solid exothermic reactions

Chemical Engineering Science 55 (2000) 6021}6036

A study on the thermal behavior of structured plate-type catalysts with metallic supports for gas/solid exothermic reactions Enrico Tronconi*, Gianpiero Groppi Dipartimento di Chimica Industriale e Ingegneria Chimica **G. Natta++, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy Received 17 April 2000; accepted 2 August 2000

Abstract The heat transfer characteristics of seven di!erent samples of coated plate-type structured catalysts with highly conductive metallic supports were investigated using the model reaction of CO oxidation over Pd/c-Al O . In the case of supports made of aluminum hot   spot temperatures were moderate, and the thermal behavior of the structured catalysts was solely controlled by the heat transfer resistance at the interface between catalyst and reactor wall. Temperature gradients were markedly more signi"cant in the case of a support with identical geometry but made of steel, due to a tenfold reduction of the intrinsic material conductivity. They were still greater in the case of a steel support with thinner plates. For aluminum supports, experiments with a fourfold more active catalytic washcoat and with a modi"ed con"guration of the structured support con"rmed that an isothermal behavior is approached even for conditions corresponding to an adiabatic temperature rise of about 8003C, and that such results can be scaled up to di!erent geometries of the structured systems if the washcoat-to-support volume ratio is conserved. Finally, the wall heat transfer coe$cient was enhanced by a design of the aluminum support with improved thermal contact at the wall. A simple 1D analysis, based on independent intrinsic kinetics, yielded estimates of the overall wall heat transfer coe$cient in the range 80}120 W/(m K).  2000 Elsevier Science Ltd. All rights reserved. Keywords: Catalyst support; Heat conduction; Isothermal; Reaction engineering; Structured catalysts; Fixed-bed reactors

1. Introduction Monolithic or structured catalyst supports and reactors are widely applied in environmental catalysis (Cybulski & Moulijn, 1994a, 1998). On the other hand, there are only a limited number of reports in the literature concerning their use in gas/solid reactors for production of chemicals (Degussa, 1989; Ragaini, De Luca, Ferrario & Della Porta, 1980; Heynderickx, Froment, Broutin, Busson & Weill, 1991; Cybulski & Moulijn, 1994b). As compared to conventional packed-bed reactors loaded with catalyst pellets, an obvious and well-established advantage of such structured reactors would be the strongly reduced pressure drops (roughly by two orders of magnitude). A second potential advantage has received much less attention in the open literature: in principle, heat transfer in structured catalysts can be more e!ective

* Corresponding author. Tel.: #39-02-23993264; fax: #39-0270638173. E-mail address: [email protected] (E. Tronconi).

because of an alternative mechanism, namely heat conduction in the connected monolith support, which is not possible in random packings of pellets. In this respect the few published studies of heat transfer in monolithic structures (Eigenberger, 1992, 1997; Cybulski & Moulijn, 1994b) have pointed out only modest improvements of their e!ective heat transfer characteristics in comparison to packed beds of pellets, possibly because they addressed only existing commercial supports: in fact neither the construction material nor the geometry of such supports is optimized in view of heat conduction. In previous papers (Groppi & Tronconi, 1996, 1998, 2000) we have shown by modeling and simulation that: (i) coated catalysts based on novel metallic honeycomb supports designed with suitable materials and geometric properties are associated with much higher e!ective radial and axial thermal conductivities than conventional packed beds of catalyst pellets; (ii) externally cooled multitubular "xed-bed reactors loaded with such structured systems can operate in principle with markedly reduced temperature gradients even in the

0009-2509/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 2 1 4 - 1

6022

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

case of very exothermic gas/solid reactions, as for example in industrial partial oxidation processes. Herein we present an experimental study of the thermal behavior of home-made structured coated metallic catalysts, using CO oxidation as a model exothermic reaction. Seven plate-type catalyst samples with di!erent structural characteristics were prepared and tested in order to investigate the in#uence of the following relevant catalyst design aspects: (i) intrinsic thermal conductivity of the support material; (ii) thickness of the slabs in the support; (iii) formulation of the catalytic washcoat; (iv) geometric con"guration of the support; (v) thermal contact of the support with the reactor wall. We also developed an engineering analysis of our structured systems with metallic supports, in order to gain a quantitative appreciation of their heat exchange characteristics. The goal of the present fundamental study is twofold: we intend to verify by experiment the previous promising theoretical analyses, and we also seek guidelines for

rational catalyst design work in view of potential industrial applications.

2. Experimental 2.1. Structured catalysts and reactor Seven plate-type catalysts (samples A}G) with coated structured metallic supports were prepared, based on three geometric con"gurations of the support and on three formulations of the catalytic washcoat. Supports * For samples A}D and E, the supports consisted of four slabs (width"46 mm, length" 200 mm) assembled with spacers 3 mm apart in order to form three parallel rectangular channels (con"guration I, shown in Fig. 1a). In all such samples, the thickness of the two outer slabs was equal to the half-thickness of the central ones, since they were coated with catalyst on one side only. The slabs were made either of aluminum (99.5% commercial purity, samples A, D and E) or of stainless steel (AISI 304, samples B and C), with halfthickness of the two central slabs"0.5 mm (samples A,

Fig. 1. Front view of the tested plate-type catalysts with metallic supports (front view): (a) con"guration I; (b) con"guration II; (c) con"guration III.

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

B, D and E) or"0.2 mm (sample C). For catalyst sample F, the support consisted of 12 0.5 mm thick slabs made of aluminum, coated on both sides, again 46 mm wide but 50 mm in length (con"guration II, shown in Fig. 1b). The support of sample G was identical to that of sample F, but for two additional appendices at the ends of each slab, which were included in order to promote heat exchange between the catalyst and the inner reactor wall (con"guration III, see Fig. 1c). Washcoats * For samples A}C the catalytic washcoat (coating I) was obtained starting from a commercial c-Al O powder impregnated with 3% w/w Pd (3PdAl)   and dissolved in a solution of sodium silicate. The resulting slurry was then spread onto the metal slabs pretreated with HNO . Calcination up to 5003C followed,  yielding adherent uniform coatings with bulk composition 40.3% SiO , 18.4% Al O , 9.3% Na w/w evaluated    by atomic adsorption. A uniform washcoat thickness of about 150}200 lm was observed in SEM micrographs. BET analysis and Hg porosimetry revealed very low porosity and speci"c surface area. Sample D was "rst coated with a proprietary Al-based primer (GDE, Novara, Italy) to improve the adherence of the catalytic coating. Subsequently, the 3PdAl powder was dispersed in a silica sol, prepared by hydrolysis of organic precursors (TEOS and TMEOS) dissolved in dioxane; fumed silica was added in order to control the viscosity. The catalytic layer (coating II) was deposited by dipping, followed by #ash heating at 2803C. The "nal composition was 40% w/w 3PdAl and 60% w/w SiO .  The layer thickness was about 20 lm, as revealed by SEM images. BET analysis showed that the coating was porous in this case, with a pore volume of 0.64 cm/g, a speci"c surface area of 140 m/g and a mean pore radius of 130 As . For samples E}G, the washcoat was deposited according to the following two steps (coating III): (a) deposition of a pseudobohemite primer, prepared by dispersing 10% w/w of a commercial aluminum hydroxide powder (Disperal, supplied by Condea Chemie) in a 0.4% w/w HNO 

