2976 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
between bubbles and particles utilizing the Boycott effect
(Boycott 1920 Dickinson et al., 2015 Ireland, 2019).
MATERIAL AND METHOD
Ore Sampling
In this research, the material was provided by KGHM
Polska Miedz S.A. The material was collected from the
crushing circuit outlet at the KGHM Polkowice Copper
Concentrator in Polkowice, Poland. The Polkowice copper
concentrator processes the ore extracted from the Polkowice-
Sieroszowice mines, which is part of the Kupferschiefer-
hosted Cu-Ag deposits in Poland. The received material was
first reduced in amount using the coning and quartering
method, then further crushed using a RETSCH BB 200
lab-scale jaw crusher prior to grinding. Wet grinding was
performed just before flotation tests in a lab scale rod mill
(ca. 33L). The particle size distribution of the ground mate-
rial was measured using a Malvern Panalytical Mastersizer
3000, the results of which are given in Figure 2. Following
grinding, the prepared slurry was then moved to the feed
tank to start conditioning for flotation tests.
Reagents
Prior to this study, various collectors were evaluated and
compared in different dosages and combinations using RFC
to identify the optimal dosage and collector type for deter-
mining the operating parameters of RFC in subsequent flo-
tation tests (Guner et al., 2024). The reagent chosen for this
investigation was AEROPHINE® 3422 at a concentration
of 50 g/t. Thivs compound is composed of isopropyl ethyl
thionocarbamate (IPETC) and dithiophosphinate (DTPi).
During the flotation tests, the frother (Nasforth 245),
which is polyethylene glycol butyl ether with the chemical
formula C4H9(C2H5O)n.OH where n ranges from 2 to 5,
was used (15 mg/L). This particular frother was provided
by NASACO and supplied by KGHM Polska Miedz S.A to
NTNU for flotation tests.
Elemental Analysis
HNO3 digestion followed by inductively coupled plasma
mass spectrometry (ICP-MS) was performed to analyze
of Cu in the feed using the Perkin Elmer Elan DRC II
ICP-MS at the Chemical/Mineralogical Laboratory at
the Department of Geoscience and Petroleum (IGP) at
NTNU. Flotation products were analyzed by A portable
X-ray fluorescence analyzer (Niton ™ XL3t, pXRF) at the
Mineral Processing Laboratory (IGP, NTNU). Based on
the analysis, the copper content in the feed was around
1.8%.
Flotation Tests in RFC
The experimental setup consists of several pieces of equip-
ment and machines, which are the RFC-100 (a 16L labo-
ratory-scale a REFLUX flotation cell), two pre-calibrated
peristaltic pumps (Flowrox ™ LPP-D25) for feed and tail-
ings flow, one pre-calibrated peristaltic pump (Flowrox ™
LPP-D15) for wash water, a wash water tank (180L),
Figure 2. Particle size distribution of ground material for flotation tests in RFC

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Extracted Text (may have errors)

2976 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
between bubbles and particles utilizing the Boycott effect
(Boycott 1920 Dickinson et al., 2015 Ireland, 2019).
MATERIAL AND METHOD
Ore Sampling
In this research, the material was provided by KGHM
Polska Miedz S.A. The material was collected from the
crushing circuit outlet at the KGHM Polkowice Copper
Concentrator in Polkowice, Poland. The Polkowice copper
concentrator processes the ore extracted from the Polkowice-
Sieroszowice mines, which is part of the Kupferschiefer-
hosted Cu-Ag deposits in Poland. The received material was
first reduced in amount using the coning and quartering
method, then further crushed using a RETSCH BB 200
lab-scale jaw crusher prior to grinding. Wet grinding was
performed just before flotation tests in a lab scale rod mill
(ca. 33L). The particle size distribution of the ground mate-
rial was measured using a Malvern Panalytical Mastersizer
3000, the results of which are given in Figure 2. Following
grinding, the prepared slurry was then moved to the feed
tank to start conditioning for flotation tests.
Reagents
Prior to this study, various collectors were evaluated and
compared in different dosages and combinations using RFC
to identify the optimal dosage and collector type for deter-
mining the operating parameters of RFC in subsequent flo-
tation tests (Guner et al., 2024). The reagent chosen for this
investigation was AEROPHINE® 3422 at a concentration
of 50 g/t. Thivs compound is composed of isopropyl ethyl
thionocarbamate (IPETC) and dithiophosphinate (DTPi).
During the flotation tests, the frother (Nasforth 245),
which is polyethylene glycol butyl ether with the chemical
formula C4H9(C2H5O)n.OH where n ranges from 2 to 5,
was used (15 mg/L). This particular frother was provided
by NASACO and supplied by KGHM Polska Miedz S.A to
NTNU for flotation tests.
Elemental Analysis
HNO3 digestion followed by inductively coupled plasma
mass spectrometry (ICP-MS) was performed to analyze
of Cu in the feed using the Perkin Elmer Elan DRC II
ICP-MS at the Chemical/Mineralogical Laboratory at
the Department of Geoscience and Petroleum (IGP) at
NTNU. Flotation products were analyzed by A portable
X-ray fluorescence analyzer (Niton ™ XL3t, pXRF) at the
Mineral Processing Laboratory (IGP, NTNU). Based on
the analysis, the copper content in the feed was around
1.8%.
Flotation Tests in RFC
The experimental setup consists of several pieces of equip-
ment and machines, which are the RFC-100 (a 16L labo-
ratory-scale a REFLUX flotation cell), two pre-calibrated
peristaltic pumps (Flowrox ™ LPP-D25) for feed and tail-
ings flow, one pre-calibrated peristaltic pump (Flowrox ™
LPP-D15) for wash water, a wash water tank (180L),
Figure 2. Particle size distribution of ground material for flotation tests in RFC

