Air and water flows in a vertical sand column

[1] The unsteady state drainage of water from a vertical sand column with and without a finer layer on the top was studied theoretically and experimentally to investigate the airflow generated by the finer layer. The sand column, saturated at its lower portion and initially in the condition of hydrostatic equilibrium, is drained at its bottom at constant head. The results show that significant vacuum can be generated in the vadose zone of the column with a finer layer on the top. The vacuum increases quickly in the earlier stage of the drainage, reaches a maximum, and gradually becomes zero. Because of the effect of the vacuum in the vadose zone, water is held in and the cumulative outflow from the column with the finer layer is much smaller than without the layer during most of the drainage process. Ordinary differential equations (ODE), which require only saturated hydraulic properties of the porous media, are derived to predict the location of the surface of saturation and vacuum in the vadose zone in air-water two-phase flow. The solutions of ODE match very satisfactorily with the experimental data and give better results than TOUGH2.

[1]  J. Parlange,et al.  Application and improvement of a recent approximate analytical solution of Richards' Equation , 2000 .

[2]  Experimental and Numerical Study of Column Drainage , 1967 .

[3]  A. Szymkiewicz.  Approximation of internodal conductivities in numerical simulation of one‐dimensional infiltration, drainage, and capillary rise in unsaturated soils , 2009 .

[4]  U. Kroszynski.  Flow in a vertical porous column drained at its bottom at constant flux , 1975 .

[5]  Hailong Li,et al.  Breathing of coastal vadose zone induced by sea level fluctuations , 2004 .

[6]  Charles R. Faust,et al.  Simulation of three‐dimensional flow of immiscible fluids within and below the unsaturated zone , 1989 .

[7]  Alain Bourgeat,et al.  TWO-PHASE FLOW IN HETEROGENEOUS POROUS MEDIA , 1991 .

[8]  A. Arbhabhirama,et al.  Approximate solutions for nonsteady column drainage , 1973 .

[9]  Y. Yortsos,et al.  On the exactly solvable equation$S_t = [ ( \beta S + \gamma )^{ - 2} S_x ]_x + \alpha ( \beta S + \gamma )^{ - 2} S_x $ Occurring in Two-Phase Flow in Porous Media , 1982 .

[10]  J. Parlange,et al.  COMPARING EXACT AND NUMERICAL SOLUTIONS OF RICHARDS' EQUATION FOR ONE‐DIMENSIONAL INFILTRATION AND DRAINAGE , 1994 .

[11]  J. Jiao,et al.  One‐dimensional airflow in unsaturated zone induced by periodic water table fluctuation , 2005 .

[12]  Charles R. Faust,et al.  Transport of Immiscible Fluids Within and Below the Unsaturated Zone: A Numerical Model , 1985 .

[13]  M. Celia,et al.  A General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation , 1990 .

[14]  J. Parker.  Multiphase flow and transport in porous media , 1989 .

[15]  G. Vachaud,et al.  Effects of air pressure on water flow in an unsaturated stratified vertical column of sand , 1973 .

[16]  Michel Vauclin,et al.  A note on estimating finite difference interblock hydraulic conductivity values for transient unsaturated flow problems , 1979 .

[17]  E. Youngs,et al.  Fundamentals of Soil Physics. , 1982 .

[18]  Dmitri Kavetski,et al.  Noniterative time stepping schemes with adaptive truncation error control for the solution of Richards equation , 2002 .

[19]  M. Vauclin.  Flow of Water and Air in Soils: Theoretical and Experimental Aspects , 1989 .

[20]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[21]  Emil O. Frind,et al.  Two‐phase flow in heterogeneous porous media: 1. Model development , 1991 .

[22]  Myron B. Allen,et al.  A Finite-Element Collocation Method for Variably Saturated Flow in Two Space Dimensions , 1986 .

[23]  H. J. Morel-Seytoux,et al.  Two-Phase Flows in Porous Media , 1973 .

[24]  R. G. Hills,et al.  Algorithms for solving Richards' equation for variably saturated soils , 1992 .

[25]  Lin A. Ferrand,et al.  Toward an improved understanding of multiphase flow in porous media , 1998 .

[26]  Hubert J. Morel-Seytoux,et al.  A Two‐Phase Numerical Model for Prediction of Infiltration: Applications to a Semi‐Infinite Soil Column , 1985 .

[27]  J. Jiao,et al.  Numerical study of airflow in the unsaturated zone induced by sea tides , 2007 .

[28]  George F. Pinder,et al.  Orthogonal collocation and alternating-direction procedures for unsaturated flow problems , 1987 .

[29]  Philip John Binning,et al.  A mass conservative numerical solution for two‐phase flow in porous media with application to unsaturated flow , 1992 .

[30]  J.-Y. Parlange,et al.  Exact nonlinear solution for constant flux infiltration , 1988 .

[31]  Cass T. Miller,et al.  Multiphase flow and transport modeling in heterogeneous porous media: challenges and approaches , 1998 .

[32]  Rainer Helmig,et al.  Numerical simulation of non-isothermal multiphase multicomponent processes in porous media.: 1. An efficient solution technique , 2002 .

