A Shrinking Particle—Shrinking Core Model for Leaching of a Zinc Ore Containing Silica

Int. J. Miner. Process. 93 (2009) 79–83

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Int. J. Miner. Process. j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j m i n p r o

A shrinking particle—shrinking core model for leaching of a zinc ore containing silica Vida Safari a, Gilnaz Arzpeyma a, Fereshteh Rashchi b, Navid Mostoufi a,⁎ a b

Department of Chemical Engineering, University of Tehran, PO Box 11155/4563, Tehran, Iran Department of Metallurgy and Materials Engineering, University of Tehran, PO Box 11155/4563, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 10 January 2009 Received in revised form 24 May 2009 Accepted 11 June 2009 Available online 23 June 2009 Keywords: Leaching Kinetics Zinc silicate Shrinking core model Gelatinous silica layer

a b s t r a c t A new mathematical model was developed for leaching of zinc ores containing silicates such as hemimorphite which produce a gel during leaching with sulfuric acid. This model is based on the shrinking core model in which the particle size and the reacting core shrink simultaneously. It was shown that the actual dissolution time of the ore particles is longer than the time corresponding to the dissolution of chemical zinc oxide itself. It was suggested that because of the existence of silicates in the ore, a gelatinous layer was formed around the reacting core. Since the gel product is soft, it breaks apart when the particles collide and as a result, the particles shrink. However, a thin gelatinous layer always covers the reacting core which increases the mass transfer resistance and increases the leaching time. This model was applied to leaching of a zinc-rich tailing containing hemimorphite and the thickness of the gelatinous layer as well as the diffusion coefficient in this layer was determined. © 2009 Elsevier B.V. All rights reserved.

1. Introduction The main source of zinc metal production is zinc sulfide ore. Currently, depletion of these sulfide ores has brought more emphasis on zinc extraction from oxides, silicates or even secondary sources. Zinc extraction is performed mainly by hydrometallurgical methods. In the hydrometallurgical process, the ore is first leached by a solvent and then before electrowinning a purification process is used to prepare the solution for eletrolysis. During the leaching process of zinc oxidized ore, soluble zinc sulfate forms which stays in solution. In this process, the lead compounds form lead sulfate precipitates which transfer to the leaching filter cake during the solid/liquid separation. Leaching of the ore at pH ca. 2, transforms the silicate compounds of the ore to colloidal silica, i.e., a gel (Matthew and Elsner, 1977). Process kinetics and optimum operating conditions have been studied for the leaching of zinc silicate ore tailings. Monhemius and Terry (1983) investigated the influence of different parameters on the kinetic of acid dissolution of both natural and synthetic willemite (Zn2SiO4) and hemimorphite (Zn4Si2O7(OH)2.H2O). Specific rate constants were estimated for leaching of both willemite and hemimorphite in different acidic media. They found that the dissolution was mixed chemical/diffusion controlled in hemimorphite and chemically controlled in the case of willemite. Abdel-Aal (2000) investigated the kinetics of sulfuric acid leaching of low-grade zinc silicate ore. In their study, diffusion through the product layer was

⁎ Corresponding author. Tel.: +98 21 6696 7797; fax: +98 21 6640 1024. E-mail address: mostoufi@ut.ac.ir (N. Mostoufi). 0301-7516/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2009.06.003

determined as the rate controlling step. Espiari et al. (2006) verified extraction of zinc from tailings of lead flotation plant. They studied the effect of different parameters on kinetics of zinc dissolution and found that the rate determining step is the physicochemical desorption process. Souza et al. (2007) studied the effect of particle size, temperature and initial acid concentration on leaching of zinc silicate ores. They concluded that the grain model with porous diffusion control is the rate controlling step. Some researchers have reported the possible existence of internal diffusion resistance. For instance, Pecina et al. (2007) have reported formation of a sulfur layer in zinc sulfide leaching with high concentration of sulfuric acid solution containing hydrogen peroxide and indicated that this layer reduces leaching efficiency. Mulak et al. (2005) found that in leaching of spent nickel oxide catalyst with sulfuric acid, an aluminium-rich layer surrounds the unreacted core of the particle and grows inward as the particle reacts. In leaching process of sphalerite containing a lower concentration of iron, the decrease in zinc dissolution rate (as compared to a greater ironcontaining sphalerite mineral) was attributed to formation and growth of a polysulfide surface layer during the initial rapid leach period (Weisener et al., 2004). Based on the above evidences, it can be concluded that when a core shrinks, an internal resistance layer, either a reaction product layer or a gel film forms around the core and results in a decrease in the extraction yield in the leaching process. However, in many cases, the size of the particle (including unreacted core and the layer) decreases with time. In other words, although the product layer forms around the core, it shrinks as the core shrinks. In all the previous studies, existence of this gelatinous layer around the particle was neglected during the kinetics calculations and its effect on the kinetics of

