Leaching of Zinc Sulﬁde Concentrate from the Ganesh–Himal Deposit of Nepal S.K. SAHU, K.K. SAHU, and B.D. PANDEY The leaching of zinc concentrate obtained from the zinc ore located in the Ganesh–Himal region of Nepal has been carried out in the presence of ammonium persulfate (APS) as an oxidant. Leaching variables such as time, temperature, acid, and oxidant concentration, Eh, and particle size of sphalerite concentrate were studied to optimize the condition and to understand the mechanism of the reaction. The zinc extraction increased up to a temperature of 333 K and a further rise in the temperature to 343 K resulted in lowering of metal extraction. A decrease in particle size and increase in oxidant concentration enhanced the dissolution rate of zinc. The leaching data best ﬁtted to the mixed controlled kinetic model. An activation energy of 43 kJ/mol was obtained for the dissolution of zinc in the temperature range 303 to 333 K with APS. The leaching mechanism was further established by characterizing the original concentrate and the leach residue by X-ray diffraction (XRD) phase identiﬁcation and scanning electron microscopy (SEM) studies.
ZINC occurs in the earth crust predominantly as sulﬁdes, and sphalerite is its most important ore. Many investigations have been reported for the beneﬁciation of zinc ore to prepare concentrate from which zinc metal is produced by pyroor hydrometallurgical processes. These processes involve a roasting step, which evolves toxic SO2 gas and requires a sulfuric acid plant to be set up in the smelter. Direct leaching under pressure has several problems associated with maintenance of autoclave.[1,2,3] Among the alternate processes to treat the sphalerite, the hydrometallurgical route without pretreatment, such as direct oxidative leaching, is considered quite attractive. Several reagents have been used for the leaching of sphalerite concentrate. These are ferric ion in chloride and sulfate media, hydrogen peroxide, manganese dioxide, nitric acid, etc. The dissolution of zinc from sphalerite in acidic ferric solution and in acidic bacterial solution containing iron has been widely studied. Kuzminkh and Yakhontova investigated the dissolution of zinc from its concentrates with ferric sulfate in the temperature range 353 to 373 K. The zinc extraction rate increased with an increase in Fe31 concentration up to three times the stoichiometric requirement. The leaching of zinc from sphalerite with ferric ion in different media and also at different hydrochloric acid concentrations was investigated. Crundwell described the kinetics of dissolution of zinc sulﬁde by electrochemical mechanisms in which the charge transfer from the solid to the oxidant was rate limiting. Fullam and co-workers reported a fused salt electrolysis process for the treatment of sphalerite concentrate on laboratory scale. The process involves electrolytic decomposition of zinc sulﬁde dissolved in a molten salt to give molten zinc at the cathode and sulfur at the anode. The S.K. SAHU and K.K. SAHU, Scientists, and B.D. PANDEY, Deputy Director, are with the Metal Extraction and Forming Division, National Metallurgical Laboratory, Jamshedpur – 831 007, India. Contact e-mail: firstname.lastname@example.org Manuscript submitted June 15, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS B
process suffers from the technical problems such as maintenance of low current densities to prevent formation of chlorides. The leaching of zinc in the presence of chloride and pressure conditions[10,11] and kinetic studies of the ZnSFe(III) system in the absence[12,13] and sometimes in the presence of NaCl have been investigated. Parameters on the extraction of zinc from its concentrates were established in hydrochloric acid, hydrogen peroxide, and ferric chloride. Sharma and co-workers[18,19] studied the preferential attack of chloride in the ferric chloride-ZnS system. The oxidation behavior of sphalerite in the presence of pyrolusite in HCl and H2SO4 has been explained[20,21,22] in terms of formation of two corrosion couples, i.e., ZnS-Fe31 and MnO-Fe21, the redox species being generated continuously in a cyclic manner. Leaching of zinc in nitric acid is enhanced with increasing the temperature and acid concentration. There are many problems associated with the regeneration of the acid as