Resumo em Inglês:

We are concerned here with the analysis and partition of uncertainty into component pieces, for a model prediction problem for flow in porous media.

Resumo em Inglês:

A numerical moment method (NMM) is applied to study groundwater flow and solute transport in a multiple-scale heterogeneous formation. The formation is composed of various materials and conductivity distribution within each material is heterogeneous. The distribution of materials in the study domain is characterized by an indicator function and the conductivity field within each material is assumed to be statistically stationary. Based on this assumption, a general expression is derived for the covariance function of the composite field in terms of the covariance of the indicator variables and the statistical properties of the composite materials. The NMM is used to investigate the effects of various uncertain parameters on flow and transport predictions in two case studies. It is shown from the study results that the two-scale stochastic processes of heterogeneity will both significantly influence the flow and transport predictions, especially for the variances of hydraulic head and solute fluxes. This study also shows that the NMM can be used to study flow and transport in complex subsurface environments. Therefore, the method may be applicable to complex environmental projects.

Resumo em Inglês:

This paper investigates the physics of two-phase, immiscible flow in stratified porous media. A review of previous studies reveals the major role played by the interaction of heterogeneity and viscous forces in the development of large-scale flow regimes. The stabilizing effects of gravity for flow in vertically layered porous media is introduced in a first order theoretical model and illustrated with the results of Monte Carlo simulations.

Resumo em Inglês:

Dissolution mechanisms in porous media may lead to unstable dissolution fronts (''wormholing''). It has been shown in the literature that Darcy-scale models may reproduce all the characteristics of such dissolution patterns. This paper considers the core-scale averaged behavior of these Darcy-scale dissolution models. The form of core-scale equations is discussed based on the volume averaging of the Darcy-scale equations. The uncertainty about the choice of the unit cell (and boundary conditions) to solve the closure problems and the impact of the dissolution history on the core-scale properties is emphasized.

Resumo em Inglês:

In this paper we consider homogenization of the diffusion, adsorption and convection of chemical species in porous media, that are transported by unsaturated single phase flows. The unsaturated flow is described by the Richards' equation. We present in details a rigorous derivation of the corresponding dual porosity model. Then we give the derivation by homogenization of first-order kinetic models for the evolution of the chemical species. Finally, numerical simulations for the Freundlich and Langmuir isotherms are presented.

Resumo em Inglês:

In this paper we consider upscaling of multiphase flow in porous media. We propose numerical techniques for upscaling of pressure and saturation equations. Extensions and applications of these approaches are considered in this paper. Numerical examples are presented.

Resumo em Inglês:

Today, the focus of physical scientists is shifting more to biology than ever before. A biological tissue is typically an ionised porous medium saturated with a solution of ions and neutral solutes. Because classical porous media theories do not account for ionisation, the present paper addresses this issue. The characteristic pore size in most biological applications is close to the molecular level and hence below the Debye-Hueckel scale. Not only pressure gradients and concentration gradients, but electrical gradients as well are intimately linked to fluid flow, ion flow and deformation.

Resumo em Inglês:

A pore scale population balance model is formulated for deep bed filtration of stable particulate suspensions in porous media. The particle capture from the suspension by the rock occurs by the size exclusion mechanism. The equations for particle and pore size distributions have been derived from the stochastic Master equation. The model proposed is a generalization of stochastic Sharma-Yortsos equations – it accounts for particle flux reduction due to restriction for large particles to move via small pores. Analytical solution for low particle concentration is obtained for any particle and pore size distributions. The averaged macro scale equations, derived from the stochastic pore scale model, significantly differ from the traditional deep bed filtration model.

Resumo em Inglês:

The prediction of the reversible evolution of macroscopic magnetostriction strain and magnetisation in ferromagnetic materials is still an open issue. Progress has been recently made in the description of the magneto-elastic behaviour of single crystals. Herein, we propose to extend this procedure to the prediction of the behaviour of textured soft magnetic polycrystals. This extension implies a magneto-mechanical homogenisation. The model proposed is discussed and the results are compared to experimental data obtained on industrial iron-silicon alloys.

Resumo em Inglês:

In this article, we numerically determine the effective stress-strain relation of some two-dimensional polycrystals. These are aggregates of a few tens of perfectly bonded single-crystal (hexagonal atomic lattice) grains, with varying orientations. Each grain obeys a given nonlinear viscoplastic stress-strain relation, which depends on the orientation of the grain. Precise calculations performed with this microscopic model are compared with calculations done with a macroscopic approximate model (in which matter has no microstructure) in order to determine the macroscopic constitutive law. We find an effective behaviour for the stationary response which appears to be also consistent for the transient response. The influence of the number of grains as well as that of the distribution of grain orientations are investigated.

Resumo em Inglês:

This paper deals with a finite strain continuum theory of elastic-brittle solids with microstructure. A single scalar microstructural field is introduced, meant to represent - even if in a summary way - the concentration of microdefects within the material. A system of microforces, dual to the microstructural field, is axiomatically introduced. The corresponding balance, augmented with suitable constitutive information, yields, inter alia, a kinetic equation for the microstructural field, criteria for damage nucleation, growth and healing as well as a failure criterion based on attainment of a critical value of the microstructural field. The theory is applied for the description of the Mullins effect.

Resumo em Inglês:

We introduce a framework for modeling elastic properties of shape memory alloy polycrystals by coupling orientational degrees of freedom with elastic strains. Our method allows us to span the length scales from single crystal to that appropriate to obtain polycrystal properties. The single crystal free energy coefficients can be determined from microscopic calculations (such as electronic structure and molecular dynamics) and/or available experimental structural, phonon and thermodynamic data. We simulate the microstructure and determine the stress-strain response of the polycrystal and compare it with that of a single crystal. For FePd parameters we find that the recoverable strain for a polycrystal is ~ 40% of that for a single crystal. The polycrystal information can, in principle, serve as input to the engineering scale of calculation, where the finite element method is appropriate.

Resumo em Inglês:

In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.

Resumo em Inglês:

This paper deals with the derivation of a macroscopic model for columnar dendritic solidification of binary mixtures using the volume averaging method with closure. The main originalities of the model are first related to the explicit description of evolving heterogeneities of the dendritic structures and their consequences on the derivation of averaged conservation equations, where additional terms involving porosity gradients are present, and on the determination of effective transport properties. These average properties are defined by the associated closure problems taking into account the geometry of the dendrites and the local intensity of the flow. The macroscopic solute transport is obtained by considering macroscale non-equilibrium giving rise to macroscopic dispersion and interfacial exchange phenomena. Mass exchange coefficients are accurately explicited as a function of the local geometry.

Resumo em Inglês:

In this paper we consider the modeling of heterogeneous aerosol coagulation where the heterogeneous aerosol particles (called droplets) contain smaller particles (enclosures). Droplets and enclosures coagulate with different collision kernels. We discuss macroscopic modeling and simulation of these processes using both deterministic and Monte-Carlo methods.