Solar Carbothermal Reduction of ZnO: Shrinking Packed-Bed Reactor

Figure 4 ZnO−C packed-bed modeled as a 1D continuum exposed to radiation at the top and undergoing shrinkage due to chemical reaction...
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Ind. Eng. Chem. Res. 2004, 43, 7981-7988

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Solar Carbothermal Reduction of ZnO: Shrinking Packed-Bed Reactor Modeling and Experimental Validation Thomas Osinga,† Gabriel Olalde,‡ and Aldo Steinfeld*,†,§ Department of Mechanical and Process Engineering, ETH - Swiss Federal Institute of Technology Zu¨ rich, CH-8092 Zu¨ rich, Switzerland, Institut de Science et de Ge´ nie des Mate´ riaux et Proce´ de´ s, CNRS-IMP, 66125 Font-Romeu Cedex, France, and Solar Technology Laboratory, Paul Scherrer Institute, CH-5232 Villigen, Switzerland

The thermodynamics and kinetics of the carbothermic reduction of ZnO are examined over the temperature range 400-1600 K. Above 1340 K, the equilibrium composition of the stoichiometric chemical system consists of an equimolar gas mixture of Zn (vapor) and CO. Assuming a firstorder rate constant for the surface reaction kinetics between ZnO(s) and CO and further applying a shrinking spherical particle model with an unreacted core, the apparent activation energy obtained by linear regression of the thermogravimetric data is EA ) 201.5 kJ/mol. A numerical model is formulated for a solar chemical reactor that uses concentrated solar radiation as the energy source of process heat. The model involves solving, by the finite-volume technique, a 1D unsteady-state energy equation that couples heat transfer to the chemical kinetics for a shrinking packed bed exposed to thermal radiation. Validation is accomplished by comparison with experimentally measured temperature profiles and Zn production rates as a function of time, obtained for a 5-kW solar reactor tested in a high-flux solar furnace. Application of the model for a scaled-up reactor predicts a large temperature gradient at the top layer, which is typical of ablation processes where heat transfer through the bed becomes the rate-controlling mechanism. Once the temperature of the top layer exceeds 1200 K, the bed shrinks at an approximately constant speed of 2.8 × 10-5 m/s as the reaction proceeds under a constant radiative flux input. 1. Introduction Zinc is a versatile metal. In addition to being a widely used commodity in the galvanizing industry, it is also a compact and safe-to-handle solid fuel that finds applications in Zn/air fuel cells and batteries. Zinc can also be reacted with water to form high-purity hydrogen, especially needed for polymer electrolyte membrane (PEM) fuel cell applications. In either case, the chemical product from these power generation processes is zinc oxide, which in turn needs to be reduced to zinc to close the material cycle. However, the current industrial production of Zn from ZnO by electrolytic and smelting furnaces is characterized by its high energy consumption and concomitant environmental pollution, derived mostly from the combustion of fossil fuels for heat and electricity generation. These emissions could be substantially reduced or completely eliminated by instead using concentrated solar power as the source of hightemperature process heat.1 Solar-made zinc further offers the possibility of storing and transporting solar energy.2 The thermal dissociation of ZnO into its elements requires temperatures above 2200 K, and the product gases Zn(g) and O2(g) need to be either quenched or separated at high temperatures to prevent their recombination.3,4 The reduction temperature can be signifi* To whom correspondence should be addressed. E-mail: [email protected]. † ETH - Swiss Federal Institute of Technology Zu ¨ rich. ‡ Institut de Science et de Ge´nie des Mate´riaux et Proce´de´s. § Paul Scherrer Institute.

cantly lowered and the recombination avoided by using carbonaceous materials as reducing agents. The solar carbothermic reduction of ZnO has been experimentally demonstrated using C(graphite)5,6 and CH47,8 as reductants. The cyclic process from solar energy to electricity via solar-processed Zn/air fuel cells is being investigated within the European Union’s project SOLZINC.9 In a previous paper,10 we described in detail the design, fabrication, and experimental investigation of a 5-kW solar chemical reactor for performing the carbothermic reduction of ZnO. The present paper addresses the modeling of this solar reactor. First, the most relevant aspects of the thermodynamics and kinetics of the pertinent reactions are briefly examined. Then, the unsteady-state energy governing equation is formulated for coupling the heat transfer to the chemical kinetics and solved for moving boundaries by the finite-volume technique. Third, numerical results are compared with those obtained experimentally. Finally, the model is used to predict the performance of a scaled-up solar reactor. 2. Thermodynamics and Kinetic Analyses The carbothermic reduction of ZnO can be represented by the overall net reaction

