Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

Ultrasonic study of water adsorbed in nanoporous glasses

Thermodynamic properties of fluids confined in nanopores differ from those observed in the bulk. To investigate the effect of nanoconfinement on water compressibility, we perform water sorption experiments on two nanoporous glass samples while concomitantly measuring the speed of longitudinal and shear ultrasonic waves in these samples. These measurements yield the longitudinal and shear moduli of the water-laden nanoporous glass as a function of relative humidity that we utilize in the Gassmann theory to infer the bulk modulus of the confined water. This analysis shows that the bulk modulus (inverse of compressibility) of confined water is noticeably higher than that of the bulk water at the same temperature. Moreover, the modulus exhibits a linear dependence on the Laplace pressure. The results for water, which is a polar fluid, agree with previous experimental and numerical data reported for nonpolar fluids. This similarity suggests that irrespective of intermolecular forces, confined fluids are stiffer than bulk fluids. Accounting for fluid stiffening in nanopores may be important for accurate interpretation of wave propagation measurements in fluid-filled nanoporous media, including in petrophysics, catalysis, and other applications, such as in porous materials characterization.

The influence law of concrete aggregate particle size on acoustic emission wave attenuation

Elastic waves have different attenuation laws when propagating in various materials, which is one of the important challenges in the application of non-destructive testing methods, such as acoustic emission (AE) technology in geotechnical engineering. The study presented in this paper investigated the influence mechanism of concrete composition materials and parameters on the propagation law of elastic waves using concrete specimens produced in six different particle sizes of sand or gravel. The burst AE signal was generated through the lead-breaking experiment, and ceramic piezoelectric sensors were used to record the signal waveform at different propagation distances. Through parameter analysis, spectrum analysis, and pattern recognition techniques, the influence of the concrete aggregate particle size on AE wave propagation and attenuation was revealed. The results show that the attenuation of elastic wave amplitude, energy spectral density, and frequency all were positively correlated with the aggregate particle size, and the elastic wave spectrum center of gravity generally decreased with the propagation distance. The ring count gradually decreased with the propagation distance, and the specimens with a larger aggregate particle size underwent a relatively faster ring count attenuation rate. The rise time increased rapidly with the propagation of the elastic wave, and the specimens with a larger aggregate particle size experienced a relatively rapid increase in rise time. In addition, in the feature spaces of ring count-amplitude and rise time–amplitude, the size of aggregate has an obvious influence on the distribution of these feature vector.

Numerical simulation of wave-induced fluid flow seismic attenuation based on the Cole-Cole model

The acoustic behavior of porous media can be simulated more realistically using a stress-strain relation based on the Cole-Cole model. In particular, seismic velocity dispersion and attenuation in porous rocks is well described by mesoscopic-loss models. Using the Zener model to simulate wave propagation is a rough approximation, while the Cole-Cole model provides an optimal description of the physics. Here, a time-domain algorithm is proposed based on the Grünwald-Letnikov numerical approximation of the fractional derivative involved in the time-domain representation of the Cole-Cole model, while the spatial derivatives are computed with the Fourier pseudospectral method. The numerical solution is successfully tested against an analytical solution. The methodology is applied to a model of saline aquifer, where carbon dioxide (CO₂) is injected. To follow the migration of the gas and detect possible leakages, seismic monitoring surveys should be carried out periodically. To this aim, the sensitivity of the seismic method must be carefully assessed for the specific case. The simulated test considers a possible leakage in the overburden, above the caprock, where the sandstone is partially saturated with gas and brine. The numerical examples illustrate the implementation of the theory.

Epidermal mechano-acoustic sensing electronics for cardiovascular diagnostics and human-machine interfaces

Physiological mechano-acoustic signals, often with frequencies and intensities that are beyond those associated with the audible range, provide information of great clinical utility. Stethoscopes and digital accelerometers in conventional packages can capture some relevant data, but neither is suitable for use in a continuous, wearable mode, and both have shortcomings associated with mechanical transduction of signals through the skin. We report a soft, conformal class of device configured specifically for mechano-acoustic recording from the skin, capable of being used on nearly any part of the body, in forms that maximize detectable signals and allow for multimodal operation, such as electrophysiological recording. Experimental and computational studies highlight the key roles of low effective modulus and low areal mass density for effective operation in this type of measurement mode on the skin. Demonstrations involving seismocardiography and heart murmur detection in a series of cardiac patients illustrate utility in advanced clinical diagnostics. Monitoring of pump thrombosis in ventricular assist devices provides an example in characterization of mechanical implants. Speech recognition and human-machine interfaces represent additional demonstrated applications. These and other possibilities suggest broad-ranging uses for soft, skin-integrated digital technologies that can capture human body acoustics.

Seismic wave attenuation and dispersion due to wave-induced fluid flow in rocks with strong permeability fluctuations

Oscillatory fluid movements in heterogeneous porous rocks induced by seismic waves cause dissipation of wave field energy. The resulting seismic signature depends not only on the rock compressibility distribution, but also on a statistically averaged permeability. This so-called equivalent seismic permeability does not, however, coincide with the respective equivalent flow permeability. While this issue has been analyzed for one-dimensional (1D) media, the corresponding two-dimensional (2D) and three-dimensional (3D) cases remain unexplored. In this work, this topic is analyzed for 2D random medium realizations having strong permeability fluctuations. With this objective, oscillatory compressibility simulations based on the quasi-static poroelasticity equations are performed. Numerical analysis shows that strong permeability fluctuations diminish the magnitude of attenuation and velocity dispersion due to fluid flow, while the frequency range where these effects are significant gets broader. By comparing the acoustic responses obtained using different permeability averages, it is also shown that at very low frequencies the equivalent seismic permeability is similar to the equivalent flow permeability, while for very high frequencies this parameter approaches the arithmetic average of the permeability field. These seemingly generic findings have potentially important implications with regard to the estimation of equivalent flow permeability from seismic data.

Velocity and attenuation of scalar and elastic waves in random media: a spectral function approach

This paper investigates the scattering of scalar and elastic waves in two-phase materials and single-mineral-cubic, hexagonal, orthorhombic-polycrystalline aggregates with randomly oriented grains. Based on the Dyson equation for the mean field, explicit expressions for the imaginary part of Green's function in the frequency-wavenumber domain (ω, p), also known as the spectral function, are derived. This approach allows the identification of propagating modes with their relative contribution, and the computation of both attenuation and phase velocity for each mode. The results should be valid from the Rayleigh (low-frequency) to the geometrical optics (high-frequency) regime. Comparisons with other approaches are presented for both scalar and elastic waves.

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.

Dispersion and attenuation due to scattering from heterogeneities of the frame bulk modulus of a poroelastic medium

While Biot theory can successfully account for the dispersion observed in sand sediments, the attenuation at high frequencies has been observed to increase more rapidly than Biot theory would predict. In an effort to account for this additional loss, perturbation theory is applied to Biot's poroelastic equations to model the loss due to the scattering of energy from heterogeneities in the sediment. A general theory for propagation loss is developed and applied to a medium with a randomly varying frame bulk modulus. The theory predicts that these heterogeneities produce an overall softening of the medium as well as scattering of energy from the mean fast compressional wave into incoherent fast and slow compressional waves. This theory is applied to two poroelastic media: a weakly consolidated sand sediment and a consolidated sintered glass bead pack. The random variations in the frame modulus do not have significant effects on the propagation through the sand sediment but do play an important role in the propagation through the consolidated medium.