Inversion for Biot-consistent material properties in subresonant oscillation experiments with fluid-saturated porous rock

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. MR67-MR79 ◽  
Author(s):  
Igor B. Morozov ◽  
Wubing Deng
Keyword(s):  
Traveling Wave ◽  
Seismic Waves ◽  
Rock Specimen ◽  
Low Frequency ◽  
P Wave ◽  
Axial Deformation ◽  
Porous Rock ◽  
Frequency Dependent ◽  
Shear Moduli ◽  
Young’S Moduli

To quantitatively interpret the results of a subresonant laboratory or numerical experiment with wet porous rock, it is insufficient to merely state the measured frequency-dependent viscoelastic moduli and [Formula: see text]-factors. The measured properties are apparent, i.e., dependent on the experimental setup such as the length of the sample and boundary conditions for pore flows. To reveal the true properties of the material, all experimental factors need to be accurately modeled and corrected for. Here, such correction is performed by developing an effective Biot’s model for the material and using it to predict driven oscillations of a cylindrical rock specimen. The model explicitly describes elastic and inertial effects, Biot’s flows, and viscous internal friction within the solid frame and pore fluid, and it approximates squirt and other wave-induced flow effects. The model predicts the dynamic permeability of the specimen, fast (traveling) and slow (diffusive) P- and axial-deformation waves, and it allows accurate modeling of any other ultrasonic or seismic-frequency experiments with the same rock. To illustrate the approach, attenuation and dispersion data from two laboratory and numerical experiments with sandstones are inverted for effective, frequency-dependent moduli of drained sandstone. Several observations from this inversion may be useful for interpreting experiments with porous rock. First, Young’s moduli measured in a short rock cylinder differ from those in a traveling wave within an infinite rod. In particular, for the modeled 8 cm long rock specimen, modulus dispersion and attenuation ([Formula: see text]) are approximately 10 times greater than for a traveling wave. Second, P-wave moduli cannot be derived from the measured Young’s and shear moduli by using conventional (visco)elastic relations. Third, because of wavelengths comparable with the size of the specimen, slow waves contribute to its quasistatic and low-frequency behaviors. Similar observations should also apply to seismic waves traveling through approximately 10 cm layering in the field.

scholarly journals Vertical to Horizontal Spectral Ratio (VHSR) Response of Seismic Wave Propagation in a Homogeneous Elastic – Poroelastic Medium Using The Spectral Finite Element Method

2021 ◽  
Vol 11 (1) ◽  
pp. 95
Author(s):  
Sudarmaji Saroji ◽  
Budi Eka Nurcahya ◽  
Nivan Ramadhan Sugiantoro
Keyword(s):  
Finite Element Method ◽  
Elastic Medium ◽  
Seismic Waves ◽  
Low Frequency ◽  
Seismic Wave Propagation ◽  
P Wave ◽  
Poroelastic Medium ◽  
Compressional Waves ◽  
Spectral Finite Element Method ◽  
Spectral Finite Element

<p>Numerical modeling of 2D seismic wave propagation using spectral finite element method to estimate the response of seismic waves passing through the poroelastic medium from a hydrocarbon reservoir has been carried out. A hybrid simple model of the elastic - poroelastic - elastic with a mesoscopic scale element size of about 50cm was created. Seismic waves which was in the form of the ricker function are generated on the first elastic medium, propagated into the poroelastic medium and then transmitted to the second elastic medium. Pororoelastic medium is bearing hydrocarbon fluid in the form of gas, oil or water. Vertical and horizontal component of velocity seismograms are recorded on all mediums. Seismograms which are recorded in the poroelastic and second elastic medium show the existence of slow P compressional waves following fast P compressional waves that do not appear on the seismogram of the first elastic medium. The slow P wave is generated when the fast P wave enters the interface of the elastic - poroelastic boundary, propagated in the poroelastic medium and is transmited to the second elastic medium. The curves of Vertical to horizontal spectrum ratio (VHSR) which are observed from seismograms recorded in the poroelastic and the second elastic medium show that the peak of VHSR values at low frequency correlated with the fluid of poroelastic reservoir. The highest VHSR value at the low frequency which is recorded on the seismogram is above the 2.5 Hz frequency for reservoirs containing gas and oil in the second elastic medium, while for the medium containing water is the highest VHSR value is below the 2.5 Hz frequency.</p>

scholarly journals On The Low-Frequency Elastic Response of Pierre Shale During Temperature Cycles