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leaching was not taken into account. In the present study, a mathematical model has been developed based on the shrinking core model in which the resistance of the gelatinous product film is also considered. This kinetic model consists of three steps: external diffusion in the liquid, internal diffusion in the gelatinous product film and chemical reaction on the surface of the core. 2. Model development Zinc silicate ore, as hemimorphite, reacts with sulfuric acid according to the following reaction: Zn4 Si2 O7 ðOHÞ2 ·H2 O þ 4H2 SO4 →4ZnSO4 þ Si2 OðOHÞ6 þ 3H2 O

ð1Þ

Zinc sulfate is soluble in water. However, disilicic acid, Si2O(OH)6, which apparently polymerizes to produce polysilicic acid, forms a gelatinous phase at specific acidic pH which remains around the particles surface and leads to a decrease in the extraction yield. The most common models considered in leaching are illustrated in Fig. 1. Fig. 1a corresponds to the case when the reaction takes place on the exposed surface of the particle and the product completely dissolves in the liquid. This shrinking particle model (SPM) has been used by researchers such as Espiari et al. (2006), Aydoğan et al. (2006) and Velardo et al. (2002). If the product does not dissolve in the liquid, the particle size would not change but the reacting core shrinks inside the particle. This situation is shown in Fig. 1b and the model is called “Shrinking Core–Constant Particle Size”. It has been used by researchers such as Liu et al. (2006), Liddell (2005) and Szubert et al. (2006). Fig. 1c demonstrates schematic of a model called “Shrinking Core–Shrinking Particle”. In this case as the reaction proceeds, the unreacted core of particle shrinks while a gelatinous silica layer forms around the core. However, since this layer is soft, it breaks apart when the particles collide. Nevertheless, a thin layer of silica remains around the core. The silica layer creates a resistance during acid transfer from the solution to the surface of the core. In the present work, the last model was considered as the base kinetic model since the silica product does not dissolve completely in the acid solution. Therefore, the internal diffusion through the gel film should be taken into account. 2.1. Assumptions

• In the absence of adequate information, the thickness of the silica layer around the core was assumed to be constant during the leaching process. • Although there exist many reactions in the leaching of zinc by sulfuric acid from the ore, for the sake of simplicity, the main reaction considered in this work is dissolution of zinc oxide in acid. In other words, the main source of zinc in the leaching was assumed to be zinc oxide. • Hemimorphite particles were considered as the source of silica responsible for the gel formation. • Other substances present in the ore do not have any significant effect on the kinetics. • The temperature remains constant during the process. • The particle and the gelatinous layer are both non-porous. Thus, mass transfer occurs through molecular/ion diffusion in these phases. 2.2. Kinetic modeling Considering all the above assumptions, the first step for developing the model is to define a criterion indicative of the advancement of reaction versus time. The rate of reaction per unit surface of the core can be related to the dissolution rate of zinc oxide as follows: M dn Rr = − ZnO ZnO Sc dt

ð2Þ

The rate of zinc oxide disappearance can be expressed as: dnZnO ρ GS dr = Ore c c dt MZnO dt

ð3Þ

It has been shown in several references that the rate of reaction for dissolution of zinc oxide, Rr, is first order with respect to the concentration of the solvent (e.g., Espiari et al., 2006; Monhemius and Terry, 1983): Rr =

kCA MZnO

ð4Þ

Therefore, the rate of shrinkage can be expressed as:

The assumptions of the model are as follows: • The particles are spherical. • During the process, the particle shrinks uniformly, thus, it maintains its spherical shape.

drc kCA =− dt ρOre G

ð5Þ

The acid concentration, CA, used in Eq. (5) should be evaluated at the surface of the core. To find the acid concentration at reaction

Fig. 1. Schematics of different mechanisms of leaching.

