XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3645
• Froth characteristics (Rf): Rf is a function of the froth
selectivity and transportation behavior which in turn
are dependent on reagents such as frother affecting
froth behavior, mineral properties in the froth phase,
cell lip length and transportation distance.
• The gangue entrainment effects are also characterized
by separating the flotation rate constant due to true
flotation and due to entrainment.
Our experience has been quite encouraging as this approach
has led to outcomes that would likely be overlooked using
the traditional approach. Despite the advantages of utiliz-
ing these two techniques, there are some drawbacks with
both the traditional and the modelling and simulation-
based approaches, as they are both kinetics based. Hence
a third methodology was developed to overcome many of
these challenges to a great extent as described below.
Non-Kinetics Based Macro Flotation Modelling for
Scale-Up and Plant Design
The traditional flotation modelling approach predomi-
nantly focuses on kinetics rate constants. It’s origin from
reactor modelling in chemical engineering is evident. The
kinetics based approach may have served well in the early
days when the ore complexities were relatively low and the
flotation machines used to be mostly mechanical. But now
with more challenging ore bodies and availability of new
non-mechanical flotation cell technologies, kinetics rate
based approach appears to have limitations, resulting in
significant errors in plant design.
Following are some reasons that illustrate the limita-
tion of kinetics based approach in modelling the flotation
process:
1. The selection of a rate constant for an ore type in
flotation scale-up is often challenging. The rate
constant is in fact not constant even for a spe-
cific ore type as the cell operating conditions have
a strong impact on it. Unless we are limiting the
cell operating conditions to a very narrow range of
operation, which is impractical from the perspec-
tive of real flotation scenario where a plant has to
deal with large variations in plant feed conditions.
Hence it doesn’t make sense to rely on rate con-
stants for plant design. Figure 1 shows the impact
of cell operating conditions for an ore type.
The importance of cell operating conditions on flota-
tion conditions has been observed even in the early days
(Agar &Stratton-Crawley, 1982), yet this is often over-
looked in flotation scale-up and plant design. Table 1 shows
the range of rate constant values fitted using different mod-
els viz. simple kinetics, rectangular, two rate constants (fast
and slow) for the same ore type and using the same chemis-
try but for a large variations in cell operating conditions as
shown in Figure 1.
Both Figure 1 and Table 1 show that the rate con-
stants vary significantly with cell operating conditions even
though this is the same ore and using the same reagent
conditions. This poses a major challenge in the selection of
the rate constant for design. It is very easy to over design
or under design using the average values. This complexity
magnifies tremendously if we were to consider different ore
types or ore variability as part of the geo-metallurgy pro-
gram. Design engineers have to use higher scale-up factors
to reduce any risks in design, that lead to higher capital
costs.
1. These rate constants and residence times don’t
make sense if we were to use different flotation
cell designs. In Pneumatic cells like the Jameson
cell for example, the residence time requirements
are just a fraction of what’s considered typically
in mechanical cells (Tabosa et al, 2020). Since all
bench tests are carried out in laboratory mechani-
cal cells like Denver or Agitair, the rate constant
parameters derived from these cells are not directly
applicable to non-mechanical cells.
It is important to realize that flotation rate is basi-
cally a reflection of inefficiency in our flotation sys-
tems. This may sound strange at first but when we
dig deeper this is quite obvious. Non-mechnaical
cell designs such as the Imhofloat, Microcel,
Jameson or Staged Flotation Reactors (SFRs) have
drifted away from conventional mechanical design,
and hence the use for kinetics based modelling
Table 1. Rate constants fitted using different models for the same ore type
K
(Simple Model)
Fraction
(Slow Floating)
K
(Fast)
K
(Slow)
K
(Rectangular)
Minimum value 0.201 0.053 0.201 0 0.451
Maximum value 1.551 0.328 1.854 0.112 4.176
Average 0.779 0.191 1.011 0.051 1.883
Standard Deviation 0.399 0.070 0.572 0.024 1.080
• Froth characteristics (Rf): Rf is a function of the froth
selectivity and transportation behavior which in turn
are dependent on reagents such as frother affecting
froth behavior, mineral properties in the froth phase,
cell lip length and transportation distance.