6023

aqueous solution; the supports were then dipped into the dispersion and dried at r.t. for 4}5 h; (b) deposition of the Pd#c-Al O washcoat: in this case 3PdAl was ob  tained by dry impregnation of a c-Al O with particle   size (0.1 lm (Sumitomo ALK-PG015) with palladium nitrate (Aldrich); this powder was dispersed in HNO  aqueous solution to give the catalytic slurry; the supports pre-coated with the pseudobohemite primer were dipped in the c-Al O slurry and #ash heated at 2803C. A layer   thickness of 70 lm was estimated from SEM images, whereas the morphological analysis yielded a pore volume of 0.48 cm/g, a speci"c surface area of 110 m/g and a mean pore radius of 80 As . Further details on the coating methods are given elsewhere (Valentini et al., 1999; Groppi, Cristiani, Valentini & Tronconi, 2000). The characteristics of the seven tested catalyst samples are summarized in Table 1. Reactor * The assembled packets of coated slabs were eventually equipped with "ve (con"guration I) or four (con"gurations II and III) 1/16 stainless-steel tubes at di!erent transverse locations, acting as thermowells for sliding J-type thermocouples, and loaded into a stainless-steel reactor tube (46;26 mm internal cross section) placed inside an oven with air recirculation (Mazzali Thermotest) driven by a proportional-integral-derivative controller. The temperature distribution along the upper and lower external reactor walls was also measured by two sliding thermocouples. The pressure drop in the reactor was negligible in all runs. 2.2. CO oxidation runs All of the structured catalyst samples were tested in CO oxidation. The reactor feed stream consisted of 0.7}8.8% v/v CO in air or air/N (O concentra  tion"4}19% v/v), with feed #ow rates in the range 150}9000 cm/min (STP), corresponding to GHSV values between 2500 and 150 000 cm/(h g ) (STP). . Under such conditions laminar #ow prevailed in the channels of the catalysts: for example we estimate

Table 1 Characteristics of the tested structured catalysts

Support material Support con"guration No. of slabs No. of coated slab faces Slab thickness, mm Gap between slabs, mm Slab width, mm Length, mm Coating type Washcoat load, g Load of 3PdAl, g

Sample A

Sample B

Sample C

Sample D

Sample E

Sample F

Sample G

Al I 4 6 0.5}1 3 46 200 I 12.8 2.44

Steel I 4 6 0.5}1 3 46 200 I 14.9 2.83

Steel I 4 6 0.2}0.4 3 46 200 I 13.2 2.50

Al I 4 6 0.5}1 3 46 200 II 1.04 0.42

Al I 4 6 0.5}1 3 46 200 III 3.84 3.84

Al II 12 24 0.5 1.5 46 50 III 4.15 4.15

Al III 12 24 0.5 1.5 46 50 III 3.98 3.98

6024

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

a Reynolds number equal to 70 for sample E operated at the maximum #ow rate of 9000 cm/min (STP) at 2503C. Analysis of reactants and products was performed by an online GC (HP 6890 Series) equipped with a Porapak Q packed column (3 m long) and a 5 As molecular sieve packed column (3 m long) in series with TCD detectors. Carbon balances of all the considered runs were within $5%.

3. Catalytic and thermal behavior of the structured catalysts 3.1. Sample A: catalytic activity and kinetics A kinetic analysis of CO oxidation over the Pd/cAl O supported catalysts was carried out prior to the   investigation of the thermal behavior of our structured systems in the said reaction. This section reports related results for sample A, prepared with catalytic coating I: such results apply as well to samples B and C, which were also washcoated with coating I (see Table 1). Kinetic data concerning catalyst samples with coatings II and III will be presented and discussed by comparison in a following section. Fig. 2 shows CO conversion data measured in CO oxidation with air over sample A at di!erent oven temperatures and CO feed contents, at the same total feed #ow. The Pd/c-Al O coating resulted fairly active in   CO combustion, with a light-o! temperature markedly increasing with increasing feed concentration of CO. This behavior corresponds to a negative reaction order with respect to CO (see below), in line with previous reports on the kinetics of CO oxidation over noble metal catalysts (Voltz, Morgan & Liederman, 1973; Subramanian & Varma, 1985).

Fig. 2. CO oxidation with air over catalyst sample A (coating I): in#uence of CO feed mole fraction and oven temperature on CO conversion; feed #ow"1000 cm/min (STP). Experimental data (symbols) versus kinetic model "t (lines).

A more detailed kinetic study was then addressed. The goal was the development of a suitable rate expression in view of its later inclusion into a mathematical model of the structured reactor by which the thermal behavior of our coated plate-type systems could be analyzed. The adopted form of the rate expression, Eq. (1), was inspired by literature kinetic studies of CO oxidation over noblemetal catalysts (Voltz et al., 1973; Subramanian & Varma, 1985; Dubien, Schweich, Mabilon, Martin & Prigent, 1998): k p p r "  !- - !- (1#k p )  !-

(mol/(ms)).

(1)

No signi"cant e!ect of CO was detected in prelimi nary dedicated runs with up to 8% v/v carbon dioxide added to the feed. Eq. (1) includes two kinetic parameters, k and k : in   order to reduce correlation in the estimation process, their Arrhenius-type temperature dependence was reparametrised as k "exp[b !b (1000/¹!1000/473)],   

(2)

k "exp[b #b (1000/¹!1000/473)].   

(3)

The four parameter estimates b were determined by GH nonlinear regression on integral data from 162 CO oxidation runs over sample A, with CO% conversion as the experimental response: a simple pseudo-homogeneous isothermal plug-#ow model of the structured reactor was used. The data covered the e!ects of temperature and of inlet feed concentrations of CO and O , and were  obtained with feed #ow rates in the range 700}2000 cm/min (STP). Only runs with less than 53C di!erence between maximum and minimum catalyst temperature readings were considered. It is worth emphasizing already at this stage that the measured temperature distributions over the structured catalyst (sample A) remained virtually #at up to large CO conversions, as discussed in more details in the following. This allowed extension of the investigation to high CO feed concentrations and feed #ow rates, both conditions being associated with large thermal loads. A similar investigation of CO oxidation over the same Pd/cAl O catalyst in the   form of powder, loaded in a conventional #ow microreactor, was constrained to a much more narrow range of conditions due to the onset of strong temperature gradients already at >3 "0.03 (Groppi et al., 2000). !Table 2 provides the estimates of the four kinetic parameters and the corresponding correlation matrix. Notice the strong correlation a!ecting the estimates of b and b , and of b and b , which prevents dis    cussion of the individual parameter estimates. The overall adequacy of the "t is documented by the comparison of experimental data (symbols) with model predictions (lines) in Fig. 2.

