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The tight oil/gas reservoirs in China have showed the great exploration prospects and high production potential, with the characteristics of low porosity, low permeability, and significant heterogeneity in formation rocks. It remains a challenge to sort out the relations between reservoir wave responses and rock physical properties, and the further studies on the wave response patterns of tight reservoirs are in an urgent demand. The shear modulus and S- (shear) wave attenuation of rocks are affected by the properties of pore fluid and confining pressure. The ultrasonic wave experiments are performed on eight partially-saturated tight sandstone samples at different confining pressures, and we estimate S-wave attenuation with the spectral-ratio method. Results show that S-wave attenuation decreases with increasing confining pressure, and the water saturation case shows more loss compared to the oil saturation case, while the gas saturation case gives the lowest attenuation. We observe the S-wave relaxation peak at an intermediate water saturation for the gas-water partial-saturation case in general. S-wave attenuation increases with increasing porosity or permeability. Based on the measured rock physical properties, and combined with the Voigt–Reuss–Hill (VRH) average, differential effective medium (DEM) model and squirt-flow model, a tight rock attenuation model is proposed for analyzing the attenuation characteristics of fluid-saturated rocks at different confining pressures. The model reasonably describes the S-wave attenuation characteristics. The model predictions of S-wave attenuation show apparent pressure- and fluid-sensitivity at full saturation and partial saturation conditions. For sample TS1-19 at full saturation with different confining pressures, the S-wave peak attenuation predicted by the model ranges from 11.6 to 69.5, and decreases with confining pressure, while the relaxation frequency shifts to high frequency end. For the partial saturation condition of the sample, the predicted S-wave peak attenuation ranges from 15.5 to 39.8 at a confining pressure of 30 MPa and increases with water saturation, while the relaxation frequency shifts to low frequency end. For all the samples at 30MPa confining pressure, the predicted S-wave attenuation ranges from 5.6 to 38.6. At the full-saturation case, the predicted S-wave attenuation increases with porosity and decreases with confining pressure. For the partial saturation case, the S-wave attenuation predicted with the model and the Voigt and Reuss bounds generally increases with water saturation, whereas the experimentally-measured attenuation exhibits the peak attenuation at an intermediate saturation. [ABSTRACT FROM AUTHOR]

The time-fractional Cattaneo (TFC) equation is a practical tool for simulating anomalous dynamics in physical diffusive processes. The existing numerical solutions to the TFC equation generally deal with the Dirichlet boundary conditions. In this paper, we incorporate the absorbing boundary condition as a complex-frequency-shifted (CFS) perfectly matched layer (PML) into the TFC equation. Then, we develop an adaptive-coefficient (AC) finite-difference frequency-domain (FDFD) method for solving the TFC with CFS PML. The corresponding analytical solution for homogeneous TFC equation with a point source is proposed for validation. The effectiveness of the developed AC FDFD method is verified by the numerical examples of four typical TFC models, including the different orders of time-fractional derivatives for both the homogeneous model and the layered model. The numerical examples show that the developed AC FDFD method is more accurate than the traditional second-order FDFD method for solving the TFC equation with the CFS PML absorbing boundary condition, while requiring similar computational costs. [ABSTRACT FROM AUTHOR]

We perform seismic and ultrasonic measurements in carbonate and shaley sandstone samples as a function of differential pressure. The velocities show a strong frequency and pressure dependence. The dispersion disappears with increasing pressure and the squirt flow in turn inhibits the pressure dependence. To model these effects, we combine the Gurevich's squirt-flow model with the Mori–Tanaka scheme and the David Zimmerman model, and extend it with third-order elastic constants, to obtain a frequency-dependent acoustoelasticity model. Comparisons between measurements from this study and literature and modelling results show that the P -wave velocity increases non-linearly first and then nearly linearly, dominated by crack closure and acoustoelasticity, respectively. The pressure dependence of wave velocities is reduced by liquid substitution and further by the squirt-flow mechanism. The effects of fluid properties and crack closure on P -wave velocity decrease with differential pressure. The results will feed a new model and help better understanding the wave propagation in pre-stressed rocks at different scales. [ABSTRACT FROM AUTHOR]

Knowledge of how temperature affects the oil–sand acoustic response is useful to exploit these reservoir rocks with seismic methods. We propose three models: double-porosity coherent potential approximation (CPA), lower-bound Hashin–Shtrikmann (HS-), and contact cement (CC), based on different spatial distributions of heavy oil and temperature and frequency-dependent empirical equations. The shear modulus and S-wave velocity are affected by temperature in all the cases. Moreover, the properties of oil sands with heavy oil as a continuous matrix and higher viscosity are more sensitive to temperature. The models can provide theoretical support for the establishment of rock physical models in heavy oil reservoirs so as to quantitatively characterize the seismic response changes caused by thermal mining. [ABSTRACT FROM AUTHOR]

Tight gas sandstone reservoirs play an important role in the field of exploration and development of unconventional oil/gas resources. However, these reservoirs typically exhibit low-porosity and poor-permeability, with pore structures of strong heterogeneity comprising connected and isolated pores. The traditional rock physics models (such as the Gassmann model) are established under the assumption of fully connected pores, which cannot reasonably describe the complexity in tight reservoirs. In this regard, this work proposes a rock physics modeling approach aimed at tight sandstone reservoirs based on a reformulated Xu–White model. Specifically, the differential effective medium model and Xu–White model are combined to analyze the influences of isolated pores on the dry rock skeleton. To characterize the general effects due to the different pore types on rock elastic moduli, the volume content of connected pores is defined as a pore-connectivity parameter. The simulated annealing algorithm is applied to invert the parameter, which is treated as a weighting coefficient for correcting the wet rock elastic moduli, thereby improving the precision of rock physics modeling. The proposed approach is tested and verified by using the log data of the work area of Sichuan Basin, West China. The result shows that, compared with the conventional method, the P- and S-wave velocities predicted by the proposed method are consistent with the log data. In addition to the inversion results of the conventional petrophysical parameters, the inverted pore-connectivity parameter can be a good auxiliary attribute that assists locating potential targets for tight gas sandstone reservoirs. [ABSTRACT FROM AUTHOR]

