Time Analysis of the Three Characteristic Behaviours of Dual-Porosity Media. I: Fluid Flow and Solute Transport

Abstract

Homogenisation of consolidation and compressible fluid flow in dual-porosity media has highlighted the existence of three characteristic macroscopic behaviours. These three behaviours are, namely, a dual-porosity description which includes memory effects, a single-porosity description with which the micro-porosity is simply ignored, and an intermediate behaviour which we refer as behaviour with reservoir effect. With this latter, the whole dual-porosity medium is represented by an equivalent single-porosity medium. In contrast with a single-porosity behaviour, the porosity of the entire dual-porosity medium is accounted for. During solute transport in dual-porosity media, while memory effects are most often experimentally observed, the homogenised model obtained for the most general values of the involved parameters leads to a model with reservoir effect. Therefore, the observed memory effects are not reproduced by this model and a clear interpretation of the origins of these effects remains an unresolved issue. The work is presented in two complementary articles. The objective of the present paper is, firstly, to determine a physical interpretation of the existence of the three characteristic behaviours of dual-porosity media. This is performed by exploring the homogenised models and their domains of validity for the analogy of heat conduction in a dual-conductivity composite. This leads to the original result that consists to relate each type of behaviour to a specific relationship between two characteristic times. This is then used for interpreting the results obtained for compressible flow in dual-porosity media. Finally, it allows to elucidate the conditions under which memory effects may occur during solute transport in dual-porosity media.

On the quasi-static effective behaviour of poroelastic media containing elastic inclusions

“…While sometimes qualified as a multiporous medium and although three distinct scales are actually involved, this composite is distinct from a double porosity microstructure (e.g. Auriault and Royer (1993), Royer and Boutin (2012), Boutin and Royer (2015)), as the distribution of the inclusions does not play the role of a porous network. Indeed, the impact of inclusions on fluid flow transfer is characterised by a purely geometrical parameter, with no reference to their fluid conductivity.…”

Numerization of a memory effect for an homogenized composite material with a large contrast in the phase thermal conductivities

“…This case is usefully interpreted with characteristic times [9,13] since the characteristic macroscopic time is expected to be s M ¼ ðC M =k M ÞðL=pÞ 2 (if C M and k M are the homogenized total thermal capacity and conductivity), while their counterparts for the microscopic S and F phases are s S ¼ ðq S c S =k S Þðl S =pÞ 2 and…”

“…Other diffusion-involved physics are also under concern: for instance the porous media flows [9] that may exhibit such delayed effects at several scales, for double permeability media, to be taken into account for contaminant dispersion in soils or for their cleaning with soil vapor extraction [28], or for oil recovery [29], the blood perfusion in biological tissues or the compact bone porous media [30].…”

“…The delayed effect is therefore directly provided by the homogenization procedure [6][7][8][9]. We proposed to study a thermal problem for illustration purpose, though the same framework also applies to different physics [10].…”

A Strategy for Solving the Non Symmetries Arising in Nonlinear Consolidation of Partially Saturated Soils

“…In the former, a horizontal multilayered soil with anisotropic permeability undergoing square load was analyzed whilst in the later a first order homogenization on RVE was adopted to overcome the heterogeneous issue. In [20], the physical interpretation of the three characteristic behaviors of homogenized dual-porosity is evaluated along with memory effects.…”