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Abstract: Induced seismicity is one of the main risks for gigaton-scale geological storage of carbon dioxide (CO2). Thus, passive seismic monitoring is often recommended as a necessary component of the monitoring systems for CO2 storage projects, with a particular forcus on risk mitigation. We present the first field study, CO2CRC Otway Project Stage 3 (Victoria, Australia), where distributed acoustic sensing (DAS) enabled high-precision tracking of the induced seismicity triggered by a small CO2 injection and also informed the reservoir models. In 610 days of passive seismic monitoring of the Stage 3 injection, we detected 17 microseismic events (maximum moment magnitude Mw 0.1) using five deep boreholes equipped with enhanced-sensitivity optical fiber. The DAS array has sensitivity sufficient for detection and location of induced events with Mw∼−2 in a monitoring borehole located up to 1500 m away. Thanks to the dense spatial sampling by the DAS, we were able to estimate the focal mechanisms for events with Mw>−1.5; although the monitoring boreholes provided very limited angular coverage. The main cluster of the events has the same location and source mechanism as the one triggered by the previous CO2 injection at the Otway Project site, Stage 2C. Surprizingly, the Stage 2C and Stage 3 events closely followed the actual movement of the CO2 saturation plume front (not the pressure front), as observed using controlled-source reflection seismic images. The nature of the plume-fault interaction remains unclear, but some alteration of the fault gouge by CO2 might be responsible for the faults’ reactivation by the pressure perturbation. Importantly, the seismogenic fault could not be identified in the seismic images and was only revealed by DAS observations, which also demonstrated the signature of fluid–rock interaction, that may control the CO2 flow.

A permanent automated continuous seismic CO2 geosequestration monitoring system for was installed at CO2CRC Otway Project site (Victoria, Australia) in early 2020. The system is composed of five deviated ∼1600 m deep wells equipped with distributed acoustic sensing (DAS) acting as seismic receivers and nine seismic orbital vibrators (SOV) as seismic sources. DAS recording is performed continuously by three iDASv3 units. Each SOV operates for 2.5 h at a time, and hence all SOVs operating sequentially (during daytime only) produce in a single vintage every two days. Each vintage consists of 45 offset VSP transects covering predicted CO2 plume migration paths over ∼0.7 km2 area. An automated data processing implemented on-site reduces data size from ∼1.3 TB/day to ∼500 MB/day with the results transmitted to the office daily. The repeatability analysis based on pre-injection data (acquired from May to October 2020 before the injection start in December 2020) shows that variability of SOV performance is the main source of non-repeatability while borehole measurements are stable. An SOV waveform could reach NRMS value from 20 to 100 % within a few days. However, deconvolution of the seismograms with the waveform of the direct wave reduces the repeatability to within 10–15 % NRMS.

CO2 sequestration projects benefit from quantitative assessment of saturation distribution and plume extent for field development and leakage prevention. In this work, we carry out quantitative analysis of time-lapse seismic by using rock physics and seismic modelling tools. We investigate the suitability of Gassmann's equation for a CO2 sequestration project with 1600 tons of CO2 injected into high-porosity, brine-saturated sandstone. We analyze the observed time delays and amplitude changes in a time-lapse vertical seismic profile dataset. Both reflected and transmitted waves are analyzed qualitatively and quantitatively. To interpret the changes obtained from the vertical seismic profile, we perform a 2.5D elastic, finite-difference modelling study. The results show a P-wave velocity reduction of 750 m/s in the proximity of the injection well evident by the first arrivals (travel-time delays and amplitude change) and reflected wave amplitude changes. These results do not match with our rock physics model using Gassmann's equation predictions even when taking uncertainty in CO2 saturation and grain properties into account. We find that time-lapse vertical seismic profile data integrated with other information (e.g., core and well log) can be used to constrain the velocity–saturation relation and verify the applicability of theoretical models such as Gassmann's equation with considerable certainty. The study shows that possible nonelastic factors are in play after CO2 injection (e.g., CO2–brine–rock interaction and pressure effect) as Gassmann's equation underestimated the velocity reduction in comparison with field data for all three sets of time-lapse vertical seismic profile attributes. Our work shows the importance of data integration to validate the applicability of theoretical models such as Gassmann's equation for quantitative analysis of time-lapse seismic data.

