# Kinetics and Mechanisms of Artificial Willemite Leaching in Low-Sulfuric-Acid Solution at Elevated Temperature

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}), hydrozincite (2ZnCO

_{3}·3Zn(OH)

_{2}), zincite (ZnO), willemite (Zn

_{2}SiO

_{4}), and hemimorphite (Zn

_{4}Si

_{2}O

_{7}(OH)

_{2}·H

_{2}O) are the main oxide ore resources of zinc and are generally found in various parts of the world [3,4,5,6].

## 2. Experimental

#### 2.1. Materials

_{2}contents of each size fraction are listed in Table 1.

#### 2.2. Apparatus and Procedure

_{2}SO

_{4}was added to the reactor chamber and then heated to the required temperature whilst being agitated at 800 rpm. When the temperature reached the preset value and remained stable, the installed sample was injected into the solution by being pushed through a pressurized air stream. At the same time, the partial pressure of air was adjusted to the desired value (usually 1.2 MPa) for the convenience of solution sampling. This moment was considered the starting time for the leaching reaction. At appropriate time intervals, about 10 mL sample of the reaction mixture was collected for the analysis of zinc dissolved in the leach liquor. The zinc in the leach liquor was analyzed by EDTA titration. Reaction extent was estimated depending on the amount of zinc released from the artificial willemite. Zinc extraction was calculated using a volume-correction formula [22].

_{i}is the zinc extraction corresponding to the sample i, V

_{0}is the initial volume of the solution, V

_{i}is the volume of the sample i withdrawn each time, C

_{i}is the concentration of zinc in the sample i, M is the initial mass of the sample added to the reactor chamber, and C

_{M}is the percentage of zinc in the solid sample.

## 3. Results and Discussion

#### 3.1. Effects of Parameters

#### 3.1.1. Effect of Leaching Time

_{2}. Chemical analysis of artificial willemite showed a content of 49.5% Zn and 35.9% SiO

_{2}. These findings seem to suggest that high-temperature leaching of willemite in low-sulfuric-acid solution is effective for the selective extraction of zinc over silica. In addition, taking into account the fact that for measuring accurately the leaching rates, a very low acid concentration (1.0 g/L) was used in the present study, it is very likely that the acid concentration was not kept constant throughout the experiment. Additionally, the reaction kinetics slowed down between 8 and 16 min, as shown in Figure 2. This indicates that the first 8 min of leaching are of primary importance for the present kinetic study.

#### 3.1.2. Effect of Agitation Speed

#### 3.1.3. Effect of Particle Size

#### 3.1.4. Effect of Sulfuric Acid Concentration

#### 3.1.5. Effect of Temperature

#### 3.2. Characterization of Leaching Residue

#### 3.3. Kinetic Analysis

_{g}and F

_{p}are respectively the shape factor for grains and particle (=3 for spheres), g(x) and p(x) defined respectively by Equations (5) and (7) are the conversion functions, b is the stoichiometric coefficient, k

_{r}is the reaction rate constant, C

_{A,b}is the initial concentration of lixiviant A in solution, ρ

_{m}is the mole density of solid B, D

_{e}is the effective diffusivity of lixiviant A in the particle, D

_{g}is the effective diffusivity of lixiviant A through the product layer around grains, and r

_{g}and r

_{0}are respectively the distance from the center of symmetry to the reaction interface in the grain; in the particle, ε

_{0}is the initial porosity of the solid (B) particle, $\stackrel{\wedge}{\sigma}$ is the generalized liquid–solid reaction modulus defined by Equation (8). ${\stackrel{\wedge}{\sigma}}_{\mathrm{g}}^{}$, defined by Equation (6), is the dimensionless modulus for the reaction of the grain.

^{2}) of the fitting curve. The results are given in Table 2.

_{A}is ${C}_{\mathrm{A},\mathrm{b}}(1-\frac{{n}_{\mathrm{B}0}x}{b{C}_{\mathrm{A},\mathrm{b}}V})={C}_{\mathrm{A},\mathrm{b}}(1-\sigma x)$ at time t but not C

_{A,b}.

_{B0}is the initial moles of solid reactant B and V is the volume of the test solution in the system, $\sigma =\frac{{n}_{\mathrm{B}0}}{b{C}_{\mathrm{A},\mathrm{b}}V}$.

_{c}, k

_{d}, and k

_{d}

^{0}—defined in Equations (12)–(14), respectively—are apparent rate constants.

