Review of Flow through Porous Media as Applied to Head Loss in Water Filters
Publication: Journal of Environmental Engineering
Volume 125, Issue 11
Abstract
This article reviews the development of our understanding of flow through porous media with a focus on understanding the clean-bed head loss in water filters. A model of the Forchheimer form is developed by typing existing empirical models to current hydrodynamic theory, and constants are developed for three filter media: glass beads, crushed silica sand, and crushed anthracite coal. Suggestions are made for future research that would improve our understanding.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ahmed, N., and Sunada, D. (1969). “Nonlinear flow in porous media.”J. Hydr. Div., ASCE, 95(6), 1847–1857.
2.
Bear, J. (1972). Dynamics of fluids in porous media. Dover, New York.
3.
Blake, F. (1923). “The resistance of packing to fluid flow.” Trans. Am. Soc. Chemical Engrg., 14, 415.
4.
Brillouin, M. (1907). Leçons sur la viscosité des liquides et des gaz. Gauthier-Villars, Paris.
5.
Brownell, L., and Katz, D. (1947). “Flow of fluids through porous media.” Chem. Engr. Prog., 43(10), 537–548.
6.
Bucharth, H., and Anderson, O. (1995). “On the one-dimensional steady and unsteady porous flow equations.” Coast. Engrg., Amsterdam, The Netherlands, 24, 233–257.
7.
Burke, S., and Plummer. W. (1928). “Gas flow through packed columns.” Ind. Engr. Chem., 20, 1196.
8.
Carman, P. (1937). “Fluid flow through granular beds.” Trans. Inst. of Chemical Engrg., 15, 150.
9.
Chang, M., Trussell, R., Guzman, V., Martinez, J., and Delaney, C. (1999). “Laboratory studies on the cleanbed headloss of filter media.” Aqua, 49(4).
10.
Chauveteau, G., and Thirriott, C. (1967). “Regimes d'ecoulement in milieu poureux et limite de la loi de Darcy.” La Houille Blanche, Grenoble, France, 2, 141 (in French).
11.
Darcy, H. (1856). Les fontaines publiques de la vile de Dijon. Victor Dalmont, Paris (in French).
12.
Dudgeon, C. (1966). “An experimental study of the flow of water through coarse granular media.” La Houille Blanche, Grenoble, France, 7, 785.
13.
Dupuit, A. (1863). Études theoretiques et pratiques sur le mouvement des eaux (in French).
14.
Ergun, S., and Orning, A. (1949). “Fluid flow through randomly packed columns and fluidized beds.” Ind. and Engrg. Chem., 41(6), 1179–1184.
15.
Ergun, S. (1952). “Fluid flow through packed columns.” Chem. Engr. Prog., 43(2), 89–94.
16.
Fair, G., and Hatch, L. (1933). “Fundamental factors governing the streamline flow of water through sand.” J. AWWA, 25, 1551.
17.
Fair, G., Geyer, J., and Okun, D. (1968). Water and wastewater engineering. Vol. 2, Water purification and wastewater treatment and disposal. Wiley, New York.
18.
Forchheimer, P. ( 1901). “Wasserbewegung durch Boden.” Forschtlft ver. D. Ing., 45, 1782–1788 (in German).
19.
Franzini, J. (1951). “Porosity factor for laminar flow through granular media.” Trans. Am. Geophys. Union, 32(3), 443.
20.
Hubbert, M. (1956). “Darcy's law and the field equations of the flow of underground fluids.” AIME Petr. Trans., 207, 222–239.
21.
Irmay, S. (1958). “On the theoretical derivation of Darcy and Forchheimer formulas.” Trans. Am. Geophys. Union, 39(4), 702–707.
22.
Kozeny, J. (1927a). “Ueger kapillare Leitung des Wassers im Boden [On capillary conduction of water in soil].” Sitzungsbericht, Akad. Wiss., Vienna, Vienna, Austria, abt. IIIa, 136, 276.
23.
Kozeny, J. (1927b). “Ueger kapillare Leitung des Wassers im Boden [On capillary conduction of water in soil].” Wasserkraft Wasserwirtschaft, 22, 67 (in German).
24.
MacDonald, I., El-Sayed, M., Mow, K., and Dullien, F. (1979). “Flow through porous media—The Ergun equation revisited.” I&EC Fundamentals, 18(3), 199–208.
25.
Nutting, P. (1930). “Physical analysis of oil sands.” Bull. Am. Assn. Petr. Geol., 14, 1337.
26.
Poiseuille, J. (1841). “Reserches experimentales sur le mouvement des liquides dans les tubes de tres petits diametres.” Comptes Rendus de l'Academie des Sciences (in French).
27.
Rose, H., and Risk, A. (1949). “Further researches in fluid flow through beds of granular material.” Proc., Instn. Mech. Engrs., London, 160, 149.
28.
Rumpf, H., and Gupte, A. (1971). “Einsflusse der Porositat und KorngroBenverteilung im Widerstandsgesetz der Porenstromun.” Chemie Ingenieur Technik, 43(6), 367–375 (in German).
29.
Saleh, S., Thovert, J. F., and Adler, P. M. (1992). Exp. Fluids, 12, 211.
30.
Scheidegger, A. (1960). The physics of flow through porous media. Macmillan, New York.
31.
Schiller, Z. (1923). Angew. Math. Mech., 3, 2 (in German).
32.
Schneebeli, G. (1955). “Experiences sur la limite de validite de la loi de Darcy et l'apparitio de la turbulence dans un ecoulement de filtration.” La Houille Blanche, Grenoble, France, 10, 414–149 (in French).
33.
Sunada, D. (1965). “Turbulent flow through porous media.” Contribution No. 103, Water Resour. Center, University of California, Berkeley.
34.
Todd, D. (1960). Hydrogeology. McGraw-Hill, New York.
35.
Topakoglu, C. (1951). “Steady laminar flow of an incompressible fluid through a curved pipe of circular cross section.” Istanbul University (in Turkish).
36.
Trussell, R., Chang, M., Lang, J., Guzman, V., and Hodges, W. (1999). “Measurement of porosity in a full-scale water filter.” J. AWWA.
37.
Wallis, R. (1939). “A photographic study of fluid flow between banks of tubes.” Proc., Instn. Mech. Engrs., London, 142, 379.
38.
Wallis, R., and White, C. (1938). “Resistance to flow through nests of tubes.” Engrg., London, 146, 605.
39.
Ward, J. (1964). “Turbulent flow in porous media.”J. Hydr. Div., ASCE, 90(5), 1–12.
40.
Weber, W., and DiGiano, F. (1996). Process dynamics in environmental systems. Wiley, New York, 115–121.
41.
White, C. (1929). “Streamline flow through curved pipes.” Proc., Royal Soc., London, Series A, 123, 645.
42.
Wright, E. (1968). “Nonlinear flow through granular media.”J. Hydr. Div., ASCE, 94(4), 851–872.
43.
Wyckoff, R., Botset, G., Muskat, M., and Reed, D. (1933). “The measurement of permeability of porous media for homogeneous fluids.” Rev. Scientific Instruments, 4, 394.
Information & Authors
Information
Published In
History
Received: Dec 1, 1998
Published online: Nov 1, 1999
Published in print: Nov 1999
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.