V. Safari et al. / Int. J. Miner. Process. 93 (2009) 79–83

surface, mass balances should be written for both the liquid film layer and the gelatinous layer. In both cases, mass transfer occurs only in radial direction and the mass transfer equation becomes:
 1 d 2 dCA r =0 2 dr dr r

ð6Þ

The boundary conditions are: r = rc + δ r = rc

hD ðCA0  CA Þ = Dg

Dg

dCA dr

ð7Þ

dCA = kCA dr

ð8Þ

Considering that the process is in quasi-steady-state conditions, the rate of reaction at the surface of the core would be equal to the rate of mass transfer to and through the gel film: hD ðCA0  CA j rc

+ δÞ

= kCA j rc

ð9Þ

Solving the differential Eq. (6) with boundary conditions (7) and (8) and then solving Eq. (9) for finding CA(rc) would result in obtaining CA: 2 CA = CA0 4 D

Dg krc2 g

krc2

+

1 rc

r

3

 r1  1r

c

c

1 + δ

Dg hD ðrc + δÞ2

+

5

ð10Þ

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It is worth mentioning that in all previous investigations on kinetics of leaching of zinc with sulfuric acid, different rate constants were reported (e.g., Espiari et al., 2006; Abdel-Aal, 2000). However, since in all these investigations the effect of gelatinous layer was not taken into account, the reported rate constant is in fact a combination of reaction rate constant and dispersion coefficient of acid in the gelatinous layer. In the present study, the effect of gelatinous layer is separated from the reaction. Therefore, only dissolution of pure zinc oxide in sulfuric acid was considered on the surface of the ore. Of course, based on the assumptions listed above, effect of other substances in the ore, on the dissolution kinetic of zinc oxide was neglected in this work. The mass transfer coefficient was calculated from (Ranz and Marshall, 1952): Sh = 2 + 0:6Sc

1=3

1=2

Re


1 = 3
 dp up 1 = 2 μ = 2 + 0:6 ρD μ

ð16Þ

Evaluation of mass transfer coefficient from Eq. (16) requires estimation of viscosity, density and diffusion coefficient of the acid solution. These properties are not simple functions of their compositions. There can be found several equations for viscosity, density and diffusion coefficient of the mixture in this process in various literatures. In the present study, the following correlations of Guerra and Bestetti (2006) were used: μ = ð0:4332344  4:998831 × 103 T + 2:174276 × 105 T 2  4:216447 × 108 T 3 + 3:072309 × 1011 T 4 Þ × expð0:6182½ZnSO4  + 0:1801½H2 SO4 

Therefore, the dissolution rate of zinc oxide can be expressed as:

Rr =

2

kCA j r = rc

=

MZnO

CA0 MZnO

4 1 k

ð17Þ

3 +

rc Dg



1 1r

c



rc + δ

+

rc2 hD ðrc + δÞ2

5

ð11Þ

2+

ρ = 1153:82 + 66748½H2 SO4  + 181:436½Zn 3+

+ 396:312½Fe

  0:55T

or in form of the shrinkage rate: 2 CA0 drc 4 =− dt ρOre G 1 + k

3 rc Dg



1 1r

c



rc + δ

+

rc2

5

ð12Þ




 r ðtÞ 3 XðtÞ = 1  c r0

ð13Þ

Therefore, the final differential equation, from which the extent of dissolution of particles as a function of time can be obtained, can be then achieved by combining Eqs. (12) and (13):

k

+

ð1XÞ2 = 3 r02 Dg

1

 1 r0 ð1−XÞ1 = 3

r



1 ð1XÞ1 = 3 + δ 0

+

ð1XÞ2 = 3 r02 hD ðr0 ð1XÞ1 = 3 + δÞ2



ð14Þ 2.3. Chemical and physical properties The only chemical reaction considered in this work on the surface of the core is dissolution of zinc oxide by sulfuric acid. Reaction rate constant for dissolution of pure zinc oxide in sulfuric acid is calculated from the following equation (Kristovnikov and Davydovskaya, 1936):

k = 6:028 × 10

−4


 13634:96 ðm = sÞ exp  RT



ð18Þ

DZnSO4 = ½8:083  7:496ð½ZnSO4  + 0:296½H2 SO4 Þ0:5 + 4:105½ZnSO4  + 3:924½H2 SO4   0:739ð½ZnSO4  + 1:615½H2 SO4 Þ1:5  × 1010

