Layers Of Different Properties Research Articles

Reduced model for the surface dynamics of a generally anisotropic elastic half-space

Near-surface resonance phenomena often arise in semi-infinite solids. For instance, when a moving load with a speed v close to the surface wave speed v R is applied to the surface of an elastic half-space, it will give rise to a large-amplitude disturbance inversely proportional to v − v R . The latter can be determined by a multiple-scale approach using an extra slow time variable. It has also been shown for isotropic elastic half-spaces that the reduced governing equation thus derived is capable of describing the surface wave contribution even for arbitrary dynamic loading. In this paper, we first derive the analogous evolution equation for a generally anisotropic elastic half-space, and then assess its applicability in the study of travelling waves in a half-space that is coated with a continuous array of spring-like vertical resonators or bonded to an elastic layer of different properties. Our results are validated by comparison with previously known results, and illustrative calculations are carried out for a fibre-reinforced half-space and a coated half-space that is subjected to a finite deformation.

Verification benchmark for a single-phase flow hydro - mechanical model comparison between COMSOL Multiphysics and DuMuX

Numerical modelling of hydromechanical processes in geological environments has become an invaluable tool in understanding and predicting system behaviour. However, due to the different algorithms and numerical schemes implemented in the different models, model reliability may vary considerably. Modelling of single- and multi-phase flow in porous media has been widely employed in various engineering applications such as geological disposal of nuclear waste, geological storage of carbon dioxide, high-temperature geothermal systems, or hydraulic fracturing for shale gas exploitation. Coupled hydro-mechanical (H-M) processes play a key role in the prediction of the behaviour of geological reservoirs during their development and testing operations. In this paper, we present a benchmark test on a single-phase flow problem in a hydrogeological reservoir with 5 horizontal layers of different properties. The aim is to compare two hydromechanical (H-M) models that use a vertex-centred finite-volume discretization and a finite element discretization. The first model is constructed with the free-open source simulator DuMuX, and the second with the commercial software COMSOL Multiphysics. The verification study suggests general confidence in the model reliability, but also highlights and discusses several areas of discrepancies between two models.

The effects of asteroid layering on ejecta mass-velocity distribution and implications for impact momentum transfer

Most bodies in the Solar System do not have a homogeneous structure. Understanding the outcome of an impact into regolith layers of different properties is especially important for NASA’s Double Asteroid Redirection Test (DART) and ESA’s Hera missions. Here we used the iSALE shock physics code to simulate the DART impact into three different target scenarios in the strength regime: a homogeneous porous half-space; layered targets with a porous weak layer overlying a stronger bedrock; and targets with exponentially decreasing porosity with depth. For each scenario we determined the sensitivity of crater morphology, ejecta mass-velocity distribution and momentum transferred from the impact for deflection, β−1, to target properties and structure. We found that for a homogeneous porous half-space, cohesion and porosity play a significant role and the DART impact is expected to produce a β−1 between 1 and 3. In a two-layer target scenario, the presence of a less porous, stronger lower layer close to the surface can cause both amplification and reduction of ejected mass and momentum relative to the homogeneous upper-layer case. For the case of DART, the momentum enhancement can change by up to 90%. Impacts into targets with an exponentially decreasing porosity with depth only produced an enhancement in the ejected mass and momentum for sharp decreases in porosity that occur within 6 m of the asteroid surface. Together with measurements of the DART crater by the Hera mission, these results can be used to test the predictive capabilities of numerical models of asteroid deflection.

Discrete element method to model cracking for two layer systems

Cracking at the fold is a serious issue for many grades of coated paper and coated board. Some recent work has suggested methods to minimize this problem by using two or more coating layers of different properties. A discrete element method (DEM) has been used to model deformation events for single layer coating systems such as in-plain and out-of-plain tension, three-point bending, and a novel moving force picking simulation, but nothing has been reported related to multiple coating layers. In this paper, a DEM model has been expanded to predict the three-point bending response of a two-layer system. The main factors evaluated include the use of different binder systems in each layer and the ratio of the bottom and top layer weights. As in the past, the properties of the binder and the binder concentration are input parameters. The model can predict crack formation that is a function of these two sets of factors. In addition, the model can predict the flexural modulus, the maximum flexural stress, and the strain-at-failure. The predictions are qualitatively compared with experimental results reported in the literature.

