XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 1725
Kinetic models. In this study, three kinetic models
were used to calculate the rate and activation energy of
precipitation reactions using ozone. These models are as
follows:
Linear Model: The linear model is an approxima-
tion and can serve as a baseline to understand the primary
behavior of the system (Oruê et al., 2021). The first-order
reaction constant in the Linear model is calculated using
Eq. 1.
Ct /C0 =k *t (1)
where k is the rate constant, and Ct and C0 are Co and Mn
concentration at the time t from the beginning and at the
start of the reaction, respectively.
Higbie Model: The Higbie model can provide a bet-
ter view of the reaction than the linear model by consider-
ing the effect of concentration gradients, and it could be
described using Eq. 2 (Oruê et al., 2021).
ln(Ct) =2k′t0.5+ Ln(C0) (2)
where k′ is a precipitation rate, and Ct and C0 are elemental
concentrations (e.g., Co and Mn) at time t from the begin-
ning and at the start of the reaction, respectively.
Pseudo-homogeneous Model: In this model, the
resistance to mass transfer from the gas phase to the liq-
uid phase is considered to be negligible, and the amount
of ozone dissolved in the liquid was regarded as abundant
(Cruz-Díaz et al., 2015 Oruê et al., 2021). Eq. 3 describes
the corresponding rate equation.
ln(Ct/C0)= –k″ *t (3)
where k″ is a precipitation rate, Ct and C0 are elemental
concentrations (e.g., Co and Mn) at time t from the begin-
ning and at the start of the reaction, respectively.
The activation energy (Eg) of the reaction was also cal-
culated through Arrhenius Eq.(4):
kg=A exp(–Eg/RT) (4)
where A is the frequency at which atoms and molecules
collide in a way that leads to a reaction, R is the gas con-
stant, T represents the temperature in Kelvin, and kg is the
temperature-dependent constant. (Lewis et al., 2015 Vaziri
Hassas et al., 2023).
Characterization and Data Analysis
Elemental analysis of the precipitates gathered at each
pH level during the staged precipitation process, and the
filtrates from each step were performed using an Agilent
7900 Inductively Coupled Plasma Mass Spectrometry
(ICP-MS). Quality control for the ICP analyses was
ensured by examining blanks, duplicate samples, standard
checks, internal standards, and different dilutions. The
elemental recovery values were calculated based on the ele-
mental concentrations and using Equation (5), where Ci is
the concentration (mg/L) of the element of interest in the
solution after filtration at each stage, and Cf is the concen-
tration of the same element in AMD at pH 7 (i.e., feed
to the ozone oxidative precipitation process). In this study,
error bars represent the 95% CI, calculated from triplicate
experiments to ensure reliability of the findings, reflect-
ing variations within a confident range under repeated
measurements.
Recovery (%)=C
C
100
f
i $d1 -n (5)
RESULTS AND DISCUSSION
Solution Chemistry Study
The saturation index was calculated to predict whether
Co-Mn hydroxides or oxides precipitate out of a solution
under specific conditions.
The saturation index is calculated using the following
Equation:
SI =log(IAP/Ksp) (6)
Here:
• IAP is the Ion Activity Product, the product of the
dissolved metal and oxide/hydroxide ions’ activities
(or concentrations) in solution.
• Ksp is the solubility product constant for the metal
hydroxide or oxide at the given temperature.
The process of manganese (II) and Cobalt (II) being
oxidized by ozone in water to form manganese (III) oxide
and cobalt (III) oxide can be written as follows:
Mn2+(aq) +½ O3(aq) +H2O(l) →
½ Mn2O3(s) +2H+(aq) +½ O2(g) (R3)
2Co2+(aq) +O3(aq) +H2O(l) →
Co2O3(s) +2H+(aq) +½ O2(g) (R4)
If SI 0, the solution is supersaturated, and there is a
potential for the precipitation of Mn2O3 and Co2O3. If SI
=0, the solution is at equilibrium. If SI 0, the solution
is undersaturated, meaning more Mn2O3 and Co2O3 can
dissolve into the solution.