the oxides of nitrogen are more hazardous and cause global warming and green house effects. In addition, the recovery of zinc from nitrate solution itself is considered a problem. At an altitude of 4420 m above mean sea level, a mineral deposit rich in zinc and lead has been located in the Ganesh–Himal region of Nepal. The reserve is estimated to be 2 million tonnes containing 16 to 19 pct zinc and lead together. M/s Nepal Metal Company Ltd. (NMCL, Katmandu) is interested in developing Ganesh–Himal zinc-lead deposit. The NML (Jamshedpur) has been engaged in studying the beneﬁciation of the ore and extraction of zinc from the zinc concentrate. For the treatment of such a small and pocket deposit at a high altitude, an ecofriendly hydrometallurgical route was considered. Earlier, the use of persulfate salts such as ammonium, sodium, and potassium was explored for the leaching of zinc from sphalerite concentrate in our laboratory.[24,25] Ammonium persulfate was found to be a better oxidant in comparison to its other analogues. Therefore, in the present investigation, ammonium persulfate has been used for the leaching of zinc from the sphalerite concentrate produced from the Nepal ore. VOLUME 37B, AUGUST 2006—541
Chemical Analysis of the Ore and Zinc Concentrate
Chemical Analysis of Ore Sample Constituents Zn Pb S Fe (total) SiO2 Al2O3 CaO MgO Cu Ag Au
Chemical Analysis of Zinc Concentrate
13.45 3.53 13.30 10.36 0.98 0.55 15.67 10.49 0.025 0.0008 nf
Zn Pb S Fe (total) Co Ni Cu Cd Ag SiO2 Al2O3 moisture
55.7 0.21 31.6 8.72 nf 0.005 0.04 0.091 0.0031 0.18 nf nil
Particle Size (mm)
Zinc Content (Pct)
106 106 to 75 75 to 63 63 to 45 ,45
5.94 10.11 11.36 26.18 46.31
56.4 57.3 56.4 56.2 54.8
Table III. XRD Identiﬁcation of Phases in Concentrate and Leach Residue at Different Time Intervals* Serial Number 1 2 3 4
Duration of Leaching (h)
before leaching 1 2 5
ZnS, FeS ZnS, FeS Zns, a-S a-S
About 5.0 tonnes of ore sample from the Ganesh–Himal region was supplied by NMCL (Katmandu). The sample was crushed and ground and was subjected to froth ﬂotation at NML to produce zinc concentrate. The concentrate was further ground and sieved to ,150-mm size, and from this, the particle size distribution was obtained. Analytical grade sulfuric acid and ammonium persulfate were used for leaching of the zinc concentrate. Other chemicals used for analysis were also analytical grade reagents. Leaching experiments were carried out in a glass vessel housed in a water bath, which was placed on a magnetic stirrer. The desired amount of zinc concentrate was added to the 2 3 104 m3 leaching solution containing ammonium persulfate maintained at the required temperature. The temperature was monitored and controlled by passing water through the bath while stirring the slurry to ensure uniform suspension of particles. During mixing, external diffusion was assumed to be negligible. At a selected time interval, a known amount of slurry was withdrawn and ﬁltered with whatman 41 ﬁlter paper; zinc and persulfate in the ﬁltrate were analyzed titrimetrically using standard methods. Based on the chemical analysis of the ﬁltrate, the percentage of zinc extraction was calculated. Residue from the leaching was sometimes analyzed to check the material balance. The redox potential (Eh) against SCE of the leach solution after ﬁltration was measured at room temperature. Phases in the concentrate and the leach residue were identiﬁed by X-ray diffraction (XRD). Surface morphology was studied by scanning electron microscopy (SEM) examination. III.
Table II. Particle Size Distribution of Zinc Concentrate
RESULTS AND DISCUSSION
The compositions of the ore and the zinc concentrate produced by ﬂotation are given in Table I. The major metallic content in the concentrate is zinc and iron analyzing 55.7 and 8.7 pct, respectively. Analysis of the concentrate may have a few unidentiﬁed residues and may have error within 2 pct. The zinc contents in various sieve fractions are incorporated in Table II. The smallest size fraction (,45 mm) was found to be the major component (46.3 pct) with 54.8 pct zinc content. The amount of coarser fraction (.106 mm) was 542—VOLUME 37B, AUGUST 2006
Minor Phase SiO2 a-S, SiO2 SiO2 ZnS, FeS, SiO2, (NH4)Fe3(SO4)2(OH)6
*Temperature: 333 K; acid: 900 mol/m3 H2SO4; oxidant: 272 kg/m3 APS; and pulp density: 100 kg/m3.