Geometric heterogeneities in tight reservoir rocks saturated with a fluid mixture may exhibit different scale distribution characteristics. Conventional models of rock physics based on poroelasticity, which usually consider single‐scale pore structure and fluid patches, are inadequate for describing elastic wave responses. A major challenge is to establish the relationship between the wave response at different spatial scales and frequencies. To address this problem, three sets of observational data over a wide frequency range were obtained from a tight oil reservoir in the Ordos Basin, China. Ultrasonic measurements were made on eight sandstone samples at partial oil‐water saturation at 0.55 MHz. Data from six borehole measurements and seismic profiles were acquired and analyzed at about 10 kHz and 30 Hz, respectively. Analysis of the cast thin sections shows that dissolution pores and microcracks generally develop, with fractal dimensions of the pores ranging from 2.45 to 2.67 for the samples with porosities between 5.1% and 10.2%. Compressional wave velocity and attenuation were estimated from the observed data. The results show that the velocity dispersion from seismic to ultrasonic frequencies is 10.02%, mostly occurring between sonic and ultrasonic frequencies. The attenuation is stronger at higher oil saturation. The relationships between velocity, attenuation, and wavelength were established and can be used for further forward modeling and seismic interpretation studies. A partial saturation model has been derived based on effective differential medium theory and a double double‐porosity model, assuming that the medium contains fractal cracks and fluid patches. The effects of scale and saturation on wave responses are prevalent. Modeling results consistent with observed data show that the radii of cracks and fluid patches range from 0.1 μm to 2.8 mm, affecting ultrasonic, acoustic, and seismic attenuation. The multiscale data and proposed model quantify the relationship between fracture and fluid distributions and attenuation and could be useful for upscaling to the reservoir scale. The study helps improve the understanding of seismic wave propagation in partially saturated rocks, which has potential applications in seismic exploration, hydrocarbon production in reservoirs, and CO2 sequestration in aquifers. Plain Language Summary: The physical properties of the rock and fluid can be inferred from the measured elastic wave responses and energy dissipation characteristics. However, the effects of heterogeneities of different sizes and at different frequencies can hinder studies to quantify wave responses in a partially saturated porous medium, which are usually based on laboratory measurements. A major problem is the difference between observed frequencies and scales: megahertz in the laboratory, 10 of kilohertz in the borehole scale, and hertz in the seismic exploration scale. In this work, the frequency‐ and saturation‐dependent compressional velocity and attenuation are investigated using three geophysical data sets from the same tight reservoirs. A strong velocity dispersion over the measured frequency range is observed. The stronger attenuation at partial saturation may be caused by the multiscale heterogeneities of the pore structure and fluid patch distribution. A fractal poroelasticity model is developed by gradually inserting inclusions of different sizes with compliant pores and liquid patches into a homogeneous host skeleton. The wave responses are significantly affected by scale distribution and saturation. The proposed model, verified by the measured data, can be useful in interpreting the anelasticity of tight heterogeneous reservoirs in a broadband range. Key Points: We investigate how fluid saturation affects wave attenuation and dispersion over a wide frequency range in tight sandstone layersA partial saturation model describes the fractal properties of the layersThe size of the cracks and fluid patches are determined by applying the fractal model to the multiscale data [ABSTRACT FROM AUTHOR]

Wave propagation in anelastic rocks is a relevant scientific topic in basic research with applications in exploration geophysics. The classical Biot theory laid the foundation for wave propagation in porous media composed of a solid frame and a saturating fluid, whose constitutive relations are linear. However, reservoir rocks may have a high-viscosity fluid, which exhibits a non-Newtonian (nN) behaviour. We develop a poroelasticity theory, where the fluid stress-strain relation is described with a Kelvin–Voigt mechanical model, thus incorporating viscoelasticity. First, we obtain the differential equations from first principles by defining the strain and kinetic energies and the dissipation function. We perform a plane-wave analysis to obtain the wave velocity and attenuation. The validity of the theory is demonstrated with three examples, namely, considering a porous solid saturated with a nN pore fluid, a nN fluid containing solid inclusions and a pure nN fluid. The analysis shows that the fluid may cause a negative velocity dispersion of the fast P (S)-wave velocities, that is velocity decreases with frequency. In acoustics, velocity increases with frequency (anomalous dispersion in optics). Furthermore, the fluid viscoelasticity has not a relevant effect on the wave responses observed in conventional field and laboratory tests. A comparison with previous theories supports the validity of the theory, which is useful to analyse wave propagation in a porous medium saturated with a fluid of high viscosity. [ABSTRACT FROM AUTHOR]

Seismic wave propagation is affected by wave‐induced local fluid flow between stiff pores and multiscale fractures. To investigate this phenomenon, forced vibration (1–100 Hz) and ultrasonic (106 Hz) measurements are performed on two tight sandstones with complex pore geometry in dry and water‐saturated scenarios. Porosity, permeability, and ultrasonic velocities were also measured at different differential pressures. The results indicate that the nonlinear behavior of these properties is strongly influenced by the presence of cracks, and the correlations between the permeability/ultrasonic velocities and porosity are different. A wave propagation model is then developed in which penny‐shaped cracks are inclusions introduced stepwise into a porous medium to describe the wave anelasticity in a wide frequency band at different pressures. As a result, the model provides good agreement with the measured P‐wave velocity dispersion, and the pore aspect ratio spectrum and crack radii are determined. We then compare the estimated crack radii and pore size distributions from nuclear magnetic resonance spectroscopy. Published data of a tight sandstone and a low porosity sandstone in the frequency range (2–200, 106) and (1–3,000) Hz at different differential pressures are also analyzed to validate the model. The aspect ratios, volume fractions, and radii of pores/cracks are used to describe the measured permeability. The present work can provide new insights into the geophysical properties of reservoir rocks with complex pore geometry. Plain Language Summary: Multiscale cracks exert an important influence on the dispersion and attenuation of broadband acoustic waves. To better understand the underlying mechanism, we measured frequency‐dependent elastic moduli and pressure‐dependent porosity, permeability, and ultrasonic wave velocities of two tight sandstones. These data show that velocity dispersion is observable in water‐saturated rock and that permeability and ultrasonic velocities are differentially correlated with porosity. A proposed wave propagation model, in which penny‐shaped cracks are inclusions introduced stepwise into a porous medium, successfully describes the experimental data and other published data on tight sandstone and low‐porosity sandstone, and aspect ratios, volume fractions, and radii of pores/cracks are determined. Key Points: We propose a model to investigate the effect of multiscale cracks on seismic waves in tight sandstonesThe pore aspect ratio and crack‐radius spectra are estimated at different differential pressuresThe permeability is obtained according to the pore geometry [ABSTRACT FROM AUTHOR]

The finite-difference frequency domain (FDFD) method is widely applied for simulating seismic wavefields, and a key to achieving successful FDFD simulation is to construct FDFD coefficients that can effectively suppress numerical dispersion. Among the existing FDFD coefficients for seismic wavefield simulation, adaptive FDFD coefficients that vary with the number of wavelengths per grid can suppress numerical dispersion to the maximum extent. The current methods for calculating adaptive FDFD coefficients involve numerical integration, conjugate gradient (CG) optimization, sequential initial value selection, and smooth regularization, which are difficult to implement and inefficient in calculations. To simplify the calculation of adaptive FDFD coefficients and improve the corresponding computational efficiency, this paper proposes a new method for calculating adaptive FDFD coefficients. First, plane-wave solutions with different discrete propagation angles are substituted in the FDFD scheme, and the corresponding least-squares problem is constructed. As this problem is ill-conditioned and obtaining smooth adaptive FDFD coefficients by the conventional solving method based on normal equations is difficult, this paper proposes solving the least-squares problem by solving the corresponding overdetermined linear system of equations through QR matrix decomposition. Compared with the existing methods for calculating adaptive FDFD coefficients based on numerical integration, CG optimization, and sequential initial value selection, the proposed method allows for a simplified computational process and considerably higher computational efficiency. Numerical wavefield simulation results show that the adaptive-coefficient FDFD method based on QR matrix decomposition can achieve the same accuracy as those based on numerical integration, CG optimization, and sequential initial value selection while requiring less computation time. [ABSTRACT FROM AUTHOR]

