Environmental Engineering Reference
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a desired BSD matching a given particle size distribution. However, controlling the
whole BSD is a complex problem belonging to the new research area of the control
of stochastic distributions. In our view, new sparger designs will play a crucial role
in increasing system controllability.
Another area which should attract research interest is the proper use of frother
dosage as a control variable. So far, some reported control strategies rely on infor-
mation coming either from froth characteristics (color, bubble size, froth velocity,
etc.
, usually inferred from image processing analysis) or from the collection zone
(gas dispersion properties). A coordinated overall control strategy seems pertinent
here. It is well known that frother content strongly affects both collection and froth
zones. Indeed, frothers modify bubble size in the collection zone and stabilize the
froth layer. Therefore, frother concentration may well turn out to be a relevant sec-
ondary variable to control. Frother is usually added at the head (front) of the flotation
stage in a concentrator plant by implementing a ratio feedforward control based on
processed tonnage, although in some places it is added at intermediate points in
the flotation circuit. Nevertheless, because of the limitations of feedforward con-
trol in the presence of modeling uncertainties and unknown disturbances, such as
frother persistency, evaporation rate and, most importantly, the effect of reprocessed
water (containing remaining frother), frother concentration in a particular flotation
machine is never precisely known, which makes its control rather complex.
Examples of column flotation control based on metallurgical objectives are rather
scarce in the technical literature. What has been proposed almost exclusively relies
on heuristic techniques, such as expert systems and fuzzy logic [61, 62, 80-82].
True model-based RTO, as described in Section 6.4.1, certainly deserves to be in-
vestigated. A
sine qua non
condition would be the availability of a mathematical
model linking primary variables (metallurgy) to secondary (operating) variables.
As mentioned earlier in this section, the effect of froth depth on recovery is rather
weak. Indeed, large froth depth set points would be required for significant effects on
this primary variable, thus, its use for optimization purposes is rather limited. At this
moment, there is still no consensus on the quantitative role played by bias rate on
grade and recovery, owing to the lack of an appropriate sensor for this variable. The
effect of
S
b
, ε
g
and
J
g
on metallurgy has been studied in-depth, with each variable
being studied separately. What is certainly missing is a comprehensive quantitative
study aiming at determining the relationships between all of the above mentioned
secondary variables and the primary variables, particularly to consider their interac-
tions. The best way to select set points of the secondary variables as a function of
the particle size distribution has not been studied either.
Reliable measurement and control of the secondary variables are required to
make up for the lack of knowledge in this area. Thorough experimental campaigns
consisting of a series of steady-state tests, each run at different values of the sec-
ondary set points would then be possible. During the tests, samples of feed, tail and
concentrate could be taken and later processed for chemical assaying to evaluate the
recovery. If available, an OSA could be used instead. These tests would allow the
development of a model to predict grade and recovery from secondary variables.
An economic criterion, such as the net smelter return, which is a function of grade
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