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Subsurface Solute Transport Models and Case Histories pp 77–119Cite as

Water Movement and Solute Transport in Unsaturated Porous Media

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Part of the book series: Theory and Applications of Transport in Porous Media ((TATP,volume 25))

Abstract

The unsaturated zone, also termed the vadose zone, is the portion of the subsurface above the groundwater table. It contains air as well as water in the pores. This zone is also high in organic matter and clay, which promotes sorption, biological degradation and transformation of contaminants. In industrial or agricultural areas, where the ground surface is contaminated by hazardouswastes or fertilizers and pesticides, the unsaturated zone may be thought of as a buffer zone, which provides protection to the underlying aquifers. Unsaturated zone is often regarded as a filter removing undesirable substances before they affect aquifers, and the hydrogeologic properties of unsaturated zone are the most important factor for groundwater deterioration induced by surface contamination (Stephens 1996; Selker et al. 1999).

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References

  • Averjanov SF (1950) About permeability of subsurface soils in case of incomplete saturation. Engineering Collection Vol VII. As quoted by PY Polubarinova-Kochina in The theory of groundwater movement (1962). Princeton University Press, Princeton, pp 19--21

    Google Scholar 

  • [Barry and Sander(1991)]{ch02:Barry1991} Barry DA, Sander GC (1991) Exact solution for water infiltration with an arbitrary surface flux or nonlinear solute adsorption. Water Resour Res 27:2667--2680

    Google Scholar 

  • [Barry et al.(1993)]{ch02:Barry1993} Barry DA, Parlange J-Y, Sander GC et al (1993) A class of exact solutions for Richards\prime equation. J Hydrol 142:29--46

    Google Scholar 

  • [Barry et al.(2005)]{ch02:Barry2005} Barry DA, Parlange J-Y, Li L et al (2005) Green--Ampt approximations. Adv Water Resour 28:1003--1009

    Google Scholar 

  • [Bear and Cheng(2010)]{ch02:Bear2010} Bear J, Cheng AH-D (2010) Modeling groundwater flow and contaminant transport. Springer, Dordrecht/Heidelberg/London/New York

    Google Scholar 

  • [Broadbridge(1990)]{ch02:Broadbridge1990} Broadbridge P (1990) Solution of nonlinear adsorption model of mixed saturated-unsaturated flow. Water Resour Res 26:2435--2443

    Google Scholar 

  • [Broadbridge and White(1988)]{ch02:Broadbridge1988} Broadbridge P, White I (1988) Constant rate rainfall infiltration: A versatile nonlinear model. 1. Analytic solution, Water Resour Res 24:145--154

    Google Scholar 

  • [Brooks and Corey(1964)]{ch02:Brooks1964} Brooks RH, Corey AT (1964) Hydraulic properties of porous media. Colo State Univ Fort Collins Hydrol Pap 3:27

    Google Scholar 

  • [Bruce and Klute(1956)]{ch02:Bruce1956} Bruce RR, Klute A (1956) The measurement of sol-water diffusivity. Soil Sci Soc Am Proc 20:458--562

    Google Scholar 

  • [Brutsaert(1967)]{ch02:Brutsaert1967} Brutsaert W (1967) Some methods of calculating unsaturated permeability. Trans ASAE 10:400--404

    Google Scholar 

  • [Brutsaert(1968)]{ch02:Brutsaert1968} Brutsaert W (1968) The permeability of a porous medium determined from certain probability laws for pore size distribution. Water Resour Res 4:425--434

    Google Scholar 

  • [Brutsaert(1976)]{ch02:Brutsaert1976} Brutsaert W (1976) The concise formulation of diffusive sorption of water in dry soil. Water Resour Res 12:1118--1124

    Google Scholar 

  • [Chahinian et al.(2005)]{ch02:Chahinian2005} Chahinian N, Moussa R, Andrieux P et al (2005) Comparison of infiltration models to simulate flood events at the field scale. J Hydrol 306:191--214

    Google Scholar 

  • [Corey(1977)]{ch02:Corey1977} Corey A (1977) Mechanics of heterogeneous fluids in porous media. Water Resources, Fort Collins

