Solute Mixing and Chaotic Transport in Unsaturated Porous Media

Abstract

Porous media are ubiquitous in the environment. It is a structural component of living organisms, being present in plants, tissues, and biofilms, and also of abiotic systems, such as soils. The latter stands out for its high environmental relevance, as it mediates the effects on the subsurface of processes occurring in the atmosphere. The unsaturated region of soils, extending from the surface until the deeper aquifers, is key in this exchange, as it controls the fate of solutes, pollutants, and nutrients entering the subsoil. This region is characterized by the combined presence of more than one fluid phase in the pore space, which translates into high spatial heterogeneity and large inherent topological complexity. As a result, some of the most relevant physical processes taking place in this region are not fully understood yet. Fluid flow and solute transport are examples of such processes, whose study has been constrained by the difficulty in both accessing these systems in a non-invasive manner and in observing and quantifying them at the required spatial and temporal resolutions. This doctoral thesis aims to provide a mechanistic understanding of the control of saturation (fraction of the pore volume occupied by the liquid phase) on the processes of fluid flow and solute transport in porous media. This was achieved through an extensive numerical and theoretical investigation at the pore scale, deeply rooted in previous experimental work. In particular, the use of synchrotron X-ray micro-tomography allowed overcoming the technical challenges mentioned above by allowing real-time observation of the movement, spreading, and mixing of an injected solute in a porous medium at different degrees of saturation and under different flow rates. Results on the impact of saturation on flow revealed an enhancement in the flow redistribution upon a decrease in saturation. This manifested itself in the stronger formation of backbones of preferential flow and in larger dead-end regions of very low velocity. The latter contributed largely to a marked change of scaling in the velocity distribution and to a sharp transition to enhanced anomalous transport, visible already after a slight desaturation in the system. A theoretical framework is presented, which successfully captured these variations from structural properties in unsaturated porous media. Results from the synchrotron X-ray experiments showed that this enhanced solute dispersion at lower saturation imparts larger amounts of deformation to the solute plume, which renders the mixing of transported solute with the resident solution more efficient. Similar outcomes were obtained upon an increase in the injection flow rate under a constant saturation degree. A fully resolved 3D numerical investigation of flow allowed explaining the physical mechanisms behind this interplay. Lower saturation alters the connectivity of the system, enhancing the streamlines convergence in the pore space and leading to backbone formation. This results in a strengthened helical flow inside the liquid phase, with large values of helicity density linked to strong streamlines deformation in the form of intensive folding and braiding. This suggests the simultaneous presence of shear- and vorticity-dominated deformation regions in the pore space, whose combination is ultimately responsible for the enhanced solute plume deformation quantified from the experimental data. Based on additional transport simulations performed on the same 3D geometries, we conclude on the occurrence of chaotic advection and chaotic mixing in the system, as initially suggested by the strong braiding and folding of streamlines visible in the vicinity of air clusters and solid boundaries. As indicated by the Lyapunov exponents, computed from the solute plume deformation reconstructed for all tested conditions, the strength of chaos in the liquid phase is enhanced upon both a decrease in saturation and an increase in flow rate. The study presented in this thesis is a major leap forward in our understanding of the physical mechanisms behind the larger flow field heterogeneity and enhanced transport dynamics characteristic of unsaturated porous media. The results here presented are relevant for a wide range of environmental and industrial applications, being especially useful in investigations on mixing and reactive transport under multiphase conditions. The outcome of this thesis will likely motivate further research in the field and will contribute to the study of complex systems and additional processes of high environmental and industrial relevance.