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Delineating Capture Zone of a Pumping Well in a Slanting Regional Groundwater Flow to a Stream with a Leaky Layer

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Abstract

In this study, analytical and semi-analytical solutions are derived to delineate capture zone of a pumping well near a stream where a leaky layer exists between the aquifer and the stream. A groundwater regional flow is considered in the aquifer and allowed to have different angles with respect to the stream axis. Three critical pumping rates are introduced. At the first pumping rate, capture zone boundary tangents the interface between the aquifer and the leaky layer; called the in-homogeneity boundary. At the second pumping rate, capture zone boundary tangents the stream boundary and if the rate is increased, a part of pumped water would be withdrawn from the stream. The third pumping rate, which may be smaller or larger than the other two, is defined as the rate at which stream water begins to enter the leaky layer; it may or may not be captured by the pumping well. Four different capture zone configurations (cases) are analyzed for different values of pumping rates, groundwater flow directions, and leaky layer’s thickness and hydraulic conductivity. The first three cases analyze hydraulic situations whereby capture zone does not reach the stream, and hence, no pumped water is withdrawn from the stream. With the lowest pumping rate in the first case, no stream water enters the leaky layer. It enters the leaky layer but not the aquifer in the second, and enters the leaky layer and the aquifer in the third case. In the fourth case, where capture zone boundary intersects the stream, the fraction of pumped stream water to total pumped water is delineated.

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Abbreviations

a :

Distance from the well to the in-homogeneity boundary

B :

Aquifer thickness

Cu and CC :

Arbitrary constants

f :

Fraction of pumped stream water to total pumped water

h and h D :

Leaky layer thickness and the dimensionless thickness, respectively

i :

\( \sqrt{-1} \)

K and K * :

Hydraulic conductivity of the aquifer and the leaky layer, respectively

β :

Ratio of the leaky layer hydraulic conductivity to that of the aquifer, K * /K

κ :

A dimensionless constant related to β

q and q * :

Specific discharge in the aquifer and in the leaky layer, respectively

Q and Q D :

Pumping rate and dimensionless pumping rate, respectively

Q DC1 and Q DC2 and Q DC3 :

The first, second, and third critical pumping rates, respectively

Q R and Q DR :

The (portion of pumping) rate pumped from the stream and its dimensionless value, respectively

x and y :

Horizontal and vertical axes of the coordinate system, respectively

x D and y D :

Dimensionless horizontal and vertical axes of the coordinate system, respectively

y DM and x DM :

Maximum y D in the capture zone boundary and x D corresponding to that point

z and z D :

Complex and dimensionless complex variables, respectively

θ and θ*:

Angle between groundwater flow direction and the line normal to the stream axis, in the aquifer and in the leaky layer, respectively (0 o  ≤ θ and θ* ≤ 90 o)

Ω and Ω D :

Aquifer complex, and dimensionless complex functions, respectively

Ω* and Ω * D :

Leaky layer complex, and dimensionless complex functions, respectively

φ :

Hydraulic head

φ 0 and φ *0 :

Constant hydraulic heads for the aquifer and the leaky layer, respectively

Φ and Φ D :

Potential and dimensionless potential functions for the aquifer, respectively

Φ 0 and Φ D0 :

Aquifer constant and dimensionless constant potential functions, respectively

Φ* and Φ* D :

Potential and dimensionless potential functions in the leaky layer, respectively

Φ *0 and Φ * D0 :

Leaky layer constant and dimensionless constant potential functions, respectively

Ψ and Ψ D :

Stream and dimensionless stream functions for the aquifer, respectively

Ψ* and Ψ * D :

Stream and dimensionless stream functions for the leaky layer, respectively

Ψ DS :

Stream function corresponding to the capture zone boundary

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Authors and Affiliations

  1. Faculty of Agriculture, Water Engineering Department, Shahrekord University, Shahrekord, Iran

    Mahdi Asadi-Aghbolaghi

  2. Civil Engineering Department, School of Engineering, Shiraz University, Shiraz, Iran

    Gholam Reza Rakhshandehroo

Authors
  1. Mahdi Asadi-Aghbolaghi
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  2. Gholam Reza Rakhshandehroo
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Corresponding author

Correspondence to Mahdi Asadi-Aghbolaghi.

Additional information

Submitted to Water Resources Management Journal on January 26, 2016

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Asadi-Aghbolaghi, M., Rakhshandehroo, G.R. Delineating Capture Zone of a Pumping Well in a Slanting Regional Groundwater Flow to a Stream with a Leaky Layer. Water Resour Manage 30, 4273–4291 (2016). https://doi.org/10.1007/s11269-016-1420-9

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