Modeling of unsaturated water flow in double-porosity soils by the homogenization approach

Lewandowska, Jolanta; Szymkiewicz, Adam; Burzyński, K.; Vauclin, Michel

doi:10.1016/j.advwatres.2003.12.004

Cited by 81 publications

(103 citation statements)

References 29 publications

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“…Lewandowska et al (2005) conducted infiltration experiments with a double-porosity medium composed of a mixture of sand and sintered clayey spheres arranged in a periodic manner. The resulting inflow and outflow observations were used to verify the DPM approach 'DPOR-1D' (Lewandowska et al, 2004). With domain specific hydraulic parameters (van Genuchten, 1980) identified independently for the sand material and clayey spheres using HYDRUS-1D (Šimůnek et al, 1998), the macroscopic prediction satisfactorily approximated observed inflow and outflow for the composite dual-permeability medium (Lewandowska et al, 2005).…”

Section: Modelling Of Preferential Flow Systemsmentioning

confidence: 95%

“…The original research model was adapted for application to field conditions (Gerke and Köhne, 2004). DPOR-1D (Lewandowska et al, 2004) employs a single integrodifferential mass balance equation that includes an integral term for water exchange between matrix and PF subdomains. Despite an increased accuracy, fewer BCs and parameters need to be defined than in DUAL.…”

Section: Capillary Pf Modelsmentioning

confidence: 99%

See 1 more Smart Citation

A review of model applications for structured soils: a) Water flow and tracer transport

Köhne

Šimůnek

2009

Journal of Contaminant Hydrology

290

224

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Section: Modelling Of Preferential Flow Systemsmentioning

confidence: 95%

Section: Capillary Pf Modelsmentioning

confidence: 99%

A review of model applications for structured soils: a) Water flow and tracer transport

Köhne

Šimůnek

2009

Journal of Contaminant Hydrology

290

224

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“…[9] A comparable approach regarding Richards' equation has been presented by Lewandowska et al [2004]. Differences in their study from the present one are that they considered the transient case, and made assumptions regarding the ratio between the hydraulic diffusivity.…”

mentioning

confidence: 99%

Two‐scale analytical homogenization of Richards' equation for flows through block inclusions

Sviercoski

Warrick

Winter

2009

Water Resources Research

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[1] In this paper we propose an analytical form for the upscaled coefficient applicable to the nonlinear Richards' equation. Block inclusions are symmetrically centered in a grid cell, and flow is dominated by capillary forces on the small scale. The nonlinear boundary value problems can be defined in a three-dimensional bounded domain, with a periodic and rapidly oscillating saturated hydraulic conductivity coefficient. The new result is derived by applying a corrector to an analytical approximation of the well-known cell problem obtained by the two-scale asymptotic expansion to the original heterogeneous nonlinear problem. The previously known analytical results for the upscaled coefficient, including the geometric average for the checkerboard geometry, can be regarded as particular cases of this new form. We perform numerical simulations to obtain the error between the fine-scale solution and the upscaled solution, respectively, as well as convergence properties of the approximation, corroborating results in the literature. There is no limitation regarding either the ratio of permeability between the matrix and inclusion or its shape for both computing the upscaled coefficient and obtaining the upscaled equation. This is illustrated by the comparison with known results and by numerically demonstrating convergence properties with a medium having square and circular inclusions in a main matrix with heterogeneity ratio of 1:100 and 1:10. Even though the derivation and applications are presented for single phase and steady state, the results are valid for multiphase and transient flow conditions. We also show that the approximation is independent of the relative saturated hydraulic relationship.

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“…The essence of this approach, together with many examples, is explained in Hornung (1997). Homogenization techniques have been successfully applied by Neuweiler and Cirpka (2005) and Lewandowska et al (2004) to upscale flows in unsaturated porous media. This article is a continuation of van Duijn et al (2002a), where two-phase flow with trapping at the microscale is considered.…”

Section: Introductionmentioning

confidence: 99%

“…One of the first qualitative studies of the effects of heterogeneities on two-phase porous media flow has been done by Kueper et al (1989). Laboratory experiments using a porous column with periodically varying permeability were performed by van Lingen (1998).…”

Section: Introductionmentioning

confidence: 99%

Effective equations for two-phase flow in porous media: the effect of trapping on the microscale

et al. 2007

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In this article, we consider a two-phase flow model in a heterogeneous porous column. The medium consists of many homogeneous layers that are perpendicular to the flow direction and have a periodic structure resulting in a one-dimensional flow. Trapping may occur at the interface between a coarse and a fine layer. Assuming that capillary effects caused by the surface tension are in balance with the viscous effects, we apply the homogenization approach to derive an effective (upscaled) model. Numerical experiments show a good agreement between the effective solution and the averaged solution taking into account the detailed microstructure.

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Modeling of unsaturated water flow in double-porosity soils by the homogenization approach

Cited by 81 publications

References 29 publications

A review of model applications for structured soils: a) Water flow and tracer transport

A review of model applications for structured soils: a) Water flow and tracer transport

Two‐scale analytical homogenization of Richards' equation for flows through block inclusions

Effective equations for two-phase flow in porous media: the effect of trapping on the microscale

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