Effects of CO 2 Injection on the Seismic Velocity of Sandstone Saturated with Saline Water

Geological sequestration (GS) of carbon dioxide (CO2) is considered as one of the most promising technologies to reduce the amount of anthropogenic CO2 emission in the atmosphere. To ensure success of CO2 GS, monitoring is essential 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 supercritical 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 distribution 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.


Introduction
There has been increasing evidence that anthropogenic release of carbon dioxide (CO 2 ) 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 CO 2 in the atmosphere from human activities is geological sequestration (GS) whereby carbon dioxide (CO 2 ) is injected and permanently stored in underground geological formations.The estimated volume of potential sequestration reservoirs is abundant [1,2].Depleted oil and gas reservoirs and abandoned mines are important candidates for CO 2 storage.Deep saline aquifers are also very promising because of their huge estimated capacities and high connectivity of pore spaces [3].
CO 2 injected in geological formations is trapped due to different mechanisms, including stratigraphic and structural trapping, residual CO 2 trapping, solubility trapping, and mineral trapping [1].A large part of injected CO 2 is initially trapped due to the structural and stratigraphic trapping mechanisms.The volume ratio of CO 2 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 CO 2 and the host rock.
To be economically feasible, CO 2 needs to displace in situ saline water efficiently.Injection of CO 2 is carried out in the form of a supercritical fluid as a result of high in situ fluid pressure and temperature.This is advantageous in terms of injectivity because supercritical CO 2 (referred to as scCO 2 in this paper) is less viscous than liquid CO 2 and denser than CO 2 vapor.However, CO 2 injection pressures, which must be greater than in situ pore pressures, can cause adverse effects in the reservoir, 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 CO 2 in water aquifers or to the atmosphere [4].Thus, one of the main technical issues in CO 2 geological sequestration is the prediction of the flow, transport and prolonged stability of CO 2 in deep saline formations.Development of field monitoring techniques for CO 2 migration is also essential for the safe and reliable operations of CO 2 sequestration.Field monitoring is crucial to determine injected CO 2 movement, volumes and locations in the sequestration reservoir.Direct monitoring techniques use observation wells and tracers to observe CO 2 migration in reservoirs.However, drilling observation 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 electric resistivity surveys can be used for economical, largescale field underground fluid monitoring.Time-lapsed seismic survey mapping can provide spatial distribution of seismic wave velocity which can be correlated with CO 2 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 sandstone cores changes with the relative volumes of water/ CO 2 in the pore space.The change in acoustic velocity is a result of the change in the bulk modulus of the pore fluid as sCO 2 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 CO 2 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 distribution of two phase fluids, particularly in terms of layering and non-uniformity in the scCO 2 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 CO 2 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 CO 2 in core samples of sandstone initially saturated with saline water.High pressure precision syringe pumps for back pressure and injection fluid pressure control, a hydraulic pump for cell pressure control, and a temperature control system allow for the injection of CO 2 at supercritical conditions.The end caps of the core holder are equipped with piezoelectric transducers to characterize ultrasonic wave velocity response of the rock core sample.

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 mechanical response and vice versa, and fluid flow field cannot be analysed separately from the mechanical response except under simple boundary conditions.(Notes: a) tensorial notation is used and repeated indices imply summation; b) a dot over a symbol indicates differentiation with respect to time; and c) all stresses are total).Biot's theory couples the poroelastic stress-strain relation for fluid-saturated porous materials: with the poroelastic fluid diffusion equation that quantifies fluid pressure changes in the same material (assuming single phase fluid flow and isotropic permeability): = strain rate tensor, = pore pressure rate, k  permeability,  = 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: 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.
(i.e., no fluid sink or source).Substituting these two conditions in Equation ( 2) and solving for gives: 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: where 3 3 = mean stress rate, and stress rate tensor.The validity of uncoupling the deviatoric and volumetric elastic response of fluid saturated porous media is investigated experimentally below.Substituting Equation (4) in Equation (5) yields: Dividing throughout by v  yields the undrained bulk modulus of a fluid-saturated porous rock 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 K u .

