Scalar mixtures in porous media

Kree, Mihkel; Villermaux, Emmanuel

doi:10.1103/physrevfluids.2.104502

Cited by 17 publications

(14 citation statements)

References 30 publications

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“…While X-ray microtomography technologies have progressed significantly (24), they still cannot resolve the fine structures produced below pore-scale. In contrast, use of visible-spectrum refractive-index matching between the solid and the fluid phases represents a viable alternative to observe solute mixing, as obtained with hydrogel beads in water (25). However, as molecular diffusion eventually masks the deformation of dyed fluid elements, a direct measurement of fluid deformation in random porous media is an outstanding challenge.…”

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confidence: 99%

Stretching and folding sustain microscale chemical gradients in porous media

Heyman

Lester

Turuban

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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Fluid flow in porous media drives the transport, mixing, and reaction of molecules, particles, and microorganisms across a wide spectrum of natural and industrial processes. Current macroscopic models that average pore-scale fluctuations into an effective dispersion coefficient have shown significant limitations in the prediction of many important chemical and biological processes. Yet, it is unclear how three-dimensional flow in porous structures govern the microscale chemical gradients controlling these processes. Here, we obtain high-resolution experimental images of microscale mixing patterns in three-dimensional porous media and uncover an unexpected and general mixing mechanism that strongly enhances concentration gradients at pore-scale. Our experiments reveal that systematic stretching and folding of fluid elements are produced in the pore space by grain contacts, through a mechanism that leads to efficient microscale chaotic mixing. These insights form the basis for a general kinematic model linking chaotic-mixing rates in the fluid phase to the generic structural properties of granular matter. The model successfully predicts the resulting enhancement of pore-scale chemical gradients, which appear to be orders of magnitude larger than predicted by dispersive approaches. These findings offer perspectives for predicting and controlling the vast diversity of reactive transport processes in natural and synthetic porous materials, beyond the current dispersion paradigm.

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mentioning

confidence: 99%

Stretching and folding sustain microscale chemical gradients in porous media

Heyman

Lester

Turuban

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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“…Thus, the derived Markov model provides a basis to account for the impact of velocity variability and diffusion on hydrodynamic dispersion. Furthermore, pore‐scale flow variability has an impact on processes such as the filtration of colloidal particles and bacteria (Liang et al, ) as well as mixing between dissolved chemicals (Kree & Villermaux, ), while these processes are also affected by other factors such as volume exclusion and interactions with the solid matrix as well as diffusion; for example, the derived stochastic model for Lagrangian particle velocities may serve as a starting point to account systematically for the effect of hydrodynamic variability.…”

Section: Discussionmentioning

confidence: 99%

Stochastic Dynamics of Lagrangian Pore‐Scale Velocities in Three‐Dimensional Porous Media

Puyguiraud

Gouze

Dentz

2019

Water Resources Research

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Upscaling dispersion, mixing, and reaction processes from the pore to the Darcy scale is directly related to the understanding of the dynamics of pore-scale particle velocities, which are at the origin of hydrodynamic dispersion and non-Fickian transport behaviors. With the aim of deriving a framework for the systematic upscaling of these processes from the pore to the Darcy scale, we present a detailed analysis of the evolution of Lagrangian and Eulerian statistics and their dependence on the injection condition. The study is based on velocity data obtained from computational fluid dynamics simulations of Stokes flow and advective particle tracking in the three-dimensional pore structure obtained from high-resolution X-ray microtomography of a Berea sandstone sample. While isochronously sampled velocity series show intermittent behavior, equidistant series vary in a regular random pattern. Both statistics evolve toward stationary states, which are related to the Eulerian velocity statistics. The equidistantly sampled Lagrangian velocity distribution converges on only a few pore lengths. These findings indicate that the equidistant velocity series can be represented by an ergodic Markov process. A stochastic Markov model for the equidistant velocity magnitude captures the evolution of the Lagrangian velocity statistics. The model is parameterized by the Eulerian velocity distribution and a relaxation length scale, which can be related to hydraulic properties and the medium geometry. These findings lay the basis for a predictive stochastic approach to upscale solute dispersion in complex porous media from the pore to the Darcy scale.

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“…A pore-scale characterization of the transport is thus necessary to understand the behavior of a waterborne contaminant flowing into a subsurface. Direct visualization of mixing in porous media via high-resolution experimental images at high Péclet numbers has recently confirmed the role of diffusive and advective forces in stretching scalar elements and determining the rate of the chaotic dispersion [11], the mixing of initially separated scalars [12] and, in turn, the intensity of the chemical gradients that control pore-scale reaction and adsorbing mechanisms [8]. Such experiments, complemented with pore-scale numerical studies, have supported the development of mathematical formulations able to predict the stretching and mixing processes of transported scalars in homogeneous and heterogeneous media [13][14][15] and their impact on reactive processes [16].…”

Section: Introductionmentioning

confidence: 94%

Transition from diffusion to advection controlled contaminant adsorption in saturated chemically heterogeneous porous subsurfaces

Maggiolo¹,

Modin²,

Kalagasidis³

2022

Preprint

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We show the impact that stretching and mixing has on the fate of plumes of waterborne contaminant solutes transported through a chemically heterogeneous, partially adsorbing porous medium, at a typical Péclet number characterizing saturated flows in subsurfaces, Pe = O(1). Via pore-scale lattice Boltzmann simulations, we follow the dynamic of a passive scalar injected in a packed bed consisting of a mixture of chemically inert and adsorbing spherical particles. By varying the fraction of the adsorbers, randomly and uniformly distributed in the porous volume, and the adsorption rate, we find that the waterborne solute forms different plumes emerging between pairs of adsorbing particles. The plumes are stretched at a rate linearly increasing with time and inversely proportional to the adsorbers' interparticle dimensionless distance * ξ = ξ /d, with d being the pore size. We provide a relationship between the characteristic small-scale scalar concentration width σB and the adsorption-induced stretching rate. The stretching process competes with diffusion broadening to asymptotically determine σB/d ∝ (Pe/ * ξ ) −1/2 and sets the characteristic scale of concentration width larger than the characteristic pore size, that is σB > d. Because of the latter condition, small scalar structures overlap among adjacent pores until mass transport and adsorption are equilibrated at a time t ξ , when the plume is well-mixed at a larger scale, corresponding to its transverse crosssection dimension. The plume mixing rate related to the average flow velocity 1/(U t ξ ) very well approximates a macrohomogenous adsorption coefficient, thus predicting the macroscopic adsorption process and the probability of solute leakage from the porous volume. On the basis of these observations, we also derive the probability of formation of large solute plume volumes, which we find to exponentially decay with large * ξ and small fraction of adsorbers.

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Scalar mixtures in porous media

Cited by 17 publications

References 30 publications

Stretching and folding sustain microscale chemical gradients in porous media

Stretching and folding sustain microscale chemical gradients in porous media

Stochastic Dynamics of Lagrangian Pore‐Scale Velocities in Three‐Dimensional Porous Media

Transition from diffusion to advection controlled contaminant adsorption in saturated chemically heterogeneous porous subsurfaces

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