A continuum model of unstable infiltration in porous media endowed with an entropy function

Beljadid, Abdelaziz; Cueto‐Felgueroso, Luis; Juanes, Rubén

doi:10.1016/j.advwatres.2020.103684

Cited by 27 publications

(29 citation statements)

References 91 publications

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“…The flow potential, Π, comprises gravitational and capillary phenomena. It is a second-gradient extension of the Richards model of unsaturated flow [2,55] that allows for unstable wetting fronts [25,26,30,56]:…”

Section: Mathematical Model Of Unsaturated Flow In Porous Mediamentioning

confidence: 99%

“…where h cap is the characteristic capillary rise, J(S w ) is the Leverett J-function [57]-a dimensionless capillary pressure function-and κ is the expansion coefficient for the second-gradient theory [30]:…”

Section: Mathematical Model Of Unsaturated Flow In Porous Mediamentioning

confidence: 99%

“…Fingering during infiltration into homogeneous sands has been extensively studied in experiments [9,[14][15][16][17][18][19][20][21][22][23][24], in numerical simulations in homogeneous soils [6,[25][26][27][28][29][30], and observed in field settings [31,32]. Controlled experiments in heterogeneous and layered soils suggest that the fingering instability persists and is not suppressed by soil heterogeneity, but rather enhanced by it [33,34].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Simulation of Unstable Preferential Flow during Water Infiltration into Heterogeneous Dry Soil

Cueto‐Felgueroso

Suárez-Navarro

et al. 2020

Water

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Water infiltration and unsaturated flow through heterogeneous soil control the distribution of soil moisture in the vadose zone and the dynamics of groundwater recharge, providing the link between climate, biogeochemical soil processes and vegetation dynamics. Infiltration into dry soil is hydrodynamically unstable, leading to preferential flow through narrow wet regions (fingers). In this paper we use numerical simulation to study the interplay between fingering instabilities and soil heterogeneity during water infiltration. We consider soil with heterogeneous intrinsic permeability. Permeabilities are random, with point Gaussian statistics, and vary smoothly in space due to spatial correlation. The key research question is whether the presence of moderate or strong heterogeneity overwhelms the fingering instability, recovering the simple stable displacement patterns predicted by most simplified model of infiltration currently used in hydrological models from the Darcy to the basin scales. We perform detailed simulations of constant-rate infiltration into soils with isotropic and anisotropic intrinsic permeability fields. Our results demonstrate that soil heterogeneity does not suppress fingering instabilities, but it rather enhances its effect of preferential flow and channeling. Fingering patterns strongly depend on soil structure, in particular the correlation length and anisotropy of the permeability field. While the finger size and flow dynamics are only slightly controlled by correlation length in isotropic fields, layering leads to significant finger meandering and bulging, changing arrival times and wetting efficiencies. Fingering and soil heterogeneity need to be considered when upscaling the constitutive relationships of multiphase flow in porous media (relative permeability and water retention curve) from the finger to field and basin scales. While relative permeabilities remain unchanged upon upscaling for stable displacements, the inefficient wetting due to fingering leads to relative permeabilities at the field scale that are significantly different from those at the Darcy scale. These effective relative permeability functions also depend, although less strongly, on heterogeneity and soil structure.

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Section: Mathematical Model Of Unsaturated Flow In Porous Mediamentioning

confidence: 99%

Section: Mathematical Model Of Unsaturated Flow In Porous Mediamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Simulation of Unstable Preferential Flow during Water Infiltration into Heterogeneous Dry Soil

Cueto‐Felgueroso

Suárez-Navarro

et al. 2020

Water

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“…The flow potential, Π (Pa), comprises gravitational and capillary phenomena. It is a second-gradient extension of the Richards model of unsaturated flow [20,[41][42][43][44][45]:…”

Section: Mathematical Model Of Unsaturated Flow In Porous Mediamentioning

confidence: 99%

“…where h cap is the characteristic capillary heigth (m), J(S w ) is the Leverett J-function [46]-a dimensionless capillary pressure function-and κ (m 3 ) is the expansion coefficient for the second-gradient theory [45]:…”

Section: Mathematical Model Of Unsaturated Flow In Porous Mediamentioning

confidence: 99%

Interplay between Fingering Instabilities and Initial Soil Moisture in Solute Transport through the Vadose Zone

Cueto‐Felgueroso

Suárez-Navarro

et al. 2020

Water

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Modeling water flow and solute transport in the vadose zone is essential to understanding the fate of soil pollutants and their travel times towards groundwater bodies. It also helps design better irrigation strategies to control solute concentrations and fluxes in semiarid and arid regions. Heterogeneity, soil texture and wetting front instabilities determine the flow patterns and solute transport mechanisms in dry soils. When water is already present in the soil, the flow of an infiltration pulse depends on the spatial distribution of soil water and on its mobility. We present numerical simulations of passive solute transport during unstable infiltration of water into sandy soils that are prone to wetting front instability. We study the impact of the initial soil state, in terms of spatial distribution of water content, on the infiltration of a solute-rich water pulse. We generate random fields of initial moisture content with spatial structure, through multigaussian fields with prescribed correlation lengths. We characterize the patterns of water flow and solute transport, as well as the mass fluxes through the soil column. Our results indicate a strong interplay between preferential flow and channeling due to fingering and the spatial distribution of soil water at the beginning of infiltration. Fingering and initial water saturation fields have a strong effect on solute diffusion and dilution into the ambient water during infiltration, suggesting an effective separation between mobile and inmobile transport domains that are controlled by the preferential flow paths due to fingering.

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A thermodynamic nonequilibrium model for preferential infiltration and refreezing of melt in snow

Moure

Jones

Pawlak

et al. 2022

Preprint

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The transport of meltwater through porous snow is a fundamental process in hydrology that remains poorly understood but essential for more robust prediction of how the cryosphere will respond under climate change. Here we propose a continuum model that resolves the nonlinear coupling of preferential melt flow and the nonequilibrium thermodynamics of ice-melt phase change at the Darcy scale. We assume that the commonly observed unstable melt infiltration is due to the gravity fingering instabililty, and capture it using the modified Richards equation that is extended with a higher-order term in saturation. Our model accounts for changes in porosity and the thermal budget of the snowpack caused by melt refreezing at the continuum scale, based on a mechanistic estimate of the ice-water phase change kinetics formulated at the pore scale. We validate the model in 1D against field data and laboratory experiments of infiltration in snow and find generally good agreement. Compared to existing theory of stable melt infiltration, our 2D simulation results show that preferential infiltration delivers melt faster to deeper depths, and as a result, changes in porosity and temperature can occur at deeper parts of the snow. The simulations also capture the formation of vertical low porosity annulus known as ice pipes, which have been observed in the field but lack mechanistic understanding to date. Our results demonstrate how melt refreezing and unstable infiltration reshape the porosity structure of snow and impacts thermal and mass transport in highly nonlinear ways, which are not captured by simpler models.

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A continuum model of unstable infiltration in porous media endowed with an entropy function

Cited by 27 publications

References 91 publications

Numerical Simulation of Unstable Preferential Flow during Water Infiltration into Heterogeneous Dry Soil

Numerical Simulation of Unstable Preferential Flow during Water Infiltration into Heterogeneous Dry Soil

Interplay between Fingering Instabilities and Initial Soil Moisture in Solute Transport through the Vadose Zone

A thermodynamic nonequilibrium model for preferential infiltration and refreezing of melt in snow

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