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XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2975
2014). Based on the residence time distribution (RTD)
measurements on RFC, it was shown that feed flux is the
key parameter determining the mean residence time and
also affects type of flow regime inside the flotation cell with
gas flux (Guner et al., 2023). The gas flux is very effective
factor in determining many hydrodynamic parameters such
as gas hold-up, bubble size, bubble surface area flux, and
each type of flotation cell has its own optimum gas flux
range (Chen et al., 2022). It was also mentioned in the lit-
erature that the increase in the gas flux affects the mass bal-
ance significantly in pneumatic flotation cells (Harbort et
al., 2003). Naturally, air bubbles introduced into a column
ascend due to their buoyancy. The upward transportation
of fines is determined by the velocity of the bubbles, while
ensuring the critical removal of unwanted gangue in the
downstream process (Wang et al., 2015). Achieving opti-
mum flotation requires minimizing these entrained gangue
particles (Drzymala, 2007). The wash water (different from
the washing water that cleans the top froth surface) moves
downward in the flotation cell, increasing the total volume
of entering the system in addition to the feed flow (Jera and
Bhondayi, 2022). An unbalance exits between the com-
bined volume of overflow and underflow leaving the system
and the total volume entering due to the additional wash
water (Finch and Dobby, 1991). This difference between the
wash water and the overflow is defined as a bias (jb) (Dobby
and Finch, 1991). The bias pushes suspended fine-sized
gangue material downward and is one of the most funda-
mental operational parameters for column and pneumatic
type flotation cells as it directly affects the gangue content
in the overflow (Öteyaka and Soto, 1995). Typically, a posi-
tive bias is more recommended for flotation cells because
it reduces the overflow volume (Finch and Dobby, 1991,
Şahbaz et al., 2008). Therefore, optimization of the bias
is essential to achieve the best possible selectivity with suf-
ficient yield (mass pull of concentrate).
The main zones and components are schematized in
Figure 1. RFC can process the feed with a high flux, reach-
ing up to 9.3 cm/s, as described by Cole et al. (2021). The
compressed air is introduced through frits at a notably high
flux, reaching up to 6.1 cm/s, as detailed by Dickinson et
al., (2015). The downcomer works as a reactor (Chen et
al., 2022 Guner et al., 2023). Within this downcomer, the
initial interaction between the gas phase and solid materi-
als takes place, and first bubble-particle attachment occurs
here, particularly under conditions of high gas volume
and high shear rates (Dickinson et al., 2019 Galvin and
Dickinson, 2014 Jiang et al., 2014). While wash water
creates a counter-current flow inside the fluidized bed of
the cell, hydrophilic particles are directed downwards into
inclined channels under the reverse fluidized bed. Notably,
there is no conventional froth zone in the upper region
of RFC (Wang et al., 2023). In the lower part of RFC,
the inclined channels are used to enhance the segregation
Figure 1. Schematic representation of RFC (not to scale) modified

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Extracted Text (may have errors)

XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2975
2014). Based on the residence time distribution (RTD)
measurements on RFC, it was shown that feed flux is the
key parameter determining the mean residence time and
also affects type of flow regime inside the flotation cell with
gas flux (Guner et al., 2023). The gas flux is very effective
factor in determining many hydrodynamic parameters such
as gas hold-up, bubble size, bubble surface area flux, and
each type of flotation cell has its own optimum gas flux
range (Chen et al., 2022). It was also mentioned in the lit-
erature that the increase in the gas flux affects the mass bal-
ance significantly in pneumatic flotation cells (Harbort et
al., 2003). Naturally, air bubbles introduced into a column
ascend due to their buoyancy. The upward transportation
of fines is determined by the velocity of the bubbles, while
ensuring the critical removal of unwanted gangue in the
downstream process (Wang et al., 2015). Achieving opti-
mum flotation requires minimizing these entrained gangue
particles (Drzymala, 2007). The wash water (different from
the washing water that cleans the top froth surface) moves
downward in the flotation cell, increasing the total volume
of entering the system in addition to the feed flow (Jera and
Bhondayi, 2022). An unbalance exits between the com-
bined volume of overflow and underflow leaving the system
and the total volume entering due to the additional wash
water (Finch and Dobby, 1991). This difference between the
wash water and the overflow is defined as a bias (jb) (Dobby
and Finch, 1991). The bias pushes suspended fine-sized
gangue material downward and is one of the most funda-
mental operational parameters for column and pneumatic
type flotation cells as it directly affects the gangue content
in the overflow (Öteyaka and Soto, 1995). Typically, a posi-
tive bias is more recommended for flotation cells because
it reduces the overflow volume (Finch and Dobby, 1991,
Şahbaz et al., 2008). Therefore, optimization of the bias
is essential to achieve the best possible selectivity with suf-
ficient yield (mass pull of concentrate).
The main zones and components are schematized in
Figure 1. RFC can process the feed with a high flux, reach-
ing up to 9.3 cm/s, as described by Cole et al. (2021). The
compressed air is introduced through frits at a notably high
flux, reaching up to 6.1 cm/s, as detailed by Dickinson et
al., (2015). The downcomer works as a reactor (Chen et
al., 2022 Guner et al., 2023). Within this downcomer, the
initial interaction between the gas phase and solid materi-
als takes place, and first bubble-particle attachment occurs
here, particularly under conditions of high gas volume
and high shear rates (Dickinson et al., 2019 Galvin and
Dickinson, 2014 Jiang et al., 2014). While wash water
creates a counter-current flow inside the fluidized bed of
the cell, hydrophilic particles are directed downwards into
inclined channels under the reverse fluidized bed. Notably,
there is no conventional froth zone in the upper region
of RFC (Wang et al., 2023). In the lower part of RFC,
the inclined channels are used to enhance the segregation
Figure 1. Schematic representation of RFC (not to scale) modified

XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2977
a feed tank (which also served as a conditioning tank), a
rotameter (Brooks® Instruments, 30LPM max), a liquid
flow meter (Brooks Instruments®, 10LPM max), and two
electromagnetic slurry flow meters (Krohne AF-E 400,
KROHNE Messtechnik GmbH) for feed and underflow.
Conditioning was applied to the ground material in the
feed tank for 3 minutes for the collector and 1 minute for
the frother. The pre-calibrated feed pump transferred mate-
rial to RFC while air flow was already supplied. Wash water,
which had the frother at the same dosage as the slurry, was
injected by the peristaltic pump. All flows were read by the
introduced flowmeters, and concentrate was collected from
the overflow chamber of RFC. The pH was measured by a
Metrohm 914 pH/Conductometer and it was not adjusted,
the natural pH of the material was used. Conditions that
were kept constant for each flotation test are introduced in
Table 1.
Table 1. Constant flotation conditions
Parameters Values
Flotation time 15 minutes
Conditioning time 3 minutes for collector, 1 minute
for frother
Frother 15 mg/L Nasforth 245
Initial pH 8.0
Circuit type Rougher
Cell volume 16L
For recovery calculations, the calculated head for Cu was
used (as shown in Eq.1 and integrated into the recovery
calculation as depicted in Eq.2. In these equations, ‘c’ rep-
resents the Cu content in the overflow product (%),‘C’ is
the portion of mass of the concentrate in total (%),‘t’ is the
assayed Cu content in the non-floated material (%),‘T’ is
the portion of the mass of the non-floated material in total
(%),‘R’ is the Cu recovery (%),‘fc’ is the calculated head
of Cu in the feed, and ‘fa’ is the assayed Cu content in the
concentrate.
%f Tt Cc
100 c =+`j (1)
*%R f
Cc
100
c
=c m (2)
Statistical Study
This research utilized the Box–Behnken design (BBD)
within the framework of Design of Experiments (DOE),
a statistical approach to exploring the relationships
between multiple factors and responses. This method is
widely recognized as one of the most common statistical
experimental design techniques for optimization purposes
(Napier-Munn, 2014). Specifically, a four-factor, three-
level study was conducted to examine the interplay among
independent variables—feed flux (jf), gas flux (jg), wash
water flux (jw), and bias flux (jb)—and their impact on the
outcome variables of grade (c, %)and recovery (R, %).The
levels of factors were presented in Table 2, and the condi-
tions of the flotation tests (DOE) were detailed in Table 3.
StdOrder represents the sequence of runs in an experiment
if conducted in a systematic order, whereas RunOrder
indicates the sequence of runs when they are arranged in a
random order. In the BBD approach, the total number of
experimental runs is calculated using the formula: N =2k(k
− 1) +C0, where ‘N’ represents the total experimental trials
needed, ‘k’ denotes the number of factors being tested, and
‘C0’ signifies the count of central points (Box and Behnken,
1960). Minitab® 21.4 was employed to conduct BBD and
further statistical analysis.
RESULTS AND DISCUSSION
Application of BDD for Flotation Optimization of
Operating Parameters
BBD extracted two empirical quadratic regression models
for recovery and grade, as shown in Eq. 3 and 4. In the
model for grade, the standard deviation of the distance
between the data values and the fitted values is 1.83, and
R2—the percentage of variation in the response that is
explained by the model—is 82.%. For the recovery, these
values are 2.86 as the standard deviation and 91% for R.
Table 2. Factors and levels of operating parameters
Factors Unit Symbol
Leves
–1 0 +1
Feed flux cm/s jf 3.00 4.00 5.00
Gas flux cm/s jg 0.50 1.50 2.50
Wash water flux cm/s jw 0.75 1.00 1.25
Bias cm/s j
b 0.00 0.25 0.50

