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

Transcription

1 International Journal o Geosciences, 01, 3, Published Online October 01 ( Eects o CO Injection on the Seismic Velocity o Sandstone Saturated with Saline Water Marte Gutierrez, Daisuke atsuki, Abdulhadi Almrabat Civil and Environmental Engineering Colorado School o Mines, St. Golden, USA mgutierr@mines.edu Received August 16, 01; accepted September 15, 01; accepted October 14, 01 ABSTRACT Geological sequestration (GS) o carbon dioxide (CO ) is considered as one o the most promising technologies to reduce the amount o anthropogenic CO emission in the atmosphere. To ensure success o CO GS, monitoring is essential on ascertaining movement, volumes and locations o injected CO in the sequestration reservoir. One technique is to use time-lapsed seismic survey mapping to provide spatial distribution o seismic wave velocity as an indicator o CO migration and volumes in a storage reservoir with time. To examine the use o time-lapsed seismic survey mapping as a monitoring tool or CO sequestration, this paper presents mathematical and experimental studies o the eects o supercritical CO injection on the seismic velocity o sandstone initially saturated with saline water. The mathematical model is based on poroelasticity theory, particularly the application o the Biot-Gassmann substitution theory in the modeling o the acoustic velocity o porous rocks containing two-phase immiscible pore luids. The experimental study uses a high pressure and high temperature triaxial cell to clariy the seismic response o a sample o Berea sandstone to supercritical CO injection under deep saline aquier conditions. Measured ultrasonic wave velocity changes during CO injection in the sandstone sample show the eects o pore luid distribution in the seismic velocity o porous rocks. CO injection was shown to decrease the P-wave velocity with increasing CO saturation whereas the S-wave velocity was almost constant. The results conirm that the Biot-Gassmann theory can be used to model the changes in the acoustic P-wave velocity o sandstone containing dierent mixtures o supercritical CO and saline water provided the distribution o the two luids in the sandstone pore space is accounted or in the calculation o the pore luid bulk modulus. The empirical relation o Brie et al. or the bulk modulus o mixtures o two-phase immiscible luids, in combination with the Biot-Gassmann theory, was ound to satisactorily represent the pore-luid dependent acoustic P-wave velocity o sandstone. eywords: Biot-Gassmann Theory; CO Geological Sequestration; Poroelasticity; Porous Rocks; Two-Phase Fluid Flow; Seismic Velocity 1. Introduction There has been increasing evidence that anthropogenic release o carbon dioxide (CO ) in the atmosphere has been one o the main causes o changes in global weather patterns. One major solution to reduce the urther release o CO in the atmosphere rom human activities is geological sequestration (GS) whereby carbon dioxide (CO ) is injected and permanently stored in underground geological ormations. The estimated volume o potential sequestration reservoirs is abundant [1,]. Depleted oil and gas reservoirs and abandoned mines are important candidates or CO storage. Deep saline aquiers are also very promising because o their huge estimated capacities and high connectivity o pore spaces [3]. CO injected in geological ormations is trapped due to dierent mechanisms, including stratigraphic and structural trapping, residual CO trapping, solubility trapping, and mineral trapping [1]. A large part o injected CO is initially trapped due to the structural and stratigraphic trapping mechanisms. The volume ratio o CO 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 ormation gets mineralized by geochemical interactions between CO and the host rock. To be economically easible, CO needs to displace in situ saline water eiciently. Injection o CO is carried out in the orm o a supercritical luid as a result o high in situ luid pressure and temperature. This is advantageous in terms o injectivity because supercritical CO (reerred to as scco in this paper) is less viscous than liquid CO and denser than CO vapor. However, CO injection pressures, which must be greater than in situ pore pressures, can cause adverse eects in the reservoir, Copyright 01 SciRes.

