XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2019
for Sn compared to Nb and Ta. The recovery and enrich-
ment ratios for Rb exhibit an almost linear evolution, rang-
ing from 0.9% recovery and 0.6 enrichment ratio to 6.7%
recovery and 0.9 enrichment ratio.
Modelling
Enrichment Ratio Models
Modelling results. Throughout the ANOVA process, a
t-test was conducted for each parameter to evaluate their
significance in the model. Parameters with a p-value exceed-
ing the selected significance level of 0.05 were deemed
non-significant
The enrichment ratio models equations are:
..21x ER x x 11.5 6.09x 3 05 4.67x 4
Sn 1 2 1 2 1
2 =-+-+(2)
.69 ..28x ER x x 9 4.50x 2 42 3.79x 2
Nb 1 2 1 2 1
2 =-+-+(3)
.29 ..30x ER x x 9 3.72x 2 66 2.52x 2
Ta 1 2 1 2 1
2 =-+-+(4)
..113 ..0653x ER x x 0 785 0 0 0684 0
Rb 1 2 1
2 =+--(5)
The assessment of the accuracy of the Enrichment Ratio
(ER) models was conducted by comparing the summary
of fit between the modelled and experimental data. Across
the four generated models, the correlation coefficients (R2)
values exceed 0.75, indicating an acceptable level of accu-
racy for the models (Table 4). Additionally, the low Root
Mean Square Errors (RMSE) and p-values further suggest
the robustness of the models.
Interpretation of the model. The Enrichment Ratio
models for Sn (ERSn), Nb (ERNb), and Ta (ERTa) are depen-
dent on the rotary speed (G) in both linear and quadratic
effects, fluidization pressure (F), and their interaction (GF).
In all three models, G and GF exert a negative impact on
the ERs, while F and G2 have a positive impact. The nega-
tive influence of the rotation speed is evident: higher rota-
tion speed leads to increased compaction in the retention
zone of the bowl, making the elimination of gangue miner-
als more challenging. Conversely, the positive impact of flu-
idization pressure is also clear: higher fluidization pressure
facilitates the ejection of gangue minerals in the retention
zone. Given that the coefficient associated with G is greater
than F, the interaction parameter globally has a negative
impact on the ERs.
Contrarily, the coefficients of the ERRb model demon-
strate an opposite influence compared to ERSn, ERNb, and
ERTa. Higher G and lower F contribute to higher ERRb.
This is because, unlike the metals with higher densities, Rb
is predominantly recovered through size classification. The
Rb grade increases if gangue micas accumulate in the con-
centrate nozzles, a scenario promoted by high G and low F
settings. Nevertheless, the ERRb intercept at 0.78 suggests
that, rather than increasing, the Rb grade in the concen-
trate decreases regardless of the applied settings.
Recovery Models
Modelling results. Recovery models were derived using
a methodology identical to that employed for the enrich-
ment ratio models but the significance level was set at 0.1
for most parameters, with the exception of Rb, where the
significance level was established at 0.05.
The recovery models equations are:
...046x R x x x 0 69 0.038 0 051 0
Sn 1 1 2 1
2 =-+-(6)
..094x R x 0 58 0.030 0
Nb 1 1
2 =--(7)
...061x R x x x 0 55 0.054 0 090 0
Ta 1 1 2 1
2 =-+-(8)
..017 ..011x R x x 0 048 0 0 011 0
Rb 1 2 1
2 =+--(9)
Interpretation of the models. The recovery models for
Sn, Nb, and Ta are solely dependent on the rotation speed
(G) in both linear and quadratic terms, as well as the inter-
action between the rotation speed and fluidization pressure
(GF). RSn, RNb, and RTa experience negative impacts from
the linear and quadratic terms of the rotation speed, while
the interaction term (GF) has a positive influence. This is
primarily due to the higher rotation speed increasing the
likelihood of trapping larger gangue particles, reducing the
available space for the recovery of heavy minerals in the
retention zone.
The coefficients of RRb exhibit the same sign as those
in the ERRb model, suggesting similar behaviour. If one
increases, the other increases, and if one decreases, the other
decreases. RRb is the only recovery model for which fluidi-
zation pressure (F) is significant. This significance arises
because Rb is recovered through size classification rather
than density separation. The more micas trapped in the
concentrate zone, the higher the grade and the recovery.
Contour Plots
Contour plots of the models within the experimental
domain indicate that RSn, RNb, and RTa did not reach a
Table 4. Summary of fit for the enrichment ratio models
(actual vs. predicted)
Model Statistics ER
Sn ER
Nb ER
Ta ER
Rb
R2 0.77 0.76 0.81 0.96
RMSE 2.36 1.72 1.36 0.0170
F 22.8 21.9 29.5 258
P .0001 .0001 .0001 .0001
for Sn compared to Nb and Ta. The recovery and enrich-
ment ratios for Rb exhibit an almost linear evolution, rang-
ing from 0.9% recovery and 0.6 enrichment ratio to 6.7%
recovery and 0.9 enrichment ratio.
