Double Porosity Research Articles

Thermodynamical interactions in a double porosity model with diffusion and microtemperatures

This manuscript investigates the disruptions occurring in a two-dimensional homogeneous, isotropic, thermoelastic medium with diffusion, double porosity and microtemperatures under Lord and Shulman (LS) theory of generalized thermoelasticity. A mechanical load is applied at the outer free surface of the solid half-space. To procure the exact expressions for various field variables, normal mode analysis is utilized. Numerical computations are performed for a particular material and the acquired results are visualized through graphical representations with the aid of MATLAB software. Comparisons are carried out to elucidate the influences of diffusion parameter, time, double porosity and intensity of load on the resulting quantities. 2010 MSC: 74A15, 80A20.

Poroelastic size dependent dynamics of viscoelastic microbeams connected via a viscoelastic layer

This article aims to investigate the dynamics of clamped-clamped porous viscoelastic double microbeams interconnected via a viscoelastic layer within the framework of the modified couple stress theory (MCST). Different types of porosity distributions are considered to examine the material imperfection effects on the dynamics of the double microbeam. A closed-cell porosity model is employed to model the variation of the material properties in the thickness plane. The coupled longitudinal and lateral equations of motion are derived using Hamilton’s principle. The governing equations of motion are solved using the modal decomposition method. The equations of motion are verified against the literature for simplified cases (i.e., a non-porous single viscoelastic microbeam and a porous single microbeam resting on a viscoelastic foundation). The numerical results are validated for simpler versions of the system using the finite element method and against the existing literature for a simplified case of a uniformly distributed porous double macrobeam connected via an elastic layer. Influences of viscoelasticity in the double microbeam, viscoelastic layer, porosity, and small-scale influences on the dynamics of the viscoelastic double microbeams are studied. It was found that increasing the material length-scale factor causes the complex fundamental lateral vibrational frequencies to increase for all the porosity patterns.

Characterisation and simulation of a general ventilation filter based on a double porosity approach

The air filters installed in ventilation systems are designed for collecting dust and particles. These filters usually consist in folded paper or textile, arranged either as a flat slab or in a V-shape frame. Some of them may also contain activated carbon in order to remove molecular compounds. Experimental results show that they can significantly attenuate the upstream sound sources such as fans or other regenerated noise. Though, these acoustic properties are not strictly speaking designed and often result from the tailored filtering capacities. The present work proposes a three-stage methodology to design and optimize the acoustic performance of these filters. The first stage is the characterization of the intrinsic acoustic parameters of the paper or textile. The second stage consists in the validation of these parameters regarding sound attenuation as measured in impedance tube. This includes analytical and finite element computations to correctly account for the mounting conditions of the specimen in the impedance tube. The final stage consists in predicting the sound attenuation measured on the full-size filter, set in shape using the porous composite material theory. The obtained results provide a satisfactory correspondence allowing for an accurate design at an early stage of the project.

Multiscale simulation study for mechanical characteristics of coral sand influenced by particle breakage

This paper investigates the mechanical response of coral sand under particle breakage using a hierarchical multiscale model combining the discrete element method (DEM) and the finite element method (FEM). This DEM-FEM model links the microscopic interaction mechanisms to macroscopic phenomena such as strain localization and failure. A cohesive contact model was first utilized to simulate compaction bands in the DEM and construct a cohesive assembly with smaller particles distributed around a larger particle to better simulate the grinding and angular breakage of coral sand. A representative volume element (RVE) that includes particle breakage was then constructed and analyzed under periodic boundary conditions. DEM analysis was performed, and the results were compared with triaxial compression test data obtained from the literature, demonstrating that the constructed RVE effectively represents the mechanical properties of coral sand. The constructed RVE was used for hierarchical multiscale simulations, which showed good agreement with existing triaxial testing of coral sand. Finally, by setting a larger cohesive force, the constructed coral sand particles were prevented from breakage, and comparative analysis revealed that particle breakage weakens the mechanical properties of coral sand. Furthermore, different shapes of coral sand particles were constructed, and RVE and hierarchical multiscale simulations of triaxial tests were performed. The results indicated that the triaxial tests of long strip-shaped coral sand particles exhibit higher peak values compared to spherical coral sand particles. Additionally, a double porosity model of coral sand was constructed to analyze the impact of internal porosity on soil mechanical properties. The results showed that the presence of internal porosity significantly weakened the mechanical properties of coral sand. These findings highlight the significant impact of particle breakage and shape on the mechanical behavior of coral sand, offering important insights for engineering applications.