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

6025

Table 2 CO oxidation over catalyst sample A: kinetic parameter estimates, Eqs. (1)}(3), with 95% con"dence limits, correlation matrix and statistical indeces Parameter estimates: b  b  b  b  Correlation matrix: 1.00000E#00 !5.81909E!01 9.94906E!01 5.48940E!01 Number of degrees of freedom"158 Average absolute error"1.700 Average percent error"5.519 Correlation index"0.9973

Lower limit !1.31244E#00 2.91771E#00 4.37907E#00 3.97559E#00

Estimate !1.22753E#00 3.99373E#00 4.44027E#00 4.79638E#00

Upper limit !1.14262E#00 5.06975E#00 4.50147E#00 5.61716E#00

1.00000E#00 !5.82298E!01 !9.89951E!01

1.00000E#00 5.56432E!01

1.00000E#00

The signi"cance of gas/solid (interphase) mass transfer limitations was ruled out a posteriori based on the evaluation of the following Damkohler number, r d Da" !- F . (4) D C !- !In Eq. (4), d represents the hydraulic diameter of the F channels in the plate-type catalyst, i.e. twice the interplate distance. The di!usivity of CO in air at temperature ¹ was evaluated according to




¹   D "D (5) !!- ¹  with D "0.32 cm/s "di!usivity of CO in air at !¹ "373 K (Reid, Prausnitz & Poling, 1987). It was  found that Da(0.1 under all the reaction conditions (both temperatures and local CO concentrations) covered in the kinetic runs. This indicates that the rate of gas/solid mass transfer in the channels of the structured catalysts was always much greater than the rate of reaction, so that di!usional limitations can be safely neglected. However, Da became of order unity for reaction temperatures in excess of 3003C: accordingly, account of external di!usion needs to be introduced when modeling the structured catalysts operated under severe, nonisothermal conditions, such as those adopted in the study of their thermal behavior. This aspect is addressed in the appendix. The signi"cance of internal mass transfer limitations was evaluated according to the Weisz criterion, taking into account the particular structure of the rate expression, Eq. (1), by means of the generalized Thiele modulus (Froment & Bischo!, 1979). We found that pore di!usion e!ects were negligible, too, in the whole range of temperatures and CO concentrations considered for the kinetic analysis.

On the basis of the parameter estimates in Table 2, the average reaction order with respect to CO in the range > "0.01}0.09 was !0.64 at 2203C, and approached !!1 at the highest CO feed contents. This further con"rms the absence of di!usional intrusions. Rate equation (1) will be applied to the kinetic analysis of CO oxidation over other catalysts samples. It will be also included in the nonisothermal structured reactor model derived in the appendix, which is applied to the analysis of thermal data in Section 4 below. 3.2. Samples A}C: inyuence of support material and slab thickness on thermal behavior We refer in the following to data collected over catalyst samples A}C, which shared the same support con"guration I as well as similar loads of the same washcoat I. As shown in Table 1, however, the slabs of the three structured catalysts di!ered both in construction material (aluminum, sample A, versus steel, samples B and C) and in thickness (1 mm, samples A and B, versus 0.4 mm, sample C). Fig. 3 compares CO conversions measured over the three samples under standard conditions. It is apparent that the three catalysts exhibited similar activities, with CO combustion starting below 1803C and approaching complete conversion above 220}2403C. This con"rms the good reproducibility of the washcoating technique. Concerning thermal behavior, the observed temperature distributions were virtually uniform and coincident with the oven temperature in the region of moderate CO conversions, as anticipated in the previous paragraph. However, upon increasing the thermal load, e.g. by incrementing the oven temperature and consequently the CO conversion, the average catalyst temperature progressively grew above the oven temperature. Such an e!ect is illustrated in Fig. 4 for catalyst sample A, and is

6026

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

Fig. 3. Comparison of the activity of catalyst samples A, B and C in CO oxidation. Reaction conditions: >3 in air, "0.05, feed #ow" !1000 cm/min (STP).

pond to adiabatic temperature rises in excess of 400 and 6003C, respectively: nonetheless, as shown in Fig. 4, the measured axial temperature pro"les under such conditions were almost #at in the case of the aluminum (intrinsic thermal conductivity k +200 W/(m K)) support K (sample A). Furthermore, the virtually identical ¹-pro"les provided by the "ve thermocouples indicated the absence of any signi"cant temperature gradients in the direction transverse to gas #ow. Fig. 5 points out however that, under the same reaction conditions, much more marked axial temperature gradients were observed in the case of sample B, which included a support having exactly the same geometry as the one of sample A but consisted of less conductive stainless steel (k +20 W/(m K)). Furthermore, over the K steel support signi"cant gradients (up to 303C) were detected also in the transverse direction, as indicated in Fig. 5 by the di!erent readings provided by the "ve thermocouples at the same axial locations. Even greater hot spot temperatures, associated with more marked gradients, were measured in the case of sample C, i.e. the structured catalyst including the steel support with the thinner slabs.

Fig. 4. Catalyst sample A (Al support): in#uence of the oven temperature on the temperature pro"les measured in CO oxidation runs. For each run, the symbols represent the readings of the "ve thermocouples at di!erent transverse locations. Reaction conditions: >3 "0.05 in air, !feed #ow"1000 cm/min (STP); CO conversion"12.3% (¹ "  1763C), 50.2% (¹ "1963C), 100% (¹ "216 and 2563C).  

clearly due to heat transfer resistances hindering removal of the increasing heat of reaction from the catalyst structure. Over Sample A, temperature di!erences between the catalyst and the oven less than 253C were measured at 100% CO conversion with >3 "0.05 in air and feed !#ow "1000 cm/min (STP); they were still below 503C for total CO conversion with >3 "0.07 and feed #ow !"2000 cm/min (STP). Notably, such conditions corres-

Fig. 5. Comparison of temperature pro"les measured in CO oxidation runs over catalyst samples A (Al support, s"0.5 mm) and B (steel support, s"0.5 mm). Reaction conditions: >3 "0.07 in air, feed !#ow"2000 cm/min (STP), CO conversion"100%. ¹ "226 (a)  and 306 (b) 3C.

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

Fig. 6. Comparison of the thermal behaviors of the three catalyst samples A, B and C: maximum catalyst temperature increment versus oven temperature. Reaction conditions: >3 "0.05 in air, feed !#ow"1000 cm/min (STP).

For the three catalysts A}C, Fig. 6 summarizes the in#uences of support material and thickness of the support slabs on the maximum observed catalyst temperature increment, plotted versus the oven temperature. In the low-temperature region, corresponding to limited CO conversions, only small positive deviations from the oven temperature were observed for all samples. Upon light-o! of the reaction, greater temperature di!erences became apparent, which exhibited an asymptotic behavior as the oven temperature was raised and total CO conversion was approached. In the high-¹ region, the lowest temperature di!erences by far were obtained over sample A, followed by sample B and then by sample C. Such di!erent behaviors are directly related to the heat transfer characteristics of the three catalysts, with Albased sample A being remarkably more e!ective than the catalysts with steel supports (B and C) in distributing and removing the heat of reaction. Likewise, the temperature moderation e!ect associated with using thicker slabs is also apparent when comparing the data of catalysts B and C in Fig. 6. The rate of heat conduction in the support is proportional to the intrinsic thermal conductivity of the support material and to the thickness of the support slabs: from these data it is apparent that an e!ective heat conduction mechanism is helpful in #attening the temperature gradients along both the transverse and the axial coordinates of the catalyst supports.

