Modeling wave propagation in cracked porous media with penny-shaped inclusions

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. WA141-WA151 ◽  
Author(s):  
Lin Zhang ◽  
Jing Ba ◽  
José M. Carcione ◽  
Weitao Sun
Keyword(s):  
Wave Propagation ◽  
Aspect Ratio ◽  
Crack Density ◽  
Low Frequency ◽  
Confining Pressure ◽  
Wave Dispersion ◽  
Fluid Viscosity ◽  
Porous Rocks ◽  
Flow Models ◽  
Dispersion And Attenuation

Understanding acoustic wave dispersion and attenuation induced by local (squirt) fluid flow between pores and cracks (compliant pores) is fundamental for better characterization of the porous rocks. To describe this phenomenon, some squirt-flow models have been developed based on the conservation of the fluid mass in the fluid mechanics. By assuming that the cracks are represented by isotropically distributed (i.e., randomly oriented) penny-shaped inclusions, this study applies the periodically oscillating squirt flow through inclusions based on the Biot-Rayleigh theory, so that the local squirt flow and global wave oscillation of rock are analyzed in the same theoretical framework of Hamilton’s principle. The governing wave-propagation equations are derived by incorporating all of the crack characteristics (such as the crack radius, crack density, and aspect ratio). In comparison with the previous squirt models, our model predicts the similar characteristics of wave velocity dispersion and attenuation, and our results are in agreement with Gassmann equations at the low-frequency limit. In addition, we find that the fluid viscosity and crack radius only affect the relaxation frequency of the squirt-flow attenuation peak, whereas the crack density and aspect ratio also affect the magnitudes of dispersion and attenuation. The application of this study to experimental data demonstrates that when the differential pressure (the difference between confining pressure and pore pressure) increases, the closure of cracks can lead to a decrease of attenuation. The results confirm that our model can be used to analyze and interpret the observed wave dispersion and attenuation of real rocks.

Analysis of wave dispersion and attenuation effects on seismic low-frequency reflections of a poroelastic layer

2020 ◽  
pp. 1-21
Author(s):  
Yan-Xiao He ◽  
Shangxu Wang ◽  
Genyang Tang ◽  
Xinyu Wu ◽  
Bo Xi
Keyword(s):  
Low Frequency ◽  
Wave Dispersion ◽  
Dispersion And Attenuation

Low-frequency seismic properties of thermally cracked and argon-saturated granite

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. F147-F159 ◽  
Author(s):  
Cao Lu ◽  
Ian Jackson
Keyword(s):  
Shear Modulus ◽  
Transient Flow ◽  
Crack Density ◽  
Fluid Pressure ◽  
Low Frequency ◽  
Confining Pressure ◽  
Seismic Properties ◽  
Aspect Ratios ◽  
In Situ Permeability

Torsional forced-oscillation techniques have been used to measure the shear modulus and strain-energy dissipation on cylindrical specimens of a fine-grained granite, Delegate aplite. The specimens were subjected to thermal cycling and associated microcracking under varying conditions of confining pressure [Formula: see text] and argon pore-fluid pressure [Formula: see text] within the low-frequency saturated isobaric regime. Complementary transient-flow studies of in-situ permeability and volumetric measurements of connected crack porosity allowed the modulus measurements to be interpreted in terms of the density and interconnectivity of the thermally generated cracks. The modulus measurements indicate that newly generated thermal cracks are closed by a differential pressure, [Formula: see text], which ranges from [Formula: see text] for temperatures of [Formula: see text]. This suggests crack aspect ratios on the order of [Formula: see text]. The covariation of in-situ permeability [Formula: see text] and thermal crack density [Formula: see text] that we infer from the modulus deficit is consistent with percolation theory. There is a well-defined threshold at [Formula: see text], beyond which [Formula: see text] increases markedly as [Formula: see text], with [Formula: see text]. At lower crack densities, it is difficult to measure the sensitivity of shear modulus to variations of confining and pore pressures because pore-pressure equilibrium is approached so sluggishly. At temperatures beyond the percolation threshold, the modulus variation is a function of the effective pressure, [Formula: see text], with the value of [Formula: see text] increasing toward one with increasing crack connectivity.

