XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2891
while vsettling,i is the hindered settling velocity of particle
type i. While providing useful insights, implementing such
models for complex industrial systems remains challenging.
The second modeling approach focuses on the degree
of entrainment, which is then used to calculate entrain-
ment flows and recovery. Ross and Van Deventer (1988)
developed a model relating the entrainment of different
mineral size fractions in a column to particle size and den-
sity. It is expressed as:
Xi =1 − 0.429[log(di) − 1][ρS − 1] (5)
where Xi is the degree of entrainment of the ith size frac-
tion, di is the particle diameter, and ρs represents the den-
sity of mineral (g/cm3). However, their model did not
account for froth retention time, an important factor in
entrainment. Subsequent empirical models were proposed
by researchers including Kirjavainen (1992) and Savassi et
al. (1998). Kirjavainen’s model incorporated factors such
as particle shape, water recovery, and slurry viscosity. But
the calculation of water recovery is required as an input.
Savassi et al.’s (1998) model related entrainment to particle
size and was found to fit some industrial data. However,
other key variables are also not included. For both models,
the restricted range of variables limits broader applicability.
Yianatos and Contreras (2010) developed a dimensionless
model correlating entrainment to particle size, calibrated
using industrial flotation cell data.
.693d exp EFi
d
,i p
d =-0
z e n o (6)
where EFi is the entrainment factor representing the
gangue/water recovery ratio, dp,i is the mean particle size of
class i, parameter δ corresponds to the mean particle size at
EFi =0.5 for each data set, while ϕ is the drainage param-
eter depending on the mineral characteristics and cell oper-
ating conditions. Their model enforces appropriate limits,
with fine particles recovering equally with water rate and
coarse particles not entraining.
The entrainment models presented incorporate various
parameters to quantify this phenomenon, including par-
ticle size, density, water recovery, impeller speed, superficial
gas velocity, froth height, and slurry viscosity. While models
incorporate the primary factors, the complex interactions
between all process variables make entrainment inherently
challenging to predict. The objective to this work is to eval-
uate the relative importance of different process conditions
for entrainment, i.e., collector concentration, frother con-
centration, impeller speed, and superficial gas velocity, and
the interactions of these variables. This is done by using a
simple model ore comprising fully liberated particles of two
phases, i.e., pyrite and quartz, termed as the binary case.
While the effect of process conditions can be evaluated
for simple particle system, in reality, the ores are mostly
complex. The complexity of ores define the properties of
particles that are to be treated by flotation which are parti-
cle size, shape, composition, surface liberation, and mineral
association. Through the existing models presented, it is
not possible to have an in-depth look at individual particles
and their flotation behavior. Hence, a complex porphyry
copper ore is utilized to study the recovery of major gangue
minerals, used as tracers for entrainment, by computing
their recovery probabilities and comparing them with par-
ticle settling velocities.
MODEL BINARY ORE METHODOLOGY
A binary mineral system composed of quartz and pyrite was
employed for the model ore. Pyrite is chosen as a relevant
sulfide mineral with lower degree of oxidation to increase
the reproducibility of results. Quartz is chosen as a typi-
cal gangue mineral and entrainment tracer. The feed mate-
rial preparation involved separate crushing and grinding
of each mineral, achieving a suitable particle size distribu-
tion (Figure 1). D80 for pyrite and quartz was found to
be 152 µm and 165 µm, respectively, as measured by wet
sieving.
In the systematic exploration of intricate relationships
among key factors and their influence on entrainment, a
comprehensive full-factorial Design of Experiments (DoE)
was implemented. This experimental design encompassed
four essential input variables: collector concentration,
frother concentration, impeller tip speed, and superficial gas
velocity, with two levels and a midpoint. Each experimental
trial was executed in triplicates. The collector used in the
study was potassium amyl xanthate (PAX), technical grade,
in the concentrations 20, 35, and 50 g/t of feed material.
Methyl Isobutyl Carbinol (MIBC), technical grade, was
used as frother in the concentrations 30, 45, and 60 g/t.
The superficial gas velocity (Jg) was set in the range 0.4,
0.45, 0.5 cm/s while the impeller tip speed (Vt) utilized was
in the range 4.7, 5.1, 5.5 m/s. pH was maintained at 6 and
pulp solids content at 30 wt. %.The input parameters used
for the experimental campaign are summarized in Table 1.
Before each test, pyrite and quartz were mixed together
(1:19, pyrite =100 grams and quartz 1900 grams) in the
rod mill to wet grind the feed material for just one minute.
