A general real-time formulation for multi-rate mass transfer problems

Silva, Orlando; Carrera, Jesús; Dentz, Marco; Kumar, Subodha; Alcolea, Andrés; Willmann, M.

doi:10.5194/hess-13-1399-2009

Cited by 63 publications

(53 citation statements)

References 70 publications

(135 reference statements)

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“…Other equivalent formulations exist (Silva et al, 2009) such the fractional ADE (Benson et al, 2000;Berkowitz et al, 2002;Schumer et al, 2003), Continuous Time Random…”

Section: Non-fickian Solutions For Rtdsmentioning

confidence: 99%

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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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“…Other equivalent formulations exist (Silva et al, 2009) such the fractional ADE (Benson et al, 2000;Berkowitz et al, 2002;Schumer et al, 2003), Continuous Time Random…”

Section: Non-fickian Solutions For Rtdsmentioning

confidence: 99%

“…Walk, Multi-Rate Mass Transfer Gouze et al, 2008;Haggerty and Gorelick, 1995), and generalized memory function approaches (Cvetkovic, 2012;Silva et al, 2009). The solution presented here is a general non-local in time formulation.…”

Section: Non-fickian Solutions For Rtdsmentioning

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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“…One might be tempted to use multirate models (Haggerty and Gorelick, 1995), which reproduce the effect of heterogeneity (Silva et al, 2009;Dentz et al, 2011). In fact, such models would probably capture the fast rebound of the TCA concentration when the recharge stopped, as observed in Fig.…”

Section: Tca and Ec Validationmentioning

confidence: 99%

Tracer test modeling for characterizing heterogeneity and local-scale residence time distribution in an artificial recharge site

Valhondo

Martinez-Landa

Carrera

et al. 2016

Hydrol. Earth Syst. Sci.

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Abstract. Artificial recharge of aquifers is a technique for improving water quality and increasing groundwater resources. Understanding the fate of a potential contaminant requires knowledge of the residence time distribution (RTD) of the recharged water in the aquifer beneath. A simple way to obtain the RTDs is to perform a tracer test. We performed a pulse injection tracer test in an artificial recharge system through an infiltration basin to obtain the breakthrough curves, which directly yield the RTDs. The RTDs turned out to be very broad and we used a numerical model to interpret them, to characterize heterogeneity, and to extend the model to other flow conditions. The model comprised nine layers at the site scaled to emulate the layering of aquifer deposits. Two types of hypotheses were considered: homogeneous (all flow and transport parameters identical for every layer) and heterogeneous (diverse parameters for each layer). The parameters were calibrated against the head and concentration data in both model types, which were validated quite satisfactorily against 1,1,2-Trichloroethane and electrical conductivity data collected over a long period of time with highly varying flow conditions. We found that the broad RTDs can be attributed to the complex flow structure generated under the basin due to three-dimensionality and time fluctuations (the homogeneous model produced broad RTDs) and the heterogeneity of the media (the heterogeneous model yielded much better fits). We conclude that heterogeneity must be acknowledged to properly assess mixing and broad RTDs, which are required to explain the water quality improvement of artificial recharge basins.

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“…MRMT models differ by the distributions of characteristic rates α i and immobile porosities ϕ i . Among the available models (Cvetkovic, 2012;Haggerty et al, 2000), we choose a uniform distribution for characteristic times (1/α i ) bounded by the two extreme rates α 1 = 1/t 1 and α N = 1/t N (t 1 < t N ) and a power-law distribution for ϕ i : The power-law distribution is consistent with observed breakthrough curves in HPM, which often display long tails that appear linear in log(c) versus log(t) Haggerty et al, 2004;Li et al, 2011;Silva et al, 2009;Willmann et al, 2008). This tailing is well modeled by a power law, such that the breakthrough concentration c evolves as c ∼ t −m .…”

Section: Multi-rate Mass Transfer Model (Mrmt)mentioning

confidence: 97%

On the validity of effective formulations for transport through heterogeneous porous media

Dreuzy

Carrera

2016

Hydrol. Earth Syst. Sci.

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Abstract. Geological heterogeneity enhances spreading of solutes and causes transport to be anomalous (i.e., nonFickian), with much less mixing than suggested by dispersion. This implies that modeling transport requires adopting either stochastic approaches that model heterogeneity explicitly or effective transport formulations that acknowledge the effects of heterogeneity. A number of such formulations have been developed and tested as upscaled representations of enhanced spreading. However, their ability to represent mixing has not been formally tested, which is required for proper reproduction of chemical reactions and which motivates our work. We propose that, for an effective transport formulation to be considered a valid representation of transport through heterogeneous porous media (HPM), it should honor mean advection, mixing and spreading. It should also be flexible enough to be applicable to real problems. We test the capacity of the multi-rate mass transfer (MRMT) model to reproduce mixing observed in HPM, as represented by the classical multi-Gaussian log-permeability field with a Gaussian correlation pattern. Non-dispersive mixing comes from heterogeneity structures in the concentration fields that are not captured by macrodispersion. These fine structures limit mixing initially, but eventually enhance it. Numerical results show that, relative to HPM, MRMT models display a much stronger memory of initial conditions on mixing than on dispersion because of the sensitivity of the mixing state to the actual values of concentration. Because MRMT does not restitute the local concentration structures, it induces smaller non-dispersive mixing than HPM. However long-lived trapping in the immobile zones may sustain the deviation from dispersive mixing over much longer times. While spreading can be well captured by MRMT models, in general nondispersive mixing cannot.

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A general real-time formulation for multi-rate mass transfer problems

Cited by 63 publications

References 70 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

Tracer test modeling for characterizing heterogeneity and local-scale residence time distribution in an artificial recharge site

On the validity of effective formulations for transport through heterogeneous porous media

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