6027

literature (Zwinkels, Jaras & Govind Menon, 1995; Xiaoding Xu & Moulijn, 1998; Twigg & Webster, 1998). As a part of the present fundamental study of structured coated catalysts, therefore, we have also developed and tested three di!erent washcoating methods. Washcoats I}III are brie#y described in the Experimental section and are herein discussed in relation to their performances in CO oxidation, with emphasis on the thermal behavior of the associated catalyst samples A, D and E, respectively. The speci"c aspects concerning preparation and physico-chemical characterization of these washcoats are addressed in a companion paper (Groppi et al., 2000). Fig. 7 compares the catalytic activities of samples A, D and E under the same operating conditions. Notice that the three samples have identical Al supports, and di!er only because of the washcoat formulation. It is apparent that catalyst E is the most active, as it completes CO conversion slightly above 1803C, while catalyst D is just starting to be active at this temperature, and the light-o! curve of catalyst A lies in between those of E and D. For proper evaluation, however, one should consider also that the actual loads of the catalytically active component (3PdAl) are quite di!erent for the three samples: as indicated in the last row of Table 1, it amounts to 2.44 g for sample A, 3.84 g for sample E, but is only 0.42 g for sample D. In fact, a more fair comparison based on the data of Fig. 7 reevaluated as CO productivities  (Valentini et al., 1999) reveals that samples A and D obtain similar performances, with CO productivities of  about 60 g/(h g ) at 1953C. On the other hand, . sample E remains signi"cantly more active, yielding the same CO productivity already at 1703C. In order to  rationalize the advantage of sample E one could consider that: (i) coating III is totally silica-free (silica may adversely a!ect the oxidation activity); (ii) coatings II and III provide porous layers of c-Al O with good speci"c   surface areas, whereas coating I is non-porous; (iii) the primer of coating II may be responsible for negative

3.3. Samples A, D and E: inyuence of washcoat formulation Deposition of an oxide layer, acting as a support for catalytically active species, onto metallic carriers is essential for the development of structured catalysts with high intrinsic conductivity: the resulting washcoat must be porous, adherent and uniform. Nevertheless, very little has been published so far on this matter in the open

Fig. 7. Comparison of the activity of catalyst samples A (coating I), D (coating II) and E (coating III) in CO oxidation. Reaction conditions: >3 "0.05 in air, feed #ow"1000 cm/min (STP). !-

6028

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

e!ects on the oxidation activity, too. It is also relevant to mention that the productivities measured over sample E were in line with those obtained in CO oxidation runs over a powder catalyst with the same composition as coating III loaded in a conventional lab-scale micro#ow-reactor (Valentini et al., 1999): thus, testing the catalyst in the form of a washcoat deposited onto a metallic carrier did not alter its intrinsic activity. Due to its encouraging performances, the catalytic behavior of sample E was further investigated by kinetic analysis, based on an extensive experimental campaign which also included CO oxidation runs at higher space velocities, corresponding to feed #ows in the range 2000}9000 cm/min (STP). For data analysis we used the same methods already applied to sample A in Section 3.1 above: in order to prevent correlation e!ects, however, two of the four rate parameters in Eqs. (1)}(3), namely b and b , i.e. the reparametrised Arrhenius constants   of k , were set to the same values obtained for sample  A and displayed in Table 2, so that only the remaining two parameters, b and b , had to be estimated. This   assumption amounts to assuming that the adsorption of CO was virtually the same onto the tested catalyst samples. Nonlinear regression results for sample E are given in Table 3, whereas the adequacy of the "t is illustrated as an example in Fig. 8. Comparison of the kinetic parameters for samples A (Table 2) and E (Table 3) reveals that the rate constant at 2003C (i.e. b ) is signi"cantly  greater over catalyst E, in line with the observed higher activity of sample E in CO combustion. According to the "gures in Tables 1}3, the rate of CO oxidation per unit mass of 3PdAl at 2003C over catalyst E is 4.2 times greater than over catalyst A, which con"rms the superior catalytic characteristics of coating III. The di!erences in catalytic activity of samples A, D and E a!ected also their thermal behaviors. In line with the similar rates of CO oxidation, the temperature distributions observed over samples A and D under the same reaction conditions were very close, and nearly #at also at total CO conversions. On the other hand, higher temperature levels and more marked longitudinal

Fig. 8. CO oxidation with air over catalyst sample E (coating III): in#uence of catalyst temperature, CO feed mole fraction and feed #ow rate on CO conversion. Experimental data (symbols) versus kinetic model "t (lines): (a) moderate feed #ows; (b) high feed #ows.

temperature gradients near the catalyst entrance were noticed on sample E at high CO conversions and high feed #ows, corresponding to large thermal loads. Transverse gradients were always negligible over all samples. Sample E exhibited also a greater sensitivity to reaction conditions. For example, as illustrated in Fig. 9,

Table 3 CO oxidation over catalyst samples E, F and G: kinetic parameter estimates, Eqs. (1)}(3), with 95% con"dence limits, and statistical indeces

b  b  b  b  Correlation. b }b   No. of dof Average absolute error Average % error Correlation index

Sample E

Sample F

Sample G

0.65660$0.10926 4.12900$0.45281 4.44027 (set) 4.79638 (set) 0.96584 98 1.163 11.60 0.98347

0.36034$0.18325 3.31167$0.56982 4.44027 (set) 4.79638 (set) 0.96529 99 1.753 23.75 0.91414

0.68253$0.11368 2.07436$0.33930 4.44027 (set) 4.79638 (set) 0.97492 91 2.687 23.41 0.94581

Represents the extra-diagonal element of the correlation matrix for the parameter estimates.

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

Fig. 9. Axial temperature pro"les measured in CO oxidation runs over catalyst sample E. Reaction conditions: >3 "0.05 in air, feed !#ow"5000 cm/min (STP).

a small increment of the oven temperature (from 166 to 1693C) resulted in a sudden light-o! of CO combustion, with the CO conversion jumping from 15% to 100%. In correspondence, the hot spot temperature exceeded 3003C, with the temperature pro"les evolving from #at to markedly steeper. Once complete CO conversion was achieved, however, further increments of the oven temperature did not alter the shape of the temperature pro"les, which were simply shifted upwards. Notably, in CO oxidation runs with high feed #ows over sample E di!erences up to 1003C were noted also between the temperature of the outer wall of the reactor tube and the oven temperature: accordingly, under such conditions of large heat loads the external heat transfer resistance starts to play a role, too. The heat transfer characteristics of sample E are addressed on a quantitative basis by modeling analysis in Section 4.2 below. 3.4. Samples E and F: inyuence of support conxguration Commercial applications to gas/solid chemical processes are likely to require structured catalysts with greater catalyst inventories per reactor volume than achieved in our home-made plate-type samples. Indeed, previous simulation studies (Groppi & Tronconi, 2000) have indicated that an optimal industrial catalyst design should be based on highly conductive honeycomb monolith supports with a small pitch, associated with high volume fractions of catalytic washcoat. On the other hand, the thermal behavior of such catalysts is expected to be controlled primarily by the washcoat-to-support volume ratio. For a given support material, in fact, such a ratio is representative of the balance between the rate of heat generation (by the reaction) and the rate of heat removal (by thermal conduction in the support). Catalyst sample F was prepared and tested in CO oxidation in order to investigate the in#uence of the