Structure Formation of Sulfur-Based Composite: The Model

In material science the simultaneous application of theoretical examination, experimental and numerical studies are often required. This is especially true for modern composite materials with extra inter-boundary nanoscale layers. Thickness of layers is usually about tens of nanometers, while diameters of particles of filler are about several hundreds of nanometers. Thus, during the theoretical study and numerical experiments the size and properties of inter-boundary layer must be taken into account. The proper choice of the model is the key factor for the adequate results of simulation. In the present work we have derived such a model. The system under investigation – disperse-filled composite material with inter-boundary layers of different properties – is represented by particle system; these classes of models can be characterized by high generality. Initial equation for the law of motion is sequentially extended with terms which account for different phenomena – conservative binary interaction, non-conservative interaction with environment, interaction with planar boundaries and non-conservative particle-particle interaction via inter-boundary layer. The reduction of the law of motion to the system of ordinary differential equations had opened the possibility for utilization of the vast majority of numerical algorithms for the prediction of the structural properties of nanomodified sulfur-based composite.

Characterization of Filter Cake Generated by Water-Based Drilling Fluids Using CT Scan

Summary Filter-cake characterization is very important in drilling and completion operations. The homogeneity of the filter cake affects the properties of the filtration process such as the volume of filtrate, the thickness of the filter cake, and the best method to remove it. Various models were used to determine the thickness and permeability of the filter cake. Most of these models assumed that the filter cake was homogeneous. The present study shows that the filter cake is not homogeneous, and consists of two layers of different properties. The objective of this study is to measure the filter-cake thickness and permeability of water-based drilling fluids by a new approach and compare the results with previous models. A high-pressure/high-temperature (HP/HT) filter press was used to perform the filtration process under static conditions (225°F and 300 psi). A computed-tomography (CT) scan was used to measure the thickness and porosity of the filter cake. Scanning electron microscopy (SEM) was used to provide the morphology of the filter cake. The results obtained from the CT scan showed that the filter cake was heterogeneous and contained two layers with different properties under static and dynamic conditions. Under static conditions, the layer close to the rock surface had a 0.06-in. thickness, 10- to 20-vol% porosity, and 0.087-pd permeability, while under dynamic conditions, this layer had a 0.04-in. thickness, 15-vol% porosity, and 0.068-pd permeability. The layer close to the drilling fluid had a 0.1-in. and 0.07-in. thickness under static and dynamic conditions, respectively, and it had zero porosity and permeability after 30 minutes under static and dynamic conditions. SEM results showed that the two layers contained large and small particles, but there was extremely poor sorting in the layer, that was close to the drilling fluid, which led to zero porosity in this layer. Previous models underestimated the thickness of the filter cake by almost 50%. A new method was developed to measure the thickness of the filter cake, and various models were screened to identify the best model that can predict our permeability measurements.

On wave propagation in laminates with two substructures

We study numerically the influence of the presence of a complex internal structure of laminates, consisting of layers of different properties and variable thickness, on the dynamic response of the material. The influence of the internal structure of laminate layers on the signal propagation is demonstrated by several examples for periodic and double periodic laminates. It is also discovered that the influence of the mutual position of layers with different internal structure can be significant.

Analysis of multiple cracks in laminate composites under anti-plane static loads

This paper investigates multiple cracking of a laminate composite subjected to anti-plane loads. The laminate composite is made up of a central layer sandwiched between two layers of different properties. There is a periodic array of cracks in the central layer along the central axis of the medium. A singular integral equation is formulated in terms of the crack-face displacement. The model developed is applied to the analysis of fibre multiple cracking in fibre-matrix laminate composites. It is also applied to the analysis of matrix cracking in fibre-matrix laminate composites. Numerical results have been given for the effects of crack spacing and constituent volume fraction on the crack tip field intensity factor and stress.

A multilayered thick cylindrical shell under internal pressure and thermal loads applicable to solid propellant rocket motors

A solid propellant rocket motor can be considered to be made of various circumferential layers of different properties. A simple procedure is described here to obtain an analytical solution for the general case of multilayered thick cyclindrical shell for internal pressure and thermal loads. This analytical procedure is useful in the preliminary design analysis of solid propellant rocket motors. Since solid propellant material is of viscoelastic behaviour an approximate viscoelastic solution methodology for the multilayered shell is described for estimation of time dependent solutions of propellant grain in a rocket motor. The analytical solution for a two layer reinforced thick cylindrical shell available in the literature is shown to be a special case of the present analytical solution. The results from the present analytical solution for multilayers is found to be in good agreement with FEA results.

