Heating Element of an Air Preheater in a Utility Boiler as an SCR

A heating element coated with V2O5-WO3/TiO2 catalyst has been prepared by a two-roll forward method as a parallel passage type reactor (PPR) for ...
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Ind. Eng. Chem. Res. 2005, 44, 707-714

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Heating Element of an Air Preheater in a Utility Boiler as an SCR Reactor Removing NO by NH3 Jae Ho Choi,† Moon Hyeon Kim,‡ and In-Sik Nam*,§ Department of Chemical Engineering/School of Environmental Science and Engineering, Pohang University of Science and Technology, P.O. Box 125, Pohang 790-600, Korea, Korea Cottrell Co., Ltd., Seoul 121-200, Korea, and Environmental Technology Institute (ETI), Research Institute of Nano Technologies, Department of Environmental Engineering, Daegu University, Gyeongsan 712-714, Korea

A heating element coated with V2O5-WO3/TiO2 catalyst has been prepared by a two-roll forward method as a parallel passage type reactor (PPR) for simultaneously exchanging heat and removing NO in the air preheater of a utility boiler. The performance of the heating element coated with the catalyst has been examined as a carrier for heat transfer and a catalytic reactor reducing NO in utility boilers. No alteration of the overall heat transfer coefficient of the heating element, PPR, due to the coating of the catalyst on the surface of the element has been observed. A reactor model has been developed for the design of a heating element as a PPR removing NO by NH3. The kinetic parameters obtained over the catalyst powder of V2O5-WO3/TiO2 are directly employed for estimating the performance of a heating element as a PPR. The model predicts NO conversion as well as NH3 slip quite well, regardless of the reactor operating conditions, including reactor space velocity, NH3/NO feed ratio, the length of the heating element, and reaction temperatures. Introduction Selective catalytic reduction of NO by NH3, i.e., NH3SCR, has been widely recognized as a commercially proven technology for removing NOx from stationary sources, including power plants. The SCR reaction commonly employs either honeycomb- or plate-shaped monoliths composed of titania-supported vanadia-based catalyst. Consequently, one of the most important aspects for the commercial application of this technology to emission sources may be the preparation of lowpressure-drop reactors, including honeycomb, and parallel passage reactors (PPR) schematically shown in Figure 1, along with high NO removal activity of the SCR catalyst itself.1 One option may be the use of a heating element installed in the air preheater of a utility boiler as an SCR reactor. Twofold advantages can be immediately attained if there is simultaneous exchange of heat and removal of NO from the stationary source, particularly a utility boiler. A few studies have involved an industrial attempt to use the heating element in a Ljungstromtype air preheater as an SCR reactor for selectively reducing NO by NH3, as shown in Figure 2.2-4 For such simultaneous roles for the heating elements as both the heat transfer media in the preheaters and the catalytic reactor, SCR catalysts should be accommodated properly onto the elements without any loss of their heat transfer capability. Previous studies on SCR reactors have focused mainly on honeycomb-type reactors, commonly employed for commercial SCR processes, due to their versatile struc* To whom correspondence should be addressed. Tel: (+82-54) 279-2264. Fax: (+82-54) 279-8299. E-mail: isnam@ postech.ac.kr. † Korea Cottrell Co., Ltd. ‡ Daegu University. § Pohang University of Science and Technology.

Figure 1. Configuration of a parallel passage reactor (PPR).

tural properties.5,6 However, the use of a PPR as a lowpressure-drop reactor for the SCR process is preferable, particularly for high-dust and -sulfur systems. It features strong resistance to dust plugging and erosion, low pressure drop, weak capability of SO2 oxidation to SO3, and simple adjustment of reactor space time according to the flue gas composition, compared to the performance over extruded honeycomb reactors.2,7,8 A PPR model based upon the lumped parameter concept only considering the axial concentration gradients was developed to describe the performance of such a slab-type reactor, prepared by simply slicing commercial plate-type reactors for NOx reduction and SO2 oxidation.9 Regardless of the usefulness of deNOx activity data obtained over the slab reactor, the model hardly predicted the performance of NOx removal by the reactor. Recently, Seijger et al.10 developed a ceramic foam type PPR and predicted pressure-drop and NOx reduction efficiency over a PPR where the crystal of Cu-

10.1021/ie0492653 CCC: $30.25 © 2005 American Chemical Society Published on Web 01/20/2005

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Table 1. Physicochemical Properties of V2O5-WO3/TiO2 Catalyst and an Optimal Composition of the Coating Slurry composition (wt %) catalyst

S

V2O5

WO3

TiO2

colloidal SiO2

methyl cellulose

starch

85% H3PO4

H2O

surface area (m2/g)

TiO2 V2O5-WO3/TiO2 coating slurry

1.8 1.8 1.8

2.0 2.0

6.0 6.0

98.2 90.2 31.0

4.0

2.0

2.0

2.0

49.2

76 61a

a

Measured after calcination at 500 °C for 5 h.