Laboratory Testing Equipment
The effects of injection of scCO 2 in the seismic velocity of porous rock were studied using a newly developed test system which consists of a high-pressure and high temperature (HPHT) triaxial cell.Figure 1 shows a schematic diagram of the testing system.The triaxial core holder has a maximum working confining pressure capacity of 70 MPa, two precision syringe pumps that control the back pressure and injection pressure, a domeloaded 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 homogenize the fluid flow.Two movable pistons controlled by hydraulic pressure are able to induce axial stress different from the confining stress.One of the syringe pumps transmits a mixture of saline water and scCO 2 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 syringes and the PID temperature controllers.The pressure and volume change of fluids in the syringe pumps are monitored and acquired in a personal computer communicating with the pumps.The back-pressure regulator is equipped with a polyimide film diaphragm providing accurate regulation of outlet pressures.Saline water produced from the end face of rock core sample during scCO 2 injection is accumulated in a vessel placed on an accurate electronic balance.The mass data of saline water accumulated is acquired by using a computer via serial communication.The complete testing system is enclosed within a constant temperature air-circulating cabinet 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.

Test Material and Procedures
caps in two individual orthogonal directions.In the center of the cap is a compressional wave transducer.
The study of the effects of scCO 2 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 sedimentary rocks.Cylindrical rock samples used for the experimental 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 scCO 2 .Saline water used is a mixture of distilled water and sodium 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 × 10 9 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 oscilloscope.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 scCO 2 injection tests is described below.A core sample dried at T = 383 K is placed inside the core holder then saturated with distilled 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 pressure P pore 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 P pore = 10 MPa and a temperature of T = 313 K to ensure that the injected CO 2 is kept in supercritical condition.Distilled water filling the pore space is displaced with saline water saturated with scCO 2 at P pore = 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 CO 2 saturated with saline water is injected into core sample at a constant rate at the prescribed conditions.The injection rates q inj of scCO 2 during the relative permeability characterization and ultrasonic wave velocity measurement are 2.0 and 0.20 cm 3 /min, respectively.The pressure values used in the paper are gage pressures.

Test Results and Discussions
Figure 3 shows the injection pressure and saline water production behavior observed during CO 2 injection at a rate of 0.2 cm 3 /min.The injection pressure is maintained at 10.00 ± 0.05 MPa through displacement.The production behavior of saline water indicates that CO 2 reaches a maximum saturation of 0.25 at the end point of displacement.
Figure 4 shows some of the waveforms of P-wave acquired during the CO 2 injection.The values in the figures indicate the average CO 2 saturation of the core sample 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 significantly from 36.0 to 36.6 ms and subsequently to 37.2 ms as the CO 2 saturation increased from 0 to 0.151 and to 0.214.
The shear waveforms acquired during CO 2 injection are shown in Figure 5.The arrival times are 64.4,64.4, and 64.0 ms corresponding to the average CO 2 saturation values of 0.0, 0.137 and 0.228, respectively.The dependency of shear wave velocity on scCO 2 saturation seems to be very different to that of the P-wave, i.e., the S-wave velocity increases slightly with increasing the CO 2 saturation, and is almost insensitive to the scCO 2 saturation.
The CO 2 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 where V p and V s 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   CO 2 is calculated from where ρ dry , 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 displacement of saline water by scCO 2 .The pore fluid bulk modulus, and correspondingly the rock undrained bulk modulus u  , and ρ sln are the bulk densities of the dry rock, CO 2 , and saline water, and  is the porosity of the rock sample.In Figure 7 and Equation ( 10 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 scCO 2 saturation from 0 to 0.25.This confirms the assumption used in Equation ( 5) to uncouple the elastic volumetric and deviatoric responses in a poroelastic medium.
To calculate the undrained bulk modulus u K in Equation (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 scCO 2 , the serial law is given as: and Wood's parallel law as: where 2

