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concentrations (calibration step). An adaptive law is then obtained using Bayes'
rule to evaluate the conditional probability of each model representing the observed
system behavior. In this way, a frother concentration estimate is calculated as a
weighted sum of model probabilities and their associated (known) frother concen-
trations. This method has been successfully tested in a two-phased system working
with Dowfroth and MIBC frothers. Extension to three-phase systems (solid-liquid
and gas) must consider the effect of solids on gas hold-up. Another concern is re-
lated to the well-known fact that some collectors or even salted water may partly
act in some degree as frothers. Unknown changes in collector dosages or salt con-
tent in process water after calibration will change the frother estimate given by the
proposed method. Therefore, the algorithm will estimate an “apparent” frother con-
centration, not necessarily resulting from the effect of frother itself.
6.3 Sensor Development and Applications
As mentioned in the beginning of Section 6.2, the first successful commercial ap-
plication of the flotation column was in Canada where it was invented. Not sur-
prisingly, the bulk of the research was initially done in Canada or more precisely
at McGill University, where a great deal of work was accomplished in the 1980s
on column flotation modeling, simulation and scale-up. In the second part of that
decade, McGill research work focused on the development of specific sensors for
adequately monitoring column operation. Various graduate students who worked
there during these years, returned to their original countries or other cities in Canada,
and the initial research work was thus spread world-wide. In the 1970s, a research
group (GRAIIM) was formed at Universite Laval to work on computer applications
for the mineral industry (modeling, simulation, data reconciliation by material bal-
ances, etc. ) This same group later became what is now known as LOOP, interested
in observation and optimization techniques, particularly automatic control. In the
1990s, these two groups (Laval and McGill) began a close collaboration regarding
sensor development and their use for automatic control of flotation columns.
For more than two decades, researchers from both McGill University and Uni-
versite Laval have been working on the development of specific sensors for the
measurement of flotation column operating variables: (a) the pulp-froth interface
position (hereafter simply refer to as interface position); (b) the bias rate; (c) the
gas hold-up, (d) the bubble diameter and its distribution (BSD); and (e) the bubble
surface area flux. The sensors developed for the first three variables are based on
the use of pulp electric conductivity, whereas the bubble distribution sensor (McGill
Bubble Viewer) applies an image analysis technique to pictures of bubbles. The
Laval research group has concentrated its efforts on the development of the first two
sensors, whereas the McGill group has focused on the last three.
This section and Section 6.4 will present some of their achievements in sensor
development and process control, as well as some others resulting from research
work elsewhere in the world.
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