ZnO + λC ) Zn + (2λ - 1)CO + (1 - λ)CO2 (1) where λ denotes the stoichiometric molar ratio C/Zn. Reaction 1 proceeds endothermically (∆H°1400K ) 352.5 kJ/mol) at temperatures above 1230 K, via the solid-

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Figure 2. Arrhenius plot obtained by applying eq 5 to the TG experimental data.

Figure 1. Thermodynamic equilibrium composition of the system 1 mol ZnO + λ mol C for (a) λ ) 1 and (b) λ ) 0.8.

gas intermediate reactions11

ZnO(s) + CO(g) ) Zn(g) + CO2(g)

(2)

CO2(g) + C(s) ) 2CO(g)

(3)

The dissociation of ZnO into its elements is omitted from consideration because its reaction rate is negligible at temperatures below 1800 K.12 The equilibrium mole fraction of ZnO(g) in the saturated vapor is at most 5 × 10-5 at 1700 K, and it is therefore neglected in this study.3,13 The thermodynamic equilibrium composition of the system ZnO + λC at 1 bar and over the range of temperatures of interest is shown in Figure 1 for λ ) 1 and 0.8, computed using the HSC Outokumpu code.14 Below about 900 K, ZnO and C are thermodynamically stable components. In the temperature range 900-1340 K, they are consumed in reactions 2 and 3. Above 1340 K, the reduction reaches completion, and the chemical system consists of a single gas phase containing an equimolar mixture of Zn(g) and CO for λ ) 1 and a 1:0.6: 0.2 molar mixture of Zn(g)/CO/CO2 for λ ) 0.8. The effect of understoichiometry on the equilibrium composition has been previously examined for λ ranging from 0 (thermal decomposition) to 1. It was found that the

Figure 3. Solar chemical reactor configuration for the carbothermic reduction of ZnO featuring two cavities in series, with the first one functioning as the solar absorber and the second as the reaction chamber.

minimum temperature requirement for which ZnO is completely converted into Zn(g) is 1623 K for λ as low as 0.6, but this minimum temperature increases sharply to above 2000 K when λ is reduced further.2 In addition to the savings in carbon and, consequently, avoidance of CO2, operation with λ < 1 would be advantageous because of the higher fraction of solar energy stored in chemical form in Zn.15 In contrast, understoichiometry might have adverse effects because high CO2 partial pressures favored Zn reoxidation,11 which can be avoided to some extent via rapid quenching using lead-spray condensers.16 When a reactive carbonaceous material is used as the reducing agent, such as the charcoal powder used in our experimental studies, the interfacial kinetics of reaction 2 become the rate-controlling mechanism. Assuming a shrinking spherical particle model with an unreacted core,17 the reaction rate of ZnO particles with CO is

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Figure 4. ZnO-C packed-bed modeled as a 1D continuum exposed to radiation at the top and undergoing shrinkage due to chemical reaction.

defined in terms of the particle surface area as

r)-

Table 1. Experimental Conditions of Solar Experimental Runs a and b

1 dnZnO 4πRp2 dt

(4)

Assuming an amount nZnO containing N particles, nZnO ) 4/3NFZnOπRp3, and assuming a first-order rate constant for the surface reaction,17 r ) kCCO, the reaction rate takes the form

(

dnZnO 3 n -2/3 ) -4π dt ZnO 4NFZnOπ

)

2/3

CCOk

(5)

or, in terms of the reaction extent, R ) 1 - nZnO/n0,ZnO

[ (

3 dR ) (1 - R)2/3k 4π dt 4NFZnOπ

)

2/3

CCOn0-1/3

]

(6)

The temperature dependency of the rate constant k is determined by imposing the Arrhenius law

k ) k0e-EA/RT

(7)