Elastic properties of sandstones can be highly pressure dependent. However, the pressure‐induced deformation of intact sandstones in X‐ray micro‐Computed Tomography (micro‐CT) images are below the resolving power of conventional image analysis methods. Also, most digital rock physics studies of the elastic properties operate with micro‐CT images acquired at ambient pressure. Here, we perform a comprehensive analysis of an intact sandstone sample with pronounced stress‐sensitivity. A purpose‐built X‐ray‐transparent pressure cell enables scanning micro‐CT images at confining pressures of up to 36 MPa. To detect the small pressure‐induced changes from these images, we design an overall deformation detection workflow with slice‐searching technique. We apply this workflow to a set of micro‐CT images of a 2 × 2 × 2 mm sample scanned at several pressures with a voxel size length of ∼1 μm. The results give the static modulus of 2.78 GPa, which is ∼0.5 times of the dynamic modulus derived from ultrasonic measurements. This ratio is consistent with literature data, showing the accuracy of the deformation detection workflow. Images scanned at different pressures are then segmented into two‐phase labels. The porosity change detected from segmented labels is consistent with the value derived from static modulus using poroelastic theory. The two‐phase segmented images are utilized to simulate the elastic properties with a finite element method. Most of the pressure dependency of elastic moduli shown in ultrasonic measurements is caused by closure of compliant pores at grain contacts, which cannot be resolved by the micro‐CT. The accuracy improvement of the estimated elastic properties from images scanned at higher pressures is negligible. Plain Language Summary: X‐ray micro‐Computed Tomography (micro‐CT) technique is the main tool for imaging three‐dimensional rock microstructure. Often, researchers attempt to substitute the real laboratory measurements on rock samples ‐ time‐consuming and expensive ‐ by numerical simulations of diverse physical processes in these images. However, such an approach ignores the effect of stress on the rock properties, because micro‐CT images are usually scanned at ambient pressures. This study estimates the stress‐induced changes on the images of a porous sandstone. To this end, we acquired a set of images of a sandstone sample at different confining pressures with a purpose‐built X‐ray‐transparent pressure cell and accompanied the images with a comprehensive laboratory data set. Standard algorithms for time‐lapse analysis of rock images failed at our data set, because the deformations are at the limit of the algorithms' sensitivity, hence, we designed a novel deformation detection workflow. The subsequent numerical elastic simulations using these images, ultrasonic measurements and petrophysical experiments suggest that the main stress effects are concentrated in thin intergranular contact that may not be resolved directly by the modern CT‐machines. Hence, the effect of stress should be estimated using indirectly from the analysis of multiphysics measurements and the images of sandstones may be taken at ambient pressure. Key Points: Micro‐Computed Tomography (micro‐CT) images of a sandstone are scanned in a X‐ray transparent pressure cell at confining pressures of up to 36 MPaAn overall deformation detection workflow is designed to track the sandstone deformation from micro‐CT imagesThe differences of the computed moduli based on scans at different pressures are demonstrated [ABSTRACT FROM AUTHOR]

