Environmental Engineering Reference
In-Depth Information
with an appropriate function
myfun
. The function is derived from the residual
condition
q
X
hðr
fit
Þ h
0
s
fit
2
rekk¼
is minimal
(12.7)
0 is considered, condition (
12.7
)
is equivalent to finding the minimum of the objective function
When the reach of the well with condition
h
0
¼
X
hðr
fit
Þþs
fit
2
eðTÞ¼
(12.8)
This has the following necessary condition:
2
X
hðr
fit
Þþs
fit
@
h
@
T
ðr
fit
Þ¼
@
e
@
T
¼
0
(12.9)
Using the Thiem formula, the derivative can be written as:
¼
@
h
@
T
¼
Q
r
r
0
h
T
log
(12.10)
2
pT
2
and thus the condition can be reformulated as follows:
X
hðr
fit
Þþs
fit
h
ð
r
fit
T
¼
0
(12.11)
The vector notation is:
hðr
fit
Þ
1
T
T
h
ðr
fit
Þþs
fit
¼
0
(12.12)
It is convenient to use the function in an M-file, which should look similar to:
function
f = myfun(T);
global
rfit sfit reach Q
% calculate Thiem solution
h = Q*log(rfit/reach)/T/2/pi;
% specify function f to vanish
f = (h+sfit)*h'/T;
352 m
2
/d, which is obtained after
The result for the example data set is:
T ¼
few iterations within the MATLAB
®
fzero
module. Figure
12.8
depicts the