2 M. GUTIERREZ ET AL. 909 such as induced seismic activity, deterioration o the capping and sealing properties o the cap rock layers, opening o ractures, and shear ailure o aults resulting in leakage o CO in water aquiers or to the atmosphere [4]. Thus, one o the main technical issues in CO geological sequestration is the prediction o the low, transport and prolonged stability o CO in deep saline ormations. Development o ield monitoring techniques or CO migration is also essential or the sae and reliable operations o CO sequestration. Field monitoring is crucial to determine injected CO movement, volumes and locations in the sequestration reservoir. Direct monitoring techniques use observation wells and tracers to observe CO migration in reservoirs. However, drilling observation wells is expensive, time consuming, provides only limited data which may not ully represent in situ conditions, and has the risk o deteriorating the sealing capacity o the cap rock [1]. Indirect geophysical methods such as seismic and electric resistivity surveys can be used or economical, largescale ield underground luid monitoring. Time-lapsed seismic survey mapping can provide spatial distribution o seismic wave velocity which can be correlated with CO migration and volumes in a storage reservoir with time. The acoustic velocity response o rock media illed with luids is primarily a unction o rock mass elasticity, porosity, and pore luid bulk modulus. These components, related to acoustic velocity, are aected by temperature, rock mass eective stresses, luid pressure, and pore luid composition (saturation). Previous studies [5,6] have shown that the acoustic velocity response o sandstone cores changes with the relative volumes o water/ CO in the pore space. The change in acoustic velocity is a result o the change in the bulk modulus o the pore luid as sco displaces saline water during the injection process. However, the evaluation o the bulk modulus o mixture o multiphase luid is still a challenge. A major reason is that the bulk modulus o a luid mixture should also depend on the degree o uniormity o the luid mixture in the rock pore space [7,8]. This paper presents mathematical and experimental investigations o the eects o supercritical CO injection on the seismic velocity o sandstone initially saturated with saline water. The mathematical model is based on application o the Biot-Gassmann poroelasticity theory [9,10] in the modelling o the acoustic velocity o porous rocks containing two-phase immiscible pore luids. The ocus o the mathematical modelling is on how the Biot- Gassmann theory can be modiied to account or the distribution o two phase luids, particularly in terms o layering and non-uniormity in the scco displacement ront, in addition to their relative volumes, in the pore space o sandstone. The experimental study uses a laboratory testing system to clariy the acoustic response o rocks to supercritical CO injection under deep saline aquier conditions. The main component o the system is a high pressure and high temperature (HPHT) triaxial cell that allows or injection o CO in core samples o sandstone initially saturated with saline water. High pressure precision syringe pumps or back pressure and injection luid pressure control, a hydraulic pump or cell pressure control, and a temperature control system allow or the injection o CO at supercritical conditions. The end caps o the core holder are equipped with piezoelectric transducers to characterize ultrasonic wave velocity response o the rock core sample.. Biot-Gassmann Theory Gassman s substitution theory [10] is the most widely used equation to describe the eects o the bulk modulus o the pore luid on the seismic velocity o deormable porous media. The original derivation o 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 irst derived by [9], provide a rigorous mathematical treatment o luid low in deormable porous media, where luid low aects mechanical response and vice versa, and luid low ield cannot be analysed separately rom 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 dierentiation with respect to time; and c) all stresses are total). Biot s theory couples the poroelastic stress-strain relation or luid-saturated porous materials: Ge p (1) ij v ij ij ij with the poroelastic luid diusion equation that quantiies luid pressure changes in the same material (assuming single phase luid low and isotropic permeability): k p v p q () s In the above equations xi, ij = stress rate tensor, v kk ijij = volumetric strain rate tensor, e ij ij ij v 3 = deviatoric strain rate tensor, ij = strain rate tensor, p = pore pressure rate, k permeability, = luid viscosity, q = luid source or sink, and G = elastic bulk and shear moduli o the porous medium, respectively, ij = ronecker delta, and s = bulk moduli o the pore luid and the solid grains o the porous medium, respectively, = porosity, and = Biot s poroelastic constant deined as: 1 (3) s Copyright 01 SciRes.

