with fluids is primarily a function of rock mass elasticity,
porosity, and pore fluid bulk modulus. These components,
related to acoustic velocity, are affected by temperature,
rock mass effective stresses, fluid pressure, and pore
fluid composition (saturation). Previous studies [5,6]
have shown that the acoustic velocity response of sand-
stone cores changes with the relative volumes of water/
CO2 in the pore space. The change in acoustic velocity is
a result of the change in the bulk modulus of the pore
fluid as sCO2 displaces saline water during the injection
process. However, the evaluation of the bulk modulus of
mixture of multiphase fluid is still a challenge. A major
reason is that the bulk modulus of a fluid mixture should
also depend on the degree of uniformity of the fluid
mixture in the rock pore space [7,8].
This paper presents mathematical and experimental
investigations of the effects of supercritical CO2 injection
on the seismic velocity of sandstone initially saturated
with saline water. The mathematical model is based on
application of the Biot-Gassmann poroelasticity theory
[9,10] in the modelling of the acoustic velocity of porous
rocks containing two-phase immiscible pore fluids. The
focus of the mathematical modelling is on how the Biot-
Gassmann theory can be modified to account for the dis-
tribution of two phase fluids, particularly in terms of lay-
ering and non-uniformity in the scCO2 displacement front,
in addition to their relative volumes, in the pore space of
sandstone. The experimental study uses a laboratory
testing system to clarify the acoustic response of rocks to
supercritical CO2 injection under deep saline aquifer
conditions. The main component of the system is a high
pressure and high temperature (HPHT) triaxial cell that
allows for injection of CO2 in core samples of sandstone
initially saturated with saline water. High pressure preci-
sion syringe pumps for back pressure and injection fluid
pressure control, a hydraulic pump for cell pressure con-
trol, and a temperature control system allow for the in-
jection of CO2 at supercritical conditions. The end caps of
the core holder are equipped with piezoelectric transduc-
ers to characterize ultrasonic wave velocity response of
the rock core sample.
2. Biot-Gassmann Theory
Gassman’s substitution theory [10] is the most widely
used equation to describe the effects of the bulk modulus
of the pore fluid on the seismic velocity of deformable
porous media. The original derivation of Gassman’s
equation is very involved and complicated. Here, it is
shown that the equation can be derived very elegantly and
succinctly using Biot’s poroelastic equations. The coupled
poroelastic equations, which were first derived by [9],
provide a rigorous mathematical treatment of fluid flow in
deformable porous media, where fluid flow affects me-
chanical response and vice versa, and fluid flow field
cannot be analysed separately from the mechanical re-
sponse except under simple boundary conditions. (Notes:
a) tensorial notation is used and repeated indices imply
summation; b) a dot over a symbol indicates differentia-
tion with respect to time; and c) all stresses are total).
Biot’s theory couples the poroelastic stress-strain relation
for fluid-saturated porous materials:
2
ijv ijijij
K
Ge p

 


 
(1)
with the poroelastic fluid diffusion equation that quanti-
fies fluid pressure changes in the same material (assum-
ing single phase fluid flow and isotropic permeability):
v
fs
kppq
KK




 
 

 
 

(2)

In the above equations i
x
 , ij



vkk
= stress rate
tensor, ijij


 
  = volumetric strain rate tensor,
3eijijij v


 
  = deviatoric strain rate tensor, ij


p

=
strain rate tensor, = pore pressure rate, k

perme-
ability,

= fluid viscosity, q = fluid source or sink,
and G = elastic bulk and shear moduli of the porous
medium, respectively, ij

K

= Kronecker delta,
f
K
and
s
K
= bulk moduli of the pore fluid and the solid grains of
the porous medium, respectively,

= porosity, and

=
Biot’s poroelastic constant defined as:
K
(3) 1
K
 
s

M. GUTIERREZ ET AL. 910
In Equation (2), single phase fluid flow and isotropic
permeability were assumed. As will be shown below,
permeability disappears in the derivation of the Biot-
Gassmann equation. For this reason and by defining the
pore pressure as the average fluid pressure, the Biot-
Gassman equation that will be derived below based on the
Equations (1) and (2) can also be used for two phase fluid
flow. Note that Equation (1) differs from conventional
elasticity in that poroelastic deformation of the solid
grains due to pore pressure changes is included in the total
deformation of the porous medium. Equation (2) also
differs from conventional fluid diffusion equation in that
it accounts for poroelastic deformation in the fluid flow in
the porous medium.
p
Under undrained conditions, two conditions are
achieved: 1)

(i.e., no fluid gradients or
Darcy fluid flow), and 2)