Laboratory experiments of ultrasonic velocities of fluid‐saturated rocks are often much higher than the predictions of the Gassmann theory. This difference is usually attributed to the velocity dispersion caused by fluid pressure relaxation between pores of different shapes and orientation. This paper proposes a simple model to characterize pressure and frequency effects on the elastic moduli of fluid‐saturated rocks in a broad frequency range. The proposed model incorporates micromechanics of wave‐induced fluid pressure relaxation at grain contacts (between crack‐like contacts and stiff pores) into pressure dependency of elastic moduli. Previously, the pressure dependency of the velocities or elastic moduli was ascribed to the progressive closure of cracks with the increasing effective pressure and expressed as an integral of crack compliance over the range of aspect ratios. For isolated cracks, this compliance is a function of crack geometry only. For cracks hydraulically connected to stiff pores, this crack compliance can be replaced by a frequency‐dependent solution of the micromechanical problem of fluid pressure relaxation between a single crack and surrounding pores. The resulting equation expresses the bulk and shear moduli of the fluid‐saturated rock as functions of both pressure and frequency. Furthermore, if pressure‐dependent moduli of both dry and fluid‐saturated moduli are known, the aspect ratio distribution can be obtained from the pressure dependency of the dry moduli, and then the saturated moduli can be computed with no adjustable parameters. The model predictions show reasonable agreement with laboratory data measured using ultrasonic and forced oscillation techniques. Key Points: A micromechanical model of wave‐induced fluid pressure relaxation is incorporated into pressure dependency of elastic moduli of porous rocksThe resulting equation expresses elastic wave dispersion and attenuation in porous rock as functions of effective pressureThe model predictions show reasonable agreement with laboratory data measured using ultrasonic and forced oscillation techniques [ABSTRACT FROM AUTHOR]

Time-lapse (4D) seismic monitoring of injected CO 2 in geological formations is being increasingly employed as the principal method for ensuring containment of the CO 2 and testing conformance of predicted plume behaviour. However, to bring further confidence in this method, the CO 2 volume detection limit in the seismic monitoring and key factors controlling it need to be quantitatively understood. The CO2CRC Otway Project attempts to improve this understanding by exploring the capability of seismic reflection method to detect and monitor a 15,000 t injection of supercritical CO 2 /CH 4 mixture in a saline aquifer at a depth of 1500 m. To increase the signal to noise ratio and to reduce the disruption to land users, seismic acquisition is performed using a buried geophone array. Seismic acquisition occurred at injection intervals of 5000, 10,000 and 15,000 t over a 5-month period. The seismic images clearly show the distribution and evolution of the stored CO 2 /CH 4 plume. The analysis confirms that signal from pure CO 2 would be of similar magnitude to the signal from CO 2 /CH 4 mixture. The results demonstrate the potential of time-lapse reflection seismic to provide key information to both operators and regulators for confirming the security and behaviour of stored CO 2 at very small volumes. [ABSTRACT FROM AUTHOR]

Time-lapse ultrasonic measurements constitute a tool to establish and calibrate rock physics models for surface seismic monitoring of partially saturated rocks. This workflow requires one to take into account seismic dispersion caused by frequency-dependent wave-induced fluid flow. We develop a theory of squirt flow in rocks saturated with a viscoelastic material containing isolated gas patches between compliant intergranular contacts. This model is valid for the entire frequency range, from seismic to ultrasonic. In the limit of full saturation the derived equations reduce to the Gassmann equations in the low-frequency regime and traditional squirt theory in the high-frequency regime. The model prediction of ultrasonic velocities versus saturation matches with experimental observations. [ABSTRACT FROM AUTHOR]

ABSTRACT Estimating the impact of solid pore fill on effective elastic properties of rocks is important for a number of applications such as seismic monitoring of production of heavy oil or gas hydrates. We develop a simple model relating effective seismic properties of a rock saturated with a liquid, solid, or viscoelastic pore fill, which is assumed to be much softer than the constituent minerals. A key feature of the model is division of porosity into stiff matrix pores and compliant crack-like pores because the presence of a solid material in thin voids stiffens the rock to a much greater extent than its presence in stiff pores. We approximate a typical compliant pore as a plane circular interlayer surrounded by empty pores. The effect of saturation of the stiff pores is then taken into account using generalized Gassmann's equations. The proposed model provides a good fit to measurements of the shear stiffness and loss factor of the Uvalde heavy-oil rock at different temperatures and frequencies. When the pore fill is solid, the predictions of the scheme are close to the predictions of the solid squirt model recently proposed by Saxena and Mavko. At the same time, the present scheme also gives a continuous transition to the classic Gassmann's equations for a liquid pore fill at low frequencies and the squirt theory at high frequencies. [ABSTRACT FROM AUTHOR]