3 910 M. GUTIERREZ ET AL. In Equation (), single phase luid low and isotropic permeability were assumed. As will be shown below, permeability disappears in the derivation o the Biot- Gassmann equation. For this reason and by deining the pore pressure p as the average luid pressure, the Biot- Gassman equation that will be derived below based on the Equations (1) and () can also be used or two phase luid low. Note that Equation (1) diers rom conventional elasticity in that poroelastic deormation o the solid grains due to pore pressure changes is included in the total deormation o the porous medium. Equation () also diers rom conventional luid diusion equation in that it accounts or poroelastic deormation in the luid low in the porous medium. Under undrained conditions, two conditions are achieved: 1) kp 0 (i.e., no luid gradients or Darcy luid low), and ) q 0 (i.e., no luid sink or source). Substituting these two conditions in Equation () and solving or p gives: v p (4) s Since the shear modulus G is independent o pore luid composition and is the same or both drained and undrained conditions [11], Equation (1) can be split into deviatoric and volumetric components: s Ge and m v p (5) ij ij where m kk 3 ijij 3 = mean stress rate, and sij ij ij m = deviatoric stress rate tensor. The validity o uncoupling the deviatoric and volumetric elastic response o luid saturated porous media is investigated experimentally below. Substituting Equation (4) in Equation (5) yields: v m v (6) s Dividing throughout by v yields the undrained bulk modulus o a luid-saturated porous rock u m v as: u (7) s Equation (7) was irst derived by [10], however, as shown above this equation can also be derived rom 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 o luid-saturated porous material as unction o the drained or dry bulk modulus o the same material, the porosity, Biot s poroelastic constant, and bulk moduli o the pore luid and the solid grains o the porous medium. The dierent parameters in Equation (7) are all constants or a rock specimen under the same eective stress and porosity except or the pore luid bulk modulus which can change with luid composition. It is important to note that the second term o the right-hand side o Equation (7) represents the eect o pore luid content on the undrained bulk modulus u. 3. Laboratory Testing Equipment The eects o injection o scco in the seismic velocity o porous rock were studied using a newly developed test system which consists o a high-pressure and high temperature (HPHT) triaxial cell. Figure 1 shows a schematic diagram o the testing system. The triaxial core holder has a maximum working conining pressure capacity o 70 MPa, two precision syringe pumps that control the back pressure and injection pressure, a domeloaded back pressure regulator, a hydraulic pump or regulating cell pressure, and a dierential pressure transducer. The sample is enclosed in a Viton sleeve. Both ends o the core sample are in contact with high permeability porous metal ilter discs in order to homogenize the luid low. Two movable pistons controlled by hydraulic pressure are able to induce axial stress dierent rom the conining stress. One o the syringe pumps transmits a mixture o saline water and scco into the rock core sample at very accurate low rates. Another syringe pump acts as the back-pressure regulator with set-point pressure. The temperatures o luids stored in the syringe pumps are regulated by using silicon rubber blanket heaters wrapped around the side walls o the syringes and the PID temperature controllers. The pressure and volume change o luids 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 ilm diaphragm providing accurate regulation o outlet pressures. Saline water produced rom the end ace o rock core sample during scco injection is accumulated in a vessel placed on an accurate electronic balance. The mass data o 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-o inrared heater and air-circulating ans. The end caps o the core holder are equipped with piezoelectric transducers or seismic compressional and shear wave velocity measurements. Figure shows a schematic o the arrangement o piezoelectric transducers. Triads o shear wave transducers shake one o the end Copyright 01 SciRes.

4 M. GUTIERREZ ET AL. 911 Figure 1. Schematic diagram o the testing system. PZT (P) Cap Porous metal ilters PZT (SH) PZT (SV) SV SH Viton sleeve Rock core sample Figure. Arrangement and polarization o piezoelectric transducers or seismic wave velocity measurement. Arrows indicate the direction o oscillation o two dierent shear waves (horizontal SH and vertical SV ), and P denotes compression wave. caps in two individual orthogonal directions. In the center o the cap is a compressional wave transducer. The natural requencies o the transducers range rom 0.5 to 1 MHz. The transducers are excited by using a square wave pulser/receiver capable o providing square pulses whose voltages are selectable between 100 and 400 V in increments o 100 V. The typical rise time o pulse is less than s. The maximum bandwidth and typical noise level o receiver are rom 1 khz to 35 MHz and 70 μv peak to peak, respectively. The seismic waveorms are converted into digital signals by using a digital oscilloscope having 100 MHz o bandwidth and s 1 o real time sample rate. The minimum time base and the vertical resolution o oscilloscope are 10 9 s/div and 8 bits. The waveorm data are acquired by using a personal computer communicating with the oscilloscope. Each waveorm acquired is the average o 16 waveorms. The resultant minimum time interval o waveorm acquisition in the personal computer is 6 s. 4. Test Material and Procedures The study o the eects o scco injection in the seismic velocity o 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 o the rock mechanical and luid low behavior o sedimentary rocks. Cylindrical rock samples used or the experimental works are cored rom a block o Berea sandstone. Both ends o the core samples are grinded to ensure that sample ends are parallel within required tolerances. The petrophysical properties o the Berea sandstone used in the tests are summarized in Table 1. Carbon dioxide having % o purity is used to prepare the scco. Saline water used is a mixture o distilled water and sodium chloride at 3.4% o salinity. The procedure or the scco injection tests is described below. A core sample dried at T = 383 is placed inside the core holder then saturated with distilled Copyright 01 SciRes.

