Squirt-flow seismic dispersion models: a comparison

2020 ◽  
Vol 222 (3) ◽  
pp. 2068-2082 ◽  
Author(s):  
Yongyang Sun ◽  
José M Carcione ◽  
Boris Gurevich
Keyword(s):  
Aspect Ratio ◽  
Pore Space ◽  
Crack Density ◽  
Fluid Pressure ◽  
Porous Rocks ◽  
Dispersion Models ◽  
Pore Characteristics ◽  
Low Frequencies ◽  
High Frequencies ◽  
Significant Difference

SUMMARY The anelastic properties of porous rocks depend on the pore characteristics, specifically, the pore aspect ratio and the pore fraction (related to the soft porosity). At high frequencies, there is no fluid pressure communication throughout the pore space and the rock becomes stiffer than at low frequencies, where the pore pressure is fully equilibrated. This causes a significant difference between the moduli at low and high frequencies, which is known as seismic dispersion and is commonly explained by the squirt-flow mechanism. In this paper, we consider and contrast three squirt-flow dispersion models: the modified Mavko–Jizba model, valid for a porous medium with arbitrary shapes of the pores and cracks, and two other models, based on idealized geometries of spheres and ellipsoids: the EIAS (equivalent inclusion-average stress) and CPEM (cracks and pores effective medium) models. We first perform analytical comparisons and then compute several numerical examples to demonstrate similarities and differences between the models. The analytical comparison shows that when the stiff pores are spherical and the crack density is small, the theoretical predictions of the three models are very close to each other. However, when the stiff pores are spheroids with an aspect ratio smaller than 1 (say, between 0.2 and 1), the predictions of inclusion based models are not valid at frequencies of ultrasonic measurements on rock samples. In contrast, the predictions of the modified Mavko–Jizba model are valid at ultrasonic frequencies of about 106 Hz, which is a typical frequency of laboratory measurements on core samples. We also introduce Zener-based bulk and shear dispersion indices, which are proportional to the difference between the high- and low-frequency stiffness moduli, and are a measure of the degree of anelasticity, closely related to the quality factors by view of the Kramers–Kronig relations. The results show that the three models yield similar moduli dispersion with very small differences when the crack density is relatively high. The indices versus crack density can be viewed as a template to obtain the crack properties from low- and high-frequency velocity measurements.

Incorporating pore geometry and fluid pressure communication into modeling the elastic behavior of porous rocks

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 106-117 ◽  
Author(s):  
Anthony L. Endres ◽  
Rosemary J. Knight
Keyword(s):  
Closed System ◽  
Elastic Moduli ◽  
Pore Space ◽  
Fluid Pressure ◽  
Continuous Distribution ◽  
Elastic Behavior ◽  
Pore Geometry ◽  
Porous Rocks ◽  
Low Frequencies ◽  
Poroelastic Theory

Inclusion‐based formulations allow an explicit description of pore geometry by viewing porous rocks as a solid matrix with embedded inclusions representing individual pores. The assumption commonly used in these formulations that there is no fluid pressure communication between pores is reasonable for liquid‐filled rocks measured at high frequencies; however, complete fluid pressure communication should occur throughout the pore space at low frequencies. A generalized framework is presented for incorporating complete fluid pressure communication into inclusion‐based formulations, permitting elastic behavior of porous rocks at high and low frequencies to be described in terms of a single model. This study extends previous work by describing the pore space in terms of a continuous distribution of shapes and allowing different forms of inclusion interactions to be specified. The effects of fluid pressure communication on the elastic moduli of porous media are explored by using simple models and are found to consist of two fundamental elements. One is associated with the cubical dilatation and governs the effective bulk modulus. Its magnitude is a function of the range of pore shapes present. The other is due to the extensional part of the deviatoric strain components and affects the effective shear modulus. This element is dependent on pore orientation, as well as pore shape. Using sandstone and granite models, an inclusion‐based formulation shows that large differences between high‐ and low‐frequency elastic moduli can occur for porous rocks. An analysis of experimental elastic wave velocity data reveals behavior similar to that predicted by the models. Quantities analogous to the open and closed system moduli of Gassmann‐Biot poroelastic theory are defined in terms of inclusion‐based formulations that incorporate complete fluid pressure communication. It was found that the poroelastic relationships between the open and closed system moduli are replicated by a large class of inclusion‐based formulations. This connection permits explicit incorporation of pore geometry information into the otherwise empirically determined macroscopic parameters of the Gassmann‐Biot poroelastic theory.

