Velocity distributions, dispersion and stretching in three-dimensional porous media

“…Ballisticules are delineated by the stretching lamella of a deforming material plane perpendicular to transport. Souzy et al (2020) show a movie of such dynamic stretching of a short material line undergoing transport in a 3-D packed bead porous medium.…”

Section: Conceptual Model Underlying Treatment Of Mixingmentioning

confidence: 99%

Mixing Ratios With Age: Application to Preasymptotic One‐Dimensional Equilibrium Bimolecular Reactive Transport in Porous Media

Gurung

Ginn

2020

Water Resources Research

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Analysis of reactive transport in natural and engineered porous media has benefited from the concept of mixing ratios, in particular as a basis for mathematical separation of transport and reactions processes. General use of solute age has also been recently explored as a way to describe solute mass transfer and/or as a proxy for reaction extent. Age here is defined as exposure time to the flow field. Pairing these concepts, we develop mixing ratio models that are structured on age. One‐dimensional transport is cast in terms of age‐structured mixing ratios in general and compared with conventional formulations of mixing ratio models, demonstrating that age is often a more natural independent variable than absolute time. Using this modeling framework, we then apply age‐structured mixing ratios to the problem of mixing‐limited reactive transport in one‐dimension by explicitly considering unmixed and mixed phases. In order to address mixing limitations under the entirety of transport including the preasymptotic dispersion timeframe, we use the same age variable to define the dispersion coefficient value in a local formulation of transport. Establishing an age‐dependent dispersion coefficient allows simulation of the whole transport time including both preasymptotic and asymptotic dispersion conditions with one model. In our application we explore use of this modeling approach to both synthetic preasymptotic data and experimental asymptotic data pertaining to one famous experiment.

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“…Still, as outlined in the following, questions of fundamental nature remain concerning both the evolution of hydrodynamic dispersion, and the dependence of asymptotic hydrodynamic dispersion coefficients on the Péclet number, which compares the diffusion and advection times over a typical pore length. Anomalous dispersion phenomena [11] have been observed in laboratory experiments [12][13][14][15][16][17], field scale tracer tests [18,19], and numerical simulations in different types of porous medium and rock structures [20][21][22][23][24][25][26]. They cannot be described by a single constant hydrodynamic dispersion coefficient.…”

mentioning

confidence: 99%

“…This phenomenology lies at the heart of nonlocal transport theories such as multitrapping and continuous time random walk (CTRW), which have been used to model anomalous and intermittent pore-scale transport behaviors [17,20,22,24,[27][28][29][30]. However, current approaches are limited to purely advective transport, or need to be constrained by the measurement of particle transition times.…”

mentioning

confidence: 99%

Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media

2021

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We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion, namely, the smoothing of intrapore velocity contrasts, the increase of the tortuosity of particle paths, and the setting of a maximum time for particle transitions. Based on these mechanisms, we derive a theory that predicts anomalous and normal hydrodynamic dispersion in terms of the characteristic pore length, Eulerian velocity distribution, and Péclet number.

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Velocity distributions, dispersion and stretching in three-dimensional porous media

Cited by 67 publications

References 37 publications

Flow and residence time in a two-dimensional aquifer recharged by rainfall

Flow and residence time in a two-dimensional aquifer recharged by rainfall

Mixing Ratios With Age: Application to Preasymptotic One‐Dimensional Equilibrium Bimolecular Reactive Transport in Porous Media

Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media

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