Two‐medium description of dispersion in heterogeneous porous media: Calculation of macroscopic properties

Cherblanc, Fabien; Ahmadi, Azita; Quintard, Michel

doi:10.1029/2002wr001559

Cited by 46 publications

(59 citation statements)

References 100 publications

(133 reference statements)

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“…When clouds grow to this scale, the horizontal heterogeneity contributes another mechanism of dispersion similar to the macrodispersion observed in groundwater flow through an array of lenses of varying conductivity (e.g., Cherblanc et al 2003;Russo 2003). The dispersion coefficient usually increases with the scale of the velocity heterogeneity (Nepf 2004).…”

Section: Analytic Developmentmentioning

confidence: 99%

Prediction of velocity profiles and longitudinal dispersion in salt marsh vegetation

2006

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To predict the behavior of solutes and suspended particles in wetlands, it is necessary to estimate advection and longitudinal dispersion. To better understand these processes, measurements were taken of stem frontal area, velocity, vertical diffusion, and longitudinal dispersion in a Spartina alterniflora salt marsh in the Plum Island Estuary in Rowley, Massachusetts. Vegetation volumetric frontal area peaked at 0.067 Ϯ 0.007 cm Ϫ1 near 10 cm from the bed. If the velocity profile in a dense emergent marsh canopy depends on the local balance between pressure forcing and vegetation drag, the velocity will vary inversely with canopy drag (i.e., velocity is minimum where the frontal area is maximum). In fact, the minimum velocity was observed at 10 cm from the bed. The momentum balance therefore provides a way to predict the velocity profile structure from canopy morphology. The vertical diffusion coefficient also depends on canopy characteristics, such that the vertical diffusion coefficient normalized by the velocity and stem diameter had a constant value of 0.17 Ϯ 0.08 at this study site. The canopy morphology also controls the longitudinal dispersion, observed in this study to be 4 to 27 cm 2 s Ϫ1. However, theoretical considerations show that dispersion coefficients of at least 540 cm 2 s Ϫ1 can occur under typical marsh conditions. Comparisons to other canopies indicate that the prediction of the velocity profile and shear dispersion from canopy morphology can be extended to other emergent canopies and that shear dispersion may vary widely between stands with different physical characteristics.

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Section: Analytic Developmentmentioning

confidence: 99%

Prediction of velocity profiles and longitudinal dispersion in salt marsh vegetation

2006

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“…There has been an extensive literature on the subject, and we comment below some major features. Considering dispersion mechanisms on a broader sense, two types of situations have been considered in the literature: mobile-immobile models (see Zhang and Smith [41] for an illustration of this idea to the problem of viscous fingering for example) or mobile-mobile models (see a review of this problem in Cherblanc et al [6]). …”

Section: Local Mass Equilibrium Dissolution (Da Large): Two-medium Ormentioning

confidence: 99%

Core-scale description of porous media dissolution during acid injection - Part I: theoretical development

Golfier¹,

Bazin²,

Lenormand³

et al. 2004

Mat. apl. comput.

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Abstract. Dissolution mechanisms in porous media may lead to unstable dissolution fronts ("wormholing"). It has been shown in the literature that Darcy-scale models may reproduce all the characteristics of such dissolution patterns. This paper considers the core-scale averaged behavior of these Darcy-scale dissolution models. The form of core-scale equations is discussed based on the volume averaging of the Darcy-scale equations. The uncertainty about the choice of the unit cell (and boundary conditions) to solve the closure problems and the impact of the dissolution history on the core-scale properties is emphasized.Mathematical subject classification: 76V05, 76S05, 80A32.

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“…The quasi-steady formulation of the upscaled system presented above is similar to that obtained by application of volume averaging to solute transport in heterogeneous porous media at larger scales [e.g., Ahmadi et al, 1998;Quintard et al, 2001;Cherblanc et al, 2003Cherblanc et al, , 2007Chastanet and Wood, 2008;Golfier et al, 2011]. Our upscaled coefficients are expressed directly in terms of pore-scale quantities and the porous medium is assumed to be homogeneous (in terms of hydraulic conductivity distribution) at the continuum scale.…”

Section: Upscaled Systemmentioning

confidence: 76%

“…[31] Here, dimensional vectorsĝ Here, we rely on the formulation (17), which has been previously suggested and employed for the analysis of heat transport [Moyne, 1997] and mass transfer in heterogeneous bimodal porous media [Ahmadi et al, 1998;Quintard et al, 2001;Cherblanc et al, 2003Cherblanc et al, , 2007Golfier et al, 2011]. Appendix A provides the details of the complete system of equations (i.e., six equations, three of which are defined inV and three inV ; note that these equations are coupled in pairs through boundary conditions (15)) which is used to compute the closure variables introduced in (17).…”

Section: Closure Systemmentioning

confidence: 99%

“…[5] Theoretical and numerical works grounded on volume averaging arguments [Ahmadi et al, 1998;Quintard et al, 2001;Cherblanc et al, 2003Cherblanc et al, , 2007Golfier et al, 2011] consider upscaling from Darcy-to field-scale in bimodal porous media, i.e., systems which are characterized by the occurrence of high-and low-hydraulic conductivity regions. These authors assume that a continuum-scale description of the transport process based on the ADE holds within each subregion.…”

Section: Introductionmentioning

confidence: 99%

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Upscaling solute transport in porous media from the pore scale to dual‐ and multicontinuum formulations

Porta

Chaynikov

Riva

et al. 2013

Water Resources Research

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[1] We provide pore to Darcy-scale theoretical upscaling of solute transport in porous media and discuss the key theoretical elements underlying double-and multirate mass transfer formulations which are typically adopted to interpret laboratory-and/or field-scale transport experiments. We model pore-scale transport by considering advective and diffusive processes. The resulting mass balance equation is subject to volume averaging relying on an unsteady closure. This leads to a nonlocal in time continuum-scale twoequation transport model, which we compare against existing double-and multirate mass transfer formulations. Coefficients appearing in our upscaled model are expressed as functions of time and pore-scale geometry and velocity distribution. We analyze in detail the scenario associated with two-dimensional flow in a plane channel and discuss the temporal dynamics and the associated asymptotic behavior of the different effective coefficients appearing in the upscaled system of equations. The relative influence of the terms included in the continuum-scale model is quantitatively assessed.Citation: Porta, G., S. Chaynikov, M. Riva, and A. Guadagnini (2013), Upscaling solute transport in porous media from the pore scale to dual-and multicontinuum formulations, Water Resour.

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Two‐medium description of dispersion in heterogeneous porous media: Calculation of macroscopic properties

Cited by 46 publications

References 100 publications

Prediction of velocity profiles and longitudinal dispersion in salt marsh vegetation

Prediction of velocity profiles and longitudinal dispersion in salt marsh vegetation

Core-scale description of porous media dissolution during acid injection - Part I: theoretical development

Upscaling solute transport in porous media from the pore scale to dual‐ and multicontinuum formulations

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