scholarly journals Laboratory measurements of low- and high-frequency elastic moduli in Fontainebleau sandstone

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. D369-D379 ◽  
Author(s):  
Emmanuel C. David ◽  
Jérome Fortin ◽  
Alexandre Schubnel ◽  
Yves Guéguen ◽  
Robert W. Zimmerman
Keyword(s):  
Bulk Modulus ◽  
Elastic Moduli ◽  
High Pressures ◽  
Low Frequency ◽  
Frequency Dispersion ◽  
Low Frequencies ◽  
High Frequencies ◽  
Fontainebleau Sandstone ◽  
Wave Velocities ◽  
Water Saturated

The presence of pores and cracks in rocks causes the fluid-saturated wave velocities in rocks to be dependent on frequency. New measurements of the bulk modulus at low frequencies (0.02–0.1 Hz) were obtained in the laboratory using oscillation tests carried out on two hydrostatically stressed Fontainebleau sandstone samples, in conjunction with ultrasonic velocities and static measurements, under a range of differential pressures (10–95 MPa), and with three different pore fluids (argon, glycerin, and water). For the 13% and 4% porosity samples, under glycerin- and water-saturated conditions, the low-frequency bulk modulus at 0.02 Hz matched well the low-frequency and ultrasonic dry bulk modulus. The glycerin- and water-saturated samples were much more compliant at low frequencies than at high frequencies. The measured bulk moduli of the tested rocks at low frequencies (0.02–0.1 Hz) were much lower than the values predicted by the Gassmann equation. The frequency dispersion of the P and S velocities was much higher at low differential pressures than at high pressures, due to the presence of open cracks at low differential pressures.

Frequency-Weighted Variable-Length Controllers Using Anytime Control Strategies

2011 ◽  
Author(s):  
Gundula B. Runge ◽  
Al Ferri ◽  
Bonnie Ferri
Keyword(s):  
Time Scale ◽  
Weighting Function ◽  
Control Strategies ◽  
Low Frequency ◽  
Low Frequencies ◽  
High Frequencies ◽  
Frequency Components ◽  
Computational Resources ◽  
Weighted Variable ◽  
Selection Of

This paper considers an anytime strategy to implement controllers that react to changing computational resources. The anytime controllers developed in this paper are suitable for cases when the time scale of switching is in the order of the task execution time, that is, on the time scale found commonly with sporadically missed deadlines. This paper extends the prior work by developing frequency-weighted anytime controllers. The selection of the weighting function is driven by the expectation of the situations that would require anytime operation. For example, if the anytime operation is due to occasional and isolated missed deadlines, then the weighting on high frequencies should be larger than that for low frequencies. Low frequency components will have a smaller change over one sample time, so failing to update these components for one sample period will have less effect than with the high frequency components. An example will be included that applies the anytime control strategy to a model of a DC motor with deadzone and saturation nonlinearities.

Numerical Study of Crosshole Electromagnetic Tunnel Detection

Geophysics ◽  
2021 ◽  
pp. 1-68
Author(s):  
John W. Neese ◽  
David R. Jackson ◽  
Yingcai Zheng ◽  
Leon A. Thomsen
Keyword(s):  
Fresh Water ◽  
Numerical Study ◽  
Low Frequency ◽  
Open Circuit ◽  
Infinite Cylinder ◽  
Optimum Frequency ◽  
Low Frequencies ◽  
Tunnel Detection ◽  
Lossy Medium ◽  
Water Saturated

Electromagnetic tunnel detection is studied numerically using a 3D analytic infinite lossy homogeneous space solution to magnetic dipole radiation and scattering from an infinite cylinder, in a crosshole context. At low frequencies this serves as a model for a transmit coil radiating a time-varying magnetic field that is then detected from the open-circuit voltage induced on a receive coil. Numerical simulations illustrate how various parameters influence the signal strength and the ability to discern the scattered signal. Tunnel detection is achieved at relatively high frequencies (but below typical GPR frequencies) for fresh water saturated sand and for weathered granite, which are lower loss media; for the coil and tunnel parameters used here, optimum frequencies appear to be between 100 kHz and 1 MHz. Tunnel detection for fresh water saturated clay, a much more lossy medium, can be achieved at a quite low frequency, with an optimum frequency between 1 and 10 kHz. These results suggest that, when a resonant coil system is employed, tunnel detection may be possible in a wider range of earth media than previously reported, when the best-suited choice of frequency is employed.

A theory of compressional wave attenuation in noncohesive sediments

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1311-1317 ◽  
Author(s):  
C. McCann ◽  
D. M. McCann
Keyword(s):  
Wave Attenuation ◽  
Compressional Wave ◽  
Solid Particles ◽  
Biot’S Theory ◽  
Attenuation Coefficients ◽  
Low Frequencies ◽  
Biot's Theory ◽  
Compressional Waves ◽  
High Frequencies ◽  
Water Saturated

Published reviews indicate that attenuation coefficients of compressional waves in noncohesive, water‐saturated sediments vary linearly with frequency. Biot’s theory, which accounts for attenuation in terms of the viscous interaction between the solid particles and pore fluid, predicts in its presently published form variation proportional to [Formula: see text] at low frequencies and [Formula: see text] at high frequencies. A modification of Biot’s theory which incorporates a distribution of pore sizes is presented and shown to give excellent agreement with new and published attenuation data in the frequency range 10 kHz to 2.25 MHz. In particular, a linear variation of attenuation with frequency is predicted in that range.

