Double Porosity Research Articles

Normal incidence sound absorption of an acoustic labyrinthine metal-fibers-based porous metamaterial at high temperature

This work studies the sound absorption performance of acoustic labyrinthine porous metamaterials (ALPM) at high temperature. The proposed metamaterial is constructed by perforating a homogeneous metal-fibers-based porous matrix with folded slits. These macroscopic perforations provide long channels for sound waves to enter the structure, allowing sound waves to enter the porous material due to the pressure diffusion effect, resulting in excellent subwavelength absorption at high temperatures. Based on the double porosity theory and temperature-dependent parameters, we develop a high-temperature theoretical model and validate it by numerical method. The results show that with the increase of temperature, the peak frequency of the ALPM moves to higher frequencies and the half-absorption bandwidth becomes wider. The discussion of sound absorption mechanism based on the pressure distribution results shows that with the increase of temperature, the pressure diffusion effect exists in a wider frequency range, which helps to suppress the propagation of long-wavelength sound waves at high temperature. The study of particle vibration velocity and energy dissipation density shows that the higher the temperature, the stronger the motion of air particles, and more sound energy is dissipated in the porous material, resulting in enhanced sound absorption. The ALPM can be regarded as a combination of homogeneous porous material and space-coiled resonator. Compared to these two components, the ALPM exhibits excellent sound absorption in the frequency range of 200Hz to 600Hz, especially at high temperatures. The proposed porous metamaterials show promising applications in low-frequency sound absorption at high temperature.

Spectral and numerical analysis for a thermoelastic problem with double porosity and second sound

We study some spectral and numerical properties of the solutions to a thermoelastic problem with double porosity. The model includes Cattaneo-type evolution law for the heat flux to remove the physical paradox of infinite propagation speed of the classical Fourier’s law. Firstly, we prove that the operator determined by the considered problem has compact resolvent and generates a C 0 -semigroup in an appropriate Hilbert space. We also show that there is a sequence of generalized eigenfunctions of the linear operator that forms a Riesz basis. By a detailed spectral analysis, we obtain the expressions of the spectrum and we deduce that the spectrum determined growth condition holds. Therefore we prove that the energy of the considered problem decays exponentially to a rate determined explicitly by the physical parameters. Finally, some numerical simulations based on Chebyshev spectral method for spatial discretization are given to confirm the exponential stability result and to show the distribution of the eigenvalues and the variables of the problem.

An a priori error analysis of a type III thermoelastic problem with two porosities

AbstractIn this work, we study, from the numerical point of view, a type III thermoelastic model with double porosity. The thermomechanical problem is written as a linear system composed of hyperbolic partial differential equations for the displacements and the two porosities, and a parabolic partial differential equation for the thermal displacement. An existence and uniqueness result is recalled. Then, we perform its a priori error numerical analysis approximating the resulting variational problem by using the finite element method and the implicit Euler scheme. The linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are shown to demonstrate the accuracy of the approximations and the dependence of the solution on a coupling coefficient.

Fracture permeability limit for double porosity and double permeability models

Fracture permeability limit for double porosity and double permeability models

Wave propagation in double-porosity thermoelastic media

The Lord-Shulman thermoporoelasticity theory couples the Biot and hyperbolic heat equations to describe wave propagation, modeling explicitly the effects of heat and fluid flows. We have extended the theory to the case of double porosity by taking into account the local heat flow (LHF) and local fluid flow (LFF) due to wave propagation. The plane-wave analysis finds the presence of the classical P and S waves and three slow P waves, namely, the slow (Biot) P1, the slow (Biot) P2, and a thermal slow P wave (or T wave). The frequency-dependent attenuation curves find that these slow waves manifest as Zener-like relaxation peaks, which are loosely related to the LFF, Biot, and LHF loss mechanisms. The viscosity and thermoelasticity properties can lead to the diffusive behavior of the three slow P modes. However, the S wave is considered to be independent of fluid and temperature influence. We examine the effect of thermophysical properties (e.g., thermal conductivity and relaxation time) on the wave velocity and attenuation of different modes. It is confirmed that the T wave is prone to be observed in media with high thermal conductivities and high homogeneity at high frequencies. Our double-porosity thermoelastic model reasonably explains laboratory measurements and well-log data from ultradeep fractured carbonates at high temperatures.

