Abstract
First order asymptotic homogenization allows to determine the effective behaviour of a porous medium by starting from the pore scale description, when there is a large separation between the pore scale and the macroscopic scale. When the scale ratio is â ˘ AIJsmall but not too small,â ˘ A ˙ I additional terms need to be taken into account, which can be obtained by exploiting higher order equations in the asymptotic homogenization procedure. The aim of the present study is to derive second order models to describe solute transport in a macroscopically homogeneous porous medium at low scale separation. The three following macroscopic transport regimes are successively considered: pure diffusion with fluid at rest, predominant diffusion with fluid in motion and advection-diffusion. The results show that while the transport regime remains of diffusive type when the fluid is at rest, low scale separation induces modification of apparent transport regime when fluid is in motion. Indeed, predominant diffusion and advection-diffusion lead to the apparent regimes of advection-diffusion and of dispersion, respectively.