Modeling solute transport through unsaturated porous media using homogenization I

Mikelić, Andro; Rosier, Carole

doi:10.1590/s0101-82052004000200006

Cited by 9 publications

(5 citation statements)

References 23 publications

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“…This article, however, does not as yet incorporate the computation of these coefficients. Another appealing aspect of homogenization (Hornung 1997;Mikelic and Rosier 2004;Sanchez-Palencia 1980) is that it does not need a closure relation for obtaining the macroscale transport equation as opposed to volume averaging (Wood 2009). However, the relevant model equations are not conventional and not easy to solve (Tardif d'Hamonville et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

2011

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This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that the longitudinal dispersion coefficient can be reasonably represented by a simple periodic unit cell (PUC), which consists of a single sphere in a cube. We present a slightly modified and simplified approach to derive the homogenized equations, which emphasizes physical aspects of homogenization. Subsequently, we give full dimensional expressions for the dispersion tensor based on a comparison with the convective dispersion equation used for contaminant transport, inclusive the correct dependence on porosity. For the PUC of choice, the dispersion relations are identical to the relations obtained for periodic media. We show that commercial finite element software can be readily used to compute longitudinal and transverse dispersion coefficients in 2D and 3D. The 3D results are for the first time obtained at relevant Peclet numbers. There is good agreement for longitudinal dispersion. The computed transverse dispersion coefficients for a single sphere in a cube are much too low. The effect of adsorption on the dispersion coefficient is also studied. Adsorption does not affect the transverse dispersion coefficient. However, adsorption enhances the longitudinal dispersion coefficient in agreement with an analysis of homogenization applied to Taylor dispersion discussed in the literature.

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Section: Introductionmentioning

confidence: 99%

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

2011

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“…This section presents the homogenization process of the transport problem, Equations (20)- (23). Introducing the asymptotic developments (5), taking into account (6), and regrouping the terms at the same powers of ε lead to:…”

Section: Homogenization Of the Problem Of Solute Transport In Unsaturmentioning

confidence: 99%

“…Based on Richard's equation [22], this model was associated with the DP approach describing unsaturated water flow. Using the same model for DP unsaturated water flow, Mikelic and Rosier [23] proposed a transport model that takes into account the convection and dispersion in the macro-porosity, coupled with adsorption at the micro-porosity external boundary. However, no solute transport in the micro-porosity was considered.…”

Section: Introductionmentioning

confidence: 99%

Two‐scale modeling of solute dispersion in unsaturated double‐porosity media: Homogenization and experimental validation

Ngoc¹,

Lewandowska²,

Vauclin³

et al. 2010

Num Anal Meth Geomechanics

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International audienceA two-scale modeling of solute transport in double-porosity (DP) media under unsaturated water flow conditions is presented. The macroscopic model was developed by applying the asymptotic homogenization method. It is based on theoretical and empirical considerations dealing with the orders of magnitude of characteristic quantities involved in the process. For this purpose a physical model that mimics the behavior of DP medium was built. The resulting two-equation model relies on a coupling exchange term between micro- and macro-porosity subdomains associated with local non-equilibrium solute concentrations. The model was numerically implemented (Comsol Multiphysics®) to simulate the macroscopic one-dimensional physical process taking place into the porous medium of 3D periodic microstructure. A series of dispersion experiments of NaCl solution under unsaturated steady-state flow conditions were performed. The experimental results were used first to calibrate the dispersion coefficient of the model, and second to validate it through two other independent experiments. The excellent agreement between the numerical simulations and the measurements of the time evolution of the non-symmetrical breakthrough curves provides a proof of predictive capacity of the developed model. Copyright © 2010 John Wiley & Sons, Ltd

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“…Auriault and Lewandowska (1995) developed the double-difusivity model allowing to capture the tailing efect. Mikelic and Rosier (2004) derived a transport model by convection and dispersion in the macroporosity domain, coupled with adsorption at the interface of micro-and macro-pore regions, but without solute transport in the micro-pore region. In these models, Richard's equation and convection-difusion/dispersion equation were employed to describe the transient low and transport in the microstructure.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of Solute Transport in Unsaturated Double-Porosity Media: Model and Numerical Validation

Ngoc

Tran

et al. 2020

Transp Porous Med

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The development of a macroscopic model for solute transport coupled with unsaturated water low in double-porosity media is presented in this work, by using the asymptotic homogenization method. The model was derived for the case in which the medium exhibits a strong contrast of transport properties by upscaling rigorously the transport mechanisms from micro-scale to macro-scale. It consists of two coupled equations for dispersion-convection processes at macroscopic level and difusion intervention from local scale that can be described by a non-Fickian behaviour of solute concentration breakthrough. The proposed model was numerically implemented in the environment of a inite element code (commercial software) and applied to 2D examples with diferent boundary conditions. To validate, a comparative analysis between the results obtained from the homogenized model and the ine scale model (reference solution obtained from explicit heterogeneous representation of the medium structure) was carried out. The obtained numerical tool for the two-scale implementation enables treating various types of two-equation models to study the macroscopic non-Fickian transport and also non-equilibrium evolution of concentration ields inside the micro-porous medium.

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Modeling solute transport through unsaturated porous media using homogenization I

Abstract: Abstract. In this paper we consider homogenization of the diffusion, adsorption and convection of chemical species in porous media, that are transported by unsaturated single phase flows. The

Cited by 9 publications

References 23 publications

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

Two‐scale modeling of solute dispersion in unsaturated double‐porosity media: Homogenization and experimental validation

Homogenization of Solute Transport in Unsaturated Double-Porosity Media: Model and Numerical Validation

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