P-wave Velocity Dispersion Research Articles

Petrophysical properties and their influencing factors of carbonates in the fourth member of Sinian Dengying Formation, Sichuan Basin, SW China

Based on the measurements of petrological, petrophysical and elastic properties of the samples of different sedimentary facies in the fourth member of Sinian Dengying Formation (Deng 4 Member) in the Sichuan Basin, the diagenetic processes of reservoirs of different sedimentary facies and their controls on the petrophysical properties were discussed. The results show that cracks and mineral composition jointly control the petrophysical properties, and both are significantly influenced by sedimentary environment and diagenesis. The microbial dolomite of mound-shoal facies mainly experienced multi-stage dolomitization, penecontemporaneous dissolution, tectonic rupture and hydrothermal/organic acid dissolution processes, giving rise to cracks and dissolved pores. The grannular dolomite of inter-mound-shoal bottomland or dolomitic lagoon facies mainly underwent mechanical compaction, burial dolomitization and tectonic-hydrothermal action, creating cracks and intercrystalline pores. The diagenesis related to crack development increases the pressure- and saturation-dependent effects of samples, leading to significant decrease in the compressional wave impedance and Poisson’s ratio. Dolomitization changes the properties of mineral particles, resulting in a Poisson’s ratio close to dolomite. The muddy, siliceous and calcareous sediments in the low-energy environment lead to the decrease of impedance and the differential change of Poisson’s ratio (significantly increased or decreased). The samples with both cracks and dissolved pores show high P-wave velocity dispersion characteristics, and the P-wave velocity dispersion of samples with only fractures or pores is the lowest.

Effects of pressure and fluid properties on P-wave velocity and attenuation of tight sandstones

Tight reservoirs are distributed in several basins in China, with great exploration prospects and high production potential. These reservoirs have low porosity and permeability and a significant spatial heterogeneity, and this complexity requires new developments on the experimental and theoretical researches of wave propagation. To this purpose, we have conducted ultrasonic experiments on seven tight sandstones collected from the shale-oil strata as a function of the confining pressure. We obtained the P-wave velocity and attenuation by using the spectral-ratio method. The results show that attenuation decreases with pressure, and increases with porosity and permeability and that oil saturation causes more losses compared to water and gas saturations. Moreover, we observe a relaxation peak at 40% water saturation in the gas-water case. Then, we develop a tight-rock model combining three theories [Voigt-Reuss-Hill (VRH), Differential Effective Medium (DEM) and double double-porosity (DDP)], where inclusions are assumed to represent cracks or grain contacts, with different porosity and compressibility as the host. The model reasonably predicts P-wave velocity dispersion and attenuation, which increase with water saturation, and the related relaxation frequency moves to low frequencies.

Prediction of organic richness in shale gas reservoirs using a novel organic-inorganic decoupling seismic inversion method

Organic richness is associated with total hydrocarbon content and influences gas generation in shale reservoirs. The prediction of organic enrichment using seismic methods provides valuable information for identifying promising shale gas areas. Current seismic methods typically estimate organic richness using empirical relationships between organic matter (OM) content and elastic properties; these may be suitable for specific areas but cannot be generalized for universal applications. Therefore, developing a physics-based method for predicting OM content in shale gas reservoirs is critical. In this study, we proposed a novel organic-inorganic decoupling amplitude variation with offset (AVO) method by integrating the classical AVO equation with solid substitution theory. OM was considered solid pore-fillings saturated in the shale matrix. The proposed decoupling equation was extended to establish a frequency-dependent inversion framework for computing OM-related dispersion attributes, allowing for direct estimations of organic richness. Theoretical analyses suggested that the accuracy of the decoupling equation could be achieved via adjustable parameters determined using the rock physics method. Model tests demonstrated that the OM-related dispersion attributes were more sensitive to variations in OM content than the traditional P-wave velocity dispersion attribute and the commonly used elastic properties. The results of real data applications validated the superiority of our proposed OM-related dispersion attributes for reliable organic richness estimation, with the estimated results agreeing well with gas production in the study area. As a result, several promising shale gas zones were identified for further exploration. Our proposed method extends traditional fluid factors and can deal with the cases of both fluid and solid saturations in hydrocarbon resources, with widespread applications for hydrocarbon identification in various unconventional reservoirs.