6029

geometric con"guration of the metallic support on the catalytic and thermal behavior of &high conductivity' structured catalysts. The characteristics of sample F, based on support con"guration II, are shown in Fig. 1 and Table 1. Its support was made of aluminum, like those of samples A, D and F; however, the slabs were four times shorter (50 versus 200 mm), more densely packed (h"1.5 versus 3 mm), and assembled to "ll the entire cross section of the reactor tube. This design was selected in order to increment the number of catalytically active faces by a factor of four (24 versus 6), so that the overall geometric surface remained the same of the samples based on support con"guration I. The silica-free coating III was used for deposition of the catalytic washcoat onto the support, and the total amount of deposited 3PdAl (+4 g) resulted very close to the load of 3PdAl on sample E. Therefore, the catalyst-to-support volume ratios of the two samples were essentially identical, too: this allows a direct comparison of the catalytic and thermal behaviors of samples E and F, any observed deviations being attributable only to the di!erent geometric arrangements of their supports. Preliminary CO oxidation tests at lower temperatures indicated that the catalytic activity of sample F was very similar to that of sample E, their light-o! curves being essentially superimposed at low feed #ows (Q(2000 cm/min), whereas the light-o! of sample F was barely anticipated (by 3}53C) at higher #ow rates (2000(Q(9000 cm/min), possibly due to its slightly greater load of 3PdAl. This was con"rmed by kinetic analysis: the rate parameters reported in Table 3 are similar to those of sample E, which incidentally proves also the good reproducibility of coating III. Temperature distributions recorded over sample F under various operating conditions closely resembled those obtained over the previous samples: as long as the CO conversion was moderate, the axial ¹-pro"les remained #at and coincident with the oven temperature. On the other hand, high CO conversions resulted in marked increments of the slab temperatures, depending on the settings of the operating variables, and in the onset of axial temperature gradients. Notice however that, under such conditions, the maximum temperature di!erence over the catalyst (about 203C) was always much smaller than the di!erence between the maximum catalyst temperature and the oven temperature, suggesting that in the case of sample F the main heat transfer resistance was still located at the boundary of the catalyst slabs. Fig. 10 compares axial temperature pro"les observed over catalysts E and F under the same reaction conditions corresponding to complete CO conversions and large heat loads. The T-readings were taken from thermocouple no. 3 for sample E, and from thermocouple no. 2 for sample F, both such thermocouples being placed in a central position of the plate-type catalysts (see Fig. 1). It is apparent from Fig. 10 that in all cases the temperature

6030

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

Fig. 10. Comparison of axial temperature pro"les measured in CO oxidation runs with air over catalyst samples E and F. CO conversion"100%. Reaction conditions: (a) >3 "0.05, feed #ow"7000 cm/ !min (STP); (b) >3 "0.025 in air, feed #ow"7000 cm/ min (STP); (c) !>3 "0.025, feed #ow"9000 cm/min (STP). !-

Fig. 11. Maximum catalyst temperature di!erences measured in CO oxidation runs with air over catalyst samples F and G. Reaction conditions: (a) >3 "0.09 in air, feed #ow"5000 cm/min (STP); (b) !>3 "0.05, feed #ow"9000 cm/min (STP). *¹ "maximum dif!  ference between catalyst and oven temperature; *¹ "corresponding  di!erence between reactor wall and oven temperature.

pro"les of catalyst F were virtually identical to those recorded along the "rst 5 cm of catalyst E, but for minor deviations due to end e!ects. Accordingly, one can conclude that the thermal behavior of the two catalyst samples is irrespective of the di!erences in the support con"guration, whereas, in line with previous theoretical analyses (Groppi & Tronconi, 2000), it is mainly governed by the washcoat-to-support volume ratio, which was in fact identical for samples E and F. Such results seem relevant in view of scale-up to industrial applications, and deserve further modeling analysis, as discussed in Section 4.3 below.

Sample G was also washcoated with the same coating III: the resulting catalytic activity was comparable to that of samples E and F, as con"rmed by the kinetic analysis (see the rate parameter estimates in Table 3). The promotion of heat transfer was con"rmed by experiment under a variety of conditions. Selected data are shown in Fig. 11, where the maximum di!erences between catalyst and oven temperatures (*¹ ) are

 compared for catalyst samples F and G: the enhanced heat exchange characteristics of sample G result in consistently lower hot spot temperatures. Taking into account the external *¹ ("¹ !¹ ), also displayed   in Fig. 11, the modi"ed design of sample G e!ects roughly a 30% reduction of the internal heat transfer resistance. A more accurate evaluation is deferred to the modeling analysis in Section 4.3. One can notice from Fig. 11 that the improved heat transfer properties of sample G result also in a slightly delayed light-o! with respect to sample F.

3.5. Samples F and G: inyuence of the wall thermal resistance Catalyst sample G was designed and tested in order to verify the feasibility of controlling and improving the heat transfer properties of the structured catalysts at the interface between catalyst slabs and inner wall of the reactor tube. The structure of the Al support of sample G was identical to that of sample F, but for the presence of small appendices along the longitudinal contour which were expected to increment the heat transfer area and to improve the thermal contact with the reactor tube walls.

4. Nonisothermal model analysis The thermal behavior of selected catalyst samples was further analyzed by means of a simple 1D heterogeneous

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

nonisothermal structured reactor model. Notably, the one-dimensional assumption implies negligible transverse ¹-gradients, i.e. all thermal resistances are associated with the wall thermal contact: as discussed in the previous sections, this was experimentally veri"ed for the samples with Al-made supports, but did not apply e.g. to samples B and C, whose supports were made of steel. Therefore, in the following the analysis will be limited to data collected over samples with Al supports, and speci"cally to those associated with the most active silica-free coating III, namely samples E}G. The CO combustion data collected over these catalysts covered a wide range of #ow rates extending towards the high values that could be expected in industrial applications. Hence, large thermal loads were associated with these runs. The derivation of the reactor model is outlined in the appendix. The model contains two adaptive, physically meaningful parameters which represent a heat transfer coe$cient at the reactor wall, a , and a heat transfer U coe$cient at the catalyst inlet, h , respectively. For each  investigated catalyst sample such parameters were estimated by nonlinear regression, "tting the catalyst temperatures calculated by the model to the experimental catalyst temperature pro"les collected during the CO oxidation runs. 4.1. Sample E Data from 40 CO oxidation runs over catalyst E were considered for the regression analysis. For each run, an axial temperature pro"le consisting of 20 temperature readings recorded by thermocouple no. 3 (at the catalyst centerline) was used as the experimental response: due to the absence of transverse ¹-gradients, no signi"cant differences were noted by adopting the readings of other thermocouples. In the regression procedure the rate parameters for CO oxidation were set to the estimates provided by the isothermal kinetic study and reported in Table 3, with no further adjustments. The regression results, including the estimates of a and h along with U  relevant statistical indeces, are given in the second column of Table 4. Figs. 12, 13 illustrate the satisfactory match between experimental and calculated temperature

