Modulus Dispersion Research Articles

Simulating squirt flow in realistic rock models using graphical processing units (GPUs)

SUMMARY Understanding the underlying mechanisms of seismic attenuation and moduli dispersion in fluid-saturated cracked porous rocks is of great importance for the development of non-invasive methods to characterize the subsurface. Wave-induced fluid flow at the pore scale, so-called squirt flow, is responsible for seismic attenuation and moduli dispersion at sonic and ultra-sonic frequencies and may be relevant at seismic frequencies. The squirt flow associated attenuation is usually quantified using analytical models. However, numerical experiments suggest that the squirt flow related dissipation is sensitive to fine details of the pore geometry, which can only be modelled numerically. Most of the existing numerical studies explore this phenomenon using simplified models, and there is a lack of numerical studies that model the physics in realistic pore geometries with sufficient numerical resolution. As a result, the impact of wave-induced fluid flow on the effective static and time-dependent mechanical characteristics in realistic settings is still poorly understood. I address these issues by developing a numerical method to model the effective mechanical properties of a hydromechanically coupled system at the pore scale suitable for graphical processing units. A numerical evaluation of attenuation and modulus dispersion due to squirt flow in models based on 3-D microtomography images of cracked Carrara marble is presented. It is shown that the local hydraulic conductivity can be quantitatively estimated from the numerically evaluated effective properties. The accuracy of the numerical results is carefully analysed. This study improves the understanding of the underlying mechanisms of attenuation and moduli dispersion in fluid-saturated cracked rocks. The new method can be applied to model squirt flow for entire laboratory samples in the centimetre scale which was not possible a decade ago.

Quantifying the influence of clay-bound water on wave dispersion and attenuation signatures of shale: An experimental study

Understanding the elastic and attenuation signatures of shales is of considerable interest for unconventional reservoir characterization and sealing capacity evaluation for CO2 sequestration and nuclear waste disposal. We have conducted laboratory measurements on seven shale samples at seismic frequencies (2–100 Hz) to study the effects of clay-bound water (CBW) on their wave dispersion and attenuation signatures. With nuclear magnetic resonance and a helium porosimeter, the volume of CBW in the shale samples is quantified. The forced-oscillation measurement reveals that Young’s modulus exhibits a continuous dispersion trend from 2 to 100 Hz. The extensional attenuation ([Formula: see text]) shows a weak frequency and pressure dependence on effective pressure ranging from 5 to 35 MPa. The magnitude of extensional attenuation shows a positive correlation with CBW, with an [Formula: see text] value of 0.89. It is found that 4% of CBW in the rock frame causes approximately a 5% modulus increase from 2 to 100 Hz. We adopt a constant [Formula: see text] model for assigning frequency-dependent bulk and shear moduli to the CBW in the rock-physics modeling, which can fit the experimental data of modulus dispersion and attenuation well, indicating that the bulk and shear moduli of CBW in shales might behave viscoelastically.

A seismic elastic moduli module for the measurements of low-frequency wave dispersion and attenuation of fluid-saturated rocks under different pressures

Knowledge about the seismic elastic modulus dispersion, and associated attenuation, in fluid-saturated rocks is essential for better interpretation of seismic observations taken as part of hydrocarbon identification and time-lapse seismic surveillance of both conventional and unconventional reservoir and overburden performances. A Seismic Elastic Moduli Module has been developed, based on the forced-oscillations method, to experimentally investigate the frequency dependence of Young's modulus and Poisson's ratio, as well as the inferred attenuation, of cylindrical samples under different confining pressure conditions. Calibration with three standard samples showed that the measured elastic moduli were consistent with the published data, indicating that the new apparatus can operate reliably over a wide frequency range of f∈[1–2000, 106] Hz. The Young's modulus and Poisson's ratio of the shale and the tight sandstone samples were measured under axial stress oscillations to assess the frequency- and pressure-dependent effects. Under dry condition, both samples appear to be nearly frequency independent, with weak pressure dependence for the shale and significant pressure dependence for the sandstone. In particular, it was found that the tight sandstone with complex pore microstructure exhibited apparent dispersion and attenuation under brine or glycerin saturation conditions, the levels of which were strongly influenced by the increased effective pressure. In addition, the measured Young's moduli results were compared with the theoretical predictions from a scaled poroelastic model with a reasonably good agreement, revealing that the combined fluid flow mechanisms at both mesoscopic and microscopic scales possibly responsible for the measured dispersion.

