XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 875
is modelled using empirical equations given by Lynch and
Rao (1975).
The objectives of optimization are to maximize the midsize
passing and throughput of the grinding circuit with con-
straints on the decision variables: slurry concentration (c),
ball filling (J), mill speed (φ), fresh feed flowrate (FF) and
sump water flowrate (W).
,,X f1 c J, FF,W Midsize Passing,
OF {=^h
,,M f c J, FF,W Throughput,
OF 2 {=^h
,^h MAX
U f f
1 2 ^h
U FF,W =^hT
,(,W )and W FF
min min max max 1 1 ^FF ^FF,W h h (20)
RESULTS AND DISCUSSION
The PBE along with selection and breakage functions is
solved using the LU decomposition method. The stepwise
details of the algorithm can be found elsewhere (Austin
et al., 1984). The output PSD of a ball mill operating at
steady state is obtained by solving Equation 8 for grind-
ing time, t=τ, where τ is mean residence time of the mill
at steady state. For our steady state simulations of a hypo-
thetical grinding circuit, τ comes from the Holdup model.
The slurry filling used in Equation 3 also comes from the
Holdup model, as shown in Figure 1.
Validation of Particle Size Distribution (PSD) Model
The proposed model is employed to predict the PSD for a
pilot scale mill (Faria et al., 2019) to test the PBM for dif-
ferent sizes of ball mills (scale up from lab to pilot scale).
The model parameters for the larger mills are scaled-up
using Equations 10–11. The predicted PSD from a pilot
scale ball mill and its comparison with published experi-
mental data (Faria et al., 2019) is shown in Figure 4 after
a grinding time of 45 minutes. The results suggest that the
model can capture the breakage phenomenon in the pilot
mill reasonably accurately.
Validation of Power Draw Model
The power draw predicted for different mills under various
conditions and their comparison with plant data is shown
in Figure 5. Diverse ball mill data with mill diameter (0.85–
5.34 m), length (1.53–8.84 m), rotational speed (0.6–
0.83), ball filling (0.069–0.48), total filling (0.069- 0.48),
discharge mechanism (grate or overflow), specific gravity of
the ore (2.6–4.6), and gross power (6.8–4100kW) is used
for comparison. It is evident from the parity plot (Figure 5),
that model predictions (R2 =0.9923) are in line with the
experimental data (Morrell 1996a).
Figure 3. Schematic diagram of the closed loop grinding circuit
is modelled using empirical equations given by Lynch and
Rao (1975).
The objectives of optimization are to maximize the midsize
passing and throughput of the grinding circuit with con-
straints on the decision variables: slurry concentration (c),
ball filling (J), mill speed (φ), fresh feed flowrate (FF) and
sump water flowrate (W).
,,X f1 c J, FF,W Midsize Passing,
OF {=^h
,,M f c J, FF,W Throughput,
OF 2 {=^h
,^h MAX
U f f
1 2 ^h
U FF,W =^hT
,(,W )and W FF
min min max max 1 1 ^FF ^FF,W h h (20)
RESULTS AND DISCUSSION
The PBE along with selection and breakage functions is
solved using the LU decomposition method. The stepwise
details of the algorithm can be found elsewhere (Austin
et al., 1984). The output PSD of a ball mill operating at
steady state is obtained by solving Equation 8 for grind-
ing time, t=τ, where τ is mean residence time of the mill
at steady state. For our steady state simulations of a hypo-
thetical grinding circuit, τ comes from the Holdup model.
The slurry filling used in Equation 3 also comes from the
Holdup model, as shown in Figure 1.
Validation of Particle Size Distribution (PSD) Model
The proposed model is employed to predict the PSD for a
pilot scale mill (Faria et al., 2019) to test the PBM for dif-
ferent sizes of ball mills (scale up from lab to pilot scale).
The model parameters for the larger mills are scaled-up
using Equations 10–11. The predicted PSD from a pilot
scale ball mill and its comparison with published experi-
mental data (Faria et al., 2019) is shown in Figure 4 after
a grinding time of 45 minutes. The results suggest that the
model can capture the breakage phenomenon in the pilot
mill reasonably accurately.
Validation of Power Draw Model
The power draw predicted for different mills under various
conditions and their comparison with plant data is shown
in Figure 5. Diverse ball mill data with mill diameter (0.85–
5.34 m), length (1.53–8.84 m), rotational speed (0.6–
0.83), ball filling (0.069–0.48), total filling (0.069- 0.48),
discharge mechanism (grate or overflow), specific gravity of
the ore (2.6–4.6), and gross power (6.8–4100kW) is used
for comparison. It is evident from the parity plot (Figure 5),
that model predictions (R2 =0.9923) are in line with the
experimental data (Morrell 1996a).
Figure 3. Schematic diagram of the closed loop grinding circuit