Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 54

efficiency (for complex plants and data sets there is a very large number of paths to
calculate separation efficiencies or recoveries, Equations 2.112 and 2.113 being just
two simple examples). A major advantage of using reconciled data is that there is
a unique efficiency value whatever the formula used for calculation. Moreover, its
estimate is more reliable.

Feed (stream 1)

Separation
unit

Tail (stream 3)

F j = flowrate in stream j

x ji = mass fraction of
species

i in stream j

Concentrate (stream 2)

Figure 2.11 A separation unit

Example 2. Let us consider again the flotation circuit of Figure 2.7. Table 2.4 com-
pares the standard deviations of the experimental and reconciled values of the min-
eral flowrates. The results show that reconciled data is more accurate than raw data.
In addition to this positive effect and to the estimation of unmeasured variables, a
drastic improvement of the process performance evaluation is usually brought on
by the reconciled data. In this example, the relative standard deviation of the metal
recovery (ratio of metal in the concentrate to metal in the feed) goes from 15% down
to 6%, an improvement that would allow much more efficient decision for plant op-
timization.

Tabl e 2. 4 Reliability of measured and reconciled values (error standard deviations) for the plant of
Figure 2.7

Stream s.d of measured value s.d. of reconciled value
1 0.6 0.44

2 0.8 0.45

3 ∞ 0.47

4 0.3 0.27

5 0.2 0.19

6 0.3 0.23

7 0.5 0.46

8 0.2 0.2

Example 3. Table 2.5 shows the results obtained for part of a copper-lead-zinc flota-
tion plant as depicted in Figure 2.12 [90]. Clearly, when using raw data, one finds
different values of the recoveries depending upon the formula used. Furthermore
some calculations are very unreliable (standard deviations of 31 and 38%). The role