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.

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.

scholarly journals Including poroelastic effects in the linear slip theory

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. A51-A56 ◽  
Author(s):  
J. Germán Rubino ◽  
Gabriel A. Castromán ◽  
Tobias M. Müller ◽  
Leonardo B. Monachesi ◽  
Fabio I. Zyserman ◽  
...  
Keyword(s):  
Viscous Friction ◽  
Seismic Wave Propagation ◽  
Seismic Attenuation ◽  
Porous Rocks ◽  
Compliance Matrix ◽  
Frequency Dependent ◽  
Attenuation Mechanism ◽  
Wave Induced ◽  
Complex Valued ◽  
Good Agreement

Numerical simulations of seismic wave propagation in fractured media are often performed in the framework of the linear slip theory (LST). Therein, fractures are represented as interfaces and their mechanical properties are characterized through a compliance matrix. This theory has been extended to account for energy dissipation due to viscous friction within fluid-filled fractures by using complex-valued frequency-dependent compliances. This is, however, not fully adequate for fractured porous rocks in which wave-induced fluid flow (WIFF) between fractures and host rock constitutes a predominant seismic attenuation mechanism. In this letter, we develop an approach to incorporate WIFF effects directly into the LST for a 1D system via a complex-valued, frequency-dependent fracture compliance. The methodology is validated for a medium permeated by regularly distributed planar fractures, for which an analytical expression for the complex-valued normal compliance is determined in the framework of quasistatic poroelasticity. There is good agreement between synthetic seismograms generated using the proposed recipe and those obtained from comprehensive, but computationally demanding, poroelastic simulations.

Seismic wave attenuation due to fluid pressure diffusion at the mesoscopic scale: an experimental and numerical study

2021 ◽  
Author(s):  
Samuel Chapman ◽  
Jan V. M. Borgomano ◽  
Beatriz Quintal ◽  
Sally M. Benson ◽  
Jerome Fortin
Keyword(s):  
Seismic Wave ◽  
Seismic Waves ◽  
Wave Attenuation ◽  
Fluid Pressure ◽  
Fluid Distribution ◽  
Mesoscopic Scale ◽  
Seismic Wave Attenuation ◽  
X Ray ◽  
Pressure Diffusion ◽  
Attenuation And Dispersion

<p>Monitoring of the subsurface with seismic methods can be improved by better understanding the attenuation of seismic waves due to fluid pressure diffusion (FPD). In porous rocks saturated with multiple fluid phases the attenuation of seismic waves by FPD is sensitive to the mesoscopic scale distribution of the respective fluids. The relationship between fluid distribution and seismic wave attenuation could be used, for example, to assess the effectiveness of residual trapping of carbon dioxide (CO2) in the subsurface. Determining such relationships requires validating models of FPD with accurate laboratory measurements of seismic wave attenuation and modulus dispersion over a broad frequency range, and, in addition, characterising the fluid distribution during experiments. To address this challenge, experiments were performed on a Berea sandstone sample in which the exsolution of CO2 from water in the pore space of the sample was induced by a reduction in pore pressure. The fluid distribution was determined with X-ray computed tomography (CT) in a first set of experiments. The CO2 exosolved predominantly near the outlet, resulting in a heterogeneous fluid distribution along the sample length. In a second set of experiments, at similar pressure and temperature conditions, the forced oscillation method was used to measure the attenuation and modulus dispersion in the partially saturated sample over a broad frequency range (0.1 - 1000 Hz). Significant P-wave attenuation and dispersion was observed, while S-wave attenuation and dispersion were negligible. These observations suggest that the dominant mechanism of attenuation and dispersion was FPD. The attenuation and dispersion by FPD was subsequently modelled by solving Biot’s quasi-static equations of poroelasticity with the finite element method. The fluid saturation distribution determined from the X-ray CT was used in combination with a Reuss average to define a single phase effective fluid bulk modulus. The numerical solutions agree well with the attenuation and modulus dispersion measured in the laboratory, supporting the interpretation that attenuation and dispersion was due to FPD occurring in the heterogenous distribution of the coexisting fluids. The numerical simulations have the advantage that the models can easily be improved by including sub-core scale porosity and permeability distributions, which can also be determined using X-ray CT. In the future this could allow for conducting experiments on heterogenous samples.</p>

The influence of mesoscopic flow on the P-wave attenuation and dispersion in a porous media permeated by aligned fractures

2013 ◽  
Vol 57 (3) ◽  
pp. 482-506 ◽  
Author(s):  
Jixin Deng ◽  
Shangxu Wang ◽  
Gengyang Tang ◽  
Jianguo Zhao ◽  
Xiangyang Li
Keyword(s):  
Porous Media ◽  
Wave Attenuation ◽  
P Wave ◽  
Attenuation And Dispersion

scholarly journals Fluid Discrimination Based on Frequency-Dependent AVO Inversion with the Elastic Parameter Sensitivity Analysis

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Pu Wang ◽  
Jingye Li ◽  
Xiaohong Chen ◽  
Kedong Wang ◽  
Benfeng Wang
Keyword(s):  
Data Interpretation ◽  
Elastic Parameter ◽  
Pore Fluid ◽  
P Wave ◽  
Frequency Dependent ◽  
Avo Inversion ◽  
Fluid Factor ◽  
Dispersion Terms ◽  
Dispersion And Attenuation ◽  
Dispersion Term

