TECHNICAL PAPERS
Dec 1, 1989

Radial Flow in Vertically Graded Hydraulic Conductivity Aquifers

Publication: Journal of Hydraulic Engineering
Volume 115, Issue 12

Abstract

Type curve expressions are derived analytically for drawdowns around a fully penetrating well in vertically graded hydraulic conductivity aquifers. A linear increase in the hydraulic conductivity with depth is adopted in this paper. Solution of the relevant groundwater movement equations are achieved by the application of Boltzmann transformation individually for the continuity and laminar flow law equations. Necessary type curves are presented for determining the aquifer parameters from an aquifer test performed in the field. The analytical results show that the conventional Theis and Jacob methods are not applicable in the cases of vertically graded hydraulic conductivity aquifers. In addition, a straight line method is proposed for the late time‐drawdown data. However, both type‐curve and straight‐line procedures developed in the paper yield the Theis and Jacob method equivalents, respectively. The application of the methodology is given for fissured and fractured hard‐rock aquifer test data obtained in the field.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Barenblatt, G. E., Zheltov, I. P., and Kochina, I. N. (1960). “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks.” Appl. Math. Mech., 24(5), 1286–1303.
2.
Bear, J. (1972). Dynamics of fluid in porous media. American Elsevier, New York, N.Y.
3.
Boulton, N. S. (1954). “The drawdown of the water table under nonsteady conditions near a pumped well in an unconfined formation.” Proc. Inst. Civ. Eng., 3, 564–579.
4.
Boulton, N. S., and Streltsova, T. D. (1977a). “Unsteady flow to a pumped well in a two layered water bearing formation.” J. Hydrol., 35, 245–256.
5.
Boulton, N. S., and Streltsova, T. D. (1977b). “Unsteady flow to a pumped well in a fissured water bearing formation.” J. Hydrol. 35, 257–269.
6.
Darcy, H. (1856). Les fontaines publiques de la Ville Dijon. Victor Dalmont, Paris, France (in French).
7.
Gale, J. E., Rouleau, A., and Atkinson, L. C. (1985). “Hydraulic properties of fractures.” Hydrology of Rocks of Low Permeability. Int. Assoc., of Hydrogeologists, 17(1), 1–16.
8.
Gringarten, A. C., and Witherspoon, P. A. (1972). “A method of analyzing pump test data from fractured aquifers.” Symp. on Perc. Fissured Rock.
9.
Hantush, M. (1964). “Hydraulics of wells.” Advances in hydrosciences, vol. 1, V. T. Chow, ed. Academic Press, 281–432.
10.
Jenkins, D. N., and Prentice, J. K. (1982). “Theory for aquifer test analysis in fractured rock under linear (non‐radial) flow conditions.” Ground Water, 20(1), 12–21.
11.
Kazemi, H. (1969). “Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution.” Soc. Pet. Eng. J., 12, 451–462.
12.
Larsson, I. (1984). “Ground water in hard rocks.” Project 8.6, UNESCO, Int. Hydrol. Program.
13.
Muskat, M. (1937). The flow of homogeneous fluids through porous media. McGraw‐Hill Book Co., New York, N.Y.
14.
Neuman, S. P., and Witherspoon, P. A. (1969). “Theory of flow in a confined two aquifer system.” Water Resour. Res., 5, 803–816.
15.
Odeh, A. S. (1965). “Unsteady‐state behaviour of naturally fractured reservoirs.” Soc. Pet. Eng. J., 3, 60–64.
16.
Stearns, D. W., and Friedman, M. (1972). “Reservoir in fractured rocks.” American Assoc. Pet. Geol. Memoir, 16, 82–106.
17.
Summers, W. K. (1972). “Specific capacities of wells in crystalline rocks.” Ground Water, 10(6), 37–47.
18.
Şen, Z. (1982). “Type curves for large diameter wells near barriers.” Ground Water, 20(3), 274–277.
19.
Şen, Z. (1985). “Volumetric approach to type curves in leaky aquifers.” J. Hydr. Engrg., ASCE, 111(3), 467–484.
20.
Şen, Z. (1986). “Aquifer test analysis in fractured rocks with linear flow pattern.” Ground Water, 24(1), 72–78.
21.
Şen, Z. (1987). “Non‐Darcian flow in fractured rocks with linear flow pattern.” J. Hydrol., 92, 43–57.
22.
Şen, Z. (1988a). “Analytical solution incorporating nonlinear radial flow in confined aquifers.” Water Resour. Res., 24(4), 601–606.
23.
Şen, Z. (1988b). “Dimensionless time‐drawdown plots of late aquifer test data.” Ground Water, 26(5), 615–618.
24.
Theim, G. (1906). Hydrologische methoden. J. M. Gebhart, Leipzig, Germany (in German).
25.
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. Geophys. Union, 2, 519–524.
26.
Zdankus, N. T. (1974). “Analysis of shallow hard rock pumping and recovery test data.” Ground Water, 12(5), 310–317.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 115Issue 12December 1989
Pages: 1667 - 1682

History

Published online: Dec 1, 1989
Published in print: Dec 1989

Permissions

Request permissions for this article.

Authors

Affiliations

Zekâi Şen
Prof., Hydrogeol. Dept., King Abdulaziz Univ., P.O. Box 1744, Jeddah 21441, Kingdom of Saudi Arabia. On leave from the Tech. Univ. of Istanbul, Inşaat Fakültesi, Ayazag¯a, Istanbul, Turkey

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share