Two‐Dimensional Dispersion from Strip Sources
Publication: Journal of Hydraulic Engineering
Volume 109, Issue 6
Abstract
A general mathematical model is developed for two‐dimensional, unsteady dispersion of a miscible second fluid from time‐dependent, nonuniform, and nonperiodic strip sources in steady, one‐dimensional seepage flow through a homogeneous and isotropic saturated porous medium. Longitudinal and lateral dispersions, radioactive decay, and linear adsorption are considered. In the mathematical analysis, Laplace transform and Fourier analysis techniques are used simultaneously and a general equation is obtained in an integral form for the distribution of concentration. Graphs are presented for two spedal cases of this general model. The solutions can be used to control groundwater contamination and quantitative predictions of spatial and temporal changes in groundwater quality.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abramowitz, M., and Stegun, I. A., “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” National Bureau of Standards, United States Government Printing Office, Washington, D.C., 1964.
2.
Al‐Niami, A. N. S., and Rushton, K. R., “Analysis of Flow Against Dispersion in Porous Media,” Journal of Hydrology, Vol. 33, 1977, pp. 87–97.
3.
Bachmat, Y., and Bear, J., “The General Equations of Hydrodynamic Dispersion in Homogeneous, Isotropic Porous Mediums,” Journal of Geophysical Research, Vol. 69, No. 12, 1964, pp. 2561–2567.
4.
Batu, V., “Flow Net for Unsaturated Infiltration from Strip Source,” Journal of the Irrigation and Drainage Division, ASCE, Vol. 105, No. IR3, Proc. Paper 14822, Sept., 1979, pp. 233–245.
5.
Bear, J., Dynamics of Fluids in Porous Media, American Elsevier, New York, N.Y., 1972.
6.
Bear, J., “Hydrodynamic Dispersion,” Flow Through Porous Media, Roger J. M. De Wiest, ed., Academic Press, New York, N.Y., 1969, pp. 109–199.
7.
Bruch, J. C., and Street, R. L., “Two‐Dimensional Dispersion,” Journal of the Sanitary Engineering Division, ASCE, Vol. 93, No. SA6, Proc. Paper 5636, Dec., 1967, pp. 17–39.
8.
Carslaw, H. S., and Jaeger, J. C., “Conduction of Heat in Solids,” 2nd ed., Clarendon Press, Oxford, England, 1959.
9.
Crank, J., The Mathematics of Diffusion, Oxford University Press, London, England, 1956.
10.
Churchill, R. V., Fourier Series and Boundary Value Problems, McGraw‐Hill Book Co., Inc., New York, N.Y., 1941.
11.
Fried, J. J., and Combarnous, M. A., “Dispersion in Porous Media,” Advances in Hydroscience, Vol. 7, Ven Te Chow, ed., Academic Press, New York, N.Y., 1971, pp. 169–282.
12.
Gupta, S. K., and Singh, S. R., “Analytical Solutions for Predicting Solute Movement and Their Interpretation in Reclamation,” Journal of Hydrology, Vol. 45, 1980, pp. 133–148.
13.
Hoopes, J. A., and Harleman, D. R. F., “Wastewater Recharge and Dispersion in Porous Media,” Journal of the Hydraulics Division, ASCE, Vol. 93, No. HY5, Proc. Paper 5425, Sept., 1967, pp. 51–71.
14.
Hunt, B. W., “Dispersion from Pit in Uniform Seepage,” Journal of the Hydraulics Division, ASCE, Vol. 99, No. HY1, Proc. Paper 9474, Jan., 1973, pp. 13–21.
15.
Jost, W., Diffusion in Solids, Liquids, Gases, Academis Press, New York, N.Y., 1960.
16.
Marino, M. A., “Distribution of Contaminants in Porous Media Flow,” Water Resources Research, Vol. 10, No. 5, Oct., 1974, pp. 1013–1018.
17.
Pinder, G. F., “A Galerkin‐Finite Elements Simulation of Groundwater Contamination on Long Island, New York,” Water Resources Research, Vol. 9, No. 6, Dec., 1973, pp. 1657–1669.
18.
Shen, H. T., “Transient Dispersion in Uniform Porous Media Flow,” Journal of the Hydraulics Division, ASCE, Vol. 102, No. HY6, Proc. Paper 12202, June, 1976, pp. 707–716.
19.
Spiegel, M. R., Theory and Problems of Laplace Transforms, Shaum's Outline Series, McGraw‐Hill Book Co., New York, N.Y., 1965.
20.
Tranter, C. J., Integral Transform in Mathematical Physics, Metheun Co. Ltd., London, England, 1951.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 109 • Issue 6 • June 1983
Pages: 827 - 841
Copyright
Copyright © 1983 ASCE.
History
Published online: Jun 1, 1983
Published in print: Jun 1983
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.