Kinetic Study and Mathematical Modeling of the Reduction of ZnO

Ind. Eng. Chem. Res. 2005, 44, 495-504

495

Kinetic Study and Mathematical Modeling of the Reduction of ZnO-PbO Mixtures by Methane H. Ale Ebrahim* and E. Jamshidi Department of Chemical Engineering, Amir-Kabir University (Tehran Polytechnic), Tehran 15875-4413, Iran

Zinc is an important industrial metal and also can be used as an energy carrier or hydrogen generator. The imperial smelting process (ISP) is the most economic method for zinc production via high-temperature reduction of ZnO-PbO concentrates with coke. The ISP method works with the high circulation rate of lead splash condensers for zinc vapor recovery. In this work, reduction of ZnO-PbO mixtures by methane at the moderate temperatures has been proposed as a new method for zinc production. The liquid zinc recoveries of this method were determined up to 88%, and therefore the lead splash condensers can be eliminated. Thermogravimetry was used for the estimation of the kinetic parameters of the reduction reactions. A mathematical model was also developed for the prediction of reduction behavior, which compared well with experimental data. Introduction Zinc and lead are two important metals with extensive industrial applications. Zinc ores are often mineralized together with lead, and these minerals must be separated by selective flotation for subsequent operations. The traditional methods of zinc production are electrolysis and also pyrometallurgical coke-based processes such as vertical retort and electrothermic furnace.1 On the other hand, lead can be produced by various methods such as blast furnace, Kaldo, Kivcet, and QSL processes.2 One of the most important metallurgical developments in the 20th century was the imperial smelting process (ISP) method for the production of zinc and lead simultaneously.1 In the ISP method, the ZnO-PbO concentrate is reduced by coke in a blast furnace at high temperatures (1100-1300 °C).3 The advantages of the ISP method are coproduction of zinc and lead in a single furnace and simplification of the flotation step for ore concentrate preparation.3 Moreover, the ISP method is the most economic zinc production method with only 44 800 MJ/ton of zinc energy consumption, as compared to 50 100 MJ/ton zinc energy consumption by the electrolysis method.1 A flow diagram of the ISP method is presented in Figure 1, which contains a moving-packed-bed reactor; the basic reducing agent is carbon monoxide, generated from the interaction of air with excess coke.3 In the ISP method, in addition to the reduction reactions, some side and secondary reactions also occur because of the existence of zinc and lead oxides and metals.4,5 The ISP method needs lead splash condensers for rapid cooling of the zinc vapor and for its complete recovery. There is a considerable amount of carbon dioxide, which can reoxidize the zinc vapor during the slow cooling. Indeed, one of the most significant problems of the ISP method is lead splash condensers requiring a very high circulation rate (400 tons of lead/ ton of zinc).1 In this work, a novel method for the reduction of ZnO-PbO mixtures by methane and coproduction of * To whom correspondence should be addressed. E-mail: [email protected].

Figure 1. Flow diagram of the ISP method.3

zinc and lead in their liquid forms has been proposed. The molten lead can retain zinc vapor in the liquid phase at moderate temperatures. This consequently would eliminate the troublesome lead splash condensers required in the ISP method.6 Moreover, the operating temperature can be decreased from about 1200 °C (used in the ISP method) to 850 °C because of the high reactivity of methane.7 In this research, the kinetic parameters of ZnO and PbO reduction by methane have been determined from pure oxide experiments. The reduction of ZnO-PbO mixtures is studied by thermogravimetry. A suitable mathematical model has also been developed to model mixed oxide reduction reactions. Thermodynamic Predictions The feasibility study for ZnO reduction by methane at moderate temperatures has been presented elsewhere.8 This study showed that methane is more reactive than coke (and carbon monoxide), and therefore it is possible to reduce ZnO by methane at a moderately high temperature of about 850 °C (K ) 2.7) as compared to coke (a common reducing agent), requiring a reduc-

10.1021/ie0496232 CCC: $30.25 © 2005 American Chemical Society Published on Web 01/08/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 3, 2005

Previous Work

Table 1. Vapor Pressure of Zinc and Lead Liquids at Various Temperatures temperature (°C) P0Zn(l) 0 PPb(l)

(mmHg) (mmHg)