0kp  
0q


p 
(i.e., no fluid sink or
source). Substituting these two conditions in Equation (2)
and solving for gives:
v
fs
KK

p









  (4)
Since the shear modulus G is independent of pore
fluid composition and is the same for both drained and
undrained conditions [11], Equation (1) can be split into
deviatoric and volumetric components:
2
ij ij
s
Ge
 and mv
K
p




 
(5)
where 33
mkk ijij

 

s
= mean stress rate, and
ijijij m

 
  = deviatoric stress rate tensor. The va-
lidity of uncoupling the deviatoric and volumetric elastic
response of fluid saturated porous media is investigated
experimentally below. Substituting Equation (4) in Equa-
tion (5) yields:
2
v
fs
KK

mv
K












 (6)
Dividing throughout by v

 yields the undrained bulk
modulus of a fluid-saturated porous rock umv K



 
as:
2
fs
KK

u
KK








 (7)
Equation (7) was first derived by [10], however, as
shown above this equation can also be derived from the
more general and earlier Biot’s poroelasticity theory. Thus,
it is only proper to call Equation (7) as the Biot-Gassmann
equation. Equation (7) gives the undrained bulk modulus
of fluid-saturated porous material as function of the
drained or dry bulk modulus of the same material, the
porosity, Biot’s poroelastic constant, and bulk moduli of
the pore fluid and the solid grains of the porous medium.
The different parameters in Equation (7) are all constants
for a rock specimen under the same effective stress and
porosity except for the pore fluid bulk modulus which can
change with fluid composition. It is important to note that
the second term of the right-hand side of Equation (7)
represents the effect of pore fluid content on the undrained
bulk modulus Ku.
3. Laboratory Testing Equipment
The effects of injection of scCO2 in the seismic velocity
of porous rock were studied using a newly developed test
system which consists of a high-pressure and high tem-
perature (HPHT) triaxial cell. Figure 1 shows a sche-
matic diagram of the testing system. The triaxial core
holder has a maximum working confining pressure ca-
pacity of 70 MPa, two precision syringe pumps that con-
trol the back pressure and injection pressure, a dome-
loaded back pressure regulator, a hydraulic pump for
regulating cell pressure, and a differential pressure
transducer. The sample is enclosed in a Viton sleeve.
Both ends of the core sample are in contact with high
permeability porous metal filter discs in order to ho-
mogenize the fluid flow. Two movable pistons controlled
by hydraulic pressure are able to induce axial stress dif-
ferent from the confining stress. One of the syringe
pumps transmits a mixture of saline water and scCO2 into
the rock core sample at very accurate flow rates. Another
syringe pump acts as the back-pressure regulator with
set-point pressure. The temperatures of fluids stored in
the syringe pumps are regulated by using silicon rubber
blanket heaters wrapped around the side walls of the sy-
ringes and the PID temperature controllers. The pressure
and volume change of fluids in the syringe pumps are
monitored and acquired in a personal computer commu-
nicating with the pumps. The back-pressure regulator is
equipped with a polyimide film diaphragm providing
accurate regulation of outlet pressures. Saline water pro-
duced from the end face of rock core sample during
scCO2 injection is accumulated in a vessel placed on an
accurate electronic balance. The mass data of saline wa-
ter accumulated is acquired by using a computer via se-
rial communication. The complete testing system is en-
closed within a constant temperature air-circulating cab-
inet that is controlled with an on-off infrared heater and
air-circulating fans.
The end caps of the core holder are equipped with
piezoelectric transducers for seismic compressional and
shear wave velocity measurements. Figure 2 shows a
schematic of the arrangement of piezoelectric transducers.
Triads of shear wave transducers shake one of the end

