Search

Poroelastic coupling between fractures and the surrounding rock is important to numerous applications in geosciences. We measure the in‐situ fluid pressure and local strain response of a fractured carbonate sample to hydrostatic pressure oscillations. A linear poroelastic model that represents the rock sample is parameterized using X‐ray imaging and ultrasonic wave transmission measurements. The numerical solution, based on Biot's quasistatic equations, is consistent with the measured frequency dependent dispersion of the apparent bulk modulus of the background matrix and the in‐situ pore pressure response, which is caused by fluid pressure diffusion from the compliant fractures into the stiffer matrix. The observed fluid pressure diffusion is causally related to the numerically quantified intrinsic attenuation at seismic frequencies, which is a major contributor to the dissipation of seismic waves. Our analysis supports the use of a simple approximation of fractures as compliant and planar inclusions in numerical simulations based on linear poroelasticity. Plain Language Summary: Fractures control the flow of fluids through rocks as well as their mechanical properties. Finding ways to accurately simulate coupled hydro‐mechanical processes in fractured rock is important to a variety of applications in geosciences (e.g., subsurface storage of carbon dioxide or enhanced geothermal energy extraction). Physics‐based simulations require accurate parameterization and validation against experiments. In our experiment on a fluid saturated fractured rock sample, we applied an oscillating confining pressure to the sample and measured the corresponding deformation and the change in the pore fluid pressure in a fracture and the porous matrix. By adjusting the frequency of the oscillations, we observed a divergence in the pore pressure amplitude in the fracture and the matrix, which is a consequence of flow from the fracture into the porous matrix becoming restricted at elevated frequencies. The laboratory measurements were in close agreement with the results of our simulations, which were based on a simplified model of the rock sample. The outcome of our work supports the use of a widely applied approximation of fractures as simple planar inclusions in numerical simulations based on linear poroelasticity. Key Points: We observe the poroelastic coupling of fractures to the rock matrix in in‐situ fluid pressure measurements during stress oscillationsThe geometrically complex fractures can be modeled as compliant and planar poroelastic inclusionsThe numerically quantified intrinsic seismic (<100 Hz) attenuation is due to fluid pressure diffusion, which is experimentally observed [ABSTRACT FROM AUTHOR]

Seismic inversion of amplitude versus offset (AVO) data in viscoelastic media can potentially provide high-resolution subsurface models of seismic velocities and attenuation from offset/angle seismic gathers. P - and S -wave quality factors (Q), whose inverse represent a measure of attenuation, depend on reservoir rock and pore fluid properties, in particular, saturation, permeability, porosity, fluid viscosity and lithology; however, these quality factors are rarely taken into account in seismic AVO inversion. For this reason, in this work, we aim to integrate quality factors derived from physically based models in AVO inversion by proposing a gradient descent optimization-based inversion technique to predict the unknown model properties (P - and S -wave velocities, the related quality factors and density). The proposed inversion minimizes the non-linear least-squares misfit with the observed data. The optimal solution is iteratively obtained by optimizing the data misfit using a second-order limited-memory quasi-Newton technique. The forward model is performed in the frequency–frequency-angle domain based on a convolution of broad-band signals and a linearized viscoelastic frequency-dependent AVO (FAVO) equation. The optimization includes the adjoint-state-based gradients with the Lagrangian formulation to improve the efficiency of the non-linear seismic FAVO inversion process. The inversion is tested on synthetic seismic data, in 1-D and 2-D, with and without noise. The sensitivity for seismic quality factors is evaluated using various rock physics models for seismic attenuation and quality factors. The results demonstrate that the proposed inversion method reliably retrieves the unknown elastic and an-elastic properties with good convergence and accuracy. The stability of the inverse solution especially seismic quality factors estimation relies on the noise level of the seismic data. We further investigate the uncertainty of the solution as a function of the variability of the initial models. [ABSTRACT FROM AUTHOR]

Wave‐induced fluid pressure diffusion (FPD) represents an important mechanism of seismic energy dissipation in fractured media. The associated effects on wave propagation are typically studied considering idealized fracture geometries. Here, we study fracture‐geometry‐related effects on FPD by numerically computing the frequency‐dependent and angle‐dependent seismic velocity and attenuation on models having fractures of realistic geometries. The geometry of the models is derived from microcomputed tomography images of a fractured Berea sandstone. By comparing the numerical results with those for an equivalent thin‐planar‐layer analytical model, we isolate fracture‐geometry effects. We found that discrepancies on the anisotropic behavior of P and S waves with respect to the simple analytical model are small except for the S wave attenuation. This is associated with the pressure gradients induced by S waves in fractures exhibiting a mild curvature. Part of this dissipation occurs inside the fracture, parallel to its walls, and is thus controlled by its permeability, which points to a possible perspective of inferring fracture hydraulic properties from S waves attenuation. Plain Language Summary: The attenuation and velocity dispersion of seismic waves propagating in rocks can be used to infer and to characterize rock heterogeneities and fluid content. Fluid pressure diffusion is an important cause of such attenuation and dispersion and can be estimated using analytical and numerical solutions based on simple representations of fractures. A broadly used approach is to represent fractures as thin‐planar poroelastic layers. However, the effects of complex fracture geometry, such as rough and curved walls and contact areas, remain largely unexplored. In this study, we numerically calculate the seismic energy dissipation due to fluid pressure diffusion in a medium containing a fracture of realistic geometry. We compare these results with those of a thin‐planar layer to study the limitations of the simple model. We show that the S wave response for normal incidence can be strongly attenuated in part due to fluid pressure diffusion occurring inside the fracture and parallel to its walls triggered by a mild fracture curvature. Such effect cannot be accounted for by a thin‐planar model. This points to the potential of estimating hydraulic fracture properties from the S wave attenuation. Key Points: The anisotropic velocity of P and S waves traveling across real fractures can be reproduced using a planar‐thin‐layer modelThe attenuation of S waves is highly affected by a squirt‐type flow prevailing inside fractures with mild curvatureOur observations can help improve the interpretation and inversion of mechanical and hydraulic properties of fractures from seismic data [ABSTRACT FROM AUTHOR]