• The gangue entrainment effects are also characterized
by separating the flotation rate constant due to true
flotation and due to entrainment.
Our experience has been quite encouraging as this approach
has led to outcomes that would likely be overlooked using
the traditional approach. Despite the advantages of utiliz-
ing these two techniques, there are some drawbacks with
both the traditional and the modelling and simulation-
based approaches, as they are both kinetics based. Hence
a third methodology was developed to overcome many of
these challenges to a great extent as described below.
Non-Kinetics Based Macro Flotation Modelling for
Scale-Up and Plant Design
The traditional flotation modelling approach predomi-
nantly focuses on kinetics rate constants. It’s origin from
reactor modelling in chemical engineering is evident. The
kinetics based approach may have served well in the early
days when the ore complexities were relatively low and the
flotation machines used to be mostly mechanical. But now
with more challenging ore bodies and availability of new
non-mechanical flotation cell technologies, kinetics rate
based approach appears to have limitations, resulting in
significant errors in plant design.
Following are some reasons that illustrate the limita-
tion of kinetics based approach in modelling the flotation
process:
1. The selection of a rate constant for an ore type in
flotation scale-up is often challenging. The rate
constant is in fact not constant even for a spe-
cific ore type as the cell operating conditions have
a strong impact on it. Unless we are limiting the
cell operating conditions to a very narrow range of
operation, which is impractical from the perspec-
tive of real flotation scenario where a plant has to
deal with large variations in plant feed conditions.
Hence it doesn’t make sense to rely on rate con-
stants for plant design. Figure 1 shows the impact
of cell operating conditions for an ore type.
The importance of cell operating conditions on flota-
tion conditions has been observed even in the early days
(Agar &Stratton-Crawley, 1982), yet this is often over-
looked in flotation scale-up and plant design. Table 1 shows
the range of rate constant values fitted using different mod-
els viz. simple kinetics, rectangular, two rate constants (fast
and slow) for the same ore type and using the same chemis-
try but for a large variations in cell operating conditions as
shown in Figure 1.
Both Figure 1 and Table 1 show that the rate con-
stants vary significantly with cell operating conditions even
though this is the same ore and using the same reagent
conditions. This poses a major challenge in the selection of
the rate constant for design. It is very easy to over design
or under design using the average values. This complexity
magnifies tremendously if we were to consider different ore
types or ore variability as part of the geo-metallurgy pro-
gram. Design engineers have to use higher scale-up factors
to reduce any risks in design, that lead to higher capital
costs.
1. These rate constants and residence times don’t
make sense if we were to use different flotation
cell designs. In Pneumatic cells like the Jameson
cell for example, the residence time requirements
are just a fraction of what’s considered typically
in mechanical cells (Tabosa et al, 2020). Since all
bench tests are carried out in laboratory mechani-
cal cells like Denver or Agitair, the rate constant
parameters derived from these cells are not directly
applicable to non-mechanical cells.
It is important to realize that flotation rate is basi-
cally a reflection of inefficiency in our flotation sys-
tems. This may sound strange at first but when we
dig deeper this is quite obvious. Non-mechnaical
cell designs such as the Imhofloat, Microcel,
Jameson or Staged Flotation Reactors (SFRs) have
drifted away from conventional mechanical design,
and hence the use for kinetics based modelling
Table 1. Rate constants fitted using different models for the same ore type
K
(Simple Model)
Fraction
(Slow Floating)
K
(Fast)
K
(Slow)
K
(Rectangular)
Minimum value 0.201 0.053 0.201 0 0.451
Maximum value 1.551 0.328 1.854 0.112 4.176
Average 0.779 0.191 1.011 0.051 1.883
Standard Deviation 0.399 0.070 0.572 0.024 1.080