The main objective of grinding was to freshen up the surface
while vsettling,i is the hindered settling velocity of particle
type i. While providing useful insights, implementing such
models for complex industrial systems remains challenging.
The second modeling approach focuses on the degree
of entrainment, which is then used to calculate entrain-
ment flows and recovery. Ross and Van Deventer (1988)
developed a model relating the entrainment of different
mineral size fractions in a column to particle size and den-
sity. It is expressed as:
Xi =1 − 0.429[log(di) − 1][ρS − 1] (5)
where Xi is the degree of entrainment of the ith size frac-
tion, di is the particle diameter, and ρs represents the den-
sity of mineral (g/cm3). However, their model did not
account for froth retention time, an important factor in
entrainment. Subsequent empirical models were proposed
by researchers including Kirjavainen (1992) and Savassi et
al. (1998). Kirjavainen’s model incorporated factors such
as particle shape, water recovery, and slurry viscosity. But
the calculation of water recovery is required as an input.
Savassi et al.’s (1998) model related entrainment to particle
size and was found to fit some industrial data. However,
other key variables are also not included. For both models,
the restricted range of variables limits broader applicability.
Yianatos and Contreras (2010) developed a dimensionless
model correlating entrainment to particle size, calibrated
using industrial flotation cell data.
.693d exp EFi
d
,i p
d =-0
z e n o (6)
where EFi is the entrainment factor representing the
gangue/water recovery ratio, dp,i is the mean particle size of
class i, parameter δ corresponds to the mean particle size at
EFi =0.5 for each data set, while ϕ is the drainage param-
eter depending on the mineral characteristics and cell oper-
ating conditions. Their model enforces appropriate limits,
with fine particles recovering equally with water rate and
coarse particles not entraining.
The entrainment models presented incorporate various
parameters to quantify this phenomenon, including par-
ticle size, density, water recovery, impeller speed, superficial
gas velocity, froth height, and slurry viscosity. While models
incorporate the primary factors, the complex interactions
between all process variables make entrainment inherently
challenging to predict. The objective to this work is to eval-
uate the relative importance of different process conditions
for entrainment, i.e., collector concentration, frother con-
centration, impeller speed, and superficial gas velocity, and
the interactions of these variables. This is done by using a
simple model ore comprising fully liberated particles of two
phases, i.e., pyrite and quartz, termed as the binary case.
While the effect of process conditions can be evaluated
for simple particle system, in reality, the ores are mostly
complex. The complexity of ores define the properties of
particles that are to be treated by flotation which are parti-
cle size, shape, composition, surface liberation, and mineral
association. Through the existing models presented, it is
not possible to have an in-depth look at individual particles
and their flotation behavior. Hence, a complex porphyry
copper ore is utilized to study the recovery of major gangue
minerals, used as tracers for entrainment, by computing
their recovery probabilities and comparing them with par-
ticle settling velocities.
MODEL BINARY ORE METHODOLOGY
A binary mineral system composed of quartz and pyrite was
employed for the model ore. Pyrite is chosen as a relevant
sulfide mineral with lower degree of oxidation to increase
the reproducibility of results. Quartz is chosen as a typi-
cal gangue mineral and entrainment tracer. The feed mate-
rial preparation involved separate crushing and grinding
of each mineral, achieving a suitable particle size distribu-
tion (Figure 1). D80 for pyrite and quartz was found to
be 152 µm and 165 µm, respectively, as measured by wet
sieving.
In the systematic exploration of intricate relationships
among key factors and their influence on entrainment, a
comprehensive full-factorial Design of Experiments (DoE)
was implemented. This experimental design encompassed
four essential input variables: collector concentration,
frother concentration, impeller tip speed, and superficial gas
velocity, with two levels and a midpoint. Each experimental
trial was executed in triplicates. The collector used in the
study was potassium amyl xanthate (PAX), technical grade,
in the concentrations 20, 35, and 50 g/t of feed material.
Methyl Isobutyl Carbinol (MIBC), technical grade, was
used as frother in the concentrations 30, 45, and 60 g/t.
The superficial gas velocity (Jg) was set in the range 0.4,
0.45, 0.5 cm/s while the impeller tip speed (Vt) utilized was
in the range 4.7, 5.1, 5.5 m/s. pH was maintained at 6 and
pulp solids content at 30 wt. %.The input parameters used
for the experimental campaign are summarized in Table 1.
Before each test, pyrite and quartz were mixed together
(1:19, pyrite =100 grams and quartz 1900 grams) in the
rod mill to wet grind the feed material for just one minute.
The main objective of grinding was to freshen up the surface