ABSTRACT CO2 sequestration projects benefit from quantitative assessment of saturation distribution and plume extent for field development and leakage prevention. In this work, we carry out quantitative analysis of time-lapse seismic by using rock physics and seismic modelling tools. We investigate the suitability of Gassmann's equation for a CO2 sequestration project with 1600 tons of CO2 injected into high-porosity, brine-saturated sandstone. We analyze the observed time delays and amplitude changes in a time-lapse vertical seismic profile dataset. Both reflected and transmitted waves are analyzed qualitatively and quantitatively. To interpret the changes obtained from the vertical seismic profile, we perform a 2.5D elastic, finite-difference modelling study. The results show a P-wave velocity reduction of 750 m/s in the proximity of the injection well evident by the first arrivals (travel-time delays and amplitude change) and reflected wave amplitude changes. These results do not match with our rock physics model using Gassmann's equation predictions even when taking uncertainty in CO2 saturation and grain properties into account. We find that time-lapse vertical seismic profile data integrated with other information (e.g., core and well log) can be used to constrain the velocity-saturation relation and verify the applicability of theoretical models such as Gassmann's equation with considerable certainty. The study shows that possible nonelastic factors are in play after CO2 injection (e.g., CO2-brine-rock interaction and pressure effect) as Gassmann's equation underestimated the velocity reduction in comparison with field data for all three sets of time-lapse vertical seismic profile attributes. Our work shows the importance of data integration to validate the applicability of theoretical models such as Gassmann's equation for quantitative analysis of time-lapse seismic data. [ABSTRACT FROM AUTHOR]

ABSTRACT A significant portion of the world's hydrocarbon reserves are found in carbonate reservoirs, yet analysis of the petrophysical properties of these reservoirs is associated with a number of challenges. Some of these challenges stem from physical and chemical interactions between the carbonate rock matrix and pore fluids, which can affect elastic properties of the rock. Hence, the study of the pore fluid effects on the elastic properties of carbonates is important for understanding a change of the field performance properties of а carbonate reservoir caused by fluid movements during hydrocarbon extraction in producing fields. In this laboratory study, we investigate the applicability of Gassmann's model for predictions of the elastic moduli of water- and hydrocarbon-saturated Savonnières limestone and the influence of partial water saturation on elastic and anelastic properties of the rock. We present the results of two sets of laboratory experiments on the Savonnières oolitic limestone where we: (i) evaluate the effect of full water and n-decane saturation on elastic moduli and attenuation at seismic (0.1 Hz-120 Hz) and ultrasonic (0.5 MHz) frequencies; and (ii) quantify the dependence of elastic moduli and extensional attenuation on water saturation at two seismic frequencies of 1 Hz and 10 Hz. We demonstrate that the change in the bulk modulus of limestone fully saturated either with n-decane or water is in agreement with Gassmann's fluid substitution theory, whereas the shear modulus is noticeably reduced. The measurements with partial saturation show that the bulk modulus decreases with increasing water saturation to a lesser extent than the Young's and shear moduli. Our results show that extensional attenuation in the samples with closed boundaries is insignificant under dry and fully saturated conditions but is influenced greatly by the liquid content when saturation is between 0 and 20% or 95% and 100%. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the effects of supercritical CO2 (scCO2) injection on the elastic and anelastic properties of sandstone at seismic and ultrasonic frequencies. We present the results of the low-frequency and ultrasonic experiments conducted on water-saturated sandstone (Donnybrook, Western Australia) flooded with scCO2. The sandstone was cut in the direction perpendicular to a formation bedding plane and tested in a Hoek triaxial pressure cell. During the experiments with scCO2, the low-frequency and ultrasonic systems and the pump dispensing scCO2 were held at a temperature of 42°C. The elastic parameters obtained for the sandstone with scCO2 at seismic (0.1 Hz-100 Hz) and ultrasonic (~0.5 MHz) frequencies are very close to those for the dry rock. The extensional attenuation was also measured at seismic frequencies for the dry, water-saturated, and scCO2-injected sandstones. The applicability of Gassmann's fluid substitution theory to obtained results was also tested during the experiments. [ABSTRACT FROM AUTHOR]

