Isotropic Porous Materials Research Articles

Simplification d'images 3D de matériaux poreux en vue de leur caractérisation physique

ABSTRACT Predicting the physical properties of porous materials is difficult due to the complexity of the underlying microstructure that determines physics at the macroscopic scales of interest to the practitioner. The study of the relation between macroscopic physics and the microstructure can be largely facilitated if simplified and physically relevant representations of the microstructure are available. Herein, it is to reduce the structural complexity of a 3D digital image of an actual sample to the only rules describing the association of pore throat sizes and shapes to adjacent pores. Such rules, shown by a variety of independent approaches to govern the main part of flow and transport are measured by image analysis and expressed in the form of a pore network model. Relying on a random model of porous microstructures, the approach can be applied to isotropic porous materials whose observation by imagery is limited to 2D due to the small spatial resolution of the porosity.

Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium

A porothermoelastic solution of the general problem of the inclined borehole in a transversely isotropic porous material is presented herein and compared with the isotropic porothermoelastic solution. The governing equations are outlined for the case of general anisotropy and specialized for a transversely isotropic poroelastic material under nonhydrostatic and nonisothermal in situ conditions. A superposition scheme is employed to obtain the analytical solutions within the isotropic and transversely isotropic poromechanics theory. The borehole generator is assumed to coincide with the material axis of symmetry, in the case of transverse isotropy, yet subjected to a three-dimensional state of stress. A systematic analysis has been carried out to evaluate the effect of the anisotropy of the poromechanical material parameters as well as the thermal material properties on stress and pore pressure distributions and the potential impact on the overall stability of deep wellbore drilling.

Influence of dynamic tortuosity and compressibility on the propagation of transient waves in porous media

This paper provides an analytical solution in the time domain for the propagation of transient ultrasonic waves in a homogeneous, isotropic porous material with a rigid frame. The originality of this propagation equation is the use of the Pride et al. and Lafarge models, which give a better description of acoustic wave attenuation. Two parameters, p and p′, are added to the description of losses in the porous material, given a modification of coefficients of the propagation equation in the time domain. The analytical solution to the wave equation has a different form as compared with that obtained from the Johnson–Allard model. This wave equation contains fractional derivative terms describing attenuation and dispersion in porous material. The Laplace transform method is used to solve the propagation equation. An experimental application to porous plastic foam is given to validate the mathematical solution to the propagation equation. One important result of this work is that the introduction of the two parameters p and p′ corrects the Johnson–Allard model by increasing attenuation with no change in dispersion. This phenomenon is much more significant for resistive porous materials.

Phase-mineral and chemical composition of coal fly ashes as a basis for their multicomponent utilization. 3. Characterization of magnetic and char concentrates

The phase-mineral and chemical composition of magnetic (MCs) and char (CCs) concentrates recovered from five fly ashes (FAs) produced in four large Spanish thermo-electric power stations was characterized. The MCs and CCs were isolated by magnetic separation, sieving and froth flotation from FAs. The MCs recovered are in the range 0.7–4.1% and their phase-mineral composition (in decreasing order of significance) commonly includes Fe-rich aluminosilicate glass, magnetite, quartz, hematite, mullite, plagioclase, ferrian spinel, char, K-feldspar, wollastonite, anhydrite, and larnite. Other Fe, Mg, Ti, Mn, and Cr accessory minerals also occur in these fractions. The MCs are enriched in As, Ba, Co, Cr, Cu, Fe, Mg, Mn, Ni, U, and Zr in comparison with the FAs. The CCs recovered are in the range 1.6–22.8% and their phase-mineral composition (in decreasing order of significance) normally includes aluminosilicate glass, char (5–47% after sieving and 42–93% after flotation), quartz, mullite, and, to a lesser extent, magnetite, cristobalite, plagioclase, K-feldspar, wollastonite, hematite, anhydrite, calcite, kaolinite, larnite, and lime. The organic matter of CCs is mainly represented by anisotropic unfused, porous and coked components. The isotropic unfused inertinite and porous materials have subordinate occurrence in char. The CCs are enriched in Ag, Al, Cl, Cs, Cu, Rb, S, Sc, Se, Sr, Tb, V, and Zr in comparison with the FAs. Some genetic features, properties, possible environmental concern and potential utilization directions related to the MCs and CCs are also discussed.