As an important geophysical data processing technique, seismic inversion estimates subsurface rock properties with seismic observations. However, anisotropic inversion, intended for a vertical transverse isotropy (VTI) media that primarily describes shale gas/oil resources, suffers from high nonlinearity. Simulated annealing is a widely used global optimization algorithm for solving nonlinear seismic inverse problems, but it involves multiple optimization parameters (e.g., initial temperature, search limit, and perturbation range). The importance of such parameters has been proven whilst the relevant analysis is limited in seismic inversion studies. This work hereby proposes a sequential anisotropic inversion method for VTI media, wherein we combine Bayesian linear and simulated annealing nonlinear inversion schemes. The simulated annealing is featured by adaptive optimization parameters aided by the linear result. Rather than the conventional method, the adaptive setting can be implemented trace by trace for complex reservoirs, which endows the method with enhanced stability and extended applicability. Synthetic tests and practical application demonstrate the validity of the method, wherein the obtained stiffness parameters facilitate the characterization of potential shale reservoirs with an improved accuracy. [ABSTRACT FROM AUTHOR]

Fracture orientation and in particular the fracture strike play an important role in guiding the accurate estimation of the orientation of in situ stress fields. Fracture strike can be extracted based on the azimuthal seismic reflection responses. Thus, the characteristics of seismic reflection responses varying with fracture strike are critical for fracture strike estimation. In this work, a set of vertical fractures with different strikes is introduced into an isotropic host matrix based on the Schoenberg linear-slip theory, and the azimuthal seismic reflection response is modeled based on the reflection/transmission analysis at a plane interface. The effect of fracture parameters, i.e., fracture density, fracture aspect ratio, and fluid infill on the seismic reflection response, is analyzed. The influences of fracture strike on the stiffness matrix are simulated, and we further discuss the impacts on the P- and S-wave velocities. The influences of fracture strike on the reflection coefficient are depicted using the rose diagram method. The proposed workflow is applied to real seismic reflection data. The method is used to estimate the fracture strike with the seismic data in the Sichuan Basin work area by assuming that all fractures are vertically oriented, and the rose diagram is obtained close to the target layer. The results show that the fracture strike predicted by the method is in good agreement with the estimation based on the well-bore imaging data. [ABSTRACT FROM AUTHOR]

We investigate the effect of temperature on the elastic properties of rocks by combining the thermal-damage factor (TDF) with the Gassmann equation. The resulting model is tested in carbonate samples by analyzing the ultrasonic wave velocity. A comparison between the estimated and measured TDF shows that the model quantitatively describes the behavior of carbonates at relatively low temperatures, while the high-temperature one is underestimated. The dry- and wet-rock TDF difference increases significantly with increasing temperature, and the TDF is highly affected by the rock permeability and microcrack aspect ratio. [ABSTRACT FROM AUTHOR]

The production of shale gas plays an important role in the global oil/gas industries, which is considered to approach about 1/3 of the total natural gas production at 2040. In recent years, Wufeng–Longmaxi Formation shale in Sichuan Basin has become a key target of gas development in China. The detection of high-quality gas-producing areas based on the relation between pore structure, mineralogy and elastic properties is the main research direction. However, the effects of depositional environment and diagenetic processes are rarely considered in the studies of these petrophysical properties. We select core samples from the two boreholes to perform X-ray diffraction experiments together with another set of cores from the target formation to obtain scanning electron microscope images and ultrasonic velocities. The mineralogy, pore structure and elastic properties are analyzed. The formation is divided into two sections based on the reservoir characteristics and sedimentary environments. Then, we study the different diagenetic processes of the upper and lower sections. Three-dimensional rock-physics templates of the shale in the two sections are built by using equivalent medium theories and elastic attributes. The templates are calibrated with the samples and well-log data. A 2D survey line and a 3D seismic block of the upper and lower sections are selected, respectively, to map the mineral component, porosity and microcrack density. The good match between the predictions and log interpretation and actual gas content reports suggests that the rock-physics template based on differential diagenesis can be effectively used for further interpretation of seismic inversion results. [ABSTRACT FROM AUTHOR]

In recent years, the Yanchang shale-oil formations of the Ordos Basin are rich in reserves with complex lithology and structure characteristics, low porosity and low permeability, and weak anomalies for oil and water discriminations, have been the key targets of unconventional oil/gas resource exploration and development in the relevant areas. The joint acoustic-electrical (AE) properties can be used to interpret reservoir lithology, mineralogy, pore structure, and fluid saturation. To conduct tests of thin section analysis, X-ray diffraction, and ultrasonic and electrical experiments at different pressures and saturation degrees, cores from the shale-oil formations in the Q area of the basin are collected. The variations in AE properties with respect to clay content, porosity, pressure (microfracture), and saturation are analyzed. The experimental results indicate that the rock physics behaviors of sandstones with different clay contents vary significantly. The AE properties of clean sandstones are basically dependent on the microfractures (pressure), while for muddy sandstones, the clay content is an important factor affecting the responses. The target reservoir consists of interbedded sandstone and shale layers. The AE equivalent medium equations and the Gurevich theory are applied to establish the joint models for the different lithologies and simulate the variations in AE properties with respect to fluid type, pore structure, and mineral components. The three-dimensional joint templates of clean and muddy sandstones, as well as shale, are developed based on the elastic and electrical attributes and then calibrated using the experimental and well-log data. The reservoir properties are estimated with the templates and validated by the log data. The results indicate that the joint templates based on lithology characteristics can effectively characterize the properties of interbedded sandstone and shale layers. Furthermore, the combined application of AE data provides more beneficial information for the assessment of rock properties, leading to precise estimates that conform with the actual formation conditions. [ABSTRACT FROM AUTHOR]

The elastic stress–strain relation of deep source rocks must account for the presence of fractures and lamination due to thermally mature kerogen layers. Clay lamination describes the variation in transverse isotropy with a vertical symmetry (VTI) characteristic of shale background, and vertical fractures induce the transverse isotropy with a horizontal symmetry (HTI) perturbations. Thus, the fractured shale rock can be described as a medium with an orthorhombic symmetry in terms of effective anisotropy. We present a new workflow for calculating the elastic constants of a pressure-dependent fractured shale rock and the effects of clay lamination and microfractures. We investigate the shale fabric that can result in the orthorhombic elastic symmetry and the effect of pressure on elastic parameters, and propose an inversion methodology. Results based on well-log data show that the proposed methodology can be effectively applied to field data. [ABSTRACT FROM AUTHOR]

The acoustic-electrical (AE) response of subsurface hydrocarbon reservoirs is highly affected by rock heterogeneity. In particular, the characterization of the microstructure of tight (low-permeability) rocks can be aided by a joint interpretation of AE data. To this purpose, we evaluate cores from a tight-oil reservoir to obtain the rock mineralogy and pore structure by X-ray diffraction and casting thin sections. Then, ultrasonic and resistivity experiments are performed under different confining pressures to analyze the effects of pores, microcracks and mineralogy on the AE properties. We have developed acoustic and electrical models based on effective-medium theories, and the Cole–Cole and triple-porosity equations, to simulate the response to total and soft (crack) porosities and clay content. The results show that these properties play a significant role. Then, a 3D rock-physical template is built and calibrated by using the core samples and well-log data. The template is applied to tight-oil reservoirs to estimate the rock properties, which are validated with log data. The good match between the predictions and these data indicates that the model can effectively explain the effects of the heterogeneous microstructure on the AE data. Article Highlights: Tight rock microstructure is analyzed with X-ray diffraction, thin sections and ultrasonic and electrical resistivity tests Rock acoustic-electrical properties are obtained by the effective-medium and triple-porosity theories Practical application is given based on an acoustic-electrical rock physics template [ABSTRACT FROM AUTHOR]