Biot's equations describe the physics of hydromechanically coupled systems establishing the widely recognized theory of poroelasticity. This theory has a broad range of applications in Earth and biological sciences as well as in engineering. The numerical solution of Biot's equations is challenging because wave propagation and fluid pressure diffusion processes occur simultaneously but feature very different characteristic time scales. Analogous to geophysical data acquisition, high resolution and three dimensional numerical experiments lately redefined state of the art. Tackling high spatial and temporal resolution requires a high‐performance computing approach. We developed a multi‐ graphical processing units (GPU) numerical application to resolve the anisotropic elastodynamic Biot's equations that relies on a conservative numerical scheme to simulate, in a few seconds, wave fields for spatial domains involving more than 1.5 billion grid cells. We present a comprehensive dimensional analysis reducing the number of material parameters needed for the numerical experiments from ten to four. Furthermore, the dimensional analysis emphasizes the key material parameters governing the physics of wave propagation in poroelastic media. We perform a dispersion analysis as function of dimensionless parameters leading to simple and transparent dispersion relations. We then benchmark our numerical solution against an analytical plane wave solution. Finally, we present several numerical modeling experiments, including a three‐dimensional simulation of fluid injection into a poroelastic medium. We provide the Matlab, symbolic Maple, and GPU CUDA C routines to reproduce the main presented results. The high efficiency of our numerical implementation makes it readily usable to investigate three‐dimensional and high‐resolution scenarios of practical applications. Key Points: We present the dimensional analysis of Biot's equationsWe perform three dimensional numerical simulations of poroelastic wave propagationWe propose a multi‐graphical processing units implementation resolving over 1.5 billion grid cells in a few seconds with near ideal parallel efficiency [ABSTRACT FROM AUTHOR]

Quantitatively assessing seismic attenuation caused by fluid pressure diffusion (FPD) in partially saturated rocks is challenging because of its sensitivity to the spatial fluid distribution. To address this challenge we performed depressurization experiments to induce the exsolution of carbon dioxide from water in a Berea sandstone sample. In a first set of experiments we used medical X‐ray computed tomography (CT) to characterize the fluid distribution. At an equilibrium pressure of approximately 1 MPa and applying a fluid pressure decline rate of approximately 0.6 MPa per minute, we allowed a change in saturation of less than 1%. The gas was heterogeneously distributed along the length of the sample, with most of the gas exsolving near the sample outlet. In a second set of experiments, at the same pressure and temperature, following a very similar exsolution protocol, we measured the frequency dependent attenuation and modulus dispersion between 0.1 and 1,000 Hz using the forced oscillation method. We observed significant attenuation and dispersion in the extensional and bulk deformation modes, however, not in the shear mode. Lastly, we use the fluid distribution derived from the X‐ray CT as an input for numerical simulations of FPD to compute the attenuation and modulus dispersion. The numerical solutions are in close agreement with the attenuation and modulus dispersion measured in the laboratory. Our approach allows for accurately relating attenuation and dispersion to the fluid distribution, which can be applied to improving the seismic monitoring of the subsurface. Key Points: Measurements of seismic wave attenuation and dispersion in a partially saturated sandstonePartial saturation was achieved by exsolution of carbon dioxide and was characterized with X‐ray computed tomographyFluid distribution was used to numerically simulate attenuation and dispersion due to fluid pressure diffusion [ABSTRACT FROM AUTHOR]

While hydro-mechanical coupling in rocks is generally well understood, exotic rock poroelastic responses—such as unexpected dependence to fluid diffusion time and low skeleton moduli—have been reported. Hydro-mechanical coupling, or poroelasticity, explains how fluid-saturated rocks respond to either confining or fluid pressure variations. This coupling is usually inferred from the apparent mechanical and hydraulic properties: mechanical properties determine the strain level experienced by the rock when submitted to pressures at a timescale when fluid pressure is equilibrated, which is in turn ruled by hydraulic properties. However, the coupling between properties might not always be straightforward, particularly for rocks in which two distinct families of pore types coexist: spherical pores and cracks. Comparing it with reported laboratory data sets on pressure-dependent hydraulic and elastic properties in sandstones of different porosity confirms that the well-known simple concepts of networks in parallel apply and yield opposite dependencies for the two properties on the two pore families. Because hydro-mechanical coupling implies that the two properties—that depend differently on the pore families—will be interdependent, we further apply the same concept of parallel network. It yields that, although under apparent drained conditions, typical poroelasticity experiments could underestimate the rock compressibility |${C_{\mathrm{ bp}}}$|⁠ , measured as a response to fluid pressure variation, and underestimate the related skeleton (or unjacketed) bulk modulus |${K_\mathrm{ s}} = \ 1/{C_\mathrm{ s}}$|⁠. [ABSTRACT FROM AUTHOR]

