928 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
models. These Scientific AI models replicate the hydrody-
namics of gas dispersion and flotation kinetics inside each of
the flotation cells, thereby creating a Digital Process Model
of the full flotation circuit. The Digital Process Model is
linked to an Optimizer that evaluates the process perfor-
mance under different possible scenarios, suggesting opera-
tors with process setpoints for airflows, froth depths, and
reagent addition that maximise a reward-based function.
METHODOLOGY
This section describes the inner workings of the simulation
model and the optimisation approach used to enable real-
time flotation optimisation.
Digital Process Model
IntelliSense.io’s approach is based on the use of a combina-
tion of first-principles and semi-empirical models to create
a Digital Process Model of any flotation circuit incorpo-
rating Virtual Sensors. Virtual Sensors refers to a software-
based entity that simulates the functionality of a physical
sensor offering observability of real-world data without the
need for actual hardware. They can provide essential opera-
tional parameters of a process that may be unmeasurable
using physical hardware. The flotation process is modelled
by a combination of Hydrodynamic Virtual Sensors and
Flotation Kinetics Virtual Sensors. These Virtual Sensors
will mimic the gas dispersion and selection phenomena
occurring in a flotation cell allowing to link process control
variables such as froth depth with performance variables
like grade. In this paper, we present the case of mechanical
cells, but our solution can also be configured for other types
of flotation equipment such as column, pneumatic and
Jameson cells. The Digital Process Model and Optimizer
here presented were developed using Python (Python
Software Foundation, 2024).
Hydrodynamic Virtual Sensors
Key flotation cell parameters are related to how the air is
dispersed inside the pulp, ensuring that hydrophobic par-
ticles can float and be collected at the froth. Gas dispersion
will depend on the cell’s specifications (e.g., geometry and
impeller speed) but also on the froth depth and airflow.
Bubble surface area flux (Sb). Gorain et al. (1998)
found that the surface area of the bubbles per unit of time
per unit of cross-sectional area is related to the impeller tip
speed vper, the superficial gas velocity Jg, particle size p80,
and impeller aspect ratio Asp. K1 is used to ensure that Sb
units are in 1/s.
S K v J Asp p ...36
b per g 1
0 29 0.73 0 07
80
0 =-(1)
Gas hold-up (Eg). Using a semi-empirical relationship
found via Computational Fluid Dynamics simulations of
different cell designs and conditions, the amount of gas
present in the pulp phase can be described by the following
equation (Shahbazi 2011), which relates to the impeller tip
speed, the gas superficial velocity and the pulp percent sol-
ids CP. K2 is used to ensure that Eg units are in %.
E K v C J .27
g per P g 2
2.204 0.004 0 =(2)
Bubble size (d32). A geometrical relation exists
between Sb and bubble size, measured as the Sauter mean
diameter d32, with units in mm.
d32 Sb
J
6 g =(3)
Flotation Kinetics Virtual Sensors
To model the recovery process in a flotation bank (a collec-
tion of flotation cells in series) we use a first-order residence
time distribution model. We have taken the description
developed by Yianatos et al. (2003), where the cumula-
tive residence time (𝜏N) experienced by a mineral species
is related to the recovery of that species (R) by Equations 4
and 5, where Vc is the volume of the cell, ρs is the density of
the slurry and Fin is the mass flow into the cell.
R R
N
KsxN
N
K
1h
1
N
s N
N 1 x
=-
-
-+
3
-J
L
K
K1
K ^x
^N
N
P
O
O
O h
:1 D
(4)
Fin
E V C 1
N
g c P s
N 1 x
t
x =
-
+
-
^h
(5)
The flotation kinetics of that species (Ks) captures all of the
phenomena involved in the process of floating and recov-
ering such species. Thus, Ks must be sensitive to hydrody-
namic and operational parameters. Following the approach
of Yoon and Luttrell (1989), the flotation kinetics of a spe-
cies is expressed as:
K K S P f
s b f hf 3 =(6)
where Pf is the probability of true flotation, which depends
on particle size, hydrodynamic conditions and bubble size.
fhf is a parameter function of froth depth and K3 is a cali-
bration factor used to match operational data (mass pull
and recovery) to the model’s metal and gangue transport
to the concentrate. Once calibrated, the flotation kinetic
model can generate plant performance Virtual Sensors,
allowing for metallurgists and operators to see in real-time
mass pulls, grades and recoveries for each one of the cells
of the circuit.
models. These Scientific AI models replicate the hydrody-
namics of gas dispersion and flotation kinetics inside each of
the flotation cells, thereby creating a Digital Process Model
of the full flotation circuit. The Digital Process Model is
linked to an Optimizer that evaluates the process perfor-
mance under different possible scenarios, suggesting opera-
tors with process setpoints for airflows, froth depths, and
reagent addition that maximise a reward-based function.
