Elastic moduli of dry and water-saturated carbonates — Effect of depositional texture, porosity, and permeability

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. N65-N78 ◽  
Author(s):  
Ida L. Fabricius ◽  
Gregor T. Bächle ◽  
Gregor P. Eberli
Keyword(s):  
Frequency Ratio ◽  
Elastic Moduli ◽  
Reference Frequency ◽  
Fluid Substitution ◽  
Water Softening ◽  
Effect Of Water ◽  
Porosity And Permeability ◽  
Gassmann Fluid Substitution ◽  
Water Saturated ◽  
Frequency Ratios

Elastic moduli of water-saturated sedimentary rocks are in some cases different from moduli derived using Gassmann fluid substitution on data for rocks in the dry state. To address this discrepancy, we use a data set representing 115 carbonate samples from different depositional settings and a wide range of porosity and permeability. Depositional texture is reflected in the effect of water on elastic moduli and in the porosity-permeability relationship. Depositional texture is taken into account when porosity and permeability are combined in the effective specific surface of pores, which is related for a given pore fluid to the reference frequency as defined by Biot. For a given frequency of elastic waves, we obtain Biot’s frequency ratio between measured ultrasonic wave frequency and Biot reference frequency. For mostsamples with a frequency ratio above 10, elastic moduli in the water-saturated case are higher than predicted from elastic moduli in the dry case by Gassmann fluid substitution. This stiffening effect of water in some cases may be described by Biot’s high-frequency model, although in heterogeneous samples, a squirt mechanism is more probable. For data representing frequency ratios of 0.01 to 1, Gassmann fluid substitution works well. For samples with frequency ratios below 0.001, elastic moduli in the water-saturated case are lower than would be expected according to Gassmann’s equations or to Biot’s theory. This water-softening effect becomes stronger with decreasing frequency ratio. Water softening or stiffening of elastic moduli may be addressed by effective-medium modeling. In this study, we used the isoframe model to quantify water softening as a function of frequency ratio.

Exploring the X-ray universe via timing: mass of the active galactic nucleus black hole XMMUJ134736.6+173403

2019 ◽  
Vol 15 (S356) ◽  
pp. 348-350
Author(s):  
Eva Šrámková ◽  
K. Goluchová ◽  
G. Török ◽  
Marek A. Abramowicz ◽  
Z. Stuchlík ◽  
...  
Keyword(s):  
Black Hole ◽  
Frequency Ratio ◽  
Active Galactic Nucleus ◽  
Periodic Modulation ◽  
X Ray ◽  
Upper Limit ◽  
M 10 ◽  
Frequency Ratios ◽  
Quasiperiodic Oscillations ◽  
Twin Peak

AbstractA strong quasi-periodic modulation has recently been revealed in the X-ray flux of the X-ray source XMMUJ134736.6+173403. The two observed twin-peak quasiperiodic oscillations (QPOs) exhibit a 3:1 frequency ratio and strongly support the evidence for the presence of an active galactic nucleus black hole (AGN BH). It has been suggested that detections of twin-peak QPOs with commensurable frequency ratios and scaling of their periods with BH mass could provide the basis for a method intended to determine the mass of BH sources, such as AGNs. Assuming the orbital origin of QPOs, we calculate the upper and lower limit on the AGN BH mass M, reaching M ≍ 107–109M⊙. Compared to mass estimates of other sources, XMMUJ134736.6+173403 appears to be the most massive source with commensurable QPO frequencies, and its mass represents the current observational upper limit on the AGN BH mass obtained from the QPO observations.

scholarly journals Revising the musical equal temperament

2016 ◽  
Vol 38 (1) ◽  
Author(s):  
Haye Hinrichsen
Keyword(s):  
Nineteenth Century ◽  
Frequency Ratio ◽  
Western Music ◽  
Equal Temperament ◽  
Frequency Ratios ◽  
High Degree

Western music is predominantly based on the equal temperament with a constant semitone frequency ratio of 21/12. Although this temperament has been in use since the nineteenth century and in spite of its high degree of symmetry, various musicians have repeatedly expressed their discomfort with the harmonicity of certain intervals. Recently it was suggested that this problem can be overcome by introducing a modified temperament with a constant but slightly increased frequency ratio. In this paper we confirm this conjecture quantitatively. Using entropy as a measure for harmonicity, we show numerically that the harmonic optimum is in fact obtained for frequency ratios slightly larger than 21/12. This suggests that the equal temperament should be replaced by a harmonized stretched temperament as a new standard.