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.

Multiaxial Low-Cycle Fatigue Damage Evaluation Using A. C. Potential Method for Alloy 738LC Superalloy

1994 ◽  
Vol 116 (4) ◽  
pp. 488-494
Author(s):  
Yoshitada Isono ◽  
Masao Sakane ◽  
Masateru Ohnami ◽  
Kazunari Fujiyama
Keyword(s):  
Crack Length ◽  
Fatigue Damage ◽  
Low Cycle Fatigue ◽  
Crack Density ◽  
Potential Method ◽  
Damage Evaluation ◽  
Cycle Fatigue ◽  
Low Frequencies ◽  
High Frequencies ◽  
Creep Fatigue

This paper studies tension/torsion multiaxial low-cycle fatigue lives and creep-fatigue damage evaluation for Alloy 738LC superalloy. Tension/torsion creep-fatigue tests were carried out using hollow cylinder specimens and multiaxial creep-fatigue lives were obtained. The Mises’ equivalent strain correlated the multiaxial low cycle fatigue lives within a factor of two scatter band. An a.c. potential method is developed to detect the creep-fatigue damage associated with crack nucleation and extension. A.c. potentials at high frequencies accurately detect the creep-fatigue damage from the early stage of life while those at low frequencies detect that in the final stage of life. A.c. potentials at high frequencies detect the crack density, defined as the total crack length per unit area, and maximum crack length more sensitively than those at low frequencies.

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.

The effect of audio–visual expectancies on stereoacuity

2012 ◽  
Vol 25 (0) ◽  
pp. 160
Author(s):  
Marina Zannoli ◽  
Pascal Mamassian
Keyword(s):  
Visual System ◽  
Sound Source ◽  
Binocular Disparity ◽  
Frequency Content ◽  
High Pitch ◽  
Low Frequencies ◽  
High Frequencies ◽  
Depth Difference ◽  
Significant Difference ◽  
Do So

Because of greater attenuation of high frequencies, a distant sound carries more low frequencies. As the distance between the listener and a sound source increases, the sound is therefore perceived as having a lower pitch. In the present study, we investigated whether there pre-exists a relationship between depth, as it is perceived by the visual system, and pitch. To do so, we measured stereoacuity (the smallest detectable depth difference that can be seen from binocular disparity). Two lines were presented sequentially at a different depth. Each line was presented along with a beep that lasted as long as the presentation of the line. The two beeps could either have the same pitch or a different pitch associated with the two depths. When the pitch was different, the high pitch could either be associated with the near (congruent with the hypothesis) or the far (incongruent) line. Five participants were asked to determine which line was nearer and instructed not to pay attention to the sound. Results showed no significant difference between the congruent and incongruent sound conditions. However, sensitivity was much better in the two different-pitch conditions compared to the same-pitch condition. In addition, we found no difference between the same-pitch condition and a control condition in which no sound was presented. To conclude, our results suggest that a difference in pitch can improve stereacuity, independent of the frequency content of the sound.

scholarly journals A quantitative interpretation of the saturation exponent in Archie’s equations

2021 ◽  
Vol 18 (2) ◽  
pp. 444-449
Author(s):  
Tong-Cheng Han ◽  
Han Yan ◽  
Li-Yun Fu
Keyword(s):  
Aspect Ratio ◽  
Pore Space ◽  
Fluid Distribution ◽  
Air Bubbles ◽  
Quantitative Interpretation ◽  
Porous Rocks ◽  
Homogeneous Fluid ◽  
Quantitative Understanding ◽  
Saturation Exponent ◽  
Wagner Theory

AbstractSaturation exponent is an important parameter in Archie’s equations; however, there has been no well-accepted physical interpretation for the saturation exponent. We have theoretically derived Archie’s equations from the Maxwell–Wagner theory on the assumption of homogeneous fluid distribution in the pore space of clay-free porous rocks. Further theoretical derivations showed that the saturation exponent is in essence the cementation exponent for the water–air mixture and is quantitatively and explicitly related to the aspect ratio of the air bubbles in the pores. The results have provided a theoretical backup for the empirically obtained Archie’s equations and have offered a more physical and quantitative understanding of the saturation exponent.

scholarly journals Rapid Lipid Content Screening in Neochloris oleoabundans Utilizing Carbon-Based Dielectrophoresis