Analysis of the viscoelasticity in coal based on the fractal theory

Coal is a complex viscoelastic porous medium with fractal characteristics at different scales. To model the macroscale structure of coal, a fractal viscoelastic model is established, and the P-wave velocity dispersion and attenuation characteristics are discussed based on the complex modulus derived from this model. The numerical simulation results indicate that the fractional order [Formula: see text] and relaxation time [Formula: see text] greatly affect the P-wave velocity dispersion and attenuation. The fractal viscoelastic model indicates a full-band velocity dispersion between 1 Hz and 104 Hz. Meanwhile, the P-wave velocity has a weaker dispersion with the fractal viscoelastic model than with the Kelvin-Voigt model and Zener model between 1 Hz and 104 Hz for the same relaxation time and elastic modulus, but the velocity at 1 Hz based on the fractal viscoelastic model is higher with the Kelvin-Voigt model and Zener model. Simultaneously, the velocities of five coal samples are tested, and the attenuation factor is calculated using a low-frequency system. The experimental results indicate a strong dispersion in coal in the range of 10–250 Hz. The classic Kelvin-Voigt model and Zener model cannot describe the dispersion characteristics of coal, but the fractal viscoelastic model can describe them well by using the appropriate fractional order and relaxation time.

Biot-spherical squirt (BISSQ) model for wave attenuation and dispersion

SUMMARYIt has been widely recognized that seismic attenuation and dispersion can be induced by various mechanisms. Wave induced fluid flow (WIFF) is one of the popular mechanisms to interpret seismic wave attenuation and dispersion, especially at microscopic scale. In this study, we focus on the local flow induced by different compliances of adjacent pores and develop a unified model called BISSQ (Biot-spherical squirt) model based upon the Biot and spherical squirt flow theories. The proposed model is an extension of BISQ (Biot-squirt) model. The P-wave velocity and attenuation of BISSQ model are influenced by two mechanisms: the Biot and spherical squirt-flow mechanisms. To evaluate the impact of these two mechanisms on seismic wave propagation, we use different parameters (e.g. squirt flow length, fluid viscosity, permeability, saturation and so on) to simulate wave attenuation and dispersion. We then apply the proposed model to Fox Hills Sandstone, which shows that the model can realistically predict P-wave velocity dispersion. To sum up, our proposed model offers an alternative squirt flow attenuation mechanism, which can describe fluid state of squirt flow reasonably and help us to assess the effect of different parameters on seismic wave attenuation.

Gas prediction using an improved seismic dispersion attribute inversion for tight sandstone gas reservoirs in the Ordos Basin, China

Predicting gas saturation is critical for identifying gas zones in tight sandstones, but poroelastic behaviours of tight sandstones with low porosity and permeability lead to complex relationships between gas saturation and elastic attributes. Thus, gas prediction based on conventional seismic methods tends to be a challenging task. However, the frequency-dependence of elastic properties associated with fluid flow in tight sandstones allows the utilisation of seismic dispersion attributes for gas prediction. This study proposes a new inversion method to compute the bulk-modulus-related dispersion attribute DK for improved gas prediction by using the sensitivity of the bulk modulus to fluids in tight sandstones. Rock physical modelling and synthetic tests indicate that the proposed DK exhibits increased sensitivity to gas saturation compared to the conventional P-wave velocity dispersion attribute DP and the commonly utilised VP/VS ratio. Real data applications demonstrate that DK represents a preferable gas identification factor for the tight sandstone gas reservoir in the Ordos Basin. Results indicate that DK shows improved apparent anomalies to gas zones and better correspondence with the actual production status of drilled wells than DP and the VP/VS ratio. A combined factor, CF, is further proposed to improve the accuracy and robustness of gas prediction by considering the sensitivity of DK while simultaneously incorporating the VP/VS ratio as an essential constraint. A close correlation between the proposed CF and gas saturation measured in boreholes justifies the applicability of the CF for the reliable identification of gas-bearing tight sandstones. Gas zones identified by the CF provide essential information for gas exploration in the region of interest. The method proposed in this study extends the existing seismic dispersion inversion for improved gas prediction. The methodology to obtain the gas identification factor can inspire the development of other practical fluid indicators.