Thermogravimetric (TG) measurements were carried out using a modified Netzsch TASC-419 thermobalance, in which an electrically heated Al2O3 tube contained a water-cooled quartz coldfinger condenser for trapping Zn vapor.18 A mixture of ZnO powder (Fluka 96479, mean particle size of 1 µm, BET surface area of 5.2 m2/ g) and carbon (beech charcoal powder from Chemivron, mean particle size of 180 µm, BET surface area of 0.38 m2/g), with a ZnO/C molar ratio of 1:0.8, was loaded on a flat alumina holder and placed in the thermobalance. Samples were heated at a rate of 10 K/min under 25 mL/min N2 carrier flow. No ZnO deposits were observed at the end of the TG experiments, performed under nonequilibrium conditions. Figure 2 shows the Arrhenius plot obtained by applying eq 5 to the TG experimental data. The apparent activation energy obtained by linear regression (R2 ) 0.978) is EA ) 201.5 kJ/mol. Note that EA is not the inherent state activation energy because it depends on the gas diffusion resistances. 3. Solar Chemical Reactor Modeling A scheme of the solar chemical reactor is shown is Figure 3.19 It features two cavities in series, with the

solar run parameter

a

b

C/ZnO molar ratio initial ZnO + C batch (kg) ZnO + C residual (kg) initial bed temperature (K) input power (kW) CPC’s entrance diameter (m) CPC’s acceptance angle (deg) reactor’s aperture diameter (m) mean solar flux at aperture (W/m2) L(t)0) (m) measured T0(t) measured TSiC(t)

0.8 0.5 0.315 300 6.2 0.08 45 0.065 1868 0.063 Figure 5a Figure 5a

0.8 0.5 0.005 300 8.7 0.08 45 0.065 2622 0.069 Figure 5b Figure 5b

first (top) one functioning as the solar absorber and the second (bottom) one as the reaction chamber. A common SiC plate separates them. The first cavity is made of SiC and contains a windowed aperture to let in concentrated solar radiation. The second cavity is a wellinsulated cylinder and contains a packed bed of a ZnO/C mixture that is subjected to irradiation emitted by the SiC plate. With this arrangement, the first cavity protects the quartz window against particles and condensable gases and further serves as a thermal shock absorber. A 3D compound parabolic concentrator (CPC20) is incorporated at the aperture to augment the solar concentration ratio by a factor of about 2, resulting in average incident radiative fluxes through the aperture exceeding 2600 suns (1 sun ) 1 kW/m2). Reactants are placed in the reaction chamber before the run for batch operation; gaseous products exit continuously via an outlet port located on the lateral wall. The reactor is specifically designed for beam-down incident radiation, as obtained through a Cassegrain optical configuration that makes use of a hyperbolical reflector at the top of the solar tower to redirect sunlight to a receiver located on the ground level.21 Generic design guidelines for such a two-cavity reactor concept have been described by Wieckert et al.22 A transient reactor model is formulated that couples radiation and conduction heat transfer with chemical kinetics. The model domain is shown in Figure 4 and consists of a packed-bed of a ZnO and C mixture. The

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q′′′V ) ∆H°

dnZnO dt

(9)

∆H° is the standard enthalpy change of eq 1, given in polynomial form as a function of temperature as14

∆H°(T) ) -6.576 × 10-6T 2 - 5.327 × 10-3T + 373.0 kJ/mol (10) and dnZnO/dt is computed using eq 5. The effective thermal conductivity, keff, of the packed bed is found by matching numerical calculated and experimentally measured temperatures. The determination of keff and its validation with measured values are described in the Appendix. The boundary conditions are

initial

T(x,t)0) ) 300 K

top

qL′′(x)L) )

bottom

T(x)0,t) ) T0(t)

σ(TSiC4 - Tx)L4) 1 1 + -1 SiC bed

(11) (12)

(13)

where TSiC(t) and T0(t) are experimentally measured. The packed bed is discretized into NCV disk-shaped layers (control volumes) as depicted in Figure 4, and the fully implicit finite-volume scheme is applied.23 The thickness of each control volume shrinks as the reaction progresses, at the rate Figure 5. Measured temperature profiles TSiC(t) and T0(t) at the boundaries for solar experimental runs a and b, described in Table 1.

dxi dnZnO,i M ) dt dt AFbed

(14)