Figure 2. Schematic diagram of (a) a Ljungstrom-type gas-gas heat exchanger with (b) sectional packing of heating element.4

ZSM-5 catalyst has grown in situ. In addition, the direct utilization of intrinsic deNOx activity data without any mass transfer limitation for the simulation of the commercial-scale reactor could offer an immediate prediction of design guidelines for industrial SCR reactors.5,6,11 The purpose of the present study is to mainly examine the promise of heating elements of an air preheater in a utility boiler as an SCR reactor capable of removing NO from the boiler. This would significantly reduce the additional technical and economical burdens associated with the installation of an SCR reactor, particularly for a process producing electricity. A reactor model has also been developed to predict the performance of the heating element as a PPR type SCR reactor for removing NO based upon a lumped parameter model directly employing the kinetic parameters obtained from the experimental data over the powder catalyst without the fabrication of a PPR. Although there has been an attempt to model the catalytic behavior of the NH3-SCR reaction over a PPR as discussed, no studies have yet been attempted on the mathematical modeling of a heating element as an SCR reactor using intrinsic reaction kinetics for NOx removal and NH3 oxidation reactions. The promise of a heating element in an air preheater of a utility boiler as a PPR has hardly been investigated as well. Experimental Section Catalyst and PPR Preparation. A solution of metatitanic acid (Hankook Titanium Co. Ltd., Korea) containing ca. 2% of sulfur was employed to obtain a TiO2 support. A V2O5-WO3/TiO2 catalyst was prepared by an incipient wetness method. The respective precursor solutions of NH4VO3 and hydrated (NH4)6W12O39 (99.99%, Aldrich) were impregnated sequentially onto TiO2 prepared from metatitanic acid solution, and this TiO2 was dried at 100 °C in air overnight and calcined at 500 °C in air for 5 h. The catalyst includes 2% V2O5 and 6% WO3, as listed in Table 1. Details of the

Figure 3. SEM images for an aluminized steel plate (a) before and (b) after thermal oxidation.

preparation method of the catalyst have been extensively described elsewhere.12,13 An aluminized steel plate, which is commonly used for the heating element of an air preheater in a utility boiler, was employed for preparing the PPR. Prior to coating of the catalyst onto the plate in a dimension of 4.5 cm width and 19.4 cm length, its surface was thermally treated at 550 °C in air for 5 h, thereby forming a uniform oxidation layer, as indicated by scanning electron microscopy (Hitachi Model S2460N). Figure 3 shows an SEM image of the aluminized steel plate before and after the thermal treatment. In contrast to the surface of a fresh plate, the thermally aged plate in Figure 3b contains a uniformly oxidized surface, containing whiskerlike protrusions, on which stronger adhesion of the catalyst would be anticipated. A composition of the catalyst slurry with organic and inorganic binders is particularly critical to allow proper coating of the catalyst onto the plate; however, such binders should not cause any appreciable loss of the catalytic activity for the deNOx reaction. The slurry

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Figure 4. Thickness of the layer of the catalyst coated with an optimal catalyst density of 0.012 g/cm2 on the plate of the PPR by SEM imaging.