MEASURING OF ELASTIC MODULI BY MEANS OF SUB-SURFACE SOUNDING METHOD

2020 ◽  
pp. 44-53
Author(s):  
A. V. Kozlov
Keyword(s):  
Elastic Moduli ◽  
Point Contact ◽  
Low Frequency ◽  
Frequency Dispersion ◽  
Surface Measurement ◽  
Longitudinal And Shear Waves ◽  
Material Sample ◽  
Dynamic Elastic Moduli ◽  
Table Data

The method of determination of elastic moduli for different materials by means of measuring of longitudinal and shear waves’ velocities is discussed in the paper. The velocities are measured by obtaining the time of flight between a pair of low frequency ultrasonic dry point contact transducers installed on the surface of the studied material sample. Factors defining the accuracy of such measurement are indicated which mainly consist of physical velocity frequency dispersion, fundamental although small differences between static and dynamic elastic moduli measurements, velocity dependence on temperature etc. Comparison between Young’s modulus and Poisson’s ratio, obtained experimentally and from table data, is given for various plastics and steel samples. It shows good agreement of different methods’ data and demonstrates the applicability of the suggested elastic moduli ultrasonic sub-surface measurement method.

Estimation of Dry-Rock Elastic Moduli Based on the Simulation of Mud-Filtrate Invasion Effects on Borehole Acoustic Logs

2009 ◽  
Vol 12 (06) ◽  
pp. 898-911 ◽  
Author(s):  
Tobiloluwa B. Odumosu ◽  
Carlos Torres-Verdín ◽  
Jesús M. Salazar ◽  
Jun Ma ◽  
Benjamin Voss ◽  
...  
Keyword(s):  
Bulk Modulus ◽  
Shear Wave ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Compressional Wave ◽  
Shear Rigidity ◽  
Spatial Distributions ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Mud Filtrate

Summary Reliable estimates of dry-rock elastic properties are critical to the accurate interpretation of the seismic response of hydrocarbon reservoirs. We describe a new method for estimating elastic moduli of rocks in-situ based on the simulation of mud-filtrate invasion effects on resistivity and acoustic logs. Simulations of mud-filtrate invasion account for the dynamic process of fluid displacement and mixing between mud-filtrate and hydrocarbons. The calculated spatial distributions of electrical resistivity are matched against resistivity logs by adjusting the underlying petrophysical properties. We then perform Biot-Gassmann fluid substitution on the 2D spatial distributions of fluid saturation with initial estimates of dry-bulk (kdry) modulus and shear rigidity (µdry) and a constraint of Poisson's ratio (?d) typical of the formation. This process generates 2D spatial distributions of compressional and shear-wave velocities and density. Subsequently, sonic waveforms are simulated to calculate shear-wave slowness. Initial estimates of the dry-bulk modulus are progressively adjusted using a modified Gregory-Pickett (1963) solution of Biot's (1956) equation to estimate a shear rigidity that converges to the well-log value of shear-wave slowness. The constraint on dynamic Poisson's ratio is then removed and a refined estimate of the dry-bulk modulus is obtained by both simulating the acoustic log (monopole) and matching the log-derived compressional-wave slowness. This technique leads to reliable estimates of dry-bulk moduli and shear rigidity that compare well to laboratory core measurements. Resulting dry-rock elastic properties can be used to calculate seismic compressional-wave and shear-wave velocities devoid of mud-filtrate invasion effects for further seismic-driven reservoir-characterization studies.

Low frequency damping and ultrasonic attenuation in Ti3Sn-based alloys

1994 ◽  
Vol 9 (6) ◽  
pp. 1441-1448 ◽  
Author(s):  
Catherine R. Wong ◽  
Robert L. Fleischer
Keyword(s):  
High Temperature ◽  
Room Temperature ◽  
Ultrasonic Attenuation ◽  
Low Frequency ◽  
Basic Mechanism ◽  
Low Frequencies ◽  
High Frequencies ◽  
Young’S Moduli ◽  
High Temperature Alloys ◽  
Damping Behavior

Studies of high-temperature alloys in the Ti-Sn system based on the intermetallic compound Ti3Sn have identified alloys that damp strongly both at low frequencies (0.1 to 10 Hz) and high frequencies (5 to 20 MHz). The low frequency damping behavior shows loss factors as high as 0.04 at room temperature and Young's moduli that rise with temperature from 40 °C to 100 °C for two alloys. Although the basic mechanism or mechanisms of energy dissipation are presently unknown, the alloys are notable for unusual shapes of microhardness indentations. The deformations imply that large reversible strains can occur at temperatures from 23 °C to 1150 °C.

