Horizontal redistribution of fluids in a porous medium: The role of interfacial area in modeling hysteresis

Pop, Sorin; Duijn, van Cj Hans; Niessner, Jennifer; Hassanizadeh, S. Majid

doi:10.1016/j.advwatres.2008.12.006

Cited by 30 publications

(36 citation statements)

References 23 publications

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“…The original idea was that this new formulation including interfacial area could account for the full hysteretic nature of the water retention characteristic. However, when analysing the model (Pop et al 2009) it was shown that for any fixed point x 0 in space, there exists a unique P c -S w curve which satisfies…”

Section: Interfacial Area Modelmentioning

confidence: 99%

“…Case (iv) is governed by the general theory in Duijn and Peletier (1977) whereas for Case (iii) we need to recall some of the arguments from Pop et al (2009), Duijn andNeef (1998) and Duijn and Peletier (1977). To show how to construct the solutions in general, let us briefly consider the unconventional Case (iii).…”

Section: Construction Of Combined Solution For Initial Conditions On mentioning

confidence: 99%

“…Although redistribution results arising from interfacial area models (Pop et al 2009) are available for general pressure and saturation initial conditions, they do not specify any directions in the induced P c -S w curves. Thus they cannot describe hysteretic redistribution in the broadest sense.…”

Section: Scanning Curvesmentioning

confidence: 99%

“…Following Philip (1991) , Raats and van Duijn (1995) and Pop et al (2009) we make the effect of hysteresis explicit in cases of horizontal redistribution. We show that the extended playtype hysteresis as described by (2.2), with H (S w ) satisfying (2.7), covers all these cases.…”

Section: Redistributionmentioning

confidence: 99%

“…In Pop et al (2009) and Duijn and Neef (1998) mathematical aspects of the Philip redistribution [Case (i)] are considered. Before analysing the other cases in detail, observe that for the extended model (S(η), u(η)) ∈ H implies that H (S(η)) + u(η) is constant which means that u = − dH dS (S)S .…”

Section: Construction Of Combined Solution For Initial Conditions On mentioning

confidence: 99%

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Hysteresis and Horizontal Redistribution in Porous Media

Duijn

Mitra

2018

Transp Porous Med

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It is well known that multiphase flow in porous media exhibits hysteretic behaviour. This is caused by different fluid-fluid behaviour if the flux reverses. For example, for flow of water in unsaturated soils the process of imbibition and drainage behaves differently. In this paper we study a new model for hysteresis that extends the current playtype hysteresis model in which the scanning curves between drainage and imbibition are vertical. In our approach the scanning curves are non-vertical and can be constructed to approximate experimentally observed scanning curves. Furthermore our approach does not require any book-keeping when the flux reverses at some point in space. Specifically, we consider the problem of horizontal redistribution to illustrate the strength of the new model. We show that all cases of redistribution can be handled, including the unconventional flow cases. For an infinite column, our analysis involves a self-similar transformation of the equations. We also present a numerical approach (L-scheme) for the partial differential equations in a finite domain to recover all redistribution cases of the infinite column provided time is not too large.

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Section: Interfacial Area Modelmentioning

confidence: 99%

Section: Construction Of Combined Solution For Initial Conditions On mentioning

confidence: 99%

Section: Scanning Curvesmentioning

confidence: 99%

Section: Redistributionmentioning

confidence: 99%

Section: Construction Of Combined Solution For Initial Conditions On mentioning

confidence: 99%

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Hysteresis and Horizontal Redistribution in Porous Media

Duijn

Mitra

2018

Transp Porous Med

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Revisiting the horizontal redistribution of water in soils: Experiments and numerical modeling

Zhuang

Hassanizadeh

Kleingeld

et al. 2017

Water Resources Research

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A series of experiments and related numerical simulations were carried out to study one‐dimensional water redistribution processes in an unsaturated soil. A long horizontal Plexiglas box was packed as homogenously as possible with sand. The sandbox was divided into two sections using a very thin metal plate, with one section initially fully saturated and the other section only partially saturated. Initial saturation in the dry section was set to 0.2, 0.4, or 0.6 in three different experiments. Redistribution between the wet and dry sections started as soon as the metal plate was removed. Changes in water saturation at various locations along the sandbox were measured as a function of time using a dual‐energy gamma system. Also, air and water pressures were measured using two different kinds of tensiometers at various locations as a function of time. The saturation discontinuity was found to persist during the entire experiments, while observed water pressures were found to become continuous immediately after the experiments started. Two models, the standard Richards equation and an interfacial area model, were used to simulate the experiments. Both models showed some deviations between the simulated water pressures and the measured data at early times during redistribution. The standard model could only simulate the observed saturation distributions reasonably well for the experiment with the lowest initial water saturation in the dry section. The interfacial area model could reproduce observed saturation distributions of all three experiments, albeit by fitting one of the parameters in the surface area production term.

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Influence of the boundary conditions on capillary flow dynamics and liquid distribution in a porous medium

Markicevic

Zand

et al. 2011

AIChE Journal

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After depositing a wetting liquid onto a porous medium surface, and under the influence of the capillary pressure, the liquid is imbibed into the porous medium creating a wetted imprint. The flow within the porous medium does not cease once all the liquid is imbibed but continues as a secondary capillary flow, where the liquid flows from large pores into small pores along the liquid interface. The flow is solved using the capillary network model, and the influence of the boundary condition on the liquid distribution within the porous medium is investigated. The pores at the porous medium boundaries can be defined as open or closed pores, where an open pore is checked for the potential threshold condition for flow to take place. In contrast, the closed pore is defined as a static entity, in which the potential condition for flow to take place is never satisfied. By defining the pores at distinct porous medium boundaries as open or closed, one is able to obtain a very different liquid distribution within the porous medium. The liquid saturation profiles along the principal flow direction, ranging from constant to steadily decreasing, to the profile with a local maximum, are found numerically. It is shown that these saturation profiles are also related to the geometrical dimension that is perpendicular to the flow principal direction, and changing the boundary type from open to closed allows the liquid distribution within the porous medium to be controlled. In addition to the liquid distribution, the influence of the boundary conditions on capillary pressure and relative permeability is investigated, where both parameters are not influenced by variation of the boundary condition types. © 2011 American Institute of Chemical Engineers AIChE J, 2012

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Horizontal redistribution of fluids in a porous medium: The role of interfacial area in modeling hysteresis

Cited by 30 publications

References 23 publications

Hysteresis and Horizontal Redistribution in Porous Media

Hysteresis and Horizontal Redistribution in Porous Media

Revisiting the horizontal redistribution of water in soils: Experiments and numerical modeling

Influence of the boundary conditions on capillary flow dynamics and liquid distribution in a porous medium

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