Calculation of Inflow and Outflow in Phreatic Aquifers
Publication: Journal of Irrigation and Drainage Engineering
Volume 127, Issue 1
Abstract
Computer algebraic routines are applied for determination of the phreatic surface from standard boundary-value problems for ordinary differential equations. The method does not require iterative steps as other methods do and therefore may be readily used by engineers. The problem of seepage from (into) an unconfined semiinfinite aquifer into (from) an adjacent reservoir that has a sudden change of water level is revised. Comparisons with the Polubarinova-Kochina series expansion are done. Superelevation of the water table in a wetting regime compared to a drainage regime is quantified by the value of sorptivity (desorptivity). The absolute values of sorptivity and desorptivity diverge as the amplitude of the reservoir level change increases. A problem of a steady flow into (from) a constant head well from (into) an unconfined leaky aquifer is also examined. The water table elevation, well rate, and volume of the cone of depression (injection) are calculated.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bahder, T. B. ( 1995). Mathematica for scientists and engineers, Addison-Wesley, Reading, Mass.
2.
Barenblatt, G. I., Entov, V. M., and Ryzhik, V. M. ( 1990). Theory of fluid flows through natural rocks, Kluwer, Dordrecht, The Netherlands.
3.
Crank, J. ( 1975). The mathematics of diffusion, Clarendon, Oxford, U.K.
4.
Emerman, S. H. ( 1996). “Asymptotic solutions for sorption of water by a heavy clay soil.” J. Hydro., Amsterdam, 187, 297–309.
5.
Hogarth, W. L., Govindaraju, R. S., Parlange, J. Y., and Koelliker, J. K. ( 1997). “Linearised Boussinesq equation for modeling bank storage—A correction.” J. Hydro., Amsterdam, 198, 377–385.
6.
Hogarth, W. L., and Parlange, J. Y. ( 1999). “Solving the Boussinesq equation using solutions of the Blasius equation.” Water Resour. Res., 35, 885–887.
7.
Hogarth, W. L., Parlange, J. Y., Parlange, M. B., and Lockington, D. ( 1999). “Approximate analytical solution of the Boussinesq equation with numerical validation.” Water Resour. Res., 35, 3193–3197.
8.
Kacimov, A. R., and Lapin, A. V. ( 1993). “Determination of seepage parameters from data of a quick water intake test and solution of the Boussinesq equation.” Hydrotechnical Constr., Moscow, 27(10), 600–607.
9.
King, J. R. ( 1988). “Approximate solutions to a nonlinear diffusion equation.” J. Engrg. Mathematics, 22, 53–72.
10.
Klute, A., Whisler, F. D., and Scott, E. J. ( 1964). “Soil water diffusivity and hysteresis data from radial flow pressure cells.” Soil Sci. Soc. Am. Proc., 28(2), 160–163.
11.
Lisle, I. G., and Parlange, J.-Y. ( 1993). “Analytical reduction for a concentration dependent diffusion problem.” Zeitschrift fur Angewandte Mathematiks und Phys., Basel, Switzerland, 44, 85–102.
12.
Lockington, D. A. (1997). “Response of unconfined aquifer to sudden change in boundary head.”J. Irrig. and Drain. Engrg., ASCE, 123(1), 24–27.
13.
Mas-Pla, J., Montaner, J., and Sola, J. ( 1999). “Groundwater resources and quality variations caused by gravel mining in coastal streams.” J. Hydro., Amsterdam, 216, 197–213.
14.
Philip, J. R. ( 1969). “Theory of infiltration.” Adv. Hydroscience, 5, 215–296.
15.
Philip, J. R. ( 1973). “Periodic nonlinear diffusion: An integral relation and its physical consequences.” Aust. J. Phys., 26, 513–519.
16.
Polubarinova-Kochina, P. Ya. ( 1977). Theory of ground water movement, Nauka, Moscow (in Russian).
17.
Ruthven, D. M. ( 1984). Principles of adsorption and adsorption processes, Wiley, New York.
18.
Samarskii, A. A., Galaktionov, V. A., Kurdjumov, S. P., and Mikhailov, A. P. ( 1981). “Peaking modes in problems for quasilinear parabolic equations.” Regimy s obostreniem b zadachakh dlja kvazilineynykh parabolicheskikh uravnenij.
19.
Samarskii, A. A., Galaktionov, S. P., Kurdjumov, S. P., and Mikhailov, A. P. ( 1987). Blow-up in quasilinear parabolic equations, Nauka, Moscow (in Russian).
20.
Samarskii, A. A., Galaktionov, V. A., Kurdjumov, S. P., and Mikhailov, A. P. ( 1995). Blow-up in quasilinear parabolic equations, Walter de Gruyter, Berlin.
21.
Serrano, S., and Workman, S. R. ( 1998). “Modeling transient stream/aquifer interaction with the non-linear Boussinesq equation and its analytical solution.” J. Hydro., Amsterdam, 206, 245–255.
22.
Smiles, D. E., and Knight, J. S. (1998). “Discussion on `Response of unconfined aquifer to sudden change in boundary layer,' by D. A. Lockington.”J. Irrig. and Drain. Engrg., ASCE, 124(3), 184–186.
23.
Stephens, D. B. ( 1996). Vadose zone hydrology, Lewis, Boca Raton, Fla.
24.
Upadhyaya, A., and Chauhan, H. S. (1998). “Solutions of Boussinesq equation in semiinfinite flow region.”J. Irrig. and Drain. Engrg., ASCE, 124(5), 265–270.
25.
Wolfram, S. ( 1996). The Mathematica book, Wolfram Media, Cambridge University Press, Cambridge, Mass.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 127 • Issue 1 • February 2001
Pages: 16 - 19
History
Received: Sep 24, 1999
Published online: Feb 1, 2001
Published in print: Feb 2001
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.