The elastic properties of rocks depend on the mineral constituents, pore structure, saturating fluids, and stress (loading) conditions. To study these properties, we measured ultrasonic P‐ and S‐wave velocities as a function of the differential (confining minus pore) pressure and propose an unrelaxed double‐porosity acoustoelasticity model, which generalizes the single‐porosity one. The new approach includes the effects of crack closure, based on the David‐Zimmerman model, and the squirt‐flow mechanism, based on the Gurevich model. When cracks are open at low differential pressures, their properties dominate the wave velocity variations, followed by the squirt‐flow mechanism. Then, a transition occurs, where cracks partially close, and the squirt‐flow effect vanishes. At high pressures, cracks close and acoustoelasticity effects prevail. This behavior is observed in sedimentary rocks, whereas in granites, which have a low crack content, the acoustoelastic effect is dominant at all pressures. Plain Language Summary: It is well known that physical properties of rocks are important factors affecting the elastic wave velocities. However, how these properties affect the velocity‐pressure relations are not well understood. We conducted laboratory experiments and observed that the variation of wave velocities is related to crack closure, squirt flow and acoustoelasticity effects. To study the combined effects of these mechanisms, we propose an unrelaxed double‐porosity acoustoelasticity model. The theoretical results compared with the experimental data shows that, in sedimentary rocks, the crack properties dominate the pressure‐dependent velocities, followed by the squirt‐flow mechanism at low differential pressures. At high pressures, cracks approach full closure and the acoustoelasticity effect is the most significant. For low porosity granites, the acoustoelasticity effect dominates at all pressures. Key Points: We measure elastic wave velocities in saturated rocks, to analyze the effects of crack closure, squirt flow and acoustoelasticityTo this purpose, we develop an unrelaxed double‐porosity acoustoelasticity modelCrack closure dominates, followed by the squirt‐flow mechanism at low differential pressures, while acoustoelasticity effects are important at high differential pressures. In granites, the last effect prevails [ABSTRACT FROM AUTHOR]

Petrophysical seismic inversion, aided by rock physics, aims at estimating reservoir properties based on reflection events, but it is generally based on the Gassmann equation, which precludes its applicability to complex reservoirs. To overcome this problem, we present a methodology based on the double-porosity Biot–Rayleigh (BR) model, which takes into account the rock heterogeneities. The volume ratio of inclusions in the BR model is treated as a spatially varying parameter, facilitating a better description of the pore microstructure. The method includes the Zoeppritz equations to extract reservoir properties from prestack data. To handle the ill-posedness of the inversion and achieve a stable solution, the algorithm is formulated as a multi-objective optimization based on the Bayes theorem, where the reservoir-property estimation is jointly conditioned to seismic and elastic data with multiple prior terms. The method is validated with field data of a tight gas sandstone reservoir, illustrating its effectiveness compared to the Gassmann-based estimation, reducing uncertainties and improving the accuracy of identifying gas zones. Article Highlights: The petrophysical seismic inversion is based on the double-porosity Biot–Rayleigh model Spatially varying inclusion volumes are used to describe complex pore structures A multi-objective optimization with joint data misfit enables stable results [ABSTRACT FROM AUTHOR]

The complex seismic responses of heterogeneous reservoirs can be related to the fabric structure, pore/microcrack shape, mineral composition and fluid distribution of the rock in situ. The pore structure refers to the geometric shape, size, spatial distribution and interconnectedness of pores, microcracks and throats. It is closely related to the storage space of reservoirs and the spatial distribution of oil/gas. Understanding the pore structure is crucial for the development of processes to increase oil/gas production capacity. Six dolomite samples from the Gaoshiti-Moxi Longwangmiao Formation are sorted out for measurements, and the ultrasonic and seismic attenuation are determined by using the spectral ratio method and the enhanced frequency shift method, respectively. When predicting the pore structure, we assume that the aspect ratio and volume fraction of pores and microcracks correspond to a normal distribution. On this basis, a model with the Voigt–Reuss–Hill average (VRH), differential effective medium (DEM) theory and infinituple-porosity media (IPM) theory is proposed. The acoustic wave responses in terms of reservoir porosity and standard deviation of normal distribution are analyzed, and multiscale 3D rock physics templates (RPT) are created. The calibrations of the templates are performed with the ultrasonic and seismic data, and then the templates are applied to the field data. The results show that the estimated porosity and pore structure (corresponding to the mean aspect ratio and standard deviation of a normal distribution, respectively) are in substantial agreement with the log data and the actual gas production results. [ABSTRACT FROM AUTHOR]

The wave-induced local fluid flow mechanism is relevant to the complex heterogeneity of pore structures in rocks. The analysis of the local fluid flow mechanism is useful for accurately describing the wave propagation characteristics in reservoir rocks. In the exploration and production of hydrocarbon reservoirs, the real stratum may be partially saturated with a multi-phase fluid mixture in general. Therefore, it is of great significance to investigate the wave velocity dispersion and attenuation features in relation to pore structures and fluids. In this work, the characteristics of fabric microstructures are obtained on the basis of pressure dependency of dry rock moduli using the effective medium theory. A novel anelasticity theoretical model for the wave propagation in a partially-saturated medium is presented by combining the extended Gurevich squirt-flow model and White patchy-saturation theory. Numerical simulations are used to analyze wave propagation characteristics that depend on water saturation, external patchy diameter, and viscosity. We consider a tight sandstone from the Qingyang area of the Ordos Basin in west China and perform ultrasonic measurements under partial saturation states and different confining pressures, where the basic properties of the rock are obtained at the full gas saturation. The comparison of experimental data and theoretical modeling results shows a fairly good agreement, indicating that the new theory is effective. [ABSTRACT FROM AUTHOR]

Ultra-deep carbonate reservoirs have low porosity, a complex pore space with microcracks of varying aspect ratio and dissolved pores, that affect the seismic and transport properties. We propose a rock-physics model based on penny-shaped inclusions in the framework of the double-porosity theory to estimate rock features, such as the crack porosity and aspect ratio, and stiff porosity. Based on this model, a 3-D rock-physics template is built, calibrated at the ultrasonic and seismic frequency bands, from attenuation, P-wave impedance and VP/VS ratio to quantitatively evaluate the effect of those features. Attenuation is estimated by using the spectral-ratio and improved frequency-shift methods. The template is applied to ultra-deep carbonates of the S work area of the Tarim Basin (China). The predictions agree with the well-log data and field production reports. In general, the higher the crack aspect ratio, the higher the storage and transport capacity of the reservoir. Therefore, these crack features can be used as indicators of these reservoir properties. [ABSTRACT FROM AUTHOR]

Seismic wave scattering dispersion and attenuation can be significant in cracked reservoirs. Many scattering models have been proposed, and the fractal (self-similar) features of the medium need to be further incorporated and analysed. We solve the P -wave scattering caused by fluid-saturated aligned cracks of finite thickness embedded in fractal media. The model is based on crack displacement discontinuities by using the Foldy approximation and representation theorem. The frequency dependence of velocity and attenuation are analysed as a function of the incidence angle and the crack and fluid properties. The results show that the crack density, thickness and radius can have a significant influence on the wave properties, as well as the fluid bulk modulus and saturation. The model requires three parameters to describe self-similar cracked media, and can be relevant in seismology, oil exploration and non-destructive testing of materials. [ABSTRACT FROM AUTHOR]

