Environmental Engineering Reference
In-Depth Information
Example.
Figure 2.7 shows a standard flotation circuit arrangement.
6
5
II
1
2
Feed
I
4
III
IV
8
3
Reject
7
Concentrate
Figure 2.7
A flotation mineral separation circuit
The state vector
X
consists of the valuable mineral flowrates in the eight streams.
There are four nodes, two recycling streams and two plant outputs, the concentrate,
which contains the valuable mineral to be sold for metal extraction, and the reject.
Table 2.2 gives the measured values
Y
of the flowrates of the mineral to be con-
centrated, as well as their reliability σ
e
(standard deviations of
e
). Table 2.2 shows
also the values of the reconciled values
X
. The reconciled values do not exactly sat-
isfy the steady-state mass conservation equations since the plant is assumed to be
operated in a stationary dynamic regime where
V
ε
is different from zero.
Tabl e 2. 2
Data for the circuit of Figure 2.7 (fifth column will be explained in Section 2.9)
X
Stream
Y
(
t
/
h
)
σ
e
σ
X
1
15,8
0,6 14,86 0,44
2
22,2
0,8 23,08 0,45
3
-
∞ 14,19 0,47
4
8,3
0,3
8,18
0,27
5
1,4
0,2
1,47
0,19
6
6,3
0,3
6,23
0,23
7
11,3
0,5 11,62 0,46
8
2,5
0,2
2,45
0,2
2.7.3 The Node Imbalance and Two-step Methods for Bilinear
Systems
In bilinear constraint cases, when either flowrates or species concentrations are as-
sumed to be exactly measured, the reconciliation procedure degenerates into a LQ
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