Characterization of a Volcanic Gas Reservoir Using Seismic Dispersion and Fluid Mobility Attributes

Abstract Seismic dispersion and fluid mobility attributes are used to characterize a volcanic gas reservoir in the Songliao Basin of China. A rock physics model is constructed to describe poroelastic behaviors associated with heterogeneous fluids saturation within the volcanic gas reservoirs, where velocity dispersion and attenuation of propagating waves are attributed to the wave-induced fluid flow described by the patchy saturation theory. Modeling results indicate that the frequency-dependent bulk modulus at the seismic frequency is more sensitive to gas saturation than the P-wave velocity dispersion. Accordingly, a new inversion method is developed to compute bulk-modulus-related dispersion attribute DK for improved characterization of volcanic gas reservoirs. Synthetic tests indicate that DK is more sensitive than traditional P-wave dispersion attribute DP to the variations of reservoir properties. The high value of dispersion attribute DK indicates the volcanic gas reservoirs with high porosity and gas saturation. At the same time, fluid mobility attribute FM can discriminate the volcanic gas reservoir as DK. Field data applications illustrate that DK and FM exhibit anomalies to the gas zones in the volcanic gas reservoir on the cross-well section. However, DK is more robust than FM to identify favorable zones on horizontal slices for specific target layers. Overall, rock physical modeling provides insights into the poroelastic behaviors of volcanic gas reservoirs, and inversion for seismic dispersion attribute DK improves hydrocarbon detection in the volcanic gas reservoir.

Prediction of sweet spots in tight sandstone reservoirs based on anisotropic frequency-dependent AVO inversion

Abstract The frequency-dependent amplitude-versus-offset (FAVO) method has become a practical method for fluid detection in sand reservoirs. At present, most FAVO inversions are based on the assumption that reservoirs are isotropy, but the application effect is not satisfactory for fractured reservoirs. Hence, we analyse the frequency variation characteristics of anisotropy parameters in tight sandstone reservoirs based on a new petrophysical model, and propose a stepwise anisotropic FAVO inversion method to extract frequency-dependent attributes from prestack seismic field data. First, we combine the improved Brie's law with the fine-fracture model to analyse frequency-dependent characteristics of velocities and Thomsen anisotropy parameters at different gas saturations and fracture densities. Then, we derive an anisotropic FAVO inversion algorithm based on Rüger's approximation formula and propose a stepwise anisotropic FAVO inversion method to obtain the dispersions of anisotropy parameters. Finally, we propose a method that combines the inversion spectral decomposition with the stepwise anisotropy FAVO inversion and apply it to tight sand reservoirs in the Xinchang area. We use P-wave velocity dispersion and anisotropy parameter ε dispersion to optimise favourable areas. Numerical analysis results show that velocity dispersion of the P-wave is sensitive to fracture density, which can be used for fracture prediction in fractured reservoirs. In contrast, anisotropic parameter dispersion is sensitive to gas saturation and can be used for fluid detection. The seismic data inversion results show that velocity dispersion of the P-wave and anisotropic parameter dispersion are sensitive to fractured reservoirs in the second member of Xujiahe Group, which is consistent with logging interpretation results.

