An Analytical Solution of Three Dimensional Transport of Contaminants in Unsaturated Porous Media

For the validation, we assumed that a porous medium with the following arbitrary transport parameters: DL=25cm2/d, DT=5cm2/d, and v=50cm/d. All concentrations were conveniently expressed as dimensionless quantities C/C0, with C0 being equal to unity. Figures shows the solution for various radioactive decay l and time according to equation, we plot a graph for C/C0vs transverse direction (x) for different values of other depths i.e., z = 50m, y = 1, 2m, decay constant l = 0.01, 0.1, 1.0 and time t = 1, 2 years. These figures show concentration profiles obtained with solution and as well as the results obtained with the half space solutions for various times. The results are almost identical to the steady state solution given above equation. Figures illustrate solute movement as a result of diffusion from the buried solute source. In figure the concentration profile is plotted for various depths below the soil surface (z) and the transverse direction (x), whereas figure contains solute concentration profiles in the xz plane. Because the source is located close to the surface, a nonsymmetrical solute profile develops in the z direction. Figures shows the solutions for various times and decay according to equation. The solution for large times is clearly identical to the steady state.  The invasion of the solute into the medium at x > 0 and the subsequent flattering of the solute front in all the three directions can clearly be observed and figure shows concentration profiles in the transverse x direction for various values of z at t = 1 for a first and third type boundary condition.

1.           Barry, D.A., Parlange, J.Y., Sander, G.C., and M. Sivaplan (1993): A class of exact solutions for Richards equation. J. of Hydrology. 142: 29-46. 2.             Basak, P and V.V.N. Murthy, (1997): Nonlinear diffusion applied to groundwater contamination problems. J. Of Hydrology, 35: 357-363. 3.           Basak, P., and V.V.N. Murthy (1979): Determination of hydrodynamic dispersion coefficients using ‘inverfc’. Journal of hydrology. Vol. 41, pp. 43-48.  4.           Bear, J (1972): Dynamics of Fluids in Porous Media. American Elsevier, New York.  5.           Bear, J., and A. Verruijt (1990): Modelling Groundwater Flow and Pollution. D Reidel Publishing Co., Tokyo.  6.           Bitton, G., Davidson, J.M., and S.R. Farrah (1979): On the value of soil columns for assessing the transport pattern of viruses through soils – A critical outlook. Water, Air and Soil Pollution. No. 12, pp. 449-457.  7.           Brandt, A., Bresler, E., Diner, N., Ben-Asher, J., Heller, J., and D. Goldberg (1971): Infiltration from a trickle source: (i) Mathematical Models. Soil Sci. Soc. Am. Proc. 35: 675-682.  8.           Carslaw H.S. &Jeager J.C. (1947), “Conduction of Heat in solids”, Oxford University Press, P 386.  9.           Fletcher (1991), Computational techniques for fluid dynamics, 2nd edition, Springer – Verlag, Berlin.  10.        Rushton, K.R. & Chan, Y.K. (1977) Numerical pumping test analysis in unconfined aquifers. J. Irrig. Drain. Div. ASCE 103(IR1), 1-12.