minimum (5.94 pct). The minor variation in the zinc content of different size fractions was observed. As regards the phases identiﬁed by XRD in the concentrate (Table III), sphalerite and iron sulﬁde (FeS) were the major minerals, while silica and pyrite (FeS2) were the minor phases. A. Oxidative Leaching of Zinc The effect of particle size on the leaching of zinc concentrate was studied at constant initial sulfuric acid concentration (900 mol/m3), temperature (333 K), pulp density (100 kg/m3), and the amount of ammonium persulfate (272 kg/m3). Figure 1 shows an increase in zinc recovery with the decrease in particle size. It was further observed that a maximum of 95 pct zinc could be recovered in 5 hours with the ﬁnest size fraction (,45 mm) of the concentrate. Also, a 90 pct Zn was dissolved when the mixed size particles (,150 mm) of the concentrate were leached. The recovery of zinc was also examined against time using the mixed particles (,150-mm size) of the concentrate while varying acid in the range 0 to 900 mol/m3 at 333 K and 100 kg/m3 pulp density. The results (Figure 2) show that the sulfuric acid has a noticeable effect on the dissolution of zinc. Zinc recovery (90 pct) was maximum with 900 mol/m3 H2SO4 in 5 hours time as compared to about 76 pct metal recovery when no acid was present. The presence of a high amount of acid aids the process of dissolution per Reaction . H2 SO4
ZnS 1 ðNH4 Þ2 S2 O8 ! ZnSO4 1 ðNH4 Þ2 SO4 1 S0  As such, the role of acid in dissolution of metal sulﬁdes in general and iron sulﬁde in particular is well documented.[28,29] In the leaching of zinc, FeS present in the concentrate reacts with sulfuric acid as FeS 1 H2 SO4 ! FeSO4 1 H2 S
The oxidation of Fe(II) in acidic solution with the available oxygen from ammonium persulfate (APS) may proceed as METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 1—Effect of particle size on the zinc extraction from zinc concentrate at different time intervals. Temperature: 333 K, acid: 900 mol/m3 H2SO4, oxidant: 272 kg/m3 APS, and pulp density: 100 kg/m3.
(Reaction ), as discussed in Section III–B. Further, the presence of acid restricts the hydrolysis of dissolved zinc; otherwise, it would precipitate as oxy/hydroxyl complexes such as ZnOH1 and Zn(OH)2 at higher pH. This is evident from the ﬁnal pH of the leach liquor with 900 mol/m3 H2SO4, which was found to be 0.2. At a constant sulfuric acid concentration (900 mol/m3) and temperature (333 K), zinc recovery (Figure 3) marginally increased with an increase in pulp density from 50 to 100 kg/m3, when 40 pct excess to the theoretical requirement of APS was added as an oxidant. This marginal increase in zinc dissolution at higher pulp density in the same volume may be attributed to increased oxidation of sphalerite because of the availability of higher amount of ZnS and APS to participate in the reaction. The recovery of zinc is presented in Figure 4 at varying APS concentration (195 to 311 kg/m3) with the concentrate of mixed size particles. The stoichiometric requirement of ammonium persulfate under the experimental condition is 195 kg/m3. Higher zinc extraction (90 pct) was observed for the oxidant concentration of 272 kg/m3, an amount greater by 40 pct than the stoichiometric requirement. A further increase in oxidant concentration to 311 kg/m3 (60 pct excess) improved zinc recovery (92 pct) marginally. Zinc recovery vs time using mixed size concentrate and 272 kg/m3 APS while varying the temperature (308 to 343 K) is presented in Figure 5. Zinc extraction increased up to 333 K, and a further rise in temperature to 343 K lowered zinc recovery. Lower zinc dissolution at higher temperature may be attributed to the decomposition of ammonium persulfate, as reported by Kolthoff and Stenger. The decomposition rate of ammonium persulfate has been carried out in our laboratory and published elsewhere. It should be mentioned that 18 pct of APS decomposes at 333 K in 1 hour as compared to its 50 pct decomposition at 343 K; these values are 22 and 58 pct, respectively, in 2 hours time. The concentration of ammonium persulfate, which included its consumption as well as decomposition with time, was estimated at different temperatures along with the zinc recovery. Increase in temperature to 343 K lowered zinc recovery (Figure 6) after 2 hours as compared to that of 333 K due to rapid consumption as well as decomposition (58 pct) of ammonium persulfate. The zinc extraction was 90 pct at 333 K and 72 pct at 343 K. At 343 K, the concentration of the oxidant was almost negligible in 2 hours and, therefore, no further zinc dissolution beyond this point was observed. B. Behavior of Iron during Leaching
Fig. 2—Effect of sulfuric acid concentration on the recovery of zinc from zinc concentrate at different time intervals. Temperature: 333 K, oxidant: 272 kg/m3 APS, pulp density: 100 kg/m3, and particle size: ,150 mm.
