Effects of hydrodynamic dispersion on plume lengths for instantaneous bimolecular reactions

Ham, P.A.S.; Schotting, R. J.; Prommer, Henning; Davis, Gordon B.

doi:10.1016/j.advwatres.2004.05.008

Cited by 77 publications

(72 citation statements)

References 18 publications

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“…The effects of transverse mixing on reaction has received some attention in micron-size channels [Nambi et al, 2003;Ottino and Wiggins, 2004;Salmon et al, 2005;Shinohara et al, 2005], homogeneous porous media [Chu et al, 2005;Gramling et al, 2002;Ham et al, 2004;Stenback et al, 2004], and layered and stochastically generated random permeability fields where other processes (e.g., longitudinal dispersivity, retardation) also affect mixing [Oya and Valocchi, 1998;Cirpka et al, 1999a;Valocchi et al, 2003]. Detailed studies of the effects of mixing on reaction in heterogeneous permeability fields characteristic of sand and gravel aquifers are lacking.…”

Section: Introductionmentioning

confidence: 99%

Enhanced mixing and reaction through flow focusing in heterogeneous porous media

Werth

Cirpka

Grathwohl

2006

Water Resources Research

145

130

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[1] Transverse dispersion across adjacent streamlines can control the amount of mixing and reaction between one or more contaminants and a limiting substrate along the fringes of groundwater plumes. Streamlines in groundwater converge and diverge in heterogeneous porous media, depending on the permeability distribution. When flow is focused in a high-permeability zone, the distance required for a solute to cross a given number of streamlines decreases, and the time allowed for mixing and reaction is reduced. Because the first effect outweighs the latter, the overall result is an enhancement of transverse mixing and reaction. Here we develop a conceptual model of heterogeneous two-dimensional structures facilitating flow focusing. We use the conceptual model to develop simple analytical expressions quantifying the extent to which mixing and reaction are enhanced when flow focusing occurs and compare these to results of numerical simulations. Significant enhancement of transverse mixing and reaction by flow focusing is observed; for the cases considered, flow focusing enhances the amount of reaction by a factor ranging from 1.8 to 11.9. The relatively simple analytical expressions demonstrate that the fraction of the domain height made up by highpermeability inclusions, the fraction of flow that passes through the inclusions, and the fringe bypassing of inclusions determine the amount of mixing and reaction enhancement for the permeability distributions considered. These results partially explain why field-scale dispersivities are larger than laboratory derived dispersivities, where homogeneous and isotropic sediments are typically used. Further work is needed to verify the theoretical results presented here with laboratory and field experiments and to expand the relatively simple analytical expressions to consider more heterogeneous three-dimensional permeability fields.Citation: Werth, C. J., O. A. Cirpka, and P. Grathwohl (2006), Enhanced mixing and reaction through flow focusing in heterogeneous porous media, Water Resour. Res., 42, W12414,

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Section: Introductionmentioning

confidence: 99%

Enhanced mixing and reaction through flow focusing in heterogeneous porous media

Werth

Cirpka

Grathwohl

2006

Water Resources Research

145

130

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“…This is of particular relevance for plumes of continuously emitted contaminants that react with compounds from ambient water, because these plumes are controlled by effective macroscopic transverse dispersion [Cirpka et al, 1999;Huang et al, 2003]. For equilibrium reactions and instantaneous irreversible reactions, it can be shown that the length of such plumes is inversely proportional to the transverse dispersivity [Ham et al, 2004;Liedl et al, 2005;Cirpka et al, 2006]. Transverse dispersion also controls the dissolution of NAPL pools [Eberhardt and Grathwohl, 2002;Chu et al, 2005] and the mass transfer of volatile compounds through the capillary fringe [Klenk and Grathwohl, 2002].…”

