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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

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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 Author(s): 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:  
https://academic.hep.com.cn/fese/EN/10.1007/s11783-008-0067-z
https://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→+∞=00≤z<+∞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=00≤z≤bGz=1b{1+2∑m=1∞cos?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
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