Skip to main content
SpringerLink
Log in

Flow to an eccentric well in a leaky circular aquifer with varied lateral replenishment

  • Published:
Geofisica pura e applicata Aims and scope Submit manuscript

Summary

An analytical solution is obtained for the flow to an eccentric well in a leaky circular aquifer with lateral replenishment, both for steady and unsteady cases. The flows for external boundary conditions of constant head and zero flux, which were treated previously, follow in the limit from a more general boundary condition. Graphs are developed to show the influence of vertical leakage and lateral replenishment on the relationship between drawdown at the well and eccentricity.

Other symbols are defined in the text as they occur.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

s :

Drawdown at any timet and at any point (r, ϑ) from the center of the aquifer in cases of eccentric wells.

s 0 :

Drawdown at any time and at any distancer from the center of the aquifer for concentric wells.

s w, sw0 :

Drawdowns respectively at the face of an eccentric and concentric well.

Q :

Discharge of well.

K :

Hydraulic conductivity of main aquifer, artesian sand.

K′, K″ :

Hydraulic conductivities of semi-confining stratum through which vertical leakage takes place in proportion to the drawdown

b :

Thickness of main aquifer.

b′, b″ :

Thicknesses of semi-confining stratum.

S :

Storage coefficient of main aquifer.

T :

Kb Transmissivity of main aquifer.

B :

\(\sqrt {Tb'/K'} \) Leakage factor (Hantush & Jacob, 1954).

r 1 :

\(\sqrt {r^2 + r_0^2 - 2rr_0 \cos \vartheta } \) Distance to any point from center of well.

a :

Radius of circular aquifer.

rw :

Radius of well.

r 0 :

Eccentricity or position of well from center of circular aquifer.

J n :

Bessel function of first kind ofnth order.

I n,K n :

Modified Bessel functions respectively of the first and second kinds ofnth order.

Y n :

Bessel function of second kind ofnth order.

H (x) :

Heaviside's unit function.

δ (x):

Dirac's delta function.

References

  • De Wiest J. M. R. (1961):On the theory of leaky aquifers. Journal of Geophys. Res., vol. 66, pp. 4257–4262.

    Google Scholar 

  • Friedman B. (1956):Principles and techniques of Applied Mathematics, pp. 315, John Wiley, New York.

    Google Scholar 

  • Hantush M. S. &Jacob C. E. (1954):Plane potential Flow of ground water with linear leakage, Trans. Am. Geophys. Union, vol. 35, pp. 917–937.

    Google Scholar 

  • Hantush M. S. (1960):Flow to an eccentric well in a leaky circular aquifer. Journal of Geophys. Research, vol. 65, pp. 3425–3431.

    Google Scholar 

  • Jacob C. E. (1946):Radial flow in a leaky artesian aquifer, Trans. Am. Geophys. Union, vol. 27, pp. 198–208.

    Google Scholar 

  • Polubarinova-Kochina P. Ya. (1952):The Theory of Groundwater Movement, State Press, Moscow, Chap. 9C, pp. 430–449. English translation 613 pp. by De Wiest, J. M. R., Princeton University Press 1962.

    Google Scholar 

  • Steggewentz J. H. & Van Nes, B. A. V. (1939):Calculating the yield of a well, taking account of replenishment of the ground water from above. Water and Water Engineering, pp. 561–563, 1939.

  • Watson G. N. (1924):A treatise on the theory of Bessel Functions. Mac Millan, New York, 1944.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering and Applied Science, Princeton University, Princeton, New Jersey

    J. M. Roger De Wiest

Authors
  1. J. M. Roger De Wiest
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Wiest, J.M.R. Flow to an eccentric well in a leaky circular aquifer with varied lateral replenishment. Geofisica Pura e Applicata 54, 87–102 (1963). https://doi.org/10.1007/BF01988258

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01988258

Keywords

Search

Navigation