Dispersion in Anisotropic, Homogeneous, Porous Media
Publication: Journal of Hydraulic Engineering
Volume 111, Issue 5
Abstract
A tensor model for the dispersion coefficient for saturated flow in anisotropic, homogeneous porous media is proposed. The tensor components are evaluated from experiments with an anisotropic, homogeneous porous medium, constructed from thin, alternating layers of two types of sand, having different mean particle sizes. Tests were conducted for flow parallel, perpendicular, and inclined at 60° to the direction of the layers. The hydraulic conductivity and the longitudinal dispersion coefficient were found to be second‐rank tensors with equal and constant eccentricities and with major and minor principal axes oriented along and perpendicular to the direction of the sand layers, respectively. The lateral dispersion coefficient was found to be a second‐rank tensor whose principal axes were orthogonal to those of the hydraulic conductivity tensor and whose eccentricity increased with increasing seepage velocity. Two values of the off‐principal diagonal dispersivities were found to be nearly equal in magnitude but opposite in sign. Experimental results support the dispersion coefficient tensor model proposed in the investigation.
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References
1.
Adams, J. R., “Dispersion in Anisotropic Porous Media,” thesis presented to Michigan State University at East Lansing, Michigan, in 1966, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
2.
Anderson, M. P., “Using Models to Simulate the Movement of Contaminants through Groundwater Flow Systems,” Critical Reviews in Environmental Control, Vol. 9, Issue 2, Nov., 1979, pp. 97–156.
3.
Bear, J., “On the Tensor Form of Dispersion in Porous Media,” Journal of Geophysical Research, Vol. 66, No. 4, Apr., 1961, pp. 1185–1197.
4.
Bear, J., Dynamics of Fluids in Porous Media, American Elsevier, New York, N.Y., 1972, 764 pp.
5.
Bear, J., and Bachmat, Y., “A Generalized Theory on Hydrodynamic Dispersion in Porous Media,” International Association of Scientific Hydrology, Publication No. 72, 1967.
6.
De Josselin de Jong, G., “The Tensor Character of the Dispersion Coefficient in Anisotropic Porous Media,” First International Symposium (1969) on Fundamentals of Transport Phenomena in Porous Media, International Association of Hydraulic Research, Elsevier Publishing Co., New York, N.Y., 1972, pp. 259–267.
7.
Fattah, Q. N., “Investigation and Verification of a Model for the Dispersion Coefficient Tensor in Flow through Anisotropic Homogeneous, Porous Media with Application to Flow from a Recharge Well through a Confined Aquifer,” thesis, presented to the University of Wisconsin, at Madison, Wisconsin, in 1974, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
8.
Gelhar, L. W., Gutjahr, A. L., and Naff, R. L., “Stochastic Analysis of Macrodispersion in a Stratified Aquifer,” Water Resources Research, Vol. 15, No. 6, Dec., 1979, pp. 1387–1397.
9.
Gelhar, L. W., and Axeness, C. L., “Three‐Dimensional, Stochastic Analysis of Macrodispersion in Aquifers,” Water Resources Research, Vol. 19, No. 1, Feb., 1983, pp. 161–180.
10.
Goad, T. L., and Greenkorn, R. A., “Permeability and Dispersion during Flow in Linear, Heterogeneous, Anisotropic Porous Media,” Purdue University, Project Report No. 16060DLL, Federal Water Pollution Control Administration, U.S. Department of Interior, 1971.
11.
Greenkorn, R. A., “Matrix Properties of Porous Materials,” Proceedings, Second Symposium of Fundamentals of Transport Phenomena in Porous Media, Vol. I, University of Guelph, Ontario, Canada, Aug., 1972.
12.
Harleman, D. R. F., Mehlhorn, P. F., and Rumer, R. R., Jr., “Dispersion‐Permeability Correlation in Porous Media,” Journal of the Hydraulics Division, ASCE, No. HY2, Mar., 1963, pp. 67–85.
13.
Harleman, D. R. F., and Rumer, R. R., “Longitudinal and Lateral Dispersion in an Isotropic Porous Medium,” Journal of Fluid Mechanics, Vol. 16, Part 3, 1963, pp. 385–394.
14.
Harr, M. E., Groundwater and Seepage, McGraw‐Hill Inc., New York, N.Y., 1962.
15.
Hoopes, J. A., and Harleman, D. R. F., discussion of “Band Diffusion with Variable Parameters along Flow,” by Wen‐Hsiung Li, Journal of the Engineering Mechanics Division, ASCE, No. EM3, June, 1965, pp. 280–283.
16.
Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Elastic Body, Holden‐Day, Inc., San Francisco, Calif., 1963, 404 pp.
17.
Lenth, E. G., and Greenkorn, R. A., “An Exploratory Study of Permeability and Dispersion Phenomena in Anisotropic Porous Media,” Project Report No. 16060DLL, Federal Water Pollution Control Administration, U.S. Department of Interior, 1970.
18.
List, E. J., and Brooks, N. H., “Lateral Dispersion in Saturated Porous Media,” Journal of Geophysical Research, Vol. 72, No. 10, May, 1967, pp. 2531–2541.
19.
Molz, F. J., Guven, O., and Melville, J. G., “An Examination of Scale‐Dependent Dispersion Coefficients,” Ground Water, Vol. 21, No. 6, Nov.–Dec., 1983, pp. 715–725.
20.
Nikolaevskii, V. N., “Convective Diffusion in Porous Media,” Journal of Applied Mathematics and Mechanics, Vol. 23, No. 6, 1959, pp. 1042–1050.
21.
Nye, J. F., Physical Properties of Crystals, Clarendon Press, Oxford, England, 1957.
22.
Ogata, A., and Banks, R. B., “A Solution of the Differential Equation of Longitudinal Dispersion in Porous Media,” USGS Professional Paper 411‐A, 1961.
23.
Pickens, J. F., and Grisak, G. E., “Scale‐Dependent Dispersion in a Stratified Granular Aquifer,” Water Resources Research, Vol. 17, No. 4, Aug., 1981, pp. 1191–1211.
24.
Saffman, P. G., “A Theory of Dispersion in Porous Medium,” Journal of Fluid Mechanics, Vol. 6, Part 3, Oct., 1959, p. 321.
25.
Saffman, P. G., “Dispersion due to Molecular Diffusion and Macroscopic Mixing in Flow through a Network of Capillaries,” Journal of Fluid Mechanics, Vol. 7, Feb., 1960, p. 194.
26.
Scheidegger, A. E., “General Theory of Dispersion in Porous Media,” Journal of Geophysical Research, Vol. 66, No. 10, Oct., 1961, pp. 3273–3278.
27.
Schwarz, F. W., “Macroscopic Dispersion in Porous Media: the Controlling Factors,” Water Resources Research, Vol. 13, No. 4, Aug., 1977.
28.
Sudicky, E. A., and Cherry, J. A., “Field Observations of Tracer Dispersion under Natural Flow Conditions in an Unconfined Sandy Aquifer,” Water Pollution Research Journal of Canada, Vol. 14, 1979.
29.
Whitaker, S., “Diffusion and Dispersion in Porous Media,” Journal of the American Institute of Chemical Engineers, Vol. 13, 1967, pp. 420–427.
Information & Authors
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Published In
Journal of Hydraulic Engineering
Volume 111 • Issue 5 • May 1985
Pages: 810 - 827
Copyright
Copyright © 1985 ASCE.
History
Published online: May 1, 1985
Published in print: May 1985
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