Scalar dispersion in a periodically reoriented potential flow: acceleration via Lagrangian chaos

Use of steady-state hydraulic tomography to inform the selection of a chaotic advection system

The concept of chaotic advection is a novel approach that has the potential to overcome some of the challenges associated with mixing of reagents that commonly occur when injection based in situ treatment techniques are used. The rotated potential mixing (RPM) flow system is one configuration which has been theorized to achieve chaotic advection in porous media, and enhance reagent mixing by periodically re-oriented dipole pumping at a series of radial wells. Prior to field implementation of chaotic advection, the selection of an RPM flow protocol will likely require a numerical model that can adequately represent groundwater flow within the zone of interest. As expected, the hydraulic conductivity (K) field is the most critical input requirement for the selected groundwater flow model. Hydraulic tomography (HT) is an innovative characterization approach that has shown potential to provide information on a K field. In this investigation, we explored whether the same well system required to invoke chaotic advection can also be applied in a HT analysis, and evaluated the use of the generated K tomogram for the selection of RPM flow parameters that can enhance reagent mixing. A series of dipole pumping tests were conducted within an area of interest as defined by the limits of the circular network of eight injection/extraction wells used to invoke chaotic advection. Hydraulic head data collected from independent dipole pumping tests were used in an inverse model to perform steady-state hydraulic tomography (SSHT) analysis to generate a K tomogram. Both the K tomogram and an effective parameter approach (i.e., a single K value assigned across the entire spatial domain as determined by single well pumping and slug tests) produced estimates of hydraulic head that closely resembled those observed due to the relative homogeneous nature of the aquifer and the small spatial scale of the area of interest. In contrast, particle tracking results showed that incorporating a heterogeneous K field significantly enhanced the spatial distribution of particle trajectories indicative of reagent mixing. These findings support the hypothesis that the same well system used to invoke chaotic advection can be combined with SSHT analysis as a viable site characterization tool for delineating the spatial variability of K. Incorporating this K tomogram in a groundwater flow model with a particle tracking engine can be used as a design tool to aid in the selection of a site-specific RPM flow protocol to achieve enhanced reagent mixing.

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918)10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Effect of the vertical component of diffusion on passive scalar transport in an isolated vortex model

On the basis of the ellipsoidal vortex model and a Monte-Carlo-type diffusion simulation, we examine the flux and ensuing distribution of passive fluid particles through the boundary of an idealized geophysical vortex. Our focus is on features that the horizontal and vertical diffusion components introduce into the fluid particle transport. We examine the concurrent effect of both components, and we compare it with the only horizontal diffusion impact. We analyze the ellipsoid vortex model in two cases: (i) the steady state when the ellipsoid is motionless, i.e., there is no variation in its axes' lengths, and consequently the exterior fluid is not being stirred; (ii) the perturbed case when the ellipsoid rotates periodically, varying it axes' lengths, which results in the appearance of stirred fluid outside the ellipsoid. Influenced by diffusion, a fluid particle is now permitted to move to another vertical horizon, thus there is an increased possibility that the particle will eventually be located in the exterior stirred region rather than in the ellipsoid vortex with the regular dynamics. This is because the area of the horizontal section of the ellipsoid vortex decreases with depth, but the region of stirred exterior fluid extends significantly deeper. Numerical calculations show that factoring in the vertical component of diffusion significantly affects scalar spreading in the horizontal plane in the perturbed case, while in the steady state the vertical component of diffusion only induces dispersion linear growth according to a Gaussian distribution.

Is chaotic advection inherent to porous media flow?

We show that chaotic advection is inherent to flow through all types of porous media, from granular and packed media to fractured and open networks. The basic topological complexity inherent to all porous media gives rise to chaotic flow dynamics under steady flow conditions, where fluid deformation local to stagnation points imparts a 3D fluid mechanical analog of the baker's map. The ubiquitous nature of chaotic advection has significant implications for the description of transport, mixing, chemical reaction and biological activity in porous media.

Toward enhanced subsurface intervention methods using chaotic advection

Many intervention activities in the terrestrial subsurface involve the need to recover/emplace distributions of scalar quantities (e.g. dissolved phase concentrations or heat) from/in volumes of saturated porous media. These scalars can be targeted by pump-and-treat methods or by amendment technologies. Application examples include in-situ leaching for metals, recovery of dissolved contaminant plumes, or utilizing heat energy in geothermal reservoirs. While conventional pumping methods work reasonably well, costs associated with maintaining pumping schedules are high and improvements in efficiency would be welcome. In this paper we discuss how transient switching of the pressure at different wells can intimately control subsurface flow, generating a range of "programmed" flows with various beneficial characteristics. Some programs produce chaotic flows which accelerate mixing, while others create encapsulating flows which can isolate fluid zones for lengthy periods. In a simplified model of an aquifer subject to balanced pumping, chaotic flow topologies have been predicted theoretically and verified experimentally using Hele-Shaw cells. Here, a survey of the key characteristics of chaotic advection is presented. Mathematical methods are used to show how these characteristics may translate into practical situations involving regional flows and heterogeneity. The results are robust to perturbations, and withstand significant aquifer heterogeneity. It is proposed that chaotic advection may form the basis of new efficient technologies for groundwater interventions.