Rock Physical Modeling and Seismic Dispersion Attribute Inversion for the Characterization of a Tight Gas Sandstone Reservoir

Gas identification using seismic data is challenging for tight gas reservoirs with low porosity and permeability due to the complicated poroelastic behaviors of tight sandstone. In this study, the Chapman theory was used to simulate the dispersion and attenuation caused by the squirt flow of fluids in the complex pore spaces, which are assumed to consist of high aspect-ratio pores (stiff pores) and low aspect-ratio microcracks (soft pores). The rock physics modeling revealed that as the gas saturation varies, P-wave velocity dispersion and attenuation occurs at seismic frequencies, and it tends to move to high frequencies as the gas saturation increases. The velocity dispersion of the tight gas sandstone causes a frequency-dependent contrast in the P-wave impedance between the tight sandstone and the overlying mudstone, which consequently leads to frequency-dependent incidence reflection coefficients across the interface. In the synthetic seismic AVO modeling conducted by integrating the rock physics model and the propagator matrix method, the variations in the amplitudes and phases of the PP reflections can be observed for various gas saturations. The tests of the frequency-dependent AVO inversion of these synthetic data revealed that the magnitude of the inverted P-wave dispersion attribute can be used to indicate gas saturation in tight sandstone reservoirs. The applications of the frequency-dependent AVO inversion to the field pre-stacked seismic data revealed that the obtained P-wave dispersion attribute is positively correlated with the gas production from the pay zone at the well locations. Thus, the methods of the rock physics modeling and the frequency-dependent AVO inversion conducted in this study have good potential for the evaluation of the gas saturation in tight gas sandstone reservoirs.

Wave Properties of Gas-Hydrate Bearing Sediments Based on Poroelasticity

Natural gas hydrates have the properties of ice with a microporous structure and its concentration in sediments highly affects the wave velocity and attenuation. Previous studies have performed investigations based on the measurements of laboratory data, sonic-log data, and field data, whereas the variation trend of wave dissipation with increasing hydrate concentration at different frequencies is still unclear. We consider two different models to study this problem, both based on the Biot-Rayleigh double-porosity theory. In the first model, hydrate is part of the pore infill, unbonded from the grains, and brine saturates the remaining pore space. In the second model, hydrate forms a second skeleton and cements the grains. We obtain the P-wave velocity dispersion and attenuation as a function of the inclusion radius, porosity, and hydrate content. The analysis shows that the predictions of both models agree with the experimental data. At sonic log frequencies, the second model predicts much more attenuation, due to wave-induced local fluid flow (mesoscopic loss), and the behavior is such that below a given hydrate concentration the dissipation increases and then decreases beyond that concentration.

Effects of pore water distributions on P-wave velocity–water saturation relations in partially saturated sandstones

SUMMARY We have developed a new method for introducing the effects of pore water distribution into the interpretation of P-wave velocity (VP) dispersion in a partially saturated rock. Pore water in an unsaturated rock is distributed as patches, and mesoscopic-scale wave-induced fluid flow (WIFF) from saturated patches to empty patches is known as a key mechanism for interpreting P-wave dispersion. Mesoscopic WIFF depends on permeability and the scale of the saturated patch, thus evaluating their influences is important for estimating the relationship between water saturation (${S_{\rm{w}}}$) and VP. The simplest and conventional law for simulating the ${S_{\rm{w}}} - {V_{{P}}}$ relation considering the mesoscopic WIFF is White's model, which describes the patch size changes proportional to the saturation. However, White's model assumes homogeneity in the size and distribution of pores, and does not consider the effects of pore water distribution in a partially saturated rock. In the rock, pore water is distributed heterogeneously according to the pore radius, causing non-linear changes in the permeability and size of the saturated patches against the water saturation. In this study, we modified White's model by introducing relative permeability and a new coefficient describing the nonlinear change of the patch size into the conventional version, and applied the modified model to better interpret our experimental ${S_{\rm{w}}} - {V_{{P}}}$ relations, which were measured by an ultrasonic technique at 200 and 500 kHz for two types of Berea sandstone samples with different permeabilities as their water saturation was decreased by evaporative drying. The relative permeabilities were determined by applying the Mualem–van Genuchten model into the capillary pressure curves from mercury intrusion porosimetry. Furthermore, we proposed a calculation method for the new coefficient using tortuosity, which corresponds to the pore water connection. The modified White's model could reproduce the experimental ${S_{\rm{w}}} - {V_{{P}}}$ relations better than other conventional models. Consequently, our modification, considering the effect of pore water distribution, would be useful for more quantitative interpretation of P-wave velocity and attenuation under coexisting multifluid conditions.

