Flow of low pressure gas through dual-porosity media

Using the theory of homogenization we derive macroscopic models for describing flow of gas at low pressure in dual-porosity media. The case of a fractured porous medium is under consideration for the study, and the existence of a representative elementary volume that consists of open connected fractures surrounded by porous matrix blocks is assumed. The local flow is governed by either Klinkenberg's law or Knudsen's diffusion law in the matrix while either a non-slip flow or a slip flow occurs in the fractures. Six new models are derived by homogenization, which are compared to the three models which were obtained for Darcy's regime in an earlier work. Each of these nine models is characterized by its macroscopic flow regime and by the type of macroscopic behavior it describes. Besides Darcy's and Klinkenberg's macroscopic flow regimes, a transition regime between Klinkenberg's and Knudsen's regimes is identified. The types of macroscopic behaviors include a dual and a single porosity description and an intermediate behavior that describes a single-porosity behavior, but in which the porosity of the entire fractured porous medium is accounted for

Dynamic behaviour of porous media saturated by a viscoelastic fluid. Application to bituminous concretes

International audienceThis paper deals with the acoustics of porous media saturated by an incompressible viscous or viscoelastic fluid. By using the homogenization method for periodic structures, we determine the macroscopically equivalent medium. We show that the heterogeneous material displays three types of behaviour: biphasic, elastic, viscoelastic, according to the contrast of the mechanical properties of the constituants. This contrast is measured by the small parameter ε, ratio of the dimension of the pores to the macroscopic wave length. Therefore the macroscopic behaviour depends also on the excitation. The calculations of the effective macroscopic coefficients are performed for a one-dimensional geometry. The results applied to a porous media saturated by an Newtonian fluid show that the type of behaviour changes with the frequency. We treat the case of a saturation by a viscoelastic fluid by considering bituminous concretes. We investigate how this material behaves according to the temperature and the excitation frequency. The applicability of a time-temperature equivalency is studied and a comparison between experimental results and the 1D model is presented

Deformable porous media with double porosity. Quasi-statics. I: Coupling effects

International audienceWe investigate the macroscopic quasi-static description of a deformable porous medium with a double porosity constituted by pores and fractures. For this purpose, we use an homogenization technique which gives the macroscopic modelling from the description at the pore and fracture levels. It appears that the macroscopic description is sensitive to the ratios between the different scales, l/l′ and l′/l″, wherel, l′ l″ are characteristic lengths of the pores, the fractures and the macroscopic medium, respectively. In the first paper we investigate the case l′/l″=(l/l′)^2, which exhibits a coupling between the flows through the pores and the fractures. The macroscopic description is shown to depend on a single pressure field and exhibits a broken symmetry. Other situations will be examined in a subsequent paper. Large spectra of pore and fracture sizes are also evoked

Deformable porous media with double porosity, quasi-statics. II: Memory effects

International audienceAs in our previous paper, we investigate the macroscopic quasi-static description of a porous medium with a double porosity constituted by pores and fractures. For this purpose, we use a homogenization technique. As expected, the macroscopic description is sensitive to the ratios between the different scales,l/l′ andl/l′ wherel, l′, l″ are characteristic lengths of the pores, the fractures, and the macroscopic medium, respectively. In the first paper, we investigated the case l′/l″=O(l^2/l′^2)≪1 (case 1) which exhibits a coupling between the flows through the pores and the fractures. In the present paper, we deal with the other homogenizable cases. The case 3 where l/l′=O(l′^2/l″^2)≪1 gives a macroscopic description similar to that of a single porosity medium. The main result, however, is the case 2, where l/l′=O(l′/l″)≪1, which exhibits memory effects. These are due to the seepage through the micropores

Deformable porous media with double porosity III: Acoustics

International audienceWe investigate the acoustics of saturated porous media with a double porosity constituted by pores and fractures. This work is the direct extension of earlier papers by Auriault and Boutin, where the quasi-static behaviour was studied. The different macroscopic descriptions of the acoustics are shown to be the quasi-static ones, completed by classical inertial terms and with a generalized seepage law for the fractures. Therefore, when the three scales, i.e. the pore, the fracture and the macroscopic scales are equally separated, the medium exhibits memory effects. Finally, we investigate the interpretation of laboratory experiments on single porosity medium under an acoustic excitation. It is shown that the viscoelastic effects which are observed when the frequency is about a few kHz have their origins in the same phenomenon. But the macroscopic description now depends on the size and the shape of the sample, and therefore it is nonspecific for the porous medium

Rayleigh scattering in elastic composite materials

International audienceThis paper is devoted to long wave propagation in heterogeneous media. More specifically, we deal with Rayleigh diffraction in elastic materials with a periodic microstructure whose heterogeneities are in finite concentration or show great contrasts in properties. This study is based on the homogenization method but contrary to the usual procedure in which only the first significant terms are used, the developments are established up to the third order. We demonstrate that the terms of a superior order successively introduce effects of polarization, of celerity dispersion and of attenuation and we thus bring to the fore a characteristic distance of mode conversion. Finally we demonstrate that the effect of dispersion alone appears in macroscopically isotropic materials

Waves in thermoelastic materials

International audienc

Acoustic and heat waves in Fourier thermoelastic materials

International audienc

Inner thermal resonance in thermoelastic geological structures

International audienceWhen investigating heterogeneous media such as composite materials or geological structures, it is convenient to replace them by macroscopic equivalent media, which simplifies computations a lot. In the paper, we look for the equivalent macroscopic model for describing seismic wave propagation and transient heat transfers in thermoelastic periodic geological structures made of rock or soil. We follow the route described in Auriault (2012), to investigating thermoelastic composite media. We use the method of multi-scale asymptotic expansions. By estimating the dimensionless numbers in the momentum and energy balances, we show that an equivalent macroscopic model exists for describing seismic waves at very low frequencies only. The model then shows a damping which is due to thermal resonance at the heterogeneity scale. At higher frequencies, such an equivalent macroscopic model does not exist. Macroscopic models for describing transient heat transfers do not exist