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.

An inclusion‐based model of elastic wave velocities incorporating patch‐scale fluid pressure relaxation

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1503-1509 ◽  
Author(s):  
S. Richard Taylor ◽  
Rosemary J. Knight
Keyword(s):  
Elastic Wave ◽  
Elastic Moduli ◽  
Effective Medium Theory ◽  
Fluid Pressure ◽  
P Wave ◽  
Pore Fluids ◽  
Wave Velocities ◽  
Wave Cycle ◽  
Dependent Flow ◽  
Patch Scale

We consider elastic wave velocities in fluid‐saturated porous media with pore fluids distributed in “patches” (i.e., heterogeneity much larger than the typical pore size). We model elastic properties of such materials using inclusion‐based effective medium theory (IBEMT). The standard IBEMT formulation assumes insufficient time during the wave cycle for pore fluids to flow in response to wave‐induced pressure gradients. Our approach accounts for this flow, incorporating wave‐frequency dependent flow effects in the definition of effective elastic moduli for patches. Effective moduli are used in conjunction with IBEMT to estimate elastic moduli of the composite material. In the low‐ and high‐frequency limits, the model reproduces previous theoretical results. At intermediate frequencies, it yields results qualitatively similar to other patch‐scale models. We demonstrate this approach, estimating elastic P‐wave velocities and attenuation in a porous rock that simultaneously contains fluid‐saturated patches of different sizes.

Effective elastic properties of rocks with transversely isotropic background permeated by a set of vertical fracture cluster

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Da Shuai ◽  
Alexey Stovas ◽  
Jianxin Wei ◽  
Bangrang Di ◽  
Yang Zhao
Keyword(s):  
Standard Deviation ◽  
Elastic Wave ◽  
Significant Influence ◽  
Transversely Isotropic ◽  
Azimuth Angle ◽  
Effective Medium ◽  
P Wave ◽  
Wave Velocities ◽  
Anisotropy Parameters ◽  
Vertical Fractures

The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium), the effective medium becomes orthorhombic. The vertical fractures, in reality, may exist in any azimuth angle which leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle, and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuth dependent, introduce a Gaussian function to describe the fractures' azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over azimuth. The numerical examples investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the ( x2, x3) plane than that in the ( x1, x3) plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can be degenerated into the VFTI medium.

The influence of pore fluids and frequency on apparent effective stress behavior of seismic velocities

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. N1-N7 ◽  
Author(s):  
Gary Mavko ◽  
Tiziana Vanorio
Keyword(s):  
Elastic Wave ◽  
Bulk Modulus ◽  
Effective Stress ◽  
High Frequency ◽  
Laboratory Data ◽  
Pore Fluids ◽  
Wave Velocities ◽  
Stress Behavior ◽  
Stress Coefficient ◽  
The Impact

Although poroelastic theory predicts that the effective stress coefficient equals unity for elastic moduli in monomineralic rocks, some rock elastic wave velocities measured at ultrasonic frequencies have effective stress coefficients less than one. Laboratory effective stress behavior for P-waves is often different than S-waves. Furthermore, laboratory ultrasonic velocities almost always reflect high-frequency artifacts associated with pore fluids, including an increase in velocities and flattening of velocity-versus-pressure curves. We have investigated the impact of pore fluids and frequency on the observed effective stress coefficient for elastic wave velocities by developing a model that calculates pore-fluid effects on velocity, including high-frequency squirt dispersion, and we have compared the model’s predictions with laboratory data. We modeled a rock frame with penny-shaped cracks for three situations: vacuum dry, saturated with helium, and saturated with brine. Even if the frame modulus depends only on the differential stress, the saturated-rock effective stress coefficient is predicted to be significantly less than one at ultrasonic frequencies because of two effects: an increase in the fluid bulk modulus with increasing pressure and the contribution of high-frequency squirt dispersion. The latter effect is most significant in soft fluids (helium in this experiment) in which the fluid-bulk modulus is less than or comparable to the thin-crack pore stiffness.

Wavefield simulation and data-acquisition-scheme analysis for LWD acoustic tools in very slow formations

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. E59-E68 ◽  
Author(s):  
Hua Wang ◽  
Guo Tao
Keyword(s):  
Wave Velocity ◽  
Cutoff Frequency ◽  
P Wave ◽  
Flexural Wave ◽  
S Wave ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Dipole System ◽  
P Wave Velocity ◽  
Wavefield Simulation