A numerical assessment of local strain measurements on the attenuation and modulus dispersion in rocks with fluid heterogeneities

SUMMARY The forced oscillation method is widely used to investigate intrinsic seismic wave dispersion and attenuation in rock samples by measuring their dynamic stress–strain response. However, using strain gauges to locally measure the strains on samples surfaces can result in errors in determining the attenuation and moduli of rocks with mesoscopic scale heterogeneities. In this study, we developed a 3-D numerical model based on Biot's poroelastic theory to investigate the effect of strain gauge location, number and size on attenuation and dispersion in response to wave-induced fluid flow. Our results show that increasing the strain gauge length, number, and size can reduce the error between local and bulk responses. In a homogeneous and isotropic rock with a quasi-fractal fluid heterogeneity at 12 per cent gas saturation, the relative error between local and bulk responses stays below 6 per cent when the strain gauge length surpasses 8.6 times the correlation length. As the gas saturation becomes larger, the ratio minimally changes non-monotonically, initially increasing and then decreasing. We also used the Monte Carlo method to demonstrate that local laboratory measurements can approximate the reservoir-scale response with a minimum relative error of 1.5 per cent as the sample number increases. Our findings provide guidance for (i) interpreting local low-frequency measurements in terms of bulk properties of rock and (ii) upscaling lab measurements to reservoir-scale properties.

Application of Computer-Aided Precious Metal Materials in Electrochemistry of Ceramic Jewelry Design

In order to solve the electrochemical application of precious metal materials in ceramic jewelry design, a computer-aided design method of precious metal materials in ceramic jewelry was proposed. First, the potential energy surface analyzed in this paper is composed of the sum of disomy and trisomy, with different proportions of disomy and trisomy. Therefore, in the fitting process, the above two relations can be used to measure the contribution of the two-body term and the three-body term, respectively; secondly, from the viewpoint of lattice dynamics, precious metals are of special significance, because they are simple fcc lattice and large and pure single crystals can be obtained. Therefore, their accurate phonon dispersion curves can be obtained experimentally; finally, the phonon dispersion curves along the highly symmetric vector direction are given, and the calculated results are in good agreement with the experimental data. This shows that the new analytical potential energy surface accurately reproduces the interactions inside these crystals. The new analytical potential energy surfaces of the three noble metals correctly reproduce the macroscopic properties of the system, including elastic modulus, cohesive energy, and phonon dispersion curve, as well as important surface features. For all three systems, the order of the surface energies of the unreconstituted surfaces is (110) > (100) > (111), which is also correct. At the same time, the new potential energy surface gives the correct relaxation behavior of the unreconstituted surface.

Mass transfer between fluids as a mechanism for seismic wave attenuation: experimental evidence from water–CO2 saturated sandstones

SUMMARY Seismic waves are typically assumed to propagate fast enough through a porous rock saturated with multiple fluid phases such that the interaction between the fluids can be considered adiabatic, or thermodynamically unrelaxed. However, at low gas saturations and when the gas is present in the form of microscopic bubbles the fluid mixture may in fact be thermodynamically relaxed at seismic frequencies. The effective fluid is then significantly more compressible. A transition from a thermodynamically relaxed to unrelaxed state of the fluids will be accompanied by frequency dependent attenuation of the wave in response to heat and/or mass transfer. We conducted experiments on two partially saturated sandstone samples to measure frequency dependent attenuation and modulus dispersion at seismic frequencies (<1000 Hz). For CO2 saturations of 0.1–0.2 per cent we observe significant attenuation and dispersion in the bulk and shear modulus, with an attenuation peak at ∼100 Hz. The bulk modulus was significantly lower than the prediction by Gassmann–Wood fluid substitution, which assumes that the fluids are thermodynamically unrelaxed. Numerical simulations in poroelastic media further indicate that a partially drained boundary condition does not adequately explain the observed attenuation and dispersion, particularly in the shear modulus. Numerical simulations at the microscopic scale support the notion that pore-scale heterogeneities could explain the observed shear attenuation and dispersion, since an external shear deformation can cause local compressions of the pore space. The observed attenuation and dispersion are interpreted to be predominantly due to a transition from a thermodynamically relaxed to unrelaxed state of the saturating fluids.