5 91 M. GUTIERREZ ET AL. Table 1. Petrophysical properties o Berea sanstone. Dry bulk density (g/cm 3) Porosity Permeability (md) water under vacuum by allowing the sample to imbibe distilled water. The conining axial and lateral stresses are isotropically increased up to 1 MPa. The pore pressure P pore is simultaneously raised to 10 MPa by keeping the eective stress less than MPa. The core sample is consolidated at desired eective stress at a pore pressure o P pore = 10 MPa and a temperature o T = 313 to ensure that the injected CO is kept in supercritical condition. Distilled water illing the pore space is displaced with saline water saturated with scco at P pore = 10 MPa and T = 313. The total volume o saline water injected is more than ten times o the pore volume o core sample. Supercritical CO saturated with saline water is injected into core sample at a constant rate at the prescribed conditions. The injection rates q inj o scco during the relative permeability characterization and ultrasonic wave velocity measurement are.0 and 0.0 cm 3 /min, respectively. 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 CO injection at a rate o 0. cm 3 /min. The injection pressure is maintained at ± 0.05 MPa through displacement. The production behavior o saline water indicates that CO reaches a maximum saturation o 0.5 at the end point o displacement. Figure 4 shows some o the waveorms o P-wave acquired during the CO injection. The values in the igures indicate the average CO saturation o the core sample when a P-wave velocity is measured. The arrival time o each wave has been determined at the irst negative rise in the waveorm. The arrival time changed signiicantly rom 36.0 to 36.6 ms and subsequently to 37. ms as the CO saturation increased rom 0 to and to The shear waveorms acquired during CO injection are shown in Figure 5. The arrival times are 64.4, 64.4, and 64.0 ms corresponding to the average CO saturation values o 0.0, and 0.8, respectively. The dependency o shear wave velocity on scco saturation seems to be very dierent to that o the P-wave, i.e., the S-wave velocity increases slightly with increasing the CO saturation, and is almost insensitive to the scco saturation. The CO saturation dependency o the bulk and shear moduli o Berea sandstone is summarized in Figure 6. The bulk and shear moduli, and G were calculated rom 4 Vp V s (8) 3 G V (9) s where V p and V s are the compressional and shear wave velocities, and ρ is the density o porous medium. The bulk density o porous rock illed with saline water and N CO Figure 3. Injection pressure and production behavior during CO injection at 0. cm 3 /min into Berea sandstone core sample presaturated with saline water. Copyright 01 SciRes.

6 M. GUTIERREZ ET AL. 913 Figure 4. Compression waveorm change depending on CO saturation observed during CO injection into Berea sandstone core sample presaturated wit saline water. Figure 5. Change o shear waveorms during CO injection at 0. cm 3 /min into Berea sandstone core sample presaturated with saline water. CO is calculated rom SCO dry SCO CO 1 sln (10) where ρ dry, CO, and ρ sln are the bulk densities o the dry rock, CO, and saline water, and is the porosity o the rock sample. In Figure 7 and Equation (10), S is CO the scco saturation which is deined as the volume o supercritical CO in the voids divided by the volume o the voids. As can be seen in Figure 7, the bulk modulus decreased rom 17.5 GPa to 13.3 GPa during the displacement o saline water by scco. The pore luid bulk modulus, and correspondingly the rock undrained bulk modulus u, decreased with increasing S because CO the scco bulk modulus is lower than saline bulk modulus. Note that most o the change in the bulk modulus occurred or SCO 0.5. This is because the irreducible Copyright 01 SciRes.