2021 ◽  
Author(s):  
Stian Rørheim ◽  
Andreas Bauer ◽  
Rune M Holt
Keyword(s):  
Wave Velocity ◽  
Low Frequency ◽  
P Wave ◽  
Rock Properties ◽  
Fluid Viscosity ◽  
S Wave ◽  
Temperature Cycles ◽  
Wave Velocities ◽  
Young’S Moduli ◽  
P Wave Velocity

Summary The impact of temperature on elastic rock properties is less-studied and thus less-understood than that of pressure and stress. Thermal effects on dispersion are experimentally observed herein from seismic to ultrasonic frequencies: Young’s moduli and Poisson’s ratios plus P- and S-wave velocities are determined by forced-oscillation (FO) from 1 to 144 Hz and by pulse-transmission (PT) at 500 kHz. Despite being the dominant sedimentary rock type, shales receive less experimental attention than sandstones and carbonates. To our knowledge, no other FO studies on shale at above ambient temperatures exist. Temperature fluctuations are enforced by two temperature cycles from 20 via 40 to 60○C and vice versa. Measured rock properties are initially irreversible but become reversible with increasing number of heating and cooling segments. Rock property-sensitivity to temperature is likewise reduced. It is revealed that dispersion shifts towards higher frequencies with increasing temperature (reversible if decreased), Young’s moduli and P-wave velocity moduli and P-wave velocity maxima occur at 40○C for frequencies below 56 Hz, and S-wave velocities remain unchanged with temperature (if the first heating segment is neglected) at seismic frequencies. In comparison, ultrasonic P- and S-wave velocities are found to decrease with increasing temperatures. Behavioural differences between seismic and ultrasonic properties are attributed to decreasing fluid viscosity with temperature. We hypothesize that our ultrasonic recordings coincide with the transition-phase separating the low- and high-frequency regimes while our seismic recordings are within the low-frequency regime.

Macroscopic mechanical properties of porous rock with one saturating fluid

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. MR223-MR239 ◽  
Author(s):  
Wubing Deng ◽  
Igor B. Morozov
Keyword(s):  
Mechanical Properties ◽  
Laboratory Experiments ◽  
Kinetic Equations ◽  
Low Frequency ◽  
Fluid Flows ◽  
Pore Fluid ◽  
P Wave ◽  
Rock Properties ◽  
Porous Rock ◽  
Arbitrary Boundary

Effective frequency-dependent moduli and [Formula: see text]-factors are broadly used for characterizing the behavior of earth media in laboratory and field seismic observations. However, such properties are wavemode- and experiment-dependent and are often incomplete and/or inaccurate for modeling realistic situations. For example, viscoelastic moduli for porous fluid-saturated rock are usually derived for primary waves, but they may not apply to cases in which secondary waves are important, such as reflections in finely layered poroelastic media or quasistatic pore-fluid flows in laboratory experiments. To obtain a model applicable to all cases, equations of mechanics should be used, and mechanical properties of the material must be identified. To reveal and measure such properties for fluid-saturated porous rock, we have developed a Biot-consistent model based on Lagrangian continuum mechanics. The model is “minimal,” purely macroscopic, and independent of the macrostructure or patterns of pore-fluid flows; thus, it could represent many existing wave-induced fluid-flow (WIFF) as well as non-WIFF models. Due to its mechanical definition, the model should be applicable to all rock-physics experiments (linear creep, pore flow, low-frequency, resonant, or ultrasonic), any waves in the field (primary, secondary, standing, surface, etc.) under arbitrary boundary conditions, and also finite-difference and finite-element numerical modeling. When based on this model, numerical simulations require no integral equations, fractional derivatives, memory variables, or additional kinetic equations. We further use the model to invert for detailed elastic and viscous properties of fluid-saturated Berea and Fontainebleau sandstones from recently published low-frequency laboratory experiments. All rock properties inferred in the model are time- and frequency-independent, comparable to other physical observations, and the model closely predicts the data. The model can be approximately pore-fluid independent, which allows performing rigorous fluid substitution with viscous pore fluids. As an illustration, P-wave velocity dispersion and attenuation in water-, oil-, and gas-saturated sandstone are simulated.

