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An analytical solution for critical withdrawal of layered fluid through a line sink in a porous medium

Published online by Cambridge University Press:  17 February 2009

H. Zhang ,
G. C. Hocking  and
D. A. Barry
H. Zhang
Affiliation:
Department of Environmental Engineering, University of Western Australia, Nedlands, WA 6907, Australia
G. C. Hocking
Affiliation:
School of Mathematics and Physical Sciences, Murdoch University, Murdoch, WA 6150, Australia
D. A. Barry
Affiliation:
Department of Environmental Engineering, University of Western Australia, Nedlands, WA 6907, Australia
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Abstract

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Fluid withdrawn through a line sink from a layered fluid in a vertically confined porous medium is considered. A hodograph method is used to obtain the shape of the interface for a given sink position at the critical flow rate. The analytical solution is compared with a more general numerical solution developed in earlier work. It was found that the surface profiles obtained by the two methods are in close agreement. However, the present work has the advantage that it gives a fully explicit solution.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 2 , October 1997 , pp. 271 - 279
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Bear, J., Dynamics of fluids in porous media (American Elsevier, New York, 1972).Google Scholar
[2]Bear, J. and Dagan, G., “Some exact solutions of interface problems by means of the hodograph method”, J. Geophys. Res. 69 (1964) 1563–1572.Google Scholar
[3]Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B. and Watt, S. M., Maple library reference manual (Springer-Verlag, New York, 1991).CrossRefGoogle Scholar
[4]Dagan, G. and Bear, J., “Solving the problem of local interface upconing in a coastal aquifer by the method of small perturbations”, J. IAHR 1 (1968) 15–44.CrossRefGoogle Scholar
[5]McCarthy, J. F., “Gas and water cresting towards horizontal wells”, J. Austral. Math. Soc. Ser. B 35 (1993) 174–197.CrossRefGoogle Scholar
[6]McCarthy, J. F., “Improved model of water cresting”, J. Austral. Math. Soc. Ser. B 35 (1993) 207–222.CrossRefGoogle Scholar
[7]Yih, C., Stratified flows (Academic Press, 1980).Google Scholar
[8]Zhang, H. and Hocking, G. C., “Withdrawal of layered fluid through a line sink in a porous medium”, J. Austral. Math. Soc. Ser. B 38 (1996) 240–254.Google Scholar