In heterogeneous media, flow and transport usually take place in preferential flow channels. Thus, it is of prime interest to take the associated physical processes into account. However, we are limited by current technology and cannot compute the transport of solute at the field scale using the equations of hydrodynamic. Thus, in order to describe solute transport at the field scale, upscaling is required. In this thesis, we study at the scale of the channels the impact of two effects usually neglected. (i) The first effect occurs when a sufficiently concentrated solute is diluted so that the density of the fluid increase significantly. As the density gradient of the solute plume locally modifies the flow field, the solute transport is impacted. In a horizontal smooth channel, the pre-asymptotic regime of dispersion is impacted and the plume is delayed. (ii) Second, when flow is fast enough (or fluid viscosity low enough), inertial effects can dramatically alter the flow field. We study their impact in channels with periodically varying apertures. When the inertial effects increase, recirculation zones grow at the location of the maximum aperture. Solute can then enter by diffusion into these zones and be trapped for a significant duration. (iii) Finally, the coupling of the effects (i) and (ii) is addressed. We reproduce numerically each effect at the hydrodynamic scale and characterize their impact as a function of the Reynolds number, the Péclet number and a dimensionless number that quantify the impact of the density gradients.
