Automatic Control of Flotation Columns - Advanced Control and Supervision of Mineral Processing Plants - page 261

each type installed in the feed and tailings streams of the column. Despite this costly
set-up, the accuracy of this estimate is very poor since bias is a very small value
calculated from two large quantities, J wt and J wf , and subjected to important error
propagation (four instruments each having its own degree of uncertainty). Assuming
a 3% error on each instrument reading, Finch and Dobby estimated a 75% relative
error on bias estimates, which is completely unacceptable [5]. As a result of this
unreliable estimation and the high cost associated with it, not a single concentrator
is presently using a bias control loop in the operation of their flotation columns.
In conclusion, this method can only be used for sensor calibration or for auditing
purposes, and only under carefully maintained steady-state conditions.
To improve the accuracy of the bias estimation through the mass balance ap-
proach, Uribe-Salas proposed to include the liquid-phase conductivity of the tails,
concentrate, feed and wash water streams [25]. This is done through the so-called
“additivity rule”, which states that the conductivity of a mixture is a weighed aver-
age of the component conductivities. He applied this concept to the concentrate
water component J wc , which is considered to be made of a wash water short-
circuiting stream J wwc and a water feed-entrainment stream J wfc , and to the tails
water-component J wt , which is assumed to be composed of a wash water downward
stream J wwt and a water-feed downward stream J wft . Then, he used these values in
the bias definition given in Equation 6.8.
Uribe-Salas claimed that this approach would in principle improve the precision
of the bias estimate compared with that obtained through the traditional form ( J b

=

J wt J wf ). However, it still requires steady-state operating conditions, otherwise the

problem of time-synchronization of the various conductivity and flow rate values
will reduce its reliability. The situation is particularly critical for low k f

−

k w ratio
values. The extensive instrumentation required, the need for the conductivity of the
liquid component of some streams, and above all, the requirement of a steady-state
operation limit the practical application of this method to laboratory set-ups mostly
working with two-phase systems in well controlled steady-state operation.
While running experiments to validate the use of temperature or conductivity
profiles in the upper part of the column for froth depth evaluation, Moys observed
that the shape of this profile changed with wash water rate variations [26]. A similar
pattern was later reported by Uribe-Salas for the conductivity profile [25] but no
attempt was made to practically implement this relationship.
Based on these observations, Perez-Garibay [27] managed to successfully re-
late the conductivity-profile change to the prevailing bias rate using an ANN. Later
on, Vermette [28] did similar work using the temperature profile. These methods
though, require the existence of a significant difference between wash water and
feed-water conductivities or temperatures, which is usually the case, at least for
northern hemisphere weather conditions. Reported experimental results (laboratory
scale) are very good for two-phase and three-phase (mixture of hematite and silica)
systems.
To verify the usefulness of this sensor for automatic control, dynamic tests were
also conducted to evaluate the capability of the proposed approach for on-line bias
estimation [27]. A 12 in diameter Plexiglas column operating with a two-phase sys-

/