Extended Gassmann Equation with Dynamic Volumetric Strain: Modeling Wave Dispersion and Attenuation of Heterogenous Porous Rocks

Geophysics ◽  
2021 ◽  
pp. 1-97
Author(s):  
Luanxiao Zhao ◽  
Yirong Wang ◽  
Qiuliang Yao ◽  
Jianhua Geng ◽  
Hui Li ◽  
...  
Keyword(s):  
Fluid Pressure ◽  
Volumetric Strain ◽  
Wave Dispersion ◽  
Heterogeneous Porous Media ◽  
Porous Rocks ◽  
Analytical Methodology ◽  
Heterogeneous Rocks ◽  
Rock Characterization ◽  
Wave Induced ◽  
Dispersion And Attenuation

Sedimentary rocks are often heterogeneous porous media inherently containing complex distributions of heterogeneities (e.g., fluid patches, cracks). Understanding and modeling their frequency-dependent elastic and adsorption behaviors is of great interest for subsurface rock characterization from multi-scale geophysical measurements. The physical parameter of dynamic volumetric strain (DVS) associated with wave-induced fluid flow is proposed to understand the common physics and connections behind known poroelastic models for modeling dispersion behaviors of heterogeneous rocks. We derive the theoretical formulations of DVS for patchy saturated rock at mesoscopic scale and cracked porous rock at microscopic grain scales, essentially embodying the wave-induced fluid pressure relaxation process. By incorporating the DVS into the classical Gassmann equation, a simple but practical “dynamic equivalent” modeling approach, extended Gassmann equation, is developed to characterize the dispersion and attenuation of complex heterogeneous rocks at non-zero frequencies. Using the extended Gassmann equation, the effect of microscopic or mesoscopic heterogeneities with complex distributions on the wave dispersion and attenuation signatures can be captured. The proposed theoretical framework provides a simple and straightforward analytical methodology to calculate wave dispersion and attenuation in porous rocks with multiple sets of heterogeneities exhibiting complex characteristics. We also demonstrate that, with the appropriate consideration of multiple crack sets and complex fluids patches distribution, the modeling results can better interpret the experimental data sets of dispersion and attenuation for heterogeneous porous rocks.

High‐ and low‐frequency elastic moduli for a saturated porous/cracked rock‐Differential self‐consistent and poroelastic theories

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 1080-1094 ◽  
Author(s):  
Mickaële Le Ravalec ◽  
Yves Guéguen
Keyword(s):  
Elastic Moduli ◽  
Laboratory Data ◽  
Crack Density ◽  
Low Frequency ◽  
Wave Dispersion ◽  
S Wave ◽  
In Situ Data ◽  
Consistent Model ◽  
Self Consistent ◽  
Theoretical Predictions

Although P‐ and S‐wave dispersion is known to be important in porous/cracked rocks, theoretical predictions of such dispersions have never been given. We report such calculations and show that the predicted dispersions are high in the case of low aspect ratio cracks [Formula: see text] or high crack density [Formula: see text]. Our calculations are derived from first‐principle computations of the high‐ and low‐frequency elastic moduli of a rock permeated by an isotropic distribution of pores or cracks, dry or saturated, with idealized geometry (spheres or ellipsoids). Henyey and Pomphrey developed a differential self‐consistent model that is shown to be a good approximation. This model is used here, but as it considers cracks with zero thickness, it can not account for fluid content effects. To remove this difficulty, we combine the differential self‐consistent approach with a purely elastic calculation of moduli in two cases: that of spherical pores and that of oblate spheroidal cracks with a nonzero volume. This leads to what we call the “extended differential, self‐consistent model” (EM). When combining these EM results with the Gassmann equation, it is possible to derive and compare the theoretical predictions for high‐ and low‐frequency effective moduli in the case of a saturated rock. Since most laboratory data are ultrasonic measurements and in situ data are obtained at much lower frequencies, this comparison is useful for interpreting seismic data in terms of rock and fluid properties. The predicted dispersions are high, in agreement with previous experimental results. A second comparison is made with the semi‐empirical model of Marion and Nur, which considers the effects of a mixed porosity (round pores and cracks together).