Rock Physics Model and Seismic Dispersion and Attenuation in Gas Hydrate-Bearing Sediments

A rock physics model was established to calculate the P-wave velocity dispersion and attenuation caused by the squirt flow of fluids in gas hydrate-bearing sediments. The critical hydrate saturation parameter was introduced to describe different ways of hydrate concentration, including the mode of pore filling and the co-existence mode of pore filling and particle cementation. Rock physical modeling results indicate that the P-wave velocity is insensitive to the increase in gas hydrate saturation for the mode of pore filling, while it increases rapidly with increasing gas hydrate saturation for the co-existence mode of pore filling and particle cementation. Meanwhile, seismic modeling results show that both the PP and mode-converted PS reflections are insensitive to the gas hydrate saturation that is lower than the critical value, while they tend to change obviously for the hydrate saturation that is higher than the critical value. These can be interpreted that only when gas hydrate begins to be part of solid matrix at high gas hydrate saturation, it represents observable impact on elastic properties of the gas hydrate-bearing sediments. Synthetic seismograms are calculated for a 2D heterogeneous model where the gas hydrate saturation varies vertically and layer thickness of the gas hydrate-bearing sediment varies laterally. Modeling results show that larger thickness of the gas hydrate-bearing layer generally corresponds to stronger reflection amplitudes from the bottom simulating reflector.

P-wave attenuation and dispersion in a fluid-saturated rock with aligned rectangular cracks

It is well known that mesoscopic-scale wave-induced fluid flow (WIFF) between cracks and surrounding porous matrix is one of significant mechanisms in causing seismic dispersion and attenuation. Previous theoretical models that were used to interpret the interaction between cracks and passing waves assumed the cracks to be circular or slit-like. However, in many actual cases, the cracks can have a shape more close to a rectangle. In this paper, we develop an effective medium model to estimate the P-wave attenuation and velocity dispersion in a saturated porous rock containing a random distribution of permeable, aligned, rectangular cracks of infinitesimal thickness. This is done by combining the far-field displacement representation of the solution of a normally incident P wave scattered by a single crack and Foldy's scattering theorem. The effective low-frequency P-wave velocity predicted by the present model is asymptotically consistent with the Gassmann's theory. It is shown that thorough knowledge of the crack shape is important for understanding seismic signatures. Specifically, the WIFF relaxation frequency is mainly determined by the crack intermediate dimension, while it is insensitive to the crack largest dimension. Moreover, P-wave velocity of the rectangular crack model can be quite different from those of the circular crack model and the slit crack model, although the overall frequency-dependent trends of the velocities for different models are very similar. Analogously to the circular crack model and the slit crack model, at the normal incidence of a fast-P wave, the WIFF is found to dominate the wave attenuation and velocity dispersion. These results are helpful to estimate formation parameters from different frequency components of observed seismic data.

Macroscopic mechanical properties of porous rock with one saturating fluid

Effective frequency-dependent moduli and [Formula: see text]-factors are broadly used for characterizing the behavior of earth media in laboratory and field seismic observations. However, such properties are wavemode- and experiment-dependent and are often incomplete and/or inaccurate for modeling realistic situations. For example, viscoelastic moduli for porous fluid-saturated rock are usually derived for primary waves, but they may not apply to cases in which secondary waves are important, such as reflections in finely layered poroelastic media or quasistatic pore-fluid flows in laboratory experiments. To obtain a model applicable to all cases, equations of mechanics should be used, and mechanical properties of the material must be identified. To reveal and measure such properties for fluid-saturated porous rock, we have developed a Biot-consistent model based on Lagrangian continuum mechanics. The model is “minimal,” purely macroscopic, and independent of the macrostructure or patterns of pore-fluid flows; thus, it could represent many existing wave-induced fluid-flow (WIFF) as well as non-WIFF models. Due to its mechanical definition, the model should be applicable to all rock-physics experiments (linear creep, pore flow, low-frequency, resonant, or ultrasonic), any waves in the field (primary, secondary, standing, surface, etc.) under arbitrary boundary conditions, and also finite-difference and finite-element numerical modeling. When based on this model, numerical simulations require no integral equations, fractional derivatives, memory variables, or additional kinetic equations. We further use the model to invert for detailed elastic and viscous properties of fluid-saturated Berea and Fontainebleau sandstones from recently published low-frequency laboratory experiments. All rock properties inferred in the model are time- and frequency-independent, comparable to other physical observations, and the model closely predicts the data. The model can be approximately pore-fluid independent, which allows performing rigorous fluid substitution with viscous pore fluids. As an illustration, P-wave velocity dispersion and attenuation in water-, oil-, and gas-saturated sandstone are simulated.

