2018 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Given that the primary objectives of the separation pro-
cess involve recovering Sn, Nb, and Ta, the key responses
under study include recovery and enrichment ratio of Sn
(RSn, ERSn), Nb (RNb, ERNb) and Ta grade (RTa, ERTa), as
well as the mass yield (Mrec). Additionally, Rb recovery and
enrichment ratio (RRb, ERRb) were examined as proxys for
Li-micas, which contain the majority of the Rb in the sam-
ple, and more broadly to monitor the behavior of gangue
minerals. Enrichment ratios (ERs) are favored over grades
to ensure the use of normalized indicators for effective trial
comparisons.
These responses, denoted as y, were modelled based
on a combination of factors using a classical second-order
model, the general form of which is:
· ·F ·
· ·F
y a a G a a G·F
a G a
0 1 2 12
11
2
22
2 f
=+++
+++
(1)
In the above equation, a a a a a a
0 1 2 12 11 22 represent
the unknown coefficients of the model, and ε is a residual
term encompassing both the lack of fit (systematic error)
and random experimental error (Goupy &Creighton,
2008). The least squares procedure was employed to deter-
mine these coefficients and the residuals based on the
experimental data.
The models proposed in this paper underwent an
Analysis of Variance (ANOVA) to optimize their signifi-
cance and calculate the coefficients (refer to Equation 1).
The initial ANOVA was conducted on a model where
all sets of factors and their interactions were considered.
Subsequently, at each step, a t-test was performed for all
factors of the model to eliminate any non-significant term.
For enrichment ratio and recovery models, the acceptance
level of significance was set to 5% and 10%, respectively.
RESULTS AND DISCUSSIONS
Repetitiveness of Trials
The central point of the Central Composite Design (CCD)
was replicated five times to evaluate the repeatability of the
experimental trials. The mean RSn and RRb are at 69.2%
and 4.8% with a standard deviation of only 0.53% and
0.13% respectively. The mean ERSn and ERRb are at 11.31
and 0.78 with a standard deviation of only 0.32 and 0.01
respectively.
Metallurgical Performances
The grade versus recovery plots, which compile data from
the 32 gravity separation trials (including both CCD
and exploratory trials), provide an overview of the ranges
of recoveries and enrichment ratios achieved for the tar-
geted metals: Sn, Nb, and Ta (Figure 2). In the majority
of tests, Sn recovery falls within the range of 65% to 73%,
accompanied by an enrichment ratio ranging from 9 to 19.
Similarly, for the majority of tests, Nb and Ta recoveries
range from 50% to 62%, with enrichment ratios spanning
from 6 to 16. Occasionally, enrichment ratios can reach 32,
23, and 21 for Sn, Nb, and Ta, respectively, but this comes
at the expense of a significant loss in recovery. Overall, met-
allurgical performances are observed to be more favorable
Figure 2. Grade vs recovery plots of Sn, Nb and Ta (left) and Rb (right) for the 32 trials
Given that the primary objectives of the separation pro-
cess involve recovering Sn, Nb, and Ta, the key responses
under study include recovery and enrichment ratio of Sn
(RSn, ERSn), Nb (RNb, ERNb) and Ta grade (RTa, ERTa), as
well as the mass yield (Mrec). Additionally, Rb recovery and
enrichment ratio (RRb, ERRb) were examined as proxys for
Li-micas, which contain the majority of the Rb in the sam-
ple, and more broadly to monitor the behavior of gangue
minerals. Enrichment ratios (ERs) are favored over grades
to ensure the use of normalized indicators for effective trial
comparisons.
These responses, denoted as y, were modelled based
on a combination of factors using a classical second-order
model, the general form of which is:
· ·F ·
· ·F
y a a G a a G·F
a G a
0 1 2 12
11
2
22
2 f
=+++
+++
(1)
In the above equation, a a a a a a
0 1 2 12 11 22 represent
the unknown coefficients of the model, and ε is a residual
term encompassing both the lack of fit (systematic error)
and random experimental error (Goupy &Creighton,
2008). The least squares procedure was employed to deter-
mine these coefficients and the residuals based on the
experimental data.
The models proposed in this paper underwent an
Analysis of Variance (ANOVA) to optimize their signifi-
cance and calculate the coefficients (refer to Equation 1).
The initial ANOVA was conducted on a model where
all sets of factors and their interactions were considered.
Subsequently, at each step, a t-test was performed for all
factors of the model to eliminate any non-significant term.
For enrichment ratio and recovery models, the acceptance
level of significance was set to 5% and 10%, respectively.
RESULTS AND DISCUSSIONS
Repetitiveness of Trials
The central point of the Central Composite Design (CCD)
was replicated five times to evaluate the repeatability of the
experimental trials. The mean RSn and RRb are at 69.2%
and 4.8% with a standard deviation of only 0.53% and
0.13% respectively. The mean ERSn and ERRb are at 11.31
and 0.78 with a standard deviation of only 0.32 and 0.01
respectively.
Metallurgical Performances
The grade versus recovery plots, which compile data from
the 32 gravity separation trials (including both CCD
and exploratory trials), provide an overview of the ranges
of recoveries and enrichment ratios achieved for the tar-
geted metals: Sn, Nb, and Ta (Figure 2). In the majority
of tests, Sn recovery falls within the range of 65% to 73%,
accompanied by an enrichment ratio ranging from 9 to 19.
Similarly, for the majority of tests, Nb and Ta recoveries
range from 50% to 62%, with enrichment ratios spanning
from 6 to 16. Occasionally, enrichment ratios can reach 32,
23, and 21 for Sn, Nb, and Ta, respectively, but this comes
at the expense of a significant loss in recovery. Overall, met-
allurgical performances are observed to be more favorable
Figure 2. Grade vs recovery plots of Sn, Nb and Ta (left) and Rb (right) for the 32 trials