Transport under advective trapping

TL;DR

This paper investigates advective trapping in heterogeneous porous media, revealing how low permeability zones influence large-scale solute transport and proposing a new upscaled model for non-Fickian dispersion.

Contribution

It introduces a novel Lagrangian-based upscaled model that captures advective trapping effects in heterogeneous media, improving prediction of solute transport.

Findings

Transport behavior shifts from streamtube-like to random trapping with increased disorder.

Upscaled model based on continuous time random walk effectively describes non-Fickian dispersion.

Mathematical formulation links trapping mechanisms to large-scale transport predictions.

Abstract

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.