700

750

800

850

900

61 0.01

123 0.02

233 0.05

414 0.14

699 0.32

tion temperature above 1000 °C. Moreover, the equilibrium constant for PbO reduction by methane at 850 °C is very high,7 and therefore this reaction can occur without any thermodynamic constraint. Thermodynamic properties of a zinc-lead binary system can be used for the prediction of the Zn vapor pressure in the presence of Pb. Using these data, the effect of molten lead on decreasing Zn vapor pressure and increasing recovery can be determined. First of all, it is necessary to know the vapor pressures of pure molten zinc and lead. The Zn and Pb vapor pressures at the various temperatures are presented in Table 1.9 As Table 1 shows, the vapor pressure of Zn at 850 °C is very high (414 mmHg). Therefore, a low zinc recovery (as a liquid phase) can be expected from ZnO reductions at about 850 °C. This prediction is in agreement with the ZnO + CH4 reaction at 850 °C, which showed about 20% liquid zinc recovery in a single-pellet reactor.8 It is necessary to point out that, in the ZnO + CH4 reduction, some of the CO (reaction product) can participate in the Boudouard reaction and produces CO2 during slow cooling. Therefore, a simple indirect condenser may not be completely successful even in this system with mostly nonoxidizing gaseous products (CO + 2H2). It seems that the nonvolatile molten lead can be a suitable solvent for Zn for decreasing its high volatility and increasing its recovery as liquid zinc in the reduction furnace. The phase diagram of the Zn-Pb system was presented in ref 10. This diagram shows that, above 798 °C, a single liquid phase appears for all Zn-Pb compositions and Zn can be dissolved in liquid Pb. However, at about 450 °C, a liquid zinc phase is formed, which is separated from the lead phase after the cooling of a lead splash condenser fluid. The activity of zinc in the Zn-Pb system versus zinc mole fraction was also presented in ref 10. Although this activity profile shows a positive deviation from Raoult’s law, when zinc and lead are mixed, it is possible to decrease the vapor pressure of Zn considerably. The Zn vapor pressure in the Zn-Pb mixture can be computed as follows:10 / 0 0 PZn(l) ) PZn(l) xZnγZn ) PZn(l) aZn

(1)

For example, in two ZnO-PbO pellets with 0.05 and 0.17 Zn-Pb weight ratios, which are rich in lead, the vapor pressures of Zn in the Zn-Pb mixture were determined. These weight ratios are equal to xZn ) 0.13 and 0.35, respectively. Therefore, from the Zn activity profile and eq 1, the vapor pressures of Zn in the mixtures at 850 °C are computed as 215 and 335 mmHg. These figures show a considerable decrease with respect to 414 mmHg of pure molten zinc. Therefore, it is possible to decrease the vapor pressure of liquid Zn to increase its recovery by this method, especially for the mixed ZnO-PbO pellets, which are rich in lead.

In this section, a brief discussion on the results of pure ZnO and PbO pellet reduction by methane is presented from our previously published papers.8,11-13 a. ZnO Reduction. The important finding on the ZnO reaction was a considerable decrease of the operating temperature from about 1200 °C (industrial cokebased plants) to about 850-900 °C by methane reduction.8 The complete kinetic study of the pure ZnO reduction with methane between 840 and 930 °C was accomplished by thermogravimetry and continuous gas analysis by a mass spectrometer.8 The kinetic parameters of this reaction were determined from the sharp interface model. The temperature dependence of the rate constant is as follows:8

kZnO ) 4.95 × 1012 exp(-67090/RgT)

(2)

The concentration dependence of the reaction between 20 and 60% CH4 was expressed by the LangmuirHinshelwood equation.8 This dependence (which is nearly first order) is as follows:8 / ) f(CCH 4

)

/ CCH 4 / 1 + 46136CCH 4

(3)

The effect of mass transfer and bulk flow on the ZnO + CH4 reaction was studied separately.11 In this paper, a complete mathematical model was introduced and successfully compared with high-temperature experimental data.11 Finally, a new method for synthesis gas preparation by the ZnO + CH4 reaction was introduced and checked with the mass spectrometer.12 In this paper, the greenhouse gas emission elimination from a metallurgical plant was also proposed.12 b. PbO Reduction. Some reports in the literature showed that the reduction of pure PbO with methane is slow and actually is accomplished by hydrogen from thermal cracking of methane.14 Our experiments also indicated a relatively slow PbO reduction by methane.7 However, in this research, the PbO pellets with 1% ZnO were produced (with PbO* symbol) and reduced by methane very quickly13 because ZnO can convert methane into CO + 2H2, which would then reduce PbO. The detection of CO2 and H2O as gaseous products by a mass spectrometer proved this assumption.13 Also kinetic experiments by the various hydrogen concentrations showed near-zero-order dependence with respect to the gaseous reactant.13 The kinetic studies between 700 and 850 °C determined the rate constant for PbO* reduction by methane as follows:13

kPbO ) 1.82 × 108 exp(-51620/RgT)

(4)

Therefore, the important finding for PbO reduction by methane was the catalytic effect of 1% ZnO on the reaction. Experimental Section 1. Raw Materials. Kinetic studies on unknown reactions must be done with pure materials. Therefore, the materials used in this work were prepared using pure raw materials. Zinc oxide was a guaranteed

Ind. Eng. Chem. Res., Vol. 44, No. 3, 2005 497

Figure 2. SEM analysis of the ZnO powder (×16 000). Figure 4. Flow diagram of the system for reduction experiments.