Wave Propagation Through Fluid Saturated Porous Rocks

1987 ◽  
Vol 54 (4) ◽  
pp. 788-793 ◽  
Author(s):  
K. Walton ◽  
P. J. Digby
Keyword(s):  
Pore Space ◽  
Low Frequency ◽  
Confining Pressure ◽  
Spherical Particles ◽  
Microstructural Properties ◽  
Porous Rocks ◽  
Wave Speeds ◽  
Expansion Technique ◽  
Effective Wave ◽  
Inviscid Compressible Fluid

A sedimentary rock is modeled by a random packing of identical spherical particles. The connected pore space is filled with an inviscid, compressible fluid. A low-frequency expansion technique is used to calculate the effective wave speeds explicitly in terms of the microstructural properties of the rock considered. The effect of both the pore fluid and the initial confining pressure to which the rock is subjected can be included in the calculations.

Pore fluid effects on seismic velocity in anisotropic rocks

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 233-244 ◽  
Author(s):  
Tapan Mukerji ◽  
Gary Mavko
Keyword(s):  
Seismic Velocity ◽  
Crack Density ◽  
Low Frequency ◽  
Rock Properties ◽  
Fluid Viscosity ◽  
Effective Pressure ◽  
Low Frequencies ◽  
High Frequencies ◽  
Fluid Saturation ◽  
Anisotropic Rocks

A simple new technique predicts the high‐ and low‐frequency saturated velocities in anisotropic rocks entirely in terms of measurable dry rock properties without the need for idealized crack geometries. Measurements of dry velocity versus pressure and porosity versus pressure contain all of the necessary information for predicting the frequency‐dependent effects of fluid saturation. Furthermore, these measurements automatically incorporate all pore interaction, so there is no limitation to low crack density. The velocities are found to depend on five key interrelated variables: frequency, the distribution of compliant crack‐like porosity, the intrinsic or noncrack anisotropy, fluid viscosity and compressibility, and effective pressure. The sensitivity of velocities to saturation is generally greater at high frequencies than low frequencies. The magnitude of the differences from dry to saturated and from low frequency to high frequency is determined by the compliant or crack‐like porosity. Predictions of saturated velocities based on dry data for sandstone and granite show that compressional velocities generally increase with saturation and with frequency. However, the degree of compressional wave anisotropy may either increase or decrease upon saturation depending on the crack distribution, the effective pressure, and the frequency at which the measurements are made. Shear‐wave velocities can either increase or decrease with saturation, and the degree of anisotropy depends on the microstructure, pressure, and frequency. Consequently great care must be taken when interpreting observed velocity anisotropy for measurements at low frequencies, typical of in situ observations, will generally be different from those at high frequencies, typical of the laboratory.

Pore Aspect Ratio Spectrum Inversion from Ultrasonic Measurements and Its Application

2015 ◽  
Vol 23 (04) ◽  
pp. 1540009 ◽  
Author(s):  
Fuyong Yan ◽  
De-Hua Han ◽  
Xue-Lian Chen
Keyword(s):  
Aspect Ratio ◽  
Carbonate Rock ◽  
Velocity Dispersion ◽  
Rock Sample ◽  
Wave Dispersion ◽  
Ratio Spectrum ◽  
Poroelastic Media ◽  
Ultrasonic Measurements ◽  
Dispersion And Attenuation ◽  
Spectrum Inversion

We have conducted simultaneous ultrasonic velocity and pore volume change measurements on a carbonate rock sample. By including of pressure dependent porosity data, we have improved Cheng’s pore aspect ratio spectrum inversion methodology and made the inverted pore aspect ratio spectrum more realistic. Tang’s unified velocity dispersion and attenuation model is modified and extended to poroelastic media with complex pore structure under undrained condition. Using improved pore aspect ratio spectra inversion methodology and modified Tang’s model, we have explored the potential application of pore aspect ratio spectrum in prediction of seismic wave dispersion and attenuation.

A laboratory study of low-frequency wave dispersion and attenuation in water-saturated sandstones

2014 ◽  
Vol 33 (6) ◽  
pp. 616-622 ◽  
Author(s):  
Vassily Mikhaltsevitch ◽  
Maxim Lebedev ◽  
Boris Gurevich
Keyword(s):  
Laboratory Study ◽  
Low Frequency ◽  
Wave Dispersion ◽  
Frequency Wave ◽  
Water Saturated ◽  
Dispersion And Attenuation
Sign in / Sign up

Export Citation Format

Share Document