CO
is the bulk modulus of scCO 2 and sln K is the bulk modulus of saline water.The serial law is applicable to the case where the two immiscible fluids are segregated perpendicular to the wave propagation direction (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 (Figure 6 7), with f K determined from either Equation (10) or Equation (1), and as: G As can be seen, p V S decreases from 3.86 km/s to approximately 3.65 km/s as  10) and (11)) are also shown in the figure.The pressure and temperature fluid bulk modulus values for scCO 2 were obtained from [13], and [5].The Biot-Gassmann equation in combination with serial law (Equation (10)) predicts rapid decrease of V S relationship has changed along the curve given by the Gassmann-Wood equation.This change can be understood by considering the following displacement process.The injected CO 2 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 CO 2 .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 shifting to a layered distribution.This is reasonable because the injected CO 2 can concentrate in the upper part of the horizontally oriented core sample due to buoyancy effect and consequently the saline water and CO 2 phases flow in two distinct layers.After that, the observed 2 CO p relationship gradually moved toward that predicted by the Gassmann-Wood equation.This transition is understandable by considering a process in which the layered fluid distribution is changing gradually to a homogeneous 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 CO 2 , and CO 2 occupies most of the pore space.It can be seen that the observed V p 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 Biot-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.
V S 

Conclusion
Ultrasonic wave velocity changes due to CO 2 saturation change were measured using Berea sandstone core sample which was initially saturated with saline water and was subjected to constant CO 2 injection rate.The results showed the effects of pore fluid distribution in determining the effects of multiphase pore fluids on the seismic velocity of porous rocks.Increasing CO 2 saturation affected the P-wave velocity which was observed to decrease whereas the S-wave velocity was almost constant during the CO 2 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 CO 2 and saline water provided the distribution of the two fluids in the sandstone 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 dependent P-wave velocity of sandstone.The observed relationship between P-wave velocity and CO 2 saturation transitioned from the relation given by the Biot-Gassman-Wood model in the initial injection phase, to the Biot-Gassmann-parallel law model, then back to the Biot-Gassmann-Wood model towards the end of the displacement process.This should correspond to the transition of spatial distribution of saline water and CO 2 in core sample as the displacement of saline water proceeded.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.

p
Under undrained conditions, two conditions are achieved: 1)  (i.e., no fluid gradients or Darcy fluid flow), and 2)

Figure 2 Figure 1 .
Figure 1.Schematic diagram of the testing system.Porous metal filters

Figure 2 .
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.

2 CONFigure 3 .
Figure 3. Injection pressure and production behavior during CO 2 injection at 0.2 cm 3 /min into Berea sandstone core sample presaturated with saline water.

Figure 4 .
Figure 4. Compression waveform change depending on CO 2 saturation observed during CO 2 injection into Berea sandstone core sample presaturated wit saline water.

Figure 5 .
Figure 5. Change of shear waveforms during CO 2 injection at 0.2 cm 3 /min into Berea sandstone core sample presaturated with saline water.

2 CO
), 2 CO is the scCO 2 saturation which is defined as the volume of supercritical CO 2 in the voids divided by the volume of K , decreased with increasing 2 CO because the scCO 2 bulk modulus is lower than saline bulk modulus.Note that most of the change in the bulk modulus occurred for .This is because the irreducible S

V
is calculated and predicted from u K (Equation
the Biot-Gassmann equation in combination with the bulk modulus values from the serial and parallel distributions (Equations (

Figure 8
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 scCO 2 saturation than experimental data.The results shown in Figure8indicate that the twophase 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 V -ray CT (Computed Tomography) imaging of scCO 2 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-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 CO 2 phase becomes predominant at lower CO 2 saturations.The value of n determined by fitting the resulting p V vs 2 CO curve to the experimental data is 4.19 with R 2 -value of 0.85.The data-fitted 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.should correspond to the transitions of the fluid distributions in the core sample.At the very early stage of displacement