Understanding the properties of cracked rocks is of great importance in scenarios involving CO2 geological sequestration, nuclear waste disposal, geothermal energy, and hydrocarbon exploration and production. Developing noninvasive detecting and monitoring methods for such geological formations is crucial. Many studies show that seismic waves exhibit strong dispersion and attenuation across a broad frequency range due to fluid flow at the pore scale known as squirt flow. Nevertheless, how and to what extent squirt flow affects seismic waves is still a matter of investigation. To fully understand its angle- and frequency-dependent behavior for specific geometries, appropriate numerical simulations are needed. We perform a three-dimensional numerical study of the fluid–solid deformation at the pore scale based on coupled Lamé–Navier and Navier–Stokes linear quasistatic equations. We show that seismic wave velocities exhibit strong azimuth-, angle- and frequency-dependent behavior due to squirt flow between interconnected cracks. Furthermore, the overall anisotropy of a medium mainly increases due to squirt flow, but in some specific planes the anisotropy can locally decrease. We analyze the Thomsen-type anisotropic parameters and adopt another scalar parameter which can be used to measure the anisotropy strength of a model with any elastic symmetry. This work significantly clarifies the impact of squirt flow on seismic wave anisotropy in three dimensions and can potentially be used to improve the geophysical monitoring and surveying of fluid-filled cracked porous zones in the subsurface. [ABSTRACT FROM AUTHOR]

We explore the impact of roughness in crack walls on the P wave modulus dispersion and attenuation caused by squirt flow. For that, we numerically simulate oscillatory relaxation tests on models having interconnected cracks with both simple and intricate aperture distributions. Their viscoelastic responses are compared with those of models containing planar cracks but having the same hydraulic aperture as the rough wall cracks. In the absence of contact areas between crack walls, we found that three apertures affect the P wave modulus dispersion and attenuation: the arithmetic mean, minimum aperture, and hydraulic aperture. We show that the arithmetic mean of the crack apertures controls the effective P wave modulus at the low‐ and high‐frequency limits, thus representing the mechanical aperture. The minimum aperture of the cracks tends to dominate the energy dissipation process and, consequently, the characteristic frequency. An increase in the confining pressure is emulated by uniformly reducing the crack apertures, which allows for the occurrence of contact areas. The contact area density and distribution play a dominant role in the stiffness of the model, and in this scenario, the arithmetic mean is not representative of the mechanical aperture. On the other hand, for a low percentage of minimum aperture or in the presence of contact areas, the hydraulic aperture tends to control the characteristic frequency. Analyzing the local energy dissipation, we can more specifically visualize that a different aperture controls the energy dissipation process at each frequency, which means that a frequency‐dependent hydraulic aperture might describe the squirt flow process in cracks with rough walls. Key Points: We solve the quasi‐static linearised Navier‐Stokes equations coupled to elasticity equationsSeismic attenuation due to squirt‐flow is strongly affected by the roughness of the crack wallsThe minimum and the hydraulic apertures significantly affect the energy dissipation process [ABSTRACT FROM AUTHOR]

In interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface‐coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi‐static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi‐static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex‐valued, frequency‐dependent stress and strain fields. An energy‐based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy‐based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P‐wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi‐static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations. [ABSTRACT FROM AUTHOR]

The technique of seismic amplitude‐versus‐angle inversion has been widely used to estimate lithology and fluid properties in seismic exploration. The amplitude‐versus‐angle inversion problem is intrinsically ill‐posed and generally stabilized by the use of L2‐norm regularization methods but with drawback of smoothing important boundaries between adjacent layers. In this study, we propose a sparse Bayesian linearized solution for amplitude‐versus‐angle inversion problem to preserve the sharp geological interfaces. In this regard, a priori constraint term with two regularization functions is presented: the sparse constraint regularization and the low‐frequency model information. In addition, to obtain high‐resolution reflectivity estimation, the model parameters decorrelation technique combined with dipole decomposition method is employed. We validate the applicability of the presented method by both synthetic and real seismic data from the Gulf of Mexico. The accuracy improvement of the presented method is also confirmed by comparing the results with the commonly used Bayesian linearized amplitude‐versus‐angle inversion. [ABSTRACT FROM AUTHOR]

Understanding the properties of cracked rocks is of great importance in scenarios involving CO2 geological sequestration, nuclear waste disposal, geothermal energy, and hydrocarbon exploration and production. Developing non-invasive detecting and monitoring methods for such geological formations is crucial. Many studies show that seismic waves exhibit strong dispersion and attenuation across a broad frequency range due to fluid flow at the pore scale known as squirt flow. Nevertheless, how and to what extent squirt flow affects seismic waves is still a matter of investigation. To fully understand its angle- and frequency-dependent behavior for specific geometries appropriate numerical simulations are needed. We perform a three-dimensional numerical study of the fluid-solid deformation at the pore scale based on coupled Lame-Navier and Navier-Stokes linear quasistatic equations. We show that seismic wave velocities exhibit strong azimuth-, angle- and frequency-dependent behavior due to squirt flow between interconnected cracks. We show that the overall anisotropy of a medium mainly increases due to squirt flow but in some specific planes the anisotropy can locally decrease. We analyze the Thomsen-type anisotropic parameters and adopt another scalar parameter which can be used to measure the anisotropy strength of a model with any elastic symmetry. This work significantly clarifies the impact of squirt flow on seismic wave anisotropy in three dimensions and can potentially be used to improve the geophysical monitoring and surveying of fluid-filled cracked porous zones in the subsurface. [ABSTRACT FROM AUTHOR]

