Reactive Transport in Heterogeneous Porous Media Under Different Péclet Numbers

We study the synergistic effects of the Péclet number and the length scale of medium heterogeneity on the evolution of bimolecular reactive transport between mobile and immobile species. We performed a suite of numerical simulations at the Darcy scale that quantify the instantaneous, irreversible bimolecular reaction A_aq+B_s→C_aq, under various transport conditions (Péclet numbers) and porous media configurations (correlation lengths). We find that the global reaction rate is sensitive to both the Péclet number and the correlation length. The total amount of product decreases with increasing Péclet number, while it increases with increasing correlation length. In addition, for all of these scenarios, the global reaction rate is shown to be time dependent and is an outcome of the anomalous transport behavior of the chemical species. The time-dependent behavior of the reaction rate is amplified with increasing Péclet number and decreasing correlation length and can be well approximated by a power law relationship. We find, too, that the transport behavior of the reaction products (C) often deviates from that of the inflowing reactant species (A), because reactions occur preferentially within the flow domain. Finally, and due to the influence of the Péclet number on reactive transport, we show that temporal variations in the magnitude of the flow field (i.e, changing the Péclet number over time) shift the reaction and transport behavior into a state measurably different than that for steady flow conditions.