METHODOLOGY
This section describes the inner workings of the simulation
model and the optimisation approach used to enable real-
time flotation optimisation.
Digital Process Model
IntelliSense.io’s approach is based on the use of a combina-
tion of first-principles and semi-empirical models to create
a Digital Process Model of any flotation circuit incorpo-
rating Virtual Sensors. Virtual Sensors refers to a software-
based entity that simulates the functionality of a physical
sensor offering observability of real-world data without the
need for actual hardware. They can provide essential opera-
tional parameters of a process that may be unmeasurable
using physical hardware. The flotation process is modelled
by a combination of Hydrodynamic Virtual Sensors and
Flotation Kinetics Virtual Sensors. These Virtual Sensors
will mimic the gas dispersion and selection phenomena
occurring in a flotation cell allowing to link process control
variables such as froth depth with performance variables
like grade. In this paper, we present the case of mechanical
cells, but our solution can also be configured for other types
of flotation equipment such as column, pneumatic and
Jameson cells. The Digital Process Model and Optimizer
here presented were developed using Python (Python
Software Foundation, 2024).
Hydrodynamic Virtual Sensors
Key flotation cell parameters are related to how the air is
dispersed inside the pulp, ensuring that hydrophobic par-
ticles can float and be collected at the froth. Gas dispersion
will depend on the cell’s specifications (e.g., geometry and
impeller speed) but also on the froth depth and airflow.
Bubble surface area flux (Sb). Gorain et al. (1998)
found that the surface area of the bubbles per unit of time
per unit of cross-sectional area is related to the impeller tip
speed vper, the superficial gas velocity Jg, particle size p80,
and impeller aspect ratio Asp. K1 is used to ensure that Sb
units are in 1/s.
S K v J Asp p ...36
b per g 1
0 29 0.73 0 07
80
0 =-(1)
Gas hold-up (Eg). Using a semi-empirical relationship
found via Computational Fluid Dynamics simulations of
different cell designs and conditions, the amount of gas
present in the pulp phase can be described by the following
equation (Shahbazi 2011), which relates to the impeller tip
speed, the gas superficial velocity and the pulp percent sol-
ids CP. K2 is used to ensure that Eg units are in %.
E K v C J .27
g per P g 2
2.204 0.004 0 =(2)
Bubble size (d32). A geometrical relation exists
between Sb and bubble size, measured as the Sauter mean
diameter d32, with units in mm.
d32 Sb
J
6 g =(3)
Flotation Kinetics Virtual Sensors
To model the recovery process in a flotation bank (a collec-
tion of flotation cells in series) we use a first-order residence
time distribution model. We have taken the description
developed by Yianatos et al. (2003), where the cumula-
tive residence time (𝜏N) experienced by a mineral species
is related to the recovery of that species (R) by Equations 4
and 5, where Vc is the volume of the cell, ρs is the density of
the slurry and Fin is the mass flow into the cell.
R R
N
KsxN
N
K
1h
1
N
s N
N 1 x
=-
-
-+
3
-J
L
K
K1
K ^x
^N
N
P
O
O
O h
:1 D
(4)
Fin
E V C 1
N
g c P s
N 1 x
t
x =
-
+
-
^h
(5)
The flotation kinetics of that species (Ks) captures all of the
phenomena involved in the process of floating and recov-
ering such species. Thus, Ks must be sensitive to hydrody-
namic and operational parameters. Following the approach
of Yoon and Luttrell (1989), the flotation kinetics of a spe-
cies is expressed as:
K K S P f
s b f hf 3 =(6)
where Pf is the probability of true flotation, which depends
on particle size, hydrodynamic conditions and bubble size.
fhf is a parameter function of froth depth and K3 is a cali-
bration factor used to match operational data (mass pull
and recovery) to the model’s metal and gangue transport
to the concentrate. Once calibrated, the flotation kinetic
model can generate plant performance Virtual Sensors,
allowing for metallurgists and operators to see in real-time
mass pulls, grades and recoveries for each one of the cells
of the circuit.