Transport under advective trapping

Advective trapping occurs when solute enters low velocity zones in heterogeneous porous media. Classical local modelling 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 behaviour to genuine random trapping as the degree of disorder of the inclusion arrangement increases. We upscale this behaviour 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. ; Data used for producing the figures can be downloaded from digital.csic.es (https://digital.csic.es/handle/10261/216991) and by solving the respective equations. The authors thank Professor T.R. Ginn and two anonymous reviewers for their comments on the paper. J.J.H. and M.D. acknowledge the support of the Spanish Ministry of Science and Innovation (project CEX2018-000794-S and project HydroPore PID2019-106887GB-C31). J.J.H. acknowledges the support of the European Social Fund and Spanish Ministry of Ministry of Science, Innovation and Universities through the ‘Ramón y Cajal’ fellowship (RYC-2017-22300). The authors thank P. Uszes for providing the code to measure the average distance between inclusions. ; Peer reviewed