coated on the surface of the thermally treated plate forms a layer of the catalyst removing NO by NH3, as depicted in Figure 4. Note that the particle size of the catalyst in the slurry was less than 200 mesh, to minimize the mass transfer limitation. In addition to earlier efforts,14 a variety of the compositions of the coating slurry were tested to minimize the effect of the binders on the catalytic activity for the NO reduction reaction; an optimal constituent of the coating slurry has been listed in Table 1. The catalyst slurry was coated onto the thermally treated plates by using the two-roll forward method employing applicator and backup rolls in the identical rotating direction, as extensively described,14 and these catalyst-coated plates were calcined at 500 °C in air for 5 h, prior to being employed for heat transfer and deNOx activity measurements. Reactor System. A set of experimental data has been observed over a fixed-bed flow reactor to establish the intrinsic reaction kinetics for NO reduction by NH3 over the V2O5-WO3/TiO2 catalyst prepared. A flowing mixture consisting of 500 ppm of NO, 5% O2, and 5% H2O in N2 was used with an NH3/NO feed ratio of 1. The inlet and outlet concentrations of NO were analyzed by an on-line chemiluminescent NO-NOx instrument (Thermo-Electron Co., Model 10A), and NH3 slip during the course of reaction was directly measured by an online NH3 analyzer (Rosemount Co., Model 880A). Such a reactor system has been well described earlier.11,15 The mass transfer limitation over V2O5-WO3/ TiO2 was also examined by varying the catalyst size employed in a fixed-bed flow reactor system. Since the catalyst particle sizes below 20/30 mesh revealed quite similar NO removal activity, the experimental data for the present kinetic analysis were collected over 35/45 mesh size of the catalyst particle to minimize the mass transfer limitation. Prior to the measurements of the NO removal activity of PPR, five catalyst-coated plates were placed in a laboratory-designed stainless steel cartridge (4.5 × 4.5 × 19.4 cm) with an equal width and pretreated in flowing 5% O2 at 500 °C for 1 h. Since an LPG gas boiler could produce flue gas containing about 50 ppm of NO, additional NO from the cylinder was injected to adjust the feed concentration of NO by using a mass flow controller (Brooks 5850E). NH3 was independently fed into the reactor system. Consequently, the feed gas stream mainly included 500 ppm of NO with an NH3/

Figure 5. Effect of the catalyst coated on PPR on (a) thermal diffusivity and (b) conductivity of the reactor.

NO feed ratio of 1, 5% O2, 5% H2O, and the rest contained in the flue gas from gas boiler. The reactor space velocity has been defined as the ratio of the gas flow rate to the volume occupied by either the catalyst powder for kinetic study or the PPR itself. A detailed description of the present reactor system has been given elsewhere.11,12,15 PPR as a Heating Medium The heat transfer capability of the PPR prepared in the present study was examined with respect to the amounts of the catalyst coated on the plate of PPR to observe whether the PPR can also be employed as a heating medium of an air preheater in a utility boiler. Thermal diffusivity and specific heat capacity before and after the catalyst coating on the plate were measured by a thermal diffusimeter (Theta Co.) and a differential scanning calorimeter (Perkin-Elmer, Model DSC7) at a heating rate of 15 °C/min in the temperature range from 100 to 300 °C. This is a typical temperature window for an air preheater operated in a utility boiler. The thermal diffusivity of the PPR depends strongly on the amounts of the catalyst coated, as revealed in Figure 5a. When ca. 0.012 g, that is, an optimal amount of the catalyst coating of the catalyst per square centimeter of each plate, is coated, its thermal diffusivity is reduced by one-third compared to that for a fresh plate. It should be noted that the optimal amount of the catalyst coated was 0.012 g/cm2 from the view of NO removal activity, as shown in Figure 6. When the thermal conductivity is calculated on the basis of the diffusivity and heat capacity data observed, it varies from half to one-tenth of that for the fresh plate, depending upon the coating density of the catalyst on the PPR, as observed in Figure 5b. This indicates that

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Figure 6. Effect of the catalyst density on the catalytic performance of PPR coated with V2O5-WO3/TiO2 for NO reduction at a reactor space velocity of 4000 h-1.

Figure 8. Overall heat transfer coefficients of PPR with and without the catalyst coated on the plate.

Figure 7. Schematic of a laboratory-designed heat transfer measurement system.