Considering poroelastic media containing periodically distributed parallel fractures, we numerically quantify the effects that fractures with variable aperture distributions have on seismic wave attenuation and velocity dispersion due to fluid pressure diffusion (FPD). To achieve this, realistic models of fractures are generated with a stratified percolation algorithm which provides statistical control over geometrical fracture properties such as density and distribution of contact areas. The results are sensitive to both geometrical properties, showing that an increase in the density of contact areas as well as a decrease in their correlation length reduce the effective seismic attenuation and the corresponding velocity dispersion. Moreover, we demonstrate that if equivalent physical properties accounting for the effects of contact areas are employed, simple planar fractures can be used to emulate the seismic response of fractures with realistic aperture distributions. The excellent agreement between their seismic responses was verified for all wave incidence angles and wave modes. [ABSTRACT FROM AUTHOR]

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

Seismic attenuation mechanisms receive increasing attention for the characterization of fractured formations because of their inherent sensitivity to the hydraulic and elastic properties of the probed media. Attenuation has been successfully inferred from seismic data in the past, but linking these estimates to intrinsic rock physical properties remains challenging. A reason for these difficulties in fluid‐saturated fractured porous media is that several mechanisms can cause attenuation and may interfere with each other. These mechanisms notably comprise pressure diffusion phenomena and dynamic effects, such as scattering, as well as Biot's so‐called intrinsic attenuation mechanism. Understanding the interplay between these mechanisms is therefore an essential step for estimating fracture properties from seismic measurements. In order to do this, we perform a comparative study involving wave propagation modelling in a transmission set‐up based on Biot's low‐frequency dynamic equations and numerical upscaling based on Biot's consolidation equations. The former captures all aforementioned attenuation mechanisms and their interference, whereas the latter only accounts for pressure diffusion phenomena. A comparison of the results from both methods therefore allows to distinguish between dynamic and pressure diffusion phenomena and to shed light on their interference. To this end, we consider a range of canonical models with randomly distributed vertical and/or horizontal fractures. We observe that scattering attenuation strongly interferes with pressure diffusion phenomena, since the latter affect the elastic contrasts between fractures and their embedding background. Our results also demonstrate that it is essential to account for amplitude reductions due to transmission losses to allow for an adequate estimation of the intrinsic attenuation of fractured media. The effects of Biot's intrinsic mechanism are rather small for the models considered in this study. [ABSTRACT FROM AUTHOR]

ABSTRACT: We measured the extensional‐mode attenuation and Young's modulus in a porous sample made of sintered borosilicate glass at microseismic to seismic frequencies (0.05–50 Hz) using the forced oscillation method. Partial saturation was achieved by water imbibition, varying the water saturation from an initial dry state up to ∼99%, and by gas exsolution from an initially fully water‐saturated state down to ∼99%. During forced oscillations of the sample effective stresses up to 10 MPa were applied. We observe frequency‐dependent attenuation, with a peak at 1–5 Hz, for ∼99% water saturation achieved both by imbibition and by gas exsolution. The magnitude of this attenuation peak is consistently reduced with increasing fluid pressure and is largely insensitive to changes in effective stress. Similar observations have recently been attributed to wave‐induced gas exsolution–dissolution. At full water saturation, the left‐hand side of an attenuation curve, with a peak beyond the highest measured frequency, is observed at 3 MPa effective stress, while at 10 MPa effective stress the measured attenuation is negligible. This observation is consistent with wave‐induced fluid flow associated with mesoscopic compressibility contrasts in the sample's frame. These variations in compressibility could be due to fractures and/or compaction bands that formed between separate sets of forced‐oscillation experiments in response to the applied stresses. The agreement of the measured frequency‐dependent attenuation and Young's modulus with the Kramers–Kronig relations and additional data analyses indicate the good quality of the measurements. Our observations point to the complex interplay between structural and fluid heterogeneities on the measured seismic attenuation and they illustrate how these heterogeneities can facilitate the dominance of one attenuation mechanism over another. [ABSTRACT FROM AUTHOR]

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

Abstract: Understanding seismic attenuation and modulus dispersion mechanisms in fractured rocks can result in significant advances for the indirect characterization of such environments. In this paper, we study attenuation and modulus dispersion of seismic waves caused by fluid pressure diffusion (FPD) in stochastic 2‐D fracture networks, allowing for a state‐of‐the‐art representation of natural fracture networks by a power law length distribution. To this end, we apply numerical upscaling experiments consisting of compression and shear tests to our samples of fractured rocks. The resulting P and S wave attenuation and modulus dispersion behavior is analyzed with respect to the density, the length distribution, and the connectivity of the fractures. We focus our analysis on two manifestations of FPD arising in fractured rocks, namely, fracture‐to‐background FPD at lower frequencies and fracture‐to‐fracture FPD at higher frequencies. Our results indicate that FPD is sensitive not only to the fracture density but also to the geometrical characteristics of the fracture length distributions. In particular, our study suggests that information about the local connectivity of a fracture network could be retrieved from seismic data. Conversely, information about the global connectivity, which is directly linked to the effective hydraulic conductivity of the probed volume, remains rather difficult to infer. [ABSTRACT FROM AUTHOR]

