Nonlinear Flow Toward Wells
Publication: Journal of Hydraulic Engineering
Volume 115, Issue 2
Abstract
A comprehensive review of the validity of Darcy's law is presented with the emphasis on the necessity for a nonlinear flow law for Reynolds numbers especially greater than one. Subsequently, the nonequilibrium formula is developed for nonlinear flow and is useful in determining either the aquifer parameters from the time drawdown observations or in predicting the drawdown variations in a confined aquifer tapped by a fully penetrating well. The derivation of the necessary formula is based on the continuity equation in terms of the specific yield and a nonlinear flow law which is adopted in this paper as the exponential law. The general solution of nonlinear flow toward wells reduces to the Theis nonequilibrium equation when the turbulence exponent is taken as equal to one. Initial and moderate portions of nonlinear flow type curves prove to be very important for the estimation of aquifer parameters, especially for the turbulence exponent and for the nonlinear flow transmissivity. It is observed that even in the same aquifer with a constant pump discharge, differences in the observation well distances to the main well give rise to different type curves. The late time drawdown data can be used only for determining the conventional linear flow related parameters such as the storativity and the transmissivity. Finally, the application of the methodology has been performed for some field data available in the literature.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anandakrishnan, M., and Varadarajulu, F. H. (1963). “Laminar and turbulent flow of water through sand.” J. Soil Mech. and Found. Engrg. Div., ASCE, 89(5), 1–15.
2.
Bakmeteff, B. A., and Feodoroff, N. V. (1937). “Flow through granular media.” J. Applied, Mech., (4A), 97–104.
3.
Basak, P. (1977). “Non‐Darcy flow and its implications to seepage problems.” J. Irr. and Drain Div., ASCE, (ID‐4), 459–473.
4.
Bear, J. (1972). Dynamics of fluids on porous media. American Elsevier, New York, N.Y.
5.
Chauveteau, G. (1965). “Essai sur la loi de Darcy et les ecoulement laminaires a perte de change non‐lineaire,” thesis presented to the Universtié de Toulouse, Toulouse, France, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
6.
Darcy, H. (1856). Les Fontaines Publique de la Ville de Dijon. Victor Dalmont, Paris, France.
7.
Dudgeon, C. R. (1964). “Flow of water through coarse granular materials.” Report No. 76, Water Res. Lab., Univ. of New South Wales, New South Wales, Australia.
8.
Ehrenberger, R. (1928). “Versuche uber die ergiebigheit von brunnen und bestimmung der durchlassigkeit des sandes.” Zeitschrift des Osterreicher Ingenieur und Architektunvereins, Heft 11/12, Austria (in German).
9.
Engelund, F. (1953). “On the laminar and turbulent flows of ground water through homogeneous sand.” Trans. No. 3, Danish Acad, of Tech. Sciences, 7–105.
10.
Escande, L. (1953). “Experiments concerning the infiltration of water through a rock mass.” Proc. Minnesota Int. Hydr. Convention.
11.
Fancher, G. H., Lewis, J. A., and Barnes, K. B. (1933). “Some physical characteristics of oil sands, “State of Pennsylvania Mineral Industries Exploration,” State College Bulletin 12.
12.
Forchheimer, P. H. (1901). “Wasserbewegung durch boden.” Zeitschrifft Ver. Dtsch. Ing., 49, 1736–1749 (in German).
13.
Givan, C. V. (1934). “Flow of water through granular materials—Initial experiments with lead‐shot,” Amer. Geophys. Union, 15th Annual Meeting, 572–579.
14.
Hantush, M. S. (1964). “Hydraulics of wells,” Advances in Hydrosciences, Academic Press, New York, N.Y., 281–432.
15.
Hickox, G. H. (1934). “Flow through granular materials.” Trans. Amer. Geophys. Union, 15th Annual Meeting, 567–571.
16.
Indri, E. (1958). “Experience sur l'ecoulement de l'eau à travers des ames de materiaux spheriques.” Acqua 3, (in French).
17.
Izbach, S. V. (1931). “O filtracii v kropnoaernstom materiale.” Izv. Nauchnoissles, Inst. Gidrotechniki (NIIG), Leningrad, USSR (in Russian).
18.
Karadi, G., and Nagy, I. V. (1961). “Investigations into the validity of the linear seepage law.” Proc. 9th Convention, Int. Assoc. Hydr. Res., Dubrovnik, Yugoslavia, 556–566.
19.
Klinge, W. (1940). “Was ist wasserwirtschaft.” Die wasserwirtschaft, 39, Heft 4 (in German).
20.