    Google Scholar 

  • [Corey(1994)]{ch02:Corey1994} Corey AT (1994) Mechanics of immiscible fluids in porous media. Water Resources, Highlands Ranch

    Google Scholar 

  • [Gandola et al.(2001)]{ch02:Gandola2001} Gandola F, Sander GC, Braddock RD (2001) One dimensional transient water and solute transport in soils. In: Ghassemi F, Post D, Sivapalan M, Vertessy R (eds) MODSIM, natural systems (Part one) vol 1, MSSANZ, Canberra

    Google Scholar 

  • [Gardner(1958)]{ch02:Gardner1958} Gardner WR (1958) Some steady state solutions of unsaturated moisture flow equations with application to evaporation from a water table. Soil Sci 85:228--232

    Google Scholar 

  • [Gelhar(1993)]{ch02:Gelhar1993} Gelhar LW (1993) Stochastic subsurface hydrology. Prentice-Hall, Englewood Clift

    Google Scholar 

  • [Green and Ampt(1911)]{ch02:Green1911} Green WH, Ampt CA (1911) Studies on soil physics: 1 flow of air and water through soils. J Agr Sci 4:1--24

    Google Scholar 

  • [Hassanizadeh et al.(2002)]{ch02:Hassanizadeh2002} Hassanizadeh SM, Celia MA, Dahle HK (2002) Dynamic effect in the capillary pressure-saturation relationship and its impacts on unsaturated flow. Vadoze Zone J1:38--57

    Google Scholar 

  • [Haverkamp et al.(1994)]{ch02:Haverkamp1994} Haverkamp R, Ross PJ, Smetten KRJ et al (1994) Three-dimensional analysis of infiltration from the disk infiltrometer. 2 Physically based infiltration equation. Water Resour Res 30:2931--2935

    Google Scholar 

  • [Ho(2001)]{ch02:Ho2001} Ho CK (2001) A semianalytical solution for steady infiltration in unsaturated fractured rock. Water Resour Res 37:2285--2289

    Google Scholar 

  • [Kao and Hunt(1996)]{ch02:Kao1996} Kao CS, Hunt JR (1996) Prediction of wetting front movement during one-dimensional infiltration into soil. Water Resour Res 32:55--64

    Google Scholar 

  • [Koo and Suh(2001)]{ch02:Koo2001} Koo M-H, Suh M-C (2001) Geotechnical and hydrogeological approaches towards conservation of Muryong Royal Tomb in Korea. Environ Geol 41:470--479

    Google Scholar 

  • [Lagan(2001)]{ch02:Lagan2001} Lagan JD (2001) Transport modeling in hydro-chemical systems. Interdisciplinary applied mathematics. Springer, New-York

    Google Scholar 

  • [Lassabat\`{e}re et al.(2006)]{ch02:Lassabatere2006} Lassabat\`{e}re L, Angulo-Jaramillo R, Soria Ugalde JM et al (2006) Beerkan estimation of soil transfer parameters through infiltration experiments -- BEST. Soil Sci Soc Am J 70:521--532

    Google Scholar 

  • [Leong and Rahardjo(1997)]{ch02:Leong1997} Leong EC, Rahardjo H (1997) Permeability functions for unsaturated soils. J Geotech Geoenviron Eng 123:1118--1126

    Google Scholar 

  • [Lessoff and Indelman(2004)]{ch02:Lessoff2004} Lessoff SC, Indelman P (2004) Analytical model of solute transport by unsteady unsaturated gravitational infiltration. J Contam Hydrol 72:85--107

    Google Scholar 

  • [Liu et al.(2002)]{ch02:Liu2002} Liu HH, Bodvarsson GS, Finsterle S (2002) A note on unsaturated flow in two-dimensional fracture networks. Water Resour Res 38:1176--1184

    Google Scholar 

  • [Mualem(1976)]{ch02:Mualem1976} Mualem Y (1976) A new model for predicating the hydraulic conductivity of unsaturated porous media. Water Resour Res 12:513--522

    Google Scholar 

  • [Nachabe et al.(1995)]{ch02:Nachabe1995} Nachabe MH, Islas AL, Illangasekare TH (1995) Analytical solutions for water flow and solute transport in the unsaturated zone. Ground Water 33(2):304--310

    Google Scholar 

  • [Narasimhan(2005)]{ch02:Narasimhan2005} Narasimhan TN (2005) Buckingham, 1907: an appreciation. Vadose Zone J 4:434--441

    Google Scholar 

  • [Neuman(1976)]{ch02:Neuman1976} Neuman ShP (1976) Wetting front pressure head in the infiltration model of Green and Ampt. Water Resour Res 12:564--566.

