Squirt Flow Research Articles

Utilization of wave attenuation in the time-lapse sonic logging at the Nagaoka site for a near well monitoring of CO2 migration

This paper discusses the seismic wave attenuation observed by time-lapse sonic logging at the Nagaoka CO2 injection site, in consideration of the many geological on-site experimental results asserting the occurrence of amplitude attenuation, as well as reduction of P-wave velocity, by CO2 invasion. The amplitude attenuation of seismic wave can be caused by a variety of physical phenomena and that the seismic data is obtained in a noisy environment, where acquisition of reliable amplitude data is technically challenging. In this paper we analyzed time-lapse sonic logging data at the Nagaoka site for evaluating the amplitude attenuation by CO2 invasion. We re-examined the semblance analysis conducted in the site using more robust methods and evaluated data quality by utilizing the obtained coherency as the quality of the waveform data. Then, we examined the P-wave amplitude from the envelope in time and spectrum domain. Although the amplitude at each logging was erroneous, averaging several logging runs revealed the amplitude attenuation. Moreover from the spectrum of P-wave, the peak frequency changed depending on the degree of CO2 saturation. We also examined the relationships that exist among the CO2 saturation, velocity reduction, and amplitude attenuation at the Nagaoka site. These relationships exhibited a dependency pattern similar to the model expected from a squirt flow. As a whole, we confirm the amplitude attenuation in the time-lapse sonic logging data, indicating that P-wave attenuation is applicable for a reliable evaluation of CO2 saturation, and for the early detection of CO2 leakage along the well.

Modeling wave propagation in cracked porous media with penny-shaped inclusions

Understanding acoustic wave dispersion and attenuation induced by local (squirt) fluid flow between pores and cracks (compliant pores) is fundamental for better characterization of the porous rocks. To describe this phenomenon, some squirt-flow models have been developed based on the conservation of the fluid mass in the fluid mechanics. By assuming that the cracks are represented by isotropically distributed (i.e., randomly oriented) penny-shaped inclusions, this study applies the periodically oscillating squirt flow through inclusions based on the Biot-Rayleigh theory, so that the local squirt flow and global wave oscillation of rock are analyzed in the same theoretical framework of Hamilton’s principle. The governing wave-propagation equations are derived by incorporating all of the crack characteristics (such as the crack radius, crack density, and aspect ratio). In comparison with the previous squirt models, our model predicts the similar characteristics of wave velocity dispersion and attenuation, and our results are in agreement with Gassmann equations at the low-frequency limit. In addition, we find that the fluid viscosity and crack radius only affect the relaxation frequency of the squirt-flow attenuation peak, whereas the crack density and aspect ratio also affect the magnitudes of dispersion and attenuation. The application of this study to experimental data demonstrates that when the differential pressure (the difference between confining pressure and pore pressure) increases, the closure of cracks can lead to a decrease of attenuation. The results confirm that our model can be used to analyze and interpret the observed wave dispersion and attenuation of real rocks.

Viscoelastic substitute models for seismic attenuation caused by squirt flow and fracture leak off

We have investigated viscoelastic substitute models for seismic attenuation caused by fluid pressure diffusion in fluid-saturated porous media. Fluid pressure diffusion may locally occur associated with fracture leak off and/or squirt flow. We use a homogenization scheme with numerical model reduction (NMR), recently established in the literature, and we derive the corresponding viscoelastic material properties that are apparent at a larger scale (i.e., the observer scale). Moreover, we find that the rheology of the resulting viscoelastic model is of the Maxwell-Zener type. Based on a series of numerical experiments, we find that this method is able to accurately and efficiently predict the overall attenuation and stiffness moduli dispersion for a range of scenarios without resolving the substructure problem explicitly. Computational homogenization, together with NMR, can be useful to simulate seismic wave propagation using a viscoelastic substitute model that accurately reproduces the energy dissipation and dispersion of a heterogeneous medium in which squirt flow and/or fracture leak-off occurs.

A multiple relaxation interpretation of the extended Biot model.