Seismic wave attenuation is frequency dependent in rocks saturated by two fluid phases and the corresponding scaling behaviour is controlled primarily by the spatial fluid distribution. We experimentally investigate the frequency scaling of seismic attenuation in Berea sandstone saturated with two fluid phases: a liquid phase, water, and a gas phase, air, carbon dioxide or nitrogen. By changing from a heterogeneous distribution of mesoscopic gas patches to a homogeneous distribution of pore scale gas bubbles, we observe a significant steepening of the high-frequency asymptote of the attenuation. A transition from one dominant attenuation mechanism to another, from mesoscopic wave-induced fluid flow to wave-induced gas exsolution dissolution (WIGED), may explain this change in scaling. We observe that the high-frequency asymptote, for a homogenous pore scale gas bubble distribution, scales in accord with WIGED. [ABSTRACT FROM AUTHOR]

Seismic investigations of geothermal reservoirs over the last 20 years have sought to interpret the resulting tomograms and reflection images in terms of the degree of reservoir fracturing and fluid content. Since the former provides the pathways and the latter acts as the medium for transporting geothermal energy, such information is needed to evaluate the quality of the reservoir. In conventional rock physics-based interpretations, this hydro-mechanical information is approximated from seismic velocities computed at the low-frequency (field-based) and high-frequency (labbased) limits. In this paper, we demonstrate how seismic properties of fluid-filled, fractured reservoirs can be modeled over the full frequency spectrum using a numerical simulation technique which has become popular in recent years. This technique is based on Biot's theory of poroelasticity and enables the modeling of the seismic velocity dispersion and the frequency dependent seismic attenuation due to waveinduced fluid flow. These properties are sensitive to key parameters such as the hydraulic permeability of fractures as well as the compressibility and viscosity of the pore fluids. Applying the poroelastic modeling technique to the specific case of a magmatic geothermal system under stress due to the weight of the overlying rocks requires careful parameterization of the model. This includes consideration of the diversity of rock types occurring in the magmatic system and examination of the confining-pressure dependency of each input parameter. After the evaluation of all input parameters, we use our modeling technique to determine the seismic attenuation factors and phase velocities of a rock containing a complex interconnected fracture network, whose geometry is based on a fractured geothermal reservoir in Iceland. Our results indicate that in a magmatic geothermal reservoir the overall seismic velocity structure mainly reflects the lithological heterogeneity of the system, whereas indicators for reservoir permeability and fluid content are deducible from the magnitude of seismic attenuation and the critical frequency at which the peak of attenuation and maximum velocity dispersion occur. The study demonstrates how numerical modeling provides a valuable tool to overcome interpretation ambiguity and to gain a better understanding of the hydrology of geothermal systems, which are embedded in a highly heterogeneous host medium. [ABSTRACT FROM AUTHOR]

Seismic investigations of geothermal reservoirs over the last 20 years have sought to interpret the resulting tomograms and reflection images in terms of the degree of reservoir fracturing and fluid content. Since the former provides the pathways and the latter acts as the medium for transporting geothermal energy, such information is needed to evaluate the quality of the reservoir. In conventional rock physics-based interpretations, this hydro-mechanical information is approximated from seismic velocities computed at the low frequency (field-based) and high frequency (lab-based) limits. In this paper, we demonstrate how seismic properties of fluid-filled, fractured reservoirs can be modeled over the full frequency spectrum using a numerical simulation technique which has become popular in recent years. It is based on Biot's theory of poroelasticity and enables the modeling of the seismic velocity dispersion and the frequency dependent seismic attenuation due to wave-induced fluid flow. These properties are sensitive to key parameters such as the hydraulic permeability of fractures as well as the compressibility and viscosity of the pore fluids. Applying the poroelastic modeling technique to the specific case of a magmatic geothermal system under stress due to the weight of the overlying rocks requires careful parameterization of the model. This includes consideration of the diversity of rock types occurring in the magmatic system and examination of the confining pressure-dependency of each input parameter. After the evaluation of all input parameters, we use our modeling technique to determine the seismic attenuation factors and phase velocities of a rock containing a complex interconnected fracture network, whose geometry is based on a fractured geothermal reservoir in Iceland. Our results indicate that in a magmatic geothermal reservoir the overall seismic velocity structure mainly reflects the lithological heterogeneity of the system, whereas indicators for reservoir permeability and fluid content are deducible from the magnitude of seismic attenuation and the critical frequency at which the peak of attenuation and maximum velocity dispersion occur. The study demonstrates how numerical modeling provides a valuable tool to overcome interpretation ambiguity and to gain a better understanding of the hydrology of geothermal systems, which are embedded in a highly heterogeneous host medium. [ABSTRACT FROM AUTHOR]

ABSTRACT Relating seismic attributes to the characteristics of mesoscopic fractures is inherently challenging, yet these heterogeneities tend to dominate the mechanical and hydraulic properties of the medium. Analytical approaches linking the effects of material properties on seismic attributes, such as attenuation and velocity dispersion, tend to be limited to simple geometries, low fracture densities, and/or non-interacting fractures. Furthermore, the influence of fluid flow within interconnected fractures on P-wave and S-wave attenuation is difficult to accommodate in analytical models. One way to overcome these limitations is through numerical upscaling. In this paper, we apply a numerical upscaling approach based on the theory of quasi-static poroelasticity to fluid-saturated porous media containing randomly distributed horizontal and vertical fractures. The inferred frequency-dependent elastic moduli represent the effective behaviour of the underlying fractured medium if the considered sub-volume has at least the size of a representative elementary volume. We adapt a combined statistical and numerical approach originally proposed for elastic composites to explore wether the overall statistical properties of simple fracture networks can be captured by computationally feasible representative-elementary-volume sizes. Our results indicate that, for the considered scenarios, this is indeed possible and thus represent an important first step towards the estimation of frequency-dependent effective moduli of realistic fracture networks. [ABSTRACT FROM AUTHOR]