hD ðrc + δÞ2

Eq. (12) can be expressed in terms of advancement of the reaction. The conversion can be determined based on the residual volume of particle as follows:

dX 3CA  = dt ρOre Gr03 1

2+

 + 158:354½Fe

ð15Þ

ð19Þ 3. Results and discussion Performance of the proposed model was examined using the experimental data reported by Espiari et al. (2006) for leaching of zinc from a zinc-rich oxide silicate tailing with sulfuric acid. Their XRF analysis results showed that the sample contained 37% zinc oxide and 23.7% silica. The leaching data reported by Espiari et al. (2006) are available as zinc recovery vs. time at various temperatures. Eq. (14) was solved for different operating conditions reported by Espiari et al. (2006). In this equation, thickness and diffusion coefficient of the gel layer were considered as fitting parameters and their values at different temperatures were determined by fitting the equation to the experimental data. Fig. 2 illustrates a sample solution of the model as well as the corresponding experimental data. This figure shows the conversion of the ore as a function of time in the batch system. It can be seen in Fig. 2 that the model fits satisfactorily to the experimental data (Espiari et al., 2006). Prediction of the conversion when the effect of the gel film was neglected (only zinc oxide reaction with acid and liquid film resistance was considered) is also shown in the same figure. As it can be seen, the particles dissolved very fast if the effect of gel film formation is neglected. However, the trend of the experimental data suggests that the leaching process is not as fast as dissolution of zinc oxide in sulfuric acid. Slower reaction can be justified by adding the

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Fig. 2. Model verification with and without gelatinous layer. Fig. 4. Comparing reaction and gel diffusion resistances.

resistance of the gel film which is modeled in the present study. Therefore, it is not possible to neglect the effect of the gel film because its effect on the leaching is substantial. Espiari et al. (2006) reported conversion vs. time at various temperatures. Using these experimental data it was found that the thickness of the layer is almost constant in the range of temperature considered in this work and its average was determined to be 1.2 μm with standard deviation of 0.8 μm. However, diffusion coefficient is a strong function of temperature. The Arrhenius plot of diffusion coefficient of the gel against temperature is shown in Fig. 3 from which temperature dependency of diffusion coefficient was found to be: ln Dg =  12:92 

28; 167:83 RT

ð20Þ

There are three terms in the denominator of Eq. (14) which correspond to resistances due to chemical reaction, diffusion through gel film and mass transfer in the liquid film, respectively. Resistance of the liquid film is negligible as compared to the other two resistances for the operating conditions considered in this work. Therefore, in order to investigate the effect of temperature on the leaching rate, only chemical reaction and diffusion through the gel were considered. Fig. 4 demonstrates the reaction and internal diffusion resistances as a function of temperature. It can be seen in this figure that both of the resistances decrease by increasing the temperature. At low temperatures, reaction resistance is negligible and kinetic mechanism would be reduced to gel diffusion control. Increasing the temperature has a

significant effect on both reaction and mass transfer rates. At high temperatures these two rates are of the same order of magnitude as shown in Fig. 4. Therefore, at high temperature, the process is controlled by both chemical reaction and diffusion though the gelatinous layer. 4. Conclusion A mathematical model was developed for leaching of zinc from a zinc ore containing silica. It was shown that considering only the chemical reaction of zinc dissolution is not sufficient for estimating the leaching time of the ore. A thin gelatinous layer was considered to cover the reacting core of the ore in order to correct the model prediction. Adding the mass transfer resistance of this layer to the model considerably improved the predictions. It was shown that the thickness of the gel is almost constant but the diffusion coefficient of the gel decreases with temperature. At low temperatures, the reaction rate is significantly lower than the rate of mass transfer through this layer which alters the mechanism to diffusion controlled. At high temperatures, both chemical reaction and mass transfer control the dissolution rate of the zinc ore particles containing silica. Acknowledgement The authors would like to thank Professor Fathi Habashi from the University of Laval, Canada, for his valuable comments during the work. References

Fig. 3. Gel diffusivity versus temperature.