7 914 M. GUTIERREZ ET AL. saline water saturation or 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 saturation rom 0 to 0.5. This conirms 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 in Equation (7), it is necessary to determine the pore luid bulk modulus. Two widely used equations to calculate the bulk modulus o mixtures o two phase immiscible luids are: 1) the serial law; and ) the Wood s (1941) parallel law [1]. For a mixture o saline water and scco, the serial law is given as: S CO CO CO 1 S (11) sln and Wood s parallel law as: 1 SCO 1 S CO CO where is the bulk modulus o scco CO and sln is the bulk modulus o saline water. The serial law is applicable to the case where the two immiscible luids are segregated perpendicular to the wave propagation direction (Figure 6(a)), and the parallel law is applicable to the case where the two immiscible luids are segregated parallel to the wave propagation direction (Figure 6(b)). The dependency o Vp on SCO o the tested Berea sandstone is shown in Figure 8. The S -dependent CO V p is calculated and predicted rom u (Equation 7), with determined rom either Equation (10) or Equation (1), and G as: sln (1) (a) Fluid 1 Fluid Fluid 1 Fluid Fluid 1 Fluid (b) Fluid 1 Fluid Figure 6. Illustration o (a) Serial and (b) Parallel distributions o two-phase luids in respect to longitudinal direction. S CO Figure 7. CO saturation dependencies o bulk and shear moduli o Berea sandstone core sample. Copyright 01 SciRes.

8 M. GUTIERREZ ET AL. 915 Figure 8. CO content dependency o compressional wave velocity during CO injection into Berea sandstone presaturated with saline water. S CO 1 4 V u G p 3 (13) As can be seen, Vp decreases rom 3.86 km/s to approximately 3.65 km/s as SCO increases rom 0 to 0.5. The V p vs SCO relationships calculated rom the Biot-Gassmann equation in combination with the bulk modulus values rom the serial and parallel distributions (Equations (10) and (11)) are also shown in the igure. The pressure and temperature luid bulk modulus values or scco were obtained rom [13], and [5]. The Biot- Gassmann equation in combination with serial law (Equation (10)) predicts rapid decrease o V p with values much lower than experimental data, while the Biot- Gassmann equation in combination with parallel law (Equation (11)) predicts a slower decrease in V p with increasing scco saturation than experimental data. The results shown in Figure 8 indicate that the twophase luids are potentially distributed neither in parallel nor serial ashion in the test specimen, although these distributions correspond to the lower and upper bound values, respectively, o the Vp vs SCO relationship in sandstone. X-ray CT (Computed Tomography) imaging o scco injection in Berea sandstone shows that the pore luid distribution is more complicated than the ideal parallel or serial distributions and is dependent on the pore structure and the relative mobilities o the two luids (Shi et al., 011). A much improved empirical equation to estimate the luid bulk modulus o mixtures two-phase luids and account or their mixing is the equation proposed by [7]: S S n 1 n sln sln sln CO (14) where Ssln 1 SCO = saline water saturation and n = empirical parameter. Note than n = 1 corresponds to the serial luid distribution. As the value o n increases, the eect o the lower bulk modulus o CO phase becomes predominant at lower CO saturations. The value o n determined by itting the resulting V p vs S curve CO to the experimental data is 4.19 with R -value o The data-itted Vp vs SCO 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 o the combined Biot-Gasmann and Brie equations. The change in the Vp S CO relationship shown in Figure 8 should correspond to the transitions o the luid distributions in the core sample. At the very early stage o displacement ( SCO 0.0 ), the observed V p S CO relationship has changed along the curve given by the Gassmann-Wood equation. This change can be understood by considering the ollowing displacement process. The injected CO phase is likely to concentrate in the inlet end o core sample at this stage. The rest o pore space should not be invaded by CO. The luids are thereore close to the series distribution to which the Wood s law is applicable. When SCO is increased rom 0.0 to 0.15, the Vp S CO relationship observed has moved close to that given by the Gassmann-parallel law model. This transition means that the luid distribution is Copyright 01 SciRes.

