Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media: A library

Hongtao WANG, Huayong WU

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PDF(343 KB)
Front. Environ. Sci. Eng. ›› 2009, Vol. 3 ›› Issue (1) : 112-128. DOI: 10.1007/s11783-008-0067-z
Research Article

Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media: A library

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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)

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Hongtao WANG, Huayong WU. Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media: A library. Front Envir Sci Eng Chin, 2009, 3(1): 112‒128 https://doi.org/10.1007/s11783-008-0067-z

References

[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[14]
DomenicoP A. An analytical model for multidimensional transport of a decaying contaminant species. J Hydrol, 1987, 91: 49–58
CrossRef Google scholar
[15]
SrinivasanV, ClementT P, LeeK K. Domenico solution-Is it valid? Ground Water, 2007, 45: 136–146
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[23]
EllsworthT R, ButtersG L. Three-dimensional analytical solutions to advection dispersion equation in arbitrary Cartisian coordinates. Water Resour Res, 1993, 29: 3215–3225
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[27]
YehG T, TsaiY J. Analytical three dimensional transient modeling of effluent discharges. Water Resour Res, 1976, 12: 533–540
CrossRef Google scholar
[28]
JonesN L, ClementT P, HansenC M. A three-dimensional analytical tool for modeling reactive transport. Ground Water, 2006, 44: 613–617
CrossRef Google scholar
[29]
GuyonnetD, NevilleC. Dimensionless analysis of two analytical solutions for 3-D solute transport in groundwater. J Contam Hydrol, 2004, 75: 141–153
CrossRef Google scholar
[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
CrossRef Google scholar

Acknowledgements

This research was supported by National Scientific Supporting Plan of China (Grand No. 2006BAC06B05).

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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