Seismic exploration of unconventional hydrocarbon reservoirs (e.g., shale rocks) must take into account the transverse isotropy with a vertical axis of symmetry (VTI) characteristics. Prestack inversion for VTI media is more complex than the isotropic case, since the forward engine is highly nonlinear and more unknowns (five instead of three) are involved, which aggravate the ill-posedness of the inverse problem. Here, we propose a hierarchical inversion scheme to improve the estimation of the five parameters, where the exact reflection coefficient is used as forward engine (instead of the commonly-used approximations which lack accuracy). To handle the highly nonlinear inverse problem, we perform the prestack anisotropic inversion in two steps, namely, a preliminary linear result is used to reduce the search window and to formulate the constrain term and initial models of the subsequent nonlinear step. Specifically, for a reasonable preliminary estimation, we introduce a data-driven model building algorithm to provide reliable initial models, and employ the limited-memory Broyden–Fletcher–Goldfarb–Shanno combined with the momentum technique (LBFGS-MT) optimization to increase the convergence speed. We derive the Fréchet derivatives of the exact forward operator with respect to the parameters, i.e., the key factors of the linear part. Besides, we introduce a hybrid global optimization, the particle swarm optimization aided by very fast simulated annealing (PSO-VFSA) to enhance the accuracy and computational efficiency of the nonlinear stage. Synthetic tests demonstrate the effectiveness and accuracy of the proposed scheme. The field application shows that the method is capable to obtain reliable elastic information of shale reservoirs. [ABSTRACT FROM AUTHOR]

Laboratory experiments on partially saturated rocks show that seismic attenuation can be significant. The main mechanism, wave‐induced local fluid flow (WILFF), is affected by the spatial fluid distribution, especially in conditions of patchy saturation at different spatial scales. We propose a theory to obtain the seismic properties of partially saturated rocks based on fractal (self‐similar) patches, leading to an effective frequency‐dependent fluid modulus. The model combines the differential effective medium and Biot‐Rayleigh theories, where the patches are inclusions incrementally added, such that the effective fluid calculated in the current addition serves as host fluid in the next one. The analysis shows that adding identical inclusions in one or several steps produces nearly the same results, but the seismic properties depend on the scale range (radius) of the inclusions, fractal dimension Df of the self‐similar distribution, parameter θ $\theta $ of the exponential distribution, mean radius r0 and variance σr2 ${\sigma }_{r}^{2}$ of the Gaussian distribution. Forced‐oscillation experiments were performed on a limestone sample under partial water‐saturation conditions at seismic frequencies (2–500 Hz), to obtain the velocity dispersion and extensional attenuation. The proposed theory provided a reasonable description of these experimental data as well as other published measurements on tight carbonate and Berea sandstone. Plain Language Summary: Seismic wave velocity dispersion and attenuation in partially saturated rock are affected by the size of the fluid patches, and their fractal dimension. To study this phenomenon, we have developed a wave propagation theory, in which the final partially saturated material is incrementally constructed by adding inclusions in size order into a homogenous frame saturated by a host fluid. We analyze the effects of wave‐induced local fluid flow due to the multi‐scale fluid heterogeneities on wave attributes. The broadband wave anelasticity predicted by the model is strongly affected by the scale range of the heterogeneities and their fractal dimension. The theory was compared with experimental data measured on different rock specimens and the fluid distribution characteristics at different saturations were estimated. Key Points: We present a wave propagation theory for partially saturated rocks with a fractal (self‐similar) distribution of fluid patchesWe analyzed the effects of wave‐induced local fluid flow on seismic attributes due to multi‐scale fluid heterogeneitiesWe estimated variations of the fluid distribution characteristics in partially‐saturated rock samples by tying the data to the low frequency measurements [ABSTRACT FROM AUTHOR]

Tight sandstone reservoirs basically have low porosity and permeability, a complex pore structure and a heterogeneous distribution of immiscible fluids. With the development of theoretical models, it is common to characterize rock properties, i.e., pore structure, microfractures, fluid type and saturation, etc., based on acoustic and electrical properties. We have taken four tight sandstone samples and performed X-ray diffraction and cast thin section analyses. We measure porosity and permeability as well as ultrasonic properties and electrical conductivity at different confining pressures and fluid saturations. These measurements show that the P-wave velocity, P-wave attenuation and conductivity strongly depend on the type and saturation of the fluid and the microstructure of the rock. We propose a combined acoustic-electrical model based on the concept of equivalent medium and on the double porosity, patchy saturation and squirt flow models. We then create rock physics templates calibrated with wellbore log data to estimate fluid saturation and equant and soft porosities, which are well corroborated by gas production reports. This work demonstrates the link between combined acoustic-electrical responses and rock properties and provides an effective approach for applications in reservoirs. [ABSTRACT FROM AUTHOR]

The exploration and exploitation of shale oil is an important aspect in the oil industry. Seismic properties and well‐log data are essential to establish wave‐propagation models. Specifically, the description of wave dispersion and attenuation under complex geological conditions needs proper lithological and petrophysical information. This complex physical mechanism has to be considered if a traditional modeling approach is adopted. In this sense, machine learning (ML) techniques provide new possibilities for this purpose. We compare two deep‐neural‐network (DNN)‐based wave propagation models. In the first (pure data‐driven), a DNN is trained to connect seismic attributes, such as wave velocities, to multivariate functions of rock‐physics properties. By training DNNs with different initial parameters, the uncertainty of the proposed method can be quantified. The second method assumes the form of the wave equations. Then, the elastic constants of the constitutive relations are predicted by DNNs. The resulting dynamical equations describe the dispersion and attenuation and wavefield simulations can be performed to obtain more information. On the basis of a test, the two kinds of wave‐propagation models yield acceptable estimations of the seismic properties, with the second approach showing a broader application because the DNN is trained without S wave data. The methodologies illustrate that the new wave‐propagation model based on ML has high precision and can be general in terms of rheological description. Plain Language Summary: We develop a model to estimate the underground conditions, based on two machine‐learning techniques by using measurement data as input. The first uses pure data‐driven surrogate models, while the second is based on the classical wave propagation model in fluid‐saturated porous medium proposed by Biot, where deep neural networks predict the elastic coefficients so that the theoretical seismic properties match the actual measurements. The two models are tested on the basis of data from five wells located in a shale‐oil reservoir area. Compared with the pure data‐driven model, the wave‐equation method may be used to predict more reservoir properties. Key Points: Machine‐learning methods are proposed to drive wave propagation based on seismic dataOptimal prediction results of seismic attributes are obtained by feeding rock‐physics properties into the trained modelsThe proposed method has the potential to obtain additional physical quantities and shows a broad application prospect [ABSTRACT FROM AUTHOR]