A qualitative analysis on the double porous thermoelastic bodies with microtemperature

This study examines a mixed initial-boundary value problem in thermoelastic materials with a double porosity structure, taking into account the effects of microtemperature. The existence of a solution is established by converting the problem into a Cauchy-type problem. Given the complexity of the equations, unknowns, and conditions, we apply contraction semigroup theory within a specific Hilbert space. We prove the existence of a solution using the Lax-Milgram theorem. Additionally, the uniqueness of the solution is demonstrated based on the Lumer-Phillips corollary, which corresponds to the Hille-Yosida theorem. In the final section, we show the continuous dependence of the solution on the mixed initial-boundary value problem for double porous thermoelasticity with microtemperature.

Comparative analysis of double and single porosity effects on SH-wave induced vibrations in periodic porous lattices

The manuscript presents a novel study comparing the impact of single and double porosity on horizontally polarized shear wave (SH-wave) propagation in corrugated elastic void materials. The considered mathematical model comprises two cases; the first one depicts SH-wave propagation through a void porous layer having creased boundaries and resting over a heterogeneous anisotropic fluid-saturated fractured porous half-space, whereas according to the second case, heterogeneous anisotropic fluid-saturated porous semi-infinite medium without fractures has been considered. In both cases, rigidity and density of the half-space vary quadratically with depth. The separable variable method is used to attain the complex frequency equation for each case that leads to two different dispersion relations associated with two distinct wave fronts. The first wave front depends on the void parameters, whereas the second wave front defines the propagation of SH-waves in an elastic layer without void pores. In each case, the complex dispersion relation has been separated into two equations that illustrate the dispersion and attenuation properties of SH-waves. Using the variations in the inhomogeneity, position, fluctuation, flatness, total porosity, and anisotropy parameters, case I and case II have been compared in each graphical execution. In addition, the surface response of shear stress and displacement have been implemented graphically.

Multiscale homogenization for dual porosity time-dependent Darcy-Brinkman/Darcy coupling and its application to the lymphnode.

We study the coupling between time-dependent Darcy-Brinkman and the Darcy equations at the microscale subjected to inhomogeneous body forces and initial conditions to describe a double porosity problem. We derive the homogenized governing equations for this problem using the asymptotic homogenization technique, and as macroscopic results, we obtain a coupling between two Darcy equations, one of which with memory effects, with mass exchange between phases. The memory effects are a consequence of considering the time dependence in the Darcy-Brinkman equation, and they allow us to study in more detail the role of time in the problem under consideration. After the formulation of the model, we solve it in a simplified setting and we use it to describe the movement of fluid within a vascularized lymph node.

Degradable biporous polymeric networks based on 2-methylene-1,3-dioxepane: Towards hierarchically structured materials meant for biomedical applications

