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

Abstract

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.

Simulation of the Infiltration of Fractured Rock in the Unsaturated Zone

“…If they are slight (<10% of the overall aperture), sheet flow remains prominent, in agreement with the conclusion of Cey et al [82]. When they are larger, fingering destabilises the wetting front and water flow in the individual fingers is accelerated (Glass [29], Kawamoto and Miyazaki [83], Nicholl and Glass [84], Cueto-Felgueroso et al [85]).…”

A Thermodynamic Nonequilibrium Model for Preferential Infiltration and Refreezing of Melt in Snow

“…3 of 26 simpler formulation while remaining robust in producing infiltration patterns consistent with experimental observations (Beljadid et al, 2020;Cueto-Felgueroso & Juanes, 2009b;Cueto-Felgueroso et al, 2020a, 2020b. The model accounts for the phase change process of melt refreezing to ice by (a) modeling a decrease in local snow porosity due to refreezing and (b) updating the thermal budget based on the release of latent heat and heat transfer between ice and water phases.…”

“…The isothermal version of our model (T i = T w = 0°C, thus solving only Equations 25 and 26) is equivalent to that proposed by Juanes (2008, 2009b);Cueto-Felgueroso et al (2020a, 2020b; Beljadid et al (2020), and we refer the reader to this body of literature for further details. Here, we briefly discuss the results of isothermal infiltration, simulated with the proposed model applied to real snow properties.…”

“…Such extension has been shown to give rise to a gravity fingering instability and requires only a small number of model parameters. In comparison to other recent models of unstable meltwater infiltration (Hirashima et al., 2014; Leroux et al., 2020; Leroux & Pomeroy, 2017), the infiltration model we adopt has a simpler formulation while remaining robust in producing infiltration patterns consistent with experimental observations (Beljadid et al., 2020; Cueto‐Felgueroso & Juanes, 2009b; Cueto‐Felgueroso et al., 2020a, 2020b). The model accounts for the phase change process of melt refreezing to ice by (a) modeling a decrease in local snow porosity due to refreezing and (b) updating the thermal budget based on the release of latent heat and heat transfer between ice and water phases.…”

Fluid flow and strain localisation in partially saturated porous media

“…The study of this phenomenon is of interest in several circumstances as the natural water infiltration of unsaturated soils, where air is the displaced phase, see e.g. [2,3], or the sealing tightness of the caprock covering aquifer reservoir rocks used in underground gas storage or CO 2 sequestration applications, see e.g. [4].…”