XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2447
[Figure 5(c)] models. The results are presented as cumula-
tive distribution functions. The vertical continuous black
line represents the R∞ value obtained with the entire data-
set. The measured cumulative recovery at t =32 min is also
presented as a vertical blue line (dashed), and as a compari-
son reference. The SFR model led to the higher variability
in the R∞ estimation, whose values were significantly lower
than the measured recovery at t =32 min. This inconsistency
indicates the limitation of the SFR model to characterize
this flotation process. The R∞ variability decreased when
assuming a Rectangular or Gamma model, being slightly
lower with the former. However, most of the R∞ estimates
(71.4%) obtained from the Rectangular model were lower
than the measured recovery R(t =32 min), which contra-
dicts the experimental results. Thus, the Gamma model
presented a good trade-off between parameter stability and
process representativeness for the system under study.
A simplified scale-up procedure (by time) was con-
ducted to determine the potential recovery in a continu-
ous flotation system. The prediction of a rougher response
was carried out, assuming a direct scalability of each model
(SFR, Rectangular, and Gamma) to an industrial opera-
tion. A scale factor of 2.5 batch/plant was applied to each
of the subsampled responses. The selected residence times
were 20 min and 30 min at plant scale, equivalent to 8
min and 12 min at laboratory scale. The recoveries at t =8
min and t =12 min at batch scale were thus directly used
as predictions for the recoveries at large scale. Cumulative
distribution functions of these recoveries are presented in
Figure 6. Figure 6(a) shows the recovery predictions at 20
min for the continuous system, whereas Figure 6(b) shows
the same scaled-up results at 30 min. The SFR model again
exhibited higher variability in the recovery predictions,
which presented negligible differences between the evalu-
ated residence times. As this model reached a plateau in
the first 5 min of flotation (see Figure 3), non-significant
recovery increases were observed by extending the flotation
time from 8 min to 12 min at lab scale. Lower and compa-
rable variabilities were obtained with the Rectangular and
Gamma models for the studied system, which is in agree-
ment with the higher stability in the R∞-f(k) estimations
presented in Figures 4 and 5.
The R∞-f(k) pairs obtained from the Rectangular and
Gamma models exhibited higher robustness to the selec-
tion of flotation intervals in lab-scale kinetic character-
izations. This robustness led to lower uncertainties when
scaling-up recoveries at large scale. These findings under-
scored the relevance of conducting sensitivity analysis in
kinetic characterizations, as a model structure less sensitive
to the experimental designs and sampling intervals reduces
uncertainties when scaling-up laboratory results to indus-
trial operations.
CONCLUSIONS
A kinetic characterization was conducted at batch scale
for the separation of Cu minerals from a porphyry ore.
The time-recovery data were modeled using the Single
Flotation Rate (SFR), Rectangular and Gamma models,
(a) (b)
0.0
0.2
0.4
0.6
0.8
1.0
75 76 77 78
Recovery at 20 min plant (8 min batch)
SFR Rectangular Gamma
0.0
0.2
0.4
0.6
0.8
1.0
75 76 77 78
Recovery at 30 min plant (12 min batch)
SFR Rectangular Gamma
Figure 6. Cumulative distribution functions of the recovery predictions from a simplified scale-up procedure:
(a) Recovery at 20 min in continuous operation (b) Recovery at 30 min in continuous operation
Cumulati
Fracti
Cumulati
Fracti
[Figure 5(c)] models. The results are presented as cumula-
tive distribution functions. The vertical continuous black
line represents the R∞ value obtained with the entire data-
set. The measured cumulative recovery at t =32 min is also
presented as a vertical blue line (dashed), and as a compari-
son reference. The SFR model led to the higher variability
in the R∞ estimation, whose values were significantly lower
than the measured recovery at t =32 min. This inconsistency
indicates the limitation of the SFR model to characterize
this flotation process. The R∞ variability decreased when
assuming a Rectangular or Gamma model, being slightly
lower with the former. However, most of the R∞ estimates
(71.4%) obtained from the Rectangular model were lower
than the measured recovery R(t =32 min), which contra-
dicts the experimental results. Thus, the Gamma model
presented a good trade-off between parameter stability and
process representativeness for the system under study.
A simplified scale-up procedure (by time) was con-
ducted to determine the potential recovery in a continu-
ous flotation system. The prediction of a rougher response
was carried out, assuming a direct scalability of each model
(SFR, Rectangular, and Gamma) to an industrial opera-
tion. A scale factor of 2.5 batch/plant was applied to each
of the subsampled responses. The selected residence times
were 20 min and 30 min at plant scale, equivalent to 8
min and 12 min at laboratory scale. The recoveries at t =8
min and t =12 min at batch scale were thus directly used
as predictions for the recoveries at large scale. Cumulative
distribution functions of these recoveries are presented in
Figure 6. Figure 6(a) shows the recovery predictions at 20
min for the continuous system, whereas Figure 6(b) shows
the same scaled-up results at 30 min. The SFR model again
exhibited higher variability in the recovery predictions,
which presented negligible differences between the evalu-
ated residence times. As this model reached a plateau in
the first 5 min of flotation (see Figure 3), non-significant
recovery increases were observed by extending the flotation
time from 8 min to 12 min at lab scale. Lower and compa-
rable variabilities were obtained with the Rectangular and
Gamma models for the studied system, which is in agree-
ment with the higher stability in the R∞-f(k) estimations
presented in Figures 4 and 5.
The R∞-f(k) pairs obtained from the Rectangular and
Gamma models exhibited higher robustness to the selec-
tion of flotation intervals in lab-scale kinetic character-
izations. This robustness led to lower uncertainties when
scaling-up recoveries at large scale. These findings under-
scored the relevance of conducting sensitivity analysis in
kinetic characterizations, as a model structure less sensitive
to the experimental designs and sampling intervals reduces
uncertainties when scaling-up laboratory results to indus-
trial operations.
CONCLUSIONS
A kinetic characterization was conducted at batch scale
for the separation of Cu minerals from a porphyry ore.
The time-recovery data were modeled using the Single
Flotation Rate (SFR), Rectangular and Gamma models,
(a) (b)
0.0
0.2
0.4
0.6
0.8
1.0
75 76 77 78
Recovery at 20 min plant (8 min batch)
SFR Rectangular Gamma
0.0
0.2
0.4
0.6
0.8
1.0
75 76 77 78
Recovery at 30 min plant (12 min batch)
SFR Rectangular Gamma
Figure 6. Cumulative distribution functions of the recovery predictions from a simplified scale-up procedure:
(a) Recovery at 20 min in continuous operation (b) Recovery at 30 min in continuous operation
Cumulati
Fracti
Cumulati
Fracti