Ground‐Water Contamination Due to Transient Sources of Pollution
Publication: Journal of Hydraulic Engineering
Volume 110, Issue 11
Abstract
This paper presents simple analytical solutions to predict the temporal and spatial distribution of concentrations in one, two, or three‐dimensional fully saturated uniform flow fields caused by instantaneous or finite‐time release of contaminants from a point, line, plane, or parallelepiped source in an isotropic porous medium. The effects of the nonflux boundaries provided by bedrock, water table, or ground‐water divides are accounted for by the method of images. The same technique is used to model the contribution of a constant concentration boundary such as the one provided by a fully penetrating perennial stream. Sensitivity analyses show the effect of the number of images considered and the time‐step size used to evaluate the Duhamel integral. An example is presented to demonstrate the use of the method to analyze the distribution of concentrations due to seepage from an ashpond located in a streamaquifer system.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bear, J., Dynamics of Fluids in Porous Media, American Elsevier Publishing Co., Inc., New York, N.Y., 1972.
2.
Bear, J., Hydraulics of Groundwater, McGraw‐Hill Book Co., Inc., New York, N.Y., 1979.
3.
Bredehoeft, J. D., and Pinder, G. F., “Mass Transport in Flowing Ground Water,” Water Resources Research, Vol. 9, No. 1, 1973, pp. 194–210.
4.
Cabrera, G., and Marino, M. A., “A Finite Element Model of Contaminant Movement in Groundwater,” Water Resources Bulletin, AWRA, Vol. 12, No. 2, Apr., 1976, pp. 317–335.
5.
Carslaw, H. S., and Jaeger, J. C., Conduction of Heat in Solids, 2nd Ed., Oxford University Press, London, England, 1959.
6.
Duguid, J. O., and Reeves, M., “Material Transport Through Porous Media: A Finite‐Element Galerkin Model,” Report No. ORNL‐4928, Oak Ridge National Laboratory, 1976.
7.
Guymon, L. R., Gary, “Mathematical Modeling of Movement of Dissolved Constituents in Ground‐Water Aquifers by the Finite‐Element Method,” thesis presented to the University of California, at Davis, Calif., in 1970, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
8.
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.
9.
Hunt, B. W., “Dispersive Sources in Uniform Ground Water Flow,” Journal of the Hydraulics Division, ASCE, Vol. 104, No. HY1, Proc. Paper 13467, Jan., 1978, pp. 75–85.
10.
Konikow, L. F., “Modeling Mass Transport in a Shallow Aquifer,” Transactions, American Geophysical Union, Vol. 55, No. 4, 1974.
11.
Konikow, L. F., and Bredehoeft, J. D., “Modeling Flow and Chemical Quality Changes in an Irrigated Stream‐Aquifer System,” Water Resources Research, Vol. 10, No. 3, 1974, pp. 546–562.
12.
Marino, M. A., “Longitudinal Dispersion in Saturated Porous Media,” Journal of the Hydraulics Division, ASCE, Vol. 100, No. HY1, Proc. Paper 10296, Jan., 1974, pp. 151–157.
13.
Marino, M. A., “Numerical and Analytical Solutions of Dispersion in a Finite, Adsorbing Porous Medium,” Water Resources Bulletin, AWRA, Vol. 10, No. 1, Feb., 1974, pp. 81–90.
14.
Marino, M. A., “Distribution of Contaminants in Porous Media Flow,” Water Resources Research, Vol. 10, No. 5, Oct., 1974, pp. 1013–1018.
15.
Marino, M. A., “Models of Dispersion in a Granular Medium,” Journal of Hydrology, Vol. 23, 1974, pp. 313–318.
16.
Marino, M. A., “Numerical Simulation of Contaminant Transport in Subsurface Systems,” Advances in Groundwater Hydrology, Z. A. Salem, ed., AWRA, Minneapolis, Minn., 1976, pp. 113–129.
17.
Marino, M. A., “Flow Against Dispersion in Nonadsorbing Porous Media,” Journal of Hydrology, Vol. 37, 1978, pp. 149–158.
18.
Marino, M. A., “Flow Against Dispersion in Adsorbing Porous Media,” Journal of Hydrology, Vol. 38, 1978, pp. 197–205.
19.
Marino, M. A., “Solute Transport in a Saturated‐Unsaturated Porous Medium,” Modeling, Identification, and Control in Environmental Systems, G. C. Vansteenkiste, ed., North‐Holland Publishing Co., Amsterdam, Holland, 1978, pp. 269–281.
20.
