Time analysis of the three characteristic behaviours of dual-porosity media. I: fluid flow and solute transport

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.