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

Aquifer pumping tests 99
Case 1: Constant head boundary (river)
To do the calculations of
drawdown, we replace the
real well-river system with
the equivalent system that
consists of the same real well
(left side in the figure below)
and an injecting image well
(right side, on the other side
of the boundary, at the same
distance from the boundary
as the real well). The injecting
image well simulates the
boundary (its effect on head
and drawdown is exactly the
same as the effect of the
river). The figure below
shows the distribution of
drawdown in this system.
Boundary effects
Note that drawdown is zero
along the river (this is expected because the river
is a constant head boundary). We demonstrate
this mathematically by calculating total drawdown
as follows:
Total:
s r
s i
---------
Q 2.25Tt
= ln---------------
4πT 2
S
r r
---------
– Q 2.25Tt
= ln--------------- 4πT 2
S
ri rr r i
Y Data
40
35
30
25
20
15
10
5
0
-2
0 5 10 15 20 25 30 35 40
X Data
Hydrogeology, 431/531 - University of Arizona - Fall 2007 Dr. Marek Zreda
-2
-4
-2
-2
Qr
real well
(discharge)
Q
s = --------ln--- =
0 because at the boundary rr = ri 2πT
rr
0
0
0
0
M
ri
2
4
2
2
2
Qi = -Qr
image well
(recharge)