Anomalous dispersion in chemically heterogeneous media induced by long-range disorder correlation

We study transport in an idealized porous medium characterized by a spatially varying retardation factor, which models linear instantaneous chemical adsorption of a solute. Using a stochastic modelling approach, we study the impact of disorder correlation on the large-scale dispersion behaviour. We consider short, long-range and intermediate-range disorder correlations, and demonstrate that (truncated) power-law correlation causes anomalous dispersion, even in the presence of weak heterogeneity. We identify different preasymptotic and asymptotic regimes of anomalous dispersion that shed new light on the disorder and local-scale transport mechanisms leading to non-Fickian behaviour. The analytical results are complemented by numerical random walk particle tracking simulations, which are found to be in good agreement with the derived dispersion behaviour. We conclude the paper by deriving an effective transport equation for this system, which can be shown to be tied to the family of continuous-time random walk models.