Contaminant Diffusion along uniform flow velocity with pulse type input sources in finite porous medium
DOI:
https://doi.org/10.18100/ijamec.74004Keywords:
Advection- diffusion equation, Contaminant, Hydrology, Porous mediumAbstract
Solute transport inside pore system occurs due to advection and diffusion which are the important mechanisms of contaminant transport in porous medium. Analytical solutions of one-dimensional advection-diffusion equation (the coefficient of second order space derivative being temporally dependent) are obtained in a finite domain for two sets of pulse type input boundary conditions. Initially the domain is not solute free. It is supposed uniformly distributed at the initial stage. The Laplace transform technique is used with the help of new space and time variables. The solutions are graphically illustrated and compared solute distribution for finite and semi-infinite domain.Downloads
References
Banks, R. B. and Jerasate, S. R. (1962). “Dispersion in unsteady porous media flow.” J. Hydraul. Div., 88, 1-21.
Ogata, A. and Banks, R. B., (1961), “A solution of differential equation of longitudinal dispersion in porous media”, U. S. Geol. Surv. Prof. Pap. 411, A1-A7.
Lin, S. H., (1977), “Longitudinal dispersion in porous media with variable porosity”, Journal of Hydrology, 34, 13–19.
Al-Niami, A. N. S., and Rushton, K. R. (1977). “Analysis of flow against dispersion in porous media.” Journal of Hydrology, 33, 87-97.
Harleman, D. R. F. and Rumer, R. R., (1963), “Longitudinal and Lateral Dispersion in an Isotropic Porous Medium”, Journal of Fluid Mechanics, 16(3), 385-394.
Bruch, J. C., (1970), “Two dimensional dispersion experiments in a porous medium”, Water Resources Research, 6, 791-800.
van Genuchten, M. Th. and Alves, W. J., (1982). “Analytical solutions of the one-dimensional convectivedispersive solute transport equation” U.S. Dept. Agriculture, Tech. Bull. No. 1661, 151p.
Chen, J. S. and Liu, C. W., (2011), “Generalized analytical solution for advection dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition”, Hydrology Earth Syst. Sci., 8, 4099-4120.
Tracy, Fred T. (1995). “1-D,2-D,3-D analytical solutions of unsaturated flow in groundwater.” J. Hydrology, 170, 199- 214.
Aral, M. M. and Liao, B., (1996), “Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficients”, Journal of Hydro. Engg. 1(1) 20-32.
Ataie-Ashtiani, B., Volker, R. E. and Lockington, D. A., (2001), “Tidal effects on groundwater dynamics in unconfined aquifers”, Hydrological Processes, 15(4), 655- 669.
Sander, G. C., and Braddock, R. D., (2005), “Analytical solutions to the transient, unsaturated transport of water and contaminants through horizontal porous media”, Advances in Water Resources, 28, 1102–1111.
Sirin, H. (2006). “Ground water contaminant transport by non divergence – free, unsteady, and non-stationary velocity fields.” J. Hydrology, 330, 564-572.
Chen, J. S. and Liu, C. W., (2011), “Generalized analytical solution for advection dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition”, Hydrology Earth Syst. Sci., 8, 4099-4120.
Yadav, R.R., Jaiswal, D. K. and Gulrana, 2012, “TwoDimensional Solute Transport for Periodic Flow in Isotropic Porous Media: An Analytical Solution”, Hydrological Processes, 26, pp. 3425-3433.
Jaiswal, D. K., Yadav, R. R. and Gulrana, 2013, “SoluteTransport under Fluctuating Groundwater Flow in Homogeneous Finite Porous Domain”, Journal of Hydrogeology and Hydrologic Engineering, vol. 2(1), 01- 07.
Sharma, P.K. (2013), “Temporal moments for solute transport through fractured porous media”, ISH Journal of Hydraulic Engineering, 19:3, 235-243. This journal is © Advanced Technology & Science 2013 IJAMEC, 2014, 2(4), 19–25 | 25
Jury, W. A. and Flühler, H., (1992), “Transport of chemicals through soils: Mechanisms, models, and field applications”, Advances in Agronomy, 47, 141-201.
Lapidus, L. and Amundson, N. R., (1952), “Mathematics of adsorption in beds, VI. The effects of longitudinal diffusion in ion-exchange and chromatographic columns”, Journal of Physical Chemistry, 56, 984-988.
Cherry, J. A., Gillham, R. W. and Barker, J. F., (1984), “Contaminants in groundwater-Chemical processes in Groundwater Contamination”, Washington, D. C., National Academy Press, 46-64.
Crank, J. (1975), “The mathematics of diffusion”, Oxford University Press, London.
Jaiswal, D.K., Kumar, A., Kumar, N. and Yadav, R.R., 2009, “Analytical solutions for temporally and spatially dependent solute dispersion of pulse type input concentration in one dimensional semi-infinite media”, Journal of Hydro-environment Research, 2(4), 254–263.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 International Journal of Applied Methods in Electronics and Computers
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
