Elsevier

Geoderma

Volume 70, Issues 2–4, April 1996, Pages 207-229
Geoderma

Modeling finger development and persistence in initially dry porous media

https://doi.org/10.1016/0016-7061(95)00086-0Get rights and content

Abstract

The mechanism for the growth and persistence of gravity-driven fingered flow of water in initially dry porous media is described. A Galerkin finite element solution of the two-dimensional Richards equation with the associated parameter equations for capillary hysteresis in the water retention function is presented. A scheme for upstream weighting of internodal unsaturated hydraulic conductivities is applied to limit smearing of steep wetting fronts. The growth and persistence of a single finger in an initially dry porous media is simulated using this numerical solution scheme. To adequately simulate fingered flow, it was found that the upstream weighting factor had to be negative, meaning that the internodal unsaturated hydraulic conductivities were weighted more by the downstream node. It is shown that the growth and persistence of a finger is sensitive to the character of the porous media water retention functions. For porous media where the water-entry capillary pressure on the main wetting function is less than the air-entry capillary pressure on the main drainage function, a small perturbation will grow into a finger, and during sequential drainage and wetting the finger will persist. In contrast, for porous media where the water-entry capillary pressure on the main wetting function is greater than the air-entry capillary pressure on the main drainage function, the same small perturbation will dissipate by capillary diffusion. The finger widths derived from the numerical simulation are similar to those predicted by analytical theory.

References (45)

  • HillS.

    Channeling in packed columns

    Chem. Eng. Sci.

    (1952)
  • LiuY. et al.

    Formation and persistence of fingered flow in coarse grained soils under different moisture contents

    J. Hydrol.

    (1994)
  • PiniG. et al.

    Is simple diagonal scaling the best preconditioner for conjugate gradients on supercomputers?

    Adv. Water Resour.

    (1990)
  • BakerR.S. et al.

    Laboratory tests of a theory of fingering during infiltration into layered soils

    Soil Sci. Soc. Am. J.

    (1990)
  • CeliaM.A. et al.

    A general mass conservative numerical solution for the unsaturated flow equation

    Water Resour. Res.

    (1990)
  • ChangW.-L. et al.

    Fractal description of wetting front instability in layered soils

    Water Resour. Res.

    (1994)
  • ChuokeR.L. et al.

    The instability of slow, immiscible, viscous liquid-liquid displacements in permeable media

    Trans. Am. Inst. Min. Metall. Pet. Eng.

    (1959)
  • DalenV.

    Immiscible flow by finite elements

  • DimentG.A. et al.

    Stability analysis of water movement in unsaturated porous materials. 2. Numerical studies

    Water Resour. Res.

    (1983)
  • DimentG.A. et al.

    Stability analysis of water movement in unsaturated porous materials. 3. Experimental studies

    Water Resour. Res.

    (1985)
  • DimentG.A. et al.

    Stability analysis of water movement in unsaturated porous materials. I. Theoretical considerations

    Water Resour. Res.

    (1982)
  • GlassR.J. et al.

    Wetting front instability. 1. Theoretical discussion and dimensional analysis

    Water Resour. Res.

    (1989)
  • GlassR.J. et al.

    Wetting front instability. 2. Experimental determination of relationships between system parameters and two-dimensional unstable flow field behavior in initially dry porous media

    Water Resour. Res.

    (1989)
  • GlassR.J. et al.

    Mechanism for finger persistence in homogeneous, unsaturated, porous media: Theory and verification

    Soil Sci.

    (1989)
  • GlassR.J. et al.

    Wetting front instability in unsaturated porous media: A three-dimensional study in initially dry soils

    Transp. Porous Media

    (1990)
  • GuptaS.P. et al.

    An experimental study of immiscible displacement with an unfavorable mobility ratio in porous media

    Water Resour. Res.

    (1974)
  • HansenR. et al.

    An operator splitting technique for two-phase immiscible flow dominated by gravity and capillary forces

  • HillD.E. et al.

    Wetting front instability in layered soils

  • HuangK. et al.

    An Eulerian-Lagrangian approach with an adaptively corrected method of characteristics to simulate variably saturated water flow

    Water Resour. Res.

    (1994)
  • KaluarachchiJ.J. et al.

    An efficient finite element method for modeling multiphase flow

    Water Resour. Res.

    (1989)
  • LiuY. et al.

    Hysteretic finger phenomena in dry and wetted sands

  • LuT.X. et al.

    Water movement in glass bead porous media, I. Experiments of capillary rise and hysteresis

    Water Resour. Res.

    (1994)
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