Sound absorption of a perforated panel backed with perforated porous material: Energy dissipation of Helmholtz resonator cavity

A new type of low-frequency sound absorbing Helmholtz resonator is proposed, which consists of a perforated rigid panel backed with gradually perforated porous material. A theoretical model is developed by dividing the structure into a multi-layer system by using the double porosity theory, which is verified by finite element simulations and experimental measurements. The sound absorption performance of the proposed acoustic metamaterial is studied by applying the theoretical model and numerical model, where the influences of the perforation diameter, panel thickness, back cavity shape and static flow resistivity of the porous material matrix on sound absorption are discussed. The results show that this new metamaterial has better sound absorption performance than the perforated panel and the perforated porous material. Finite element simulations show that this new acoustic metamaterial absorbs sound energy almost entirely through Helmholtz cavity resonance, which accelerates the diffusion of sound into the porous material for dissipation. An energy dissipation compensation mechanism is found between the perforated panel and the perforated porous material, which enables the metamaterial to always achieve near-perfect sound absorption performance over a wide range of neck diameters. This new resonance metamaterial provides another avenue for the design of low-frequency sound absorbers.

A modeling approach for electrokinetic transport in double-porosity media

Electrokinetic techniques have attracted considerable attention due to their competitive advantage in enhancing transport phenomena and remediation of low permeability soils. However, many types of low-permeability porous media, such as active clays like bentonite, present a double porosity structure that strongly affects mass transfer processes. In this work, we develop a modeling approach to simulate electrokinetic transport in double porosity media. The proposed model is based on the previously released code M4EKR and explicitly considers the transport due to electromigration as well the effects of the electrical diffuse layer in charged porous media. For this purpose, two modeling levels have been established: one associated with the soil macrostructure (bulk water) and the other with the microstructure (diffuse layer). At the latter level, the effect of the electrostatic interactions imposed by the negative charge of the clay particles is modeled with a Donnan approach. The comparison of the results between synthetic cases in single and double porosity systems shows the fundamental role of the microstructural modeling level. High enrichment of cations and, therefore, high cationic fluxes are produced in such microstructural level. These mechanisms significantly modify the extent of cation transport by electromigration and, thus, directly influence the transport of other species determined by the electrostatic interactions.

Groundwater flow in karstic aquifer: analytic solution of dual-porosity fractional model to simulate groundwater flow

ABSTRACT Karst aquifers have a very complex flow system because of their high spatial heterogeneity of void distribution. In this manuscript, flow simulation has been used to investigate the flow mechanism in a fissured karst aquifer with double porosity, revealing how to connect exchange and storage coefficients to the volumetric density of the highly permeable form of media. The governing space-time differential equations of the dual-porosity model are modified by using the Caputo–Fabrizio fractional derivative operator for time memory. The sensitivity of exchange and storage coefficients has been demonstrated using numerical studies with theoretical karst systems in this hybrid system. When dealing with highly heterogeneous systems, it is demonstrated that porosity storage and exchange coefficients are required. The analytical model could possibly reveal some of the karstic network's essential structural features.

Taking advantage of a 3D printing imperfection in the development of sound-absorbing materials

At first glance, it seems that modern, inexpensive additive manufacturing (AM) technologies can be used to produce innovative, efficient acoustic materials with tailored pore morphology. However, on closer inspection, it becomes rather obvious that for now this is only possible for specific solutions, such as relatively thin, but narrow-band sound absorbers. This is mainly due to the relatively poor resolutions available in low-cost AM technologies and devices, which prevents the 3D-printing of pore networks with characteristic dimensions comparable to those found in conventional broadband sound-absorbing materials. Other drawbacks relate to a number of imperfections associated with AM technologies, including porosity or rather microporosity inherent in some of them. This paper shows how the limitations mentioned above can be alleviated by 3D-printing double-porosity structures, where the main pore network can be designed and optimised, while the properties of the intentionally microporous skeleton provide the desired permeability contrast, leading to additional broadband sound energy dissipation due to pressure diffusion. The beneficial effect of additively manufactured double porosity and the phenomena associated with it are rigorously demonstrated and validated in this work, both experimentally and through precise multiscale modelling, on a comprehensive example that can serve as benchmark.

Predicting the soil freezing characteristic curve of the expansive soil with double porosity accounting for hydraulic effects

Based on the similarity between the drying-wetting process and freezing-thawing process in the soil, a physically based equation predicting the soil freezing characteristic curve (SFCC) can be formulated combining the generalized Clapeyron equation. In this paper, by introducing the weighing factors in two scales of pore sizes, the physically based equation for single-porosity soil is extended for double-porosity soil, with the ability in well characterizing the bimodality of the SFCC. A systematic approach formulating the SFCC of the expansive soil is presented accounting for the pore size distribution and its evolution in two scenarios of the hydraulic conditions. Good agreements can be found between model predictions and experimental data for both scenarios. The effects of hydraulic condition on the pore structure of an expansive soil, as well as the consequences of the evolved pore structure on the SFCC, are emphasized and quantified. In addition, the framework presented herein demonstrates how an initially bimodal SFCC evolves into a unimodal shape along hydration and provides the theoretical SFCCs at different levels of saturation, which contributes to modelling the water-heat transfer in the freezing process of the unsaturated expansive soil.