Figure 3. SEM analysis of the PbO powder (×400). Table 2. Zn-Pb Ratios Used in Mixed Pellets mineral name Angouran, Irankooh, lead and Mansour concentrate Kooshk Abad Ahangaran of Zanjan Zn-Pb weight ratio mixed pellet no.

4.50

1.56

0.17

0.05

1

2

3

4

reagent from Merck (art. no. 8849). Lead oxide was also a guaranteed reagent from Merck (art. no. 7401). The scanning electron microscopy (SEM) analysis of ZnO and PbO powders is presented in Figures 2 (×16 000) and 3 (×400), respectively. From these figures, the average particle size for ZnO and PbO powders are computed as 0.23 and 14.9 µm. Methane was purchased from Air Products with 99.95% purity. The nitrogen (inert gas) is also 99.999% grade. The proportions of Zn-Pb in the mixed pellets are presented in Table 2. These ratios were selected similarly to a series of Iranian mines. 2. Equipment Description. The usual system for the kinetic study of noncatalytic gas-solid reactions is a single-pellet reactor with an excess gas stream.15 The flow diagram of the system is presented in Figure 4. The solid pellet was put on a wire basket cell in a highcapacity thermogravimeter (TGH). The TGH is from Rheometric Scientific Co., works up to 1500 °C, and is a stable isothermal facility. The system is heated to the desired temperature under a nitrogen gas stream (gas 1). Then the isothermal period begins, and after temperature stabilization, the reducing gas, a mixture of

CH4-N2 (through gas 2), is introduced to the TGH. The outlet gas stream leaves the system from the top through a bubbler for slight positive pressure control. At this isothermal temperature, the weight of the ZnO-PbO pellet is plotted versus time. Because there is an attached alumina drip tray under the basket cell, the weight loss is only due to the oxygen removal from the pellet by reduction or partial liquid zinc evaporation. 3. Producing of Pellets. Small cylindrical pellets of ZnO-PbO mixtures were built by high-pressure (2000 bar) hydraulic press and are similar to those with slablike geometry. For the kinetic study of unknown reactions (pure ZnO or PbO reduction by methane), it is common to use nonporous pellets. Because modeling of nonporous reactions has an analytical solution and leads to simple conversion-time relations, it is suitable for estimation of the kinetic parameters.16 Therefore, our sintering process for the pure pellets was performed under extreme conditions for elimination of the internal pores. For example, the sintering at 1000 °C and 5 h was used to reduce the porosity from 53% to less than 1% for ZnO pellets.8 On the other hand, for ZnO-PbO mixed pellets, it is desirable to obtain the maximum reduction rate, and therefore high porosity is favorable. Thus, sintering of mixed pellets was carried out under mild conditions (about 700 °C and 5 h) just to increase their mechanical strength. A photograph of the pure and mixed pellets before and after sintering is presented in Figure 5. Some of the properties of ZnO-PbO mixed pellets after sintering were determined by mercury porosimetry and are presented in Table 3. 4. Reduction versus Time Profiles. As mentioned above, part of the produced Zn evaporates during the reduction because of molten zinc volatility. Therefore, conversion versus time profiles must be calculated as follows:7

X(t) )

W0 - W(t) MO + (1 - Rec)MZnSZnO W0 MZnOSZnO + MPbOSPbO

(5)

The term Rec in eq 5 is the recovery of produced zinc in the liquid form. This term was evaluated from wet chemical analysis on the spherical metal droplets, which were collected in the drip tray under the cell.