Hardness measurements of Ti and TiC multilayers: a model

Microhardness measurements of thin films have to face the problem of the influence of the substrate on the measurement. Numerous models which take into account this behaviour are available in the literature. When the film is composed of several layers of different properties, it is more difficult to solve this problem because of the multiple influences of the different layers and the substrate. Little work on this subject has been already done; we propose here an extension to multilayers of two models: that of Jönsson and Hogmark, based on the relative deformed areas under the indent, and a model we have developed on the basis of plastically deformed volumes in the substrate and in the film. Starting from the hardness determination of Ti and TiC monolayer films, it is shown that it is possible to use either one or the other model to determine the composite superficial hardness of multilayer Ti–TiC films.

Macroscopic equations for vapor transport in a multi-layered unsaturated zone

Using the method of homogenization, we present a systematic derivation of the macroscopic equations for air flow and chemical vapor transport in an unsaturated zone with a periodic structure of heterogeneity. The effective specific discharge and hydrodynamic dispersion coefficient are expressible in terms of some cell functions, whose analytical solutions are sought for the simple case of alternate stacking of two strictly plane layers of different properties. For this kind of bi-layered composite, the effects of convection velocity and layer property contrasts on the longitudinal and transverse components of the hydrodynamic dispersion coefficient are investigated.

ANALYSIS OF A BILAYERED POROUS RADIANT BURNER

A theoretical study of the heating effectiveness of a composite porous radiant burner (PRB) is conducted. A one-dimensional laminar premixed flame model incorporating a radiatively participating inert porous medium consisting of two layers of different properties is used to describe the heat release/transfer processes. Combined conductive, convective, and radiative heat transfer is considered. The spherical harmonics method with the P-3 approximation is used to model the radiation part. A multistep reaction mechanism for premixed methane-air combustion is employed. A parametric study is carried out to determine the effect of the radiative properties of the two porous layers on burner performance. Calculations indicate that a significant improvement in the radiative output of a PRB can be attained by optimizing the burner properties upstream and downstream of the flame. Generally, the upstream layer should be of lower porosity, shorter length, and higher optical thickness than the downstream layer. Also, the upstream layer should be highly scattering, while the downstream layer should be nonscattering.

Dynamic response of a multi‐layered poroelastic medium

AbstractAn exact stiffness matrix method is presented to evaluate the dynamic response of a multi‐layered poroelastic medium due to time‐harmonic loads and fluid sources applied in the interior of the layered medium. The system under consideration consists of N layers of different properties and thickness overlying a homogeneous half‐plane or a rigid base. Fourier integral transform is used with respect to the x‐co‐ordinate and the formulation is presented in the frequency domain. Fourier transforms of average displacements of the solid matrix and pore pressure at layer interfaces are considered as the basic unknowns. Exact stiffness (impedance) matrices describing the relationship between generalized displacement and force vectors of a layer of finite thickness and a half‐plane are derived explicitly in the Fourier‐frequency space by using rigorous analytical solutions for Biot's elastodynamic theory for porous media. The global stiffness matrix and the force vector of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces. The numerical solution of the global equation system for discrete values of Fourier transform parameter together with the application of numerical quadrature to evaluate inverse Fourier transform integrals yield the solutions for poroelastic fields. Numerical results for displacements and stresses of a few layered systems and vertical impedance of a rigid strip bonded to layered poroelastic media are presented. The advantages of the present method when compared to existing approximate stiffness methods and other methods based on the determination of layer arbitrary coefficients are discussed.