The height of the bed is thus top of the bed is exposed to radiation emitted by the SiC plate, which is assumed to be a gray emitter at a uniform time-dependent temperature TSiC(t), measured experimentally. Radiative heat absorbed at the top is transferred by conduction and radiation through the bed. The bottom boundary condition is given by the experimentally measured time-dependent temperature T0(t). The bed is modeled as a 1D continuum undergoing shrinking due to the chemical reaction. The shrinking of the bed is caused from the endothermic chemical transformation of solid-phase reactants (ZnO and C) into gas-phase products (Zn, CO, and CO2). The 1D approximation is supported by preliminary 2D axialsymmetric simulations of a nonshrinking packed bed that predicted a uniform temperature in the radial direction, as well as by experimental measurements that showed uniform bed shrinkage in the vertical direction.10 The chemical reaction rate is given by eq 5, with the Arrhenius parameters determined by TG (see section 2). For simplicity, convection heat transfer to the gas products is omitted from consideration. Total pressure is constant and equal to 1 bar. Governing Equations. The 1D unsteady-state energy conservation equation is given by

FbedCp

dT dT d ) keff + q′′′ dt dx dx

(8)

where q′′′ is the volumetric heat sink due to the endothermic reaction

N

L(t) )

∆xi ∑ i)0

(15)

The system of eqs 8-15 is solved iteratively using the time division multiplexing algorithm (TDMA).23 The simulation program employs a mesh generator that produces a finer grid in the upper part of the bed where the heat flux and chemical reaction have their maximal amplitudes. The iterative solution at the upper boundary is under-relaxed to ensure convergence. The accuracy of the numerical simulation is estimated by calculating the relative difference in the reaction extent R for NCV ) 600 and 1200. This relative difference is equal to 10-5. 4. Experimental Validation Solar tests over the temperature range 1350-1600 K were performed with a 5-kW reactor prototype at PSI’s solar furnace24 and ETH’s high-flux solar simulator.25 Details of the fabrication of the reactor prototype, the experimental setup, and experimental results have been described by Osinga et al.10 The results produced by the model are compared to two solar experimental runs, a and b, carried out under the experimental conditions of Table 1. Note that the boundary conditions at the top and bottom are given by eqs 12 and 13, respectively, where TSiC(t) and T0(t) are experimentally measured and shown in Figure 5. For run a, the temperature of the SiC plate increases from 300 K to a maximum of 1572 K after 87 min. For run b, the

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Figure 6. Calculated temperature profiles along the packed bed determined every 10 min for solar experimental runs a and b. The points correspond to the measured values.

Figure 7. Calculated and measured temperature variation with time at a height of 30 mm for solar experimental runs a and b, described in Table 1.

temperature reaches a maximum at 1723 K after 80 min. Afterward, the shutter controlling the incoming solar radiation is closed, and the SiC plate undergoes cooling. Figure 6a,b shows the calculated temperature profiles along the bed as a function of time (every 10 min), for runs a and b, respectively. Three stages are observed. During the first 40 min, the upper portion of the bed is heated from ambient temperature to above 1000 K, but temperatures are not high enough for the reaction to occur. Afterward, the temperature at the top exceeds 1200 K, and the reaction proceeds at reasonable rates. The right ends of the temperature curves are shifted to the left with time because of the shrinking of the bed. Finally, after 87 min for run a and after 90 min for run b, the shutter is closed, the bed undergoes cooling, and the reaction stops. L (t ) 110 min) equals 3.9 and 0.1 cm for runs a and b, respectively. The remaining height of the bed is greater for run a because temperatures are about 200 K lower than those for run b. Also shown in Figure 6 (points) is the temperature measured by a thermocouple submerged in the bed at a height of 30 mm. Figure 7 shows the variation of the temperature with time at a height of 30 mm for both runs a and b of Table 1. Solid curves represent the numerical predictions; dotted curves represent the measurements. The agree-

ment between calculated and measured values is within 1.6 ( 1% for run a and 3.5 ( 3.9% for run b (mean difference ( standard deviation). Note in Figure 6b that, for run b, the thermocouple was destroyed after 70 min, when the bed shrunk below it and exposed it to direct irradiation and corrosive Zn(g). The calculated (solid curve) and measured (dotted curve) rates of ZnO decomposition are shown in Figure 8 for both experimental runs a and b. The calculated values are the result of the integration over the bed of the reaction rate for each control volume at each time step (given by eq 5). The experimental values are determined by the sum of the number of moles of CO and twice the number of moles of CO2 (CO + 2CO2), recorded by on-line gas chromatography. The agreement between model and experiment is remarkably good. 5. Scaled-up Reactor The validated model is now used to predict the performance of a scaled-up reactor with a reaction chamber of 0.5-m height, designed for a load of 464 kg of a ZnO + C mixture. T0 is set to a constant 300 K. TSiC is increased from 300 to 1600 K at a rate of 50 K/min and then set to a constant 1500, 1600, or 1700 K during the rest of the simulation. keff is taken equal to the values determined by the radial heat flow method

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Figure 9. Temperature profiles along the bed as a function of reaction time (given in minutes) for a scaled-up reactor and for TSiC ) 1600 K.