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Extracted Text (may have errors)

XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2977
a feed tank (which also served as a conditioning tank), a
rotameter (Brooks® Instruments, 30LPM max), a liquid
flow meter (Brooks Instruments®, 10LPM max), and two
electromagnetic slurry flow meters (Krohne AF-E 400,
KROHNE Messtechnik GmbH) for feed and underflow.
Conditioning was applied to the ground material in the
feed tank for 3 minutes for the collector and 1 minute for
the frother. The pre-calibrated feed pump transferred mate-
rial to RFC while air flow was already supplied. Wash water,
which had the frother at the same dosage as the slurry, was
injected by the peristaltic pump. All flows were read by the
introduced flowmeters, and concentrate was collected from
the overflow chamber of RFC. The pH was measured by a
Metrohm 914 pH/Conductometer and it was not adjusted,
the natural pH of the material was used. Conditions that
were kept constant for each flotation test are introduced in
Table 1.
Table 1. Constant flotation conditions
Parameters Values
Flotation time 15 minutes
Conditioning time 3 minutes for collector, 1 minute
for frother
Frother 15 mg/L Nasforth 245
Initial pH 8.0
Circuit type Rougher
Cell volume 16L
For recovery calculations, the calculated head for Cu was
used (as shown in Eq.1 and integrated into the recovery
calculation as depicted in Eq.2. In these equations, ‘c’ rep-
resents the Cu content in the overflow product (%),‘C’ is
the portion of mass of the concentrate in total (%),‘t’ is the
assayed Cu content in the non-floated material (%),‘T’ is
the portion of the mass of the non-floated material in total
(%),‘R’ is the Cu recovery (%),‘fc’ is the calculated head
of Cu in the feed, and ‘fa’ is the assayed Cu content in the
concentrate.
%f Tt Cc
100 c =+`j (1)
*%R f
Cc
100
c
=c m (2)
Statistical Study
This research utilized the Box–Behnken design (BBD)
within the framework of Design of Experiments (DOE),
a statistical approach to exploring the relationships
between multiple factors and responses. This method is
widely recognized as one of the most common statistical
experimental design techniques for optimization purposes
(Napier-Munn, 2014). Specifically, a four-factor, three-
level study was conducted to examine the interplay among
independent variables—feed flux (jf), gas flux (jg), wash
water flux (jw), and bias flux (jb)—and their impact on the
outcome variables of grade (c, %)and recovery (R, %).The
levels of factors were presented in Table 2, and the condi-
tions of the flotation tests (DOE) were detailed in Table 3.
StdOrder represents the sequence of runs in an experiment
if conducted in a systematic order, whereas RunOrder
indicates the sequence of runs when they are arranged in a
random order. In the BBD approach, the total number of
experimental runs is calculated using the formula: N =2k(k
− 1) +C0, where ‘N’ represents the total experimental trials
needed, ‘k’ denotes the number of factors being tested, and
‘C0’ signifies the count of central points (Box and Behnken,
1960). Minitab® 21.4 was employed to conduct BBD and
further statistical analysis.
RESULTS AND DISCUSSION
Application of BDD for Flotation Optimization of
Operating Parameters
BBD extracted two empirical quadratic regression models
for recovery and grade, as shown in Eq. 3 and 4. In the
model for grade, the standard deviation of the distance
between the data values and the fitted values is 1.83, and
R2—the percentage of variation in the response that is
explained by the model—is 82.%. For the recovery, these
values are 2.86 as the standard deviation and 91% for R.
Table 2. Factors and levels of operating parameters
Factors Unit Symbol
Leves
–1 0 +1
Feed flux cm/s jf 3.00 4.00 5.00
Gas flux cm/s jg 0.50 1.50 2.50
Wash water flux cm/s jw 0.75 1.00 1.25
Bias cm/s j
b 0.00 0.25 0.50