Automatic Control of Flotation Columns - Advanced Control and Supervision of Mineral Processing Plants - page 258

6.3.1 Interface Position Sensor

A combination of a float and an ultrasonic sensor to measure the froth depth is now
commonly used in industrial flotation plants because of the simplicity of its concept
and its non-invasive implementation (the sensor's electronics are not in contact with
the pulp). Even though its accuracy is limited by the assumption of uniform pulp and
froth densities and by the absence of the accumulation of solids on the float gage, its
use seems satisfactory to industrial flotation column practitioners. Pressure gages
have also been used to measure the interface position [5]. Theoretically, a single
pressure transducer should suffice, as long as the average value of collection zone
(ρ c ) and froth zone (ρ f ) specific gravity are known, as shown in Equation 6.6, where
H P indicates the position of the pressure transducer measured from the column lip,
P the pressure reading, and g the gravitational constant:

ρ c gH P − P

H =

) .

(6.6)

g ( ρ c − ρ f

Unfortunately, ρ c and ρ f depend on time-varying operating conditions and con-
sequently froth depth values calculated from initial pressure transducer calibration
may not represent later operating conditions.
The use of multiple pressure transducers partially solves this problem since it
provides the extra necessary information to estimate the average value of both den-
sities at prevailing operating conditions. Normally three pressure transducers are
used, one located in the uppermost part of the froth zone, and the other two in the
collection zone, one close to the interface and the other well below. If one assumes
that the collection and froth zone specific gravities are uniform up to or from the
interface, often an unrealistic situation [18], the resulting three-equation system can
be solved for H as shown in Equation 6.7, where P i and H i are the pressure mea-
surement and the position (distance) of transducer i , measured from the top of the
column:

( − )− ( − )

H 1 P 1 P 3 P 1 H 1 H 2

H = H 3

) .

(6.7)

H 3 ( P 1 − P 2 )− P 3 ( H 1 − H 2

Despite the improvement in froth depth estimation provided by this method,
some problems still remain unsolved. Assuming a uniform specific gravity in each
zone might lead to incorrect results, particularly in the case of the froth density,
which is very dependent on operating conditions [18]. Moreover, the solution of the
system of equations requires that the interface be located above the intermediate
transducer otherwise the system of equations becomes underdetermined. To over-
come these problems, some researchers have looked at methods based on intensive
properties of the pulp involved. Moys et al. [19] first reported a method for measur-
ing froth depth based on conductivity and temperature profiles across the interface.
Since the former has been studied in depth, it will be discussed in the next few
paragraphs. To measure the conductivity profile across the interface, Gomez et al.
[20] proposed a probe consisting of a series of modules mounted around a stainless