The biphasic extended Biot poroviscoelastic model takes into account the squirt flow in grain-grain contacts and introduces the bulk and shear relaxation modes associated with it. This model has been criticized for its empirical approach, but here the constitutive equations and the time domain wave equations of the model are derived. This also makes it possible to find single phase viscoelastic equivalents for all three wave solutions of the extended Biot model. Particularly, the viscoelastic equivalents for shear wave propagation can be obtained with considerably fewer parameters than the original model. These equivalents are linear viscoelastic models with springs and dampers for the low frequencies and contain half-order spring-pots for high frequencies. For high frequencies, the non-physicality of the shear relaxation mode is highlighted. The relaxation modes of the extended Biot model are interpreted in the framework of multiple relaxation mechanisms showing that the P- and S-wave modes of the model are not much more complex than that for seawater. The model's near linear frequency dependent attenuation in the intermediate frequency range is the result of weighting each relaxation mechanism appropriately.

Reflection dispersion signatures due to wave-induced pressure diffusion in heterogeneous poroelastic media

ABSTRACTWe have studied the reflection dispersion signatures of a heterogeneously patchy saturated reservoir exhibiting attenuation and velocity dispersion in a seismic range of frequency. A modified patchy saturation model is employed to predict velocity dispersion and intrinsic attenuation behaviour associated with wave-induced pressure diffusion due to the presence of both mesoscopic and microscopic heterogeneities. Understanding the combined effects of microscopic squirt flow and wave-induced fluid flow related to mesoscopic heterogeneities on wave attenuation and associated dispersion would be important for determining the relative contribution of both of the interdependent energy loss mechanisms. The acoustic properties from the modified patchy saturation model were then employed in combination with an approximate expression for the frequency-dependent normal-incidence reflection coefficient of a dispersive reservoir rock, to give insights into the impacts of attenuation (and its associated velocity dispersion) and acoustic impedance contrast on the reflection dispersion characteristics. Analysis of the results indicates that the dispersion attribute of reflection coefficients and the associated cross-plot are more sensitive to fluid saturation and porosity than the magnitude of the reflection coefficient, and hence provide a promising approach to characterise fluid saturation and porosity in heterogeneous hydrocarbon reservoirs.

Ultrasonic wave attenuation dependence on saturation in tight oil siltstones

Ultrasonic P-wave attenuation was measured in tight oil siltstones, carbonates and a tight sandstone with two independent estimation methods. The dependence on saturation in gas-water partially-saturated siltstones at in-situ conditions shows a different behavior compared to the other rocks. The siltstones in our experiments exhibit a behavior characterized by a gradual decrease of attenuation with increasing water saturation in the presence of gas, and full-gas saturation shows more attenuation than full-oil and full-water saturations. However, previous theoretical and experimental studies show that gas-water saturated carbonates and sandstones have the highest attenuation at high water saturations, and generally, a liquid-saturated rock shows more attenuation than a gas-saturated one. Poroelasticity theory shows that the two dominant loss mechanisms (due to fabric heterogeneity and patchy saturation) have peaks at different frequencies for siltstones, resulting in a gradual decrease of attenuation with water saturation, while these mechanisms overlap at ultrasonic frequencies for carbonates and sandstones, leading to an attenuation peak at high water saturations. The predicted attenuation dependence on fluid type agrees with the measurement for most samples. Regarding the tight oil siltstones, although the model fails to explain the experimental results for oil-water saturation, it can be concluded that for gas-water saturation the squirt flow caused by fabric heterogeneity dominates the attenuation, which differs from carbonates and sandstones. Experimental studies show that the attenuation dependence on saturation in tight oil reservoirs can be associated with fabric texture. The theory describes these behaviors, which can potentially improve the practices of detecting and monitoring multi-phase fluids in the reservoirs.

Linear and half order fractional viscoelastic equivalents of the extended Biot model

The extended Biot poro-viscoelastic model [Chotiros and Isakson, JASA (2014)] like the standard Biot poroelastic model is biphasic and predicts two compressional waves (fast and slow) and one shear wave. Taking squirt flow into account, the model introduces two additional relaxation modes apart from the Biot crossover relaxation mode (global flow). The frequency dependent relaxation processes and a high number of independent parameters make the finite element implementation and the inversion of parameters for reconstruction a challenge. To overcome this challenge, we identify single phase viscoelastic equivalents for all three wave solutions of the extended Biot model from its dispersion relations. Considering squirt flow and high-frequency turbulent flow, the fast compressional wave and the shear wave solutions at low frequencies are equivalent to a non-standard solid model with eight parameters (four springs and four dashpots) and six parameters (Three springs and three dashpots), respectively. At high frequencies, the Kelvin-Voigt model used for tangential contact stiffness (shear relaxation) leads to non-physical equivalents. Neglecting this shear relaxation mode, the fast compressional wave and the shear wave solutions at high frequencies are equivalent to a fractional half-order solid model of order three and two, respectively. Alternative models for tangential contact stiffness are discussed.