Micromachines ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1023
Author(s):  
Cynthia Galicia-Medina ◽  
Matías Vázquez-Piñón ◽  
Gibran Alemán-Nava ◽  
Roberto Gallo-Villanueva ◽  
Sergio Martínez-Chapa ◽  
...  
Keyword(s):  
Glassy Carbon ◽  
Lipid Content ◽  
Low Cost ◽  
Lipid Production ◽  
Neochloris Oleoabundans ◽  
Element Analysis ◽  
Low Frequencies ◽  
High Frequencies ◽  
Significant Difference ◽  
Pdms Microchannel

In this study, we carried out a heterogeneous cytoplasmic lipid content screening of Neochloris oleoabundans microalgae by dielectrophoresis (DEP), using castellated glassy carbon microelectrodes in a PDMS microchannel. For this purpose, microalgae were cultured in nitrogen-replete (N+) and nitrogen-deplete (N−) suspensions to promote low and high cytoplasmic lipid production in cells, respectively. Experiments were carried out over a wide frequency window (100 kHz–30 MHz) at a fixed amplitude of 7 VPP. The results showed a statistically significant difference between the dielectrophoretic behavior of N+ and N− cells at low frequencies (100–800 kHz), whereas a weak response was observed for mid- and high frequencies (1–30 MHz). Additionally, a finite element analysis using a 3D model was conducted to determine the dielectrophoretic trapping zones across the electrode gaps. These results suggest that low-cost glassy carbon is a reliable material for microalgae classification—between low and high cytoplasmic lipid content—through DEP, providing a fast and straightforward mechanism.

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.

scholarly journals Use of Image Correlation to Measure Macroscopic Strains by Hygric Swelling in Sandstone Rocks

2021 ◽  
Vol 11 (6) ◽  
pp. 2495
Author(s):  
Belén Ferrer ◽  
María-Baralida Tomás ◽  
David Mas
Keyword(s):  
Cross Correlation ◽  
Pore Space ◽  
Digital Camera ◽  
Experimental Methods ◽  
Image Correlation ◽  
Rock Surface ◽  
Experimental Setup ◽  
Porous Rocks ◽  
Porous Sandstone ◽  
Variable Displacement

Some materials undergo hygric expansion when soaked. In porous rocks, this effect is enhanced by the pore space, because it allows water to reach every part of its volume and to hydrate most swelling parts. In the vicinity, this enlargement has negative structural consequences as adjacent elements support some compressions or displacements. In this work, we propose a normalized cross-correlation between rock surface texture images to determine the hygric expansion of such materials. We used small porous sandstone samples (11 × 11 × 30 mm3) to measure hygric swelling. The experimental setup comprised an industrial digital camera and a telecentric objective. We took one image every 5 min for 3 h to characterize the whole swelling process. An error analysis of both the mathematical and experimental methods was performed. The results showed that the proposed methodology provided, despite some limitations, reliable hygric swelling information by a non-contact methodology with an accuracy of 1 micron and permitted the deformation in both the vertical and horizontal directions to be explored, which is an advantage over traditional linear variable displacement transformers.

Effect of Blowing Agent on Cell Morphology and Acoustic Absorption of Natural Rubber Foam

2015 ◽  
Vol 804 ◽  
pp. 25-29 ◽  
Author(s):  
Wanlop Harnnarongchai ◽  
Kantima Chaochanchaikul
Keyword(s):  
Natural Rubber ◽  
Cell Size ◽  
Cell Morphology ◽  
Foam Cell ◽  
Adsorption Coefficient ◽  
Low Frequencies ◽  
Potassium Oleate ◽  
High Frequencies ◽  
Blowing Agent ◽  
Open Cell Foam

The sound absorbing efficiency of natural rubber (NR) foam is affected by the cell morphology of foam. Potassium oleate (K-oleate) and sodium bicarbonate (NaHCO3) were used as blowing agents to create open-cell foam. Amounts of the blowing agent were varied from 0.5 to 8.0 part per hundred of rubber (phr) to evaluate cell size and number of foam cell as well as sound adsorption coefficient of NR foam. The NR foam specimens were prepared using mould and air-circulating oven for vulcanizing and foaming processes. The results indicated that K-oleate at 2.0 phr and NaHCO3 at 0.5 phr led to form NR foam with the smallest cell size and the largest number of foam cell. At low frequencies, the optimum sound adsorption coefficient of NR foam was caused by filling K-oleate 2 phr. However, that of NR foam at high frequencies was provided by 0.5 phr-NaHCO3 addition.

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