The dead volume effect on the elastic moduli measurements using the forced‐oscillation method

ABSTRACTIn low‐frequency laboratory experiments conducted on fluid‐saturated rocks, the boundary conditions of rock samples can significantly affect the results of the measurements of elastic moduli and acoustic attenuation. Generally, in laboratory measurements, the dead fluid volume associated with the fluid storage formed by the segments of the fluid line adjacent to a rock specimen cannot bе completely eliminated. Depending on the size, this fluid storage can significantly affect the elastic moduli measurements. We investigate the impact of the dead volume on (i) the quasistatic measurements of the elastic moduli of a fully fluid‐saturated rock specimen and (ii) the dispersion and attenuation measurements conducted on the same specimen at seismic frequencies. We present the results of the laboratory tests conducted at seismic frequencies on an n‐decane–saturated porous rock with the dead volume gradually changed from 2 to 260 cm3, as well as with the open‐pore‐fluid line. To take into account the dead volume, we developed a modified Gassmann theory and demonstrated that predictions of this theory are in good agreement with the measurements at lower frequencies. The Young's modulus dispersion and extensional attenuation observed at higher frequencies were explained on the basis of a one‐dimensional model considering the guided slow P‐waves in the rock specimen with boundary conditions specific to the experiment.

Theoretical prediction of elastic modulus at different states and squirt-flow-related attenuation: extension of Cracks-Pores Effective Medium model

SUMMARYSquirt flow plays an essential role in elastic modulus dispersion and attenuation for fluid-saturated cracked porous rocks. The Mavko–Jizba model and relevant modified models can describe the squirt flow well based on the related elastic moduli, such as dry/drained bulk modulus. However, when these elastic moduli are challenging to attain, it is impossible to model the squirt-flow-related elastic moduli and attenuations with the models. On the other hand, the effective medium theory (EMT) model can estimate these elastic moduli, but cannot predict the undrained/relaxed and partially relaxed saturated elastic moduli and the squirt-flow-related attenuations. This paper extended an EMT model—Cracks–Pores Effective Medium (CPEM) model—to cover the undrained/relaxed and partially relaxed states following the elastic–viscoelastic correspondence principle. The proposed model [i.e. frequency-dependent CPEM (CPEMF) model] can thus estimate the elastic moduli over the different states (dry/drained, undrained/relaxed, partially relaxed and unrelaxed) and associated attenuations. It agrees well with the prediction of the modified Mavko–Jizba–Gurevich model (MJGZ-HF) at unrelaxed state and is precisely consistent with the prediction of Gassmann at undrained/relaxed state. Also, it analytically shows good consistency with the modified Mavko–Jizba–Gurevich model (MJGZ-MF) at partially relaxed state. The numerical simulations of CPEM/CPEMF models and MJGZ-HF/MJGZ-MF models show good agreement at the different states. Furthermore, we interpreted the experimental data on a basaltic sample and a sandstone sample with the CPEM/CPEMF models. The CPEMF model's predictions of elastic modulus at different states and associated modulus dispersion/attenuation are in good agreement with the corresponding measured ones, suggesting that the proposed CPEMF model can efficiently predict the elastic moduli at different states (dry/drained, undrained/relaxed, partially relaxed and unrelaxed) and quantify the squirt-flow-related elastic modulus dispersion and attenuation among different states well.

Effects of porosity, orientation and connectivity of microcracks on dispersion and attenuation of fluid-saturated rocks using an upscaling numerical modelling of the squirt flow mechanism

Squirt flow is a wave-induced fluid flow mechanism to account for the velocity dispersion and attenuation of fluid-saturated porous media. Theoretical models of squirt flow cannot deal with complex microcrack-pore networks and thus cannot give accurate dispersion and attenuation curves with respect to frequency. We adopt a numerical oscillatory compressibility test method, based on the quasi-static poroelastic equation of Biot, to model the squirt flow and calculate corresponding P-wave modulus dispersion and attenuation. We also designed nine porous medium models containing different crack-pore configurations and investigated the effects of microcrack porosity, orientation and connectivity on the elastic responses. Modelling results show that not only microcrack porosity but also their orientation has control on the magnitude of the P-wave modulus dispersion and attenuation. Preferentially aligned microcracks may cause frequency-dependent anisotropy in the P-wave modulus and attenuation. Microcrack connectivity has a negligible influence on the dispersion and attenuation magnitude but a large influence on the characteristic frequency of the squirt flow, which is not predicted by theoretical models based on simple representative element volume of crack-pore structure. Therefore, detailed geometry of crack-pore network, of which microcrack porosity, orientation, aspect ratio and connectivity are vital factors, dictates the unique variations in the elastic modulus and associated attenuation with frequency caused by the squirt flow. Pore structure obtained by CT scanning representative of that of the whole rock is needed to obtain more accurate poroelastic responses of the rock with the numerical oscillatory compressibility test method. In this regard, we provide a powerful tool for evaluating dispersion and attenuation of fluid-saturated rock media with complex crack-pore structure, which have potential applications in seismic exploration of hydrocarbon in the subsurface.

