2558 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
Pilot and Industrial Scale
The pilot-scale flotation tests were carried out using a con-
tinuous flotation machine (CFM), the CPT Mini Pilot
Plant from Eriez ®. The first cell of the flotation machine
was used for conditioning. A feed of 30 kg/h with a solids
content of 33% was processed. The pH value was measured
and regulated in the first cleaning flotation stage and in
the first post-flotation stage, and measured in the last post-
flotation cell as shown in Figure 3.
Each test required about 2.5 to 3 hours to reach steady
state. The final concentrate and tailings masses are weighed
continuously. The steady-state is reached when the time-
dependent increase in the two masses is almost constant. At
this point, samples are taken for analyses for one minute in
each stream and analysed with pXRF and XRD.
Transition from Batch to Continuous Operation and
Principle of the Methodology
The idea is based on combining DoE methodology in batch
flotation with the Nelder Mead simplex algorithm in pilot
and industrial scale. The Nelder-Mead simplex algorithm,
also known as the downhill simplex method, is a versatile
and relatively simple optimization algorithm (Nelder and
Mead 1965). However, it has some drawbacks, such as
sensitivity to the initial simplex and slow convergence in
some cases. Therefore, it is often used in combination with
other optimization methods or modified in various ways to
improve its performance.
The algorithm starts with an initial “simplex,” a geo-
metric shape in parameter space. The simplex has dimen-
sion n+1, where “n” is the number of parameters to be
optimized. Each vertex in the simplex is used to evaluate
the function to be optimized. The vertices are arranged
according to the function values they represent. The worst
vertex is mirrored by the centre of gravity of the other ver-
tices to create a new vertex. The worst vertex is replaced if
the function value at this mirrored vertex is better than the
second worst vertex, but not better than the best vertex.
The algorithm continues these steps until a termination cri-
terion is met, such as a maximum number of iterations or a
small convergence tolerance.
Figure 3. Process flow diagram of the flotation process at pilot scale
Table 3. Levels of variables investigated for the tests with
colloidal silica (23 full factorial design). These process
conditions were applied separately to each of the colloidal
silica modifications (c.f. Table 1)
Parameter Unit
Factor level
– +
pH — 8 10
Collector dosage g/t 100 400
Depressant dosage g/t 50 550
Pilot and Industrial Scale
The pilot-scale flotation tests were carried out using a con-
tinuous flotation machine (CFM), the CPT Mini Pilot
Plant from Eriez ®. The first cell of the flotation machine
was used for conditioning. A feed of 30 kg/h with a solids
content of 33% was processed. The pH value was measured
and regulated in the first cleaning flotation stage and in
the first post-flotation stage, and measured in the last post-
flotation cell as shown in Figure 3.
Each test required about 2.5 to 3 hours to reach steady
state. The final concentrate and tailings masses are weighed
continuously. The steady-state is reached when the time-
dependent increase in the two masses is almost constant. At
this point, samples are taken for analyses for one minute in
each stream and analysed with pXRF and XRD.
Transition from Batch to Continuous Operation and
Principle of the Methodology
The idea is based on combining DoE methodology in batch
flotation with the Nelder Mead simplex algorithm in pilot
and industrial scale. The Nelder-Mead simplex algorithm,
also known as the downhill simplex method, is a versatile
and relatively simple optimization algorithm (Nelder and
Mead 1965). However, it has some drawbacks, such as
sensitivity to the initial simplex and slow convergence in
some cases. Therefore, it is often used in combination with
other optimization methods or modified in various ways to
improve its performance.
The algorithm starts with an initial “simplex,” a geo-
metric shape in parameter space. The simplex has dimen-
sion n+1, where “n” is the number of parameters to be
optimized. Each vertex in the simplex is used to evaluate
the function to be optimized. The vertices are arranged
according to the function values they represent. The worst
vertex is mirrored by the centre of gravity of the other ver-
tices to create a new vertex. The worst vertex is replaced if
the function value at this mirrored vertex is better than the
second worst vertex, but not better than the best vertex.
The algorithm continues these steps until a termination cri-
terion is met, such as a maximum number of iterations or a
small convergence tolerance.
Figure 3. Process flow diagram of the flotation process at pilot scale
Table 3. Levels of variables investigated for the tests with
colloidal silica (23 full factorial design). These process
conditions were applied separately to each of the colloidal
silica modifications (c.f. Table 1)
Parameter Unit
Factor level
– +
pH — 8 10
Collector dosage g/t 100 400
Depressant dosage g/t 50 550