Bulk modulus for fluid-saturated rocks at intermediate frequencies: Modification of squirt flow model proposed by Gurevich et al.

2021 ◽  
Author(s):  
Liming Zhao ◽  
Tongjun Chen ◽  
Genyang Tang
Keyword(s):  
Bulk Modulus ◽  
Flow Model ◽  
Full Range ◽  
Total Porosity ◽  
Wave Dispersion ◽  
Intermediate Frequency ◽  
Original Model ◽  
Frequency Range ◽  
The Matrix ◽  
Pore Fraction

Summary Squirt flow is an essential cause of wave dispersion and attenuation in saturated rocks. The squirt flow model, proposed by Gurevich et al. (2010), has been widely applied to explain the wave dispersion and associated attenuation for saturated rocks at sonic and seismic frequency bands. In this model, the saturated bulk modulus is obtained by taking the partially relaxed frame bulk modulus as the dry frame modulus into Gassmann's formula with the mineral bulk modulus as the matrix bulk modulus. However, because of the weakening effect of soft pores on rock matrix bulk modulus, the model cannot accurately predict the saturated bulk modulus when the soft-pore fraction (the ratio of the soft porosity to total porosity) becomes large. We modified this model following Gurevich et al. (2010) by setting a different boundary condition. The modified squirt flow model can obtain correct saturated bulk modulus for large soft-pore fractions in the full range of frequencies, showing excellent consistency with the predictions of Gassmann and Mavko & Jizba (modified) at both low- and high-frequency limits, respectively. Modeling results show that the saturated bulk moduli and their dispersions calculated by the original and modified models exhibit little difference when the soft-pore fraction is small. Under this condition, the original model is as effective and accurate as the modified one. When the soft-pore fraction becomes larger, the differences in the bulk moduli and their dispersions become substantial, suggesting the original model is not applicable any longer. Furthermore, the differences calculated for the intermediate frequency range is even more obvious than other ranges, suggesting that the modified model should be used to calculate the bulk modulus and the dispersion in this frequency range. In summary, the modified squirt flow model can extend the original model's applicable range in terms of soft-pore fraction and has a potential application in rocks having a relatively large amount of soft-pore fraction such as basalts.

Bulk modulus for fluid-saturated rocks at high frequency: Modification of squirt flow model proposed by Mavko & Jizba

2021 ◽  
Author(s):  
Liming Zhao ◽  
Tongjun Chen ◽  
Tapan Mukerji ◽  
Genyang Tang
Keyword(s):  
Bulk Modulus ◽  
High Frequency ◽  
Flow Model ◽  
Crack Density ◽  
Total Porosity ◽  
Original Matrix ◽  
The Matrix ◽  
Potential Applications ◽  
Applicable Range ◽  
Pore Fraction

Summary The squirt flow model, proposed by Mavko & Jizba, has been widely used in explaining the frequency-related modulus and velocity dispersion between ultrasonic and seismic measurements. In this model, the saturated bulk modulus at high frequency is obtained by taking the so-called unrelaxed frame bulk modulus into Biot's or Gassmann's formula. When using Gassmann's formula, the mineral bulk modulus is taken as matrix bulk modulus. However, the soft pores (cracks) in rocks have a weakening effect on the matrix bulk modulus. The saturated bulk modulus at high frequency calculated with mineral bulk modulus as matrix bulk modulus is higher than the real values. To overcome this shortcoming we propose a modified matrix bulk modulus based on the Betti-Rayleigh reciprocity theorem and non-interaction approximation. This modification takes the weakening effect of soft pores (cracks) into consideration and allows calculating the correct saturated bulk modulus at high frequency under different soft-pore fractions (the ratio of soft porosity to total porosity) or crack densities. We also propose an alternative expression of the modified matrix bulk modulus, which can be directly obtained from laboratory measurements. The numerical results show that the saturated bulk modulus at high frequency using the original matrix bulk modulus (i.e. mineral bulk modulus) is approximated to that using the modified one only for rocks containing a small amount of soft-pore fraction. However, as the soft-pore fraction becomes substantial, using the original bulk matrix modulus is not applicable, but the modified one is still applicable. Furthermore, the results of the modified squirt flow model show good consistency with published numerical and experimental data. The proposed modification extends the applicable range of soft-pore fraction (crack density) of the previous model, and has potential applications in media having a relatively substantial fraction of soft pores or almost only soft pores, such as granite, basalt, and thermally-cracked glasses.