Frequency dependent anisotropy of porous rocks with aligned fractures

One of the main issues in the characterization of any reservoir is the ability to predict the effect of fluid properties on seismic characteristics. This effect is studied by modelling fractures as very thin and highly porous layers in a porous background. Elastic moduli of a porous rock permeated by a system of such fractures distributed periodically are obtained using the result of Norris for elastic properties of layered poroelastic media. When both pores and fractures are dry, such material is equivalent to a transversely isotropic elastic porous material with linear-slip interfaces. When saturated with a liquid this material exhibits significant attenuation and velocity dispersion due to wave induced fluid flow between pores and fractures. At low frequencies the material properties are equal to those obtained by anisotropic Gassmann theory applied to a porous material with linear-slip interfaces. At high frequencies the results are equivalent to those for fractures in a solid (non-porous) background. The characteristic frequency of the attenuation and dispersion depends on the background permeability, fluid viscosity, as well as fracture density and spacing.

Solution in time domain of ultrasonic propagation equation in a porous material

This paper provides an analytical solution in the time domain for the propagation of transient ultrasonic waves in a homogeneous isotropic porous material having a rigid frame. The coefficients of the propagation equation are constant and depend only on the acoustical parameters of the porous material. The propagation equation contains fractional derivative terms that describe viscous and thermal interactions between the solid and the fluid. The dynamic response of the material is obtained using the Laplace transform method. An experimental application to porous plastic foams is given to validate the solution of the propagation equation.

Macroscopic strain potentials in nonlinear porous materials

By taking a hollow sphere as a representative volume element (RVE), the macroscopic strain potentials of porous materials with power-law incompressible matrix are studied in this paper. According to the principles of the minimum potential energy in nonlinear elasticity and the variational procedure, static admissible stress fields and kinematic admissible displacement fields are constructed, and hence the upper and the lower bounds of the macroscopic strain potential are obtained. The bounds given in the present paper differ so slightly that they both provide perfect approximations of the exact strain potential of the studied porous materials. It is also found that the upper bound proposed by previous authors is much higher than the present one, and the lower bounds given by Cocks is much lower. Moreover, the present calculation is also compared with the variational lower bound of Ponte Castaneda for statistically isotropic porous materials. Finally, the validity of the hollow spherical RVE for the studied nonlinear porous material is discussed by the difference between the present numerical results and the Cocks bound.

Elasticity and Viscosity of Isotropic Porous Materials

Theoretical dependences of elasticity moduli, Poisson's ratio, and the shear and volumetric viscosity of porous isotropic materials on their relative density are generalized. An approximate description is suggested for the elasticity and viscosity of isotropic porous materials on the basis of analyzing these dependences for spherical, needle- and disk-shaped pores, and also experimental data for the elasticity moduli of sintered nickel, iron, and boron carbide taking account of mesostructural imperfection of powder bodies, and also of data for amorphous glass sintered under pressure in a vacuum.

A model of the short-term damageability of a transversally isotropic material

The effective deformation properties and the stress–strain state of a material are determined on the basis of the stochastic equations of elastic theory, which allow for the random nature of microdamages. The problem on the stress-strain state of a porous transversally isotropic material under uniform loading with specified strains is solved using the model proposed. To this end, a numerical–analytical algorithm is proposed. This algorithm is based on the stochastic method of conditional moment functions and the combined iteration method, which is used to solve a transcendental equation. Using this approach, as an example, a nonlinear macrodeformation diagram is plotted and the behavior of a transversally isotropic porous material under biaxial tension is studied

A lattice gas automaton simulation of the nonlinear diffusion equation: A model for moisture flow in unsaturated porous media