Figure 8. Calculated and measured reaction rate vs time for solar experimental runs a and b, described in Table 1.

Figure 10. Zn production rate vs time for TSiC ) 1500, 1600, and 1700 K.

for the temperature range 500-900 K and to the values determined by the Zehner et al. method28 for 9001700 K (see the Appendix). The total simulation time is 5 h. Figure 9 shows the temperature profiles along the bed as a function of time for TSiC ) 1600 K. Analogously to the small-scale reactor, the temperature at the top exceeds 1200 K after 30 min, and the bed shrinks at an approximately constant speed of 2.8 × 10-5 m/s as the reaction progresses. A large temperature gradient is obtained in the top layer, which is typical of ablation processes where heat transfer through the bed becomes the rate-controlling mechanism. After 5 h of operation, the bed had shrunk by 87%. Figure 10 shows the predicted rate of Zn production for the three different SiC plate temperatures. The rate is approximately constant, except for the 30-min startup heating phase. For TSiC ) 1700 K, the reactor is emptied after 194 min. Gravity pressure differences might influence the predicted bed shrinkage because a higher bed density increases the thermal conductivity. Thermoconductivity measurements made with the setup described in the Appendix showed that a 50% increase in Fbed produces a 20% increase in keff, which in turn results in model

prediction of a 5% increase in the Zn output rate. In contrast, an increase of Fbed augments the gas diffusion resistance, which in turn reduces the Zn yield. Summary and Conclusions The carbothermic reduction of ZnO proceeds endothermically at temperatures above 1200 K via two solid-gas intermediate reactions: ZnO + CO and Boudouard. Assuming the interfacial kinetics of the former to be rate-controlling for the shrinkage of spherical particles with an unreacted core, we determined the kinetic rate constant by thermogravimetric measurements. The 1D transient energy conservation equation was solved numerically by the finite-volume technique for a shrinking packed bed of a ZnO/C mixture. Validation was accomplished with experimentally measured temperature profiles and ZnO decomposition rates as a function of time, obtained for a 5-kW solar reactor subjected to high-flux radiation in the range 1870-2620 kW/m2. The effective thermal conductivity of the packed bed is compared to data measured using the radial heat flow method. The model is further used to predict the performance of a scaled-up reactor. After a startup

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heating phase, whose duration depends on the boundary and initial conditions, the temperature at the top exceeds 1200 K, and the bed shrinks at an approximately constant speed as the reaction progresses at reasonable rates. Conditions are typical of ablation processes, where heat transfer through the bed becomes the rate-controlling mechanism. Acknowledgment This study was performed within the framework of the European Union research project SOLZINC. We gratefully acknowledge the financial support from the BBW, Swiss Federal Office of Education and Science. We thank A. Hofmann and M. Brack for the thermal conductivity measurements and T. Ro¨thlisberger and R. Mueller for the TG measurements and kinetic analysis. Nomenclature A ) bed horizontal surface, m2 C ) molar concentration, mol/m3 Cp ) specific heat, J/kg‚K EA ) activation energy, J/mol ∆H ) enthalpy change, J/mol k ) rate constant for surface reaction, m/s k0 ) preexponential factor in the Arrhenius law, m/s keff ) effective thermal conductivity, W/m‚K L ) height of bed, m LH ) length of central heater, m n ) number of moles, mol M ) ZnO + C molar mass, kg/mol N ) number of particles NCV ) number of control volumes P ) power delivered to the central electric heater, W q′′ ) heat flux, W/m2 q′′′ ) volumetric heat sink, W/m3 r ) reaction rate, mol/s‚m2 r1 ) radius of the inner cylinder, m r2 ) radius of the outer cylinder, m R ) ideal gas constant, J/mol‚K Rp ) particle radius, m t ) time, s T ) temperature, K