498


Figure 5. Photograph of the initial and sintered pellets. Table 3. Characteristics of the ZnO-PbO Sintered Pellets mixed pellet no.

total pore volume (cm3/g)

average pore radius (nm)

porosity (%)

2 3

0.145 0.031

104 100

51 22

Table 4. Recovery of Liquid Zinc from Mixed Pellets Zn-Pb ratio in mixed pellets recovery of liquid zinc (%)

4.50 20

1.56 22

0.17 54

0.05 88

The wet chemical analysis consists of complete dissolution of the produced metal droplets in nitric acid, then precipitation of lead as sulfate, and weighing in a sintered glass filter. The zinc ion in the filtrate was determined by ethylenediaminetetraacetic acid titration in the presence of xylenol orange.17 This method showed a good accuracy for a known premade Zn-Pb mixture. The liquid zinc recoveries for methane reduction of the various ZnO-PbO mixed pellets at 850 °C are presented in Table 4. As this table shows, there is a significant increase in the Zn recovery for lead-rich

mixed pellets. This matter is one of the important findings of this work, as is also predicted in the Thermodynamic Predictions section. However, the Zn recovery of zinc-rich mixed pellets in the thermogravimeter is similar to the pure ZnO reduction. Results presented in Table 4 suggest that molten lead is a suitable solvent for retaining the volatile zinc in the liquid phase and improving its recovery. These results were further substantiated by the recovery of a trace amount of zinc vapor in the molten lead via reduction of ZnO-PbO mixtures by carbon monoxide at high temperatures (1000-1200 °C).18 5. Thermogravimetry of ZnO-PbO Mixtures in Methane. The thermogravimetric curves for the reduction of mixed ZnO-PbO pellets at 850 °C by methane are presented in Figures 6-9. These figures present the graphs for mixed pellet nos. 1-4, respectively. A photograph of partially reduced pellets with spherical balls of the liquid products is presented in Figure 10. From Figures 6-9, it is apparent that the liquid product resistance on the pellet surface is negligible and the reduction of pellets continues without any liquid film layer problem. However, some oscillations in the leadrich tests with high amounts of liquid products are observed (Figures 8 and 9). This phenomenon can be attributed to the aggregation of liquid metal from internal pores to a big liquid droplet on the pellet surface, which then trickles to the drip tray. Therefore, a free pore path for the reducing gas is produced and accelerates the weight loss curves for a short time. Such oscillation behaviors were also reported for high-temperature SH2 adsorption by zinc oxide.19 The droplet form for the liquid products can also be predicted from surface tension values. The surface tension of molten lead is high (470 dyn/cm)20 and is about the same as the surface tension of mercury. The liquid zinc (with a surface tension of 761 dyn/cm)20 could improve the surface tension of Pb(l)-Zn(l) and produce

Figure 6. Thermogravimeter result for ZnO-PbO mixture (no. 1) reduction at 850 °C by 50% CH4-N2.




complete spherical droplets (Figure 10) with respect to semispherical droplets of the pure molten lead.13 These complete spherical droplets can simply separate from the surface of the pellets, and the problem of a liquid film layer does not appear in this system. Mathematical Modeling A complete review of mathematical models for the noncatalytic gas-solid reactions has been presented by

Ramachandran and Doraiswamy.21 A suitable model for the pellets, which are produced by pressing of fine powder, is the grain model.21 The grain model of Szekely and co-workers22,23 considers the gas diffusion in the pellet and reaction on the surface of grains. It seems that the grain model can be used as a framework for mathematical modeling of this system. However, the ZnO-PbO mixture reduction by methane is a complex gas-solid reaction, and the common

500



Figure 10. Photograph of the partially reduced pellets of ZnOPbO mixtures (nos. 2 and 3) with metal droplets.

grain model must be extended for this case. Some references exist in the literature for complex reactions such as the following: (1) the reduction of NiO-Fe2O3 mixtures with hydrogen,24 (2) the general model for two solids with a gas reaction,25 (3) the general model for a solid reaction with two gases,26 (4) the reaction of a gas product with the second solid,27 and (5) the presence of two solids with different grain sizes in a pellet.28 The above-mentioned references can be used as guidelines for developing the mathematical model to predict the reduction reactions presented in this paper. The main chemical reactions of this system are as follows:

(1) The ZnO reduction by methane is a first-order irreversible reaction. (2) The PbO reduction can be expressed by zero-order and irreversible reactions. (3) The reactions are isothermal. (4) The pellet has a slablike geometry. (5) The big PbO and small ZnO spherical grains exist in the pellet. (6) The pseudo-steady-state approximation is valid. (7) The external mass-transfer resistance is negligible. (8) The effect of structural changes of internal pores is small with respect to the presence of liquid products between the grains. (9) The product layer resistance on the surface of the pellet and grains is negligible because of the droplet form of the liquid metals. (10) The bulk gas concentration of methane is constant in a single-pellet reactor. (11) The diffusion coefficients in the multicomponent gas mixture must be determined by the StefanMaxwell method. However, in a similar system of COCO2-Zn(g), an approximate method has been used for diffusivity calculations.29 Therefore, the diffusion coefficients in this mathematical model can be regarded as free of composition dependence. Now the conservation equations of methane, hydrogen, and carbon monoxide can be expressed as follows:

∂2a/∂y2 ) fZnOσZnO2r/ZnO2a

(9)

/ 2 ∂2a′/∂y2 ) fPbO(D′′p/D′p)σPbO2rPbO - 2fZnOσZnO2r/ZnO2a (10)

ZnO + CH4 f Zn(l) + CO + 2H2

(6)

PbO + H2 f Pb(l) + H2O

(7)

PbO + CO f Pb(l) + CO2

(8)

/ 2 ∂2a′′/∂y2 ) fPbOσPbO2rPbO - fZnOσZnO2r/ZnO2a (11)

The assumptions used for developing the mathematical model are as follows:

In the above equations, the dimensionless parameters are defined as follows:

Ind. Eng. Chem. Res., Vol. 44, No. 3, 2005 501 / a ) CCH4/CCH 4

(12)

XZnO ) 1 -

∫01r/ZnO3 dy

(34)

/ a′ ) CH2/CCH 4

(13)

XPbO ) 1 -

/ 3 dy ∫01rPbO

(35)

/ a′′ ) CCO/CCH 4

(14)

y ) L/Lp

(15)

fZnO ) SZnOFj/FZnO

(16)

fPbO ) SPbOFj/FPbO

(17)

σZnO2 ) σPbO2 )

( ) ( )

Lp 23kZnO(1 - ) 2 DzrZnO

(18)

Lp 23kPbO(1 - ) 2 C/ D′′r CH4 p PbO

(19)

r/ZnO ) rcz/rZnO

(20)

/ ) rcp/rPbO rPbO

(21)

In the above equations, three different effective diffusivities are used. Dz is for methane diffusion in the pellet to ZnO grains, and D′p and D′′p are for H2 and CO diffusion to PbO grains. Also, mole fractions of ZnO and PbO in the pellet and the average molar density of the mixed pellet can be computed as follows:7

SZnO ) 0.0153ω/(0.0153ω + 0.0048)

(22)

SPbO ) 0.0048/(0.0153ω + 0.0048)

(23)

Fj ) 1/(SZnO/FZnO + SPbO/FPbO)

(24)

The differential equations for the ZnO and PbO grains are as follows:

∂r/ZnO/∂θZnO ) -a

(25)

/ ∂rPbO /∂θPbO

(26)

) -1

Dimensionless times are also defined as follows: / t/FZnOrZnO θZnO ) kZnOCCH 4

(27)

θPbO ) kPbOt/FPbOrPbO

(28)

Finally, the initial and boundary conditions for the above equations are expressed as follows:

θZnO ) θPbO ) 0 y)0

/ r/ZnO ) rPbO )1

∂a ∂a′ ∂a′′ ) ) )0 ∂y ∂y ∂y y)1 a)1

(29) (30) (31)

y)1

a′ )

/ / /CCH CH 4 2

(32)

y)1

/ a′′ ) C/CO/CCH 4

(33)

The above-coupled partial differential equations must be solved by numerical analysis. Then the conversion of each component can be determined as follows:24

The overall pellet conversion is also expressed as follows:24

Xov ) SZnOXZnO + SPbOXPbO

(36)

The ZnO and PbO reduction, which produces liquid metals, can lead to internal pore blockage, and consequently diffusion of gaseous reactant becomes the controlling step. The system under diffusion control conditions does not show any selectivity, and two components react equally as follows:24

Xov ) XZnO ) XPbO

(37)

Therefore, for this system with liquid products, it is predicted that the overall conversion of the mixed pellet is approximately equal to the conversion of the slower reaction. The accuracy of this prediction will be discussed in the following section. Comparison of Experimental Results with Model Prediction An important conversion-time profile for the ZnOPbO mixture (with Zn-Pb ) 0.17) reduction at 850 °C by methane is presented in Figure 11. In this figure, model predictions for pure ZnO and PbO reduction as well as a prediction for the mixed pellet reduction (from eq 36) are presented. As Figure 11 shows, the experimental data of the mixed pellet falls on the ZnO reduction prediction curve (slower reaction). Therefore, the diffusion control regime for the mixed pellet, or uniform reactions without any selectivity, is verified. This means that the liquid products block most of the internal pores of the pellet, and consequently the faster intrinsic reaction of PbO cannot appear. Indeed, diffusion of methane in the pellet is the controlling step, and production of CO and H2 by eq 6 controls the rate of PbO reduction (faster reaction). Under such a diffusion control regime, the approximate solution of Sohn is valid, and the conversion-time profile for the mixed pellets can be predicted from the following equation:22