We investigate a two-dimensional lattice gas automaton (LGA) for simulating the nonlinear diffusion equation in a random heterogeneous structure. The utilility of the LGA for computation of nonlinear diffusion arises from the fact that, the diffusion coefficient in the LGA depends on the local density ρ of ‘fluid’ particles which statistically determines the collision rate and thus, the mean free path λ of the particles at the microscopic scale. The LGA may therefore be used as a physical analogue to simulate moisture flow in unsaturated porous media. The capability of the LGA to account for unsaturated flow is tested through a set of numerical experiments simulating one-dimensional infiltration in a simplified semi-infinite homogenous isotropic porous material. Different mechanisms of interactions are used between the fluid and the solid phase to simulate various fluid–solid interfaces. The heterogeneous medium, initially at low density is submitted to a steep density gradient by continuously injecting fluid particles at high concentration and zero velocity along one face of the model. The propagation of the infiltration front is visualized at different time steps through concentration profiles parallel to the applied concentration gradient and the infiltration rate is measured continuously until steady-state flow is reached. The numerical results show close agreement with the classical theory of flow in unsaturated porous media. The cumulative absorption exhibits the expected t 1/2 dependence. The evolution of the effective diffusion coefficient with the particle concentration is estimated from the measured density profiles for the various porous materials. Depending on the applied fluid–solid interactions, the macroscopic effective diffusivity may vary by more than two orders of magnitude with density.

A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials

A method for evaluating the acoustical properties of homogeneous and isotropic porous materials that may be modeled as fluids having complex properties is described here. To implement the procedure, a conventional, two-microphone standing wave tube was modified to include: a new sample holder; a section downstream of the sample holder that accommodated a second pair of microphone holders and an approximately anechoic termination. Sound-pressure measurements at two upstream and two downstream locations were then used to estimate the two-by-two transfer matrix of porous material samples. The experimental transfer matrix method has been most widely used in the past to measure the acoustical properties of silencer system components. That procedure was made more efficient here by taking advantage of the reciprocal nature of sound transmission through homogeneous and isotropic porous layers. The transfer matrix of a homogeneous and isotropic, rigid or limp porous layer can easily be used to identify the material's characteristic impedance and wave number, from which other acoustical quantities of interest can be calculated. The procedure has been used to estimate the acoustical properties of a glass fiber material: good agreement was found between the estimated acoustical properties and those predicted by using the formulas of Delany and Bazley.

A computational model for the finite element analysis of thermoplasticity coupled with ductile damage at finite strains

An updated Lagrangian implicit FEM model for the analysis of large thermo-mechanically coupled hyperelastic-viscoplastic deformations of isotropic porous materials is considered. An appropriate framework for constitutive modelling is introduced that includes a stress-free thermally expanded configuration and a plastically deformed unstressed damaged configuration. A two-level iterative scheme is employed at each time increment to solve the field equations governing the conservation of momentum (mechanical step) and the conservation of energy (thermal step) for the coupled thermo-mechanical problem. Exact linearizations for the calculation of the tangent stiffness are performed in each of these solution steps. A fully implicit, thermo-mechanically coupled and incrementally objective Euler-backward radial return based map is developed for the time integration of the constitutive equations. The present model is used to analyse a number of benchmark examples including metal forming processes wherein temperature and the accumulated damage play an important role in influencing the deformation mechanism and the nature of the deformed workpiece. Copyright © 1999 John Wiley & Sons, Ltd.

Solutions for Hollow Cylinders in Transversely Isotropic Porous Materials

Solutions for Hollow Cylinders in Transversely Isotropic Porous Materials

Sound transmission through multilayer structures with isotropic elastic porous materials

This paper discusses the prediction of transmission loss through multilayer structures with porous materials. First, a brief review of recent formulations for multilayer structures with poroelastic materials is presented. Second, the transmission loss problem is described and formulated using a coupled finite element and boundary element procedure. Issues such as poroelastic-elastic coupling, poroelastic-fluid coupling, and radiation from a poroelastic material will be addressed. The developed model is validated through numerical examples. Its advantages and limitations are discussed. Finally, typical results showing the vibroacoustic effects of several parameters such as the multilayer configuration, the types of porous materials, and the mounting conditions are presented. [Work supported by Bombardier, Inc., Canadair and N.S.E.R.C.]