6031

Fig. 12. Axial temperature pro"les in CO oxidation runs with air over catalyst sample E at moderate #uxes: experimental data (symbols) versus model "t (lines). Reaction conditions: (a) ¹ "2163C,  >3 "0.085; (b) Q"1000 cm/min (STP), >3 "0.05. !!-

distributions for a variety of reaction conditions, including large feed #ows. It is worth emphasizing that the agreement in Figs. 12, 13 was achieved with only two adaptive thermal parameters. The estimates of a and h are comparable to typical U  wall heat transfer coe$cients for packed bed reactors (Doraiswamy & Sharma, 1984). Notably, the thermal resistance associated with a is still at least one order of U magnitude greater than typical thermal contact resistances for metallic interfaces (Incropera & De Witt, 1996): therefore, improvement seems possible in this respect. 4.2. Samples F and G The same procedure presented in the previous paragraph was applied also to the analysis of the temperature pro"les measured over samples F and G. For each of them, the rate parameters for CO combustion were set to the estimates of Table 3, and the thermal parameters a and h in the structured reactor model were evaluated U  by nonlinear regression on the ¹-readings of an internal thermocouple: their estimates and the relevant statistical

Table 4 CO oxidation over catalyst samples E, F and G: estimates of heat transfer parameters in nonisothermal reactor model, a and h in Eqs. (A.1)}(A.20), U  with 95% con"dence limits and statistical indeces Sample E a , W/(mK) U h , W/(mK)  Correlation between parameters Average absolute error Average % error Correlation index

Sample F

86.4$1.3 128.5$7.7 !0.93822 3.202 1.182 0.99705

Represents the extra-diagonal element of the correlation matrix for the parameter estimates.

84.5$0.6 90.2$6.5 !0.46885 6.892 2.365 0.99368

Sample G 118.6$2.9 112.1$9.6 !0.84907 4.274 1.493 0.99642

6032

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

the calculated temperature pro"les, but of course in the vicinity of the reactor inlet. So we can expect that the unavoidable errors in recording the catalyst temperature in the case of steep gradients in the entrance region may be responsible for the dispersion of the h values. 

5. Conclusions

Fig. 13. Axial temperature pro"les in CO oxidation runs with air over catalyst sample E at high #uxes: experimental data (symbols) versus model "t (lines). Reaction conditions: (a) Q"9000 cm/min (STP); (b) Q"5000 cm/min (STP).

Fig. 14. Axial temperature pro"les in CO oxidation runs with air over catalyst sample F at 100% CO conversion: experimental data (symbols) versus model "t (lines). Reaction conditions: ¹ "1663C, >3 "0.05.  !-

indeces are given in Table 4. The goodness of "t was satisfactory for both catalysts: a representative plot of model versus data for sample F is shown in Fig. 14. Inspection of Table 4 points out that the estimate of the wall heat transfer coe$cient a for sample F is U quite similar to that of sample E. On the other hand, and in line with the data presented in Section 3.5, the estimate of a for sample G is signi"cantly greater U (#39%): so, the model analysis con"rms on a quantitative basis the improved heat transfer characteristics of support con"guration III, associated with sample G, as compared to con"gurations I and II, associated with samples E and F. The estimates of h in Table 4 are somewhat scattered,  with no clear trend: a sensitivity analysis showed a posteriori that they do not in#uence to a great extent

A systematic study has been carried out to elucidate the heat transfer characteristics of novel, `high conductivitya structured catalysts for gas/solid reactions. We have shown by experiment that heat conduction in the supports of structured metallic catalysts can be exploited to remove e!ectively the heat generated by strongly exothermic reactions: however, both the intrinsic conductivity of the support material and the geometry of the support are critical for this purpose. Structured catalyst supports constructed with highly conductive metals and reasonably thick walls (i.e. according to a design vastly di!erent from those of available commercial metallic supports for structured catalysts) are able to grant excellent e!ective thermal conductivities, which result in limited temperature gradients even for large heats of reaction. For example our data for the Al-based sample A indicate temperature di!erences less than 303C along the axial coordinate (20 cm), and negligible temperature di!erences along the transverse coordinate (&5 cm), for reaction conditions corresponding to an adiabatic temperature rise in excess of 6003C. Such catalyst properties could a!ord new opportunities for improvement of existing gas/solid catalytic processes involving strongly exothermic reactions, where operation of externally cooled multitubular packed-bed reactors is often limited by the onset of severe hot spots. Nearisothermal behavior of gas/solid reactors without the intrinsic complications of #uidized beds is expectedly an interesting perspective. On the other hand, the present work demonstrates also a number of aspects in this area which require further developments. (i) With the very high thermal conductivity of the supports #attening the transverse and axial temperature pro"les, most of the residual heat transfer resistances are con"ned at the catalyst}reactor interface, where the temperature di!erences observed in our experiments were still quite signi"cant in the case of large thermal loads. So, future catalyst design work should be aimed also at minimizing such residual resistances: our data for sample G suggest that this goal could be possibly achieved by an ad hoc design of the support con"guration, e.g. optimizing the thermal contact between the catalyst support and the inner wall of the reactor tubes.

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

(ii) Easy scale-up is a desired feature of catalyst/reactor systems: in this respect `high-conductivitya structured catalysts are quite interesting, as their virtually isothermal behavior, at least along the transverse coordinate, greatly simpli"es analysis; furthermore, the well-de"ned mechanism of heat transport, namely conduction in the catalyst support, avoids the well-known complications associated with the analysis of convective heat transfer in packed-bed reactors, and its relationships with #uid dynamics. Our data were successfully represented by a simple onedimensional reactor model including only two adaptive thermal parameters: the same model is potentially applicable to the design of full-scale structured reactors, too. (iii) The system con"guration is also a relevant issue, which remains to be addressed: e.g. the length of the structured catalyst elements loaded in the reactor tubes and the extent of mixing in between these segments are two parameters requiring additional investigation. The similarity of the thermal behaviors observed in our experiments over samples E and F are encouraging in view of a modular approach to the design of `high conductivitya structured reactors. (iv) An intrinsic di$culty associated with the adoption of structured catalysts in reactors for chemicals production is the limited volume fraction of catalytically active material as compared to packed beds of catalyst pellets. In this respect, however, one should consider that the e!ectiveness factors of the thin catalytic washcoats in structured catalysts are generally greater than those of pellets, and typically close to one; besides, in view of the greatly enhanced e!ective thermal conductivities, the mean temperature level of the catalyst bed could be raised, thus enhancing its overall activity, without increasing however the hot spot temperatures. Nevertheless, structured catalyst con"gurations a!ording large loads of washcoat per unit reactor volume are de"nitely of interest: extruded metallic honeycomb monoliths similar to the ceramic supports of catalytic mu%ers, with their large cell densities (Brundage & Rajnick, 1995; Harada, Mizuno, Abe & Ohashi, 1995), may represent a valuable perspective in this respect (Groppi & Tronconi, 2000).

