XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 941
interactions (x*y), and pure second-order terms (x2). This
model was constructed from 1st and 2nd order interac-
tions of the 8 first order terms listed. The 45 starting terms
from full response surface model (intercept, 8 first order,
36 second order) were trimmed down using forward step-
wise regression to identify and eliminate statistically insig-
nificant terms.
Importantly, Figure 8 identifies statistically significant
factors and their interactions. More importantly, these fac-
tors can be classified into distinctively different aggregates,
chemically, physically, or both, or indirectly thermody-
namic and kinetic, like reagents (thermodynamic), particles
(feed rate, kinetics), bubbles (texture, froth velocity), ore
(mill feed XRF Cu% and Pb% readings), and Pb recov-
ery (XRF Pb% readings in tail and Pb concentrate). Most
importantly, Digital One can control and optimize these
bubbles, froth, particles, XRF assays, and interactions
among them to increase Pb recovery.
This model explains 85% variance in the data and is
very comprehensive since there are many combinations of
factors, reflecting changes throughout the two-day period
the data is collected, which can influence factor interac-
tions and Pb recovery, with two such examples shown in
Figures 14 and 15. (The behavior of this model, or flotation
in general, is extraordinarily rich and dynamic since any
subset of factors from any periods within two days could
form numerous models, or opportunities to improve Pb
recovery.)
Figure 14 shows the impact of changing mill feed rate
and dichromate on the Pb recovery, at conditions of 0.16%
feed Cu, 1.74% feed Pb, 4.25 cm/s froth velocity in the first
Cu rougher, ZnSO4 addition of 3855 ccm, a Pb cleaner 1
bubble texture of 0.42, and a Pb cleaner 1 froth velocity of
12.0 cm/s.
Figure 14 indicates that particles (mill feed rate) inter-
act with reagents (dichromate), impacting flotation (Pb
recovery). Lower mill feed rates and lower dichromate flow-
rate tend to increase Pb recovery (direction of dots).
Figure 12. Whole model Regression plot, actual versus
predicted Pb recoveries
Figure 13. Studentized residuals of predicted vs actual Pb recoveries
Table 7.Whole Model ANOVA
Source DF Sum of Squares Mean Square F Ratio
Model 16 592.90380 37.0565 74.2184
Error 209 104.35151 0.4993
C. Total 225 697.25531 p 0.0001
interactions (x*y), and pure second-order terms (x2). This
model was constructed from 1st and 2nd order interac-
tions of the 8 first order terms listed. The 45 starting terms
from full response surface model (intercept, 8 first order,
36 second order) were trimmed down using forward step-
wise regression to identify and eliminate statistically insig-
nificant terms.
Importantly, Figure 8 identifies statistically significant
factors and their interactions. More importantly, these fac-
tors can be classified into distinctively different aggregates,
chemically, physically, or both, or indirectly thermody-
namic and kinetic, like reagents (thermodynamic), particles
(feed rate, kinetics), bubbles (texture, froth velocity), ore
(mill feed XRF Cu% and Pb% readings), and Pb recov-
ery (XRF Pb% readings in tail and Pb concentrate). Most
importantly, Digital One can control and optimize these
bubbles, froth, particles, XRF assays, and interactions
among them to increase Pb recovery.
This model explains 85% variance in the data and is
very comprehensive since there are many combinations of
factors, reflecting changes throughout the two-day period
the data is collected, which can influence factor interac-
tions and Pb recovery, with two such examples shown in
Figures 14 and 15. (The behavior of this model, or flotation
in general, is extraordinarily rich and dynamic since any
subset of factors from any periods within two days could
form numerous models, or opportunities to improve Pb
recovery.)
Figure 14 shows the impact of changing mill feed rate
and dichromate on the Pb recovery, at conditions of 0.16%
feed Cu, 1.74% feed Pb, 4.25 cm/s froth velocity in the first
Cu rougher, ZnSO4 addition of 3855 ccm, a Pb cleaner 1
bubble texture of 0.42, and a Pb cleaner 1 froth velocity of
12.0 cm/s.
Figure 14 indicates that particles (mill feed rate) inter-
act with reagents (dichromate), impacting flotation (Pb
recovery). Lower mill feed rates and lower dichromate flow-
rate tend to increase Pb recovery (direction of dots).
Figure 12. Whole model Regression plot, actual versus
predicted Pb recoveries
Figure 13. Studentized residuals of predicted vs actual Pb recoveries
Table 7.Whole Model ANOVA
Source DF Sum of Squares Mean Square F Ratio
Model 16 592.90380 37.0565 74.2184
Error 209 104.35151 0.4993
C. Total 225 697.25531 p 0.0001