Solute diffusion in fractured porous media with memory effects due to adsorption

Modelling of solute transport in fractured porous media is a subject of intensive research in many engineering disciplines, such as petroleum engineering, water resources management, civil engineering. Recent field and laboratory experiments show that, in presence of strong adsorption, the behaviour of solute penetrating into the fractured porous medium diverges from classical hypotheses, rendering impossible the adjustment of classical transport models. The aim of this paper is to develop a mathematical continuous model of solute transport, when strong adsorption of solute occurs on the grains of the porous matrix. The macroscopic model is obtained by upscaling the pore and the fracture behaviours, by using the multiple scale expansion method. We obtain a non-standard diffusion behaviour of solute which shows local non-equilibrium between transport in the fractures and in the porous matrix, as well as memory effects. To cite this article: J. Lewandowska et al., C. R. Mecanique 330 (2002) 879–884.