Integral and Closed-Form Analytical Solutions to the Transport Contaminant Equation Considering 3D Advection and Dispersion
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: International Journal of Geomechanics
Volume 13, Issue 5
Abstract
Even though numerical procedures have been tremendously enhanced over the last years, analytical closed-form solutions are of special interest to water resources scientists. In general, these solutions are used to check the consistency and validate numerical routines. Bibliographical research reveals that up-to-date analytical solutions only take into account one-dimensional (1D) advection, even when three-dimensional (3D) dispersion is considered. This assumption creates an axis dependency because the flux is assumed to be parallel to one of the three possible orthogonal directions, which does not apply to all practical situations in which diagonal advection is present. In this work an analytical solution is derived for the 3D advective-dispersive equation (ADE) by means of Fourier and Laplace integral transforms. The solution allows the contaminant plume to move angularly with respect to the coordinate axes.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors acknowledge the University of Brasilia and the Brazilian Research Council (CNPq) for funding this research.
References
Bear, J. (1972). Hydraulics of groundwater, McGraw Hill, New York.
Booker, J. R., and Rowe, R. K. (1987). “One-dimensional advective–dispersive transport into a deep layer having a variable surface concentration.” Int. J. Numer. Anal. Methods Geomech., 11(2), 131–141.
Chakraborty, R., and Ghosh, A. (2011). “Finite difference method for computation of 1D pollutant migration through saturated homogeneous soil media.” Int. J. Geomech., 11(1), 12–22.
Domenico, P. A., and Robbins, G. A. (1985). “A new method of contaminant plume analysis.” Ground Water, 23(4), 476–485.
El-Zein, A. (2003). “Contaminant transport in fissured soils by three-dimensional boundary elements.” Int. J. Geomech., 3(1), 75–83.
El-Zein, A. H., Carter, J. P., and Airey, D. W. (2005). “Multiple-porosity contaminant transport by finite-element method.” Int. J. Geomech., 5(1), 24–34.
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.” J. Hydro-Environ. Res., 2(4), 254–263.
Leij, F. J., and Dane, J. H. (1990). “Analytical solutions of the one-dimensional advection equation and two- or three-dimensional dispersion equation.” Water Resour. Res., 26(7), 1475–1482.
Leij, F. J., Skaggs, T. H., and Van Genuchten, M. Th. (1991). “Analytical solutions for solute transport in three-dimensional semi-infinite porous media.” Water Resour. Res., 27(10), 2719–2733.
Mathai, A. M., Saxena, R. K., and Haubold, H. J. (2010). The H-function: Theory and applications, Springer, New York.
Ogata, A. (1970). “Theory of dispersion in granular medium.” U.S. Geol. Survey Series 411-I, U.S. Govt. Printing Office, Washington, DC.
Ogata, A., and Banks, R. B. (1961). “A solution of the differential equation of longitudinal dispersion in porous media; fluid movement in earth materials.” U.S. Geol. Survey Series 411-A, U.S. Govt. Printing Office, Washington, DC.
Sheng, D., and Smith, D. W. (2002). “2D finite element analysis of multicomponent contaminant transport through soils.” Int. J. Geomech., 2(1), 113–134.
Van Genuchten, M. T., and Alves, W. J. (1982). “Analytical solutions of the one-dimensional convective-dispersive solute transport equation.” Rep. 1661, U.S. Dept. of Agriculture, Washington, DC.
Wexler, E. J. (1992). “Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow.” Chapter 3, Applications of hydraulics, USGS Publishing Network, Washington, DC.
Winter, T. C., Harvey, J. W., Franke, O. L., and Alley, W. M. (1998). “Ground water and surface water a single resource.” U.S. Geol. Surv. Circular 1139, U.S. Dept. of the Interior, Denver.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 13 • Issue 5 • October 2013
Pages: 686 - 691
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Sep 23, 2011
Accepted: Aug 9, 2012
Published online: Aug 23, 2012
Published in print: Oct 1, 2013
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.