Seismic Wave Attenuation and Dispersion Due to Partial Fluid Saturation: Direct Measurements and Numerical Simulations Based on X‐Ray CT

AbstractQuantitatively assessing seismic attenuation caused by fluid pressure diffusion (FPD) in partially saturated rocks is challenging because of its sensitivity to the spatial fluid distribution. To address this challenge we performed depressurization experiments to induce the exsolution of carbon dioxide from water in a Berea sandstone sample. In a first set of experiments we used medical X‐ray computed tomography (CT) to characterize the fluid distribution. At an equilibrium pressure of approximately 1 MPa and applying a fluid pressure decline rate of approximately 0.6 MPa per minute, we allowed a change in saturation of less than 1%. The gas was heterogeneously distributed along the length of the sample, with most of the gas exsolving near the sample outlet. In a second set of experiments, at the same pressure and temperature, following a very similar exsolution protocol, we measured the frequency dependent attenuation and modulus dispersion between 0.1 and 1,000 Hz using the forced oscillation method. We observed significant attenuation and dispersion in the extensional and bulk deformation modes, however, not in the shear mode. Lastly, we use the fluid distribution derived from the X‐ray CT as an input for numerical simulations of FPD to compute the attenuation and modulus dispersion. The numerical solutions are in close agreement with the attenuation and modulus dispersion measured in the laboratory. Our approach allows for accurately relating attenuation and dispersion to the fluid distribution, which can be applied to improving the seismic monitoring of the subsurface.

A Laboratory Forced-Oscillation Apparatus for Measurements of Elastic and Anelastic Properties of Rocks at Seismic Frequencies

In presented paper, we describe the technical and physical aspects of the application of a low-frequency (LF) apparatus based on a longitudinal type of forced oscillations. In particular, we investigate the influence of the strain gauge position on a tested sample on measurement results, we also examine the creep effect associated with the mineralogy of rocks, as well as the dispersion and attenuation in a liquid-saturated rock sample caused by the presence of the volume of pore fluid exterior to the sample (dead volume). The effect of the position of the strain gauges is investigated using a cylindrical acrylic sample and two pairs of strain gauges fixed in the middle and at one of the sample ends under a uniaxial pressure of 15 MPa. The obtained results demonstrate that elastic and anelastic parameters of the tested sample are independent from the location of the strain gauges. The impact of the creep phenomenon on elastic moduli was studied using three room-dry samples of Savonnieres limestone, Berea sandstone and Eagle Ford shale. The measurements were conducted for 120 h at a frequency of 2 Hz under a uniaxial pressure of 10 MPa and demonstrated that the LF moduli of all rocks were noticeably reduced with time. The effect of dead volume was investigated at seismic frequencies using limestone saturated with n-decane. It was found that the Young’s and bulk moduli exhibit strong dispersion at frequencies above 10 Hz if the dead volume is close to or greater than the pore volume of the sample. We also found that the characteristic frequency of dispersion corresponding to the attenuation peak is independent of the size of the dead volume and determined only by the physical parameters of the sample and pore fluid. We present also the results of the Young’s modulus and attenuation measurements conducted at seismic frequencies on vertical and horizontal shale samples saturated with water. It was shown that the relationship between the extensional attenuation and the Young’s modulus dispersion observed in the samples saturated at a relative humidity of 97.5% is consistent with the Kramers–Kronig relation.

Squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids.