Understanding and quantifying seismic energy dissipation in fluid-saturated porous rocks is of considerable interest because it offers the perspective of extracting information with regard to the elastic and hydraulic rock properties. An important, if not dominant, attenuation mechanism prevailing in the seismic frequency band is wave-induced fluid pressure diffusion in response to the contrasts in elastic stiffness in the mesoscopic-scale range. An effective way to estimate seismic velocity dispersion and attenuation related to this phenomenon is through the application of numerical upscaling procedures to synthetic rock samples of interest. However, the estimated seismic properties are meaningful only if the underlying sample volume is at least of the size of a representative elementary volume (REV). In the given context, the definition of an REV and the corresponding implications for the estimation of the effective seismic properties remain largely unexplored. To alleviate this problem, we have studied the characteristics of REVs for a set of idealized rock samples sharing high levels of velocity dispersion and attenuation. For periodically heterogeneous poroelastic media, the REV size was driven by boundary condition effects. Our results determined that boundary condition effects were absent for layered media and negligible in the presence of patchy saturation. Conversely, strong boundary condition effects arose in the presence of a periodic distribution of finite-length fractures, thus leading to large REV sizes. The results thus point to the importance of carefully determining the REV sizes of heterogeneous porous rocks for computing effective seismic properties, especially in the presence of strong dry frame stiffness contrasts. [ABSTRACT FROM AUTHOR]

The presence of mesoscopic heterogeneities in fluid-saturated porous rocks can produce measurable seismoelectric signals due to wave-induced fluid flow between regions of differing compressibility. The dependence of these signals on the petrophysical and structural characteristics of the probed rock mass remains largely unexplored. In this work, we derive an analytical solution to describe the seismoelectric response of a rock sample, containing a horizontal layer at its centre, that is subjected to an oscillatory compressibility test. We then adapt this general solution to compute the seismoelectric signature of a particular case related to a sample that is permeated by a horizontal fracture located at its centre. Analyses of the general and particular solutions are performed to study the impact of different petrophysical and structural parameters on the seismoelectric response. We find that the amplitude of the seismoelectric signal is directly proportional to the applied stress, to the Skempton coefficient contrast between the host rock and the layer, and to a weighted average of the effective excess charge of the two materials. Our results also demonstrate that the frequency at which the maximum electrical potential amplitude prevails does not depend on the applied stress or the Skempton coefficient contrast. In presence of strong permeability variations, this frequency is rather controlled by the permeability and thickness of the less permeable material. The results of this study thus indicate that seismoelectric measurements can potentially be used to estimate key mechanical and hydraulic rock properties of mesoscopic heterogeneities, such as compressibility, permeability and fracture compliance. [ABSTRACT FROM AUTHOR]

Biot's equations of poroelasticity were solved to study the effects of fracture connectivity on S-wave attenuation caused by wave-induced fluid flow at the mesoscopic scale. The methodology was based on numerical quasistatic pure-shear experiments performed on models of water-saturated rocks containing pairs of either connected or unconnected fractures of variable inclination. Each model corresponded to a representative elementary volume of a periodic medium. Inertial terms were neglected, and hence, the observed attenuation was entirely due to wave-induced fluid flow at the mesoscopic scale. We found that when fractures are not connected, fluid flow in the embedding matrix governs S-wave attenuation, whereas fluid flow through highly permeable fractures, from one fracture into the other one, may dominate when fractures are connected. Each of these energy-dissipation phenomena has a distinct characteristic frequency, with the S-wave attenuation peak associated with flow through connected fractures occurring at higher frequencies than that associated with flow in the embedding matrix. Exploring a range of geometric arrangements of either connected or unconnected fractures at different inclinations, we also observed that the magnitude of S-wave attenuation at both characteristic frequencies shows a strong dependence on fracture inclination. For comparison, we performed quasistatic uniaxial compressibility tests to compute P-wave attenuation in the same models. We found that the attenuation patterns of S-waves tend to differ fundamentally from those of P-waves with respect to fracture inclination. The attenuation characteristics of P- and S-waves in fractured media are thus, largely complementary. With respect to fracture connectivity, we observed that S-wave attenuation tends to follow a specific pattern, indeed, more consistently than that of the P-waves. Our results point to the promising perspective of combining estimates of attenuation of P- and S-waves to infer information on fracture connectivity as well as on the effective permeability of fractured media. [ABSTRACT FROM AUTHOR]