Analytical well-test model for hydraulicly fractured wells with multiwell interference in double porosity gas reservoirs

Interference resulting from infill wells in multiwell systems becomes a common issue in interpreting well tests data from hydraulicly fractured wells in tight carbonate gas reservoirs. Current single-well pressure transient approaches may falsely interpret well interferences as the composite reservoir or boundary effects, leading to significant errors in reservoir parameter estimation. Additionally, the most semi-analytical and numerical solutions used for fractured wells are computationally demanding and inconvenient to use. This work presents a novel and simple analytical well-test model for hydraulicly fractured wells with multiwell interference in double porosity gas reservoirs with significantly less computational time and effort than the existing methods. The analytical solution for a hydraulically fractured well with finite conductivity fracture in a multiwell system with well interference is presented based on the superposition principle, the early-time approximate solutions of trilinear flow and the infinite-conductivity fracture model. A systematic verification is conducted to ensure the validity of the presented solution. The solution is valid when the dimensionless fracture conductivity is greater than 1 (FcD>1) with ∼1% error in pressure and derivative. Furthermore, we offer a criterion of identifying well interference using the pressure derivative of the late-time approximation of the proposed analytical solution. Finally, a case study is conducted in the Sichuan Basin, indicating the proposed solution's applicability.

Water retention behavior and double porosity model study of GMZ bentonite considering temperature effects

The current study investigates the influence of temperature on the water retention capacity of Gaomiaozi (GMZ) bentonite by conducting free swelling tests at different temperatures. The experimental results reveal that the equilibration time, as well as the water retention capacity, decreases significantly with temperature. A constitutive model for predicting the water retention characteristics was derived and the temperature effects were taken into account. More consistent with previous studies, the model divides the pore space into microstructural pore space (always saturated) and macrostructural pore space (presence of capillary water), with the macroscale quantifying temperature effects on water retention capacity by incorporating the suction variation and the microscale considering the introduction of a temperature-dependent microstructural deformation coefficient. The efficiency of the model was also verified using experimental data. For the GMZ bentonite with the initial dry density of 1.70 g/cm3, the threshold value for the transition from adsorbed water to capillary water is greater than 22 MPa. The microstructural deformation coefficient shows a linearly increasing relationship with temperature. The presented model allows an effective application to the hydraulic characteristics of bentonite artificial barriers for the long-term operation of nuclear waste repositories.

Integrated static and dynamic geophysical and geomechanical data for characterization of transport properties

The observatory of transfers in the vadose zone (OZNS-France) offers a unique support for characterizing the Beauce limestone aquifer at various spatial and temporal scales. This observatory consists of a large well associated with external boreholes dedicated to imaging, monitoring, and understanding mass and heat transfers through the vadose zone. An initial geological characterization of core samples gave valuable information on the facies encountered within the vadose zone. It is composed of highly incoherent limestones down to 7 m-depth and a massive and altered limestone rock layer from 7 to 20 m-depth. The latter presents fracturation and karstification increasing with depth. This study focuses on the hard limestone rock units and aims to quantify the level of heterogeneity through static and dynamic laboratory tests performed on core samples. Along 20 m of three boreholes, representative samples are tested through uniaxial or triaxial conditions. Elastic wave velocities are also measured. The obtained Young’s modulus, compression strength, and P- and S-wave velocities highlight strong variations with depth. For example, at 14 m-depth, uniaxial maximal strength ranges from 13 to 123 MPa. In addition, at 16 m-depth, P-wave velocities are distributed from 3,650 to 5,700 m.s −1 . These large scatterings confirm the strong heterogeneity of the geological formations. It is interpreted in terms of a high porosity, degree of fracturation and/or initiate active karstification. The double porosity is discussed from the difference between the static and dynamic Young’s modulus. Their variations are interpreted in terms of connected porosity and important crack density. This last parameter is estimated from the P- and S- wave velocities, and ranges from 0 to 0.43, with an extremum value of 1.21 around 19 m-depth. These values and variations are in good correlation with log imaging and independent permeability laboratory measurements made on the hard limestone rock units. • Coupled methods allow to characterize transport property of heterogeneous limestones. • Comparison of static and dynamic data shows a strong variation in double porosity. • High heterogeneities are in good correlation with permeability measurements.