M. GUTIERREZ ET AL. 911
Figure 1. Schematic diagram of the testing syste m.
Porous metal filters
Viton sleeveRock core sample
PZT (SH)
PZT (SV)SV
SH
PZT (P) Cap
Figure 2. Arrangement and polarization of piezoelectric transducers for seismic wave velocity measurement. Arrows indicate
the direction of oscillation of two different shear waves (horizontal “SH” and vertical “SV”), and “P” denotes compression
wave.
4. Test Material and Procedures
caps in two individual orthogonal directions. In the cen-
ter of the cap is a compressional wave transducer. The study of the effects of scCO2 injection in the seismic
velocity of porous rock initially saturated with saline
water was conducted using Berea sandstone, which is a
well-known and widely used test material in the study of
the rock mechanical and fluid flow behavior of sedimen-
tary rocks. Cylindrical rock samples used for the experi-
mental works are cored from a block of Berea sandstone.
Both ends of the core samples are grinded to ensure that
sample ends are parallel within required tolerances. The
petrophysical properties of the Berea sandstone used in
the tests are summarized in Table 1. Carbon dioxide
having 99.9999% of purity is used to prepare the scCO2.
Saline water used is a mixture of distilled water and so-
dium chloride at 3.4% of salinity.
The natural frequencies of the transducers range from
0.25 to 1 MHz. The transducers are excited by using a
square wave pulser/receiver capable of providing square
pulses whose voltages are selectable between 100 and
400 V in increments of 100 V. The typical rise time of
pulse is less than 1.0 × 10–8 s. The maximum bandwidth
and typical noise level of receiver are from 1 kHz to 35
MHz and 70 μV peak to peak, respectively. The seismic
waveforms are converted into digital signals by using a
digital oscilloscope having 100 MHz of bandwidth and
1 × 109 s–1 of real time sample rate. The minimum time
base and the vertical resolution of oscilloscope are 2 ×
10–9 s/div and 8 bits. The waveform data are acquired by
using a personal computer communicating with the os-
cilloscope. Each waveform acquired is the average of 16
waveforms. The resultant minimum time interval of
waveform acquisition in the personal computer is 6 s.
The procedure for the scCO2 injection tests is de-
scribed below. A core sample dried at T = 383 K is
placed inside the core holder then saturated with distilled

M. GUTIERREZ ET AL. 912
Table 1. Petrophysical properties of Berea sanstone.
Dry bulk density (g/cm3) Porosity Permeability (mD)
2.2 0.17 20 - 30
water under vacuum by allowing the sample to imbibe
distilled water. The confining axial and lateral stresses
are isotropically increased up to 12 MPa. The pore pres-
sure Ppore is simultaneously raised to 10 MPa by keeping
the effective stress less than 2 MPa. The core sample is
consolidated at desired effective stress at a pore pressure
of Ppore = 10 MPa and a temperature of T = 313 K to en-
sure that the injected CO2 is kept in supercritical condi-
tion. Distilled water filling the pore space is displaced
with saline water saturated with scCO2 at Ppore = 10 MPa
and T = 313 K. The total volume of saline water injected
is more than ten times of the pore volume of core sample.
Supercritical CO2 saturated with saline water is injected
into core sample at a constant rate at the prescribed con-
ditions. The injection rates qinj of scCO2 during the rela-
tive permeability characterization and ultrasonic wave
velocity measurement are 2.0 and 0.20 cm3/min, respec-
tively. The pressure values used in the paper are gage
pressures.
5. Test Results and Discussions
Figure 3 shows the injection pressure and saline water
production behavior observed during CO2 injection at a
rate of 0.2 cm3/min. The injection pressure is maintained
at 10.00 ± 0.05 MPa through displacement. The produc-
tion behavior of saline water indicates that CO2 reaches a
maximum saturation of 0.25 at the end point of dis-
placement.
Figure 4 shows some of the waveforms of P-wave
acquired during the CO2 injection. The values in the fig-
ures indicate the average CO2 saturation of the core sam-
ple when a P-wave velocity is measured. The arrival time
of each wave has been determined at the first negative
rise in the waveform. The arrival time changed signifi-
cantly from 36.0 to 36.6 ms and subsequently to 37.2 ms
as the CO2 saturation increased from 0 to 0.151 and to
0.214.
The shear waveforms acquired during CO2 injection
are shown in Figure 5. The arrival times are 64.4, 64.4,
and 64.0 ms corresponding to the average CO2 saturation
values of 0.0, 0.137 and 0.228, respectively. The de-
pendency of shear wave velocity on scCO2 saturation
seems to be very different to that of the P-wave, i.e., the
S-wave velocity increases slightly with increasing the
CO2 saturation, and is almost insensitive to the scCO2
saturation.
The CO2 saturation dependency of the bulk and shear
moduli of Berea sandstone is summarized in Figure 6.
The bulk and shear moduli, K and G were calculated
from
22
4
3
ps
KVV 




2
(8)
s
GV (9) 

where Vp and Vs are the compressional and shear wave
velocities, and ρ is the density of porous medium. The
bulk density of porous rock filled with saline water and
2
CO
N
Figure 3. Injection pressure and production behavior during CO2 injection at 0.2 cm3/min into Berea sandstone core sample
presaturated with saline wa ter.

