Environmental Engineering Reference
In-Depth Information
1
(
T
i
−
T
i
2
σ
T
i
+
c
i
2
n
i
2
ρ
i
2
)
(
c
i
−
)
(
n
i
−
)
(
ρ
i
−
)
∑
i
J
(
X
)=
+
+
=
σ
c
i
σ
n
i
σ
ρ
i
(2.94)
2
σ
F
1
+
(
F
1
(
F
1
−
)
P
m
2
P
−
)
+
,
σ
P
where the superscript
m
stands for the measured value of the process variable (
Y
)
and the subscript
i
for the stream number. The minimization of
J
(
)
subject to
the bilinear and trilinear constraints (2.92) and (2.93) can be performed with a PNL
algorithm applied to the substitution method. The independent variables are selected
as
X
=
F
1
F
2
F
3
T
1
T
2
T
3
ρ
1
ρ
2
c
1
c
2
n
1
n
2
T
X
ind
.
(2.95)
The dependent variables are then
=
ρ
3
c
3
n
3
P
T
X
dep
.
(2.96)
The minimization algorithm is depicted in Figure 2.9. It requires an initialization
of the independent variables, which can be estimated from the conservation con-
straints and the measured values, using, for instance, the node imbalance method.
J
Figure 2.9
Algorithm for the calculation of the reconciled values by the substitution/PNL method
The results of the reconciliation procedure appear in Table 2.3. The simultane-
ous negative and positive corrections of, respectively, power and stream 3 temper-
ature indicate that thermal losses should be taken into account. Repetition of the
measurement campaign as well as application of FDI techniques (see Section 2.12)
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