Page 242 - Materials Chemistry, Second Edition

Groundwater Remediation 225

extraction well is equal to ±Q/4Bu. In other words, the distance between the
dividing streamlines at the line of the well is equal to Q/2Bu. The asymp-
totic value of y (where x = ∞) is equal to ±Q/2Bu. Thus, the distance between
the streamlines far upstream from the pumping well is Q/Bu.
Note that the parameter in Equation (6.3), (Q/Bu), has a dimension of
length. To draw the envelope of the capture zone, Equation (6.3) can be rear-
ranged as:

y
x = forpositive y values
+−
tan[ 1( 2 Bu y )]π (6.4)
Q
y
x = fornegative y values
−−
tan[ 1( 2 Bu y )]π (6.5)
Q
A set of (x, y) values can be obtained from these equations by first specifying
a value of y. The envelope is symmetrical about the x-axis.

Example 6.5: Draw the Envelope of a Capture Zone of
a Groundwater Pumping Well
Delineate the capture zone of a groundwater recovery well with the following
information:

• Q = 60 gpm
• Hydraulic conductivity = 2,000 gpd/ft 2
• Groundwater gradient = 0.01
• Aquifer thickness = 50 ft

Solution:
(a) Determine the groundwater velocity, u:
u = (K)(i) = [(2,000 gpd/ft )(1 day/1,440 min)(1 ft /7.48 gal)](0.01)
3
2
= 1.86 ×10 ft/min
−3
(b) Determine the value of the parameter, Q/Bu:
3
Q = (60gal/min)(1 ft /7.48gal)
−3
Bu (50ft)(1.86 × 10 ft/min)
60 gal/min
= = 86.4 ft
2
(50ft)[(2,000 gal/d/ft )(1d/1, 440min)(0.01)]
(c) Establish a set of (x, y) values using Equation (6.4). First
specify values of y (select smaller intervals for small y values).