Modulus—porosity relations, Gassmann’s equations, and the low‐frequency elastic‐wave response to fluids

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1355-1363 ◽  
Author(s):  
Richard C. Nolen‐Hoeksema

Gassmann’s equations relate the low‐frequency drained and undrained elastic‐wave response to fluids. This tutorial explores how different modulus—porosity relationships affect predictions of the low‐frequency elastic‐wave response to fluids based on Gassmann’s equations. I take different modulus—porosity relations and substitute them into Gassmann’s equations through the framework moduli. The results illustrate the range of responses to fluids and can be summarized in a nomograph of the effective fluid coefficient, which quantifies the change in the pore‐space modulus ([Formula: see text]) in response to a change in fluid modulus ([Formula: see text]). Two ratios control the effective fluid coefficient: the ratio of the fluid modulus to the solid‐grain modulus ( [Formula: see text]) and the ratio of the Biot coefficient to porosity ([Formula: see text]). The effective fluid coefficient nomograph is a convenient tool for estimating how low‐frequency elastic‐wave properties will respond to changes in reservoir fluids.

2020 ◽  
Author(s):  
Srisharan Shreedharan ◽  
◽  
David Chas Bolton ◽  
Jacques Riviere ◽  
Chris Marone

2020 ◽  
Vol 12 (1) ◽  
pp. 299-306
Author(s):  
Jiang Jia ◽  
Shizhen Ke ◽  
Junjian Li ◽  
Zhengming Kang ◽  
Xuerui Ma ◽  
...  

AbstractLow-frequency resistivity logging plays an important role in the field of petroleum exploration, but the complex resistivity spectrum of rock also contains a large amount of information about reservoir parameters. The complex resistivity spectra of 15 natural sandstone cores from western China, with different water saturations, were measured with an impedance analyzer. The pore space of each core was saturated with NaCl solution, and measurements were collected at a frequency range of 40–15 MHz. The results showed a linear relationship between the real resistivity at 1 kHz and the maximum values of imaginary resistivity for each core with different water saturations. The slopes of the linear best-fit lines had good linear relationships with the porosity and the permeability of cores. Based on this, a permeability estimation model was proposed and tested. In addition, the maxima of imaginary resistivity had power exponential relationships with the porosity and the water saturation of the cores. A saturation evaluation model based on the maxima of imaginary resistivity was established by imitating Archie’s formula. The new models were found to be feasible for determining the permeability and saturation of sandstone based on complex resistivity spectrum measurements. These models advance the application of complex resistivity spectrum in petrophysics.


2021 ◽  
Vol 11 (7) ◽  
pp. 3124
Author(s):  
Alya Alhammadi ◽  
Jin-You Lu ◽  
Mahra Almheiri ◽  
Fatima Alzaabi ◽  
Zineb Matouk ◽  
...  

A numerical simulation study on elastic wave propagation of a phononic composite structure consisting of epoxy and tungsten carbide is presented for low-frequency elastic wave attenuation applications. The calculated dispersion curves of the epoxy/tungsten carbide composite show that the propagation of elastic waves is prohibited inside the periodic structure over a frequency range. To achieve a wide bandgap, the elastic composite structure can be optimized by changing its dimensions and arrangement, including size, number, and rotation angle of square inclusions. The simulation results show that increasing the number of inclusions and the filling fraction of the unit cell significantly broaden the phononic bandgap compared to other geometric tunings. Additionally, a nonmonotonic relationship between the bandwidth and filling fraction of the composite was found, and this relationship results from spacing among inclusions and inclusion sizes causing different effects on Bragg scatterings and localized resonances of elastic waves. Moreover, the calculated transmission spectra of the epoxy/tungsten carbide composite structure verify its low-frequency bandgap behavior.


Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 854-859 ◽  
Author(s):  
Xiao Ming Tang

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.


2021 ◽  
Author(s):  
Lucile Turc ◽  
Markus Battarbee ◽  
Urs Ganse ◽  
Andreas Johlander ◽  
Yann Pfau-Kempf ◽  
...  