scholarly journals Development of a Vibroacoustic Stochastic Finite Element Prediction Tool for a CLT Floor

2019 ◽  
Vol 9 (6) ◽  
pp. 1106 ◽  
Author(s):  
Cheng Qian ◽  
Sylvain Ménard ◽  
Delphine Bard ◽  
Juan Negreira
Keyword(s):  
Material Properties ◽  
Deterministic Model ◽  
Low Frequency ◽  
Stochastic Approach ◽  
Calibration Method ◽  
Sound Insulation ◽  
Wood Structures ◽  
Shear Moduli ◽  
Young’S Moduli ◽  
Impact Noise

Low frequency impact sound insulation is a challenging task in wooden buildings. Low frequency prediction tools are needed to access the dynamic behavior of a wooden floor in an early design phase to ultimately reduce the low frequency impact noise. However, due to the complexity of wood and different structural details, accurate vibration predictions of wood structures are difficult to attain. Meanwhile, a deterministic model cannot properly represent the real case due to the uncertainties coming from the material properties and geometrical changes. The stochastic approach introduced in this paper aims at quantifying the uncertainties induced by material properties and proposing an alternative calibration method to obtain a relative accurate result instead of the conventional manual calibration. In addition, 100 simulations were calculated in different excitation positions to assess the uncertainties induced by material properties of cross-laminated-timber A comparison between the simulated and measured results was made in order to extract the best combination of Young’s moduli and shear moduli in different directions of the CLT panel.

Integration of Multi-geophysical Approaches to Identify Potential Pathways of Heavy Metals Contamination - A Case Study in Zeida, Morocco

2020 ◽  
Vol 25 (3) ◽  
pp. 415-423
Author(s):  
Ahmed Lachhab ◽  
El Mehdi Benyassine ◽  
Mohamed Rouai ◽  
Abdelilah Dekayir ◽  
Jean C. Parisot ◽  
...  
Keyword(s):  
Heavy Metals ◽  
Seismic Velocity ◽  
Seismic Refraction ◽  
Geophysical Methods ◽  
Low Frequency ◽  
Electrical Current ◽  
P Wave ◽  
Low Resistivity ◽  
Refraction Tomography ◽  
Geophysical Surveys

The tailings of Zeida's abandoned mine are found near the city of Midelt, in the middle of the high Moulouya watershed between the Middle and the High Atlas of Morocco. The tailings occupy an area of about 100 ha and are stored either in large mining pit lakes with clay-marl substratum or directly on a heavily fractured granite bedrock. The high contents of lead and arsenic in these tailings have transformed them into sources of pollution that disperse by wind, runoff, and seepage to the aquifer through faults and fractures. In this work, the main goal is to identify the pathways of contaminated water with heavy metals and arsenic to the local aquifers, water ponds, and Moulouya River. For this reason, geophysical surveys including electrical resistivity tomography (ERT), seismic refraction tomography (SRT) and very low-frequency electromagnetic (VLF-EM) methods were carried out over the tailings, and directly on the substratum outside the tailings. The result obtained from combining these methods has shown that pollutants were funneled through fractures, faults, and subsurface paleochannels and contaminated the hydrological system connecting groundwater, ponds, and the river. The ERT profiles have successfully shown the location of fractures, some of which extend throughout the upper formation to depths reaching the granite. The ERT was not successful in identifying fractures directly beneath the tailings due to their low resistivity which inhibits electrical current from propagating deeper. The seismic refraction surveys have provided valuable details on the local geology, and clearly identified the thickness of the tailings and explicitly marked the boundary between the Triassic formation and the granite. It also aided in the identification of paleochannels. The tailings materials were easily identified by both their low resistivity and low P-wave velocity values. Also, both resistivity and seismic velocity values rapidly increased beneath the tailings due to the compaction of the material and lack of moisture and have proven to be effective in identifying the upper limit of the granite. Faults were found to lie along the bottom of paleochannels, which suggest that the locations of these channels were caused by these same faults. The VLF-EM surveys have shown tilt angle anomalies over fractured areas which were also evinced by low resistivity area in ERT profiles. Finally, this study showed that the three geophysical methods were complementary and in good agreement in revealing the pathways of contamination from the tailings to the local aquifer, nearby ponds and Moulouya River.

