Plume deformation, mixing, and reaction kinetics: An analysis of interacting helical flows in three-dimensional porous media

Chaotic Transport of Solutes in Unsaturated Porous Media

Unsaturated porous media, characterized by the combined presence of several immiscible fluid phases in the pore space, are highly relevant systems in nature, because they control the fate of contaminants and the availability of nutrients in the subsoil. However, a full understanding of the mechanisms controlling solute mixing in such systems is still missing. In particular, the role of saturation in the development of chaotic solute mixing has remained unexplored. Using three-dimensional numerical simulations of flow and transport at the pore scale, built upon X-ray tomograms of a porous medium at different degrees of liquid (wetting)-phase saturation, we show the occurrence of chaotic dynamics in both the deformation of the solute plume, as characterized by computed chaos metrics (Lyapunov exponents), and the mixing of the injected solute. Our results show an enhancement of these chaotic dynamics at lower saturation and their occurrence even under diffusion-relevant conditions over the medium's length, also being strengthened by larger flow velocities. These findings highlight the dominant role of the pore-scale spatial heterogeneity of the system, enhanced by the presence of an immiscible phase (e.g., air), on the mixing efficiency. This represents a stepping stone for the assessment of mixing and reactions in unsaturated porous media.

Evolution of plume geometry, dilution and reactive mixing in porous media under highly transient flow fields at the surface water-groundwater interface

Highly transient boundary conditions affect mixing of dissolved solutes in groundwater. An example of these transient boundary conditions occurs at the surface water-groundwater interface, where the water level in rivers can change rapidly due to the operation of hydropower plants, leading to a regime known as hydropeaking. Inspired by this phenomenon, this work studies at laboratory scale the effects of fluctuating surface water bodies on solute transport in aquifers. We performed flow-through experiments at two different flow velocities and under steady and transient flow conditions where a conservative tracer was injected in the system and its concentration measured with optical imaging methods. The experimental results were quantitatively interpreted with numerical simulations implementing a non-linear velocity-dependent dispersive transport model. We estimated plume dilution by computing the dilution index and its evolution as well as two key geometrical metrics of the transient plumes: the perimeter and the area. We further investigated reactive mixing and mixing enhancement considering mixing-controlled bimolecular reactions using different critical mixing ratios. In general, highly transient boundary conditions lead to a larger area, perimeter and plume dilution and the results show greater relative enhancement for the scenarios with low groundwater flow velocity. A linear relationship was observed between the evolution of the area and the dilution index of the plumes for the transient flow scenarios investigated. Considering reactive transport and mixing-limited reactions at the surface water-groundwater interface, we identified different dilution and reaction dominated regimes, characterized, respectively, by increasing and decreasing plume entropies at different mixing ratios of the reactants. Furthermore, reactive mixing was enhanced by transient flows leading to a faster degradation of contaminant plumes compared to corresponding steady flow conditions.

Linking mixing and flow topology in porous media: An experimental proof

Transport processes in porous media are controlled by the characteristics of the flow field which are determined by the porous material properties and the boundary conditions of the system. This work provides experimental evidence of the relation between mixing and flow field topology in porous media at the continuum scale. The setup consists of a homogeneously packed quasi-two-dimensional flow-through chamber in which transient flow conditions, dynamically controlled by two external reservoirs, impact the transport of a dissolved tracer. The experiments were performed at two different flow velocities, corresponding to Péclet numbers of 191 and 565, respectively. The model-based interpretation of the experimental results shows that high values of the effective Okubo-Weiss parameter, driven by the changes of the boundary conditions, lead to high rates of increase of the Shannon entropy of the tracer distribution and, thus, to enhanced mixing. The comparison between a hydrodynamic dispersion model and an equivalent pore diffusion model demonstrates that despite the spatial and temporal variability in the hydrodynamic dispersion coefficients, the Shannon entropy remains almost unchanged because it is controlled by the Okubo-Weiss parameter. Overall, our work demonstrates that under highly transient boundary conditions, mixing dynamics in homogeneous porous media can also display complex patterns and is controlled by the flow topology.