Automatic Control of Flotation Columns - Advanced Control and Supervision of Mineral Processing Plants - page 265

A different approach for evaluating gas hold-up was developed by Uribe-Salas
[38] using the Maxwell equation for a mixture of a dispersed non-conducting phase
(air) in a continuous conducting phase (pulp). In this method, either phase concen-
tration is related to its electrical conductivity. The final relation for air hold-up is
given in Equation 6.10, where k slg is the conductivity of the mixture pulp air and
k sl is the conductivity of the pulp without air. Whereas the evaluation of the former
does not cause a problem, the latter ( k sl ) represents the major challenge in using this
method. In fact, this is the same problem encountered in the hydrostatic pressure
method where the measurement of ρ sl is required.

k sl

− k slg

ε gK = 100 · . (6.10)

k sl + 0 . 5 · k slg

Various methods have been proposed for measuring k sl , the simplest being the
use of the tailing (or feed) stream conductivity [38, 39]. However, this estimate
does not correspond to the same position where k slg is measured and might lead to
errors. Two other methods of evaluating k sl close to the k slg measurement have been
proposed. The first is the “standard addition method” consisting of adding a known
amount of dielectric material in a second cell and solving a system of two equations
(such as Equation 6.10) and two unknowns, k gk and k sl [40, 41]. The second method
uses an open cell for measuring k slg and a parallel cell (called siphon cell), designed
to avoid air bubbles suction, therefore providing an adequate measure of k sl [42].
Figure 6.7 shows the concept of this method. This approach seems to provide more
precise estimates of air hold-up, since the solution of the system of equations in the

0.2

0.15

0.1

0.05

0.3

0.25

1.6

1.5

1.4

J ww (cm/s)

0.2

1.3

1.2

1.1

J g (cm/s)

1

Figure 6.6 Effect of J g and J ww on bias rate