Wave-velocity dispersion and rock microstructure

Porosity, fluid type and rock texture significantly affect acoustic wave propagation, since velocity dispersion and attenuation in fluid saturated rocks are mainly caused by wave-induced local fluid flow between microcracks and intergranular pores. We analyze P-wave velocity dispersion as a function of porosity to obtain information about the rock microstructure. The P-wave velocities in water-saturated rocks are predicted from measurements in gas-saturated rocks, using the Gassmann fluid substitution equation (the relaxed state). The dispersion is estimated from the difference between this predicted velocity and the measured one, where the latter corresponds to the unrelaxed state. We evaluate the wave dispersion as a function of porosity for 112 carbonates, 128 sandstones and 56 volcanic rocks, including our measurements for 86 tight rocks, showing that dispersion increases with porosity in the low porosity range, but decreases in the high porosity range. The dispersion peak occurs at a porosity of approximately 15%. Double-porosity poroelasticity modeling based on the local fluid-flow mechanism confirms this behavior. The microcrack radius has a peak in the porosity range 15–19% for all the lithologies from our collection, while the behavior of microcrack porosity is less evident. The dispersion peak may reveal the characteristics of lithological units, in particular porosity, fluid type and rock microstructure.

Dispersion and attenuation of compressional waves in tight oil reservoirs: Experiments and simulations

We performed ultrasonic experiments in specimens from a tight oil reservoir. The P-wave attenuation of fluid-saturated specimens was estimated by the spectral ratio method. The results suggest that at ultrasonic frequencies, most specimens have stronger attenuation under gas-saturated conditions than at water- or oil-saturated conditions. The P-wave attenuation positively correlates with permeability. Scanning electron microscopy observations and the triple-porosity structure model were used to simulate the wave propagation. The P-wave velocity dispersion and attenuation are discussed on the basis of the Biot, Biot-Rayleigh double-porosity medium, and the triple-porosity structure models. The results suggest that the Biot and Biot-Rayleigh models cannot explain the attenuation, whereas the triple-porosity structure model is in agreement with the experimental data. Furthermore, we infer that microcracks are common in a porosity of 5%–10%, and the size of microcracks increases in samples with higher porosity. However, the volume ratios of microcracks and clay inclusions remain constant regardless of porosity variations. The size of microcracks is significantly larger than the clay inclusions, and the bulk modulus of microcracks is lower than the bulk modulus of clays.

Velocity dispersion in rocks: A laboratory technique for direct measurement of P-wave modulus at seismic frequencies.

Fluid saturated rocks exhibit a dependence of acoustic velocities on frequency, which is called velocity dispersion. For some rocks, e.g., shales, velocity dispersion is rather strong and has to be taken into account when interpreting and comparing data from seismic surveys, sonic logs, and ultrasonic measurements on core plugs in the laboratory. In this work, a new laboratory technique has been developed that allows the direct measurement of the P-wave modulus at seismic frequencies from which the P-wave velocities can be derived. Together with ultrasonic velocity measurements that are carried out simultaneously, the P-wave velocity dispersion between seismic and ultrasonic frequencies is obtained.