Section: Introductionmentioning

confidence: 99%

Experimental determination of transverse dispersivity in a helix and a cochlea

Benekos

Cirpka

Kitanidis

2006

Water Resources Research

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[1] In porous media, transverse dispersion plays a decisive role in the dilution of conservative solutes, the decay of concentration fluctuations, and the mixing of reactive solutes. One possible approach for measuring the transverse dispersivity of homogeneous isotropic porous media is based on the principle of Taylor-Aris dispersion, where the longitudinal macrodispersion coefficient is inversely proportional to the pore-scale transverse dispersion coefficient. Taylor-Aris dispersion requires a shear flow situation. To achieve the latter in porous media, we use a helix, as previously proposed, and also a cochlea, which is spiral-shaped cavity resembling the interior a nautilus shell. We obtain experimental breakthrough curves from conservative tracer experiments and compare them to results of numerical simulation. By fitting the model we obtain the values of transverse dispersivity in various tracer tests. In our experiments we investigate porous media with relatively uniform particle distributions. Estimates of the transverse dispersivity are obtained for each experiment, and the relative advantages of each device are discussed. The two devices yield similar results. The estimated ratio of transverse dispersivity to longitudinal dispersivity agrees with the higher ratios reported in the literature.

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“…This approach can be applied when the concentrations of the reacting species stand in algebraic relationships, and the coefficients describing physical mixing in the system coincide for all compounds. The former requirements are met by systems either in local chemical equilibrium or instantaneous, complete, irreversible reactions (Ham et al 2004;Liedl et al 2005) and can also be used for specific cases of kinetic reactions (Molins et al 2004;Cirpka and Valocchi 2007). A methodology to compute directly homogeneous and heterogeneous reaction rates under instantaneous equilibrium has been presented recently by De Simoni et al (2005.…”

Section: Introductionmentioning

confidence: 99%

“…Upon considering both linear and nonlinear kinetic rate laws, they found an approximation for an effective rate constant describing the change in mean concentration with time. Cirpka et al (2008) start from recognizing that knowledge of the spatial distribution of mixing ratios of waters of different chemical composition can be unambiguously mapped onto reactive species concentrations (Ham et al 2004;Liedl et al 2005;Cirpka et al 2006;De Simoni et al 2007). In their study, Cirpka et al (2008) assumed the pdf of mixing ratios to be known and adopted the Beta distribution.…”

Section: Introductionmentioning

confidence: 99%

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

2008

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This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes (and associated reaction rates) evolving in a randomly heterogeneous aquifer. Most existing approaches to solute transport in heterogeneous media focus on providing expressions for space-time moments of concentrations. In general, only low order moments (unconditional or conditional mean and covariance) are computed. In some cases, this allows for obtaining a confidence interval associated with predictions of local concentrations. Common applications, such as risk assessment and vulnerability practices, require the assessment of extreme (low or high) concentration values. We start from the well-known approach of deconstructing the reactive transport problem into the analysis of a conservative transport process followed by speciation to (a) provide a partial differential equation (PDE) for the (conditional) pdf of conservative aqueous species, and (b) derive expressions for the pdf of reactive species and the associated reaction rate. When transport at the local scale is described by an Advection Dispersion Equation (ADE), the equation satisfied by the pdf of conservative species is non-local in space and time. It is similar to an ADE and includes an additional source term. The latter involves the contribution of dilution effects that counteract dispersive fluxes. In general, the PDE we provide must be solved numerically, in a Monte Carlo framework. In some cases, an approximation can be obtained through suitable localization of the governing equation. We illustrate the methodology to depict key features of transport in randomly stratified media in Math Geosci the absence of transverse dispersion effects. In this case, all the pdfs can be explicitly obtained, and their evolution with space and time is discussed.

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Effects of hydrodynamic dispersion on plume lengths for instantaneous bimolecular reactions

Cited by 77 publications

References 18 publications

Enhanced mixing and reaction through flow focusing in heterogeneous porous media

Enhanced mixing and reaction through flow focusing in heterogeneous porous media

Experimental determination of transverse dispersivity in a helix and a cochlea

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

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