Advective trapping in the flow through composite heterogeneous porous media

We study the mechanisms of advective trapping in composite porous media that consist of circular inclusions of distributed permeability embedded in a high conductivity matrix. Advective trapping occurs when solute enters low velocity regions in the media. Transport is analyzed in terms of breakthrough curves measured at the outlet of the system. The curve's peak behavior depends on the volume fraction occupied by the inclusions, while the tail behavior depends on the distribution of permeability values. In order to quantify the observed behaviors we derive two equivalent upscaled transport models. First, we  derive a Lagrangian trapping model using the continuous time random walk framework that is parameterized in terms of volume fraction and the distribution of conductivites in the inclusions. Second, we establish a non-local partial differential equation for the mobile solute concentration by volume averaging of the microscale transport equation. We show the equivalence between the two models as well as (first-order) multirate mass transfer models. The upscaled approach, parameterized by medium and flow properties captures all features of the observed solute breakthrough curves, and sheds new light on the modeling of advective trapping in heterogeneous media.