<p>The foreshock, extending upstream of the quasi-parallel shock and populated with shock-reflected particles, is home to intense wave activity in the ultra-low frequency range.<em> </em>The most commonly observed of these waves are the “30 s” waves, fast magnetosonic waves propagating sunward in the plasma rest frame, but carried earthward by the faster solar wind flow. These waves are thought to be the main source of Pc3 magnetic pulsations (10 – 45 s) in the dayside magnetosphere. A handful of case studies with suitable spacecraft conjunctions have allowed simultaneous investigations of the wave properties in different geophysical regions, but the global picture of the wave transmission from the foreshock through the magnetosheath into the magnetosphere is still not known. In this work, we use global simulations performed with the hybrid-Vlasov model Vlasiator to study the Pc3 wave properties in the foreshock, magnetosheath and magnetosphere for different solar wind conditions. We find that in all three regions the wave power peaks at higher frequencies when the interplanetary magnetic field strength is larger, consistent with previous studies. While the transverse wave power decreases with decreasing Alfvén Mach number in the foreshock, the compressional wave power shows little variation. In contrast, in the magnetosheath and the magnetosphere, the compressional wave power decreases with decreasing Mach number. Inside the magnetosphere, the distribution of wave power varies with the IMF cone angle. We discuss the implications of these results for the propagation of foreshock waves across the different geophysical regions, and in particular their transmission through the bow shock.</p>


Author(s):  
Matthew Blyth ◽  
◽  
Naoki Sakiyama ◽  
Hiroshi Hori ◽  
Hiroaki Yamamoto ◽  
...  

A new logging-while-drilling (LWD) acoustic tool has been developed with novel ultrasonic pitch-catch and pulse-echo technologies. The tool enables both high-resolution slowness and reflectivity images, which cannot be addressed with conventional acoustic logging. Measuring formation elastic-wave properties in complex, finely layered formations is routinely attempted with sonic tools that measure slowness over a receiver array with a length of 2 ft or more depending upon the tool design. These apertures lead to processing results with similar vertical resolutions, obscuring the true slowness of any layering occurring at a finer scale. If any of these layers present significantly different elastic-wave properties than the surrounding rock, then they can play a major role in both wellbore stability and hydraulic fracturing but can be absent from geomechanical models built on routine sonic measurements. Conventional sonic tools operate in the 0.1- to 20-kHz frequency range and can deliver slowness information with approximately 1 ft or more depth of investigation. This is sufficient to investigate the far-field slowness values but makes it very challenging to evaluate the near-wellbore region where tectonic stress redistribution causes pronounced azimuthal slowness variation. This stress-induced slowness variation is important because it is also a key driver of wellbore geomechanics. Moreover, in the presence of highly laminated formations, there can be a significant azimuthal variation of slowness due to layering that is often beyond the resolution of conventional sonic tools due to their operating frequency. Finally, in horizontal wells, multiple layer slownesses are being measured simultaneously because of the depth of investigation of conventional sonic tools. This can cause significant interpretational challenges. To address these challenges, an entirely new design approach was needed. The novel pitch-catch technology operates over a wide frequency range centered at 250 kHz and contains an array of receivers having a 2-in. receiver aperture. The use of dual ultrasonic technology allows the measurement of high-resolution slowness data azimuthally as well as reflectivity and caliper images. The new LWD tool was run in both vertical and horizontal wells and directly compared with both wireline sonic and imaging tools. The inch-scale slownesses obtained show characteristic features that clearly correlate to the formation lithology and structure indicated by the images. These features are completely absent from the conventional sonic data due to its comparatively lower vertical resolution. Slowness images from the tool reflect the formation elastic-wave properties at a fine scale and show dips and lithological variations that are complementary to the data from the pulse-echo images. The physics of the measurement are discussed, along with its ability to measure near-wellbore slowness, elastic-wave properties, and stress variations. Additionally, the effect of the stress-induced, near-wellbore features seen in the slowness images and the pulse-echo images is discussed with the wireline dipole shear anisotropy processing.


2013 ◽  
Vol 31 (11) ◽  
pp. 1159-1167 ◽  
Author(s):  
B. Keshavarzi ◽  
R. Karimi ◽  
I. Najafi ◽  
M. H. Ghazanfari ◽  
M. Amani ◽  
...  

2004 ◽  
Vol 270-273 ◽  
pp. 1645-1652
Author(s):  
Shinichi Hattori ◽  
Toshiro Kamada ◽  
Takashi Shimada ◽  
Yasuhiro Takemura ◽  
Kanji Matsuhashi

Author(s):  
Shinichi Hattori ◽  
Takashi Shimada ◽  
Ryousuke Taniguchi ◽  
Kanji Matsuhashi

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