XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 3443
kinetic model to the data. A candidate expression for the
rate of reaction at constant temperature and acid concen-
tration is given by Eq. [4]. It is acknowledged that this is
not a proposal for a chemical pathway, but merely a mecha-
nism to explore the possibility of a reverse reaction domi-
nating at lower concentrations of ferrous ions.
k k-1 rate Fe^IIh@2p^O
1 2 =^IIIh@ h- 6 6Fe (4)
This expression was fitted to the experimental data. The
fit was obtained using the CycadProcess ® software (www.
cycadprocess.com) which implements the Levenberg-
Marquardt algorithm to minimize the relative sum of
squared differences between the model and the data.
The fit of Equation [4] to the experimental data was
compared to the fit of the second-order model without a
reverse reaction, given by Equation [5].
k rate
1 2 =h@2p^O h 6Fe^II (5)
The results for the parameter estimation are discussed
in the next section.
Parameter Estimation and Model Fit
Both the data set for data reported here and that of
Chmielewski and Charewicz (1984) were studied. The
results of this kinetic modelling are shown in Figure 11 for
the data from this work and in Figure 12 for the data from
Chmielewski and Charewicz (1984). Equation [4] models
the deviation from second-order kinetics seen in the data
whereas the Equation [5] fails to describe the low concen-
tration region.
The parameters fitted to each of these datasets is given
in Table 4. Both models have good sensitivity to parameter
k1, but parameter k–1 shows lower sensitivity even when
relative sum of squares was used. There is clustering of the
parameter k1 for the dataset of Chmielewski and Charewicz
Figure 11. Fit of Equations [4] and [5] to data reported here. The grey curve represents Equation [4], while the orange curve
represents Equation [5]
kinetic model to the data. A candidate expression for the
rate of reaction at constant temperature and acid concen-
tration is given by Eq. [4]. It is acknowledged that this is
not a proposal for a chemical pathway, but merely a mecha-
nism to explore the possibility of a reverse reaction domi-
nating at lower concentrations of ferrous ions.
k k-1 rate Fe^IIh@2p^O
1 2 =^IIIh@ h- 6 6Fe (4)
This expression was fitted to the experimental data. The
fit was obtained using the CycadProcess ® software (www.
cycadprocess.com) which implements the Levenberg-
Marquardt algorithm to minimize the relative sum of
squared differences between the model and the data.
The fit of Equation [4] to the experimental data was
compared to the fit of the second-order model without a
reverse reaction, given by Equation [5].
k rate
1 2 =h@2p^O h 6Fe^II (5)
The results for the parameter estimation are discussed
in the next section.
Parameter Estimation and Model Fit
Both the data set for data reported here and that of
Chmielewski and Charewicz (1984) were studied. The
results of this kinetic modelling are shown in Figure 11 for
the data from this work and in Figure 12 for the data from
Chmielewski and Charewicz (1984). Equation [4] models
the deviation from second-order kinetics seen in the data
whereas the Equation [5] fails to describe the low concen-
tration region.
The parameters fitted to each of these datasets is given
in Table 4. Both models have good sensitivity to parameter
k1, but parameter k–1 shows lower sensitivity even when
relative sum of squares was used. There is clustering of the
parameter k1 for the dataset of Chmielewski and Charewicz
Figure 11. Fit of Equations [4] and [5] to data reported here. The grey curve represents Equation [4], while the orange curve
represents Equation [5]