The aim of this dissertation is to establish a framework to describe multi-scale transport through porous media. Transport of mass and momentum in porous media can be studied at two different scales: the macro-scale (averaged-, continuum-or Darcy-scale) and the micro-scale (pore-scale). Particularly challenging from the modeling perspective are coupled systems (e.g. channel-matrix systems) and/or inherently unstable phenomena (e.g. multiphase transport). The former require multiscale approaches since the quantities of interest on one scale (e.g. macro-scale) may depend on the properties or physics at another scale (e.g. micro-scale). The latter challenge the very basic concept of system reproducibility as well as the perturbative approaches on which upscaling methods are generally based upon.

The first part of this dissertation focuses on multi-scale mass transport in a two-dimensional channel embedded between two porous surfaces. By means of perturbation theory and asymptotic analysis, we first derive the set of upscaled equations describing mass transport in the coupled channel-matrix system and an analytical expression relating the macro-scale dispersion coefficient with the surface properties, namely porosity and permeability. Our analysis shows that their impact on dispersion coefficient strongly depends on the magnitude of Peclet number, i.e., on the interplay between diffusive and advective mass transport. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transversal mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Peclet number. Then, we compare the upscaled model against experiments conducted on microchannels with surfaces patterned with different topologies. The experimental data are in agreement with the developed theory and quantitatively confirm the impact of the matrix geometry on tranverse dispersion at different Peclet numbers.

The second part of this dissertation focuses on experimentally quantifying and improving the reproducibility of pore-scale multiphase flow experiments. The unstable nature of multiphase flows in porous media questions the basic concepts of both reproducibility and experimental benchmarking for numerical codes' validation and calibration. Subpore-scale heterogeneity and temporal fluctuations of experimental equipment can strongly control two-phase flow displacement data. We experimentally demonstrate that the introduction of spatial heterogeneity in pore-scale microfluidic models improves the reproducibility of multiphase flow experiments, and variability in fluid displacement between different realizations of the same experimental pore structure can be numerically captured by stochastic numerical simulations. The latter appears to be a more appropriate framework to describe unstable pore-scale displacement in multiphase transport.