Fluid discrimination is an extremely important part of seismic data interpretation. It plays an important role in the refined description of hydrocarbon-bearing reservoirs. The conventional AVO inversion based on Zoeppritz’s equation shows potential in lithology prediction and fluid discrimination; however, the dispersion and attenuation induced by pore fluid are not fully considered. The relationship between dispersion terms in different frequency-dependent AVO equations has not yet been discussed. Following the arguments of Chapman, the influence of pore fluid on elastic parameters is analyzed in detail. We find that the dispersion and attenuation of Russell fluid factor, Lamé parameter, and bulk modulus are more pronounced than those of P-wave modulus. The Russell fluid factor is most prominent among them. Based on frequency-dependent AVO inversion, the uniform expression of different dispersion terms of these parameters is derived. Then, incorporating the P-wave difference with the dispersion terms, we obtain new P-wave difference dispersion factors which can identify the gas-bearing reservoir location better compared with the dispersion terms. Field data application also shows that the dispersion term of Russell fluid factor is optimal in identifying fluid. However, the dispersion term of Russell fluid factor could be unsatisfactory, if the value of the weighting parameter associated with dry rock is improper. Then, this parameter is studied to propose a reasonable setting range. The results given by this paper are helpful for the fluid discrimination in hydrocarbon-bearing rocks.

Incorporating mechanisms of fluid pressure relaxation into inclusion‐based models of elastic wave velocities

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1173-1181 ◽  
Author(s):  
S. Richard Taylor ◽  
Rosemary J. Knight
Keyword(s):  
Elastic Wave ◽  
Water Saturation ◽  
Laboratory Data ◽  
Fluid Pressure ◽  
P Wave ◽  
Porous Rocks ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Exact Agreement ◽  
Flow Through

Our new method incorporates fluid pressure communication into inclusion‐based models of elastic wave velocities in porous rocks by defining effective elastic moduli for fluid‐filled inclusions. We illustrate this approach with two models: (1) flow between nearest‐neighbor pairs of inclusions and (2) flow through a network of inclusions that communicates fluid pressure throughout a rock sample. In both models, we assume that pore pressure gradients induce laminar flow through narrow ducts, and we give expressions for the effective bulk moduli of inclusions. We compute P‐wave velocities and attenuation in a model sandstone and illustrate that the dependence on frequency and water‐saturation agrees qualitatively with laboratory data. We consider levels of water saturation from 0 to 100% and all wavelengths much larger than the scale of material heterogeneity, obtaining near‐exact agreement with Gassmann theory at low frequencies and exact agreement with inclusion‐based models at high frequencies.

Seismic wave attenuation and modulus dispersion in sandstones

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. D211-D231 ◽  
Author(s):  
James W. Spencer ◽  
Jacob Shine
Keyword(s):  
Wave Attenuation ◽  
High Viscosity ◽  
P Wave ◽  
S Wave ◽  
Local Flow ◽  
Shear Moduli ◽  
Low Viscosity ◽  
Confining Pressures ◽  
Wave Induced ◽  
Dispersion And Attenuation

We have conducted laboratory experiments over the 1–200 Hz band to examine the effects of viscosity and permeability on modulus dispersion and attenuation in sandstones and also to examine the effects of partial gas or oil saturation on velocities and attenuations. Our results have indicated that bulk modulus values with low-viscosity fluids are close to the values predicted using Gassmann’s first equation, but, with increasing frequency and viscosity, the bulk and shear moduli progressively deviate from the values predicted by Gassmann’s equations. The shear moduli increase up to 1 GPa (or approximately 10%) with high-viscosity fluids. The P- and S-wave attenuations ([Formula: see text] and [Formula: see text]) and modulus dispersion with different fluids are indicative of stress relaxations that to the first order are scaling with frequency times viscosity. By fitting Cole-Cole distributions to the scaled modulus and attenuation data, we have found that there are similar P-wave, shear and bulk relaxations, and attenuation peaks in each of the five sandstones studied. The modulus defects range from 11% to 15% in Berea sandstone to 16% to 26% in the other sandstones, but these would be reduced at higher confining pressures. The relaxations shift to lower frequencies as the viscosity increased, but they do not show the dependence on permeability predicted by mesoscopic wave-induced fluid flow (WIFF) theories. Results from other experiments having patchy saturation with liquid [Formula: see text] and high-modulus fluids are consistent with mesoscopic WIFF theories. We have concluded that the modulus dispersion and attenuations ([Formula: see text] and [Formula: see text]) in saturated sandstones are caused by a pore-scale, local-flow mechanism operating near grain contacts.

scholarly journals Seismic velocity change in sandstone during CO2 injection

2020 ◽  
Vol 205 ◽  
pp. 02001
Author(s):  
Marte Gutierrez ◽  
Daisuke Katsuki ◽  
Abdulhadi Almrabat
Keyword(s):  
Wave Velocity ◽  
Supercritical Co2 ◽  
Seismic Velocity ◽  
Saline Water ◽  
Pore Fluid ◽  
P Wave ◽  
Co2 Injection ◽  
Porous Rocks ◽  
Deep Saline Aquifer ◽  
P Wave Velocity

This paper presents analytical and experimental studies of the effects of supercritical CO2 injection on the seismic velocity of sandstone initially saturated with saline water. The analytical model is based on poroelasticity theory, particularly the application of the Biot-Gassmann substitution theory in the modeling of the acoustic velocity of porous rocks containing two-phase immiscible fluids. The experimental study used a high pressure and high temperature triaxial cell to clarify the seismic response of samples of Berea sandstone to supercritical CO2 injection under deep saline aquifer conditions. Measured ultrasonic wave velocity changes during CO2 injection in the sandstone sample showed the effects of pore fluid distribution in the seismic velocity of porous rocks. CO2 injection was shown to decrease the P-wave velocity with increasing CO2 saturation whereas the S-wave velocity was almost constant. The results confirm that the Biot-Gassmann theory can be used to model the changes in the acoustic P-wave velocity of sandstone containing different mixtures of supercritical CO2 and saline water provided the distribution of the two fluids in the sandstone pore space is accounted for in the calculation of the pore fluid bulk modulus.

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