Notation C !C N D !Da d F

concentration of CO, mol/m gas speci"c heat, J/(g K) molecular di!usivity of CO in air, m/s




r d Damkohler number " !- F D C !- !2h, hydraulic diameter, m



F h h  h U k E k K k KR k Q ¸ ¸e N

Nu p G Pr Q R r !Re S Sh ¹ ¹ E ¹  > G v = z

6033

molar #ow rate, mol/s slab spacing in plate-type catalysts, m heat transfer coe$cient at the reactor inlet, W/(m K) gas-solid heat transfer coe$cient, W/(m K) gas thermal conductivity, W/(m K) intrinsic thermal conductivity of support material, W/(m K) gas/solid mass transfer coe$cient, m/s thermal conductivity of catalyst, W/(m K) length of plate-type catalyst, m a /D , molecular Lewis number for CO in air  !number of catalytically coated surfaces in plate-type catalysts











h d Nusselt number " U F k E partial pressure of species i, bar C k Prandtl number " N k E volumetric #ow rate, m/s ideal gas constant, J/(mol K) rate of CO oxidation, mol/(m s)






ovd Reynolds number " F k half-thickness of slabs in plate-type catalyst, m






k d Sherwood number " KR F D !catalyst temperature, K gas temperature, K oven temperature, K mole fraction of species I gas velocity, m/s slab width in plate-type catalyst, m axial coordinate, m

Greek symbols a thermal di!usivity, m/s  a wall heat transfer coe$cient, W/(m K) U !*H heat of reaction, J/mol 0 g fractional CO conversion !k gas viscosity, kg/(m s) o gas density, kg/m E Subscripts
K w

and superscripts inlet conditions average at the catalyst surface

Acknowledgements Financial support from CNR } Rome is gratefully acknowledged. The authors thank Dr. Cinzia Cristiani,

6034

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

Ing. Michela Valentini and Mr. Giuseppe Airoldi for the preparation of the catalyst samples.

Appendix A. Nonisothermal heterogeneous 1D model of plate-type structured catalysts We assume steady-state plug-#ow conditions with negligible axial dispersion of heat and mass and negligible pressure drop in the gas phase within the channels of the structured catalysts. We further assume that the temperature pro"les of the gas and solid phase develop only along the axial coordinate of the catalyst, whereas uniform temperature pro"les are established across the width of each catalyst slab (1D approximation). The gas phase can exchange heat with the solid phase (catalyst) only: heat exchange with the reactor walls is neglected in view of the very large aspect ratio of the catalyst channels. Accordingly, the following steady-state di!erential enthalpy balance applies, with symbols explained in the Notation. A.1. Enthalpy balance, gas phase d¹ 2 o CK pv E "h (¹!¹ ) . % U E h dz

(A.1)

A.2. Enthalpy balance, solid phase Besides exchange with the gas phase, heat transfer mechanisms in the solid phase also include axial heat conduction along the metallic support, and heat exchange at the interface between the catalyst and the inner wall of the reactor tube. In addition, heat is generated in the catalyst washcoat by CO combustion. Hence, upon considering the generation, conduction, and heat exchange contributions, the steady-state di!erential energy balance per unit volume of solid is given by d ¹ (!*Hr)r h  ! U (¹!¹ ) k  # Q dz E S S






2a h ! U ) (¹!¹ ) 1# "0,  = 2S

(A.7)

where !*Hr is the heat of reaction, and k is the Q thermal conductivity of the solid phase. In all the calculations we have assumed k "200 W/(m K), correspondQ ing to the intrinsic thermal conductivity of aluminum (Incropera & De Witt, 1996), and !*Hr"283.8 kJ/ mol, corresponding to the heat of CO combustion in the ¹-range 150}4003C (Reid et al., 1987). Notice that the heat transfer coe$cient a in Eq. (A.7) refers to the total U area of the reactor wall.

The interphase (gas}solid) heat transfer coe$cient h is U estimated according to Nu"Nu(zH)"1.233H(zH)\#0.4,

zH)10\,

Nu"Nu(zH)"7.541#6.874H(10zH)\ H exp(!24.5HzH), zH'10\, which is applicable for fully developed laminar velocity pro"le and developing temperature pro"le between parallel plates or in rectangular ducts with in"nite aspect ratio (Shah & London, 1978). In Eq. (A.2), Nu"h d /k U F E is a Nusselt number, and zH is a dimensionless axial coordinate z 1 z*" (A.3) d Re Pr F d "2h being the hydraulic diameter of the channels. F By setting N=k E , A "  2Qho CK p % one gets zH"A z   and d¹ E "A Nu(zH)(¹!¹ ).  E dz with initial condition ¹ (z"0)"¹ . E 

(A.4)

(A.2)

On introducing the following constants (!*Hr) A " ,  Sk Q




(A.8)



2a h , A " U 1#  k= 2S Q Kg A " ,  2hSk Q

(A.9)

(A.10)

Eq. (A.7) is rearranged to (A.5)

(A.6)

d¹ "!A r #A Nu(z)(¹!¹ )  ! E dz #A (¹!¹ ).  

(A.11)

In view of possible heat dissipation at the inlet section of the structured catalyst, we set up the following

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

boundary condition: d¹ K Q dz








h "h (¹!¹ ) 1# ,   2S

(A.12) 8 where the heat transfer coe$cient h refers to the whole  cross-sectional area of the structured reactor. On the other hand, assuming negligible heat #ux at the catalyst outlet, the remaining boundary condition results in d¹ dz



"0. (A.13) 8* The assumed boundary conditions (A.12) and (A.13) are consistent with the shape of the experimental catalyst temperature pro"les near the entrance and exit catalyst sections. It is worth noticing that both a (wall heat transfer U coe$cient) in Eq. (A.7) and h (inlet heat transfer coe$c  ient) are regarded as adaptive parameters: accordingly, they must be estimated by "tting the calculated ¹(z) distributions to experimental catalyst temperature pro"les. Preliminary calculations assuming power-law dependences of a and h on the feed #ow rate showed no U  signi"cant improvement, so it was concluded that assuming a and h to be constant is acceptable within the U  scopes of the present work. A.3. CO material balance The enthalpy balances must be coupled with a suitable di!erential material balance for the reactant CO. To account for the onset of gas/solid di!usional resistances associated with severe reaction conditions, and in line with the heterogeneous nature of the present reactor model, we consider herein that the CO partial pressure at the catalyst surface, pU , may di!er form the bulk gas!phase CO concentration, p . This leads to the following !two mass balance equations for CO in the gas and in the solid phases, respectively: dg k !- "A KR (p !pU ), (A.14)  !R¹ !dz E k k pU p KR (p !pU )"  !- - . (A.15) !R¹ !(1#k pU ) E  !The constant A in Eq. (A.14) is de"ned as  N= A " . (A.16)  FM >M  !Notice that the rate of CO combustion in Eq. (A.14) is evaluated according to Eq. (1) but as a function of pU rather than of p . Eq. (A.15) can be rearranged to !!  pU #P pU #P pU #P "0, (A.17) ! ! !