θZnO ) 1 - (1 - Xov)1/3 + fZnOσZnO2Xov2/6

(38)

In the above equation, the only unknown parameter is Dz or the effective diffusivity of methane through internal pores of the mixed pellets. This parameter can be determined from the comparison of eq 38 with experimental data. Comparisons between the model predictions and experimental data of the mixed ZnO-PbO pellet reduction are presented in Figures 12-15. These figures present the reduction of ZnO-PbO mixtures with ZnPb ) 4.50, 1.56, 0.17, and 0.05, respectively, in methane at 850 °C. Experimental reduction versus time profiles were obtained from the TGH results (Figures 6-9) and eq 5. As Figures 12-15 show, there is a good agreement between the developed mathematical model predictions and the experimental data. However, some deviations

502


Figure 11. Plot of % conversion of ZnO, PbO*, and their mixtures (Zn-Pb ) 0.17) versus time for run 68 at 850 °C and 50% CH4N2 [(s) model prediction and (9) experimental data of mixture no. 3].

Figure 14. Plot of % conversion of ZnO-PbO mixture (no. 3, run 69, Zn-Pb ) 0.17) reduction at 850 °C by 50% CH4-N2 and mathematical model prediction: (s) mathematical model; (9) experimental data.

Figure 12. Plot of % conversion of ZnO-PbO mixture (no. 1, run 71, Zn-Pb ) 4.50) reduction at 850 °C by 50% CH4-N2 and mathematical model prediction: (s) mathematical model; (9) experimental data.

Figure 15. Plot of % conversion of ZnO-PbO mixture (no. 4, run 67, Zn-Pb ) 0.05) reduction at 850 °C by 50% CH4-N2 and mathematical model prediction: (s) mathematical model; (9) experimental data. Table 5. Effective Diffusivities of Methane Zn-Pb ratio in the pellets Dz (cm2/min)

0.05 0.00027

0.17 0.00046

1.56 0.018

4.50 0.063

was a successful equation in predicting the experimental data of this work. However, the ZnO-PbO mixed pellets can be produced with large internal pores (for example, by the addition of ammonium carbonate) for increasing the rate of reaction. In such a condition, the above mathematical model must be used with eq 36. Finally, the Dz values (Table 5) with the developed model equations can be used for the design of an industrial plant for ZnO-PbO mixture reduction by methane. Figure 13. Plot of % conversion of ZnO-PbO mixture (no. 2, run 70, Zn-Pb ) 1.56) reduction at 850 °C by 50% CH4-N2 and mathematical model prediction:: (s) mathematical model; (9) experimental data.

exist in Figures 12-15 and can be attributed to the model assumptions. The liquid form of the metal products with their surface tension interactions may be the most forcible factor. Finally, the fitting parameter Dz (in eq 38) for the various ZnO-PbO mixed pellets is presented in Table 5. These data show that the effective diffusivity of methane increases with increasing Zn-Pb ratio in the mixed pellets. This trend is due to the higher volatility of the liquid products for the zinc-rich pellets. Therefore, at the mild pore blockage condition, the methane diffusion is increased to the internal pellet pores. Consequently, the developed mathematical model leads to eq 38 for the diffusion control regime, which

Conclusions In recent years, much attention has been focused on the zinc metal because of its applicability in clean fuels and the transportation of energy. For example, zinc metal can be used as a chemical hydrogen storage device (as the water splitter) and as an energy carrier for the fuel cells.30-34 The most economic zinc production method is high-temperature (1200 °C) reduction of the ZnO-PbO concentrate by coke in an ISP furnace, which requires troublesome lead splash condensers. In this work, a new method has been proposed to produce zinc metal based on the moderate temperature reduction of ZnO-PbO mixtures by methane. In this method, the molten lead dissolves the zinc vapor at about 850 °C, and therefore the requirement of the lead splash condensers can be eliminated. Liquid zinc recoveries of 54-88% were obtained for the lead-rich ZnO-


PbO mixture reduction in a single-pellet reactor. The remaining zinc, which evaporates, can be used for the production of pure zinc oxide similarly to the American method.35 The complete kinetic study of the pure ZnO, pure PbO, and ZnO-PbO mixture reduction with methane using thermogravimetry has been presented. A comprehensive mathematical model has been developed for the complex ZnO-PbO reduction reactions in methane. The experimental data compared well with the mathematical model. Therefore, the mathematical model along with kinetic parameters can be used to design industrial plants based on this reduction method. In the extension of this research, it is necessary to build a small packed-bed reactor as a pilot plant for the determination of actual zinc recoveries. In a packedbed reactor, more liquid zinc recovery is predicted with respect to the single-pellet reactor because of the high zinc production rate. The required heat of reaction in this method can be supplied externally, or even by combustion of a small part of the methane with preheated air. Because the operating temperature of this method (about 850 °C) is less than the ISP furnace temperature (1200 °C), the heat requirements can be achieved with less difficulty. Finally, the actual residence time must be determined and compared with the model prediction for verification of its assumptions.