Permeability and borehole Stoneley waves: Comparison between experiment and theory

Geophysics ◽  
1989 ◽  
Vol 54 (1) ◽  
pp. 66-75 ◽  
Author(s):  
Kenneth W. Winkler ◽  
Hsui‐Lin Liu ◽  
David Linton Johnson
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Theoretical Models ◽  
Oil Field ◽  
Stoneley Wave ◽  
Biot Theory ◽  
Frequency Dependent ◽  
Low Frequencies ◽  
High Frequencies ◽  
Theoretical Predictions

We performed laboratory experiments to evaluate theoretical models of borehole. Stoneley wave propagation in permeable materials. A Berea sandstone and synthetic samples made of cemented glass beads were saturated with silicone oils. We measured both velocity and attenuation over a frequency band from 10 kHz to 90 kHz. Our theoretical modeling incorporated Biot theory and Deresiewicz‐Skalak boundary conditions into a cylindrical geometry and included frequency‐dependent permeability. By varying the viscosity of the saturating pore fluid, we were able to study both low‐frequency and high‐frequency regions of Biot theory, as well as the intermediate transition zone. In both low‐frequency and high‐frequency regions of the theory, we obtained excellent agreement between experimental observations and theoretical predictions. Velocity and attenuation (1/Q) are frequency‐dependent, especially at low frequencies. Also at low frequencies, velocity decreases and attenuation increases with increasing fluid mobility (permeability/viscosity). More complicated behavior is observed at high frequencies. These results support recent observations from the oil field suggesting that Stoneley wave velocity and attenuation may be indicative of formation permeability.

scholarly journals Application of a mixture theory to stress waves in snow

1993 ◽  
Vol 18 ◽  
pp. 274-280
Author(s):  
George E. Austiguy ◽  
Robert L. Brown
Keyword(s):  
Wave Speed ◽  
Mixture Theory ◽  
Continuum Theory ◽  
Elastic Solid ◽  
Stress Waves ◽  
Low Frequencies ◽  
High Frequencies ◽  
Wave Velocities ◽  
Rotational Wave ◽  
Theory Of Mixtures

A continuum theory of mixtures is applied to model snow as a mixture of an elastic solid and an elastic fluid. Three wave types, two dilational and one rotational, are shown to exist. Numerical evaluation shows velocity and attenuation increasing with frequency for all three waves. Wave velocity increases with increasing density while attenuation decreases with increasing density for all three waves. The first dilational wave is associated with the pore fluid, has a slow wave speed and is highly attenuated. This wave exhibits diffusive behavior at low frequencies and nondispersive behavior at high frequencies. The second dilation wave is associated with the solid ice material. It is the fastest of the three wave types and does not appreciably attenuate. Nondispersive wave behavior characterizes this wave at low and high frequencies. The rotational wave occurs only in the solid, is the least attenuated of all three waves, and propagates at velocities greater than that of the first, but less than that of the second, dilational wave. The rotational wave exhibits nondispersive behavior at low and high frequencies. Wave velocities and attenuation show behavior that is in agreement with existing experimental data.

scholarly journals High Frequency Performance of Piezoelectric Diaphragms for Impedance-Based SHM Applications

2020 ◽  
Vol 2 (1) ◽  
pp. 16
Author(s):  
Guilherme Rezende ◽  
Fabricio Baptista
Keyword(s):  
High Frequency ◽  
Structural Damage ◽  
Low Cost ◽  
Low Frequency ◽  
Experimental Tests ◽  
Piezoelectric Transducers ◽  
Low Frequencies ◽  
High Frequencies ◽  
Electromechanical Impedance ◽  
Damage Indices

Piezoelectric transducers are used in a wide variety of applications, including damage detection in structural health monitoring (SHM) applications. Among the various methods for detecting structural damage, the electromechanical impedance (EMI) method is one of the most investigated in recent years. In this method, the transducer is typically excited with low frequency signals up to 500 kHz. However, recent studies have indicated the use of higher frequencies, usually above 1 MHz, for the detection of some types of damage and the monitoring of some structures’ characteristics that are not possible at low frequencies. Therefore, this study investigates the performance of low-cost piezoelectric diaphragms excited with high frequency signals for SHM applications based on the EMI method. Piezoelectric diaphragms have recently been reported in the literature as alternative transducers for the EMI method and, therefore, investigating the performance of these transducers at high frequencies is a relevant subject. Experimental tests were carried out with piezoelectric diaphragms attached to two aluminum bars, obtaining the impedance signatures from diaphragms excited with low and high frequency signals. The analysis was performed using the real part of the impedance signatures and two basic damage indices, one based on the Euclidean norm and the other on the correlation coefficient. The experimental results indicate that piezoelectric diaphragms are usable for the detection of structural damage at high frequencies, although the sensitivity decreases.

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