scholarly journals Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A147-75A164 ◽  
Author(s):  
Tobias M. Müller ◽  
Boris Gurevich ◽  
Maxim Lebedev
Keyword(s):  
Fluid Flow ◽  
Velocity Dispersion ◽  
Wave Attenuation ◽  
Field Measurements ◽  
Theoretical Models ◽  
Seismic Attenuation ◽  
P Wave ◽  
Induced Flow ◽  
Wave Induced ◽  
Attenuation And Dispersion

One major cause of elastic wave attenuation in heterogeneous porous media is wave-induced flow of the pore fluid between heterogeneities of various scales. It is believed that for frequencies below [Formula: see text], the most important cause is the wave-induced flow between mesoscopic inhomogeneities, which are large compared with the typical individual pore size but small compared to the wavelength. Various laboratory experiments in some natural porous materials provide evidence for the presence of centimeter-scale mesoscopic heterogeneities. Laboratory and field measurements of seismic attenuation in fluid-saturated rocks provide indications of the role of the wave-induced flow. Signatures of wave-induced flow include the frequency and saturation dependence of P-wave attenuation and its associated velocity dispersion, frequency-dependent shear-wave splitting, and attenuation anisotropy. During the last four decades, numerous models for attenuation and velocity dispersion from wave-induced flow have been developed with varying degrees of rigor and complexity. These models can be categorized roughly into three groups ac-cording to their underlying theoretical framework. The first group of models is based on Biot’s theory of poroelasticity. The second group is based on elastodynamic theory where local fluid flow is incorporated through an additional hydrodynamic equation. Another group of models is derived using the theory of viscoelasticity. Though all models predict attenuation and velocity dispersion typical for a relaxation process, there exist differences that can be related to the type of disorder (periodic, random, space dimension) and to the way the local flow is incorporated. The differences manifest themselves in different asymptotic scaling laws for attenuation and in different expressions for characteristic frequencies. In recent years, some theoretical models of wave-induced fluid flow have been validated numerically, using finite-difference, finite-element, and reflectivity algorithms applied to Biot’s equations of poroelasticity. Application of theoretical models to real seismic data requires further studies using broadband laboratory and field measurements of attenuation and dispersion for different rocks as well as development of more robust methods for estimating dissipation attributes from field data.

Pore fluid effects on S-wave attenuation caused by wave-induced fluid flow

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. L13-L23 ◽  
Author(s):  
Beatriz Quintal ◽  
Holger Steeb ◽  
Marcel Frehner ◽  
Stefan M. Schmalholz ◽  
Erik H. Saenger
Keyword(s):  
Fluid Flow ◽  
Wave Attenuation ◽  
Pore Space ◽  
Seismic Attenuation ◽  
P Wave ◽  
S Wave ◽  
Hydrocarbon Reservoir ◽  
Saturated Media ◽  
Water Saturated ◽  
Wave Induced

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 reservoir. 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.

Seismic wave attenuation and dispersion due to wave-induced fluid flow in rocks with strong permeability fluctuations

2013 ◽  
Vol 134 (6) ◽  
pp. 4742-4751 ◽  
Author(s):  
J. Germán Rubino ◽  
Leonardo B. Monachesi ◽  
Tobias M. Müller ◽  
Luis Guarracino ◽  
Klaus Holliger
Keyword(s):  
Fluid Flow ◽  
Seismic Wave ◽  
Wave Attenuation ◽  
Seismic Wave Attenuation ◽  
Wave Induced ◽  
Attenuation And Dispersion

Anisotropic P-SV-wave dispersion and attenuation due to inter-layer flow in thinly layered porous rocks

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA135-WA145 ◽  
Author(s):  
Fabian Krzikalla ◽  
Tobias M. Müller
Keyword(s):  
Wave Attenuation ◽  
Fluid Pressure ◽  
Pore Fluid ◽  
P Wave ◽  
Angle Of Incidence ◽  
Porous Rocks ◽  
Frequency Dependent ◽  
Symmetry Properties ◽  
Wave Induced ◽  
Attenuation And Dispersion

Elastic upscaling of thinly layered rocks typically is performed using the established Backus averaging technique. Its poroelastic extension applies to thinly layered fluid-saturated porous rocks and enables the use of anisotropic effective medium models that are valid in the low- and high-frequency limits for relaxed and unrelaxed pore-fluid pressures, respectively. At intermediate frequencies, wave-induced interlayer flow causes attenuation and dispersion beyond that described by Biot’s global flow and microscopic squirt flow. Several models quantify frequency-dependent, normal-incidence P-wave propagation in layered poroelastic media but yield no prediction for arbitrary angles of incidence, or for S-wave-induced interlayer flow. It is shown that generalized models for P-SV-wave attenuation and dispersion as a result of interlayer flow can be constructed by unifying the anisotropic Backus limits with existing P-wave frequency-dependent interlayer flow models. The construction principle is exact and is based on the symmetry properties of the effective elastic relaxation tensor governing the pore-fluid pressure diffusion. These new theories quantify anisotropic P- and SV-wave attenuation and velocity dispersion. The maximum SV-wave attenuation is of the same order of magnitude as the maximum P-wave attenuation and occurs prominently around an angle of incidence of [Formula: see text]. For the particular case of a periodically layered medium, the theoretical predictions are confirmed through numerical simulations.