A Novel Fault-location Method for HVDC Transmission Lines Based on Concentric Relaxation Principle and Wavelet Packet

2020 ◽  
Vol 13 (5) ◽  
pp. 705-716
Author(s):  
Congshan Li ◽  
Ping He ◽  
Feng Wang ◽  
Cunxiang Yang ◽  
Yukun Tao ◽  
...  
Keyword(s):  
Transmission Lines ◽  
Traveling Wave ◽  
Fault Location ◽  
Wave Attenuation ◽  
Wavelet Packet ◽  
Low Frequency ◽  
Evaluation Process ◽  
Location Method ◽  
Hvdc Transmission ◽  
Instantaneous Energy

Background: A novel fault location method of HVDC transmission line based on a concentric relaxation principle is proposed in this paper. Methods: Due to the different position of fault, the instantaneous energy measured from rectifier and inverter are different, and the ratio k between them is the relationship to the fault location d. Through the analysis of amplitude-frequency characteristics, we found that the wave attenuation characteristic of low frequency in the traveling wave is stable, and the amplitude of energy is larger, so we get the instantaneous energy ratio by using the low-frequency data. By using the method of wavelet packet decomposition, the voltage traveling wave signal was decomposed. Results: Finally, calculate the value k. By using the data fitting, the relative function of k and d can be got, that is the fault location function. Conclusion: After an exhaustive evaluation process considering different fault locations, fault resistances, and noise on the unipolar DC transmission system, four-machine two-area AC/DC parallel system, and an actual complex grid, the method presented here showed a very accurate and robust behavior.

scholarly journals Hearing at threshold intensities: by slow mechanical traveling waves or by fast cochlear fluid pressure waves

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Haim Sohmer
Keyword(s):  
Soft Tissue ◽  
Hair Cells ◽  
Traveling Wave ◽  
Basilar Membrane ◽  
Fluid Pressure ◽  
Low Frequency ◽  
Frequency Discrimination ◽  
Outer Hair Cells ◽  
Common Mechanism ◽  
Frequency Stimulation

The three modes of auditory stimulation (air, bone and soft tissue conduction) at threshold intensities are thought to share a common excitation mechanism: the stimuli induce passive displacements of the basilar membrane propagating from the base to the apex (slow mechanical traveling wave), which activate the outer hair cells, producing active displacements, which sum with the passive displacements. However, theoretical analyses and modeling of cochlear mechanics provide indications that the slow mechanical basilar membrane traveling wave may not be able to excite the cochlea at threshold intensities with the frequency discrimination observed. These analyses are complemented by several independent lines of research results supporting the notion that cochlear excitation at threshold may not involve a passive traveling wave, and the fast cochlear fluid pressures may directly activate the outer hair cells: opening of the sealed inner ear in patients undergoing cochlear implantation is not accompanied by threshold elevations to low frequency stimulation which would be expected to result from opening the cochlea, reducing cochlear impedance, altering hydrodynamics. The magnitude of the passive displacements at threshold is negligible. Isolated outer hair cells in fluid display tuned mechanical motility to fluid pressures which likely act on stretch sensitive ion channels in the walls of the cells. Vibrations delivered to soft tissue body sites elicit hearing. Thus, based on theoretical and experimental evidence, the common mechanism eliciting hearing during threshold stimulation by air, bone and soft tissue conduction may involve the fast-cochlear fluid pressures which directly activate the outer hair cells.

The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 309-318 ◽  
Author(s):  
Jorge O. Parra
Keyword(s):  
Wave Equation ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Seismic Waves ◽  
Transversely Isotropic ◽  
P Wave ◽  
Fluid Properties ◽  
Permeability Anisotropy ◽  
Attenuation And Dispersion ◽  
Maximum Permeability

