  Advective trapping occurs when solute enters low velocity zones in
heterogeneous porous media. Classical local modeling approaches combine the
impact of slow advection and diffusion into a hydrodynamic dispersion
coefficient and many temporally non-local approaches lump these mechanisms into
a single memory function. This joint treatment makes parameterization difficult
and thus prediction of large scale transport a challenge. Here we investigate
the mechanisms of advective trapping and their impact on transport in media
composed of a high conductivity background and isolated low permeability
inclusions. Breakthrough curves show that effective transport changes from a
streamtube-like behavior to genuine random trapping as the degree of disorder
of the inclusion arrangement increases. We upscale this behavior using a
Lagrangian view point, in which idealized solute particles transition over a
fixed distance at random advection times combined with Poissonian advective
trapping events. We discuss the mathematical formulation of the upscaled model
in the continuous time random walk and mobile-immobile mass transfer
frameworks, and derive a model for large scale solute non-Fickian dispersion.
These findings give new insight into transport in highly heterogeneous media.