Permeability variation with porosity, pore space geometry, and cement type: A case history from the Snøhvit field, the Barents Sea

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. D43-D49 ◽  
Author(s):  
Sissel Grude ◽  
Jack Dvorkin ◽  
Martin Landrø
Keyword(s):  
Grain Size ◽  
Elastic Moduli ◽  
Barents Sea ◽  
Pore Space ◽  
Rock Physics ◽  
Additional Information ◽  
Order Of Magnitude ◽  
Porosity And Permeability ◽  
Lower Permeability ◽  
Permeability Variation

Laboratory permeability data from the brine-filled Tubåen Formation in the Snøhvit field show an order of magnitude permeability variation for approximately the same porosity. This variation in permeability is explained by a modified Kozeny-Carman equation that exploits the relationships among permeability, porosity, cementation, and pore geometry. The expression correlates the slope in a logarithmic plot of porosity versus permeability with the amount of contact cement and sorting, and the intercept with the grain size. Additional information about sorting and/or cementation can be used to better constrain the slope of the plot. Based on this equation, we found that the grain size and the amount of contact cement increased with depth in the lowermost Tubåen 1–3 sandstone units, this led to an increasing permeability with depth, in the same porosity range. The permeability variation in the shallowest Tubåen 4 sandstone unit was affected by sorting to a larger degree than the remaining Tubåen intervals, which influenced the cementation factor, porosity, and permeability simultaneously. These findings were supported by the depositional environment of the formation, a petrology study of grain size and sorting and a rock-physics study. The rock-physics study indicated that the samples with higher permeability had higher elastic moduli compared with the samples with lower permeability. This correlation between permeability and elastic moduli can be explained by the increasing amount of contact cement for the stiffer, high-permeability samples.

Lock-On Vortex Shedding Patterns and Bifurcation Analysis of the Forced Streamwise Oscillation of the Cylinder Wake

2015 ◽  
Vol 25 (09) ◽  
pp. 1530022
Author(s):  
N. Nabatian ◽  
N. W. Mureithi
Keyword(s):  
Frequency Ratio ◽  
Transverse Velocity ◽  
Lift Coefficient ◽  
Oscillation Amplitude ◽  
Vortex Formation ◽  
Excitation Frequency ◽  
Immersed Boundary ◽  
Cylinder Wake ◽  
Single Vortex ◽  
Frequency Ratios

The two-dimensional numerical simulation of the flow over a cylinder forced to oscillate in the streamwise direction for Re = 200 is performed in CFX ANSYS. The controlled-vibration comprises of prescribed inline vibration from displacement amplitude-to-cylinder diameter A/D = 0.05 up to 0.5 with the excitation frequency ratios of 1, 1.5 and 2 including the harmonic and superharmonic excitation regions. The immersed boundary method is used to model the cylinder oscillation. Modal decomposition of the transverse velocity field via the proper orthogonal decomposition (POD) method is applied to uncover the interaction of symmetric and antisymmetric modes of the near wake. A model using the first two POD modes is developed based on symmetry group equivariance. The model predicts the mode interactions and bifurcated solution branches for all cases, and is shown to be in good agreement with numerical as well as previous experimental results. Lock-on is determined for a range of values of the oscillation amplitudes and frequency ratios. It is shown that the lock-on range widens with increasing nondimensional oscillation amplitude. The asymmetric 2S, P + S and symmetric pattern S with symbol S for a single vortex and P for a vortex pair shed per cycle, as well as a regime in which vortex formation is not synchronized with cylinder motion are observed in the cylinder wake depending on the combination of oscillation amplitude and frequency ratio. The frequency ratio variation from 1 to 2 leads to the switching from asymmetric to symmetric modes. The symmetric flow pattern corresponds to a near zero lift coefficient on the cylinder.

scholarly journals Formation of double emulsion micro-droplets in a microfluidic device using a partially hydrophilic–hydrophobic surface

RSC Advances ◽  
2021 ◽  
Vol 11 (56) ◽  
pp. 35653-35662
Author(s):  
Ampol Kamnerdsook ◽  
Ekachai Juntasaro ◽  
Numfon Khemthongcharoen ◽  
Mayuree Chanasakulniyom ◽  
Witsaroot Sripumkhai ◽  
...  
Keyword(s):  
Flow Rate ◽  
Frequency Ratio ◽  
Encapsulation Efficiency ◽  
Double Emulsion ◽  
Hydrophobic Surface ◽  
Water Droplets ◽  
Oil In Water ◽  
Rate Ratios ◽  
Frequency Ratios ◽  
Ratio Range

(a) Droplet encapsulation efficiency & inner and outer diameters of water-in-oil-in-water droplets at various frequency ratios and flow rate ratios and (b) Images of water-in-oil-in-water droplets over a frequency-ratio range of fr = 0.73–1.30

Sign in / Sign up

Export Citation Format

Share Document