Power law attenuation modeled as multiple relaxation

Wave equations with non-integer order derivatives may model power law behavior in medical and sediment acoustics. As experiments only support a finite bandwidth, there is a limit to how much physical insight that can be gained from such models. Other ways to model a power law are with a fractional heat law, hierarchical ladder models for polymer chains, and the non-Newtonian rheology of grain shearing. Multiple relaxation processes may be motivated by a hierarchy of substructures at different scales. It is also inherent in soft glassy materials, such as cells, with disordering and metastability. Even the Biot model with contact squirt flow and shear drag (BICSQS) may be interpreted as a multiple relaxation model. A weighted sum of relaxation processes will approximate a power law over a limited band, and an even distribution of relaxation frequencies on a logarithmic frequency axis, and with equal relaxation strengths, will give a power law attenuation with unit power, y = 1. This can be generalized to other power laws if the contribution from each relaxation process varies in proportion to the relaxation frequency to the power of y - 1. This scale-invariant distribution may hint at some fractal medium properties.

Scattering and intrinsic attenuation as a potential tool for studying of a fractured reservoir

Intrinsic attenuation is mainly caused by the frictional movement induced by seismic waves during their passage between fluids contained in subsurface pores and solid grains. In contrast, scattering attenuation is due to small reflections caused by subsurface heterogeneities. Since porosity and fractures are important sources of heterogeneity and fluids, scattering and intrinsic attenuation are suitable seismic attributes for investigating porous and fractured subsurface zones, such as oil and gas reservoirs. In the present study, we accurately estimated scattering and intrinsic attenuation from zero-offset vertical seismic profiling (VSP) and sonic data acquired from three wells that cross a reservoir zone of an oilfield located in Abu Dhabi in the United Arab Emirates. In addition, we properly separated scattering and intrinsic attenuation. The attenuation profiles show high variation with depth. Furthermore, the scattering is frequency dependent and has a significant contribution to the total attenuation. This is due to the high heterogeneous property of carbonate rocks, which dominate the lithology of the reservoir zone. This means that the variation of attenuation can be used as an indicator of the heterogeneity degree of reservoir zone. The VSP and sonic intrinsic attenuations exhibit high anomalies in oil-rich zones, and the ratio of the compressional sonic attenuation to the shear attenuation exhibits a high anomaly in gas-rich zones, but not in oil-rich zones, because the presence of oil influences the compressional and shears attenuations in a similar fashion. However, the presence of gas attenuates compressional waves much more than the shear waves. Therefore, can be used to distinguish oil- and gas-rich zones. The highly fractured reservoir units display negative VSP intrinsic attenuation anomalies and strong scattering, which reveals a strong interference phenomenon. This phenomenon leads to an increase in amplitude of the downgoing wave versus depth, which results in negative attenuation. Hence, strong negative intrinsic attenuation accompanied by strong scattering can be an indicator of a highly fractured zone. The VSP and sonic intrinsic attenuations in such zones have a large discrepancy, which might be due to the squirt flow mechanism due to the inter-crack fluid flow due to the compressional stress induced by seismic waves on the fractures. This mechanism attenuates the waves propagating at low frequencies less, because the fluid pressure has sufficient time to reach equilibrium, which is not the case at high frequencies. This explains why the VSP intrinsic attenuation is much smaller than the sonic attenuation in highly fractured zones. As such, a large discrepancy between VSP and sonic intrinsic attenuations also indicates a highly fractured reservoir.

Forced oscillation measurements of seismic wave attenuation and stiffness moduli dispersion in glycerine‐saturated Berea sandstone

ABSTRACTFluid pressure diffusion occurring on the microscopic scale is believed to be a significant source of intrinsic attenuation of mechanical waves propagating through fully saturated porous rocks. The so‐called squirt flow arises from compressibility heterogeneities in the microstructure of the rocks. To study squirt flow experimentally at seismic frequencies the forced oscillation method is the most adequate, but such studies are still scarce. Here we present the results of forced hydrostatic and axial oscillation experiments on dry and glycerine‐saturated Berea sandstone, from which we determine the dynamic stiffness moduli and attenuation at micro‐seismic and seismic frequencies (0.004–30 Hz). We observe frequency‐dependent attenuation and the associated moduli dispersion in response to the drained–undrained transition (∼0.1 Hz) and squirt flow (>3 Hz), which are in fairly good agreement with the results of the corresponding analytical solutions. The comparison with very similar experiments performed also on Berea sandstone in addition shows that squirt flow can potentially be a source of wave attenuation across a wide range of frequencies because of its sensitivity to small variations in the rock microstructure, especially in the aspect ratio of micro‐cracks or grain contacts.