P-wave seismic attenuation by slow-wave diffusion: Effects of inhomogeneous rock properties

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. O1-O8 ◽  
Author(s):  
José M. Carcione ◽  
Stefano Picotti
Keyword(s):  
Fluid Flow ◽  
Wave Attenuation ◽  
Fluid Pressure ◽  
Seismic Attenuation ◽  
P Wave ◽  
Rock Properties ◽  
Stratified Medium ◽  
P Waves ◽  
Low Frequencies ◽  
Attenuation Mechanism

Recent research has established that the dominant P-wave attenuation mechanism in reservoir rocks at seismic frequencies is because of wave-induced fluid flow (mesoscopic loss). The P-wave induces a fluid-pressure difference at mesoscopic-scale inhomogeneities (larger than the pore size but smaller than the wavelength, typically tens of centimeters) and generates fluid flow and slow (diffusion) Biot waves (continuity of pore pressure is achieved by energy conversion to slow P-waves, which diffuse away from the interfaces). In this context, we consider a periodically stratified medium and investigate the amount of attenuation (and velocity dispersion) caused by different types of heterogeneities in the rock properties, namely, porosity, grain and frame moduli, permeability, and fluid properties. The most effective loss mechanisms result from porosity variations and partial saturation, where one of the fluids is very stiff and the other is very compliant, such as, a highly permeable sandstone at shallow depths, saturated with small amounts of gas (around 10% saturation) and water. Grain- and frame-moduli variations are the next cause of attenuation. The relaxation peak moves towards low frequencies as the (background) permeability decreases and the viscosity and thickness of the layers increase. The analysis indicates in which cases the seismic band is in the relaxed regime, and therefore, when the Gassmann equation can yield a good approximation to the wave velocity.

scholarly journals NUMERICAL ALGORITHM OF SEISMIC ATTENUATION ESTIMATION IN ANISOTROPIC FRACTURED POROUS FLUID-SATURATED MEDIA

2021 ◽  
Vol 2 (2) ◽  
pp. 186-195
Author(s):  
Mikhail A. Novikov ◽  
Vadim V. Lisitsa
Keyword(s):  
Fluid Flow ◽  
Seismic Wave ◽  
Numerical Algorithm ◽  
Wave Attenuation ◽  
Seismic Attenuation ◽  
Staggered Grid ◽  
Filling Material ◽  
Seismic Wave Attenuation ◽  
Saturated Media ◽  
Wave Induced

In our work we investigate the effect of transport and elastic properties anisotropy on seismic attenuation due to fracture-to-fracture wave-induced fluid flow using numerical algorithm of estimation of seismic wave attenuation in anisotropic fractured porous fluid-saturated media. Algorithm is based on numerical solution of anisotropic Biot equations using finite-difference scheme on staggered grid. We perform a set of numerical experiments to model wave propagation in fractured media with anisotropic fractured-filling material providing wave-induced fluid flow within interconnected fractures. Recorded signals are used for numerical estimation of inverse quality factor. Results demonstrate the effect of fracture-filling material anisotropy on seismic wave attenuation.

Seismic attenuation: Effects of pore fluids and frictional‐sliding

Geophysics ◽  
1982 ◽  
Vol 47 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Kenneth W. Winkler ◽  
Amos Nur
Keyword(s):  
Fluid Flow ◽  
Strain Amplitude ◽  
Seismic Wave ◽  
Wave Attenuation ◽  
Velocity Ratio ◽  
Seismic Attenuation ◽  
P Wave ◽  
Amplitude Dependence ◽  
S Wave ◽  
Frictional Sliding