Modeling dispersion and attenuation of elastic waves in fluid-saturated rocks due to squirt flow requires the knowledge of a number of geometrical parameters of the pore space, in particular, the characteristic aspect ratio of the pores. These parameters are usually interred by fitting measurements on saturated rocks to model predictions. To eliminate such fitting and thus make the model more predictive, we propose to recover the geometrical parameters of the pore space from the pressure dependency of elastic moduli on dry samples. Our analysis showed that the pressure dependency of elastic properties of rocks (and their deviation from Gassmann's prediction) at ultrasonic frequencies is controlled by the squirt flow between equant, stiff, and so-called intermediate pores (with aspect ratios between 10-3-2 X 10-1) Such intermediate porosity is expected to close at confining pressures of between 200 and 2000 MPa, and thus cannot be directly obtained from ultrasonic experiments performed at pressures below 50 MPa. However, the presence of this intermediate porosity is inferred from the significant linear trend in the pressure dependency of elastic properties of the dry rock and the difference between the bulk modulus of the dry rock computed for spherical pores and the measured modulus at 50 MPa. Moreover, we can infer the magnitude of the intermediate porosity and its characteristic aspect ratio. Substituting these parameters into the squirt model, we have computed elastic moduli and velocities of the water-satnrated rock and compared these predictions against laboratory measmements of these velocities. The agreement is good for a number of clean sandstones, but not unexpectedly worse for a broad range of shaley sandstones. Our predictions showed that dispersion and attenuation caused by the squirt flow between compliant and stiff pores may occur in the seismic frequency band. Confirmation of this prediction requires laboratory measurements of elastic properties at these frequencies. [ABSTRACT FROM AUTHOR]

Exponential increase of seismic velocities with effective stress has usually been explained by presence of pores with a broad distribution of aspect ratios. More recently, a stress-related closure of soft pores with a narrow distribution of compliances (e.g. grain contacts) has been suggested to be sufficient to explain such exponential stress dependency. This theoretical interpretation has been verified here using laboratory measurements on dry sandstones. On the basis of these experimental data, linear dependency of elastic compressibility on soft porosity and exponential decay of soft porosity and elastic compressibility with effective stress up to 60 MPa is confirmed. Soft porosity, estimated from the fitting coefficients of elastic compressibilities, is on the same order of magnitude but slightly lower than obtained from strain measurements. The results confirm applicability of the previously proposed stress sensitivity model and provide justification for using this approach to model stress dependency of elastic properties. [ABSTRACT FROM AUTHOR]

Heavy oils have high densities and extremely high viscosities, and they exhibit viscoelastic behavior. Traditional rock physics based on Gassmann theory does not apply to materials saturated with viscoelastic fluids. We use an effective-medium approach known as coherent potential approximation (CPA) as an alternative fluid-substitution scheme for rocks saturated with viscoelastic fluids. Such rocks are modeled as solids with elliptical fluid inclusions when fluid concentration is small and as suspensions of solid particles in the fluid when the solid concentration is small. This approach is consistent with concepts of percolation and critical porosity, and it allows one to model sandstones and unconsolidated sands. We model the viscoelastic properties of a heavy-oil-saturated rock sample using CPA and a measured frequency-dependent complex shear modulus of the heavy oil. Comparison of modeled results with measured properties of the heavy-oil rock reveals a large discrepancy over a range of frequencies and temperatures. We modify the CPA scheme to account for the effect of binary pole structure by introducing a compliant porosity term. This dramatically improves the predictions. The predicted values of the effective shear modulus of the rock are in good agreement with laboratory data for the range of frequencies and temperatures. This confirms that our scheme realistically estimates the frequency- and temperature-dependent properties of heavy-oil rocks and can be used as an approximate fluid-substitution approach for rocks saturated with viscoelastic fluids. [ABSTRACT FROM AUTHOR]

