Anomalous transport and chaotic advection in homogeneous porous media

Lester, Daniel; Metcalfe, Guy; Trefry, M. G.

doi:10.1103/physreve.90.063012

Cited by 36 publications

(39 citation statements)

References 33 publications

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“…This result is generic to any macroscopic concentration distribution, hence exponentially accelerated mixing persists in both heterogeneous and homogeneous media. Likewise macroscopic longitudinal dispersion is also strongly augmented by chaotic advection (Lester et al 2014). These results have significant implications for the development of macroscopic models of dispersion and dilution which recover the pore-scale mechanisms which arise from chaotic mixing in 3D porous media.…”

Section: Discussionmentioning

confidence: 99%

“…While the impact of broad transit time distributions on the spatial spreading of transported elements is well understood, their control on mixing dynamics is still an open question. As shown in (Lester et al 2014), Lagrangian chaos generates ergodic particle trajectories at the pore-scale, and the associated decaying correlations allows the advection process to be modelled as a stochastic process. During advection through the pore-space, fluid elements undergo punctuated stretching and folding (transverse to the mean flow direction) events at stagnation points, leading to persistent chaotic advection in random porous media.…”

Section: Introductionmentioning

confidence: 99%

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Chaotic mixing in three-dimensional porous media

2016

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Under steady flow conditions, the topological complexity inherent to all random 3D porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a three-dimensional (3D) fluid mechanical analogue of the baker's map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW) which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We find that chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with longitudinal advection, whereas the topological constraints associated with 2D porous media limits mixing to scale algebraically. These results decipher the role of wide transit time distributions and complex topologies on porous media mixing dynamics, and provide the building blocks for macroscopic models of dilution and mixing which resolve these mechanisms.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chaotic mixing in three-dimensional porous media

2016

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“…These phenomena persist in the presence of additional pore-scale features outlined above [26], which only act to alter the quantitative aspects of transport and dispersion. As the network model considered herein is the simplest representation of porous media with non-trivial pore-scale topology (which is common to all porous media), we contend that the qualitative transport dynamics of this model are universal.…”

Section: Flow and Transport In A Model Open Porous Networkmentioning

confidence: 97%

“…In Lester et al [26] we formalized this CTRW in terms of the displacements ∆x and transition times ∆t over each pore branch and merge element of the flow (shown in Figure 6) which are populated from the CFD computations outlined in Section 4. If we consider the evolution of a fluid particle propagating in the mean flow direction z, then in the absence of diffusion the longitudinal position z and residence time t of fluid particle evolves via the CTRW as t n+1 = t n + ∆t n ,…”

Section: Impact Of Chaotic Advection Upon Longitudinal Dispersionmentioning

confidence: 99%

Chaotic advection at the pore scale: Mechanisms, upscaling and implications for macroscopic transport

Lester

Trefry

Metcalfe

2016

Advances in Water Resources

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The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion leading to persistent hydrodynamic dispersion is well accepted, this paradigm is inherently two-dimensional (2D) in nature and neglects important three-dimensional (3D) phenomena. We discuss how the kinematics of steady 3D flow at the porescale generate chaotic advection-involving exponential stretching and folding of fluid elements-the mechanisms by which it arises and implications of microscopic chaos for macroscopic dispersion and mixing. Prohibited in steady 2D flow due to topological constraints, these phenomena are ubiquitous due to the topological complexity inherent to all 3D porous media. Consequently 3D porous media flows generate profoundly different fluid deformation and mixing processes to those of 2D flow. The interplay of chaotic advection and broad transit time distributions can be incorporated into a continuous-time random walk (CTRW) framework to predict macroscopic solute mixing and spreading. We show how these results may be generalised to real porous architectures via a CTRW model of fluid deformation, leading to stochastic models of macroscopic dispersion and mixing which both honour the pore-scale kinematics and are directly conditioned on the pore-scale architecture.

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“…In a Markov process the particle motion can be seen as a correlated continuous time random walk (CTRW). Using a correlated CTRW, several signatures of anomalous transport behavior were accurately reproduced such as the long tails of the first passage time distribution [6], the non-linear scaling of the second centered moment of the particles longitudinal and transverse displacements [3,6,8], the probability distribution function of the Lagrangian velocity increments for different time lags among others [1].…”

Section: Introductionmentioning

confidence: 97%

Simulating anomalous dispersion in porous media using the unstructured lattice Boltzmann method

et al. 2015

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Flow in porous media is a significant challenge to many computational fluid dynamics methods because of the complex boundaries separating pore fluid and host medium. However, the rapid development of the lattice Boltzmann methods and experimental imaging techniques now allow us to efficiently and robustly simulate flows in the pore space of porous rocks. Here we study the flow and dispersion in the pore space of limestone samples using the unstructured, characteristic based off-lattice Boltzmann method. We use the method to investigate the anomalous dispersion of particles in the pore space. We further show that the complex pore network limits the effectivity by which pollutants in the pore space can be removed by continuous flushing. In the smallest pores, diffusive transport dominates over advective transport and therefore cycles of flushing and no flushing, respectively, might be a more efficient strategy for pollutant removal.

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Anomalous transport and chaotic advection in homogeneous porous media

Cited by 36 publications

References 33 publications

Chaotic mixing in three-dimensional porous media

Chaotic mixing in three-dimensional porous media

Chaotic advection at the pore scale: Mechanisms, upscaling and implications for macroscopic transport

Simulating anomalous dispersion in porous media using the unstructured lattice Boltzmann method

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