2FeSO4 1H2 SO4 1 0:5O2 ! Fe2 ðSO4 Þ3 1 H2 O
ZnS 1 Fe2 ðSO4 Þ3 ! ZnSO4 1 2FeSO4 1 S0
After consumption of APS in the oxidation of ZnS, Fe31 participated in dissolution of residual zinc from sphalerite METALLURGICAL AND MATERIALS TRANSACTIONS B
The results of iron dissolution with time at two temperatures, viz. 333 and 343 K, particularly as Fe(III) and Fe(II) in the solution with the corresponding Eh, are presented in Figures 7 and 8. At both temperatures, iron was initially present in the form of Fe(III), which exhibited high redox potential. The Fe(III) level increased continuously to 2 and 1 hour at 333 and 343 K, respectively, indicating the oxidation of sphalerite primarily by APS with minimum participation of Fe(III). The relevant APS concentration vs time at 333 and 343 K may be seen from Figure 6. After 1 hour of leaching at 343 K (Figure 8), the Fe(III) level in the solution started decreasing sharply with the VOLUME 37B, AUGUST 2006—543
Fig. 3—Effect of pulp density on the recovery of zinc from zinc concentrate at different time intervals. Temperature: 333 K, oxidant: 272 kg/m3 APS, acid: 900 mol/m3 H2SO4, and particle size: ,150 mm.
Fig. 5—Effect of temperature on the recovery of zinc from zinc concentrate at different time intervals. Acid: 900 mol/m3 H2SO4, oxidant: 272 kg/m3 APS, pulp density: 100 kg/m3, and particle size: ,150 mm.
Fig. 6—Effect of temperature on the recovery of zinc from zinc concentrate and consumption as well as decomposition of APS at different time intervals. Acid: 900 mol/m3 H2SO4, oxidant: 272 kg/m3 APS, pulp density: 100 kg/m3, and particle size: ,150 mm.
Fig. 4—Effect of oxidant concentration on the recovery of zinc from zinc concentrate at different time intervals. Temperature: 333 K, acid: 900 mol/m3 H2SO4, pulp density: 100 kg/m3, and particle size: ,150 mm.
corresponding increase in Fe(II) concentration. Beyond 2 hours time, the Fe(III) in the leach solution became almost negligible, and Fe(II) concentration remained almost steady. At 333 K, beyond 3 hours of leaching (Figure 7), Fe(III) concentration in the leach solution decreased gradually with rapid increase in the Fe(II) level, indicating the participation 544—VOLUME 37B, AUGUST 2006
of Fe(III) in oxidizing sphalerite due to low availability of APS. As a result, the zinc extraction was 90 pct at 333 K as compared to 72 pct at 343 K (Figure 6). Higher zinc extraction at 333 K may also be correlated with the higher Eh value (400 mV) acquired in 5 hours than that observed (Eh: 320 mV) at the higher temperature (343 K). The iron concentration in the leach liquor at 333 K was 7.1 kg/m3. C. Kinetics of Dissolution The rate of zinc dissolution was tested against diffusion control, chemical control, and mixed control models. METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 7—Behavior of iron(II) and iron(III) and role of Eh during leaching of zinc concentrate with APS. Pulp density: 100 kg/m3, particle size: ,150 mm, acid: 900 mol/m3 H2SO4, oxidant: 272 kg/m3 APS, and temperature: 333 K. Fig. 9—Diffusion-controlled kinetic model of zinc dissolution under oxidation with APS at different temperatures. Acid: 900 mol/m3 H2SO4, oxidant: 272 kg/m3 APS, pulp density: 100 kg/m3, and particle size: ,150 mm.