    Google Scholar 

  • [Neuman(2005)]{ch02:Neuman2005} Neuman ShP (2005) Trends, prospects and challenges in quantifying flow and transport through fractured rocks. Hydrogeol J 13:124--147

    Google Scholar 

  • [Ng and Menzies(2007)]{ch02:Ng2007} Ng CWW, Menzies B (2007) Advanced unsaturated soil mechanics and engineering. Taylor {&} Francis, London

    Google Scholar 

  • [Nielsen(1991)]{ch02:Nielsen1991} Nielsen DM (1991) Practical handbook of ground-water monitoring. Lewis Publishers, Chelsea

    Google Scholar 

  • [Nielsen et al.(1986)]{ch02:Nielsen1986} Nielsen DR, van Genuchten MTh, Biggar JW (1986) Water flow and solute transport processes in the unsaturated zone. Water Resour Res 22(9):89--108

    Google Scholar 

  • [Padilla et al.(1999)]{ch02:Padilla1999} Padilla IY, Yeh T-CJ, Coonklin H (1999) The effect of water content on solute transport in unsaturated porous media. Water Resour Res 35:3303--3313

    Google Scholar 

  • [Parlange(1971a)]{ch02:Parlange1971a} Parlange J-Y (1971a) Theory of water movement in soils: 1 one-dimensional absorption. Soil Sci 111:134--137

    Google Scholar 

  • [Parlange(1971b)]{ch02:Parlange1971b} Parlange J-Y (1971b) Theory of water movement in soils: 2 one-dimensional infiltration. Soil Sci 111:170--174

    Google Scholar 

  • [Parlange(1980)]{ch02:Parlange1980} Parlange J-Y (1980) Water transport in soil. Annu Rev Fluid Mech 12: 77--102

    Google Scholar 

  • [Parlange et al.(1985)]{ch02:Parlange1985} Parlange J-Y, Haverkamp R, Touma J (1985) Infiltration under ponded conditions. Part 1 optimal analytical solution and comparison with experimental observations. Soil Sci 139:305--311

    Google Scholar 

  • [Parlange et al.(1992)]{ch02:Parlange1992} Parlange J-Y, Barry DA, Haverkamp R (1992) Comment on “A simple approximate solution for horizontal infiltration in a Brook--Corey medium” by R.W. Zimmerma and G.S. Bodvarsson. Transp Porous Media 9:297--301

    Google Scholar 

  • [Parlange et al.(1997)]{ch02:Parlange1997} Parlange J-Y, Barry DA, Parlange MB (1997) New approximate analytical technique to solve Richards equation for arbitrary surface boundary conditions. Water Resour Res 33:903--906

    Google Scholar 

  • [Parlange et al.(1999)]{ch02:Parlange1999} Parlange J-Y, Hogarth WL, Barry DA (1999) Analytical approximation to the solution of Richards\prime equation with application to infiltration, ponding, and time compression approximation. Adv Water Resour 23:187--194

    Google Scholar 

  • [Parlange et al.(2002)]{ch02:Parlange2002} Parlange J-Y, Barry DA, Haverkamp R (2002) Explicite infiltration equations and the Lambert W-function. Adv Water Resour 25:1119--1124

    Google Scholar 

  • [Pease and Stormont(1996)]{ch02:Pease1996} Pease RE, Stormont JC (1996) Increasing the diversion length of capillary barriers. In: Proceedings of the HSRC/WERC joint conference of the environment, May 1996, Kansas State University, Manhattan

    Google Scholar 

  • [Philip(1957a)]{ch02:Philip1957a} Philip JR (1957a) The theory of infiltration: 1 the infiltration equation and its solution. Soil Sci 83:345--357

