PART 12 Aquifer pumping tests - Dr. M. Zreda - University of Arizona

Aquifer pumping tests 93
The solution of equation 1 is (Theis, 1935)
where u defined as
is called similarity variable, and W(u) is called Theis well function in hydrology (tabulated in
hydrogeology books; for example on p. 318 of Freeze and Cherry) or exponential integral in
mathematics (tabulated in mathematics books). The exponential integral is calculated as
where γ = 0.57721566..... is the Euler's number
s
∞
u
e –
Q
= --------- ------ du
=
4πT u
∫
u
u
=
Wu ( ) = – lnu – γ –
r 2 -------
S
4Tt
∞
∑
k = 1
---------W
Q
( u)
4πT
Plot the solution on a log-log graph (this is the Theis type curve; left panel below). If Q, T and S
are known, s(r, t) can be calculated and plotted on a log-log graph (these are the pumping test
data; right panel below). Note that the shapes of the two graphs, W(u) vs. u and s vs. t, are the
same. We can, therefore, use them together to determine S and T. The procedure used is called the
curve matching method.
log W(u) Theis type curve
log 1/u
Hydrogeology, 431/531 - University of Arizona - Fall 2007 Dr. Marek Zreda
u k
------ ( – 1)
kk!
k
log s Pumping test data
log t