Fig. 8—Behavior of iron(II) and iron(III) and role of Eh during leaching of zinc concentrate with APS. Pulp density: 100 kg/m3, particle size: ,150 mm, acid: 900 mol/m3 H2SO4, oxidant: 272 kg/m3 APS, and temperature: 343 K.
Attempts were made to ﬁt the kinetic data to diffusion control and chemical control models. The kinetic data (Figure 9) appear to ﬁt well into the diffusion-controlled shrinking core model (Eq. ) assuming the participation of spherical particles of the zinc sulﬁde as core while establishing the interface with the product layer. 1 2=3x ð1 xÞ
¼ kd t
2 hours of leaching, beyond which discontinuity was observed with the change in slope of the straight line. 1 ð1 xÞ1=3 ¼ k c t
However, the activation energy value (Ea 5 71 kJ/mol) was found to be on the much higher side (Figure 10). On the other hand, kinetic data showed a good ﬁt to the chemicalcontrolled model (Figure 11), according to Eq. , up to METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 10—Arrhenius plot for the diffusion-controlled model for leaching of zinc concentrate with APS.
The break in the straight line with different slope and intercept beyond 2 hours indicated an alteration in the mode of the dissolution process. Arauco and Doyle reported that the kinetics of sphalerite leaching under oxidizing conditions below the melting point of sulfur (386 K) follow the VOLUME 37B, AUGUST 2006—545
Fig. 11—Chemical-controlled kinetic model of zinc dissolution under oxidation with APS at different temperatures. Acid: 900 mol/m3 H2SO4, oxidant: 272 kg/m3 APS, pulp density: 100 kg/m3, and particle size: ,150 mm.
chemical control model, whereas after 60 pct of leaching, the development of a porous layer of sulfur brings the reaction under diffusion control. Therefore, the data were ﬁtted to the mixed controlled kinetic model (Eq. ): 1 ð1 xÞ1=3 1 B½1 2=3x ð1 xÞ2=3 5 k m t
where B 5 kc / kd and km 5 2bMDC/rr and a good ﬁt to the mixed-controlled leaching model was observed (Figure 12). Thus, in the initial stage, the leaching might be limited by the chemical surface reaction. With the growth of the elemental sulfur on the surface of the particle, the diffusion of the reactants through this layer might become the rate controlling step. The rate constants (Table IV) for zinc dissolution increased with an increase in temperature up to 333 K, which may be attributed to the gradual rise in availability of the oxygen level (from the lixiviant) and diffusion coefﬁcient. The increased oxygen level available in the solution improved oxidation of sphalerite (ZnS). This also enhanced iron dissolution from FeS initially as Fe(II), which was then oxidized to Fe(III). Once APS was consumed, Fe(III) participated in the oxidation process for zinc leaching (Figure 7). Due to the enhanced rate of decomposition of ammonium persulfate with the increase in temperature above 333 K, as discussed earlier, the leaching rate data showed poor ﬁt to the model and hence are not included in the plot. The kinetic data (Figure 13) for various size particles of zinc concentrate also ﬁt well to the mixed control model. The rate constant values increased with the decrease in the 2
546—VOLUME 37B, AUGUST 2006
Fig. 12—Mixed-controlled kinetic model of zinc dissolution under oxidation with APS at different temperatures. Acid: 900 mol/m3 H2SO4, oxidant: 272 kg/m3 APS, pulp density: 100 kg/m3, and particle size: ,150 mm.
Rate Constant Values Corresponding to Different Leaching Models
Temperatue (K) 333 323 313 308
0.148 0.1002 0.062 0.0379
0.0394 0.024 0.0092 0.0049
3.756 4.175 6.74 7.73
0.2518 0.1772 0.1062 0.070
*Corresponding to 2 h of leaching.
particle size, which may be attributed to the increase in surface area with the decrease in particle size. Inverse proportionality of the rate constant values with the radius squared (r2) plotted in Figure 14 further suggested that the leaching of zinc followed a mixed control model. The Arrhenius plot (Figure 15) for the mixed particles (,150 mm) was obtained in the temperature range 308 to 333 K. The activation energy was calculated to be 43 kJ/mole. This is well within the value of the activation energy reported for the reaction of the mixed control model. The XRD phase identiﬁcation and SEM images provide support for a mixed control mechanism, the surface reaction of sphalerite and persulfate diffusion through a predominantly sulfur product layer both being important. The chemical analysis and XRD pattern of zinc concentrate and leach residues collected at different time intervals, viz. 1, 2, and 5 hours at 333 K, showed the progress of the reaction. In the zinc concentrate, sphalerite (ZnS) and FeS were the major phases along with other minor phases. The peak height for zinc sulﬁde as well as that of FeS decreased METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 13—Effect of particle size on the rate of zinc dissolution from the concentrate with APS. Temperature: 333 K, acid: 900 mol/m3 H2SO4, oxidant: 272 kg/m3 APS, and pulp density: 100 kg/m3.
