Automatic Control of Flotation Columns - Advanced Control and Supervision of Mineral Processing Plants - page 256

cial bubblers). The gas superficial velocity can easily be measured using commer-
cially available gas flow meters. However, the frother concentration measurement
presents a major challenge, since no sensor exists for a continuous measurement.
Some alternatives are possible though, as will be explained later. Nesset et al. [11]
proposed empirical models relating D 10 and D 32 to both superficial gas velocity and
frother concentration for forced air mechanical cells. Both models are only valid un-
der steady-state conditions where a large number of bubbles are counted, typically
10000.

J g

D 32 = D 0 + C · . (6.3)

In this relationship D 0 , C and n are parameters to be adjusted. This is a modified
version of that proposed by Dobby and Finch [12] for porous spargers in columns,
where the term D 0 was not included. In this way, the S b can be estimated for a given
frother concentration as follows:

6 · J g

=

J g .

S b (6.4)

D 0 + C ·

To model the effect of frother concentration on bubble size, an empirical model
was proposed by Finch et al. [13]. An exponentially decreasing function plus a
constant was proposed for modeling the Sauter mean diameter D 32 in terms of the
normalized frother concentration (Equation 6.5). In this equation, D I , a , b are ad-
justable parameters, C is the frother concentration and CCC is a parameter called
“critical coalescence concentration” [14], defined as the frother concentration where
the Sauter mean diameter D 32 is no longer affected by a further increase in frother
concentration.

exp

CCC

b · C

D 32 = D I + a · − . (6.5)

The effect of frother type and concentration on the bubble size has also been
explored [15, 16]. This dependence was found to be similar for various types of
frothers (n-pentanol, MIBC, DF-250, F-150, F-140). The impact of frother con-
centration on the whole BSD is only described qualitatively by looking at the his-
tograms generated. It is observed that an initially bi-modal BSD at very low frother
concentration becomes narrower and a uni-modal shape is obtained as the frother
concentration increases. In these works, no information regarding the shape of the
BSD was provided, as histograms are only being used for visualization purposes.
To gain some insight into the nature of the BSD, a plot of D 32 against D 10 was
proposed by Nesset et al. [11]. If the points ( D 32 , D 10 ) belonged to a very narrow
distribution, they would sit on a unitary-slope straight line, the scatter from such a
line would indicate the degree of dispersion of the size distribution. However this
type of analysis does not provide any information about the actual size distribution
shape.
An adaptive observer has been recently proposed to on-line estimate frother con-
centration [17]. It consists of identifying a set of linear dynamic models representing
the effect of gas rate on the collection zone gas hold-up at different known frother