M. GUTIERREZ ET AL. 913
Figure 4. Compression waveform change depending on CO2 saturation observed during CO2 injection into Berea sandstone
core sample presaturated wit saline water.
Figure 5. Change of shear waveforms during CO2 injection at 0.2 cm3/min into Berea sandstone core sample presaturated
with saline water.
CO2 is calculated from


2
CO sln
S 


22
dryCO CO1S
 

 
 (10)
where ρdry, 2
CO
the voids. As can be seen in Figure 7, the bulk modulus
decreased from 17.5 GPa to 13.3 GPa during the dis-
placement of saline water by scCO2. The pore fluid bulk
modulus, and correspondingly the rock undrained bulk
modulus u

, and ρsln are the bulk densities of the
dry rock, CO2, and saline water, and  is the porosity of
the rock sample. In Figure 7 and Equation (10), 2
CO is
the scCO2 saturation which is defined as the volume of
supercritical CO2 in the voids divided by the volume of
K
, decreased with increasing 2
CO because
the scCO2 bulk modulus is lower than saline bulk mod-
ulus. Note that most of the change in the bulk modulus
occurred for . This is because the irreducible
S
2
CO 0.25S
S

M. GUTIERREZ ET AL. 914
saline water saturation for the tested sample is about 75%.
In contrast to the bulk modulus, Figure 7 shows that the
shear modulus is nearly constant during the increase in
scCO2 saturation from 0 to 0.25. This confirms the as-
sumption used in Equation (5) to uncouple the elastic
volumetric and deviatoric responses in a poroelastic me-
dium.
To calculate the undrained bulk modulus u
K
in Equ-
ation (7), it is necessary to determine the pore fluid bulk
modulus
f
K
. Two widely used equations to calculate
the bulk modulus of mixtures of two phase immiscible
fluids are: 1) the serial law; and 2) the Wood’s (1941)
parallel law [12]. For a mixture of saline water and
scCO2, the serial law is given as:

2
CO sln
1
22
CO COf
K
SK
and Wood’s parallel law as:
S K (11)
22
2
CO CO
CO sln
1
1
f
SS
KK K


K
(12)
where 2
CO is the bulk modulus of scCO2 and sln
K
is
the bulk modulus of saline water. The serial law is appli-
cable to the case where the two immiscible fluids are
segregated perpendicular to the wave propagation direc-
tion (Figure 6(a)), and the parallel law is applicable to
the case where the two immiscible fluids are segregated
parallel to the wave propagation direction (F i gure 6( b)).
The dependency of
p
VS
S
on 2
CO of the tested Berea
sandstone is shown in Figure 8. The 2
CO -dependent
p
V is calculated and predicted from u
K
(Equation 7),
with
f
K
determined from either Equation (10) or Equ-
ation (1), and as: G
Fluid1Fluid2
Fluid1Fluid2
Fluid1
Fluid2
Fluid1
Fluid2
(a)
(b)
Figure 6. Illustration of (a) Serial and (b) Parallel distributions of two-phase fluids in respect to longitudinal direction.
2
CO
S
Figure 7. CO2 saturation dependencies of bulk and shear moduli of Berea sandstone c ore sample.

M. GUTIERREZ ET AL. 915
2
CO
S
Figure 8. CO2 content dependency of compressional wave velocity during CO2 injection into Berea sandstone presaturated
with saline water.
14
3
u
VKG





p (13)
As can be seen,
p
V
S
decreases from 3.86 km/s to ap-
proximately 3.65 km/s as 2
CO increases from 0 to 0.25.
The
p
V vs 2
CO relationships calculated from the Bi-
ot-Gassmann equation in combination with the bulk
modulus values from the serial and parallel distributions
(Equations (10) and (11)) are also shown in the figure.
The pressure and temperature fluid bulk modulus values
for scCO2 were obtained from [13], and [5]. The Biot-
Gassmann equation in combination with serial law (Equ-
ation (10)) predicts rapid decrease of
S
p
V with values
much lower than experimental data, while the Biot-
Gassmann equation in combination with parallel law
(Equation (11)) predicts a slower decrease in
p
V with
increasing scCO2 saturation than experimental data.
The results shown in Figure 8 indicate that the two-
phase fluids are potentially distributed neither in parallel
nor serial fashion in the test specimen, although these
distributions correspond to the lower and upper bound
values, respectively, of the
p
VS

2
slnslnslnCO
1
nn
f
KSK SK
1SS
vs 2
CO relationship in
sandstone. X-ray CT (Computed Tomography) imaging
of scCO2 injection in Berea sandstone shows that the
pore fluid distribution is more complicated than the ideal
parallel or serial distributions and is dependent on the
pore structure and the relative mobilities of the two fluids
(Shi et al., 2011). A much improved empirical equation
to estimate the fluid bulk modulus of mixtures two-phase
fluids and account for their mixing is the equation pro-
posed by [7]:
(14)
where 2
sln CO