Dependence of the Frequency Spectrum of a Circular Disk on Poisson’s Ratio

1957 ◽  
Vol 24 (1) ◽  
pp. 53-54
Author(s):  
R. L. Sharma
Keyword(s):  
Frequency Spectrum ◽  
Poisson’S Ratio ◽  
Circular Disk ◽  
Intermediate Frequency ◽  
Poisson's Ratio ◽  
Axially Symmetric ◽  
Frequency Range ◽  
Flexural Vibrations ◽  
Circular Disks

Abstract The results of computations of frequencies of axially symmetric flexural vibrations of circular disks are given for an intermediate frequency range and for several values of Poisson’s ratio.

A Comparison of Rotordynamic-Coefficient Predictions for Annular Honeycomb Gas Seals Using Three Different Friction-Factor Models

2002 ◽  
Vol 124 (3) ◽  
pp. 524-529 ◽  
Author(s):  
Rohan J. D’Souza ◽  
Dara W. Childs
Keyword(s):  
Friction Factor ◽  
Flow Model ◽  
Factor Model ◽  
Control Volume ◽  
Bulk Flow ◽  
Shear Stresses ◽  
Steam Turbines ◽  
Frequency Range ◽  
Rotordynamic Coefficients ◽  
Rotordynamic Coefficient

A two-control-volume bulk-flow model is used to predict rotordynamic coefficients for an annular, honeycomb-stator/smooth-rotor gas seal. The bulk-flow model uses Hirs’ turbulent-lubrication model, which requires a friction factor model to define the shear stresses at the rotor and stator wall. Rotordynamic coefficients predictions are compared for the following three variations of the Blasius pipe-friction model: (i) a basic model where the Reynolds number is a linear function of the local clearance, fs=ns Rems (ii) a model where the coefficient is a function of the local clearance, and (iii) a model where both the coefficient and exponent are functions of the local clearance. The latter models are based on data that shows the friction factor increasing with increasing clearances. Rotordynamic-coefficient predictions shows that the friction-factor-model choice is important in predicting the effective-damping coefficients at a lower frequency range (60∼70 Hz) where industrial centrifugal compressors and steam turbines tend to become unstable. At a higher frequency range, irrespective of the friction-factor model, the rotordynamic-coefficient predictions tend to coincide. Blasius-based Models which directly account for the observed increase in stator friction factors with increasing clearance predict significantly lower values for the destabilizing cross-coupled stiffness coefficients.

scholarly journals Parallel PWMs Based Fully Digital Transmitter with Wide Carrier Frequency Range

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Zhou ◽  
Kun Zhang ◽  
Wenbiao Zhou ◽  
Yanjun Zhang ◽  
Dake Liu
Keyword(s):  
Carrier Frequency ◽  
Pulse Width ◽  
Power Efficiency ◽  
Intermediate Frequency ◽  
Delay Lines ◽  
Error Vector Magnitude ◽  
Frequency Range ◽  
Digital Transmitter ◽  
High Power Efficiency ◽  
Vector Magnitude

The carrier-frequency (CF) and intermediate-frequency (IF) pulse-width modulators (PWMs) based on delay lines are proposed, where baseband signals are conveyed by both positions and pulse widths or densities of the carrier clock. By combining IF-PWM and precorrected CF-PWM, a fully digital transmitter with unit-delay autocalibration is implemented in 180 nm CMOS for high reconfiguration. The proposed architecture achieves wide CF range of 2 M–1 GHz, high power efficiency of 70%, and low error vector magnitude (EVM) of 3%, with spectrum purity of 20 dB optimized in comparison to the existing designs.

Modification of DDES Based on SST kω Model for Tip Leakage Flow in Turbomachinery

2020 ◽  
Author(s):  
Yanfei Gao ◽  
Yangwei Liu
Keyword(s):  
Reynolds Number ◽  
Flow Model ◽  
Turbulence Modeling ◽  
Streamwise Vortex ◽  
Original Model ◽  
Leakage Flow ◽  
Mean Flow ◽  
Tip Leakage Flow ◽  
Modified Model ◽  
Tip Leakage

Abstract Both LES and DDES are conducted in a low-Reynolds number tip leakage flow model. The DDES uses the SST kω model and employs the same grid with the LES, but the turbulence field diverges from the LES result. Referring to the comparison between LES and DDES, a modification of the zonal function in the DDES model is proposed, which enhances the dissipation of the modeled turbulence thus promote the transition to fully LES in the tip region when the mesh is fine enough. It can generate much finer vortex structure than the original model, including the primary streamwise vortex, induced vortices and the vortex fragments after breakdown. The modification fixes the underestimation of the vorticity and pressure drop at the formation stage of the tip leakage vortex, and generates more reasonable turbulence field and energy spectra. The modified model is introduced to a real rotor simulation at engineering Reynolds number. Compared with the original model on both mean flow field and turbulence field, the modified model shows favorable agreements with the measurements. The study also gives a practical example of using the tip leakage flow model in turbulence modeling.

Sign in / Sign up

Export Citation Format

Share Document