Modelling
Enrichment Ratio Models
Modelling results. Throughout the ANOVA process, a
t-test was conducted for each parameter to evaluate their
significance in the model. Parameters with a p-value exceed-
ing the selected significance level of 0.05 were deemed
non-significant
The enrichment ratio models equations are:
..21x ER x x 11.5 6.09x 3 05 4.67x 4
Sn 1 2 1 2 1
2 =-+-+(2)
.69 ..28x ER x x 9 4.50x 2 42 3.79x 2
Nb 1 2 1 2 1
2 =-+-+(3)
.29 ..30x ER x x 9 3.72x 2 66 2.52x 2
Ta 1 2 1 2 1
2 =-+-+(4)
..113 ..0653x ER x x 0 785 0 0 0684 0
Rb 1 2 1
2 =+--(5)
The assessment of the accuracy of the Enrichment Ratio
(ER) models was conducted by comparing the summary
of fit between the modelled and experimental data. Across
the four generated models, the correlation coefficients (R2)
values exceed 0.75, indicating an acceptable level of accu-
racy for the models (Table 4). Additionally, the low Root
Mean Square Errors (RMSE) and p-values further suggest
the robustness of the models.
Interpretation of the model. The Enrichment Ratio
models for Sn (ERSn), Nb (ERNb), and Ta (ERTa) are depen-
dent on the rotary speed (G) in both linear and quadratic
effects, fluidization pressure (F), and their interaction (GF).
In all three models, G and GF exert a negative impact on
the ERs, while F and G2 have a positive impact. The nega-
tive influence of the rotation speed is evident: higher rota-
tion speed leads to increased compaction in the retention
zone of the bowl, making the elimination of gangue miner-
als more challenging. Conversely, the positive impact of flu-
idization pressure is also clear: higher fluidization pressure
facilitates the ejection of gangue minerals in the retention
zone. Given that the coefficient associated with G is greater
than F, the interaction parameter globally has a negative
impact on the ERs.
Contrarily, the coefficients of the ERRb model demon-
strate an opposite influence compared to ERSn, ERNb, and
ERTa. Higher G and lower F contribute to higher ERRb.
This is because, unlike the metals with higher densities, Rb
is predominantly recovered through size classification. The
Rb grade increases if gangue micas accumulate in the con-
centrate nozzles, a scenario promoted by high G and low F
settings. Nevertheless, the ERRb intercept at 0.78 suggests
that, rather than increasing, the Rb grade in the concen-
trate decreases regardless of the applied settings.
Recovery Models
Modelling results. Recovery models were derived using
a methodology identical to that employed for the enrich-
ment ratio models but the significance level was set at 0.1
for most parameters, with the exception of Rb, where the
significance level was established at 0.05.
The recovery models equations are:
...046x R x x x 0 69 0.038 0 051 0
Sn 1 1 2 1
2 =-+-(6)
..094x R x 0 58 0.030 0
Nb 1 1
2 =--(7)
...061x R x x x 0 55 0.054 0 090 0
Ta 1 1 2 1
2 =-+-(8)
..017 ..011x R x x 0 048 0 0 011 0
Rb 1 2 1
2 =+--(9)
Interpretation of the models. The recovery models for
Sn, Nb, and Ta are solely dependent on the rotation speed
(G) in both linear and quadratic terms, as well as the inter-
action between the rotation speed and fluidization pressure
(GF). RSn, RNb, and RTa experience negative impacts from
the linear and quadratic terms of the rotation speed, while
the interaction term (GF) has a positive influence. This is
primarily due to the higher rotation speed increasing the
likelihood of trapping larger gangue particles, reducing the
available space for the recovery of heavy minerals in the
retention zone.
The coefficients of RRb exhibit the same sign as those
in the ERRb model, suggesting similar behaviour. If one
increases, the other increases, and if one decreases, the other
decreases. RRb is the only recovery model for which fluidi-
zation pressure (F) is significant. This significance arises
because Rb is recovered through size classification rather
than density separation. The more micas trapped in the
concentrate zone, the higher the grade and the recovery.
Contour Plots
Contour plots of the models within the experimental
domain indicate that RSn, RNb, and RTa did not reach a
Table 4. Summary of fit for the enrichment ratio models
(actual vs. predicted)
Model Statistics ER
Sn ER
Nb ER
Ta ER
Rb
R2 0.77 0.76 0.81 0.96
RMSE 2.36 1.72 1.36 0.0170
F 22.8 21.9 29.5 258
P .0001 .0001 .0001 .0001