For the first time, the preparation of doubly porous “poly(ε-caprolactone)-like” networks through free-radical ring-opening copolymerization of 2-methylene-1,3-dioxepane with divinyl adipate was achieved via a double porogen templating approach. This versatile strategy allowed for the formation of macropores of around 150 μm generated by removal of sieved and sintered NaCl particles in water, while smaller pores in the 1–10 μm range were created by phase separation during the copolymerization process through a syneresis mechanism in the presence of a porogenic solvent. The chemical nature of the as-obtained scaffolds was evidenced by Raman spectroscopy. The two distinct porosity levels could be examined by scanning electron microscopy and mercury intrusion porosimetry. The nature of the porogenic solvent as well as its volume proportion and the amount of crosslinking agent in the polymerization feed allowed for finely tuning the porous features of the micropores. The crucial role of the double porosity of such biporous scaffolds on their water uptake and mechanical properties under compression was assessed by comparing them with their monoporous analogues, while their degradability was investigated in different alkaline aqueous media. The double porosity enabled a synergistic effect regarding the water uptake of the resulting scaffolds when compared to their monoporous counterparts. Doubly porous polymeric materials with appropriate mechanical properties were obtained, possessing high compressibility and shape memory behavior upon consecutive compression cycles. Finally, these materials display degradation rates that could be controlled depending on medium pH.

Influence of dry density and wetting–drying cycles on the soil–water retention curve of compacted loess: experimental data and modeling

AbstractIn this paper, the EC-5 water sensor and the MPS-6 water potential sensor were used to measure water content and suction, respectively, to investigate the evolution of soil–water retention properties of compacted loess samples prepared at different dry densities and subjected to different numbers of wetting–drying cycles. The water retention data were integrated with a detailed microstructural investigation, including morphological analysis (by scanning electron microscopy) and pore size distribution determination (by nuclear magnetic resonance). The microstructural information obtained shed light on the double porosity nature of compacted loess, allowing the identification of the effects of compaction dry density and wetting–drying cycles at both intra- and inter-aggregate levels. The information obtained at the microstructural scale was used to provide a solid physical basis for the development of a simplified version of the water retention model presented in Della Vecchia et al. (Int J Numer Anal Meth Geomech 39: 702–723, 2015). The model, adapted for engineering application to compacted loess, requires only five parameters to capture the water retention properties of samples characterized by different compaction dry densities and subjected to different numbers of wetting–drying cycles. The comparison between numerical simulations and experimental results, both original and from the literature, shows that only one set of parameters is needed to reproduce the effects of dry density variation, while the variation of only one parameter allows the reproduction of the effects of wetting and drying cycles. With respect to the approaches presented in the literature, where ad hoc calibrations are often used to fit density and wetting–drying cycle effects, the model presented here shows a good compromise between simplicity and predictive capabilities, making it suitable for practical engineering applications.

Thermoelastic diffusion based on a nonlocal three-phase-lag diffusion model with double porosity structure

This work aims to develop a new diffusion-elasticity-based model using Eringen’s nonlocal elasticity theory under the purview of the three-phase-lag (TPL) model of hyperbolic thermoelasticity. This problem is treated in the context of a double porosity structure in a homogeneous, isotropic thermoelastic medium. By considering the phase laggings of the diffusion flux vector and using nonlocal continuum mechanics, new constitutive and field equations are derived. The problem is solved by employing the normal mode analysis technique which gives the exact results of all the physical variables. To illustrate the theoretical results, different physical quantities are calculated numerically and presented graphically with respect to distance and time. The influences of different thermoelastic models like TPL (three-phase-lag model), GN-III (Green-naghdi model), DPL (dual-phase-lag model), LS (Lord-Shulman model), and CT (coupled thermoelasticity) on the physical quantities are shown graphically. Additionally, the effects of nonlocal parameters, double voids, and diffusion on the physical quantities are represented graphically. Some limiting and particular cases are also derived from the governing equations and those results have been compared with the existing results available in the literature. Some 3D surface curves are also presented to study the impact of diffusion, nonlocality, and double voids on various physical quantities.