Regularization is effective in mitigating the ill-condition existing in inverse problems. With respect to the ill-conditioned prestack seismic inversion, regularization aims to stabilize the multiple inverted results and, essentially, reconstruct structural features of subsurface parameter (model) as realistic as possible. Among variants of regularization method, Markov random field (MRF) is an effective approach in formulating prior constraint. However, standard MRF-based or other methods often require prior knowledge of the structural features of desired models, e.g., smoothness, blockiness, and sparsity, after which the prior constraint is formulated. Therefore, such a model-driven regularization method lacks applicability to the cases with geological complexity or limited prior knowledge. In this article, we propose a data-driven regularization scheme for prestack seismic inversion. The MRF-based constraints formulated by multiple orders are quantitatively integrated into the inversion procedure driven by seismic data. In order to endow the method with high adaptation to geological complexity, we iteratively adjust the regularization parameters of multiple orders via the maximum likelihood estimator. Besides, we incorporate the multivariate Gaussian distribution among elastic parameters into the model update/perturbation in fast simulated annealing, by which the objective function is optimized while the multiple results are correlated and stabilized. Synthetic tests indicate that the proposed method is capable of revealing structural details and achieving multiple results with less uncertainty. Field application provides further validation, wherein the results distinctly reveal structural details within the target formation. [ABSTRACT FROM AUTHOR]

In the field of Granular Computing (GrC), feature selection is an attractive task. Some basics of GrC such as information granulation and granularity have well guided the explorations of feature selection technique. Nevertheless, some challenges to perform feature selection such as high computational costs of repeating information granulation and multi-granularity structure in the process of searching qualified features may also arise. In this study, to improve the efficiency and effectiveness of feature selector, a novel framework named Glee : Granularity fiLter for fEature sElection , is reported. Firstly, the value of granularity related to each feature is calculated. Secondly, all features are reordered by the corresponding values of granularity. Finally, following such a derived sequence, features will be added into the selection pool one by one until the termination condition is achieved. Glee can not only eliminate the iterative calculations of information granulation in the whole process of selecting, but also provide sequence of features which may be insensitive to data perturbation. It should also be emphasized that Glee is a general framework, and most existing termination conditions to feature selection can be embedded into it. To validate the effectiveness of Glee , it is compared with several well-established feature selection schemes in elapsed time of selecting features, stability of selected features and classification performance. Experimental results over 20 UCI datasets with both raw features and 3 different ratios of noisy features demonstrate that our framework is superior as it yields better robustness with satisfactory elapsed time. [ABSTRACT FROM AUTHOR]

Understanding the effect that multiscale heterogeneities have on the wave responses of rocks at different frequencies is essential in the interpretation of seismic data. In fact, the behaviors of ultrasonic and seismic waves differ because the experiments involve different spatial scales. Then, a solution is to apply a theory that establishes a relation between the wave properties at different frequency bands considering a size range of heterogeneities. To investigate this problem, we have measured the compressional wave (P-wave) anelasticity (velocity and attenuation) of tight reservoir rocks at ultrasonic, sonic and seismic frequencies. The wave behavior as a function of porosity or clay content shows a consistent trend. With increasing confining pressure, the effect of porosity on attenuation decreases, while that of clay content gradually becomes important. To interpret the data, we propose a double-fractal poroelasticity model by incorporating the self-similarity characteristics of cracks and clay minerals. The comparison between the experimental data and model results reveals the fractality of the clay inclusions and cracks, with radii range of [10−6, 10−1.5] m and [10−6, 10−3.1] m, respectively, which is responsible for the anelastic behavior of the waves on a wide frequency band. [ABSTRACT FROM AUTHOR]

SUMMARY: We consider surface-wave propagations at an interface separating a fluid layer and a double-porosity medium embedded with cracks. The theory is based on a generalization of the Biot-Rayleigh model from spherical cavities to penny-shaped cracks randomly embedded into a host medium, where mesoscopic local fluid flow (LFF) plays an important role. We derive closed-form dispersion equations of surface waves, based on potentials and suitable boundary conditions (BCs), to obtain the phase velocity and attenuation by using numerical iterations. Two special cases are considered by letting the thickness of the fluid (water) layer to be zero and infinity. We obtain pseudo-Rayleigh and pseudo-Stoneley waves for zero and infinite thickness and high-order surface modes for finite nonzero thickness. Numerical examples confirm that the LFF affects the propagation at low frequencies, causing strong attenuation, whereas the impact of BCs is mainly observed at high frequencies, due to the propagation of slow wave modes. The crack density mainly affects the level of attenuation, whereas the aspect ratio the location of the relaxation peak. The fundamental mode undergoes a significant velocity dispersion, whose location moves to low frequencies as the thickness increases. In all cases, there also exist two slower surface modes that resemble the two slow body waves, only present for sealed BCs. [ABSTRACT FROM AUTHOR]

The prediction of the pore geometrical properties is important in the exploration and development of tight-sandstone hydrocarbon reservoirs. To investigate this topic, we have measured the porosity, permeability, P- and S-wave velocities, electrical conductivity, and axial and radial strains as a function of differential (confining minus pore) pressure of tight-sandstone samples, collected from the Zhongjiang gas field of Sichuan, in West China. The results show that the closure of cracks with pressure highly affects these properties. Then, we propose a multiphase reformulated differential effective-medium (R-DEM) model that employs the unified pore geometry (the same pores or cracks with different aspect ratios and volume fractions) for both elastic and electrical modeling. The model gives the pressure-dependence of the P- and S-wave velocities and electrical conductivity, and the experimental porosity and static moduli are used as constraints to estimate the pore geometry. The model describes the elastic properties of sandstones saturated with nitrogen gas, and the electrical conductivity when the pore fluid is brine. The prediction of the wet-rock S-wave velocities is less accurate, due to the presence of shear stiffening and weakening effects. Furthermore, we compare the results with those of the joint elastic-electrical inversion by using the dynamic instead of the static stiffness modulus. The results show that the latter provides a better agreement between theory and experiment. Subsequently, we show that the pore geometry estimated from the elastic or the electrical measurements separately (unjoint inversion) present discrepancies, indicating that a joint inversion is required. The published experimental data are also used to illustrate the model, and the results are satisfactory. • We have measured the porosity, velocities, electrical conductivity, and axial and radial strains of tight sandstones. • The data are interpreted by a multiphase reformulated differential effective-medium modelwith a unified pore geometry. • The results show that the proposed model successfully explains those properties. [ABSTRACT FROM AUTHOR]

Attribute reduction is a critical topic in the field of rough set theory. Currently, to further enhance the stability of the derived reduct, various attribute selectors are designed based on the framework of ensemble selectors. Nevertheless, it must be pointed out that some limitations are concealed in these selectors: (1) rely heavily on the distribution of samples; (2) rely heavily on the optimal attribute. To generate the reduct with higher stability, a novel beam-influenced selector (BIS) is designed based on the strategies of random partition and beam. The scientific novelty of our selector can be divided into two aspects: (1) randomly partition samples without considering the distribution of samples; (2) beam-based selections of features can save the selector from the dependency of the optimal attribute. Comprehensive experiments using 16 UCI data sets show the following: (1) the stability of the derived reducts may be significantly enhanced by using our selector; (2) the reducts generated based on the proposed selector can provide competent performance in classification tasks. [ABSTRACT FROM AUTHOR]

