On matrix diffusion: formulations, solution methods and qualitative effects

Carrera, Jesús; Sánchez-Vila, Xavier; Benet, I.; Medina, A.; Galarza, G.; Guimerà, Jordi

doi:10.1007/s100400050143

Cited by 328 publications

(475 citation statements)

References 22 publications

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“…The primary features of non-Fickian transport are fast arrivals and/or late time tailing, relative to a Fickian model, for which the RTD analog would be short and long residence times, respectively. The fast arrivals are the result of preferential flow through uncharacterized fast pathways and late time tailing may be caused by mass transfer, back diffusion, or broad ranges of velocities (Benson et al, 2000;Carrera et al, 1998;Haggerty and Gorelick, 1995). Much of this terminology originates from subsurface solute transport literature but similar analogies can be made for other systems.…”

Section: Non-fickian Systemsmentioning

confidence: 99%

Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

Leray

Engdahl

Massoudieh

et al. 2016

Journal of Hydrology

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Steady-state analytical RTDs contaminant transport, and ecosystem preservation. Analytical solutions are often adopted as a model of the RTD and a broad spectrum of models from many disciplines has been applied. Although these solutions are typically reduced in dimensionality and limited in complexity, their ease of use makes them preferred tools, specifically for the interpretation of tracer data. Our review begins with the mechanistic basis for the governing equations, highlighting the physics for generating a RTD, and a catalog of analytical solutions follows. This catalog explains the geometry, boundary conditions and physical aspects of the hydrologic systems, as well as the sampling conditions, that altogether give rise to specific RTDs. The similarities between models are noted, as are the appropriate conditions for their applicability. The presentation of simple solutions is followed by a presentation of more complicated analytical models for RTDs, including serial and parallel combinations, lagged systems, and non-Fickian models. The conditions for the appropriate use of analytical solutions are discussed, and we close with some thoughts on potential applications, alternative approaches, and future directions for modeling hydrologic residence time.

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Section: Non-fickian Systemsmentioning

confidence: 99%

Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

Leray

Engdahl

Massoudieh

et al. 2016

Journal of Hydrology

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“…These recirculation zones represent low velocity regions that can have a significant impact on effective solute transport and, in particular, on the asymptotic dispersion, both for reactive 32 and inert solute transport, 7 depending on typical mass transfer time scales. [43][44][45] In this work, considering an idealized pore geometry, we focus on flow regimes at Reynolds numbers larger than 1, where inertial effects become significant. However, we do not consider situations where the Reynolds number becomes sufficiently large for the flow to become turbulent.…”

Section: -2mentioning

confidence: 99%

The impact of inertial effects on solute dispersion in a channel with periodically varying aperture

et al. 2012

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We investigate solute transport in channels with a periodically varying aperture, when the flow is still laminar but sufficiently fast for inertial effects to be nonnegligible. The flow field is computed for a two-dimensional setup using a finite element analysis, while transport is modeled using a random walk particle tracking method. Recirculation zones are observed when the aspect ratio of the unit cell and the relative aperture fluctuations are sufficiently large; under non-Stokes flow conditions, the flow in non-reversible, which is clearly noticeable by the horizontal asymmetry in the recirculation zones. After characterizing the size and position of the recirculation zones as a function of the geometry and Reynolds number, we investigate the corresponding behavior of the longitudinal effective diffusion coefficient. We characterize its dependence on the molecular diffusion coefficient D m , the Péclet number, the Reynolds number, and the geometry. The proposed relation is a generalization of the well-known Taylor-Aris relationship relating the longitudinal dispersion coefficient to D m and the Péclet number for a channel of constant aperture at sufficiently low Reynolds number. Inertial effects impact the exponent of the Péclet number in this relationship; the exponent is controlled by the relative amplitude of aperture fluctuations. For the range of parameters investigated, the measured dispersion coefficient always exceeds that corresponding to the parallel plate geometry under Stokes conditions; in other words, boundary fluctuations always result in increased dispersion. The transient approach to the asymptotic regime is also studied and characterized quantitatively. We show that the measured characteristic time to attain asymptotic conditions is controlled by two competing effects: (i) the trapping of particles in the near-immobile zone and, (ii) the enhanced mixing in the central zone where most of the flow takes place (mainstream), due to its thinning. C 2012 American Institute of Physics. [http://dx

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“…Matrix diffusion as a retention process is largely described in the literature. [Carrera et al, 1998] sum up the major properties of the system based on breakthrough curves: for low matrix diffusion, peak arrival time is weakly delayed, peak level slightly decreases and a long tail appears. For large matrix diffusion effects, the breakthrough curve is strongly delayed.…”

Section: Main Results From Single Fracture Casementioning

confidence: 99%

Assessment of Retention Processes for Transport in a Fractured System at Äspö (Sweden) Granitic Site: from Short-Time Experiments to Long-Time Predictive Models

Grenier¹,

Fourno²,

Mouche³

et al. 2013

Dynamics of Fluids and Transport in Fractured Rock

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On matrix diffusion: formulations, solution methods and qualitative effects

Cited by 328 publications

References 22 publications

Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

The impact of inertial effects on solute dispersion in a channel with periodically varying aperture

Assessment of Retention Processes for Transport in a Fractured System at Äspö (Sweden) Granitic Site: from Short-Time Experiments to Long-Time Predictive Models

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