T0 ) temperature at x ) 0, K T1 ) temperature at the radius r1, K T2 ) temperature at the radius r2, K TSiC ) temperature of the SiC plates, K V ) volume, m3 x ) space coordinate, m R ) reaction extent λ ) stoichiometric molar ratio of C to Zn SiC ) emissivity of the SiC plate bed ) emissivity of the bed material FZnO ) ZnO molar density, mol/m3 Fbed ) ZnO + C bulk density, kg/m3 σ ) Stephan-Boltzmann constant, W/m2‚K4

Appendix: Effective Thermal Conductivity The effective thermal conductivity of a ZnO + C powder mixture was experimentally determined by the radial heat flow method.26 The apparatus is depicted in Figure 11. It features two concentric cylinders of radii r1 and r2, the inner one containing the central electric heater of length LH, and the powder placed between the two cylinders. The power P produced in this heater induces a temperature gradient in the powder. An additional shell heater coiled around the outer cylinder is used to adjust the temperature gradient. Four guard heaters at the side boundaries guarantee heat flux in the radial direction. Thus, the effective thermal conductivity of the ZnO + C sample is calculated as

keff )

P ln(r2/r1) 2πLH(T1 - T2)

(16)

Measurements were carried out for a ZnO + C powder mixture (ZnO, mean particle size of 5.2 µm and BET surface area of 2.3 m2/g; carbon, beech charcoal powder from Chemivron with a mean particle size of 180 µm and BET surface area of 0.38 m2/g). keff is plotted as a function of temperature in Figure 12.27 Also shown in Figure 12 are the curve calculated by the model of

Figure 11. Radial heat flow apparatus used to measure the effective thermal conductivity of the ZnO + C powder mixture.

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Figure 12. Effective thermal conductivity vs temperature for ZnO + C powder.

Zehner et al.28 and the two curves that give the best match between numerical and experimental measured temperatures for runs a and b, Figure 7. Literature Cited (1) Steinfeld, A. High-Temperature Solar Chemistry for CO2 Mitigation in the Extractive Metallurgical Industry. EnergysInt. J. 1997, 22, 311. (2) Steinfeld, A.; Weidenkaff, A.; Brack, M.; Mo¨ller, S.; Palumbo, R. Solar Thermal Production of Zinc: Program Strategy and Status of Research. High-Temperature Material Processes. 2000, 4 (3), 405-416. (3) Palumbo, R.; Lede, J.; Boutin, O.; Elorza Ricart, E.; Steinfeld, A.; Mo¨ller, S.; Weidenkaff, A.; Fletcher, E. A.; Bielicki, J. The Production of Zn from ZnO in a Single Step High-Temperature Solar Decomposition ProcesssI. The Scientific Framework for the Process. Chem. Eng. Sci. 1998, 53, 2503-2517. (4) Steinfeld, A. Solar Hydrogen Production via a 2-Step WaterSplitting Thermochemical Cycle based on Zn/ZnO Redox Reactions. Int. J. Hydrogen Energy 2002, 27, 611-619. (5) Murray, J. P.; Steinfeld, A.; Fletcher, E. A. Metals, Nitrides, and Carbides Via Solar Carbothermal Reduction of Metals Oxides. EnergysInt. J. 1995, 20 (7), 695-704. (6) Adinberg, R.; Epstein, M. Experimental study of solar reactors for carboreduction of zinc oxide. Energy 2004, 29, 757769. (7) Steinfeld, A.; Frei, A.; Kuhn, P.; Wuillemin, D. Solarthermal Production of Zinc and Syngas Via Combined ZnO-Reduction and CH4-Reforming Processes. Int. J. Hydrogen Energy 1995, 20 (10), 793-804. (8) Steinfeld, A.; Brack, M.; Meier, A.; Weidenkaff, A.; Wuillemin, D., A Solar Chemical Reactor for the Co-Production of Zinc and Synthesis Gas. Energy 1998, 23, 803-814. (9) Wieckert, C.; Epstein, M.; Olalde, G.; Palumbo, R.; Pauling, H. J.; Reichardt, H. U.; Robert, J. F.; Santen, S.; Steinfeld, A. The SOLZINC Project for Solar Carbothermic Production of Zn from ZnO. In Proceedings of the 11th SolarPACES International Symposium; Steinfeld, A., Ed.; Zu¨rich, Switzerland, 2002; pp 239245. (10) Osinga, T.; Frommherz, U.; Steinfeld, A.; Wieckert, C. Experimental Investigation of the Solar Carbothermic Reduction