Mechanical waves, which are commonly employed for the noninvasive characterization of fluid-saturated porous media, tend to induce pore-scale fluid pressure gradients. The corresponding fluid pressure relaxation process is commonly referred to as squirt flow and the associated viscous dissipation can significantly affect the waves' amplitudes and velocities. This, in turn, implies that corresponding measurements contain key information about flow-related properties of the probed medium. In many natural and applied scenarios, pore fluids are effectively non-Newtonian, for which squirt flow processes have, as of yet, not been analyzed. In this work, we present a numerical approach to model the attenuation and modulus dispersion of compressional waves due to squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids. In particular, we explore the effective response of a medium comprising an elastic background with interconnected cracks saturated with a Maxwell-type non-Newtonian fluid. Our results show that wave signatures strongly depend on the Deborah number, defined as the relationship between the classic Newtonian squirt flow characteristic frequency and the intrinsic relaxation frequency of the non-Newtonian Maxwell fluid. With larger Deborah numbers, attenuation increases and its maximum is shifted towards higher frequencies. Although the effective plane-wave modulus of the probed medium generally increases with increasing Deborah numbers, it may, however, also decrease within a restricted region of the frequency spectrum.

Seismic dispersion and attenuation in Mancos shale – laboratory measurements

ABSTRACTWe present the results of a low‐frequency study of Mancos shale, where we first elaborate a stress–strain methodology of laboratory low‐frequency experiments to estimate the elastic moduli of shales, and then apply this methodology to investigate the influence of partial water saturation on the elastic and anelastic parameters, velocities and P‐wave anisotropy of Mancos shale. We also analyse the applicability of the anisotropic Gassmann theory for predictions of the stiffness tensor components of the water‐saturated shale with non‐expandable clay content presented in our case by illite (33%) and chamosite (9.1%) minerals. The effect of water saturation was studied using two samples drilled in vertical and parallel directions to the formation bedding. The experiments were carried out at a confining pressure of 10 MPa in the frequency range from 0.1 to 100 Hz. Prior to measurements, the samples were saturated in desiccators at six different values of relative humidity ranging from 9% to 97.5%. The results of our study demonstrate a reduction of Young's modulus and P‐wave anisotropy with saturation accompanied by a decrease in shear stiffnesses. The latter indicates the inapplicability of the anisotropic Gassmann theory to Mancos shale. Our measurements of attenuation carried out on the vertical and horizontal samples saturated at a relative humidity of 97.5% revealed prominent attenuation peaks associated with partial saturation. We showed that the measurement results of the attenuation and Young's modulus dispersion are consistent with the causality principle presented by the Kramers–Kronig relations.

Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading

This paper presents a mathematical model that reflects the nature of the dynamic Young’s modulus of a dry sedimentary rock during nonstationary uniaxial loading. The model is based on an idealized model of a system suggested by Jaeger J.C. A rock sample is considered as a spring with stiffness, the bottom point of which is fixed, while the upper point carries a mass. A sample experiences dynamic load and the rock matrix response. Displacement of the mass from the equilibrium state sets the variation of the sample’s length. Displacement of all the sample’s points goes according to the same law regardless of the point location. The response of a rock to a disturbing nonstationary load is selected based on the combination of conditions of each experiment, such as the load frequency and amplitude and the mass, length, and diameter of a sample. The mathematical model is consistent with experimental data, according to which an increase in load frequency leads to an increase in the dynamic Young’s modulus for each value of the load. The accuracy of the models is evaluated. The relations underlying the model can be used as a basis to describe the Young’s modulus dispersion of sedimentary rocks under the influence of nonstationary loads.

Structural and dielectric characterization of (PVP/PEO)/Al2O3 nanocomposites for biodegradable nanodielectric applications

Polymer host matrix and inorganic nanofiller comprising hybrid nanocomposites of integrated promising properties are the most appealing multifunctional materials for developing advanced flexible-type electrical and electronic devices and also a variety of daily life quality products. This research reports the structural parameters and dielectric properties of biodegradable poly(vinyl pyrrolidone)/poly(ethylene oxide) (PVP/PEO) blend matrix and alumina (Al2O3) nanoparticle–based polymer nanocomposite (PNC) films. Porous spherulitic morphology of the host PVP/PEO matrix, polymer-polymer interactions, and the structures of PEO crystallites are found largely influenced by the Al2O3 nanofiller, whereas the degree of crystallinity of the PNC films increases slightly. The dielectric permittivity of the PNC films over 20 Hz to 1 MHz frequency range confirmed some increase in dielectric polarization, but they exhibited anomalous behavior when the Al2O3 content increases in gradual steps from 1 to 5 wt%. In these hybrid materials, the interfacial polarization and dielectric relaxation predominantly contributed in the dielectric permittivity and electric modulus dispersion at the lower frequencies. The detailed analysis of dielectric properties authenticates that these nanocomposites could be used as prominent biodegradable nanodielectrics for polymer nanotechnology-based eco-friendly future-generation numerous types of flexible devices/products.