Reservoir parameters, such as porosity, saturation, and clay volume, are directly related to the hydrocarbon-bearing properties of potential reservoirs, of which estimation is one of the ultimate goals of data processing for seismic exploration. However, the complex pore structure of tight sandstone presents difficulty in evaluating reservoir properties. This study proposes a novel reservoir parameter inversion method intended for tight sandstone reservoirs. The method builds the forward operator by combining the rock physics model and the seismic reflectivity equation, enabling the direct inversion of reservoir parameters from observed seismic data. In particular, the (sand- and clay-related) pore aspect ratios of rock frame are treated as internal variables, which are iteratively updated during the inversion process. The varying aspect ratios address the complex pore structure, which facilitates the improved accuracy in rock physics modeling of tight sandstone reservoirs. Besides, the Bayesian inversion constrained by the prior Gaussian mixture model considers the complex prior distributions of reservoir parameters in different lithofacies, which stabilizes the inversion process and achieves the optimal solution. The method is tested by the synthetic data which exhibits less uncertainty. The application to the field data from tight sandstone gas reservoirs in southwestern China demonstrates the method has the good capability of indicating the gas-bearing areas. • Seismic rock physics inversion method is proposed for tight sandstone reservoirs. • Reservoir property parameters can be directly inverted from seismic data. • Varying pore aspect ratio describes the complex pore structures in the inversion. • The estimated reservoir parameters can be good indicators for gas-bearing areas. [ABSTRACT FROM AUTHOR]

S-wave attenuation in porous media is affected by the presence and properties of saturating fluids. We measured the ultrasonic S-wave velocities of three types of tight rocks (siltstone, dolomite, and sandstone) under partial fluid saturation conditions using the pulse-transmission technique. The S-wave attenuation is estimated by the centroid frequency shift and spectral-ratio methods. The fluid-saturated test results show that the attenuation of most water-saturated dolomites is stronger than that of gas- or oil-saturated dolomites, whereas no apparent relationship exists between attenuation and fluid type in siltstone. The attenuation of siltstone and dolomite increases with increasing porosity and permeability, as well as with clay content for siltstone with clay contents less than 6%. The maximum attenuation of rocks partially saturated with gas and water occurs at high water saturation (55%–100%) in most siltstones. The attenuation of most dolomites shows an increasing trend with water saturation, but remains nearly unchanged in partially saturated sandstone. The attenuation of rocks partially saturated with oil and water is strongest at the partial saturation state in siltstone, but remains essentially constant with water saturation in dolomite. A squirt flow model is used to predict the S-wave attenuation of the fluid-saturated sample. Based on rock property and microstructure analyses, wave attenuation in the fluid-saturated rocks measured in this study can be explained by squirt flow mechanisms and the scattering effect owing to heterogeneities of water patches and grain clusters. [ABSTRACT FROM AUTHOR]

Low porosity-permeability structures and microcracks, where gas is produced, are the main characteristics of tight sandstone gas reservoirs in the Sichuan Basin, China. In this work, an analysis of amplitude variation with offset (AVO) is performed. Based on the experimental and log data, sensitivity analysis is performed to sort out the rock physics attributes sensitive to microcrack and total porosities. The Biot–Rayleigh poroelasticity theory describes the complexity of the rock and yields the seismic properties, such as Poisson's ratio and P-wave impedance, which are used to build rock-physics templates calibrated with ultrasonic data at varying effective pressures. The templates are then applied to seismic data of the Xujiahe formation to estimate the total and microcrack porosities, indicating that the results are consistent with actual gas production reports. [ABSTRACT FROM AUTHOR]

The rheological models of Lomnitz and Jeffreys have been widely used in earthquake seismology (to simulate a nearly constant Q medium) and to describe the creep and relaxation behavior of rocks as a function of time. Other similar models, such as those of Becker, Scott Blair and Kolsky, show similar properties, particularly the Scott Blair model describes a perfectly constant Q as a function of frequency. We first give a historical overview of the main scientists and the development and versions of the various models and priorities of discovery. Then, we clarify the relationship between the different versions of these models in terms of mathematical expressions of the complex modulus and calculate the phase velocity and quality factor Q as a function of frequency, illustrating the various special cases. In addition, we give useful hints for the numerical calculation of these moduli, which include special cases of the hypergeometric function. [ABSTRACT FROM AUTHOR]

Petrophysics and fluid-flow simulations are used to build a realistic pre- and post- CO 2 injection geological model for the Utsira formation at the Sleipner field, and the Fourier pseudospectral method is employed to compute synthetic seismograms. The methodology can be used to perform a seismic sensitivity analysis for the detection of carbon dioxide. We built the model solely based on the porosity and clay content of the formations with the aid of fluid-flow and seismic simulations. The pressure map before the injection is assumed to be hydrostatic for which a reference porosity map is defined. The injection induces pore pressure variations and partial saturation, which affect the poroelastic properties and hence the associated seismic response. A proper porosity–permeability–clay content relation is one of the key factors since permeability determines the preferential flow directions and the distribution of the CO 2 plume. The petrophysical model is based on a shaly sandstone (or sandy shale) to represent the caprock, Utsira Sand and embedded mudstone layers. The composite permeability (anisotropic) is analogous to the inverse electrical resistance model. Gas viscosity depends on pressure and temperature. The P- and S-wave velocities are obtained from Gassmann equation (pre-injection) and White's mesoscopic model (post-injection), which also yields the P-wave quality factor in the case of partial (patchy) saturation. To model a realistic situation, we implement a fractal variation of the porosity and clay content, based on the von Kármán correlation function. We then compare the real and synthetic seismograms (pre-injection and post-injection) and show the effect of attenuation on the seismic data. Simulations and real data show a remarkable match. [ABSTRACT FROM AUTHOR]

Mesoscopic P-wave attenuation in layered, partially saturated thermo-poroelastic media is analyzed by combining the theories of Biot poroelasticity and Lord–Shulman thermoelasticity (BLS). The attenuation is quantified by estimating the quality factor Q. The mesoscopic attenuation effect, commonly referred to as wave-induced fluid flow (WIFF), is the process that converts fast compressional and shear waves into slow diffusive Biot waves at mesoscopic heterogeneities larger than the pore scale, but much smaller than the dominant wavelengths. This effect was first modeled in White's isothermal theory by quantifying the seismic response of a periodic sequence of planar porous layers that are alternately saturated with gas or water. This work presents a numerical extension of White's theory for the non-isothermal case in this type of sequence. For this purpose, an initial-boundary-value problem (IBVP) for the BLS wave propagation equations is solved using the finite element method, where the particle velocity field is recorded at uniformly distributed receivers. The quality factor is estimated using spectral-ratio and frequency-shift methods. The Q-estimates show that thermal effects influence the attenuation of the P-wave and the velocity dispersion compared to the isothermal case. [ABSTRACT FROM AUTHOR]

We study the anelastic properties (attenuation and velocity dispersion) of surface waves at an interface between a finite water layer and a porous medium described by Biot theory including the frequency-dependent effects due to mesoscopic flow. A closed-form dispersion equation is derived, based on potential functions and open and sealed boundary conditions (BC) at the interface. The analysis indicates the existence of high-order surface modes for both BCs and a slow true surface mode only for sealed BC. The formulation reduces to two particular cases in the absence of water and with infinite-thickness water layer, with the presence of pseudo-versions of Rayleigh and Stoneley waves. The mesoscopic flow affects the propagation of all the pseudo-surface waves, causing significant velocity dispersion and attenuation, whereas the effect of the BC is mainly evident at high frequencies, due to the presence of the slow Biot wave. The mesoscopic-flow peak moves to low frequencies as the thickness of the water layer increases. In all cases, the true surface wave resembles the slow P2 wave, and is hardly affected by the flow. [ABSTRACT FROM AUTHOR]

