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Frontiers of Environmental Science & Engineering

ISSN 2095-2201

ISSN 2095-221X(Online)

CN 10-1013/X

Postal Subscription Code 80-973

2018 Impact Factor: 3.883

Front Envir Sci Eng Chin    2009, Vol. 3 Issue (1) : 112-128    https://doi.org/10.1007/s11783-008-0067-z
Research Article |
Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media: A library
Hongtao WANG(), Huayong WU
Department of Environmental Science and Engineering, Tsinghua University
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Abstract

The purpose of this study is to present a library of analytical solutions for the three-dimensional contaminant transport in uniform flow field in porous media with the first-order decay, linear sorption, and zero-order production. The library is constructed using Green's function method (GFM) in combination with available solutions. The library covers a wide range of solutions for various conditions. The aquifer can be vertically finite, semi-infinitive or infinitive, and laterally semi-infinitive or infinitive. The geometry of the sources can be of point, line, plane or volumetric body; and the source release can be continuous, instantaneous, or by following a given function over time. Dimensionless forms of the solutions are also proposed. A computer code FlowCAS is developed to calculate the solutions. Calculated results demonstrate the correctness of the presented solutions. The library is widely applicable to solve contaminant transport problems of one- or multiple- dimensions in uniform flow fields.

Keywords solution library      contaminant transport      analytical solution      dispersion and advection      porous media      type curve      Green's function method (GFM)     
Corresponding Authors: WANG Hongtao,Email:htwang@tsinghua.edu.cn   
Issue Date: 05 March 2009
 Cite this article:   
Hongtao WANG,Huayong WU. Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media: A library[J]. Front Envir Sci Eng Chin, 2009, 3(1): 112-128.
 URL:  
http://academic.hep.com.cn/fese/EN/10.1007/s11783-008-0067-z
http://academic.hep.com.cn/fese/EN/Y2009/V3/I1/112
directionconditiondirectional solution
xC|x±=0-<x<+Gx=12πDx(t-τ)exp?{-[(x-x')-u(t-τ)]24Dx(t-τ)}
C|x=0={C0, (y,z)source0, otherwise0<x<+Gx=x-x'2πDx(t-τ)exp?{-[x-x'-u(t-τ)]24Dx(t-τ)}
yC|y±=0-<y<+Gy=12πDy(t-τ)exp?[-(y-y')24Dy(t-τ)]
C|y=0={C0, (x,z)source0, otherwise0<y<+Gy=y-y'2πDy(t-τ)exp?[-(y-y')24Dy(t-τ)]
zC|z±=0-<z<+Gz=12πDz(t-τ)exp?[-(z-z')24Dz(t-τ)]
?C/?z|z=0=0C|z+=00z<+Gz=12πDz(t-τ){exp?[-(z-z')24Dz(t-τ)]+exp?[-(z+z')24Dz(t-τ)]}
?C/?z|z=0=0?C/?z|z=b=00zbGz=1b{1+2m=1cos?mπ(z0-z')bcos?mπ(z-z')bexp?[-Dzn2π2b2(t-τ)]}
C|z=0={C0, (x,y)source0, otherwise0<z<+Gz=z-z'2πDz(t-τ)exp?[-(x-x')24Dz(t-τ)]
Tab0  Directional solutions for the instantaneous point sources
Fig0  Schematic representation of imaging method near a linear boundary
1 ZhengC, BennettG D. Applied Contaminant Transport Modeling. New York, USA: John Wiley & Sons, Inc., 2002
2 WangH T. Dynamics of Fluid Flow and Contaminant Transport in Porous Media. Beijing: Higher Education Press, 2008(in Chinese)
3 ClearyR W, AdrianD D. Analytical solution of the convective-dispersive equation for cation adsorption in soils. Soil Sci Soc Amer Proc , 1973, 37: 197–199
4 SautyJ P, PierreJ. Analysis of hydro-dispersive transfer in aquifers. Water Resour Res , 1980, 16: 145–158
doi: 10.1029/WR016i001p00145
5 Van GenuchtenM T. Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-order decay. J Hydrol , 1981, 49: 213–233
doi: 10.1016/0022-1694(81)90214-6
6 HuntB W. Dispersive sources in uniform groundwater flow. ASCE J Hydraul Div , 1978, 104(HY1): 75–85
7 LatinopoulosP, TolikasD, MylopoulosY. Analytical solutions for two-dimensional chemical transport in aquifer. J Hydrol , 1988, 98: 11–19
doi: 10.1016/0022-1694(88)90202-8
8 WilsonJ L, MillerP J. Two-dimensional plume in uniform ground-water flow. ASCE J Hydraul Div , 1978, 4: 503–514
9 BatuV. A generalized two-dimensional analytical solute transport model in bounded media for flux-type finite multiple sources. Water Resour Res , 1993, 29: 2881–2892
doi: 10.1029/93WR00977