Reflection and transmission of plane waves from the interface of a porothermoelastic solid and a double porosity solid

Reflection and transmission of plane waves from the interface of a porothermoelastic solid and a double porosity solid

Topology optimization with a parametric level set method for double porosity poroelastic sound-absorbing structures

Topology optimization with a parametric level set method for double porosity poroelastic sound-absorbing structures

Effect of Electromagnetic Field on Vibrations of Nonlocal Elastic Cylinders with Double Porosity

Effect of Electromagnetic Field on Vibrations of Nonlocal Elastic Cylinders with Double Porosity

Theory of elastic wave propagation in a fluid-saturated multi-porous medium with multi-permeability

This paper establishes the concept of elastic wave propagation in a multi-porous medium with different permeabilities by assuming there are n distinct pore fluid phases. The dynamic equation of motion of elastic wave propagation through this multi-porous medium is derived based on Lagrangian mechanics. In this regard, the generalized form of mass coefficients and then the energy loss due to the fluid phases in terms of dissipation coefficients are presented for low-frequency limits with the help of Darcy’s Law of multi-phases system. The elastic coefficients of the constitutive equation in terms of compliance matrix are identified using a series of Gedanken experiments. Some significant results regarding the compressional and rotational waves in a multi-porosity medium are derived. The validation of the theory has been shown by comparing it with the existing theory of single and double porosity. It is observed that there are ( n + 1 ) compressional waves corresponding to solid and fluid phases, whereas only one rotational wave is associated with the solid phase. The concept of multi-porosity theory can contribute to a deeper understanding of wave behaviour in a porous medium.

Hydromechanical coupling in unsaturated clayey rocks with double porosity based on a multiscale homogenization procedure

Shales and clay rocks are porous media with multiscale microstructures used in many engineering applications. Intact clay rocks often exhibit a bimodal pore size distribution in which the nanopores are related to the interlayer spacing in the clay platelet and the micropores are related to the interparticle pores between clay particles. The double-porosity microstructure has significant implications for the hydromechanical behavior of these rocks especially in unsaturated conditions. In this study, we develop a double-porosity hydromechanical framework incorporating a homogenization scheme to simulate fluid flow and elastic deformation in anisotropic clay rocks. The homogenization scheme provides an enriched description of the elastic behavior of clay rocks during changes in the degree of saturation by bridging the nano, micro, and macroscale characterizations. We also model the nanopores and micropores as two independent pore networks with distinct fluid flow mechanisms and permeabilities. The proposed framework is cast into a three-field mixed finite element formulation for solving fully coupled flow and deformation problems. Numerical examples of free and confined swelling in Opalinus clay samples are presented to demonstrate the impacts of a multiscale microstructure on wetting processes in clay rocks.

Catalytic decomposition of sulphuric acid in Iodine-Sulphur and Hybrid-Sulphur processes for Hydrogen production: Estimation of effectiveness factor of catalyst

High endothermic heat of SO3 decomposition reaction (ΔHR∼+98 kJ mol−1) can lead to significant thermal gradients (lower temperatures) inside the catalyst particle, depending up on mass diffusion, heat conduction and intrinsic reaction kinetics in the particle. The lower catalyst effectiveness (due to thermal gradients) leads to lower decomposition conversions in Packed Bed Reactors (PBR), which has to be maximized. In this study, a multi-scale model (Double Porosity Model, DPM) is used for the estimation of non-isothermal effectiveness factor (η) of Cr-Fe2O3 catalyst types; less porous pellet and porous foam types. η obtained using DPM (foam∼0.249 and pellet∼0.147) are found to be in good agreement with experimental data and also with the results of derived model (Weisz model). Further, effect of porosity and size/diameter on η are studied and obtained the optimum porosity required for maximum η. The present study is useful for estimation and optimization of non-isothermal η of catalysts.

Groundwater flow modelling in Neoproterozoic carbonate karst based on dye tracer pathways

