Mixing, spreading and reaction in heterogeneous media: A brief review

Dentz, Marco; Borgne, Tanguy Le; Englert, Andreas; Bijeljic, Branko

doi:10.1016/j.jconhyd.2010.05.002

Cited by 469 publications

(454 citation statements)

References 178 publications

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“…Recharged water flows initially upstream and then laterally around and below recently recharged water. This complexity stretches flow tubes and favors mixing (Dentz et al, 2011). This effect is enhanced by temporal fluctuations in recharge and was observed in both the homogeneous and heterogeneous models.…”

Section: Resultsmentioning

confidence: 85%

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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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Section: Resultsmentioning

confidence: 85%

“…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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“…The influence of incomplete mixing on mixing-induced reactions has recently won much attention and been reported in many literatures [36][37][38][39][40][41]. The key point for this is that a fundamental difference exists between spreading and mixing processes.…”

Section: Reactants Mixing and Reaction Productmentioning

confidence: 99%

Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture

et al. 2018

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This pore-scale modeling study in single self-affine fractures showed that the heterogeneous flow field had a significant influence on the mixing-induced reaction transport. We generated the single self-affine fracture by the successive random additions (SRA) technique. The pore-scale model was developed by coupling the Navier-Stoke equation (NSE) and advection-diffusion equation with reaction (ADER). Eddies were captured in the self-affine fracture due to the increasing Reynolds number and the sudden expansion of aperture. The flux-weighted breakthrough curves (BTCs) of reaction product showed the typical non-Fickian characteristics (i.e., "early arrival" and "heavy tail"). It was found that the reactant was involved in eddies and then reacted inside the eddy-controlled domain. Consequently, eddies played a significant role in delaying the mass exchange process between the eddycontrolled domain and the main flow channel, which resulted in the "heavy tail" in BTCs. As the Reynolds number increased, the breakthrough time increased while the concentration peaks of BTCs decreased. Furthermore, the dilution index presenting the exponential of the Shannon entropy of a concentration probability distribution was used to quantify the degree of reactant mixing. The results showed that the quantification of dilution for nonreaction transport was in good agreement with the outcomes of mixing-induced reaction transport. The high Reynolds number and Peclet number had a negative influence on the mixing process at the early time whereas they led to the enhanced mixing process at the late time.

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“…One can develop an evolution equation for the productc AγcBγ , which is frequently done. [50][51][52] Although this shows that the evolution ofc AγcBγ depends upon the scalar dissipation rate, this in itself is not entirely helpful because one does not know the scalar dissipation rate a priori either. Additionally, the expression forc AγcBγ exhibits the typical hierarchy problem for nonlinear equations; thus, it is not technically possible to close and expression for this product without significant approximations.…”

Section: A Localization Of the Closure Problemsmentioning

confidence: 99%

A non-scale-invariant form for coarse-grained diffusion-reaction equations

Ostvar

Wood

2016

The Journal of Chemical Physics

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The process of mixing and reaction is a challenging problem to understand mathematically. Although there have been successes in describing the effective properties of mixing and reaction under a number of regimes, process descriptions for early times have been challenging for cases where the structure of the initial conditions is highly segregated. In this paper, we use the method of volume averaging to develop a rigorous theory for diffusive mixing with reactions from initial to asymptotic times under highly segregated initial conditions in a bounded domain. One key feature that arises in this development is that the functional form of the averaged differential mass balance equations is not, in general, scale invariant. Upon upscaling, an additional source term arises that helps to account for the initial configuration of the reacting chemical species. In this development, we derive the macroscopic parameters (a macroscale source term and an effectiveness factor modifying the reaction rate) defined in the macroscale diffusion-reaction equation and provide example applications for several initial configurations.

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Mixing, spreading and reaction in heterogeneous media: A brief review

Cited by 469 publications

References 178 publications

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

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

Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture

A non-scale-invariant form for coarse-grained diffusion-reaction equations

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