Phase Saturation Control on Mixing-Driven Reactions in 3D Porous Media

Abstract

Transported chemical reactions in unsaturated porous media are relevant to environmental and industrial applications. Continuum scale models are based on equivalent parameters derived from analogy with saturated conditions and cannot appropriately account for incomplete mixing. It is also unclear how the third dimension controls mixing and reactions. We obtain three-dimensional (3D) images by magnetic resonance imaging using an immiscible nonwetting liquid as a second phase and a fast irreversible bimolecular reaction. We study the impact of phase saturation on the dynamics of mixing and the reaction front. We quantify the temporally resolved effective reaction rate and describe it using the lamellar theory of mixing, which explains faster than Fickian (t 0.5 ) rate of product formation by accounting for the deformation of the mixing interface between the two reacting fluids. For a given Pećlet, although stretching and folding of the reactive front enhance as saturation decreases, enhancing the product formation, the product formation is larger as saturation increases. After breakthrough, the extinction of the reaction takes longer as saturation decreases because of the larger nonmixed volume behind the front. These results are the basis for a general model to better predict reactive transport in unsaturated porous media not achievable by the current continuum paradigm.

Mixing Controlled Adsorption at the Liquid-Solid Interfaces in Unsaturated Porous Media

“…Similar air cluster size distributions (Iglauer et al 2010(Iglauer et al , 2012Scheffer et al 2021) and a similar flow structure, displaying a clear separation of liquid flow in stagnation regions and preferential paths (Holzner et al 2015), have also been described in three-dimensional conditions. It has also been shown previously that the mixing dynamics in 3D unsaturated porous media follow the same scaling laws as in 2D unsaturated flows (Markale et al 2021). Therefore, we expect the adsorption mechanisms we describe for these 2D flow structures to remain valid for 3D conditions.…”

“…It has also been shown previously that the mixing dynamics in 3D unsaturated porous media follow the same scaling laws as in 2D unsaturated flows (Markale et al. 2021 ). Therefore, we expect the adsorption mechanisms we describe for these 2D flow structures to remain valid for 3D conditions.…”

“…For the duration of the simulations, a transition toward a Fickian condition (t 0.5 ) is only observed for the fully saturated case at around t∕t a = 3.0 . This is caused by the diffusion-controlled coalescence of fingers formed at early times, as developed theoretically (Le Borgne et al 2013) and observed experimentally (de Anna et al 2014;Jiménez-Martínez et al 2015;Markale et al 2021). This transition is usually referred to as mixing time, after which the porous medium behaves as a diffusive system with regards to liquid mixing.…”

“… 2015 ; Markale et al. 2021 ). This transition is usually referred to as mixing time, after which the porous medium behaves as a diffusive system with regards to liquid mixing.…”

Morphogenesis of Biofilms in Porous Media and Control on Hydrodynamics

“…This revealed that the presence of biofilm increases the fluid flow velocity heterogeneity and the spreading of a transported solute . Furthermore, in abiotic porous media, the mosaic of high and low velocities within porous media enhances the reactivity, due to the enhanced creation of concentration gradients. , Despite these advances, the temporal evolution of the permeability field within porous media during bioclogging, its relation with the aggregation process of biofilm clusters, and its dependency on pore size and flow rate have remained largely unknown.…”