A triple porosity scheme for fluid/solid substitution: theory and experiment

ABSTRACTQuantifying the effects of pore‐filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid‐octadecane‐saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so‐called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects.

Modeling the Effect of Microscopic and Mesoscopic Heterogeneities on Frequency-Dependent Attenuation and Seismic Signatures

At seismic and sonic frequencies, the major cause of wave attenuation and dispersion in fluid-saturated rocks might be the wave-induced fluid flow on microscopic and mesoscopic scales. However, it is challenging to assess these effects as the attenuation mechanisms related to both heterogeneities that cannot be expected to be independent. This is due to the fact that, fluid flow taking placing at the mesoscopic scale may be impacted by squirt flow mechanism in the presence of microscopic heterogeneities via modifying the dry rock to be frequency-dependent complex moduli. Understanding the integrated effects, related to microscopic squirt flow and wave-induced fluid flow of mesoscopic heterogeneities, would be important for quantifying the relative contribution of the interdependent energy loss mechanisms. We introduce a procedure in this letter to estimate the frequency-dependent seismic attenuation and dispersion by considering the combined presence of microscopic and mesoscopic heterogeneities. The corresponding seismic reflections of a finely stratified model with a dispersive reservoir are calculated using a propagator matrix method in the frequency domain to study the sensitivity of seismic signatures to pore-fluid mobility and rock heterogeneities.

Sensitivity of seismic properties to temperature variations in a geothermal reservoir

Geophysical characterization plays a key role for the definition of the deep structures of geothermal reservoirs and the consequent assessment and validation of the geothermal conceptual model. Seismic methods may provide a valuable contribution for this purpose. This involves a deep and reliable understanding of the sensitivity of seismic-wave propagation to physical and temperature variations, with complex interactions. We present the theory and sensitivity analysis based on rock's mechanical Burgers model including Arrhenius temperature equations, integrated with Gassmann model for fluid saturated porous rocks, pressure effects for bulk and shear moduli, as well as permeability and squirt flow effects. Assuming a temperature gradient model, the analysis applied at low seismic frequencies compares the interpretation of the sensitivity effects for different typical seismic elastic quantities, showing the different performance in relation to physical effects, including melting, supercritical conditions, and observability obtained in different temperature regions. With a quantification of the physical properties, the results of the study show that in deeper zones the main expected contributions in terms of variations in seismic velocity, moduli and seismic attenuation due to temperature come from melting transition, while in shallower porous fluid-saturated formations the trends are governed by pressure effects, with minor contributions of permeability and possible effects related to soft porosity. The new calculated elastic moduli are complex-valued and frequency-dependent, and temperature dependent through the fluid properties. In this complex scenario, not always the increments in the velocity and elastic wave moduli correspond to an increment in the temperature. Moreover, with mobility decreasing as a function of depth, the analysis shows that the shear quality factor is sensitive to permeability, which introduces moderate effects for velocity and attenuation of shear waves. The analysis applies to active exploration seismic and passive seismology.

A Modified Biot/Squirt Model of Sound Propagation in Water-Saturated Sedment

A modified Biot/Squirt flow model was developed. The difference between MBISQ and BISQ models is the expression for the porosity differential. Numerical analysis shows that the acoustic dispersion predicted by MBISQ is much higher than by BISQ. Investigations of the effects of permeability, viscosity, and squirt flow length on velocity and attenuation indicate that the behavior of MBISQ agrees with that of the BISQ model. The result of sediment acoustic inversion based on MBISQ was more reasonable than the result of BISQ model.