In the past few decades, great attention has been focused on uncovering the physics of seismic wave attenuation in fluid-saturated rocks. However, the relationship among many variables affecting attenuation is still not completely clear. For instance, although the role of strain in enhancing friction dissipation is relatively well known for dry rocks, it remains unclear how and how much it affects attenuation in fluid-saturated rocks. We experimentally measured attenuation in the extensional mode in Berea sandstone at strains between 7.8×10-7 and 1.9×10-5, and at frequencies in the seismic bandwidth (1-100 Hz). These strains were similar to those typically observed in seismic exploration (~10-6). We also measured the transient fluid pressure caused when a stepwise stress was applied resulting in such strains. For the studied strain range, our results indicated that: (1) the overall attenuation in dry Berea sandstone increased linearly with strain, (2) the frequency-dependent component of attenuation, which was associated with fluid saturation, was approximately insensitive to strain, and (3) the overall attenuation can be considered as a sum of a frequency-independent and a frequency-dependent components. [ABSTRACT FROM AUTHOR]

To better understand the effects of fluid saturation on seismic attenuation, we combined numerical modeling in poroelastic media and laboratory measurements of seismic attenuation in partially saturated Berea sandstone samples. Although in laboratory experiments many physical mechanisms for seismic attenuation take place simultaneously, with numerical modeling we separately studied the effect of a single physical mechanism: wave-induced fluid flow on the mesoscopic scale. Using the finite-element method, we solved Biot's equations of consolidation by performing a quasistatic creep test on a 3D poroelastic model. This model represents a partially saturated rock sample. We obtained the stress-strain relation, from which we calculated frequency-dependent attenuation. In the laboratory, we measured attenuation in extensional mode for dry and partially water-saturated Berea sandstone samples in the frequency range from 0.1 to 100 Hz. All the measurements were performed at room pressure and temperature conditions. From numerical simulations, we found that attenuation varies significantly with fluid distribution within the model. In addition to binary distributions, we used spatially continuous distributions of fluid saturation for the numerical models. Such continuous saturation distribution was implemented using properties of an effective single-phase fluid. By taking into account the matrix anelasticity, we found that wave-induced fluid flow on the mesoscopic scale due to a continuous distribution of fluid saturation can reproduce seismic attenuation data measured in a partially saturated sample. The matrix anelasticity was the attenuation measured in the room-condition dry sample. [ABSTRACT FROM AUTHOR]

A novel laboratory technique is proposed to investigate wave-induced fluid flow on the mesoscopic scale as a mechanism for seismic attenuation in partially saturated rocks. This technique combines measurements of seismic attenuation in the frequency range from 1 to 100 Hz with measurements of transient fluid pressure as a response of a step stress applied on top of the sample. We used a Berea sandstone sample partially saturated with water. The laboratory results suggest that wave-induced fluid flow on the mesoscopic scale is dominant in partially saturated samples. A 3-D numerical model representing the sample was used to verify the experimental results. Biot's equations of consolidation were solved with the finite-element method. Wave-induced fluid flow on the mesoscopic scale was the only attenuation mechanism accounted for in the numerical solution. The numerically calculated transient fluid pressure reproduced the laboratory data. Moreover, the numerically calculated attenuation, superposed to the frequency-independent matrix anelasticity, reproduced the attenuation measured in the laboratory in the partially saturated sample. This experimental—numerical fit demonstrates that wave-induced fluid flow on the mesoscopic scale and matrix anelasticity are the dominant mechanisms for seismic attenuation in partially saturated Berea sandstone. [ABSTRACT FROM AUTHOR]

We have modeled numerically the seismic response of a poroelastic inclusion with properties applicable to an oil reservoi r that interacts with an ambient wavefield. The model includes wave-induced fluid flow caused by pressure differences between mesoscopic-scale (i.e., in the order of centimeters to meters) heterogeneities. We used a viscoelastic approximation on the macroscopic scale to implement the attenuation and dispersion resulting from this mesoscopic-scale theory in numerical simulations of wave propagation on the kilometer scale. This upscaling method includes finite-element modeling of wave-induced fluid flow to determine effective seismic properties of the poroelastic media, such as attenuation of P- and S-waves. The fitted, equivalent, viscoelastic behavior is implemented in finite-difference wave propagation simulations. With this two-stage process, we model numerically the quasi- poroelastic wave-propagation on the kilometer scale and study the impact of fluid properties and fluid saturation on the modeled seismic amplitudes. In particular, we addressed the question of whether poroelastic effects within an oil reservoir may be a plausible explanation for low-frequency ambient wavefield modifications observed at oil fields in recent years. Our results indicate that ambient wavefield modification is expected to occur for oil reservoirs exhibiting high attenuation. Whether or not such modifications can be detected in surface recordings, however, will depend on acquisition design and noise mitigation processing as well as site-specific conditions, such as the geologic complexity of the subsurface, the nature of the ambient wavefield, and the amount of surface noise. [ABSTRACT FROM AUTHOR]

Synchrotron radiation X-ray tomographic microscopy is a nondestructive method providing ultra-high-resolution 3D digital images of rock microstructures. We describe this method and, to demonstrate its wide applicability, we present 3D images of very different rock types: Berea sandstone, Fontainebleau sandstone, dolomite, calcitic dolomite, and three-phase magmatic glasses. For some samples, full and partial saturation scenarios are considered using oil, water, and air. The rock images precisely reveal the 3D rock microstructure, the pore space morphology, and the interfaces between fluids saturating the same pore. We provide the raw image data sets as online supplementary material, along with laboratory data describing the rock properties. By making these data sets available to other research groups, we aim to stimulate work based on digital rock images of high quality and high resolution. We also discuss and suggest possible applications and research directions that can be pursued on the basis of our data. [ABSTRACT FROM AUTHOR]