We simulate variations in the P- and S-wave velocities due to CO2 injection in basalt, caused by water replacement and mineralization in the form of carbonate cements. Carbonization can be monitored with seismic data on the basis of changes in velocity. We consider basalts composed of (Fe, Ca and Mg) minerals mainly, and the pore space is assumed to be initially saturated with water. The mineralization is based on a model that estimates the volume of precipitated cement and resulting porosity loss, and the velocities as a function of injection time are calculated with a patchy cement model. In the example, there are two stages: 1 week of CO2 injection and 29 weeks of frame cementation. After 1 week, water has been replaced by CO2, where density and P-wave velocity decrease, and cementation implies an increase in bulk density, P-wave velocity, whereas porosity and surface area are reduced. To our knowledge there are no models relating the effects of carbon mineralization on seismic properties. The present model can be applied to other rocks, where CO2 injection induces mineralization and storage. [ABSTRACT FROM AUTHOR]

There is a mathematical analogy between the poroelastic and thermoelastic behavior of the compressional P wave, whose dissipation is due to the coupling between the elastic deformation and the phenomenon of pressure and heat diffusion, represented by Darcy's law and heat conduction, respectively. This attenuation effect is more pronounced in heterogeneous media, where conversion of the fast P wave to the slow (Biot) and thermal diffusive modes occurs at material interfaces. Specifically, the problem is to obtain the P-wave properties of a porous medium due to temperature gradients between the solid and fluid phases. Then, we consider a simplified one-dimensional porous medium and obtain the quality factor, Q, and phase velocity as a a function of frequency, based on an isostress condition and using Gassmann equation and the Kramers Kronig relations.The model allows for the incorporation of a relaxation time to simulate a proper wave-like behavior at high frequencies, avoiding in this way infinite velocities. Moreover, we perform a complete analysis varying the different parameters, namely, the heat conduction, the specific heat, the thermal expansion, the types of solid and fluid and the pore size. [ABSTRACT FROM AUTHOR]

We obtain the amplitude and energy reflection coefficients of seismic waves in porous media with penny-shaped inclusions, based on the generalized Biot-Rayleigh model that takes into account the attenuation due to mesoscopic local fluid flow (LFF). We consider two cases, including a contact between two porous media having either different fluids (gas–water contact) or crack density and aspect ratio, as well as a water half-space overlying a porous medium, and study the frequency-dependent reflection-transmission (scattering) coefficients for open- and sealed-pore boundary conditions. Our examples show that the LFF mechanism mainly reduces the reflection coefficients (amplitude and energy) at the gas–water contact and at a water–porous medium interface for frequencies less than 10 kHz, due to the fact that the velocity in the lower medium decreases. For the latter case, if the fluid is gas, the LFF effect becomes only important at frequencies between 0.0001 and 10 Hz for the open-pore case. This is due to the fact that the acoustic impedance contrast between water and gas is high. At frequencies less than 0.0001 Hz, the interface is equivalent to a water–elastic medium one, and hence the results are the same as those of the sealed-pore case. Moreover, the crack density and aspect ratio affect the mesoscopic attenuation and relaxation frequency, and therefore the reflection coefficients. [ABSTRACT FROM AUTHOR]

We simulate the effects of diagenesis, cementation and compaction on the elastic properties of shales and sandstones with four different petro-elastic theories and a basin-evolution model, based on constant heating and sedimentation rates. We consider shales composed of clay minerals, mainly smectite and illite, depending on the burial depth, and the pore space is assumed to be saturated with water at hydrostatic conditions. Diagenesis in shale (smectite/illite transformation here) as a function of depth is described by a fifth-order kinetic equation, based on an Arrhenius reaction rate. On the other hand, quartz cementation in sandstones is based on a model that estimates the volume of precipitated quartz cement and the resulting porosity loss from the temperature history, using an equation relating the precipitation rate to temperature. Effective pressure effects (additional compaction) are accounted for using the Athy equation and the Hertz–Mindlin model. The petro-elastic models yield similar seismic velocities, despite the different levels of complexity and physics approaches, with increasing density and seismic velocities as a function of depth. The methodology provides a simple procedure to obtain the velocity of shales and sandstones versus temperature and pressure due to the diagenesis-cementation-compaction process. [ABSTRACT FROM AUTHOR]

We present a novel numerical upscaling technique for modeling the wave response of gas-hydrate bearing sediments composed of a rock frame, gas-hydrate and water, where the hydrate consists of ice-like lattice of water molecules with methane trapped inside. These sediments are highly heterogeneous at mesoscopic scales, much smaller than the wavelength but much larger than the pore size, inducing substantial seismic wave attenuation and dispersion due to mode conversions. The proposed numerical upscaling procedure simulates the wave-induced fluid-flow loss mechanism by computing an average effective viscoelastic medium having the same behavior of the original sediment. The method determines the complex stiffness coefficients associated with the viscoelastic medium by solving numerically boundary value problems formulated in the space-frequency domain, representing compressibility and shear experiments. The procedure is applied to composite media with regions of different amounts of hydrate with patchy or periodic-layer distributions, which define an anisotropic effective viscoelastic medium, respectively. The examples demonstrate that variations in hydrate content induce strong attenuation and dispersion effects on seismic waves due to the mesoscopic loss mechanism. [ABSTRACT FROM AUTHOR]

We study the wave anelasticity (attenuation and velocity dispersion) of a periodic set of three flat porous layers saturated by two immiscible fluids. The fluids are very dissimilar in properties, namely gas, oil, and water, and, at most, three layers are required to study the problem from a general point of view. The sequence behaves as viscoelastic and transversely isotropic (VTI) at wavelengths much longer than the spatial period. Wave propagation causes fluid flow and slow P modes, inducing anelasticity. The fluids are characterized by capillary forces and relative permeabilities, which allow for the existence of two slow modes and the presence of dissipation, respectively. The methodology to study the physics is based on a finite-element uspcaling approach to compute the complex and frequency-dependent stiffnesses of the effective VTI medium. The results of the experiments indicate that there is higher dissipation and anisotropy compared to the widely used model based on an effective fluid that ignores the effects of surface tension (capillarity) and viscous flow interference between the two fluid phases. [ABSTRACT FROM AUTHOR]

We compare the exact normal-incidence PP reflection coefficient [Geertsma–Smit expression] to approximations reported by several authors, based on open-pore boundary conditions at a plane interface between two porous media. The approximations correspond to low frequencies. Two of them are derived from the low-frequency Biot theory below the Biot characteristic frequency, but the results show significant differences much below the Biot frequency. Then, we extend the Geertsma–Smit equations by including the high-frequency viscodynamic operator (i.e., the full-frequency range Biot theory), showing that there are additional substantial differences at the high-frequency range. Use of this latter expression is required to honor the physics in the whole frequency range. We further generalize the Geertsma–Smit equations to the case of general boundary conditions other than the open-pore interface. At the seismic band, it is shown that the lossless (elastic) expression based on the Gassmann P-wave impedance is the reflection coefficient to use for practical applications. It is inferred that interpretations based on the frequency dependency of these approximations can be misleading, since this dependency does not provide a suitable description of the physics. [ABSTRACT FROM AUTHOR]