Abdel-Aal, E.A., 2000. Kinetics of sulfuric acid leaching of low-grade zinc silicate ore. Hydrometallurgy 55, 247–254. Aydoğan, S., Erdemoğlu, M., Aras, A., Uçar, G., Özkan, A., 2006. Dissolution kinetics of celestite (SrSO4) in HCl solution with BaCl2. Hydrometallurgy 84, 239–246. Espiari, S., Rashchi, F., Sadrnezhaad, S.K., 2006. Hydrometallurgical treatment of tailings with high zinc content. Hydrometallurgy 82, 54–62. Guerra, E., Bestetti, M., 2006. Physicochemical properties of ZnSO4–H2SO4–H2O electrolytes of relevance to zinc electrowinning. J. Chem. Eng. Data 51, 1491–1497. Kristovnikov, A.H., Davydovskaya, E.A., 1936. Zh. Fiz. Khim (In Russian) 8, 77–84. Liddell, K.C., 2005. Shrinking core models in hydrometallurgy: what students are not being told about the pseudo-steady approximation. Hydrometallurgy 79, 62–68. Liu, Y., Qi, T., Chu, J., Tong, Q., Zhang, Y., 2006. Decomposition of ilmenite by concentrated KOH solution under atmospheric pressure. Int. J. Miner. Process. 81, 79–84. Matthew, G., Elsner, D., 1977. Hydrometallurgical treatment of zinc silicate ores. Metall. Trans. 8B, 73–83. Monhemius, A.J., Terry, 1983. Acid dissolution of willemite and hemimorphite. Metall. Trans. 14B, 335–346. Mulak, W., Miazga, B., Szymczycha, A., 2005. Kinetics of nickel leaching from spent catalyst in sulphuric acid solution. Int. J. Miner. Process. 77, 231–235. Pecina, T., Franco, T., Castillo, P., Orrantia, E., 2007. Leaching of zinc concentrate in H2SO4 solutions containing H2O2 and complexing agents. Miner. Eng. 21 (1), 23–30.

V. Safari et al. / Int. J. Miner. Process. 93 (2009) 79–83 Ranz, W.E., Marshall, W.R., 1952. Evaporation from drops: part 1. Chem. Eng. Prog. 48, 141–150. Souza, A.D., Peina, P.S., Lima, E.V.O., daSilva, C.A., Leão, V.A., 2007. Kinetics of sulphuric acid leaching of a zinc silicate calcine. Hydrometallurgy 89, 337–345. Szubert, A., Łupiński, M., Sadowski, Z., 2006. Application of shrinking core model to bioleaching of black shale particles. Physicochem. Prob. Miner. Process. 40, 211–225. Velardo, A., Giona, M., Adrover, A., Pagnanelli, F., Toro, L., 2002. Two-layer shrinkingcore model: parameter estimation for the reaction order in leaching processes. Chem. Eng. J. 90, 231–240. Weisener, C.G., Smart, R.St.C., Gerson, A.R., 2004. A comparison of the kinetics and mechanism of acid leaching of sphalerite containing low and high concentrations of iron. Int. J. Miner. Process. 74, 239–249.

Glossary CA: acid concentration at the surface of the core (kg m− 3) CA0: acid concentration in the bulk (kg m− 3) dp: particle diameter (m) Dg: diffusivity of gel (m2 s− 1) DZnSO4: diffusion coefficient of zinc sulfate in solution (m2 s− 1) G: zinc oxide grade hD: mass transfer coefficient (m s− 1)

k: reaction rate constant (m s− 1) MZnO: zinc oxide molecular weight (kg kmol− 1) nZnO: moles of zinc oxide (k mol) rc: core radius (m) r0: initial radius of the particle (m) R: gas constant (8.314 J mol− 1 K− 1) Rr: rate of reaction for dissolution of zinc oxide (kg m− 2 s− 1) Re: Reynolds number; Re = ρupdp/µ Sc: surface of the core (m2) Sc: Schmidt number; Sc = µ/ρDZnSO4 Sh: Sherwood number; Sh = hDdp/µ t: time (s) T: temperature (K) up: terminal velocity (m s− 1) X: volumetric conversion

Greek letters δ: gelatinous layer thickness (m) µ: viscosity of solution (kg m− 1 s− 1) ρOre: density of zinc ore (kg m− 3) ρ: density of solution (kg m− 3)

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