Mixing and dispersion upscaling from a 2D pore scale characterization of Lagrangian velocities

Mixing and reactive transport are primarily controlled by the interplay between diffusion, advection and reaction at the pore scale. Yet, how heterogeneity of the pore scale velocity field impacts these processes is still an open question. Here we present an experimental investigation of the distribution and correlations in pore scale velocities and their relation to upscaled dispersion and mixing, for different pore geometries. We use a quasi two-dimensional (2D) horizontal set up, consisting of two glass plates filled with cylinders representing the grains of the porous medium : the cell is built using soft lithography, which allows for full control of the system geometry. The local velocity field is quantified from particle tracking velocimetry using microsphere solid tracers. Their displacement is purely advective, as the particle size is chosen sufficiently large so as to neglect diffusion. We thus obtain particle trajectories and lagrangian velocities in the entire system. The experimental results are compared with and validated by finite element numerical simulations performed with comsol. The measured velocity fields show the existence of a network of preferential flow paths in channels with high velocities, as well as very low velocity in stagnation zones, with a non Gaussian probability density function of the velocities. Lagrangian velocities are long range correlated in time, which implies a non-fickian scaling of the longitudinal variance of particle positions. The analysis of Lagrangian velocities is used to upscale both dispersion and mixing. The predictions of these upscaled models, parameterized by the velocity field properties, are compared to conservative tracer tests data, performed in the same porous media.