We develop a new model for elastic properties of rocks saturated with heavy oil. The heavy oil is represented by a viscoelastic material, which at low frequencies and/or high temperatures behaves as a Newtonian fluid, and at high frequencies and/or low temperatures as a nearly elastic solid. The bulk and shear moduli of a porous rock saturated with such viscoelastic material are then computed using approximate extended Gassmann equations of Ciz and Shapiro by replacing the elastic moduli of the pore filling material with complex and frequency-dependent moduli of the viscoelastic pore fill. We test the proposed model by comparing its predictions with numerical simulations based on a direct finite-difference solution of equations of dynamic viscoelasticity. The simulations are performed for the reflection coefficient from an interface between a homogeneous fluid and a porous medium. The numerical tests are performed both for an idealized porous medium consisting of alternating solid and viscoelastic layers, and for a more realistic 3-D geometry of the pore space. Both sets of numerical tests show a good agreement between the predictions of the proposed viscoelastic workflow and numerical simulations for relatively high viscosities where viscoelastic effects are important. The results confirm that application of extended Gassmann equations in conjunction with the complex and frequency-dependent moduli of viscoelastic pore filling material, such as heavy oil, provides a good approximation for the elastic moduli of rocks saturated with such material. By construction, this approximation is exactly consistent with the classical Gassmann's equation for sufficiently low frequencies or high temperature when heavy oil behaves like a fluid. For higher frequencies and/or lower temperatures, the predictions are in good agreement with the direct numerical solution of equations of dynamic viscoelasticity on the microscale. This demonstrates that the proposed methodology provides realistic estimates of elastic properties of heavy oil rocks. [ABSTRACT FROM AUTHOR]

Digital rock methodology combines modern microscopic imaging with advanced numerical simulations of the physical properties of rocks. Modeling of elastic-wave propagation directly from rock microstructure is integral to this technology. We survey recent development of the rotated staggered grid (RSG) finite-difference (FD) method for pore-scale simulation of elastic wave propagation in digital rock samples, including the dynamic elastic properties of rocks saturated with a viscous fluid. Examination of the accuracy of this algorithm on models with known analytical solutions provide an additional accuracy condition for numerical modeling on the microscale. We use both the elastic and viscoelastic versions of the RSG algorithm to study gas hydrates and to simulate propagation of Biot's slow wave. We apply RSG methodology to examine the effect of gas hydrate distributions in the pore space of a rock. We compare resulting P-wave velocities with experimentally measured data, as a basis for building an effective-medium model for rocks containing gas hydrates. We then perform numerical simulations of Biot's slow wave in a realistic 3D digital rock model, fully saturated with a nonviscous fluid (corresponding to the high-frequency limit of poroelasticity), and placed inside a bulk fluid. The model clearly demonstrates Biot's slow curve when the interface is open between the slab and bulk fluid. We demonstrate slow wave propagation in a porous medium saturated with a viscous fluid by analyzing an idealized 2D porous medium represented alternating solid and viscous fluid layers. Comparison of simulation results with the exact solution for this layered system shows good agreement over a broad frequency range. [ABSTRACT FROM AUTHOR]