the conduction efficiency of the PPR is closely related to the thickness of the catalyst layer coated on the PPR. Variation in the overall heat transfer coefficient before and after coating the catalyst on PPR was examined by using a self-designed heat transfer unit, as shown in Figure 7. One or two PPRs were placed in the unit completely insulated with mortar and fiberglass to prevent any heat loss to the surroundings. Air was heated and controlled in a separate chamber of the unit equipped with mass flow controllers (Brooks 5850E) in order to adjust the amount of air feed to the heat transfer unit. The overall heat transfer coefficient for the plate was calculated by the logarithmic mean temperature difference (LMTD) method as a function of heat flow.16 The coefficient, as depicted in Figure 8, was not altered at all on the basis of the amount of the catalyst coated onto the heating element. This result is primarily due to a thin layer of the catalyst coating prepared in the present study; therefore, the change in the conduction hardly affects the overall heat transfer performance of the PPR. Of course, the performance strongly depends on the thickness of the catalyst layer attributed to the amount of the catalyst coated on the PPR. Note that there is an optimal thickness of the catalyst on the plate from the view of NO removal activity, as mentioned. It definitely excludes the concern about the inefficiency of the PPR as a heating element of a preheater for a utility boiler to remove NO by NH3.14

Figure 9. TPD profile for NH3 and NO adsorbed on V2O5-WO3/ TiO2 catalyst. The carrier gas He was used at a flow rate of 50 cm3/min.

Reactor Modeling of a Heating Element as a PPR Reaction Kinetics. Temperature-programmed desorption (TPD) was conducted to establish an appropriate kinetic model based on the extent of the adsorption of NO, NH3, and O2 on the surface of V2O5-WO3/TiO2. Figure 9 shows the desorption profiles of NO, NH3, and O2 during TPD. NH3 could be predominantly adsorbed on the catalyst surface, while negligible amounts of NO and O2 were adsorbed on the surface compared to the amount of NH3. This indicates that NO reduction over the catalyst mainly occurs according to the Eley-Rideal mechanism, which is commonly observed for V2O5/TiO2 catalyst.17-20 Through an independent experiment clarifying the oxidation route of NH3 over V2O5-WO3/STiO2 toward NOx (NO + NO2), N2, and/or N2O at high reaction temperature, only N2 with H2O was produced. This agrees well with the earlier results over V2O5WO3/TiO2 catalyst.21 With the Hougen-Watson formalism based upon the Eley-Rideal mechanism confirmed by both TPD analysis and the catalytic oxidation of NH3, the present SCR reaction would occur according to the following reaction

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scheme, where S represents an active reaction site on the catalyst surface:

NH3 + S T NH3-S

(1)

NH3-S + NO + 1/4O2 f N2 + 3/2H2O + S

(2)

NH3-S + 3/4O2 f 1/2N2 + 3/2H2O + S

(3)

Although tens of possible reactions for SCR could occur,22 two primary kinetic equations postulated from eqs 1-3 can be derived:

-rNO )

-rNH3 )

kNOKNH3CNOCNH3

(4)

1 + KNH3CNH3

kNOKNH3CNOCNH3 1 + KNH3CNH3

+

kNH3KNH3CNH3 1 + KNH3CNH3

(5)

where KNH3 is the equilibrium constant for NH3 adsorption, kNO is the reaction rate constant for NO reduction, and kNH3 is the reaction rate constant for NH3 oxidation. PPR Model. The assumptions including steady state, isothermal conditions, nonaxial dispersion, symmetry at a channel axis, and only convection flow may be sufficient to develop the lumped parameter model for the PPR developed in the present study.11,15,23 A material balance for bulk flow at any axial position x in a reactor length L may lead to

dCbNO -u ) km,NOAe(CbNO - CsNO) dx -u

dCbNH3 dx

) km,NH3Ae(CbNH3 - CsNH3)

(6)

(7)

with the initial conditions at x ) 0: CbNO ) Cb,0NO and CbNH3 ) Cb,0NH3. A material balance for both diffusion and catalytic reactions over a coated layer, dy, on the PPR surface at any flow-directed position x is

-rNO ) De,NO

d2CNO

(8)

dy2

d2CNH3 -rNH3 ) De,NH3 dy2 at y ) 0:

dCNO )0 dy

at y ) t: CNO ) CsNO

dCNH3 dy

(9)