We studied seismic attenuation of P- and S-waves caused by the physical mechanism of wave-induced fluid flow at the mesoscopic scale. Stress relaxation experiments were numerically simulated by solving Biot's equations for consolidation of 2D poroelastic media with finite-element modeling. The experiments yielded time-dependent stress-strain relations that were used to calculate the complex moduli from which frequency-dependent attenuation was determined. Our model consisted of periodically distributed circular or elliptical heterogeneities with much lower porosity and permeability than the background media, which contained 80% of the total pore space of the media. This model can represent a hydrocarbon reservoir, where the porous background is fully saturated with oil or gas and the low-porosity regions are always saturated with water. Three different saturation scenarios were considered: oil-saturated (80% oil, 20% water), gas-saturated (80% gas, 20% water), and fully water-saturated media. Varying the dry bulk and shear moduli in the background and in the heterogeneities, a consistent tendency was observed in the relative behavior of the S-wave attenuation among the different saturation scenarios. First, in the gas-saturated media the S-wave attenuation was very low and much lower than in the oil-saturated or in the fully water-saturated media. Second, at low frequencies the S-wave attenuation was significantly higher in the oil-saturated media than in the fully water-saturated media. The P-wave attenuation exhibited a more variable relative behavior among the different saturation degrees. Based on the mechanism of wave-induced fluid flow and on our numerical results, we suggest that S-wave attenuation could be used as an indicator of fluid content in a reservoil: Additionally, we observed that impermeable barriers in the background can cause a significant increase in S-wave attenuation. This suggests that S-wave attenuation could also be an indicator of permeability changes in a reservoir due to, for example, fracturing operations. [ABSTRACT FROM AUTHOR]

The impact of changes in saturation on the frequency-dependent reflection coefficient of a partially saturated layer was studied. Seismic attenuation and velocity dispersion in partially saturated (i.e., patchy saturated) poroelastic media were accounted for by using the analytical solution of the ID White's model for wave-induced fluid flow. White's solution was applied in combination with an analytical solution for the normal-incidence reflection coefficient of an attenuating layer embedded in an elastic or attenuating background medium to investigate the effects of attenuation, velocity dispersion, and tuning on the reflection coefficient. Approximations for the frequency-dependent quality factor, its minimum value, and the frequency at which the minimum value of the quality factor occurs were derived. The approximations are valid for any two alternating sets of petrophysical parameters. An approximation for the normal-incidence reflection coefficient of an attenuating thin (compared to the wavelength) layer was also derived. This approximation gives insight into the influence of contrasts in acoustic impedance and]or attenuation on the reflectivity of a thin layer. Laboratory data for reflections from a water-saturated sand layer and from a dry sand layer were further fit with petrophysical parameters for unconsolidated sand partially saturated with water and air. The results showed that wave-induced fluid flow can explain low-frequency reflection anomalies, which are related to fluid saturation and can be observed in seismic field data. The results further indicate that reflection coefficients of partially saturated layers (e.g., hydrocarbon reservoirs) can vary significantly with frequency, especially at low seismic frequencies where partial saturation may often cause high attenuation. [ABSTRACT FROM AUTHOR]

The 1D interlayer-flow (or White's) model is based on Biot's theory of poroelasticity and explains low-frequency seismic wave attenuation in partially saturated rocks by wave-induced fluid flow between two alternating poroelastic layers, each saturated with a different fluid. We have developed approximate equations for both the minimum possible value of the quality factor, Q, and the corresponding fluid saturation for which Q is minimal. The simple approximate equations provide a better insight into the dependence of Q on basic petrophysical parameters and allow for a fast assessment of the minimal value of Q. The approximation is valid for a wide range of realistic petrophysical parameter values for sandstones partially saturated with gas and water, and shows that values of Q can be as small as two. We applied the interlayer-flow model to study the reflection coefficient of a thin (i.e., between 6 and 11 times smaller than the incident wavelength) layer that is partially saturated with gas and water. The reflection coefficient of the layer, caused only by a contrast in attenuation between the layer and the nonattenuating background medium, can be larger than 10% for Q < 4 within the layer. The reflection coefficient was calculated with finite difference simulations of wave propagation in heterogeneous, poroelastic solids and in equivalent viscoelastic solids. The reflection coefficient of the layer is also estimated with an analytical solution using a complex velocity for the layer. The numerical and analytical results agree well. Our results indicate that reflection coefficients of gas reservoirs can be significantly increased and frequency dependent in the low-frequency range because of attenuation within the reservoir caused by wave-induced flow. [ABSTRACT FROM AUTHOR]

Biot's theory describes the coupled solid-fluid interaction in a porous medium. In the earth sciences, poroelasticity is essential in many applications, for example, in hydrogeology, in seismic monitoring of CO2 reservoirs, etc. In the present work, we solve Biot's equations for particle velocity and stress in the time domain with a finite difference approach on a staggered grid. Depending on the medium's properties, besides the elastic compressional and shear waves, one may observe the propagating slow wave or the diffusive static slow mode. In such a case, when the diffusive slow mode is present, the time-stepping should be very small in order to reach a stable simulation of Biot's equations. We present a new treatment of this problem based on the so-called pseudo-transient method. The idea is that at each time step, another pseudo iteration causes the slow mode to attenuate quickly. As a result, very fine time-stepping is unnecessary and the time-stepping is controlled by a standard Courant stability condition for the fast P-wave. Furthermore, we accelerate a finite-difference code using an NVIDIA graphics card with the CUDA programming language. [ABSTRACT FROM AUTHOR]