Propagating wavefields from monopole, dipole, and quadrupole acoustic logging-while-drilling (LWD) tools in very slow formations have been studied using the discrete wavenumber integration method. These studies examine the responses of monopole and dipole systems at different source frequencies in a very slow surrounding formation, and the responses of a quadrupole system operating at a low source frequency in a slow formation with different S-wave velocities. Analyses are conducted of coherence-velocity/slowness relationships (semblance spectra) in the time domain and of the dispersion characteristics of these waveform signals from acoustic LWD array receivers. These analyses demonstrate that, if the acoustic LWD tool is centralized properly and is operating at low frequencies (below 3 kHz), a monopole system can measure P-wave velocity by means of a “leaky” P-wave for very slow formations. Also, for very slow formations a dipole system can measure the P-wave velocity via a leaky P-wave and can measure the S-wave velocity from a formation flexural wave. With a quadrupole system, however, the lower frequency limit (cutoff frequency) of the drill-collar interference wave would decrease to 5 kHz and might no longer be neglected if the surrounding formation becomes a very slow formation, with S-wave velocities at approximately 500 m/s.

scholarly journals An effective-medium model for P-wave velocities of saturated, unconsolidated saline permafrost

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. EN33-EN50 ◽  
Author(s):  
Shan Dou ◽  
Seiji Nakagawa ◽  
Douglas Dreger ◽  
Jonathan Ajo-Franklin
Keyword(s):  
Laboratory Data ◽  
Parameter Tuning ◽  
Effective Medium ◽  
P Wave ◽  
Mixing Ratios ◽  
Wave Velocities ◽  
Effective Medium Model ◽  
Medium Model ◽  
P Wave Velocities ◽  
Ice Content

To better understand the relationship between P-wave velocities and ice content in saturated, unconsolidated saline permafrost, we constructed an effective-medium model based upon ultrasonic P-wave data that were obtained from earlier laboratory studies. The model uses a two-end-member mixing approach in which an ice-filled, fully frozen end member and a water-filled, fully unfrozen end member are mixed together to form the effective medium of partially frozen sediments. This mixing approach has two key advantages: (1) It does not require parameter tuning of the mixing ratios, and (2) it inherently assumes mixed pore-scale distributions of ice that consist of frame-strengthening (i.e., cementing and/or load-bearing) ice and pore-filling ice. The model-predicted P-wave velocities agree well with our laboratory data, demonstrating the effectiveness of the model for quantitatively inferring ice content from P-wave velocities. The modeling workflow is simple and is largely free of calibration parameters — attributes that ease its application in interpreting field data sets.

A rock-physics model to determine the pore microstructure of cracked porous rocks

2020 ◽  
Vol 223 (1) ◽  
pp. 622-631
Author(s):  
Lin Zhang ◽  
Jing Ba ◽  
José M Carcione
Keyword(s):  
Crack Density ◽  
Rock Physics ◽  
Differential Pressure ◽  
P Wave ◽  
Porous Rocks ◽  
S Wave ◽  
Wave Velocities ◽  
Pore Microstructure ◽  
Physics Model ◽  
Rock Physics Model

SUMMARY Determining rock microstructure remains challenging, since a proper rock-physics model is needed to establish the relation between pore microstructure and elastic and transport properties. We present a model to estimate pore microstructure based on porosity, ultrasonic velocities and permeability, assuming that the microstructure consists on randomly oriented stiff equant pores and penny-shaped cracks. The stiff pore and crack porosity varying with differential pressure is estimated from the measured total porosity on the basis of a dual porosity model. The aspect ratio of pores and cracks and the crack density as a function of differential pressure are obtained from dry-rock P- and S-wave velocities, by using a differential effective medium model. These results are used to invert the pore radius from the matrix permeability by using a circular pore model. Above a crack density of 0.13, the crack radius can be estimated from permeability, and below that threshold, the radius is estimated from P-wave velocities, taking into account the wave dispersion induced by local fluid flow between pores and cracks. The approach is applied to experimental data for dry and saturated Fontainebleau sandstone and Chelmsford Granite.

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.

Seismic velocities and electrical resistivity of recent volcanics and their dependence on porosity, temperature, and water saturation

Geophysics ◽  
1981 ◽  
Vol 46 (10) ◽  
pp. 1415-1422 ◽  
Author(s):  
A. W. Ibrahim ◽  
George V. Keller
Keyword(s):  
Water Saturation ◽  
Strong Dependence ◽  
Electric Resistivity ◽  
P Wave ◽  
Seismic Velocities ◽  
Fine Grained ◽  
Wave Velocities ◽  
Electrical Resistivities ◽  
P Wave Velocities ◽  
Water Saturated

Variation of P‐wave velocities and electrical resistivities of several suites of water‐saturated recent volcanics was investigated. Both P‐velocities and resistivities exhibited strong dependence on porosity. Resistivity was also dependent upon degree of water saturation and temperature. P‐wave velocities, while showing a strong dependence on porosity, appear to be independent of water saturation and temperature. Volcanics, in general, exhibit higher resistivities compared to other igneous rocks and sediments. Electric resistivity of fine‐grained basalts is anomalously low, probably due to higher content of disseminated iron. Pyroclastics and volcanic breccia, on the other hand, exhibit higher resistivities in relation to fine‐grained basalts.

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