)0

CNH3 ) CsNH3

t, the thickness of the catalyst layer coated onto the surface of the PPR, depends on the amounts of catalyst slurry coated, and it is closely associated with the NO removal activity of the PPR system, as shown in Figure 6. About 2.0 g of catalyst coated onto each plate corresponding to a catalyst density of 0.012 g/cm2 with a thickness of 0.018 cm (see Figure 4) revealed the best reactor performance for removing NO by NH3 without any alteration of its heat transfer capability, as confirmed in Figure 8. Five PPR plates contained in a

reactor cartridge containing identical coating densities of the catalyst on the plate were employed as a reactor for the test of deNOx performance of the PPR. With identical boundary conditions derived for eqs 8 and 9, a material balance at any axial position x of the PPR from bulk gas flow becomes

km,NO(CbNO - CsNO) ) De,NO

( ) dCNO dy

km,NH3(CbNH3 - CsNH3) ) De,NH3

(10)

s

( ) dCNH3 dy

s

(11)

where calculations of De,NH3 and De,NO were based on the random pore model assuming a monodispersed pore size distribution.24 The pore size distribution of the catalyst coated on the plate was measured by a BET apparatus (Micrometrics ASAP 10C). Although there have been a variety of approaches to calculate an external mass transfer coefficient for a monolith-type catalytic reactor,7,25,26 the present study employed the Hawthorn correlation, which is quite versatile regardless of the types of monolith reactor, mainly due to the shape factor of the reactor in the correlation extending the range of the application of the formula. The external mass transfer coefficient can then be reformulated:

km,NO )

(

)

Dh D C 1 + 0.095 ReSc Dh L

0.45

(12)

where C is a limiting value of the Nusselt number depending on the geometry of the PPR channel and 7.54 has been commonly employed for a parallel plate in a PPR.23 To simultaneously solve the models developed, Gear’s method and a quasi-Newton method were employed for the coupled ordinary and partial differential equations along with the finite difference method (FDM). Estimates of the kinetic parameters were obtained by minimizing the residual sum of squares from the difference in experimental and calculated values for NO and NH3 conversions. Nonlinear regression was done by using the Levenberg-Marquardt algorithm in the IMSL (International Mathematical and Statistical Library, version 1.1) subroutine. A total of 150 or more initial values were used to avoid local minima by the regression. Details of the procedures for the present numerical data analysis have already been well described.11,15 Results Intrinsic DeNOx SCR Kinetics. Figure 10 shows the validity of the kinetic model in eqs 4 and 5 developed for NO reduction by NH3 over the catalyst particles of V2O5-WO3/TiO2 in a fixed-bed flow reactor. The model well predicts the experimental observation for NO reduction as well as NH3 consumption, regardless of the reactor space velocity. The kinetic parameters estimated from the model are listed in Table 2. The activation energy for NO reduction is 15.1 kcal/ mol, which is quite consistent with previous work on a similar catalytic system.5,6,11 The oxidation of NH3 over the catalyst requires an activation energy of 48.8 kcal/ mol, reasonably comparable to that obtained for the commercial systems V2O5-WO3-MoO3/TiO227 and V2O5-

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Figure 10. Prediction of NO conversion and NH3 slip by the kinetic model (eqs 4 and 5) as a function of reactor space velocity: (a) 100 0000 h-1 and (b) 200 000 h-1. Table 2. Kinetic Parameters Determined from the Experimental Data for NO Reduction in the Fixed-Bed Reactor kinetic param

est value

Ea,NO (kcal/mol) Ea,NH3 (kcal/mol) ∆HNH3 (kcal/mol) kNO (1/s) kNH3 (cm3/(mol s)) KNH3 (cm3/mol)

15.1 48.8 16.0 9.2 × 107 1.5 × 103 2.3 × 102

WO3/TiO2.11 The activation energy for NH3 oxidation is 3 times greater than that for NO reduction. Such a significant distinction in activation energies for both reactions also agrees well with earlier work.11,28 This difference mainly causes a bell-shaped NO conversion with respect to the reaction temperatures, which is commonly observed for an SCR catalytic system. Reactor Model. The kinetic parameters in Table 2 have been directly utilized for predicting the performance of a heating element as a PPR by the reactor model developed in the present study, including the effect of both geometric and diffusional resistances due to the layer of the catalyst coated onto the element. The model reasonably predicts the trend of NO conversion and NH3 slip as a function of the reaction temperatures with respect to the reactor space velocity, as shown in Figure 11. At the reactor space velocity of 2500 h-1 shown in Figure 11a, the model well predicts the experimental observation for NO removal activity but exhibits somewhat poor fitness for NH3 slip, particularly at high reaction temperature. Note that the reactor space

Figure 11. Prediction of NO conversion and NH3 slip by the PPR model (eqs 6-11) as a function of reactor space velocity: (a) 25 000 h-1 and (b) 5000 h-1. The thickness of the catalyst layer coated on PPR was ca. 0.018 cm.