_{e}>> D

_{g}, which indicates that the diffusion of the liquid reactant through the product layer around the individual grains is the main rate-controlling step.

_{d}, it must be directly proportional to $\frac{1}{{r}_{\mathrm{g}}^{2}}$. Combining Equations (13) and (15), it is found that the apparent rate constant k

_{d}is also proportional to $\frac{1}{{r}_{0}^{2}\left(1-{\epsilon}_{0}\right)}$. The k

_{d}values for the five sizes are calculated from Figure 9 and plotted in Figure 13 against $\frac{1}{{r}_{0}^{2}\left(1-{\epsilon}_{0}\right)}$. A straight line with a regression coefficient of 0.97 is obtained. This result may be taken as the indirect evidence to support the conclusion that the leaching process follows the grain model with the product layer diffusion control.

_{d}values for each sulfuric acid concentration are determined from Figure 10. From the k

_{d}and sulfuric acid concentration values, a plot of lnk

_{d}versus ln[H

_{2}SO

_{4}] is given in Figure 14. As seen in Figure 14, the reaction order with respect to sulfuric acid concentration was found to be 1.6472, with a correlation coefficient of 0.9891.

_{a}is the apparent activation energy of the reaction, R is the universal gas constant, and T is the absolute temperature.

_{d}values for different temperatures are calculated from the slopes of the straight lines in Figure 12. The Arrhenius plot of lnk

_{d}versus 1/T is an approximate line with a regression coefficient of 0.9828 where the slop is (−E

_{a}/R), as shown in Figure 15. From E

_{a}/R, the apparent activation energy of the leaching reaction was determined to be 22.06 KJ/mol. From the intercept of the straight line in Figure 15, the Arrhenius pre-exponential factor is found to be 43.55 min

^{−1}.

#### 3.4. High-Temperature Leaching Reaction of Willemite with Sulfuric Acid

_{2}SiO

_{4}(s) + 2H

_{2}SO

_{4}(aq) → 2ZnSO

_{4}(aq) + Si(OH)

_{4}(aq)

_{4}) produced in Equation (16) polymerizes over time to produce polysilicic acid, forming a gel [12] which impairs or totally disrupts pulp filtration and limits the mobility of liquid relative to solid phase in the pulp, leading to the reduction of zinc extraction in the solution.

_{4}(aq) = SiO

_{2}(s, crystalline) + 2H

_{2}O(g)

_{2}SiO

_{4}(s) + 2H

_{2}SO

_{4}(aq) → 2ZnSO

_{4}(aq) + SiO

_{2}(s, cristobalite) + 2H

_{2}O(g).

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Effect of leaching time on zinc extraction (particle size −57 + 53 μm, sulfuric acid concentration 1.0 g/L, agitation speed 800 rpm, and temperature 393 K).

**Figure 3.**XRD patterns of the sample before leaching and after leaching of different durations (conditions as per Figure 2).

**Figure 4.**Effect of agitation speed on zinc extraction (conditions as per Figure 2).

**Figure 5.**Effect of particle size on zinc extraction (conditions as per Figure 2).

**Figure 6.**Effect of sulfuric acid concentration on zinc extraction (conditions as per Figure 2).

**Figure 7.**Effect of temperature on zinc extraction (conditions as per Figure 2).

**Figure 8.**SEM image and EDS analysis of leaching residue after 16 min leaching (conditions as per Figure 2).

**Figure 14.**Plot for the determination of reaction order with respect to sulfuric acid concentration.

**Figure 17.**SEM images ((

**a**) ×200 times and (

**b**) ×5000 times) and EDS patterns of leaching residue from the experiment No. 2 (1-residual willemite, 2-franklinite, 3-quartz).

**Table 1.**Chemical analysis, surface area, and D

_{e}/D

_{g}values of each size fraction from artificial willemite.