The previous study by the authors on the effect of vari-
ous ligands/oxidative on Co-Mn showed that ozone was
the most effective oxidizing agent for the recovery of these
elements from AMD. To further explore how ozone can
Kinetic models. In this study, three kinetic models
were used to calculate the rate and activation energy of
precipitation reactions using ozone. These models are as
follows:
Linear Model: The linear model is an approxima-
tion and can serve as a baseline to understand the primary
behavior of the system (Oruê et al., 2021). The first-order
reaction constant in the Linear model is calculated using
Eq. 1.
Ct /C0 =k *t (1)
where k is the rate constant, and Ct and C0 are Co and Mn
concentration at the time t from the beginning and at the
start of the reaction, respectively.
Higbie Model: The Higbie model can provide a bet-
ter view of the reaction than the linear model by consider-
ing the effect of concentration gradients, and it could be
described using Eq. 2 (Oruê et al., 2021).
ln(Ct) =2k′t0.5+ Ln(C0) (2)
where k′ is a precipitation rate, and Ct and C0 are elemental
concentrations (e.g., Co and Mn) at time t from the begin-
ning and at the start of the reaction, respectively.
Pseudo-homogeneous Model: In this model, the
resistance to mass transfer from the gas phase to the liq-
uid phase is considered to be negligible, and the amount
of ozone dissolved in the liquid was regarded as abundant
(Cruz-Díaz et al., 2015 Oruê et al., 2021). Eq. 3 describes
the corresponding rate equation.
ln(Ct/C0)= –k″ *t (3)
where k″ is a precipitation rate, Ct and C0 are elemental
concentrations (e.g., Co and Mn) at time t from the begin-
ning and at the start of the reaction, respectively.
The activation energy (Eg) of the reaction was also cal-
culated through Arrhenius Eq.(4):
kg=A exp(–Eg/RT) (4)
where A is the frequency at which atoms and molecules
collide in a way that leads to a reaction, R is the gas con-
stant, T represents the temperature in Kelvin, and kg is the
temperature-dependent constant. (Lewis et al., 2015 Vaziri
Hassas et al., 2023).
Characterization and Data Analysis
Elemental analysis of the precipitates gathered at each
pH level during the staged precipitation process, and the
filtrates from each step were performed using an Agilent
7900 Inductively Coupled Plasma Mass Spectrometry
(ICP-MS). Quality control for the ICP analyses was
ensured by examining blanks, duplicate samples, standard
checks, internal standards, and different dilutions. The
elemental recovery values were calculated based on the ele-
mental concentrations and using Equation (5), where Ci is
the concentration (mg/L) of the element of interest in the
solution after filtration at each stage, and Cf is the concen-
tration of the same element in AMD at pH 7 (i.e., feed
to the ozone oxidative precipitation process). In this study,
error bars represent the 95% CI, calculated from triplicate
experiments to ensure reliability of the findings, reflect-
ing variations within a confident range under repeated
measurements.
Recovery (%)=C
C
100
f
i $d1 -n (5)
RESULTS AND DISCUSSION
Solution Chemistry Study
The saturation index was calculated to predict whether
Co-Mn hydroxides or oxides precipitate out of a solution
under specific conditions.
The saturation index is calculated using the following
Equation:
SI =log(IAP/Ksp) (6)
Here:
• IAP is the Ion Activity Product, the product of the
dissolved metal and oxide/hydroxide ions’ activities
(or concentrations) in solution.
• Ksp is the solubility product constant for the metal
hydroxide or oxide at the given temperature.
The process of manganese (II) and Cobalt (II) being
oxidized by ozone in water to form manganese (III) oxide
and cobalt (III) oxide can be written as follows:
Mn2+(aq) +½ O3(aq) +H2O(l) →
½ Mn2O3(s) +2H+(aq) +½ O2(g) (R3)
2Co2+(aq) +O3(aq) +H2O(l) →
Co2O3(s) +2H+(aq) +½ O2(g) (R4)
If SI 0, the solution is supersaturated, and there is a
potential for the precipitation of Mn2O3 and Co2O3. If SI
=0, the solution is at equilibrium. If SI 0, the solution
is undersaturated, meaning more Mn2O3 and Co2O3 can
dissolve into the solution.
The previous study by the authors on the effect of vari-
ous ligands/oxidative on Co-Mn showed that ozone was
the most effective oxidizing agent for the recovery of these
elements from AMD. To further explore how ozone can