Page 105 - Materials Chemistry, Second Edition

88 Practical Design Calculations for Groundwater and Soil Remediation

T = aquifer transmissivity (in gpd/ft or m /day)
2
t = time since pumping started (in days)
The infinite-series term in Equation (3.15) (the terms inside the square
bracket) is often called the well function and designated as W(u). Tabulated
values of W(u) as a function of u can be found in groundwater hydrol-
ogy books. (The well function tables have become obsolete because of the
convenience of hand calculators and personal computers.) A type-curve
approach is often developed to match the time and drawdown data to the
curve of W(u) versus 1/u. From the match points, the transmissivity and
storativity can be determined. There are computer programs commercially
available for Theis curve matching. This subsection will provide one exam-
ple of using the Theis equation, but no examples for the curve matching
will be given.

Example 3.13: Estimate Unsteady-State Drawdown of a
Confined Aquifer Using the Theis Equation
A pumping well is installed in a confined aquifer. Use the following infor-
mation to estimate the drawdown at a distance 20 ft away from the well after
one day of pumping:

• Aquifer thickness = 30.0 ft
• Groundwater extraction rate = 20 gpm
• Aquifer hydraulic conductivity = 400 gpd/ft 2
• Aquifer storativity = 0.005

Solution:
(a) T = Kb = (400)(30) = 12,000 gpd/ft
(b) Inserting the data into Equation (3.16), we obtain
2
2
1.87 rS 1.87(20ft) (0.005)
u = = = 3.12 10× − 4
Tt (12,000 gpd/ft)(1 day)
(c) Substitute the value of u in the well function to obtain its value:
−
 (3.12 × 10 )
42
−
−
4
4
+
−
Wu() = − 0.5772 ln(3.12 × 10 )(3.12 × 10 )− 22!

⋅

−
−
43
44
(3.12 × 10 ) (3.12 × 10 ) 
+ − +  
⋅
⋅
33! 44! 
= 7.50