Contaminant Transport Through Single Fracture With Porous Obstructions

Transport of contaminant through a single fracture, modeled as a closely spaced parallel plates aperture, is analyzed theoretically and numerically. Permeable contact regions between the plates are modeled as fixed packs of homogeneous, isotropic, and inert porous material. A nondimensional theoretical expression for estimating the equivalent global permeability of the aperture is presented in terms of the relative volume occupied by the contact regions. Transient transport of contaminant (solute) through this heterogeneous system is analyzed considering injection of fluid with uniform concentration at the inlet of the fracture. For natural systems, it is verified that relative volume and distribution of contact regions affect clean-up time, defined as the time necessary for the complete removal of contaminant, only indirectly by varying the equivalent permeability of the system, otherwise their effect is negligible. The clean-up time of a clear (of contact regions) fracture, is correlated with the Peclet number for 10−1 ≤ Pe ≤ 106.

Mechanical properties of isotropic porous materials. IV. The effect of mesostructural defects

Mechanical properties of isotropic porous materials. IV. The effect of mesostructural defects

An unstructured mesh cell-centered control volume method for simulating heat and mass transfer in porous media: Application to softwood drying, part I: The isotropic model

Drying is one of the most energy intensive industrial processes with applications in a wide variety of industries including the timber industry, the food industry, and the construction industry. In order to understand the physics of drying at a fundamental level it is necessary to analyze the motion of liquid and gas through a capillary porous medium. The governing transport equations are comprised of a set of tightly coupled, highly nonlinear partial differential equations for the dynamic system variables of moisture content, temperature, and internal gaseous pressure. Due to the complexity of this system of equations there is usually little alternative but to employ a numerical solution technique. In this work an innovative scheme known as the unstructured mesh cell-centered control volume method will be analyzed and subsequently applied to high temperature drying of softwood. The method will be tested for a wide range of meshes each having differently shaped polygonal control volumes or cells. This new method will lay the foundation for studying problems that concern heat and mass transfer in porous media defined on complex geometries, or more importantly, for drying problems that include a stress analysis implemented on a dynamically distorting mesh. The work consists of two parts: Part I is devoted to the study of isotropic porous materials using a two-node and a four-node formulation for the discretization of the equations on an unstructured mesh; in Part II the numerical discretization associated with the complex problem of an anisotropic porous material is presented.

Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements

In this paper the development of a two-dimensional elastic-absorption finite element model of isotropic elastic porous noise control materials is described. A method for coupling elastic-absorption finite elements with conventional acoustic finite elements is also presented for the cases when the interface between the adjacent air space and the foam is either unfaced or sealed by a membrane. The accuracy of the acoustic/elastic-absorption model has been verified by comparing its predictions with analytical solutions for the case of wave propagation in a foam-filled waveguide. Further, the finite element model has been used to investigate the effect of edge constraints on the surface normal impedance of a foam sample in a standing-wave tube. As expected, edge constraints were found to stiffen the foam acoustically at low frequencies.

Second-order constitutive relations for transversely isotropic piezoelectric porous materials

Based on the theory of invariants, polynomial constitutive relations for transversely isotropic piezoelectric porous materials are derived from the polynomial integrity bases for an energy density function depending on a symmetric second-order tensor and two vectors. They are assumed to be smooth functions of their arguments, are expanded about the values their arguments take in the reference configuration and all terms up to the quadratic terms in the gradients of the mechanical displacement, the electric potential, and the gradients of the volume fraction are kept. The second-order constitutive relations so obtained are then specialized to the case of infinitesimal deformations and weak electric fields, and also to the case of infinitesimal deformations and strong electric fields.

Validity of Finite Element Unit Cell Model for Studying Yield Condition of Isotropic Porous Materials.

Assuming a spherical void in an infinite rigid plastic material, Gurson proposed a yield function for isotropic porous solids. It is, however, well known that the Gurson model gives harder response than those predicted by experimentation on actual porous solids. In numerical studies to check the validity of Gurson's model, most of the past researchers have introduced a cubic unit cell model, in which a spherical void is placed at the center of the cube. The cubic model can be a good approximation of a porous solid, if the void volume fraction is very small. The cubic model, however, may be not appropriate for the study of porous solids with high ratio of void volume fraction since the model automatically introduces an orthotropy effect due to the geometrically repetitive distribution of voids in three orthogonal axis directions. This research will propose a new unit cell model which is appropriate for the study of the yield functions for isotropic porous materials. The model is also favorable for the study of the anisotropic effect due to the void shape because the unit cell includes less of the anisotropy based on the distribution than the cubic model does.