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
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