Reactive Transport with Fluid–Solid Interactions in Dual-Porosity Media

Abstract

We study pore-scale dynamics of reactive transport in heterogeneous, dual-porosity media, wherein a reactant in the invading fluid interacts chemically with the surface of the permeable grains, leading to the irreversible reaction $A_{aq} + B_{s} \rightarrow C_{aq}$. A microfluidic porous medium was synthesized, consisting of a single layer of hydrogel pillars (grains), chemically modified to contain immobilized enzymes on the grain surfaces. Fluorescence microscopy was used to monitor the spatiotemporal evolution of the reaction product $C_{aq}$ at different flow rates (P\'eclet values), and to characterize the impact on its transport. The experimental set-up enables delineation of three key features of the temporal evolution of the reaction product within the domain: (\textit{i}) the characteristic time until the rate of $C_{aq}$ production reaches steady state, (\textit{ii}) the magnitude of the reaction rate at steady state, and (\textit{iii}) the rate at which $C_{aq}$ is flushed from the system. These features, individually, are found to be sensitive to the value of the P\'eclet number, because of the relative impact of diffusion (versus advection) on the production and spatiotemporal evolution of $C_{aq}$ within the system. As the P\'eclet number increases, the production of $C_{aq}$ is reduced and the transport becomes more localized within the vicinity of the grains. The dual-porosity feature causes the residence time of the transported species to increase --- by forming stagnant zones and diffusive-dominant regions within the flow field --- thus enhancing the reaction-potential of the system. Using complementary numerical simulations, we explore these effects for a wider range of P\'eclet and Damk{\"o}hler numbers, and propose non-linear scaling laws for the key features of the temporal evolution of $C_{aq}$.