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One-dimensional uniform and time varying solute dispersion along transient groundwater flow in a semi-infinite aquifer

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An analytical solution for the space-time variation of contaminant concentration in one-dimensional transient groundwater flow in a homogenous semi-infinite aquifer, subjected to time-dependent source contamination, is derived. The uniform and time varying dispersion along transient groundwater flow is investigated under two conditions. First, the flow velocity distribution in the aquifer is considered as a sinusoidally varying function, and second, the flow velocity distribution is treated as an exponentially increasing function of time. It is assumed that initially the aquifer is not solute free, so the initial background concentration is considered as an exponentially decreasing function of the space variable which is tending to zero at infinity. It is assumed that dispersion is directly proportional to the square of the velocity, noting that experimental observations indicate that dispersion is directly proportional to the velocity with a power ranging from 1 to 2. The analytical solution is illustrated using an example and may help benchmark numerical codes and solutions.
Czasopismo
Rocznik
Strony
872--892
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
autor
autor
  • Department of Biological and Agricultural Engineering, Zachry Department of Civil Engineering, Texas A&M University, College Station, USA, vsingh@tamu.edu
Bibliografia
  • 1.Aral, M.M., and B. Liao (1996), Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficients, J. Hydrol. Eng. 1, 1, 20-32, DOI: 10.1061/(ASCE)1084-0699(1996)1:1(20).
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  • 5.Crank, J. (1975), The Mathematics of Diffusion, 2nd ed., Oxford University Press, Oxford.
  • 6.De Smedt, F. (2006), Analytical solutions for transport of decaying solutes in rivers with transient storage, J. Hydrol. 330, 3-4, 672-680, DOI: 10.1016/j.jhydrol.2006.04.042.
  • 7.Freeze, R.A., and J.A. Cherry (1979), Groundwater, Prentice-Hall, Englewood Cliffs, 604 pp.
  • 8.Ghosh, N.C., and K.D. Sharma (eds.) (2006), Groundwater Modelling and Management, Capital Publishing Co., New-Delhi.
  • 9.Jaiswal, D.K., A. Kumar, N. Kumar, and R.R. Yadav (2009), Analytical solutions for temporally and spatially dependent solute dispersion of pulse type input concentration in one-dimensional semi-infinite media, J. Hydro-Env. Res. 2, 4, 254-263, DOI: 10.1016/j.jher.2009.01.003.
  • 10.Jaiswal, D.K., A. Kumar, N. Kumar, and M.K. Singh (2011), Solute transport along temporally and spatially dependent flows through horizontal semi-infinite media: dispersion proportional to square of velocity, J. Hydrol. Eng. 16, 3, 228-238, DOI: 10.1061/(ASCE)HE.1943-5584.0000312.
  • 11.Kumar, A., D.K. Jaiswal, and N. Kumar (2010), Analytical solutions to onedimensional advection-diffusion equation with variable coefficients in semi-infinite media, J. Hydrol. 380, 3-4, 330-337, DOI: 10.1016/j.jhydrol.2009.11.008.
  • 12.Kumar, G.S., M. Sekhar, and D. Misra (2006), Time dependent dispersivity behavior of non-reactive solutes in a system of parallel fractures, Hydrol. Earth Syst. Sci. Discuss. 3, 895-923, DOI: 10.5194/hessd-3-895-2006.
  • 13.Kumar, N., and M. Kumar (1998), Solute dispersion along unsteady groundwater flow in a semi-infinite aquifer, Hydrol. Earth Syst. Sci. 2, 93-100, DOI:10.5194/hess-2-93-1998.
  • 14.Lai, S.-H., and J.J. Jurinak (1971), Numerical approximation of cation exchange in miscible displacement through soil columns, Soil Sci. Soc. Am. J. 35, 6, 894-899, DOI: 10.2136/sssaj1971.03615995003500060017x.
  • 15.Lindstrom, F.T., and L. Boersma (1989), Analytical solutions for convectivedispersive transport in confined aquifers with different initial and boundary conditions, Water Resour. Res. 25, 2, 241-256, DOI: 10.1029/WR025i002p00241.
  • 16.Mitchell, J.K. (1976), Fundamentals of Soil Behavior, JohnWiley & Sons, New York.
  • 17.Ogata, A. (1970), Theory of Dispersion in a Granular Medium: Fluid Movement in Earth Materials, US Geological Survey Professional Papers, 411-I, 34 pp.
  • 18.Sander, G.C., and R.D. Braddock (2005), Analytical solutions to the transient, unsaturated transport of water and contaminants through horizontal porous media, Adv. in Water Resour. 28, 10, 1102-1111, DOI: 10.1016/j.advwatres.2004.10.010.
  • 19.Scheidegger, A.E. (1957), The Physics of Flow through Porous Media, MacMillan, London.
  • 20.Singh, M.K., V.P. Singh, P. Singh, and D. Shukla (2009), Analytical solution for conservative solute transport in one-dimensional homogeneous porous formations with time-dependent velocity, J. Eng. Mech. 135, 9, 1015-1021,DOI: 10.1061/(ASCE)EM.1943-7889.0000018.
  • 21.Singh, M.K., S. Ahamad, and V.P. Singh (2012), Analytical solution for onedimensional solute dispersion with time-dependent source concentration along uniform groundwater flow in a homogeneous porous formation, J. Eng. Mech. 138, 8, 1045-1056, DOI: 10.1061/(ASCE)EM.1943-7889.0000384.
  • 22.Sneddon, I.N. (1974), The Use of Integral Transforms, Tata McGraw-Hill, New Delhi, 539 pp.
  • 23.Srinivasan, V., and T.P. Clement (2008), Analytical solutions for sequentially coupled one-dimensional reactive transport problems – Part I: Mathematical derivations, Adv. Water Resour. 31, 2, 203-218, DOI: 10.1016/j.advwatres.2007.08.002.
  • 24.Thangarajan, M. (ed.) (2006), Groundwater: Resource Evaluation, Augmentation, Contamination, Restoration, Modeling and Management, Capital, New Delhi.
  • 25.van Genuchten, M.Th., and W.J. Alves (1982), Analytical solutions of the onedimensional convective-dispersive solute transport equation, US Dept. of Agriculture, Techn. Bull. No. 157268.
  • 26.Wexler, E.J. (1992), Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow. In: Techniques of Water-Resources Investigations, Vol. 3, Ch. B7, U.S. Geological Survey.
  • 27.Zheng, C., and G.D. Bennett (1995), Applied Contaminant Transport Modeling: Theory and Practice, Van Nostrand-Reinhold, New York, 440 pp.
  • 28.Zoppou, C., and J.H. Knight (1999), Analytical solution of a spatially variable coefficient advection-diffusion equation in up to three dimensions, App. Math. Model. 23, 9, 667-685, DOI: 10.1016/S0307-904X(99)00005-0.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6f5ccf8c-3116-4893-a882-03f502da04be
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