[33]  M. Menziani,et al.  Analytical solutions of the linearized Richards equation for discrete arbitrary initial and boundary conditions , 2007 .

[34]  J. Parlange,et al.  AIR AND WATER FLOW IN A SEALED, PONDED VERTICAL SOIL COLUMN: EXPERIMENT AND MODEL , 1984 .

[35]  K. Pruess,et al.  TOUGH2 User's Guide Version 2 , 1999 .

[36]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[37]  Y. Mualem.  A New Model for Predicting the Hydraulic Conductivity , 1976 .

[38]  J. R. Philip.  General Method of Exact Solution of the Concentration?Dependent Diffusion Equation , 1960 .

[39]  Hussein Hoteit,et al.  Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures , 2008 .

[40]  E. Weeks.  The Lisse Effect Revisited , 2002, Ground water.

[41]  Linda M. Abriola,et al.  Mass conservative numerical solutions of the head‐based Richards equation , 1994 .

[42]  J. Parlange,et al.  New approximate analytical technique to solve Richards Equation for arbitrary surface boundary conditions , 1997 .

[43]  G. Hornberger,et al.  A Moving Boundary Model of a One‐Dimensional Saturated‐Unsaturated, Transient Porous Flow System , 1970 .

[44]  W. Kissling,et al.  The influence of airflow on the vertical infiltration of water into soil , 1992 .

[45]  J. Parlange,et al.  Exact solutions to radially symmetric two-phase flow for an arbitrary diffusivity , 2005 .

[46]  E. Youngs.  The drainage of liquids from porous materials , 1960 .

[47]  B. Mohanty,et al.  A new convergence criterion for the modified Picard iteration method to solve the variably saturated flow equation , 1996 .

[48]  S. E. Buckley,et al.  Mechanism of Fluid Displacement in Sands , 1942 .

[49]  E. C. Childs.  Dynamics of fluids in Porous Media , 1973 .

[50]  H. Bouwer,et al.  Delayed aquifer yield as a phenomenon of delayed air entry , 1978 .

[51]  Ruben Juanes,et al.  Nonlocal interface dynamics and pattern formation in gravity-driven unsaturated flow through porous media. , 2008, Physical review letters.

[52]  C. Tsakiroglou,et al.  A multi-flowpath model for the interpretation of immiscible displacement experiments in heterogeneous soil columns. , 2009, Journal of contaminant hydrology.

[53]  Airflow induced by pumping tests in unconfined aquifer with a low‐permeability cap , 2009 .

[54]  J. Jiao,et al.  Rain-induced subsurface airflow and Lisse effect , 2008 .

[55]  C. Popa,et al.  Nonlinear Multigrid Methods for Numerical Solution of the Unsaturated Flow Equation in Two Space Dimensions , 2010 .

[56]  Ken'ichirou Kosugi,et al.  Comparison of Three Methods for Discretizing the Storage Term of the Richards Equation , 2008 .

[57]  Christos Babajimopoulos,et al.  Revisiting the Douglas-Jones method for modelling unsaturated flow in a cultivated soil , 2000, Environ. Model. Softw..

[58]  Jack C. Parker,et al.  A parametric model for constitutive properties governing multiphase flow in porous media , 1987 .

[59]  P. Broadbridge,et al.  Analytical model of infiltration under constant‐concentration boundary conditions , 2010 .

[60]  L. A. Richards.  Capillary conduction of liquids through porous mediums , 1931 .

[61]  Y. Fujioka,et al.  Approximate solution of a vertical drainage problem , 1964 .

[62]  David L. Clements,et al.  On two phase filtration under gravity and with boundary infiltration: application of a bäcklund transformation , 1983 .

[63]  Vincenzo Casulli,et al.  A Nested Newton-Type Algorithm for Finite Volume Methods Solving Richards' Equation in Mixed Form , 2010, SIAM J. Sci. Comput..

[64]  K. H. Tan,et al.  Soil sampling, preparation, and analysis , 1995 .

[65]  Michal Beneš,et al.  An Improved Semi‐Analytical Solution for Verification of Numerical Models of Two‐Phase Flow in Porous Media , 2007 .

[66]  S. Sherif,et al.  Groundwater Hydraulics and Pollutant Transport , 1999 .

[67]  David B. McWhorter,et al.  Exact integral solutions for two‐phase flow , 1990 .

[68]  D. R. Nielsen,et al.  Two‐phase flow infiltration equations accounting for air entrapment effects , 1997 .

[69]  Jack C. Parker,et al.  Finite‐element analysis of multiphase immiscible flow through soils , 1987 .

[70]  Fred J. Molz,et al.  A physically based, two-dimensional, finite-difference algorithm for modeling variably saturated flow , 1994 .

[71]  Michel Vauclin,et al.  Experimental and numerical analysis of two-phase infiltration in a partially saturated soil , 1986 .

[72]  Mladen Jurak,et al.  Modeling and Numerical Simulations of Immiscible Compressible Two-Phase Flow in Porous Media by the Concept of Global Pressure , 2010 .

[73]  S. M. Hassanizadeh,et al.  A model for two‐phase flow in porous media including fluid‐fluid interfacial area , 2008 .