Toward enhanced subsurface intervention methods using chaotic advection

Trefry, M. G.; Lester, Daniel; Metcalfe, Guy; Ord, Alison; Regenauer-Lieb, Klaus

doi:10.1016/j.jconhyd.2011.04.006

Cited by 57 publications

(79 citation statements)

References 21 publications

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“…The limiting role of mixing to the overall transformation rates of contaminants in the subsurface is increasingly recognized as well as the importance of mixing enhancement by natural flow and transport processes (e.g., Rolle et al, 2009;Werth et al, 2006) and engineered approaches (Kitanidis and McCarty, 2012;Mays and Neupauer, 2012;Trefry et al, 2012). Moreover, there is a clear need to distinguish between true mixing processes, depending on aqueous diffusion, and processes such as advective heterogeneities, which may lead to squeezing, stretching and meandering of a solute plume but do not directly contribute to physical mixing.…”

Section: Metrics Of Mixingmentioning

confidence: 99%

On the importance of diffusion and compound-specific mixing for groundwater transport: An investigation from pore to field scale

Rolle

Chiogna

Hochstetler

et al. 2013

Journal of Contaminant Hydrology

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Section: Metrics Of Mixingmentioning

confidence: 99%

On the importance of diffusion and compound-specific mixing for groundwater transport: An investigation from pore to field scale

Rolle

Chiogna

Hochstetler

et al. 2013

Journal of Contaminant Hydrology

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“…The studies in Lester et al (2009), Metcalfe et al (2010, Trefry et al (2012) concern time-periodic flows with this particular structure and reveal that the underlying reorientation is essential for the accomplishment of chaotic advection. The reorientation of the pumping scheme under anisotropic conditions no longer transfers to the internal flow and, in consequence, structure (1) is broken.…”

Section: General Configurationmentioning

confidence: 99%

“…The step-wise Darcy velocity described by (11), in consequence, becomes a potential flow: u k = −∇ p. Moreover, the period-wise flow under isotropic conditions consists of reorientations of base flow u 1 following (1). Thus the system becomes the rotated potential mixing (RPM) flow employed in the studies by Lester et al (2009), Metcalfe et al (2010), Trefry et al (2012) with the base flow given analytically by…”

Section: Flow Field: General Properties and Numerical Treatmentmentioning

confidence: 99%

“…Recent studies by Lester et al (2009), Metcalfe et al (2010), Trefry et al (2012) on the so-called rotated potential mixing (RPM) flow demonstrated that well configurations and pumping schemes designed on the basis of chaos theory enable systematic and efficient distribution of the production fluids throughout the entire reservoir. Key to this is chaotic advection, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Lagrangian Transport and Chaotic Advection in Two-Dimensional Anisotropic Systems

2017

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Enhanced geothermal systems (EGSs) are a promising concept to make geothermal power generation available in many regions worldwide. However, in current EGSs generally only a fraction of the geothermal reservoir is effectively accessed by the production fluid, resulting in suboptimal performance. Recent studies in the literature on a two-dimensional Darcy flow in a circular reservoir driven by reoriented injector-producer wells demonstrated that well configurations and pumping schemes designed on the basis of chaos theory enable efficient distribution of the production fluids throughout the entire reservoir. Key to this is accomplishment of chaotic advection, i.e. the rapid dispersion and stretching of material fluid regions, by a "proper" flow forcing. However, these studies concern isotropic reservoirs, while geothermal reservoirs typically are highly anisotropic. Our theoretical/computational study expands on said studies by investigating the impact of anisotropy on fundamental aspects of the Lagrangian transport of production fluids. This reveals that anisotropy generically eliminates key organizing mechanisms in the Lagrangian transport, viz. symmetries, and thus tends to promote disorder and, inherently, chaotic advection. However, symmetries are partially preserved-and thus order and coherence partially restored-in non-generic cases such as pumping schemes employing an even number of injector-producer wells and well configurations aligned with the anisotropy. Symmetry associated with well alignment in fact appears crucial to an intriguing "order within chaos" observed only in such cases: prolonged confinement of fluid to subregions of chaotic areas.

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“…Article (12) where λ ≡ Cd̅ 2 /(Sδ) and A is an integration constant determined by the relative volume of particle species i in the chute (e.g., ∫ −1 0 c i (z) dz̃= 0.5 for an equal volume mixture). Note that λ combines all the relevant length scales in the problem: S for percolation, d̅ for diffusion and δ for chute geometry.…”

Section: Industrial and Engineering Chemistry Researchmentioning

confidence: 99%

On Mixing and Segregation: From Fluids and Maps to Granular Solids and Advection–Diffusion Systems

Schlick

Isner

Umbanhowar

et al. 2015

Ind. Eng. Chem. Res.

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In fluids, diffusive transport and fluid parameters are determined by the thermally driven movement of molecules, whereas in granular media, thermal effects play no role in transport. Despite this fundamental difference, mixing in fluids and mixing and segregation in granular solids share many similarities. The advection−diffusion equation formalism unites the two systems and can be used in both cases to predict and understand how and when mixing occurs, through the use of strategic simplifications. We illustrate this connection with a fluid mixing example (the rotated potential mixer) and a granular segregation example (the segregation of a bidisperse mixture flowing in a chute). ■ INTRODUCTIONMixing in fluids and granular materials shares similarities, but also crucial differences. Every problem involving fluid motion, diffusion, and even reaction, can, in principle, be understood in terms of the Navier−Stokes equations and the advection− diffusion equation. However, it is rare that analytic solutions and their accompanying insights exist; instead, the coupled partial differential equations (PDEs) are solved numerically for one set of parameters at a time. In contrast to fluids, there is not yet a universal continuum description that fully captures flow and mixing in granular systems. Instead, discrete element method (DEM) simulations provide a powerful computational microscope that can reveal nearly all details for flows involving millions of particles. These details on their own, although useful for a particular set of parameters, lack the power to provide a deeper understanding of the principles governing granular flow and mixing. To advance our knowledge on both frontsfluid flow and granular flowother approaches are needed that are both accurate and sufficiently elegant to reveal the fundamental nature of the mechanisms driving mixing, and, in the case of granular solids, segregation as well. We present two examples, representing extremes, and show how they connect.The foundation of understanding fluid mixing rests on maps. Repeated applications of the right types of maps in certain mixing systems leads to stretching and folding and chaos. 1 The map route, a purely kinematical approach to mixing, was crucial over the last two decades to understanding fluid mixing via chaotic advection. Only lately have computational algorithms advanced to the point that directly solving the Navier−Stokes and advection−diffusion equations has become possible and practical. Here, we present an example that sits midway between the two approaches: simple enough that the structure created by the repeated applications of maps is evident, but rich enough, when one adds diffusion, that it serves as a test bed for the application of recent algorithms based on the advection− diffusion formalism. 2 In fact, the repeated application of a map to solve the advection−diffusion equation has provided a methodology to solve problems in which chaotic advection is accompanied by diffusion. 3−7 The method uses operator splitting, which allows...

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Toward enhanced subsurface intervention methods using chaotic advection

Cited by 57 publications

References 21 publications

On the importance of diffusion and compound-specific mixing for groundwater transport: An investigation from pore to field scale

On the importance of diffusion and compound-specific mixing for groundwater transport: An investigation from pore to field scale

Lagrangian Transport and Chaotic Advection in Two-Dimensional Anisotropic Systems

On Mixing and Segregation: From Fluids and Maps to Granular Solids and Advection–Diffusion Systems

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