    Google Scholar 

  • [Philip(1957b)]{ch02:Philip1957b} Philip JR (1957b) The theory of infiltration: 4 sorptivity and algebraic infiltration equations. Soil Sci 8:257--264

    Google Scholar 

  • [Philip(1957c)]{ch02:Philip1957c} Philip JR (1957c) The theory of infiltration: 2 the profile at infinity. Soil Sci 83:435--448

    Google Scholar 

  • [Philip(1987)]{ch02:Philip1987} Philip JR (1987) The infiltration joining problem. Water Resour Res 23:2239--2245

    Google Scholar 

  • [Polyanin et al.(2005)]{ch02:Polyanin2005} Polyanin AD, Zaitsev VF, Zhurov AI (2005) Methods of solving nonlinear equations of the mathematical physics and mechanics. Fizmatlit, Moscow

    Google Scholar 

  • [Pruess(1999)]{ch02:Pruess1999} Pruess K (1999) A mechanistic model for water seepage through thick unsaturated zones of fractured rocks of low permeability. Water Resour Res 35:1039--1052

    Google Scholar 

  • [Raats and Genuchten(2006)]{ch02:Raats2006} Raats PAC, van Genuchten MTh (2006) Milestone in soil physics. Soil Sci. 171:S21--S28

    Google Scholar 

  • [Ravi and Williams(1998)]{ch02:Ravi1998} Ravi V, Williams JR (1998) Estimation of infiltration rate in the vadose zone: compilation of simple mathematical models. Report EPA/600/R-97/128a, vol 1. Environmental Protection Agency, Washington, DC

    Google Scholar 

  • [Richards(1931)]{ch02:Richards1931} Richards LA (1931) Capilary conduction of liquids through porous mediums. Physics 1:318--333

    Google Scholar 

  • [Ross and Parlange(1994)]{ch02:Ross1994} Ross PJ, Parlange JY (1994) Comparing exact and numerical solutions of Richards equation for one-dimensional infiltration and drainage. Soil Sci 157:341--344

    Google Scholar 

  • [Salvucci(1996)]{ch02:Salvucci1996} Salvucci GD (1996) Series solution for Richards equation under concentration boundary conditions and uniform initial conditions. Water Resour Res 32:2401--2407

    Google Scholar 

  • [Salvucci and Entekhabi(1994)]{ch02:Salvucci1994} Salvucci GD, Entekhabi D (1994) Explicit expression for Green-Ampt (delta function diffusivity) infiltration rate and cumulative storage. Water Resour Res 30:2661--2663

    Google Scholar 

  • [Selker et al.(1999)]{ch02:Selker1999} Selker JS, Keller CK, McCord JT (1999) Vadose zone processes. CRC Press LLC, Boca Raton

    Google Scholar 

  • [Singh(1997)]{ch02:Singh1997} Singh VP (1997) Kinematic wave modeling in water resources: environmental hydrology. Wiley, New York

    Google Scholar 

  • [Smiles et al.(1978)]{ch02:Smiles1978} Smiles DE, Philip JR, Knight LH et al (1978) Hydrodynamic dispersion during absorption of water by soil. Soil Sci. Soc Am 42:229--234

    Google Scholar 

  • [Stephens(1996)]{ch02:Stephens1996} Stephens DB (1996) Vadose zone hydrology. Lewis Publishers, New York

    Google Scholar 

  • [Van Dam et al.(2004)]{ch02:VanDam2004} Van Dam JC, De Rooij GH, Heinen M, Stagnitti F (2004) Concepts and dimensionality in modeling unsaturated water flow and solute transport. In: Feddes RA, de Rooij GH, van Dam JC (eds) Unsaturated-zone Modeling: progress, challenges and applications. Kluwer, Wageningen, pp 1--36

    Google Scholar 

  • [Van Genuchten(1980)]{ch02:VanGenuchten1980} Van Genuchten MTh (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892--898.