velocity has been defined as the ratio of the flow rate to the reactor volume occupied by the PPR cartridge. When the space velocity is increased to 7500 h-1, the model slightly underestimates NO conversion within the reaction temperatures covered, as observed in Figure 11b. The difference between the model prediction and the experimental observation is probably due to the direct use of the kinetic parameters estimated over the catalyst particles. The agreement could be significantly improved if the adjustable parameters of the PPR model were estimated from the experimental data over the PPR. Regardless, the direct use of the kinetic parameter contains enormous technical advantages over the estimation of the kinetic parameters with the PPR experimental data.11 The performance of a heating element as an SCR reactor can be predicted without fabrication of the PPR. It can be done only with the kinetic results on the catalyst powder. The validation of the model developed has been also examined to describe the trend of NO removal activity as a function of NH3/NO feed ratio to the reactor. The model reasonably predicts the reactor performance for both NO conversion and NH3 oxidation at the reactor space velocity of 5000 h-1, as shown in Figure 12. The slight deviation of the simulated performance of the PPR model developed may be again due to the direct use of the kinetic parameters evaluated from the experimental data over the catalyst powder, as discussed. However, it is quite worthwhile from the viewpoint of the efforts to experimentally evaluate the catalytic activity of the PPR through its fabrication, although the developed model somewhat under- and/or overestimates the reactor performance. The NO removal

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Nomenclature Ae ) geometric surface area of PPR, 2n/w, where n ) number of plates and w ) width of plate (cm2/cm3) B ) roughness constant b ) distance between plates (cm) Ci ) concentration of i species (mol/cm3) Dh ) hydraulic diameter of monolith channel (cm) De,i ) diffusivity of i species (cm2/s) Ea,i ) activation energy for either reduction or oxidation of i species k ) thermal conductivity (W/(cm °C)) kNO ) reaction rate constant of NO reduction (1/s) kNH3 ) reaction rate constant of NH3 oxidation (cm3/(mol s)) km,i ) mass transfer coefficient of i species (cm/s) KNH3 ) adsorption equilibrium constant for NH3 (cm3/mol) L ) reactor length (cm) ri ) reaction rate for i species based on catalytic volume (cm2/cm3) t ) thickness of catalyst layer coated onto a plate surface (cm) u ) average gas velocity at reactor inlet (cm/s) y ) catalytic wall coordinate from the center of the wall outward (cm) Sub- and Superscripts b ) bulk s ) surface Greek Symbols Figure 12. Prediction of NO conversion and NH3 slip by the PPR model (eqs 6-11) at a reactor space velocity of 5000 h-1 as a function of NH3/NO feed ratio: (a) NH3/NO ) 1.0; (b) NH3/NO ) 0.8. The thickness of the layer coated by the catalyst was ca. 0.018 cm.

activity of the PPR can be easily anticipated only with the kinetic data obtained from the catalyst powder, even without the PPR fabrication and performance test. The data can be immediately utilized for obtaining information on the commercial design of the PPR to remove NO by NH3 without time-consuming efforts in the fabrication of a heating element and the performance test as an SCR reactor. Conclusions A heating element can be successfully prepared for the effective heating medium of an air preheater in a utility boiler and used for the selective catalytic reduction of NO by NH3 over V2O5-WO3/TiO2 as an SCR reactor. The element reveals high performance of NO removal activity along with a negligible alteration of heat transfer efficiency, due to the thin layer of the catalyst coating on the plate. The reactor model, including the reaction kinetics derived in the present study, reasonably predicts the performance of the element as a PPR with respect to the configuration and operating conditions of the reactor, even though the model directly employs the kinetic parameters estimated from the reaction kinetics. It indicates that the significant efforts to re-estimate the kinetic parameters from the experimental data observed over a commercial scale reactor can be excluded, and the performance of the reactor can be easily evaluated only with the kinetic data examined over the powder of the catalyst.

F ) gas density (g/cm3) µ ) gas viscosity (g/cm s) Dimensionless Group Re ) Reynolds number, uDhF/µ Sc ) Schmidt number, µ/FD Pe ) Peclet number, ReSc ) µDh/D Sh ) Sherwood number, kmDh/D

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Received for review August 12, 2004 Revised manuscript received November 26, 2004 Accepted November 29, 2004 IE0492653