Prestack Stochastic Frequency-Dependent Velocity Inversion With Rock-Physics Constraints and Statistical Associated Hydrocarbon Attributes

Previous studies have demonstrated that P-wave velocity dispersion at seismic frequencies is often related to hydrocarbons, which results in frequency-dependent P-wave reflection coefficients. This effect is neglected in the conventional amplitude-versus-angle (AVA) inversion, or reduced in most AVA inversion involving seismic dispersion due to the linearization of either the forward modeling or the inversion objective function. As a consequence, there are times when nonnegligible error exists in the inverted dispersion-associated result, which is probably nonnegligible in some cases. In this letter, we adopt the propagator matrix forward modeling derived from the wave equation and the particle swarm optimization (PSO)-based inversion to solve the uncollapsed objective function to avoid any linearization operator at the cost of probably more computational complexity and inversion ill-posedness. To address the ill-posedness, in both the forward modeling and inversion, we introduce rock-physics constraints of frequency-independent S-wave velocity and limited variations of P-wave velocity with frequency. Furthermore, we statistically derive the average frequency-dependent P-wave velocity attribute, the P-wave velocity dispersion intensity attribute, and the characteristic frequency attribute corresponding to the maximum velocity dispersion gradient from multiple experimental inverted dispersive P-wave velocity results. These attributes can be directly applied to detect hydrocarbons. A synthetic data example and a real data example through a drilling well are used to demonstrate that PSO-based prestack stochastic inversion method with rock-physics constraints is effective, and that the statistical attributes derived from the multiple inverted dispersive P-wave velocities can be utilized to favorably indicate gas reservoirs.

Effect of CO2 on P- and S-wave velocities at seismic and ultrasonic frequencies

Time-lapse seismic is a widely used technology for monitoring the geological sequestration of carbon dioxide (CO2), consisting of mapping its movement in the subsurface and of demonstrating that the CO2 is safely stored in the reservoir (Xue and Ohsumi, 2004). In this work, the effect of CO2 on P- and S-wave velocities was investigated. Laboratory measurements were performed with Castlegate sandstone both at seismic frequencies (1–155 Hz), and at ultrasonic frequency (around 500 kHz). Different CO2 saturations between 2% and 10% were obtained by controlled depressurization of CO2-saturated water with which the sandstone sample had been saturated with. At seismic frequencies, the results of the experiments revealed that P-wave velocity is strongly reduced in the presence of free gas CO2 in the pore space, whereas at ultrasonic frequency, the P-wave velocity changed only slightly. Therefore, the presence of free CO2 gas increased significantly the P-wave dispersion between seismic and ultrasonic frequencies. The S-wave velocity, on the other hand, was hardly affected by the pore fluid at seismic frequencies. At seismic frequencies, P- and S-wave velocities were consistent with the Biot–Gassmann model. The P-wave velocity dispersion and corresponding attenuation were simulated by applying the Cole–Cole model. The transition frequency was found around 200 kHz.

Effects of ellipsoidal heterogeneities on wave propagation in partially saturated double-porosity rocks

Reservoir rocks are heterogeneous porous media saturated with multiphase fluids, in which strong wave dissipation and velocity dispersion are closely associated with fabric heterogeneities and patchy saturation at different scales. The irregular solid inclusions and fluid patches are ubiquitous in nature, whereas the impact of geometry on wave dissipation is still not well-understood. We have investigated the dependence of wave attenuation and velocity on patch geometry. The governing equations for wave propagation in a porous medium, containing fluid/solid heterogeneities of ellipsoidal triple-layer patches, are derived from the Lagrange equations on the basis of the potential and kinetic energies. Harmonic functions describe the wave-induced local fluid flow of an ellipsoidal patch. The effects of the aspect ratio on wave velocity are illustrated with numerical examples and comparisons with laboratory measurements. The results indicate that the P-wave velocity dispersion and attenuation depend on the aspect ratio of the ellipsoidal heterogeneities, especially in the intermediate frequency range. In the case of Fort Union sandstone, the P-wave velocity increases toward an upper bound as the aspect ratio decreases. The example of a North Sea sandstone clearly indicates that introducing ellipsoidal heterogeneities gives a better description of laboratory data than that based on spherical patches. The unexpected high-velocity values previously reported and ascribed to sample heterogeneities are explained by varying the aspect ratio of the inclusions (or patches).