Solution of the Advection-Dispersion Equation: Continuous Load of Finite Duration
Publication: Journal of Environmental Engineering
Volume 122, Issue 9
Abstract
Field studies of solute fate and transport in streams and rivers often involve an experimental release of solutes at an upstream boundary for a finite period of time. A review of several standard references on surface-water-quality modeling indicates that the analytical solution to the constant-parameter advection-dispersion equation for this type of boundary condition has been generally overlooked. Here an exact analytical solution that considers a continuous load of finite duration is compared to an approximate analytical solution presented elsewhere. Results indicate that the exact analytical solution should be used for verification of numerical solutions and other solute-transport problems wherein a high level of accuracy is required.
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References
1.
Bear, J. (1972). Dynamics of fluids in porous media . Elsevier, New York, N.Y.
2.
Broshears, R. E., Bencala, K. E., Kimball, B. A., and McKnight, D. M. (1993). “Tracer-dilution experiments and solute-transport simulations for a mountain stream, Saint Kevin Gulch, Colorado.”Water Res. Investigative Rep. 92-4081, U.S. Geological Survey, Denver, Colo.
3.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H. (1979). Mixing in inland and coastal waters . Academic Press, San Diego, Calif.
4.
James, A. (1993). An introduction to water quality modeling, 2nd Ed., John Wiley & Sons, West Sussex, England.
5.
Maidment, D. R. (1993). Handbook of hydrology . McGraw-Hill, New York, N.Y.
6.
McCutcheon, S. C. (1989). Water quality modeling, Vol. 1, transport and surface exchange in rivers, R. H. French, ed., CRC Press, Boca Raton, Fla.
7.
Ogata, A. (1964). “Mathematics of dispersion with linear adsorption isotherm.”Profl. Paper No. 411-H, U.S. Geological Survey, Washington, D.C.
8.
Ogata, A., and Banks, R. B. (1961). “A solution of the differential equation of longitudinal dispersion in porous media.”Profl. Paper No. 411-A, U.S. Geological Survey, Washington, D.C.
9.
O'Loughlin, E. M., and Bowmer, K. H.(1975). “Dilution and decay of aquatic herbicides in flowing channels.”J. Hydrol., 26, 217–235.
10.
Rathbun, R. E. (1979). “Estimating the gas and dye quantities for modified tracer technique measurements of stream reaeration coefficients.”Water Resour. Invest., U.S. Geological Survey, 27–79.
11.
Rose, D. A.(1977). “Dilution and decay of aquatic herbicides in flowing channels—comments.”J. Hydrol., 32, 399–400.
12.
Runkel, R. L., and Bencala, K. E. (1995). “Transport of reacting solutes in rivers and streams.”Environmental hydrology, V. P. Singh, ed., Kluwer, Dordrecht, The Netherlands.
13.
Rutherford, J. C. (1994). River mixing . John Wiley & Sons, Chichester, England.
14.
Thomann, R. V., and Mueller, J. A. (1987). Principles of surface water quality modeling and control . Harper & Row, New York, N.Y.
15.
van Genuchten, M. T., and Alves, W. J. (1982). “Analytical solutions of the one-dimensional convective-dispersive solute transport equation.”Tech. Bull. 1661. U.S. Dept. of Agriculture, Washington, D.C.
16.
Walton, R., and Webb, M.(1994). “QUAL2E simulations of pulse loads.”J. Envir. Engrg., ASCE, 120(5), 1017–1031.
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Copyright © 1996 American Society of Civil Engineers.
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Published online: Sep 1, 1996
Published in print: Sep 1996
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