Size Fraction (μm) | Zn (%) | SiO_{2}(%) | Surface Area (m^{2}/g) | Total Pore Volume (mm ^{3}/g) | Pore Average Diameter (Å) | Initial Porosity (ε_{0}) of Particle (%) | $\frac{{\mathit{D}}_{\mathbf{e}}}{{\mathit{D}}_{\mathbf{g}}}(\times {10}^{4})$ |
---|---|---|---|---|---|---|---|

−246 + 147 | 48.7 | 34.8 | 0.459 | 1.1 | 16.10 | 0.44 | 0.96~3.8 |

−147 + 98 | 49.1 | 36.1 | 0.431 | 0.9 | 15.97 | 0.36 | 0.37~1.5 |

−98 + 74 | 49.5 | 35.4 | 0.469 | 1.0 | 16.13 | 0.4 | 0.15~0.6 |

−74 + 57 | 49.3 | 36.5 | 0.569 | 1.0 | 17.94 | 0.4 | 0.087~0.35 |

−57 + 53 | 49.5 | 35.9 | 0.644 | 1.0 | 19.53 | 0.4 | 0.078~0.31 |

Temp. (K) | Kinetics Expression | |||||
---|---|---|---|---|---|---|

$1-{(1-\mathit{x})}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{}^{\u2020}$ | $1-3{(1-\mathit{x})}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+2(1-\mathit{x}){}^{\u2020}$ | ψ* ^{‡} | ψ^{‡} | |||

3 min | 8 min | 3 min | 8 min | 8 min | 8 min | |

373 | 0.9165 | 0.8799 | 0.9813 | 0.9835 | 0.965 | 0.9982 |

383 | 0.9046 | 0.8217 | 0.9694 | 0.9428 | 0.928 | 0.9792 |

393 | 0.9107 | 0.7719 | 0.9761 | 0.9025 | 0.9041 | 0.9701 |

403 | 0.9052 | 0.8031^{(6min)} | 0.9807 | 0.925^{(6min)} | 0.9185^{(6min)} | 0.9766^{(6min)} |

413 | 0.8962 | 0.797^{(6min)} | 0.9841 | 0.9252^{(6min)} | 0.9216^{(6min)} | 0.9791^{(6min)} |

^{†}: Assuming that the sulfuric acid concentration remains constant during leaching.

^{‡}: The sulfuric acid concentration changes as the reaction proceeds.

**Table 3.**Chemical components of willemite concentrate and leaching residue under the optimal conditions studied.

Experiment No. | 1 | 2 | 3 | 4 | Average | Willemite Concentrate | |
---|---|---|---|---|---|---|---|

Chemical composition of leaching residue (wt.%) | Zn | 2.15 | 1.63 | 1.97 | 1.74 | 1.87 | 43.96 |

Fe | 2.13 | 1.89 | 2.06 | 1.95 | 2.01 | 1.23 | |

Pb | 0.94 | 1.13 | 1.03 | 1.2 | 1.07 | 0.78 | |

As | <0.1 | <0.1 | <0.1 | <0.1 | <0.1 | <0.1 | |

SiO_{2} | 77.04 | 75.6 | 76.3 | 74.69 | 75.9 | 38.9 | |

Al_{2}O_{3} | 1.09 | 1.22 | 1.18 | 1.27 | 1.19 | 0.91 | |

K_{2}O | 0.53 | 0.52 | 0.42 | 0.48 | 0.49 | 1.06 | |

MgO | 0.2 | 0.22 | 0.23 | 0.22 | 0.22 | 0.27 | |

CaO | 2.26 | 2.3 | 2.04 | 2.1 | 2.2 | 1.22 |

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**MDPI and ACS Style**

Xu, H.; Qian, Y.; Zhou, Q.; Wei, C.; Wang, Q.; Zhao, W.; Zhu, B.; Wu, J.; Ren, F.; Xu, J.
Kinetics and Mechanisms of Artificial Willemite Leaching in Low-Sulfuric-Acid Solution at Elevated Temperature. *Metals* **2022**, *12*, 2031.
https://doi.org/10.3390/met12122031

**AMA Style**

Xu H, Qian Y, Zhou Q, Wei C, Wang Q, Zhao W, Zhu B, Wu J, Ren F, Xu J.
Kinetics and Mechanisms of Artificial Willemite Leaching in Low-Sulfuric-Acid Solution at Elevated Temperature. *Metals*. 2022; 12(12):2031.
https://doi.org/10.3390/met12122031

**Chicago/Turabian Style**

Xu, Hongsheng, Yanan Qian, Quanfa Zhou, Chang Wei, Qi Wang, Wenjie Zhao, Binglong Zhu, Juan Wu, Fang Ren, and Jingxu Xu.
2022. "Kinetics and Mechanisms of Artificial Willemite Leaching in Low-Sulfuric-Acid Solution at Elevated Temperature" *Metals* 12, no. 12: 2031.
https://doi.org/10.3390/met12122031