Fig. 15—Arrhenius plot for mixed-controlled model for leaching of zinc concentrate with APS.
the presence of zinc-sulﬁde–rich phase along with FeS and pyrite (FeS2). The micrograph of the leach residue in Figures 16(b) and (c) shows an increase in dissolution of zinc sulﬁde with time and the formation of a signiﬁcant amount of sulfur. After 5 hours, leach residue (Figure 16(d)) became quite rich in sulfur containing cavities. The morphology of the leach residue implies that the zinc dissolution proceeds initially by surface reaction and subsequently by the diffusion of lixiviant through the pores of the sulfur-rich reaction product. Thus, the leaching process is governed by the mixed control shrinking core model. IV.
Fig. 14—Plots of rate constant vs 1/r2 (radius of the particle) during the dissolution of zinc from the concentrate with APS. Temperature: 333 K, acid: 900 mol/m3, oxidant: 272 kg/m3 APS, and pulp density: 100 kg/m3.
with time. A peak corresponding to a-S appeared in all of the leach residues. The phases identiﬁed by XRD are listed in Table III. The iron phase also appeared as ammonium jarosite in a minor amount in the ﬁnal leach residue. The a-S was the major phase in the last residue. The SEM images of zinc concentrate and leach residues are presented in Figures 16(a) through (d). The surface morphology of the concentrate (Figure 16(a)) indicates METALLURGICAL AND MATERIALS TRANSACTIONS B
Ammonium persulfate—a strong oxidant—has been used for leaching of zinc concentrate from the Ganesh– Himal lead-zinc ore of Nepal. The effects of various leaching parameters such as particle size, acid concentration, temperature, pulp density, and oxidant concentration with time were studied. Using the concentrate of mixed size particle (,150 mm) with 900 mol/m3 sulfuric acid at 100 kg/m3 pulp density, 90 pct zinc is extracted in the presence of 272 kg/m3 APS at 333 K. The recovery of zinc increases with the rise in temperature from 308 to 333 K. However, above 333 K, zinc dissolution decreases due to rapid consumption as well as decomposition of the oxidant. With the ﬁner size (,45 mm) of the concentrate, higher zinc recovery (95 pct) is obtained. The leaching of zinc with time at the optimum temperature (333 K) may be correlated with the concentration of Fe(III) and Fe(II) and the value of redox potential (Eh). The kinetic data for zinc dissolution show a good ﬁt to the mixed control model, and the rate is governed by the surface reaction plus mass transport of the lixiviant through the porous sulfur layer, which is generated as the reaction VOLUME 37B, AUGUST 2006—547
Fig. 16—(a) through (d) SEM photographs of zinc concentrate and leach residues: (a) concentrate, (b) residue—1 h, (c) residue—2 h, and (d) residue—5 h (Sp: sphalerite, Py: pyrite, FeS: iron sulﬁde, and S: sulfur).
product in the temperature range 308 to 333 K. An activation energy of 43 kJ/mole is acquired. The characterization of the leach residue with the help of XRD and SEM corroborates the mixed control leaching mechanism. ACKNOWLEDGMENTS The authors are thankful to the Director, NML (Jamshedpur), for giving permission to publish the article. Thanks are also due to Dr. C.K. Chakraborty, NMCL (Nepal), for providing the ore sample. NOMENCLATURE kd kc km x t b
diffusion-controlled rate constant (h1) chemical-controlled rate constant (h1) mixed-controlled rate constant (h1) fraction reacted time in h stoichiometric coefﬁcient (dimensionless)
548—VOLUME 37B, AUGUST 2006
M D C r r
molecular weight of major zinc mineral diffusion coefﬁcient of zinc ions in porous medium (m2/h) concentration of lixiviant (kg/m3) density of zinc ore (kg/m3) radius of unreacted particles (m)
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