9 916 M. GUTIERREZ ET AL. shiting to a layered distribution. This is reasonable because the injected CO can concentrate in the upper part o the horizontally oriented core sample due to buoyancy eect and consequently the saline water and CO phases low in two distinct layers. Ater that, the observed Vp SCO relationship gradually moved toward that predicted by the Gassmann-Wood equation. This transition is understandable by considering a process in which the layered luid distribution is changing gradually to a homogeneous one as the luid displacement proceeds. More speciically, the volume o the saline water occupying the outlet end o the core sample has now been gradually displaced by CO, and CO occupies most o 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 o displacement. This suggests that the luid distribution still has some heterogeneity at the end point o displacement. On the average, the Biot-Gassmann-Brie et al. equation with an exponent o 4.19 provides a very good representation o the pore luid dependent P-wave velocity o Berea sandstone. 6. Conclusion Ultrasonic wave velocity changes due to CO saturation change were measured using Berea sandstone core sample which was initially saturated with saline water and was subjected to constant CO injection rate. The results showed the eects o pore luid distribution in determining the eects o multiphase pore luids on the seismic velocity o porous rocks. Increasing CO saturation aected the P-wave velocity which was observed to decrease whereas the S-wave velocity was almost constant during the CO injection. The results conirm that the Biot-Gassmann theory can be used to model the changes in the acoustic P-wave velocity o sandstone containing dierent mixtures o supercritical CO and saline water provided the distribution o the two luids in the sandstone pore space is accounted or in the calculation o the pore luid bulk modulus. Two-phase luids distributed parallel and in series in the voids relative to the wave propagation direction correspond to the lower and upper bound values, respectively, o the luid saturation dependent P-wave velocity o sandstone. The observed relationship between P-wave velocity and CO saturation transitioned rom 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 o the displacement process. This should correspond to the transition o spatial distribution o saline water and CO in core sample as the displacement o saline water proceeded. The empirical relation o Brie et al. [7] or the bulk modulus o mixtures o two-phase immiscible luids, in combination with the Biot-Gassmann theory, was ound to satisactorily represent the pore-luid dependent acoustic P-wave velocity o sandstone. 7. Acknowledgements Financial support provided by the Department o Energy under Grant No. DE-FE is grateully acknowledged. The author thanks Dr. Mike Batzle and Mr. Weiping Wang on their advice and help on the ultrasonic velocity testing, and Mr. Brian Asbury or his technical support in coring o the rock samples. REFERENCES [1] IPCC Intergovernmental Panel on Climate Change, Special Report on Carbon Dioxide Capture and Storage, Chapter 5, 005. [] S. M. Benson and D. R. Cole, CO Sequestration in Deep Sedimentary Formations, Elements, Vol. 4, No. 5, 008, pp doi:10.113/gselements [3] S. Bachu, Screening and Ranking o Sedimentary Basins or Sequestration o CO in Geological Media in Response to Climate Change, Environmental Geology, Vol. 44, No. 3, 003, pp doi: /s [4] J. Sminchak, N. Gupta, C. Byrer and P. Bergman, Issues Related to Seismic Activity Induced by the Injection o CO in Deep Saline Aquiers, Journal o Energy and Environmental Research, Vol., 00, pp [5] J.. im, J. Xue and T. Matsuoka, Experimental Study on CO Monitoring and Saturation with Combined P-Wave Velocity and Resistivity, SPE Journal, 010, pp. SPE doi:10.118/13084-ms [6] J. Q. Shi, Z. Q. Xue and S. Durucan, Seismic Monitoring and Modelling o Supercritical CO Injection into a Water-Saturated Sandstone: Interpretation o P-Wave Velocity Data, International Journal o Greenhouse Gas Control, Vol. 1, No. 4, 007, pp doi: /s (07) [7] A. Brie, F. Pampuri, A. F. Marsala and O. Meazza, Shear Sonic Interpretation in Gas-Bearing Sands, Proceedings o SPE Annual Technical Conerence and Exhibition, Dallas, -5 October 1995, p doi:10.118/30595-ms [8] A. L. Endres and R. night, The Eects o Pore-Scale Fluid Distribution on the Physical-Properties o Partially Saturated Tight Sandstones, Journal o Applied Physics, Vol. 69, No., 1991, pp doi: / [9] M. Biot, General Theory o Three-Dimensional Consolidation, Journal o Applied Physics, Vol. 1, 1941, pp doi: / [10] F. Gassmann, Über die Elastizität Poröser Medien, Viertel Naturorsch Ges Zürich, Vol. 96, 1951, pp [11] J. G. Berryman, Origin o Gassmann s Equations, Geophysics, Vol. 64, 1999, pp Copyright 01 SciRes.

10 M. GUTIERREZ ET AL. 917 doi: / [1] A. B. Wood, A Textbook o Sound, Bell and Sons LTD., London, [13] M. Batzle and Z. J. Wang, Seismic Properties o Pore luids, Geophysics, Vol. 57, No. 11, 199, pp doi: / Copyright 01 SciRes.