10 BatuV. A generalized two-dimensional analytical solution for hydrodynamic dispersion in bounded media with the first-type boundary condition at the source. Water Resour Res , 1989, 25: 1125–1132
doi: 10.1029/WR025i006p01125
11 QuezadaC R, ClementT P, LeeK K. Generalized solution to multi-dimensional multi-species transport equations coupled with a first-order reaction network involving distinct retardation factors. Adv Water Res , 2004, 27: 508–521
12 SrinivasanV, ClementT P. Analytical solutions for sequentially coupled one-dimensional reactive transport problems-Part I: Mathematical derivations. Adv Water Res , 2008a, 31: 203–218
doi: 10.1016/j.advwatres.2007.08.002
13 SrinivasanV, ClementT P. Analytical solutions for sequentially coupled one-dimensional reactive transport problems-Part II: Special cases, implementation and testing. Adv Water Res , 2008b, 31: 219–232
doi: 10.1016/j.advwatres.2007.08.001
14 DomenicoP A. An analytical model for multidimensional transport of a decaying contaminant species. J Hydrol , 1987, 91: 49–58
doi: 10.1016/0022-1694(87)90127-2
15 SrinivasanV, ClementT P, LeeK K. Domenico solution-Is it valid? Ground Water , 2007, 45: 136–146
doi: 10.1111/j.1745-6584.2006.00281.x
16 NevilleC J. Compilation of Analytical Solutions for Solute Transport in Uniform Flow, S.S. Bethesda, MD, USA: Papadopus & Associates, 1994
17 LeijF J, SkaggsT H, van GenuchtenM T. Analytical solutions for solute transport in three- dimensional semi-infinite porous media. Water Resour Res , 1991, 27(10): 2719–2733
doi: 10.1029/91WR01912
18 LeijF J, TorideN, van GenuchtenM T. Analytical solutions for non-equilibrium solute transport in three-dimensional porous media. J Contam Hydrol , 1993, 151: 193–228
19 LeijF J, PriesackE, SchaapM G. Solute transport modeled with Green's functions with application to persistent solute sources. J Contam Hydrol , 2000, 41: 155–173
doi: 10.1016/S0169-7722(99)00062-5
20 ParkE, ZhanH. Analytical solutions of contaminant transport from finite one-, two-, and three-dimensional sources in a finite-thickness aquifer. J Contam Hydrol , 2001, 53: 41–61
doi: 10.1016/S0169-7722(01)00136-X
21 SagarB. Dispersion in three dimensions: Approximate analytic solutions. ASCE J Hydraul Div , 1982, 108(HY1): 47–62
22 GoltzM N, RobertsP V. Three-dimensional solutions for solute transport in an infinite medium with mobile and immobile zones. Water Resour Res , 1986, 22(7): 1139–1148
doi: 10.1029/WR022i007p01139
23 EllsworthT R, ButtersG L. Three-dimensional analytical solutions to advection dispersion equation in arbitrary Cartisian coordinates. Water Resour Res , 1993, 29: 3215–3225
doi: 10.1029/93WR01293
24 ChrysikopoulosC V. Three-dimensional analytical models of contaminant transport from nonaqueous phase liquid pool dissolution in saturated subsurface formations. Water Resour Res , 1995, 31: 1137–1145
doi: 10.1029/94WR02780
25 SimY, ChrysikopoulosC V. Analytical solutions for solute transport in saturated porous media with semi-infinite or finite thickness. Adv Water Res , 1999, 22(5): 507–519
doi: 10.1016/S0309-1708(98)00027-X
26 LuoJ, CirpkaO A, FienenM N, WuW M, MehlhornT L, CarleyJ, JardineP M, CriddleC S, KitanidisP K. A parametric transfer function methodology for analyzing reactive transport in nonuniform flow. J Contam Hydrol , 2006, 83: 27–41
doi: 10.1016/j.jconhyd.2005.11.001
27 YehG T, TsaiY J. Analytical three dimensional transient modeling of effluent discharges. Water Resour Res , 1976, 12: 533–540
doi: 10.1029/WR012i003p00533
28 JonesN L, ClementT P, HansenC M. A three-dimensional analytical tool for modeling reactive transport. Ground Water , 2006, 44: 613–617
doi: 10.1111/j.1745-6584.2006.00206.x
29 GuyonnetD, NevilleC. Dimensionless analysis of two analytical solutions for 3-D solute transport in groundwater. J Contam Hydrol , 2004, 75: 141–153
doi: 10.1016/j.jconhyd.2004.06.004
30 BearJ. Dynamics of Fluids in Porous Media. New York, USA: Elsevier, 1972
31 HuyakornP, UngsM, MulkeyL, SudickyE. A three-dimensional analytical method for predicting leachate migration. Ground Water , 1987, 25(5): 588–598
doi: 10.1111/j.1745-6584.1987.tb02889.x
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