Effect of the orientation distribution of thin highly conductive inhomogeneities on the overall electrical conductivity of heterogeneous material

Many natural composite materials contain systems of partially oriented thin low-resistivity inclusions (for example, water-saturated microcracks in a double porosity sedimentary formation). We have calculated the components of the electrical conductivity tensor of such materials as a function of crack density. The results were obtained for thin ellipsoidal inclusions with conductivity (electrical or thermal) much larger than the matrix conductivity. To calculate the effective conductivity, we have used the effective field method (EFM). We have obtained the explicit expressions for the effective parameters of inhomogeneous materials. The application of the EFM allows one to describe the influence of the peculiarities in the spatial distribution of inclusions on the effective properties of the medium. General explicit expressions, obtained in this work, are illustrated by calculation examples for inclusions, homogeneously distributed in the sector [-Beta, Beta], where Beta is the disorientation angle, and some continuous angle distribution functions. The calculations have shown that the spatial distribution of the crack-like inclusions strongly affects the conductive properties of the effective medium and the symmetry of their tensor.

Generalized Effective Biot Theory and Seismic Wave Propagation in Anisotropic, Poroviscoelastic Media

AbstractThe interior of the Earth is quite complex due to the actual geometrical structure and the presence of complex rheological materials, including viscoelastic rocks, porous sediments and the presence of anisotropy. Seismic wavefield forward modeling in such media forms the basis of most wave equation‐based methods for investigating the structure of the Earth and processing and imaging of seismic data, e.g., seismic full waveform inversion. Numerical modeling using Biot's equations that describe the physics of poroelasticity provides a useful framework to investigate wave attenuation and dispersion. Poroelasticity describes the interaction between the deformation of an elastic porous solid and the fluid flow in the porous structure. We present a time‐domain finite‐difference method for seismic wavefield modeling, taking into account both attenuation and anisotropy of poroviscoelastic Earth structure. The mathematical formulations and modeling methods are based on (a) the linear Biot's poroelastic theory and double porosity models in anisotropic media and (b) a relaxation function that uses the generalized standard linear solid model with anisotropic τ parameter for magnitude of attenuation and nearly constant Q model. Using a modified relaxation function that is suggested to describe the anisotropy attenuation, we develop a generalized anisotropic Biot model in the anisotropic, viscoelastic media. In addition to the anisotropic poroelasticity based on Biot theory, we implement the generalized anisotropic Biot model with complex moduli for an effective Biot's model in which the attenuative anisotropic viscoelastic model with the generalized standard linear solid model is used to approximate the attenuation factor function. The method generalizes the linear poroviscoelastic model based on effective Biot theory for seismic wave modeling to the attenuative, anisotropic case. In the anisotropic, poroviscoelastic model, we represent the bulk modulus and shear modulus of the solid frame by the modified relaxation function. We present time‐domain finite‐difference modeling for seismic wavefields in anisotropic, viscoelastic porous media including transversely isotropic media with a vertical, tilted or horizontal symmetry axis (VTI, TTI, and HTI). We also consider the extension of the two new models to nearly constant Q viscoelastic anisotropy.

Propagation of Vibrations in a Plane Angular Sector of Double Porosity Elliptic Cone

Propagation of Vibrations in a Plane Angular Sector of Double Porosity Elliptic Cone

Micromechanical schemes for Stokes to Darcy homogenization of permeability based on generalized Brinkman inhomogeneity problems

Mean field homogenization schemes are formulated for the Stokes to Darcy upscaling of the permeability on the basis of generalized inhomogeneity problems in which flow is described by Brinkman equations. The average velocity and drag force concentrations for flow in a potentially composite inclusion are characterized in terms of a permeability contribution tensor and an equivalent permeability, which allow for the direct transposition to Stokes to Darcy upscaling of most homogenization schemes available in elasticity (self-consistent, differential, Mori–Tanaka, Maxwell, …). The unified framework extends existing effective medium and cell model permeability estimates. Its flexibility is illustrated on a panel of microstructures of porous media: granular or fibrous materials, materials with spanning cylindrical or crack-like pores, double porosity materials with disconnected or connected meso-porosity and compared with existing or newly produced full field simulation results.

The theory of generalized micropolar thermoelastic diffusion with double porosity

The main purpose of the paper is to derive the constitutive relations and field equations for anisotropic micropolar thermoelastic medium with mass diffusion and double porosity. In addition to this, the fundamental solution of system of equations in case of steady oscillations is also constructed.

Numerical Analysis of a Problem Involving a Viscoelastic Body with Double Porosity

Numerical Analysis of a Problem Involving a Viscoelastic Body with Double Porosity

Investigation of an Oscillatory Multiphase Flow in a Double Porosity Medium with a Chemically Active Skeleton

Investigation of an Oscillatory Multiphase Flow in a Double Porosity Medium with a Chemically Active Skeleton