Seismic wave attenuation in rocks was studied experimentally, with particular attention focused on frictional sliding and fluid flow mechanisms. Sandstone bars were resonated at frequencies from 500 to 9000 Hz, and the effects of confining pressure, pore pressure, degree of saturation, strain amplitude, and frequency were studied. Observed changes in attenuation and velocity with strain amplitude are interpreted as evidence for frictional sliding at grain contacts. Since this amplitude dependence disappears at strains and confining pressures typical of seismic wave propagation in the earth, we infer that frictional sliding is not a significant source of seismic attenuation in situ. Partial water saturation significantly increases the attenuation of both compressional (P) and shear (S) waves relative to that in dry rock, resulting in greater P‐wave than S‐wave attenuation. Complete saturation maximizes S‐wave attenuation but causes a reduction in P‐wave attenuation. These effects can be interpreted in terms of wave induced pore fluid flow. The ratio of compressional to shear attenuation is found to be a more sensitive and reliable indicator of partial gas saturation than is the corresponding velocity ratio. Potential applications may exist in exploration for natural gas and geothermal steam reservoirs.

scholarly journals Dynamic permeability of porous rocks and its seismic signatures

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. E149-E158 ◽  
Author(s):  
Tobias M. Müller ◽  
Gracjan Lambert ◽  
Boris Gurevich
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Dispersion Model ◽  
Seismic Attenuation ◽  
Flow In Porous Media ◽  
Equivalent Permeability ◽  
Dynamic Equivalent ◽  
Wave Induced ◽  
Attenuation And Dispersion ◽  
The Impact

In inhomogeneous porous media, the mechanism of wave-induced fluid flow causes significant attenuation and dispersion of seismic waves. In connection with this phenomenon, we study the impact of spatial permeability fluctuations on the dynamic behavior of porous materials. This heterogeneous permeability distribution further complicates the ongoing efforts to extract flow permeability from seismic data. Based on the method of statistical smoothing applied to Biot’s equations of poroelasticity, we derive models for the dynamic-equivalent permeability in 1D and 3D randomly inhomogeneous media. The low-frequency limit of this permeability corresponds to the flow permeability governing fluid flow in porous media. We incorporate the dynamic-equivalent permeability model into the expressions for attenuation and dispersion of P-waves, also obtained by the method of smoothing. The resulting attenuation and dispersion model is confirmed by numerical computations in randomly layered poroelastic structures. The results suggest that the effect of wave-induced fluid flow can be observed in a broader frequency range than previously thought. The peak attenuation shifts along the frequency axis depending on the strength of the permeability fluctuations. We conclude that estimation of flow permeability from seismic attenuation is only possible if permeability fluctuations are properly accounted for.

The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 309-318 ◽  
Author(s):  
Jorge O. Parra
Keyword(s):  
Wave Equation ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Seismic Waves ◽  
Transversely Isotropic ◽  
P Wave ◽  
Fluid Properties ◽  
Permeability Anisotropy ◽  
Attenuation And Dispersion ◽  
Maximum Permeability

The transversely isotropic poroelastic wave equation can be formulated to include the Biot and the squirt‐flow mechanisms to yield a new analytical solution in terms of the elements of the squirt‐flow tensor. The new model gives estimates of the vertical and the horizontal permeabilities, as well as other measurable rock and fluid properties. In particular, the model estimates phase velocity and attenuation of waves traveling at different angles of incidence with respect to the principal axis of anisotropy. The attenuation and dispersion of the fast quasi P‐wave and the quasi SV‐wave are related to the vertical and the horizontal permeabilities. Modeling suggests that the attenuation of both the quasi P‐wave and quasi SV‐wave depend on the direction of permeability. For frequencies from 500 to 4500 Hz, the quasi P‐wave attenuation will be of maximum permeability. To test the theory, interwell seismic waveforms, well logs, and hydraulic conductivity measurements (recorded in the fluvial Gypsy sandstone reservoir, Oklahoma) provide the material and fluid property parameters. For example, the analysis of petrophysical data suggests that the vertical permeability (1 md) is affected by the presence of mudstone and siltstone bodies, which are barriers to vertical fluid movement, and the horizontal permeability (1640 md) is controlled by cross‐bedded and planar‐laminated sandstones. The theoretical dispersion curves based on measurable rock and fluid properties, and the phase velocity curve obtained from seismic signatures, give the ingredients to evaluate the model. Theoretical predictions show the influence of the permeability anisotropy on the dispersion of seismic waves. These dispersion values derived from interwell seismic signatures are consistent with the theoretical model and with the direction of propagation of the seismic waves that travel parallel to the maximum permeability. This analysis with the new analytical solution is the first step toward a quantitative evaluation of the preferential directions of fluid flow in reservoir formation containing hydrocarbons. The results of the present work may lead to the development of algorithms to extract the permeability anisotropy from attenuation and dispersion data (derived from sonic logs and crosswell seismics) to map the fluid flow distribution in a reservoir.

Sign in / Sign up

Export Citation Format

Share Document