Pressure Transient Testing of the Heterogeneous Reservoirs

Abstract Over the years, attempts have been made to include system heterogeneities into mathematical descriptions and to determine their effect on pressure response. In this study, a general case of a system with layers of non-uniform thicknesses is considered. The mathematical description is based on assuming radial flow within individual layers and pseudosteady-state cross flow between the adjacent layers. Since the angle of the interphasing plane may assume any angle between 0 and 90 degrees, layered (uniform thicknesses) and composite systems constitute the lim iting cases. The analytical solution is found in Laplace space and the numerical inversion to real space is obtained by using the Stehfest algorithm. The model is verified for several simpler subsystems and its sensitivity to reservoir parameters is investigated. Solutions are presented in a graphical form for a selected set of parameters. Based on this model a method of well test data analysis is proposed. Introduction Well testing is a valuable source of information on reservoir properties and well conditions. Test data are interpreted on the basis of pressure transient theory, which is deve1oped for various physical concepts of the reservoir flow conditions. In this study, modeling of complex reservoir systems is attempted in order to enhance the quality of the well test data analysis. It is well recognized that all petroleum reservoirs are heterogeneous to a certain degree. The heterogeneity manifests itself-in terms of variable rock and/or fluid properties, which occur due to either natural processes or human activities. Heterogeneities may be observed both in the radial and the vertical directions. Modelling of heterogeneous systems is usually approached by considering several subsystems each with properties lumped at some characteristic value. Such an approach has been used over the years and has given rise to the concepts of composite and the layered reservoir models. Literature Review In this section, only the key papers are mentioned. A complete review of the work done on the subject of multilayer pressure transient theory was published by Ehlig-Economides and Joseph(l) in 1985; the contributions made by individual authors are categorized according to the solution method, number of layers, existence of the formation crosstlow and types of the boundary conditions. The models describing the pressure response of layered reservoirs may be classified into two groups depending whether or not the interlayer flow is considered. One of the first descriptions of crossflow between two layers was introduced by Barrenblatt et al(2), who proposed the double porosity model for naturally fractured reservoirs. Such systems are featured by pressure imbalance between high diffusivity fractures and low diffusivity matrix blocks: the resultant fluid transfertends to equalize pressures in the two subsystems. Assuming the lump parameter concept, the flow between a matrix and a fracture is proportional to their pressure difference. This approach has been successfully used in simulating crossflow between layers of different properties.

Interfacial instability of density-stratified two-layer systems under initial stress

The onset of interfacial instability in two coherent semi-infinite layers of different properties and the corresponding critical wavelength are found by solving a static bifurcation problem in finite plane strain. Subsequently, the stability of perturbations of any wavelength is determined from the appropriate linearized equations of motion. For gravitationally stable or unstable density stratifications, the critical stress at which the interface is destabilized is shown to depend on the wavelength of a perturbation ; it is also determined in a complex manner by initial stress gradients perpendicular to the layer interface and by layer stiffness, as is illustrated here in detail for the examples of a hyperelastic solid and an elastoplastic solid, both resting on an inviscid fluid of different density. The very large wavelength that is predicted for the gravitational instability of a semi-infinite elastic solid on a buoyant fluid substratum brings forward the essential role of pre-stress and associated stiffness reduction as well as that of a finite layer thickness in destabilizing geological and geophysical two-layer systems.

Solute transport through layered soil profiles: Zero and perfect travel time correlation models

In this paper the problem of solute transport through layered soil is modeled with a transfer function, representing the travel time to any depth in the soil as the sum of the travel times through the individual layers. The probability density function (pdf) of this travel time depends on the joint pdfs of the travel times through the individual layers, and hence on the correlation structure as well as the layer properties. Analytic expressions are derived for the flux and resident concentrations in layered soil for two limiting cases of correlation structure, for both convective-dispersive and stochastic-convective model representations of transport within the individual layers. These models are contrasted to the layered convection-dispersion model, which asumes continuous resident fluid concentration at the interface. Calculated concentrations are used to illustrate features of the different models, as well as to suggest experiments that might deduce the appropriate boundary condition to use at the interface between layers of different properties. The physical significance of various boundary condition assumptions is also discussed.

Propagation of a compressional pulse in a layered solid

In this investigation we solve the problem of propagation of a compressional pulse in a solid half‐space which is overlain by a solid layer of different properties. The point source is situated at the depth ½H, H denoting the thickness of the layer. Theoretical seismograms of the vertical displacement w at the surface are evaluated out to ranges r = 20H. The solution is obtained by the exact ray theory. The displacement Wo due to the source was assumed to have a shape which at large distances reduces to a sawtooth. The once‐reflected waves from the interface, PP and PS, are strongly marked. The Rayleigh wave is already recognizable at r = 5H and is fully developed at r = 20H. The method of ‘ray theory’ was applied here far into the region where the normal mode theory converges well. The theoretical seismograms are illustrated. The properties assumed for the layer (1) and for the half‐space (2) are λ1 = μ1 μ2 = 2μ1cs2 ≡ c2 = 1.1cs1 ≡ 1.1c1cp2 > cp1 > c2 > c1