Type Curves for Two‐Regime Well Flow
Publication: Journal of Hydraulic Engineering
Volume 114, Issue 12
Abstract
Nonequilibrium analytical solutions are presented for fully penetrating wells by incorporating the concept of the existence of a non‐Darcy flow regime around the pumping well and a Darcian flow regime away from the well. For this purpose, an approximate procedure is proposed to find the distance to which the non‐Darcy flow extends. This distance is referred to as the critical well radius, which divides the whole flow domain into nonlinear and linear flow zones with distinctive hydraulic characteristics. The nonlinear flow law is characterized by the Forchheimer equation. Detailed expressions are derived separately for the specific discharge calculations for each zone. Depending on the observation well locations, drawdown distributions and subsequently relevant type curves are developed mathematically for each zone. Various limiting cases are discussed and their physical implications in the practical applications are exposed. In general, linear regime zone type curves converge asymptotically, for large times as well as distances, to the Theis type curve, whereas such a convergence is valid for the nonlinear flow regime, but for small times only.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abromovitz, M., and Stegun, I. A. (1972). Handbook of mathematical functions. Dover Publ. New York, N.Y.
2.
Albertson, M. L., Barton, J. R., and Simon, D. B. (1960). Fluid mechanics for engineers. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
3.
Basak, P. (1978). “Analytical solutions for two‐regime well flow problems.” J. Hydrology, 38, 147–159.
4.
Bear, J. (1972). Dynamics of fluids in porous media. Elsevier, New York, N.Y.
5.
Boulton, N. S. (1963). “Analysis of data from non‐equilibrium pumping test allowing for delayed yield and storage.” Proc., Inst. of Civ. Engrs., 26(6693), London, U.K., 469–482.
6.
Darcy, H. (1856). Les fontaines publique de la Ville de Dijon. Victor Dalmond, Paris, France.
7.
Dudgeon, C. R., Huyakorn, P. S., and Swan, W. H. C. (1973). “Hydraulics of flow near wells in unconsolidated sediments.” Water Res. Rept., 76, Univ. New South Wales, Australia.
8.
Engelund, F. (1953). “On the laminar and turbulent flows of groundwater through homogeneous sand.” Bulletin No. 4, Tech. Univ. of Denmark, Copenhagen, Denmark.
9.
Forchheimer, P. H. (1901). “Wasserbewegung durch Boden.” Zeitschrift, Vereins Deut., 1749–1782.
10.
Hantush, M. S. (1964). “Hydraulics of wells.” Advances in Hydrosciences, Academic Press, V. T. Chow, ed., 1, 282–437.
11.
Huyakorn, P. S., and Dudgeon, C. R. (1962). “Investigation of two‐regime well flow.” J. Hydr. Div., ASCE, 102(HY9), 1149–1165.
12.
Huyakorn, P. S., and Pinder, G. F. (1983). Computational methods in subsurface flow. Academic Press, Inc.
13.
Irmay, S. (1958). “On the theoretical derivation of Darcy and Forchheimer formulas.” Trans., Amer. Geophysical Union, 39, 702–707.
14.
Kirkham, C. E. (1967). “Turbulent flow in porous media. An analytical and experimental model study.” Bull. 11, Water Res. Foundation of Australia.
15.
Kristianovich, S. A. (1940). “Movement of groundwater violating Darcys' law.” J. Appl. Mathematics and Mech., 4, 33–52.
16.
Kritz, G. J., Scott, V. H., and Burgy, R. H. (1966). “Graphical determination of confined aquifer parameters.” J. Hydr. Div., ASCE, 92(HY5), 39–48.
17.
Mackie, C. D. (1983). “Determination of Nonlinear formation losses in pumping wells.” Int. Conf. Groundwater and Man, 1, Sydney, Australia, 199–209.
18.
Morris, D. A., and Johnson, A. I. (1967). “Summary of hydrologic and physical properties of rock and soil materials as analyzed by the U.S. geological survey 1948‐1960.” Water Supply Paper, 1839‐D, U.S. Geological Survey.
19.
Neuman, S. P. (1972). “Theory of flow in unconfined aquifers considering delayed response of the water table.” Water Resour. Res., 8(4), 1031–1045.
20.
Prickett, T. A. (1975). “Modelling Techniques for Groundwater Evaluation,” Advances in Hydroscience, 10, Academic Press, edited by V. T. Chow, ed.
21.
Scholnikoff, I. S., and Redheffer, R. M. (1966). Mathematics of physics of modern engineering. McGraw‐Hill, New York, N.Y.
22.
Şen, Z. (1983). “Volumetric approach to type curves in leaky aquifers.” J. Hydr. Div., 111(HY3), 467–484.
23.
Şen, Z., (1986). “Volumetric approach to non‐Darcy flow in confined aquifers.” J. of Hydrology, 87, 337–350.
24.
Şen, Z., (1987). “Non‐Darcian flow in fractured rocks with linear flow pattern.” J. of Hydr., 92, 43–57.
25.
Şen, Z., (1987). “Type Curves in Patchy Aquifers,” J. of Hydrology, 95, 277–287.
26.
Stark, K. P., and Volker, R. E. (1967). “Nonlinear flow through porous materials—Some theoretical aspects.” Res. Bull. No. 1.
27.
Streltsova, T. D. (1978). “Well hydraulics in heterogeneous aquifer formations.” Advances in Hydroscience, 11, Academic Press, V. T. Chow, ed., 357–423.
28.
Sunada, D. K. (1965). “Turbulent flow through porous media.” Contribution 103, Univ. of California, Berkeley, Water Resour. Center.
29.
Theis, C. V. (1935). “The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage.” Trans., Amer. Geophysical Union, 2, 519–524.
30.
Williams, D. E. (1985). “Modern techniques in water well design.” Amer. Water Works Assoc.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 114 • Issue 12 • December 1988
Pages: 1461 - 1484
Copyright
Copyright © 1988 ASCE.
History
Published online: Dec 1, 1988
Published in print: Dec 1988
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.