/ ) dimensionless radius of the unreacted core in ZnO rZnO grains Rec ) percentage of the zinc recovery in the liquid form Rg ) gas constant (cal/gmol‚K) SPbO ) mole fraction of PbO in the mixed pellet SZnO ) mole fraction of ZnO in the mixed pellet t ) time (min) T ) reaction temperature (K) W0 ) initial weight of the pellet (mg) W(t) ) weight of the pellet at each time (mg) xZn ) mole fraction of molten zinc in the Zn-Pb mixture Xov ) overall predicted conversion from the model XPbO ) conversion of PbO XZnO ) conversion of ZnO X(t) ) experimental conversion in each time y ) dimensionless position in the porous pellet γZn ) activity coefficient of molten zinc in the mixture ) pellet porosity θPbO ) dimensionless time for PbO θZnO ) dimensionless time for ZnO FPbO ) true molar density of PbO (gmol/cm3) FZnO ) true molar density of ZnO (gmol/cm3) Fj ) true molar density of the mixed pellet (gmol/cm3) σPbO ) Thiele modulus for PbO σZnO ) Thiele modulus for ZnO ω ) weight ratio of Zn-Pb in the mixed pellet

Nomenclature

(1) Kirk-Othmer Encyclopedia of Chemical Technology; Wiley: New York, 1991; Vol. 25, pp 789-839. (2) Kirk-Othmer Encyclopedia of Chemical Technology; Wiley: New York, 1991; Vol. 15, pp 69-113. (3) Moore, J. J. Chemical Metallurgy; Butterworth: London, 1981; pp 236-241. (4) Creese, R. C.; Healy, G. W. A Chemical Equilibrium Model of the Imperial Smelting Blast Furnace. Can. Metall. Q. 1975, 14, 175-181. (5) Cox, A.; Fray, D. J. Zinc Reoxidation in the Shaft of a ZincLead Imperial Smelting Furnace: II. Zinc-Carbon-Oxygen System in Combination with Sinter and Coke Substrates. Trans. Inst. Min. Metall. 2000, 109, C105-C111. (6) Ale Ebrahim, H.; Jamshidi, E. Omitting of Lead Splash Condensers in the Zinc Producing Furnaces. Iranian Patent No. 25993, 1998. (7) Ale Ebrahim, H. Kinetic Study and Mathematical Modeling of ZnO-PbO Mixtures Reduction with Methane. Ph.D. Thesis, Amir-Kabir University, Tehran, Iran, 1998. (8) Ale Ebrahim, H.; Jamshidi, E. Kinetic Study of Zinc Oxide Reduction by Methane. Trans. Inst. Chem. Eng. 2001, 79A, 6270. (9) Kubaschewski, O.; Alcock, C. B. Metallurgical Thermochemistry; Pergamon: Oxford, U.K., 1979. (10) Mackowiak, J. Physical Chemistry for Metallurgists; Elsevier: New York, 1965; pp 146-193. (11) Ale Ebrahim, H.; Jamshidi, E. Effect of Mass Transfer and Bulk Flow on the Zinc Oxide Reduction by Methane. Ind. Eng. Chem. Res. 2002, 41, 2630-2636. (12) Ale Ebrahim, H.; Jamshidi, E. Synthesis Gas Production by Zinc Oxide Reaction with Methane: Elimination of Greenhouse Gas Emission from a Metallurgical Plant. Energy Convers. Manage. 2004, 45, 345-363. (13) Ale Ebrahim, H.; Jamshidi, E. Kinetic Study of Lead Oxide Reduction by Methane. Sixth Iranian Congress of Chemical Engineering, Isfahan Industrial University, 2001. (14) Chizhikov, D. M.; Tsvetkov, Yu. V.; Kusaev, Yu. I.; Karyazina, I. N. Reduction of Nonferrous Metal Oxides by Natural Gas. Termodin. Kinet. Protsessov Vosstanov. Met. Mater. Konf. 1972, 22-27 (Russian). (15) Smith, J. M. Chemical Engineering Kinetics; McGrawHill: New York, 1981. (16) Szekely, J.; Evans, J. W.; Sohn, H. Y. Gas-Solid Reactions; Academic Press: New York, 1976. (17) Vogel, A. I. A Text-Book of Quantitative Inorganic Analysis; Longmans: London, 1961; pp 443-444.