6035

where P , P and P are constants de"ned by    P "2/k !p , (A.18)   !(1#k p)R¹ 2p  - E ! !- , P " (A.19)  k k KR  P "!p /k , (A.20)  !-  Eq. (A.17), a cubic equation in pU , is conveniently solved !analytically (Beyer, 1979) to give pU as a function of p , !!thus eliminating one of the model equations. Finally, the mass transfer coe$cient k is evaluated KR from a Sherwood number, Sh"k d /D . For the KR F !CO}air system, the molecular Lewis number ¸e"a /D is approximately unity: e.g. at 2003C the  !following estimates apply for the thermal di!usivity of air and for the molecular di!usivity of CO in air: a "5;10\ cm/s and D "4.9;10\ cm/s, re !spectively. Accordingly, the simple analogy Sh"Nu can be invoked, so that Sh is computed from Eq. (A.2), too. A.4. Numerical solution The structured reactor model is constituted by the three ODEs Eqs. (A.6), (A.11) and (A.14), which form a boundary value problem. Numerical solution has been based on a relaxation method involving "nite di!erence approximations (Press, Teukolsky, Vetterling & Flannery, 1992). The resulting system of nonlinear algebraic equations was then solved by a homotopy continuation method (Wayburn & Seader, 1987), taking advantage of its block tridiagonal structure. Convergence of the solution was achieved with 81 equispaced knots on the longitudinal coordinate z. The overall e$ciency of the numerical solution was adequate to allow incorporation of the model into a robust global nonlinear regression routine (Donati & Buzzi-Ferraris, 1974; Villa, Forzatti, Buzzi-Ferraris, Garone & Pasquon, 1985) which required model solutions for all of the CO oxidation runs included in the experimental set at every step of the regression procedure.

References Beyer, W. H. (1979). CRC standard mathematical tables (25th ed.). Boca Raton: CRC Press. Brundage, K. R., & Rajnick, L. S. (1995). Extrusion of metal honeycombs, US Patent No. 5,466,415 to Corning Inc., Corning, NY. Cybulski, A., & Moulijn, J. A. (1994a). Monoliths in heterogeneous catalysis. Catalysis Reviews-Science Engineering, 36(2), 179}270. Cybulski, A., & Moulijn, J. A. (1994b). Modelling of heat transfer in metallic monoliths consisting of sinusoidal cells. Chemical Engineering Science, 49, 19}27. Cybulski, A., & Moulijn, J. A. (1998). Structured catalysts and reactors. New York: M. Dekker. Degussa Aktengesellschaft. (1989). Wacker Chemie GMBH, Europ. Pat. 0369439A2 (16.11.1989).

6036

E. Tronconi, G. Groppi / Chemical Engineering Science 55 (2000) 6021}6036

Donati, G., & Buzzi-Ferraris, G. (1974). Powerful method for HougenWatson model parameter estimation with integral conversion data. Chemical Engineering Science, 29, 1504}1509. Doraiswamy, L. K., & Sharma, M. M. (1984). Heterogeneous reactions: analysis, examples and reactor design, vol. 1. New York: Wiley. Dubien, C., Schweich, D., Mabilon, G., Martin, B., & Prigent, M. (1998). Three-way catalytic converter modelling: Fast- and slow-oxidizing hydrocarbons, inhibiting species, and steam reforming reaction. Chemical Engineering Science, 53, 471}481. Eigenberger, G. (1992). Fixed-bed reactors. In Ullmann's encyclopedia of industrial chemistry, vol. B4 (p. 199). Weinheim: VCH Publs. Eigenberger, G. (1997). Reaction engineering. In: G. Ertl, H. Knozinger, & J. Weitkamp (Eds.), Handbook of heterogeneous catalysis, vol. 3 (pp. 1399}1425). Weinheim: Wiley-VCH. Froment, G. F., & Bischo!, K. B. (1979). Chemical reactor analysis and design. New York: Wiley. Groppi, G., Cristiani, C., Valentini, M., & Tronconi E. (2000). Development of novel structured catalytic reactors for highly exothermic reactions. In: A. Corma, F. V. Melo, S. Mendioroz, & J. L. G. Fierro (Eds.), Proceedings of 12th International congress on catalysis, Granada, Spain, Studies in surface science and catalysis, vol. 130 (pp. 2747}2752). Amsterdam: Elsevier. Groppi, G., & Tronconi, E. (1996). Continuous vs. discrete models of nonadiabatic monolith catalysts. A.I.Ch.E. Journal, 42, 2382}2387. Groppi, G., & Tronconi, E. (1998). A study of monolith catalysts for highly exothermic reactions. Kinetika i Kataliz, 39, 701. Groppi, G., & Tronconi, E. (2000). Design of novel monolith honeycomb catalyst supports for gas/solid reactions with heat exchange. Chemical Engineering Science, 55, 2161}2171. Harada, T., Mizuno, H., Abe, F., & Ohashi, T. (1995). Heat-resistant metal monolith and manufacturing method therefor. US patent No. 5,445,786 to NGK Insulator, Ltd., Japan. Heynderickx, G. J., Froment, G., Broutin, P. S., Busson, C. R., & Weill, J. E. (1991). Modelling and simulation of a honeycomb reactor for high severity thermal cracking. A.I.Ch.E. Journal, 37, 1354}1364. Incropera, F. P., & De Witt, D. P. (1996). Introduction to heat transfer. New York: Wiley. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). Numerical recipes. The art of scientixc computing. New York: Cambridge University Press.

Ragaini, V., De Luca, G., Ferrario, B., & Della Porta, P. (1980). A Mathematical model for a tubular reactor performing ethylene oxidation to ethylene oxide by a catalyst deposited on metallic strips. Chemical Engineering Science, 35, 2311}2319. Reid, R. C., Prausnitz, J. M., & Poling, B. E. (1987). The properties of gases and liquids (IV ed.). New York: Mc Graw-Hill. Shah, R. K., & London, A. L. (1978). Laminar yow forced convection. New York: Academic Press. Subramanian, B., & Varma, A. (1985). Reaction kinetics on a commercial three-way catalyst: The CO-NO-O -H O System. Industrial   and Engineering Chemistry, Process Design and Design and Development, 24, 512}516. Twigg, M. V., & Webster, D. E. (1998). Metal and coated-metal catalysts. In A. Cybulsky, & J. A. Moulijn (Eds.), Structured catalysts and reactors (pp. 59}90). New York: Marcel Dekker, and references therein contained. Valentini, M., Airoldi, G., Cristiani, C., Groppi, G., Tronconi, E., & Forzatti, P. (1999). Coating of ceramic and metallic structured catalysts supports. In Book of abstracts 4th European congress on catalysis (EUROPACAT-IV), Rimini, Italy (p. 813). Villa, P. L., Forzatti, P., Buzzi-Ferraris, G., Garone, G., & Pasquon, I. (1985). Synthesis of alcohols from carbon monoxide and hydrogen. 1. Kinetics of the low-pressure methanol synthesis. Industrial and Engineering Chemistry, Production Research and Development, 24, 12}19. Voltz, S. E., Morgan, C. R., & Liederman, B. A. (1973). Kinetic study of carbon monoxide and propylene oxidation on platinum catalysts. Industrial and Engineering Chemistry, Process Design and Design and Development, 12, 294}301. Wayburn, T. C., & Seader, J. D. (1987). Homotopy continuation methods for computer-aided process design. Computers & Chemical Engineering, 11, 7}25. Xiaoding Xu, & Moulijn, J. A. (1998). Transformation of a structured carrier into structured catalyst. In: A. Cybulsky, & J. A. Moulijn (Eds.), Structured catalysts and reactors (pp. 599-615). New York: Marcel Dekker and references therein contained. Zwinkels, M. F. M., Jaras, S., & Govind Menon, P. (1995). Preparation of combustion catalysts by washcoating alumina whiskers-covered metal monoliths using a sol-gel method. In: G. Poncelet et al. (Eds.), Preparation of catalysts VI (pp. 85}94). Amsterdam: Elsevier.