XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3161
Since recovery information for individual particles is
not readily available, model validation is done by compar-
ing the predicted mass and composition of each processing
product to that observed in the test, for example by means
of enrichment factor vs. recovery plots. For that, a boot-
strap approach is used:
• Resample the validation particle dataset with the
same number of particles and replacement,
• Predict the probability of recovery of individual par-
ticles with the trained model,
• Assign particles to each processing stream based on
the computed probabilities,
• Compute the bulk mass and composition of each
processing stream,
• Compare to observed values.
This process is repeated 100 times to capture model and
process uncertainties. Uncertainties of observed stream
composition values are captured by resampling their par-
ticle dataset, as proposed by Blannin et al. (2021).
With the recovery probabilities of individual parti-
cles in the different concentrates of each flotation experi-
ment, the classical first-order flotation rate constant model
(Polat and Chander, 2000, Eq. (2)) is fit to each particle.
Parameters Rmax, the recovery expected at infinite time,
and k, the flotation rate constant, which are computed as a
function of flotation time (t) and recovery at time t (Rt), can
then be evaluated to understand the flotation behaviour of
individual particles according to the properties (e.g., size).
*R R e 1
max t =--kt ^h (3)
Besides, the entrainment degree (ENT) can be calculated
based on the cumulative water (Rw) and individual CAM-
particle recoveries (RCAM)—Eq. (3)—as an adaptation of
the typically entrainment degree functions based on par-
ticle sizes (Savassi, 1998). This approach does not imply
that all CAM particles are solely recovered via entrainment.
One must surely be careful with interpreting these results
since each phase has a distinct density and surface wetta-
bility. It can anyway provide meaningful information for
understanding the mechanism of recovery of these phases
ENT Rw
R
CAM =(4)
RESULTS
Figure 1 displays the reconstructed modal mineralogy of the
feed material used in each flotation test. The reconstructed
modal mineralogy results match well with mass ratio of
the distinct phases used in each experiment (Table 1). The
larger variations are observed for quartz (6 wt.% measured
and 10 wt. %used) and aluminium (6 wt.% measured and
3 wt. %used). These variations might be caused by the
Figure 1. Modal composition of the feed of each experiment, reconstructed based on the product samples. Results from the MLA
Since recovery information for individual particles is
not readily available, model validation is done by compar-
ing the predicted mass and composition of each processing
product to that observed in the test, for example by means
of enrichment factor vs. recovery plots. For that, a boot-
strap approach is used:
• Resample the validation particle dataset with the
same number of particles and replacement,
• Predict the probability of recovery of individual par-
ticles with the trained model,
• Assign particles to each processing stream based on
the computed probabilities,
• Compute the bulk mass and composition of each
processing stream,
• Compare to observed values.
This process is repeated 100 times to capture model and
process uncertainties. Uncertainties of observed stream
composition values are captured by resampling their par-
ticle dataset, as proposed by Blannin et al. (2021).
With the recovery probabilities of individual parti-
cles in the different concentrates of each flotation experi-
ment, the classical first-order flotation rate constant model
(Polat and Chander, 2000, Eq. (2)) is fit to each particle.
Parameters Rmax, the recovery expected at infinite time,
and k, the flotation rate constant, which are computed as a
function of flotation time (t) and recovery at time t (Rt), can
then be evaluated to understand the flotation behaviour of
individual particles according to the properties (e.g., size).
*R R e 1
max t =--kt ^h (3)
Besides, the entrainment degree (ENT) can be calculated
based on the cumulative water (Rw) and individual CAM-
particle recoveries (RCAM)—Eq. (3)—as an adaptation of
the typically entrainment degree functions based on par-
ticle sizes (Savassi, 1998). This approach does not imply
that all CAM particles are solely recovered via entrainment.
One must surely be careful with interpreting these results
since each phase has a distinct density and surface wetta-
bility. It can anyway provide meaningful information for
understanding the mechanism of recovery of these phases
ENT Rw
R
CAM =(4)
RESULTS
Figure 1 displays the reconstructed modal mineralogy of the
feed material used in each flotation test. The reconstructed
modal mineralogy results match well with mass ratio of
the distinct phases used in each experiment (Table 1). The
larger variations are observed for quartz (6 wt.% measured
and 10 wt. %used) and aluminium (6 wt.% measured and
3 wt. %used). These variations might be caused by the
Figure 1. Modal composition of the feed of each experiment, reconstructed based on the product samples. Results from the MLA