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Capture Zone of a Partially Penetrating Well with Skin Effects in Confined Aquifers

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Abstract

The analysis of the capture zone of wells is useful to design pumping systems and wellhead protection programs. In this study, an analytical solution for the head distribution of a partially penetrating well, and semi-analytical methods to determine the geometry of the capture surface are presented. The analytical solution is derived based on an infinitesimal radius under a constant pumping rate in a two-zone confined aquifer. Using the developed solution, a sensitivity analysis is performed to study the influence of skin on the drawdown, location of the stagnation point, maximum horizontal and vertical extent of the capture surface. The results show the efficiency of a partially penetrating well in the plume removal process is different for positive and negative skins. Also it can be concluded, the skin effect will decrease as the degree of penetration and pumping discharge of the well increase. Generally, the thickness of the skin zone is an influential factor in well hydraulics and hydraulic head distribution. However, it can be seen where the skin zone is less than some specific values, the skin effect is not a significant factor, thus, the geometry of the capture surface can be obtained by assuming a single-zone aquifer. Moreover, the effects of different parameters (pumping rates, degree of penetration of the well, thickness of the skin zone, etc.) on the capture zone are studied.

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Abbreviations

Q :

Constant pumping rate [L3 T−1]

K r :

Horizontal hydraulic conductivity of the aquifer [LT−1]

K z :

Vertical hydraulic conductivity of the aquifer [LT−1]

K :

Hydraulic conductivity of isotropic aquifer [LT−1]

H(r, z):

Drawdown [L]

\({\tilde {H}(r,n)}\) :

Drawdown in Fourier domain

R :

Radial distance from the well [L]

Z :

Vertical distance [L]

U :

Darcy velocity [LT−1]

r s :

Radius of the skin zone [L]

r w :

Radius of the capture well [L]

R :

Radius of the influence of the well [L]

L :

Thickness of the aquifer [L]

B 1 :

Upper limit of the screen of the well [L]

B 2 :

Lower limit of the screen of the well [L]

n :

Fourier transform of variable z

\({\phi_u}\) :

Velocity potential due to regional flow [L2 T−1]

\({\phi_w}\) :

Velocity potential due to pumping well [L2 T−1]

U :

Discharge component in x direction [LT−1]

V :

Discharge component in y direction [LT−1]

W :

Discharge component in z direction [LT−1]

I 0(u):

Modified Bessel function of the first kind of order zero

K 0(u):

Modified Bessel function of the second kind of order zero

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Authors and Affiliations

  1. Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

    B. Ataie-Ashtiani, B. Shafei & H. Rashidian-Dezfouli

  2. National Centre for Groundwater Research and Training, Flinders University, Adelaide, SA, Australia

    B. Ataie-Ashtiani

  3. Department of Physics, University of Tehran, Tehran, Iran

    M. Mohamadzadeh

Authors
  1. B. Ataie-Ashtiani
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  2. B. Shafei
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  3. H. Rashidian-Dezfouli
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  4. M. Mohamadzadeh
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Correspondence to B. Ataie-Ashtiani.

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Ataie-Ashtiani, B., Shafei, B., Rashidian-Dezfouli, H. et al. Capture Zone of a Partially Penetrating Well with Skin Effects in Confined Aquifers. Transp Porous Med 91, 437–457 (2012). https://doi.org/10.1007/s11242-011-9853-3

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