Automatic Control of Flotation Columns - Advanced Control and Supervision of Mineral Processing Plants - page 264

the oldest and simplest technique for evaluating gas hold-up. It consists of measur-
ing the hydrostatic pressure at two points in the collection zone, distant Δ L cm. If
P 1 and P 2 are the corresponding pressure values and ρ sl is the average density of the
pulp between the two sensors, then the gas hold-up is calculated through

100 1

P 1 − P 2

= − .

ε gP (6.9)

ρ sl · g · Δ L

Since the slurry density value ρ sl is hard to measure in industrial columns, the
practical implementation of this method requires assuming a constant value, e.g. ,
feed or tail density. However, this fact could lead to erroneous estimates in practice
as indicated hereafter.
When comparing this method with the conductivity-based one for two- and three-
phase system in a well-controlled laboratory column, Nu nez et al. [37] observed
that for the two-phase case, both methods gave similar results whereas for the three-
phase system the pressure-based method provided continuously varying estimates as
a result of the assumption of a constant slurry density used in the air hold-up calcu-
lation. This was clearly observed when the column solid content changed as the fed
pulp replaced the initial water-only content, in that the ε gP estimate reflected this
pulp-density effect whereas the conductivity-based estimate ε gK was not affected.
During time periods where test conditions were stable, both methods provided con-
sistent estimates not identical but having the same trend, as the respective sensors
were installed at different column positions.

0.4 J b = J wt − J wf

J b = a ε ww +b

0.3

0.2

0.1

0

−0.1

0 20 40 60 80 100 120 140

time (min)

0.3

0.2

0.1

0 J b = J wt − J wf

J b = a ε ww +b

−0.1

0 20 40 60 80 100 120 140 160 180

time (min)

Figure 6.5 Dynamic bias estimation