a ) dimensionless concentration of methane a′ ) dimensionless concentration of hydrogen a′′ ) dimensionless concentration of carbon monoxide aZn ) activity of zinc in a Zn-Pb mixture CCH4 ) concentration of methane in the pellet (gmol/cm3) / CCH ) concentration of methane in the bulk gas (gmol/ 4 cm3) CCO ) concentration of CO in the pellet (gmol/cm3) C/CO ) concentration of CO in the bulk gas (gmol/cm3) CH2 ) concentration of H2 in the pellet (gmol/cm3) / CH ) concentration of H2 in the bulk gas (gmol/cm3) 2 D′p ) effective diffusivity of H2 in the pores (cm2/min) D′′p ) effective diffusivity of CO in the pores (cm2/min) Dz ) effective diffusivity of methane in the pores (cm2/min) fPbO ) volume fraction of PbO in the mixed pellet fZnO ) volume fraction of ZnO in the mixed pellet / f(CCH ) ) concentration dependence of the reaction (gmol/ 4 cm3) kPbO ) rate constant for the PbO reaction (gmol/cm2‚min) kZnO ) rate constant for the ZnO reaction (cm/min) K ) equilibrium constant for the ZnO reaction L ) position of each point in the pellet (cm) Lp ) thickness of the slab pellet (cm) MO ) molecular weight of oxygen (g/gmol) MPbO ) molecular weight of PbO (g/gmol) MZn ) molecular weight of zinc (g/gmol) MZnO ) molecular weight of ZnO (g/gmol) 0 ) vapor pressure of pure molten lead (mmHg) PPb(l) 0 PZn(l) ) vapor pressure of pure molten zinc (mmHg) / PZn(l) ) vapor pressure of molten zinc in the Zn-Pb mixture (mmHg) rcp ) radius of the unreacted core in PbO grains (cm) rcz ) radius of the unreacted core in ZnO grains (cm) rPbO ) radius of PbO grains (cm) rZnO ) radius of ZnO grains (cm) r/PbO ) dimensionless radius of the unreacted core in PbO grains

Literature Cited

504


(18) Karwan, T.; Kotula, K. Rate of Reduction of Mixtures of Zinc and Lead Oxides in a Carbon Monoxide Atmosphere. Pr. Inst. Met. Niezelaz. 1976, 5, 187-194 (Polish). (19) Gibson, J. B.; Harrison, D. P. The Reaction between Hydrogen Sulfide and Spherical Pellets of Zinc Oxide. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 231-237. (20) Lide, D. R. Handbook of Chemistry and Physics; CRC Press: Boston, 1998. (21) Ramachandran, P. A.; Doraiswamy, L. K. Modeling of Noncatalytic Gas-Solid Reactions. AIChE J. 1982, 28, 881-900. (22) Sohn, H. Y.; Szekely, J. A Structural Model for Gas-Solid Reactions with a Moving Boundary: III. A General Dimensionless Representation of the Irreversible Reaction between a Porous Solid and a Reactant Gas. Chem. Eng. Sci. 1972, 27, 763-778. (23) Georgakis, C.; Chang, C. W.; Szekely, J. A Changing Grain Size Model for Gas-Solid Reactions. Chem. Eng. Sci. 1979, 34, 1072-1075. (24) Szekely, J.; Hastaoglu, A. Reduction of Nickel OxideHematite Mixture with Hydrogen. Trans. Inst. Min. Metall. 1976, 85, C78-C87. (25) Sohn, H. Y.; Braun, R. L. Simultaneous Fluid-Solid Reactions in Porous Solids: II. Reactions between One Fluid and Two Solid Reactants. Chem. Eng. Sci. 1984, 39, 21-30. (26) Sohn, H. Y.; Braun, R. L. Simultaneous Fluid-Solid Reactions in Porous Solids: Reactions between One Solid and Two Fluid Reactants. Chem. Eng. Sci. 1980, 35, 1625-1635. (27) Sohn, H. Y.; Rajamani, K. Successive Gas-Solid Reactions in a Porous Pellet: Application to the Reaction of Metal Sulfides in the Presence of Lime. Chem. Eng. Sci. 1977, 32, 1093-1101.

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Received for review May 6, 2004 Revised manuscript received November 12, 2004 Accepted November 15, 2004 IE0496232

Kinetic Study and Mathematical Modeling of the Reduction of ZnO

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