Page 106 - Materials Chemistry, Second Edition

Plume Migration in Aquifer and Soil 89

(d) The drawdown can then be determined from Equation (3.15):

s = (114.6)(20)(7.50)/(12,000) = 1.43 ft

Discussion:
For small u values, the third and later terms in the well function can be
truncated without causing a significant error.

3.4.2 Cooper–Jacob’s Straight-Line Method
As shown in Example 3.13, the higher terms in the well function become
negligible for small u values. Cooper and Jacob (1946) [6] pointed out that,
for small u values, the Theis equation can be modified to the following form
without significant errors:

264 Q  0.3 Tt 
s = log (AmericanPractical Units)
T   r 2 S  
0.183 Q  2.25 Tt 
= log  2  (SIUnits) (3.17)
T  r S 

where the symbols represent the same terms as in Equation (3.15).
As shown in Equation 3.16, the value of u becomes small as t increases
and r decreases. So Equation (3.17) is valid after sufficient pumping
time and at a short distance from the well (u < 0.05). It can be seen from
Equation (3.17) that, at any specific location (r = constant), s varies linearly
with log[(constant)t]. The Cooper–Jacob straight-line method is to plot
drawdown vs. pumping-time data from a pumping test on semilog paper;
most of the data should fall on a straight line. From the plot, the slope, Δs
(the change in drawdown per one log cycle of time), and the intercept, t ,
0
of the straight line at zero drawdown can be derived. The following rela-
tionships can then be used to determine the transmissivity and storativity
of the aquifer:

264 Q 0.183 Q
T = (AmericanPractical Units) = (SIUnits) (3.18)
s ∆ s ∆
0.3 2.25
S = Tt 0 (AmericanPractical Units) = Tt 0 (SIUnits) (3.19)
r 2 r 2

where Δs is in ft or m, t in days, and the other symbols represent the same
0
terms as in Equation (3.15).