 = saline water saturation and n =
empirical parameter. Note than n = 1 corresponds to the
serial fluid distribution. As the value of n increases, the
effect of the lower bulk modulus of CO2 phase becomes
predominant at lower CO2 saturations. The value of n
determined by fitting the resulting
p
V vs 2
CO curve
to the experimental data is 4.19 with R2-value of 0.85.
The data-fitted
S
p
VS

0.02S 
S

vs 2
CO curve corresponding to the
combined Biot-Gasmann and Brie equations is shown in
Figure 8 together with the experimental data. As can be
seen, a good agreement is obtained indicating the validity
of the combined Biot-Gasmann and Brie equations.
The change in the 2
COp
VS relationship shown in
Figure 8 should correspond to the transitions of the fluid
distributions in the core sample. At the very early stage
of displacement (2
CO ), the observed 2 COp
VS
relationship has changed along the curve given by the
Gassmann-Wood equation. This change can be under-
stood by considering the following displacement process.
The injected CO2 phase is likely to concentrate in the
inlet end of core sample at this stage. The rest of pore
space should not be invaded by CO2. The fluids are
therefore close to the series distribution to which the
Wood’s law is applicable. When 2
CO is increased from
0.02 to 0.15, the 2
COp
VS relationship observed has
moved close to that given by the Gassmann-parallel law
model. This transition means that the fluid distribution is

M. GUTIERREZ ET AL. 916
shifting to a layered distribution. This is reasonable be-
cause the injected CO2 can concentrate in the upper part
of the horizontally oriented core sample due to buoyancy
effect and consequently the saline water and CO2 phases
flow in two distinct layers. After that, the observed
2
COp relationship gradually moved toward that pre-
dicted by the Gassmann-Wood equation. This transition
is understandable by considering a process in which the
layered fluid distribution is changing gradually to a ho-
mogeneous one as the fluid displacement proceeds. More
specifically, the volume of the saline water occupying the
outlet end of the core sample has now been gradually
displaced by CO2, and CO2 occupies most of the pore
space. It can be seen that the observed Vp remains higher
than that predicted by the Gassmann-Wood equation
even at the end point of displacement. This suggests that
the fluid distribution still has some heterogeneity at the
end point of displacement. On the average, the Bi-
ot-Gassmann-Brie et al. equation with an exponent of
4.19 provides a very good representation of the pore fluid
dependent P-wave velocity of Berea sandstone.
VS
6. Conclusion
Ultrasonic wave velocity changes due to CO2 saturation
change were measured using Berea sandstone core sam-
ple which was initially saturated with saline water and
was subjected to constant CO2 injection rate. The results
showed the effects of pore fluid distribution in determin-
ing the effects of multiphase pore fluids on the seismic
velocity of porous rocks. Increasing CO2 saturation af-
fected the P-wave velocity which was observed to de-
crease whereas the S-wave velocity was almost constant
during the CO2 injection. The results confirm that the
Biot-Gassmann theory can be used to model the changes
in the acoustic P-wave velocity of sandstone containing
different mixtures of supercritical CO2 and saline water
provided the distribution of the two fluids in the sand-
stone pore space is accounted for in the calculation of the
pore fluid bulk modulus. Two-phase fluids distributed
parallel and in series in the voids relative to the wave
propagation direction correspond to the lower and upper
bound values, respectively, of the fluid saturation de-
pendent P-wave velocity of sandstone. The observed
relationship between P-wave velocity and CO2 saturation
transitioned from the relation given by the Biot-Gass-
man-Wood model in the initial injection phase, to the
Biot-Gassmann-parallel law model, then back to the Bi-
ot-Gassmann-Wood model towards the end of the dis-
placement process. This should correspond to the transi-
tion of spatial distribution of saline water and CO2 in
core sample as the displacement of saline water pro-
ceeded. The empirical relation of Brie et al. [7] for the
bulk modulus of mixtures of two-phase immiscible fluids,
in combination with the Biot-Gassmann theory, was
found to satisfactorily represent the pore-fluid dependent
acoustic P-wave velocity of sandstone.
7. Acknowledgements
Financial support provided by the Department of Energy
under Grant No. DE-FE0000730 is gratefully acknowl-
edged. The author thanks Dr. Mike Batzle and Mr.
Weiping Wang on their advice and help on the ultrasonic
velocity testing, and Mr. Brian Asbury for his technical
support in coring of the rock samples.
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