of ZnO Using a Two-Cavity Solar Reactor. ASME J. Solar Energy Eng. 2004, 126, 633-637. (11) Berman, A.; Epstein, M. The Kinetic Model for Carboreduction of Zinc Oxide. J. Physics IV 1999, 9, 319-324. (12) Mo¨ller, S.; Palumbo, R. Solar thermal decomposition kinetics of ZnO in the temperature range 1950-2400 K. Chem. Eng. Sci. 2001, 56, 4505-4515. (13) Watson, L.; R., Thiem; T. L.; Dressler, R. A.; Salter, R. H.; Murad, E. High-temperature mass spectrometric studies of the bond energies of gas-phase ZnO, NiO, and CuO. J. Phys. Chem. 1993, 97, 5577-5580. (14) Roine, A. Outokumpu HCS Chemistry 5.0; Outokumpu Research Oy: Pori, Finland, 1997. (15) Wieckert, C.; Steinfeld, A. Solar Thermal Reduction of ZnO using CH4:ZnO and C:ZnO Molar Ratios Less than 1. J. Solar Energy Eng. 2002, 124, 55-62. (16) Graf, G. G. Zinc. In Ullmann’s Encyclopedia of Industrial Chemistry, 5th ed.; Gerhartz, W., Ed.; VCH: Weinheim, Germany, 1996; p A28. (17) Levenspiel, O. Chemical Reaction Engineering, 3rd ed.; Wiley: New York, 1999. (18) Ro¨thlisberger, T. Thermographimetrische Analyse des Zinkoxid-Kohle Prozesses. Semester Thesis, ETH Zu¨rich, Zu¨rich, Switzerland, 2002. (19) Bruesewitz, M.; Semrau, G.; Epstein, M.; Vishnevetsky, I.; Frommherz, U.; Kra¨upl, S.; Palumbo, R.; Wieckert, C.; Olalde, G.; Robert, J.-F.; Osinga, T.; Steinfeld, A.; Sante´n, S. Solar Carbothermic Production of Zinc and Power Generation via ZnOZn Cyclic Process. Presented at the ISES Solar World Congress, Go¨teborg, Sweden, June 16-19, 2003. (20) Welford, W. T.; Winston, R. High Collection Nonimaging Optics; Academic Press: San Diego, 1989. (21) Yogev, A.; Kribus, A.; Epstein, M.; Kogan, A. Solar “Tower Reflector” Systems: A new Approach for High-Temperature Solar Plants. Int. J. Hydrogen Energy 1998, 23, 239-245. (22) Wieckert, C.; Meier, A.; Steinfeld, A. On Indirectly Irradiated Solar Receiver-Reactors for High-Temperature Thermochemical Processes. ASME J. Solar Energy Eng. 2003, 125, 120123. (23) Patankar, S. V. Numerical Heat Transfer and Fluid Flow; Hemisphere: New York, 1980. (24) Haueter, P.; Seitz, T.; Steinfeld, A. A New High-Flux Solar Furnace for High-Temperature Thermochemical Research. ASME J. Solar Energy Eng. 1999, 121, 77-80. (25) Hirsch, D.; v. Zedtwitz, P.; Osinga, T., Kinamore, J.; Steinfeld, A. A New 75 kW High-Flux Solar Simulator For HighTemperature Thermal and Thermochemical Research. ASME J. Solar Energy Eng. 2003, 125, 117-120. (26) Flynn, D. R. Thermal Conductivity of Loose-Fill Materials by a Radial-Heat-Flow Method; Compendium of Thermophysical Property Measurement Methods; Plenum Press: New York, 1992; Vol. 2. (27) Hofmann, A. Messung der effektiven Wa¨rmeleitfa¨higkeit von Zinkoxid (ZnO) mit Kohle (C), Kalkstein (CaCO3) und Kalk (CaO). Diploma Thesis, ETH Zu¨rich, Zu¨rich, Switzerland, 2004. (28) Tsotsas, E.; Martin, H. Thermal Conductivity of Packed Beds: A Review. Chem. Eng. Process. 1987, 22, 19-37.

Received for review May 8, 2004 Revised manuscript received July 21, 2004 Accepted September 28, 2004 IE049619Q