Squirt flow due to interfacial water films in hydrate bearing sediments

Abstract. Sediments containing gas hydrate dispersed in the pore space are known to show a characteristic seismic anomaly which is a high attenuation along with increasing seismic velocities. Currently, this observation cannot be fully explained albeit squirt-flow type mechanisms on the microscale have been speculated to be the cause. Recent major findings from in situ experiments, using the gas in excess and water in excess formation method, and coupled with high-resolution synchrotron-based X-ray micro-tomography, have revealed the systematic presence of thin water films between the quartz grains and the encrusting hydrate. The data obtained from these experiments underwent an image processing procedure to quantify the thicknesses and geometries of the aforementioned interfacial water films. Overall, the water films vary from sub-micrometer to a few micrometers in thickness. In addition, some of the water films interconnect through water bridges. This geometrical analysis is used to propose a new conceptual squirt flow model for hydrate bearing sediments. A series of numerical simulations is performed considering variations of the proposed model to study seismic attenuation caused by such thin water films. Our results support previous speculation that squirt flow can explain high attenuation at seismic frequencies in hydrate bearing sediments, but based on a conceptual squirt flow model which is geometrically different than those previously considered.

Integrating the Biot-Stoll model with contact squirt flow and shear drag (BICSQS) in the Biot viscosity extended framework

The viscosity extended Biot theory [Sahay, Geophysics (2008)] incorporates pore fluid viscosity in the constitutive relation of the classical Biot theory. The strain rate term due to pore fluid viscosity turns the zero velocity slow S wave mode into a diffusive process. In this framework, it is claimed that fast P and S waves bleed energy when the slow S wave is generated at an interface or at a discontinuity. On the other hand, the Biot-Stoll model with contact squirt flow and shear drag (BICSQS) [Chotiros and Isakson, JASA (2004)] models the grain to grain contact as compression and shear relaxation processes and obtains a causal poro-elastic frame response. In this work, we incorporated the grain to grain contact physics in the constitutive relation of the Biot theory and integrated it into the viscosity extended Biot framework. With realistic parameters, the fast S wave phase velocity and attenuation in the integrated model show a significant difference over a range of frequencies when compared to BICSQS. Additionally, this integrated model may provide a more accurate match for the measured reflection coefficient.

Ultrasonic P- and S-Wave Attenuation and Petrophysical Properties of Deccan Flood Basalts, India, as Revealed by Borehole Studies

Petrophysical properties and ultrasonic P- and S-wave attenuation measurements on 35 Deccan basalt core specimens, recovered from Killari borehole site in western India, provide unique reference data-sets for a lesser studied Deccan Volcanic Province. These samples represent 338-m-thick basaltic column, consisting four lava flows each of Ambenali and Poladpur Formations, belonging to Wai Subgroup of the Deccan volcanic sequence. These basalt samples are found to be iron-rich (average FeOT: 13.4 wt%), but relatively poor in silica content (average SiO2: 47.8 wt%). The saturated massive basalt cores are characterized by a mean density of 2.91 g/cm3 (range 2.80–3.01 g/cm3) and mean P- and S-wave velocities of 5.89 km/s (range 5.01–6.50 km/s) and 3.43 km/s (range 2.84–3.69 km/s), respectively. In comparison, saturated vesicular basalt cores show a wide range in density (2.40–2.79 g/cm3) as well as P-wave (3.28–4.78 km/s) and S-wave (1.70–2.95 km/s) velocities. Based on the present study, the Deccan volcanic sequence can be assigned a weighted mean density of 2.74 g/cm3 and a low Vp and Vs of 5.00 and 3.00 km/s, respectively. Such low velocities in Deccan basalts can be attributed mainly to the presence of fine-grained glassy material, high iron contents, and hydrothermally altered secondary mineral products, besides higher porosity in vesicular samples. The measured Q values in saturated massive basalt cores vary enormously (Qp: 33–1960 and Qs: 35–506), while saturated vesicular basalt samples exhibit somewhat lesser variation in Qp (6–46) as well as Qs (5–49). In general, high-porosity rocks exhibit high attenuation, but we observed the high value of attenuation in some of the massive basalt core samples also. In such cases, energy loss is mainly due to the presence of fine-grained glassy material as well as secondary alteration products like chlorophaeite, that could contribute to intrinsic attenuation. Dominance of weekly bound secondary minerals might also be responsible for the generation of microcracks, which may generate squirt flow in saturated samples. Hence, we argue that the Deccan basalts attenuate seismic energy significantly, where its composition plays a major role.