The transversely isotropic poroelastic wave equation can be formulated to include the Biot and the squirt‐flow mechanisms to yield a new analytical solution in terms of the elements of the squirt‐flow tensor. The new model gives estimates of the vertical and the horizontal permeabilities, as well as other measurable rock and fluid properties. In particular, the model estimates phase velocity and attenuation of waves traveling at different angles of incidence with respect to the principal axis of anisotropy. The attenuation and dispersion of the fast quasi P‐wave and the quasi SV‐wave are related to the vertical and the horizontal permeabilities. Modeling suggests that the attenuation of both the quasi P‐wave and quasi SV‐wave depend on the direction of permeability. For frequencies from 500 to 4500 Hz, the quasi P‐wave attenuation will be of maximum permeability. To test the theory, interwell seismic waveforms, well logs, and hydraulic conductivity measurements (recorded in the fluvial Gypsy sandstone reservoir, Oklahoma) provide the material and fluid property parameters. For example, the analysis of petrophysical data suggests that the vertical permeability (1 md) is affected by the presence of mudstone and siltstone bodies, which are barriers to vertical fluid movement, and the horizontal permeability (1640 md) is controlled by cross‐bedded and planar‐laminated sandstones. The theoretical dispersion curves based on measurable rock and fluid properties, and the phase velocity curve obtained from seismic signatures, give the ingredients to evaluate the model. Theoretical predictions show the influence of the permeability anisotropy on the dispersion of seismic waves. These dispersion values derived from interwell seismic signatures are consistent with the theoretical model and with the direction of propagation of the seismic waves that travel parallel to the maximum permeability. This analysis with the new analytical solution is the first step toward a quantitative evaluation of the preferential directions of fluid flow in reservoir formation containing hydrocarbons. The results of the present work may lead to the development of algorithms to extract the permeability anisotropy from attenuation and dispersion data (derived from sonic logs and crosswell seismics) to map the fluid flow distribution in a reservoir.

Anisotropic correction of sonic logs in wells with large relative dip

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. E1-E5 ◽  
Author(s):  
Lev Vernik
Keyword(s):  
Reservoir Characterization ◽  
Low Frequency ◽  
P Wave ◽  
Amplitude Variation With Offset ◽  
Seismic Amplitude ◽  
Avo Inversion ◽  
Pore Pressure Prediction ◽  
Siliciclastic Rocks ◽  
Dip Angle ◽  
Sonic Logs

Seismic reservoir characterization and pore-pressure prediction projects rely heavily on the accuracy and consistency of sonic logs. Sonic data acquisition in wells with large relative dip is known to suffer from anisotropic effects related to microanisotropy of shales and thin-bed laminations of sand, silt, and shale. Nonetheless, if anisotropy parameters can be related to shale content [Formula: see text] in siliciclastic rocks, then I show that it is straightforward to compute the anisotropy correction to both compressional and shear logs using [Formula: see text] and the formation relative dip angle. The resulting rotated P-wave sonic logs can be used to enhance time-depth ties, velocity to effective stress transforms, and low-frequency models necessary for prestack seismic amplitude variation with offset (AVO) inversion.

A PHASE-PLANE DESCRIPTION OF NONLINEAR TRAVELING WAVES IN BUBBLY LIQUIDS

1999 ◽  
Vol 07 (02) ◽  
pp. 71-82
Author(s):  
A. NADIM ◽  
D. GOLDMAN ◽  
J. J. CARTMELL ◽  
P. E. BARBONE
Keyword(s):  
Equation Of State ◽  
Fixed Points ◽  
Traveling Wave ◽  
Phase Plane ◽  
Volume Fraction ◽  
Low Frequency ◽  
Traveling Wave Solutions ◽  
Bubbly Liquid ◽  
Phase Plane Analysis ◽  
Bubbly Liquids

One-dimensional traveling wave solutions to the fully nonlinear continuity and Euler equations in a bubbly liquid are considered. The elimination of velocity from the two equations leaves a single nonlinear algebraic relation between the pressure and density profiles in the mixture. On assuming the bubbles to have identical size and taking the volume fraction of bubbles in the medium to be small, an equation of state which relates the mixture pressure to the density and its first two material time-derivatives is derived. When this equation of state is linearized and combined with the laws of conservation of mass and momentum, a nonlinear, second-order, ordinary differential equation is obtained for the density as a function of the single traveling wave coordinate. A phase-plane analysis of this equation reveals the existence of two fixed points, one of which is a saddle and the other a node. A single trajectory connects the two fixed points and corresponds to a traveling shock wave solution when the Mach number of the wave, defined as the ratio of traveling wave speed to the low-frequency speed of sound in the bubbly liquid, exceeds unity. The analysis provides a qualitative explanation of the oscillations behind shocks seen in experiments on bubbly liquids.

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