Kriz, G. J., Scott, V. H., and Burgy, R. H. (1966). “Graphical determination of confined aquifer parameters.” J. Hydr. Div., ASCE, 92(HY5), 39–48.
21.
Krusemann, G. P., and deRidder, N. A. (1979). “Analysis and evaluation of pumping test data.” Int. Inst. Land Reclamation Impr., Bulletin 11, Wageningen, Netherlands.
22.
Lindquist, E. (1933). “On the flow of water through porous soil.” ler Congress des Grandes Barrages, 5–81.
23.
Missbach, A. (1967). “Nonlinear flow through porous materials.” Research Bulletin No. 1, K. P. Stark, and R. E. Volker, eds., Univ. College of Townsville, Dept. of Civ. Engrg., Apr.
24.
Parkin, A. K. (1962). “Rock‐fill dams with inbuilt spillways, part I‐hydraulic characteristics.” Dept. Civ. Engrg., Univ. of Melbourne, Australia.
25.
Philip, J. R. (1957). “Fluid flow in porous media from the point of classical hydrodynamics.” 2nd Austrian Conf. Soil Sci., Austria.
26.
Rose, H. E. (1945). “An investigation into the laws of flow of fluids through beds of granular materials.” Proc., Inst. Mech. Engrg., 153, 141–148.
27.
Rose, H. E., and Rizk, A. M. A. (1949). “Further research in fluid flow through beds of granular material,” Proc., Inst. Mech. Engrg., 160, 493–511.
28.
Rosenshein, J., and Bennett, G. D. (1984). “Groundwater hydraulics,” Water Resour. Monograph 9, Amer. Geophys. Union.
29.
Scheidegger, A. E. (1954). “Statistical hydrodynamics in porous media.” J. Applied Physics, 25(8).
30.
Scheidegger, A. E. (1960). The physics of flow through porous media. University of Toronto Press, Toronto, Ont., Canada.
31.
Schneebeli, G. (1955). “Experience sur la limite de validite de la loi de Darcy et l'application de la turbulence dans un ecoulement de filtration.” La Houille Blanche, 2 (in French).
32.
Slepicka, F. (1961). “The laws of filtration and limits of their validity.” Proc. 9th Convention, Int. Association Hydr. Res., 383–394.
33.
Smreker, O. (1878). “Entwicklung eines gesetzes fur den widerstand bei der bewegung des grundwassers.” Zeitschrift des Vereines Deutscher Ingenieurws, (in German).
34.
Sokolnikoff, I. S., and Redheffer, R. M. (1966). Mathematics of physics and modern engineering. McGraw‐Hill Book Company, Inc., New York, N.Y.
35.
Streltsova, T. D. (1978). “Well hydraulics in heterogeneous aquifer formations.” Advances in Hydrosciences, V. T. Chow, Ed., Academic Press, New York, N.Y., 357–423.
36.
Sen, Z. (1985). “Volumetric approach to type curves in leaky aquifers.” J. Hydr. Div., ASCE, 111(3), 467–484.
37.
Sen, Z. (1986). “Aquifer test analysis in fractured rocks with linear flow pattern.” Ground Water, 24(1), 72–78.
38.
Sen, Z. (1987). “Non‐Darcian flow in fractured rocks with linear flow pattern.” J. Hydro., 92, 43–57.
39.
Theis, C. V., (1935). “The relationship between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground water storage.” Trans., Amer. Geophys. Union, 16, 516–524.
40.
Todd, D. K. (1980). Groundwater Hydrology. John Wiley and Sons, New York, N.Y.
41.
Tuin, V. D. H. (1960). “La perméabilité et les applications pratiques des materiaux gross.” Hydr. Souterraine, Soc. Hydrotech., France, 17–23 (in French).
42.
Veronese, A. (1941). “Interpretazione della prove di permeabilita nelle sabie et ghiaie,” L'ingeniere, 15, 463–470 (in Italian).
43.
White, A. M. (1955). Trans. Amer. Inst. Chem. Engrg., 31.
44.
Wilkins, J. S. (1935). “Flow of water through rock‐fill and its application to the design of dams.” New Zealand Engineering, 382–387.
45.
Wright, D. E. (1964). “Nonlinear flow through granular media.” J. Fluid Mech., 19, 103–112.
46.
Williams, D. E. (1985). Modern techniques in water well design. Amer. Water Works Association, Denver, Colo.
47.
Zunker, F. (1920). “Das allgemeine grundwasserflissgesetz.” Gasbeleuchtung und Wasserversorgung, (in German).
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 115 • Issue 2 • February 1989
Pages: 193 - 209
Copyright
Copyright © 1989 ASCE.
History
Published online: Feb 1, 1989
Published in print: Feb 1989
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.