Résumé
Upscaling transport in porous media from the pore- to the Darcy scale is a challenge. Transport often displays non-Fickian behaviors due to porescale heterogeneity that can cause a wide range of solute transition times due to advective heterogeneity and samll scale diffusion. To understand these mechanisms, we run particle tracking simulations on digitized rocks in order to investigate transport properties through a wide range of Peclet regimes. At infinite Peclet, transport is anomalous and the breakthrough curves (BTC) exhibit early peaks and large tailings. This is partly due to Lagrangian intermittency: particles spend large times in low velocity zones but travel rapidly in high velocity zones. This is a result of the fact that porescale velocities vary on a characteristic length scale. We use a 1D Continuous Time Random Walk (CTRW) based on a spatial Markov process for the prediction of particle velocities. This velocity process relies on a relaxation scheme that forces the velocity to decorrelate on a spatial scale related to the mean pore length of the sample. The transport behavior changes in the presence of diffusion. BTCs exhibit new features such as earlier arrivals, delayed peaks, intermediate time retention, and a large time cutoff. Those are linked to three mechanisms contained in the diffusion process. The perpendicular-to-the-flow diffusive motion enforces particles to jump from a pathline to another, and thus modifies the spatial and temporal velocity series. The parallel-to-the-flow diffusive motion shortens or lengthens the duration of spatial transitions. Finally, particles may jump diffusively into very low velocity zones in the wake of grains causing long retention times (trapping). To upscale these behaviors, we use a 1D CTRW model coupling an advective velocity change (occurring at constant spatial rate) and a diffusive velocity change (occurring at constant temporal rate). The model reproduces the results of direct numerical simulations for a wide range of Peclet regimes.