The current study consisted of the development of a hydrogeological numerical model in the Lagoa Santa Karst Environmental Protection region, in order to represent the conduit-flow karst springs in the most well-studied karst system in Brazil. Once carbonate aquifers are characterized by a complex 3D pattern with a combination of a double porosity of matrix and conduits, two different modelling approaches were used: Equivalent Porous Medium (EPM), based on Darcy’s law, to represent laminar flow in the fractured massif and Conduit Network (CN), using Manning-Stricker Law and the discrete feature tool, to represent the karst conduits with turbulent flow. Modeling was calibrated in a steady-state and simulations of groundwater flow and an evaluation of water exchanges between the karstic aquifer and the other hydrogeological units, were conducted. The model was developed based on data available for many studies carried out in the area, including tracer-derived route data. The calibration results for spring discharges, water levels and mass balance were satisfactory and aligned with modeling good practices. In turn, the hydraulic conductivities and recharge rates obtained by back-analysis were in agreement with literature references. The regional groundwater flow was well represented and indicated how external water entrances can be relevant to explain the higher discharge rates observed in some karstic springs. In addition, the representation of conduits allowed for the simulation of tracer pathways, enabling the inference of potential flow rates to the karstic springs from the particle simulations.

3D rock physics template-based probabilistic estimation of tight sandstone reservoir properties

Quantitative prediction of reservoir properties (e.g., gas saturation, porosity, and shale content) of tight reservoirs is of great significance for resource evaluation and well placements. However, the complex pore structures, poor pore connectivity, and uneven fluid distribution of tight sandstone reservoirs make the correlation between reservoir parameters and elastic properties more complicated and thus pose a major challenge in seismic reservoir characterization. We have developed a partially connected double porosity model to calculate elastic properties by considering the pore structure and connectivity to analyze these factors' influences on the elastic behaviors of tight sandstone reservoirs. The modeling results suggest that the bulk modulus is likely to be affected by the pore connectivity coefficient, while the shear modulus is sensitive to the volumetric fraction of stiff pores. By comparing the model predictions with the acoustic measurements of the dry and saturated quartz sandstone samples, the volumetric fraction of stiff pores and the pore connectivity coefficient can be determined. Based on the calibrated model, we have constructed a 3D rock physics template that accounts for the reservoir properties’ impacts on the P-wave impedance, S-wave impedance, and density. The template combined with Bayesian inverse theory is used to quantify gas saturation, porosity, clay content, and their corresponding uncertainties from elastic parameters. The application of well-log and seismic data demonstrates that our 3D rock physics template-based probabilistic inversion approach performs well in predicting the spatial distribution of high-quality tight sandstone reservoirs in southwestern China.

Reflection of plane waves in a rotating micropolar double porous thermoelastic medium with temperature dependent properties

AbstractThe objective of this empirical investigation is to explore the behavior of different waves reflected in a homogenous isotropic double porous structured micropolar thermoelastic medium with rotation and temperature‐dependent characteristics. Three‐phase‐lag theory of thermoelasticity is adopted to acquire the governing equations of the model. Six coupled plane waves have been found to propagate across the medium at distinct velocities. Derivation for energy and amplitude ratios of reflected waves were carried out by employing appropriate boundary conditions. For different angles of incidence, the outcomes for energy partition were determined numerically and displayed graphically. It is found that amplitude ratios associated with various reflected waves are affected by angular velocity, temperature‐dependent properties, micropolar parameter, and double porosity. Also, it has been discovered that throughout the reflection phenomena there is no dissipation of energy. Furthermore, this study concludes with a summary of the findings and subsequent observations. The current investigation has yielded inferences regarding specific cases that are of particular interest.

Influence of thermal load on a rotating thermoelastic medium with diffusion and double porosity

In the present work, we have studied the thermodynamical interactions in a two-dimensional thermoelastic medium with diffusion, rotation and double porosity in the context of Green–Lindsay theory. A thermal load is applied at the outer free surface of the medium. The normal mode technique is employed to derive the analytic expressions of the field quantities such as stresses, displacement components, temperature field and mass concentration. Numerical computations are performed with the help of MATLAB software for a specific material for illustrating the results. To the author’s best knowledge, no attempt has been made to investigate the therodynamical interactions in a rotating double porous thermoelastic medium with diffusion under the influence of a thermal load. Comparisons of the physical quantities are shown in figures to study the effects of time, double porosity, rotation, thermal load and diffusion. Some particular cases of interest have also been inferred from the present problem. The theoretical and numerical computations are found to be in close agreement.