Effect of pore structure on the dispersion and attenuation of fluid-saturated tight sandstone

The pore structure of tight sandstones has significant influence on the elastic properties, and also determines the fluid-flow-related wave dispersion and attenuation mechanisms. However, in those velocity dispersion models, only the compliant pore or crack with fixed aspect ratio and concentration has been taken into account, which is not completely realistic in reservoir rock. A procedure is presented to obtain the pore aspect distribution of compliant pore (crack) from the pressure dependence of velocities. Based on the pore aspect distribution of compliant pore, the existing squirt fluid model of Gurevich is extended to consider complex pore structure of reservoir sandstones, especially when the aspect ratio has a relatively wide distribution. The extended Gurevich's squirt-flow model is consistent with Gassmann's equation at low-frequency limit, and with Mavk-Jizba model at high-frequency. To illustrate the validation of the extended Gurevich's squirt-flow model, we compare predictions of our squirt model with laboratory measurement of two water-saturated tight sandstones at ultrasonic frequency. The new model on the basis of the pore structure is more accurate in predicting the pressure dependence of compression and shear velocities for these two samples. Considering aspect ratio distribution of compliant pore in the tight sandstone samples, the new model for predicting dispersion curve shows a relatively wide squirt-flow relaxation frequency range, which even covers the typical seismic frequency and sonic logging frequency. This observation suggests that squirt flow be still important even in the seismic frequency band for tight sandstone with special pore structure.

Inversion for Biot-consistent material properties in subresonant oscillation experiments with fluid-saturated porous rock

To quantitatively interpret the results of a subresonant laboratory or numerical experiment with wet porous rock, it is insufficient to merely state the measured frequency-dependent viscoelastic moduli and [Formula: see text]-factors. The measured properties are apparent, i.e., dependent on the experimental setup such as the length of the sample and boundary conditions for pore flows. To reveal the true properties of the material, all experimental factors need to be accurately modeled and corrected for. Here, such correction is performed by developing an effective Biot’s model for the material and using it to predict driven oscillations of a cylindrical rock specimen. The model explicitly describes elastic and inertial effects, Biot’s flows, and viscous internal friction within the solid frame and pore fluid, and it approximates squirt and other wave-induced flow effects. The model predicts the dynamic permeability of the specimen, fast (traveling) and slow (diffusive) P- and axial-deformation waves, and it allows accurate modeling of any other ultrasonic or seismic-frequency experiments with the same rock. To illustrate the approach, attenuation and dispersion data from two laboratory and numerical experiments with sandstones are inverted for effective, frequency-dependent moduli of drained sandstone. Several observations from this inversion may be useful for interpreting experiments with porous rock. First, Young’s moduli measured in a short rock cylinder differ from those in a traveling wave within an infinite rod. In particular, for the modeled 8 cm long rock specimen, modulus dispersion and attenuation ([Formula: see text]) are approximately 10 times greater than for a traveling wave. Second, P-wave moduli cannot be derived from the measured Young’s and shear moduli by using conventional (visco)elastic relations. Third, because of wavelengths comparable with the size of the specimen, slow waves contribute to its quasistatic and low-frequency behaviors. Similar observations should also apply to seismic waves traveling through approximately 10 cm layering in the field.

CO2-brine flow-through on an Utsira Sand core sample: Experimental and modelling. Implications for the Sleipner storage field

Sleipner (North Sea) is the world’s first commercial-scale carbon capture and storage (CCS) project, active since 1996, with ∼17 million tonnes of CO2 stored. The main reservoir, Utsira Sand, constitutes an ideal host formation of exceptionally high porosity-permeability and large lateral extent. However, the extensive seismic time-lapse, gravity and electromagnetic monitoring surveys deployed at Sleipner have not been well-supported by laboratory measurements. Here, we investigate the geophysical and geomechanical response of an Utsira core sample for the first time, using controlled inflation/depletion cycles at variable CO2-to-brine fractional flow rates. Ultrasonic P-wave velocities and attenuations are measured together with electrical resistivity (converted into CO2-saturation), along with continuous axial and radial strain monitoring. Ultrasonic velocity and attenuation data were simultaneously inverted and results extrapolated to field-scale seismic-frequencies using a new rock physics theory, which combines patchy fluid distribution and squirt flow effects. It provides a velocity-saturation relationship of practical importance to CO2 plume monitoring. Furthermore, by combining ultrasonic and deformation data, we report empirical relations between pore pressure changes and geomechanical effects in the reservoir, for different saturation ranges. Our dataset complements and constrains existing geophysical monitoring surveys at Sleipner and, more generally, improves the understanding of shallow weakly-cemented sand reservoirs.