Marino, M. A., “Analysis of the Transient Movement of Water and Solutes in Stream‐Aquifer Systems,” Journal of Hydrology, Vol. 49, 1981, pp. 1–17.
21.
Marino, M. A., “Saturated‐Unsaturated Modeling of Groundwater Quality in Unconfined Aquifer Systems,” Quality of Groundwater, Studies in Environmental Science, W. van Duijvenbooden, P. Glasbergen, and H. van Lelvyveld, eds., Vol. 17, Mar., 1981, pp. 979–984.
22.
Marino, M. A., and Matanga, G. B., “A Galerkin‐Finite Element Simulation of Solute Transport in Subsurface Drainage Systems,” Finite Elements in Water Resources, C. A. Brebbia, W. G. Gray, and G. F. Pinder, eds., Ch. 1, Pentech, London, 1978, pp. 51–67.
23.
Phillips, K., and Gelhar, L. W., “Contaminant Transport to Deep Wells,” Journal of the Hydraulics Division, ASCE, Vol. 104, No. HY6, Proc. Paper 13824, June, 1978, pp. 807–819.
24.
Pinder, G. F., “A Galerkin‐Finite Element Simulation of Ground Water Contamination on Long Island, New York,” Water Resources Research, Vol. 9, No. 6, Dec., 1973, pp. 1657–1669.
25.
Prakash, A., “Convective‐Dispersion Through Adsorbing Porous Media,” Journal of the Hydraulics Division, ASCE, Vol. 102, No. HY3, Proc. Paper 11995, Mar., 1976, pp. 379–396.
26.
Prakash, A., “Convective‐Dispersion in Perennial Streams,” Journal of the Environmental Engineering Division, ASCE, Vol. 103, No. EE2, Proc. Paper 12891, Apr., 1977, pp. 321–340.
27.
Prakash, A., “Finite‐Element Solutions of the Non‐Self‐Adjoint Convective Dispersion Equation,” International Journal for Numerical Methods in Engineering, Vol. 11, No. 2, Feb., 1977, pp. 269–287.
28.
Prakash, A., “Ground‐Water Contamination Due to Vanishing and Finite‐Size Continuous Sources,” Journal of the Hydraulics Division, ASCE, Vol. 108, No. HY4, Proc. Paper 17010, Apr., 1982, pp. 572–590.
29.
Prakash, A., “Dispersion in Three Dimensions: Approximate Analytic Solutions,” by B. Sagar, discussion, Journal of Hydraulic Engineering, ASCE, Vol. 109, No. 3, Proc. Paper 16806, Mar., 1983, pp. 500–501.
30.
Reddell, D. L., and Sunada, D. K., “Numerical Simulation of Dispersion in Groundwater Aquifers,” Hydrology Paper No. 41, Colorado State University, Fort Collins, Colo., June, 1970.
31.
Rubin, J., and James, R. V., “Dispersion‐Affected Transport of Reacting Solutes in Saturated Porous Media: Galerkin Method Applied to Equilibrium Controlled Exchange in Unidirectional Steady Water Flow,” Water Resources Research, Vol. 9, Oct., 1973, pp. 1332–1356.
32.
Sagar, B., “Dispersion in Three Dimensions: Approximate Analytic Solutions,” Journal of the Hydraulics Division, ASCE, Vol. 108, No. HY1, Proc. Paper 16806, Jan., 1982, pp. 47–62.
33.
Sauty, J. P., “An Analysis of Hydrodispersive Transfer in Aquifers,” Water Resources Research, Vol. 16, No. 1, Feb., 1980, pp. 145–158.
34.
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. 707–718.
35.
Wilson, J. L., and Miller, P. J., “Two‐Dimensional Plume in Uniform Ground Water Flow,” Journal of the Hydraulics Division, ASCE, Vol. 104, No. HY4, Proc. Paper 13665, Apr., 1978, pp. 503–514.
36.
Wilson, J. L., and Miller, P. J., “Two‐Dimensional Plume in Uniform Ground Water Flow,” closure, Journal of the Hydraulics Division, ASCE, Vol. 135, No. HY12, Proc. Paper 13665, Dec., 1979, pp. 1567–1570.
37.
Wolanski, E. J., “Dispersion From Pit in Uniform Seepage,” by B. W. Hunt, discussion, Journal of the Hydraulics Division, ASCE, Vol. 99, No. HY7, Proc. Paper 9474, July, 1973, pp. 1198–1199.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 110 • Issue 11 • November 1984
Pages: 1642 - 1658
Copyright
Copyright © 1984 ASCE.
History
Published online: Nov 1, 1984
Published in print: Nov 1984
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.