Spring-Depletion Solution
Publication: Journal of Hydrologic Engineering
Volume 9, Issue 2
Abstract
Pumping from a well beside a spring also drains water from the spring in a process that is termed spring depletion. A solution is obtained for this problem by assuming that the spring partially penetrates an aquitard that overlies the pumped aquifer. The Boulton solution for delayed-yield flow to a well and the Duhamel superposition theorem are used to obtain a Volterra integral equation of the second kind, and the Laplace transform is used to solve this integral equation. Numerical values computed from this solution are checked with a direct numerical solution of the integral equation. Flow depleted from the spring depends upon dimensionless time and four dimensionless parameters, and the solution is illustrated by showing in plots the effect of changing time and one parameter while holding all other parameters constant. The plotted results appear physically reasonable.
Get full access to this article
View all available purchase options and get full access to this article.
References
Amit, H., Lyakhovsky, V., Katz, A., Starinsky, A., and Burg, A.(2002). “Interpretation of spring recession curves.” Ground Water, 40(5), 543–551.
Anderson, M. P., and Woessner, W. W. (1992). Applied groundwater modeling: Simulation of flow and advective transport, Academic, New York, 122–130.
Angelini, P., and Dragoni, W.(1997). “The problem of modeling limestone springs: The case of Baguara (North Apennines, Italy).” Ground Water, 35(4), 612–618.
Avery, W. H., Donovan, J. J., and Ketchum, J. N.(1999). “Recharge estimation by stage-discharge interpolation of springflows from cross-correlated well measurements.” Ground Water, 37(3), 332–337.
Bear, J. (1979). Hydraulics of groundwater, McGraw-Hill, New York, 53–57.
Bhar, A. K., and Mishra, G. C.(1997). “One-dimensional springflow model for time variant recharge.” Hydrol. Sci. J., 42(3), 381–390.
Boulton, N. S.(1963). “Analysis of data from non-equilibrium pumping tests allowing for delayed yield from storage.” Proc., Inst. Civil Eng.,26, Paper No. 6693, 469–482.
Eisenlohr, L., Kiraly, L., Bouzelboudjen, M., and Rossier, Y.(1997). “Numerical simulation as a tool for checking the interpretation of karst spring hydrographs.” J. Hydrol., 193(1–4), 306–315.
Estrela, T., and Sahuquillo, A.(1997). “Modeling the response of a karstic spring at Arteta aquifer in Spain.” Ground Water, 35(1), 18–24.
Fetter, C. W. (1994). Applied hydrogeology, 3rd Ed., Prentice-Hall, Upper Saddle River, N.J., 289–290.
Hildebrand, F. B. (1976). Advanced calculus for applications, Prentice-Hall, Englewood Cliffs, N.J., 463–467, 622–628.
Hunt, B.(2003). “Unsteady stream depletion when pumping from semiconfined aquifer.” J. Hydrologic Eng., 8(1), 12–19.
Hunt, R. J., Steuer, J. J., Mansor, M. T. C., and Bullen, T. D.(2001). “Delineating a recharge area for a spring using numerical modeling, Monte Carlo techniques, and geochemical investigation.” Ground Water, 39(5), 702–712.
Jian, W., Yao, H., Wen, X., and Chen, B.(1998). “A nonlinear time series model for spring flow: An example from Shanxi Province, China.” Ground Water, 36(1), 147–150.
Perez, E. S.(1999). “Simulation of spring management with quasi-aggregated model.” J. Hydrologic Eng., 4(1), 77–79.
Soliz, J. G., and Acebo, H. L.(2001). “A model of cells as practical approach to simulate spring flow in the Itxina karstic aquifer: Basque country, Spain.” Ground Water, 39(2), 339–347.
Todd, D. K. (1980). Groundwater hydrology, 2nd Ed., Wiley, New York, 47–50.
Wicks, C. M., and Hoke, J. A.(2000). “Prediction of the quality and quantity of Maramec spring water.” Ground Water, 38(2), 218–225.
Information & Authors
Information
Published In
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Oct 2, 2002
Accepted: Jun 23, 2003
Published online: Feb 19, 2004
Published in print: Mar 2004
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.