Evolutive Models for the Geometry and Heat Conductivity of an Intumescent EVA-ATH Composite during Its Thermal Degradation.

Reliable predictions from numerical simulations in fire safety applications require knowledge of the combustible materials' properties in their initial and thermally degraded states. The thermal conductivity of the sheath material of electrical cables, present in massive amounts in industrial plants, is addressed here. An evolutive conceptual model is proposed for the morphology of this intumescent polymer composite during its thermal degradation.

Propagation of acoustic waves through saturated porous media.

The homogenization approach to wave propagation through saturated porous media is extended in order to include the compressibility of the interstitial fluid and the existence of several connected pore components which may or not percolate. The necessary theoretical developments are summarized and the Christoffel equation whose solutions provide the wave velocities is presented. Some analytical developments are proposed for isotropic media.

Thermal convection in three-dimensional fractured porous media.

Thermal convection is numerically computed in three-dimensional (3D) fluid saturated isotropically fractured porous media. Fractures are randomly inserted as two-dimensional (2D) convex polygons. Flow is governed by Darcy's 2D and 3D laws in the fractures and in the porous medium, respectively; exchanges take place between these two structures.

Percolation in three-dimensional fracture networks for arbitrary size and shape distributions.

The percolation threshold of fracture networks is investigated by extensive direct numerical simulations. The fractures are randomly located and oriented in three-dimensional space. A very wide range of regular, irregular, and random fracture shapes is considered, in monodisperse or polydisperse networks containing fractures with different shapes and/or sizes.

Transport properties of a Bentheim sandstone under deformation.

The mechanical and transport properties of a Bentheim sandstone are studied both experimentally and numerically. Three classical classes of loads are applied to a sample whose permeability is measured. The elasticity and the Stokes equations are discretized on unstructured tetrahedral meshes which precisely follow the deformations of the sample.

Solid matrix partition by fracture networks.

The geometrical properties of the matrix blocks formed by a random fracture network are investigated numerically, for a wide range of fracture shapes and for fracture densities ranging from the dilute limit to well above the threshold where the material is entirely partitioned into finite blocks. The main block characteristics are the density and volume fraction, the mean volume and surface area, and their number of faces. In the dilute limit, general expressions for these characteristics are obtained, which provide a good approximation of the numerical data for any fracture shape.

Interaction between a fracture network and a cubic cavity.

The intersection between a network of polygonal fractures and a cubic cavity is numerically studied. Several probabilities are defined and particular attention is paid to the probabilities of intersection or not of the percolating cluster with the cavity; they depend on the size of the domain, on the fracture density, and on the relative size of the fractures and of the cavity. These probabilities are extrapolated to infinite domains.

Percolation and permeability of fracture networks in excavated damaged zones.

Generally, the excavation process of a gallery generates fractures in its immediate vicinity. The corresponding zone which is called the excavated damaged zone (EDZ), has a larger permeability than the intact surrounding medium. Therefore, some of its properties are of crucial importance for applications such as the storage of nuclear wastes.

Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities.

The asymptotic behaviors of the permeability of isotropic fracture networks at small and large densities are characterized, and a general heuristic formula is obtained which complies with the limiting behaviors and accurately predicts the permeability of these networks over the whole density range. Theses developments are based on extensive numerical calculations and on theoretical arguments inspired by the examination of the flow distribution in the fractures at large densities. Then, the results are extended to anisotropic networks with a Fisher distribution of the fracture orientations, to polydisperse networks, and to fractured porous media.

Trace analysis for fracture networks with anisotropic orientations and heterogeneous distributions.

Since only intersections with lines or planes are usually available to quantify the properties of real fracture networks, a stereological analysis of these intersections is a crucial issue. This article-the second of a series-is devoted to the derivation of the direct relations between the properties and the observable quantities. First, this derivation is achieved for anisotropic networks whose orientations obey a Fisher probability distribution function; second, it is extended to networks which are heterogeneous in space, i.

Transport properties of real metallic foams.

Three dimensional samples of three different foams are obtained by microtomography. The macroscopic conductivity and permeability of these foams are calculated by three different numerical techniques based on either a finite volume discretization or Lattice Boltzmann algorithm. Permeability is also measured and an excellent agreement is obtained between the various estimations.

Random packings of spiky particles: geometry and transport properties.

Spiky particles are constructed by superposing spheres and oblate ellipsoids. The resulting star particles (but nonconvex) are randomly packed by a sequential algorithm. The geometry, the conductivity, and the permeability of the resulting packings are systematically studied.

Percolation and permeability of networks of heterogeneous fractures.

Networks composed by heterogeneous fractures whose local permeability is a binary correlated random field are generated. The percolation and permeability properties of a single heterogeneous fracture are strongly influenced by finite size effects when the correlation length is of the order of the fracture size. For fracture networks, a mean-field approximation is derived which approximates well the macroscopic permeability while an empirical formula is proposed for the percolation properties.

Geometrical and transport properties of random packings of polydisperse spheres.

Loose packings of spheres with bidisperse or log-normal distributions are generated by random sequential deposition. Porosity, conductivity, and permeability are determined. The porosities correspond to loose packings, but they follow the usual trends for bidisperse packings.

Wave propagation through saturated porous media.

The homogenization procedure is applied to the problem of wave propagation in the biphasic mode in porous media saturated with a Newtonian fluid. The local problems corresponding to the solid and fluid phases have been solved separately for complex three-dimensional media. The effective rigidity tensor, some effective coefficients, the dynamic permeability, the celerities, and the attenuation of the three waves are systematically determined.

Effective permeability of fractured porous media with power-law distribution of fracture sizes.

The permeability of geological formations which contain fractures with a power-law size distribution is addressed numerically by solving the coupled Darcy equations in the fractures and in the surrounding porous medium. Two reduced parameters are introduced which allow for a unified description over a very wide range of the fracture characteristics, including their shape, density, size distribution, and possibly size-dependent permeability. Two general models are proposed for loose and dense fracture networks, and they provide a good representation of the numerical data throughout the investigated parameter range.

Percolation of three-dimensional fracture networks with power-law size distribution.

The influence of various parameters such as the domain size, the exponent of the power law, the smallest radius, and the fracture shape on the percolation threshold of fracture networks has been numerically studied. For large domains, the adequate percolation parameter is the dimensionless fracture density normalized by the product of the third moment of fracture radii distribution and of the shape factor; for networks of regular polygons, the dimensionless critical density depends only slightly on the parameters of radii distribution and on the shape of fractures; a model is proposed for the percolation threshold for fractures with elongated shapes. In small domains, percolation is analyzed in terms of the dimensionless fracture density normalized by the sum of two reduced moments of the radii distribution; this provides a general description of the network connectivity properties whatever the dominating percolation mechanism; the fracture shape is taken into account by using excluded volume in the definition of dimensionless fracture density.

Macroscopic permeability of three-dimensional fracture networks with power-law size distribution.

Fracture network permeability is investigated numerically by using a three-dimensional model of plane polygons uniformly distributed in space with sizes following a power-law distribution. Each network is triangulated via an advancing front technique, and the flow equations are solved in order to obtain detailed pressure and velocity fields. The macroscopic permeability is determined on a scale which significantly exceeds the size of the largest fractures.

Two-phase flow through fractured porous media.

Two-phase flow in fractured porous media is investigated by means of a direct and complete numerical solution of the generalized Darcy equations in a three-dimensional discrete fracture description. The numerical model applies to arbitrary fracture network geometry, and to arbitrary distributions of permeabilities in the porous matrix and in the fractures. It is used here in order to obtain the steady-state macroscopic relative permeabilities of random fractured media.