Modeling the Effect of Pressure on the Moduli Dispersion in Fluid‐Saturated Rocks

AbstractLaboratory experiments of ultrasonic velocities of fluid‐saturated rocks are often much higher than the predictions of the Gassmann theory. This difference is usually attributed to the velocity dispersion caused by fluid pressure relaxation between pores of different shapes and orientation. This paper proposes a simple model to characterize pressure and frequency effects on the elastic moduli of fluid‐saturated rocks in a broad frequency range. The proposed model incorporates micromechanics of wave‐induced fluid pressure relaxation at grain contacts (between crack‐like contacts and stiff pores) into pressure dependency of elastic moduli. Previously, the pressure dependency of the velocities or elastic moduli was ascribed to the progressive closure of cracks with the increasing effective pressure and expressed as an integral of crack compliance over the range of aspect ratios. For isolated cracks, this compliance is a function of crack geometry only. For cracks hydraulically connected to stiff pores, this crack compliance can be replaced by a frequency‐dependent solution of the micromechanical problem of fluid pressure relaxation between a single crack and surrounding pores. The resulting equation expresses the bulk and shear moduli of the fluid‐saturated rock as functions of both pressure and frequency. Furthermore, if pressure‐dependent moduli of both dry and fluid‐saturated moduli are known, the aspect ratio distribution can be obtained from the pressure dependency of the dry moduli, and then the saturated moduli can be computed with no adjustable parameters. The model predictions show reasonable agreement with laboratory data measured using ultrasonic and forced oscillation techniques.

Squirt-flow seismic dispersion models: a comparison

SUMMARY The anelastic properties of porous rocks depend on the pore characteristics, specifically, the pore aspect ratio and the pore fraction (related to the soft porosity). At high frequencies, there is no fluid pressure communication throughout the pore space and the rock becomes stiffer than at low frequencies, where the pore pressure is fully equilibrated. This causes a significant difference between the moduli at low and high frequencies, which is known as seismic dispersion and is commonly explained by the squirt-flow mechanism. In this paper, we consider and contrast three squirt-flow dispersion models: the modified Mavko–Jizba model, valid for a porous medium with arbitrary shapes of the pores and cracks, and two other models, based on idealized geometries of spheres and ellipsoids: the EIAS (equivalent inclusion-average stress) and CPEM (cracks and pores effective medium) models. We first perform analytical comparisons and then compute several numerical examples to demonstrate similarities and differences between the models. The analytical comparison shows that when the stiff pores are spherical and the crack density is small, the theoretical predictions of the three models are very close to each other. However, when the stiff pores are spheroids with an aspect ratio smaller than 1 (say, between 0.2 and 1), the predictions of inclusion based models are not valid at frequencies of ultrasonic measurements on rock samples. In contrast, the predictions of the modified Mavko–Jizba model are valid at ultrasonic frequencies of about 106 Hz, which is a typical frequency of laboratory measurements on core samples. We also introduce Zener-based bulk and shear dispersion indices, which are proportional to the difference between the high- and low-frequency stiffness moduli, and are a measure of the degree of anelasticity, closely related to the quality factors by view of the Kramers–Kronig relations. The results show that the three models yield similar moduli dispersion with very small differences when the crack density is relatively high. The indices versus crack density can be viewed as a template to obtain the crack properties from low- and high-frequency velocity measurements.

Squirt Flow in Cracks with Rough Walls

AbstractWe explore the impact of roughness in crack walls on the P wave modulus dispersion and attenuation caused by squirt flow. For that, we numerically simulate oscillatory relaxation tests on models having interconnected cracks with both simple and intricate aperture distributions. Their viscoelastic responses are compared with those of models containing planar cracks but having the same hydraulic aperture as the rough wall cracks. In the absence of contact areas between crack walls, we found that three apertures affect the P wave modulus dispersion and attenuation: the arithmetic mean, minimum aperture, and hydraulic aperture. We show that the arithmetic mean of the crack apertures controls the effective P wave modulus at the low‐ and high‐frequency limits, thus representing the mechanical aperture. The minimum aperture of the cracks tends to dominate the energy dissipation process and, consequently, the characteristic frequency. An increase in the confining pressure is emulated by uniformly reducing the crack apertures, which allows for the occurrence of contact areas. The contact area density and distribution play a dominant role in the stiffness of the model, and in this scenario, the arithmetic mean is not representative of the mechanical aperture. On the other hand, for a low percentage of minimum aperture or in the presence of contact areas, the hydraulic aperture tends to control the characteristic frequency. Analyzing the local energy dissipation, we can more specifically visualize that a different aperture controls the energy dissipation process at each frequency, which means that a frequency‐dependent hydraulic aperture might describe the squirt flow process in cracks with rough walls.