Fractures in a porous rock can be modelled as very thin and highly porous layers in a porous background. First, a dispersion equation for a P wave propagating in periodically layered poroelastic medium is obtained using propagator matrix approach applied to Biot equations of poroelasticity with periodic coefficients. Then in the limit of low stiffness and thickness this dispersion equation yields an expression for the effective P-wave modulus of the fractured porous material. When both pores and fractures are dry, this material is equivalent to a transversely isotropic elastic porous material with linear–slip interfaces. When saturated with a liquid this material exhibits significant attenuation and velocity dispersion due to wave-induced fluid flow between pores and fractures. In the low-frequency limit the material properties are equal to those obtained by anisotropic Gassmann (or Brown–Korringa) theory applied to a porous material with linear-slip interfaces. At low frequencies inverse quality factor scales with the first power of frequency ω. At high frequencies the effective elastic properties are equal to those for isolated fluid-filled fractures in a solid (non-porous) background, and inverse quality factor scales with . The magnitude of both attenuation and dispersion strongly depends on both the degree of fracturing and background porosity of the medium. The characteristic frequency of the attenuation and dispersion depends on the background permeability, fluid viscosity, as well as fracture density and spacing. [ABSTRACT FROM AUTHOR]

Spatial heterogeneity of hydrocarbon reservoirs causes significant attenuation and dispersion of seismic waves due to wave-induced flow of the pore fluid between more compliant and less compliant areas. This paper investigates the interaction between a plane elastic wave in a poroelastic medium with a spherical inhomogeneity of another porous material. The behaviour of both the inclusion and the background medium is described by the low-frequency variant of Biot's equations of poroelasticity with the standard boundary conditions at the inclusion surface, and for the inclusion size much smaller than the wavelength of the fast compressional wave. The scattering problem is formulated as a series expansion of displacements expressed in the spherical harmonics. The resulting scattered wavefield consists of the scattered normal compressional and shear waves and Biot's slow wave, which attenuates rapidly with distance from the inclusion and represents the main difference from the elastic case. This study concentrates on the attenuation effects caused by the mode conversion into Biot's slow wave. The solution obtained for Biot's slow wave is well described by the two terms of orderandof the scattering series. The scattering amplitude for the term of orderis given by a simple expression. The full expression for the term of orderis very complicated, but can be simplified assuming that the amplitude of the scattered fast (normal) compressional and shear waves are well approximated by the solution of the equivalent elastic problem. This assumption yields a simple approximation for the amplitude of the scattered slow wave, which is accurate for a wide range of material properties and is sufficient for the analysis of the scattering amplitude as a function of frequency.In the low-frequency limit the scattering amplitude of the slow wave scales withω3/2, and reduces to the asymptotic long-wavelength solution of, which is valid for inclusions much smaller than the wavelength of Biot' slow wave. For inclusions larger than the wavelength of Biot's slow wave, the scattering amplitude is proportional toω1/2, which is consistent with the results of, which were derived by the Born approximation and therefore were limited to a weak contrast between the inclusion and the background medium. Our general solution, however, does not require these assumptions on frequency and material properties. The obtained results can be used in the analysis of the effective properties, attenuation and dispersion of elastic waves in randomly inhomogeneous porous materials. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the effects of supercritical CO2 (scCO2) injection on the elastic and anelastic properties of sandstone at seismic and ultrasonic frequencies. We present the results of the low-frequency and ultrasonic experiments conducted on water-saturated sandstone (Donnybrook, Western Australia) flooded with scCO2. The sandstone was cut in the direction perpendicular to a formation bedding plane and tested in a Hoek triaxial pressure cell. During the experiments with scCO2, the low-frequency and ultrasonic systems and the pump dispensing scCO2 were held at a temperature of 42°C. The elastic parameters obtained for the sandstone with scCO2 at seismic (0.1 Hz-100 Hz) and ultrasonic (~0.5 MHz) frequencies are very close to those for the dry rock. The extensional attenuation was also measured at seismic frequencies for the dry, water-saturated, and scCO2-injected sandstones. The applicability of Gassmann's fluid substitution theory to obtained results was also tested during the experiments. [ABSTRACT FROM AUTHOR]