    Google Scholar 

  • [Van Genuchten and Nielsen(1985)]{ch02:VanGenuchten1985} Van Genuchten MTh, Nielsen DR (1985) On describing and predicting the hydraulic properties of unsaturated soil. Ann Geophys 3:615--628

    Google Scholar 

  • [Vanderborght et al.(2000a)]{ch02:Vanderborght2000a} Vanderborght J, Timmerman A, Feyen J (2000a) Solute transport for steady-state and transient flow in soils with and without macropores. Soil Sci Soc Am J 64:1305--1317

    Google Scholar 

  • [Vanderborght et al.(2000b)]{ch02:Vanderborght2000b} Vanderborght J, Jacques D, Feyen J (2000b) Deriving transport parameter from transient flow leaching experiments by approximate steady-state flow convection-dispersion models. Soil Sci Soc Am J 64:1317--1327

    Google Scholar 

  • [Vanderborght et al.(2005)]{ch02:Vanderborght2005} Vanderborght J, Kasteel R, Herbst M et al (2005) A set of analytical benchmarks to test numerical models of flow and transport in soils. Vadose Zone J 4:206--221

    Google Scholar 

  • [Wang et al.(2003)]{ch02:Wang2003} Wang Q, Horton R, Shao M (2003) Algebraic model for one-dimensional infiltration and soil water distribution. Soil Sci 168:671--676

    Google Scholar 

  • [Wang et al.(2006)]{ch02:Wang2006} Wang Q-J, Zhang J-H, Jun F (2006) An analytical method for relationship between hydraulic diffusivity and soil sorptivity. Pedosphere 16:444--450

    Google Scholar 

  • [Wang et al.(2009)]{ch02:Wang2009} Wang Q-J, Horton R, Fan J (2009) An analytical solution for one-dimensional water infiltration and redistribution in unsaturated soil. Pedosphere 19:104--110

    Google Scholar 

  • [Weight(2008)]{ch02:Weight2008} Weight WD (2008) Hydrogeology field manual, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • [Williams et al.(1998)]{ch02:Williams1998} Williams JR, Ouyang Y et al (1998) Estimation of infiltration rate in the vadose zone: application of selected mathematical models. Report EPA/600/R-97/128d, vol 2. Environmental Protection Agency, Washington, DC

    Google Scholar 

  • [Wilson and Gelhar(1981)]{ch02:Wilson1981} Wilson JL, Gelhar LW (1981) Analysis of longitudinal dispersion in unsaturated flow. The analytical method. Water Resour Res 17:122--130

    Google Scholar 

  • [Wiltshire and El-Kafri(2004)]{ch02:Wiltshire2004} Wiltshire R, El-Kafri M (2004) Non-classical and potential symmetry analysis of Richard’s equation for moisture flow in soil. J Phys A Math Gen 37:823--839

    Google Scholar 

  • [Witelski(1998)]{ch02:Witelski1998} Witelski TP (1998) Horizontal infiltration into wet soil. Water Resour Res 34:1859--1863

    Google Scholar 

  • [Witelski(2005)]{ch02:Witelski2005} Witelski TP (2005) Motion of wetting front moving into partially pre-wet soil. Adv Water Resour 28:1133--1141

    Google Scholar 

  • [Youngs(1957)]{ch02:Youngs1957} Youngs EG (1957) Moisture profiles during vertical infiltration. Soil Sci 84:283--287

    Google Scholar 

  • [Zhang et al.(2004)]{ch02:Zhang2004} Zhang O, Volker RE, Lockington DA (2004) Numerical investigation of seawater intrusion at Gooburrum, Bundaberg, Queensland, Australia. Hydrogeol J 12:674--687

    Google Scholar 

  • [Zlotnik et al.(2007)]{ch02:Zlotnik2007} Zlotnik VA, Wang T, Nieber JL (2007) Verification of numerical solutions of the Richards equation using a traveling wave solution. Adv Water Resour 30:1973--1980

    Google Scholar 

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  1. Geological Department, The Russian Academy of Sciences Institute of Environmental Geology Saint Petersburg Division Saint Petersburg State University, Sredniy Ave., 41, of 519, 199004, St. Petersburg, Russian Federation

    Vyacheslav G. Rumynin

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Rumynin, V.G. (2011). Water Movement and Solute Transport in Unsaturated Porous Media. In: Subsurface Solute Transport Models and Case Histories. Theory and Applications of Transport in Porous Media, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1306-2_2

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