Poroelastic Relaxation in Thermally Cracked and Fluid‐Saturated Glass

AbstractTo test theoretical models of modulus dispersion and dissipation in fluid‐saturated rocks, we have investigated the broadband mechanical properties of four thermally cracked glass specimens of simple microstructure with complementary forced‐oscillation (0.004–100 Hz) and ultrasonic techniques (~1 MHz). Strong pressure dependence of moduli (bulk, Young's, and shear), axial strain, and ultrasonic wave speeds for dry conditions attests to essentially complete crack closure at a confining pressure of 15 MPa—consistent with ambient‐pressure crack aspect ratios ≤2 × 10−4. Oscillation of the confining pressure reveals bulk modulus dispersion and a corresponding dissipation peak, near 0.002 Hz only at the lowest effective pressure (2.5 MPa)—attributed to the transition with increasing frequency from the drained to saturated‐isobaric regime. The observations are consistent with Biot‐Gassmann's theory, with dispersion and dissipation adequately represented by Zener model. Above the draining frequency, axial forced‐oscillation tests show dispersion of Young's modulus and Poisson's ratio, and an associated broad dissipation peak centered near 0.3 Hz, thought to reflect local “squirt” flow and adequately modeled with a continuous distribution of relaxation times over two decades. Observations of Young's and shear moduli dispersion and dissipation from complementary flexural and torsional oscillation measurements for differential pressure ≤10 MPa provide supporting evidence of the transition with increasing frequency from the saturated‐isobaric to the saturated‐isolated regime—also probed by ultrasonic technique. These findings validate predictions from theoretical models of dispersion in cracked media and emphasize need for caution in the seismological application of laboratory ultrasonic data for cracked media.

Influence of SnO2 nanoinclusions on the structural and dielectric properties of (PVA–PEO)/SnO2 nanocomposites

Nanofiller concentration dependent, tunable-type structural, dielectric, thermo-mechanical, and optical properties of the polymer nanocomposites (PNCs) have established them as technologically smart multifunctional materials for advances in stretchable and flexible-type organoelectronic, optoelectronic, and energy harvesting/storage devices. In this work, organic-inorganic hybrid PNC films comprising poly(vinyl alcohol) (PVA) and poly(ethylene oxide) (PEO) blend as host matrix (PVA–PEO; 50–50 wt%) dispersed with varying concentration of tin oxide (SnO 2 ) nanoparticles up to 5 wt% have been prepared by the solution-cast method. The influence of SnO 2 loading on the percent crystallinity of the host matrix and the structural parameters of the PEO crystallites has been examined by the X-ray diffraction (XRD) measurements of the PNC films. The results reveal that the percent crystallinity of the semicrystalline (PVA–PEO) matrix gradually enhanced, whereas the interlayer spacing, crystallite size, and interchain separation of the PEO crystallites varied anomalously with the increase of SnO 2 concentration in the PNC films. The complex dielectric permittivity, alternating current (ac) electrical conductivity, and electric modulus dispersion over the broad frequency range (20 Hz–1 MHz) of these (PVA–PEO)/SnO 2 films has been characterized by employing the dielectric relaxation spectroscopy (DRS). It has been observed that 1 wt% SnO 2 nanoinclusion abruptly reduced the interfacial, dipole polarizations, and also electrical conduction of the host matrix, whereas considerably enhanced hindrance to the PEO chain segmental motion studied at 30 °C. The temperature dependent study (30–60 °C) of the representative PNC film of 3 wt% nanofiller reveals its thermally activated non-linear dielectric polarization at fixed frequency and also Arrhenius behaviour of the dielectric relaxation processes of significantly low activation energy (≃ 0.14 eV). The structural, dielectric, and electrical properties of the (PVA–PEO)/SnO 2 films have been critically analyzed for their suitability as controllable low dielectric permittivity polymer nanodielectric (PNDs) materials for biodegradable electronic devices.