Mass-Transfer Characterization of Metallic Foams as Supports for

Feb 9, 2005 - foams with different cell sizes were coated with a thin layer of ... in a 9-mm inner diameter tubular reactor by performing the catalyti...
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Ind. Eng. Chem. Res. 2005, 44, 4993-5002

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Mass-Transfer Characterization of Metallic Foams as Supports for Structured Catalysts Leonardo Giani, Gianpiero Groppi, and Enrico Tronconi* Centro di Eccellenza per l’Ingegneria dei Materiali e delle Superfici Nanostrutturate, Dipartimento di Chimica, Materiali ed Ingegneria Chimica “G. Natta”, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

Open-celled metal foams have been characterized as supports for structured catalysts, considering their utilization in gas-solid catalytic processes with short contact times and high reaction rates, typically controlled by gas-solid diffusional mass transport. Examples of such processes are found in the field of environmental catalysis, including, e.g., catalytic combustion, selective catalytic reduction (SCR-DeNOx), and automotive exhaust gas after treatment. In this work, foams with different cell sizes were coated with a thin layer of palladium-alumina and tested in a 9-mm inner diameter tubular reactor by performing the catalytic oxidation of CO at empty tube velocities in the range of 0.8-2.6 m/s. The coated foams exhibited sufficient catalytic activity to achieve mass-transfer-limited operation in the temperature range of 300-450 °C. Under such conditions, mass-transfer coefficients were determined according to a simple one-dimensional model of the test reactor. Adopting the average diameter of the foam struts as the characteristic length, we obtained a dimensionless correlation for the estimation of mass-transfer coefficients, which correlates all the data: it closely resembles semitheoretical literature correlations for heat transfer in flow across banks of tubes at low Reynolds numbers. Pressure drop measurements across foam samples were also collected for air velocities in the range of 1-16 m/s. The performances of foams, packed beds of pellets, and honeycomb monoliths as catalyst supports were compared on the basis of a dimensionless merit index, which accounts for the tradeoff between pressure drop and mass-transfer properties. Foams are largely superior to packed beds, because of their high voidage, but perform slightly worse than honeycomb monoliths. On the other hand, foams can afford marked reductions of reactor volume and weight, with respect to honeycombs, in fast, diffusion-controlled processes where pressure drop is of minor concern. 1. Introduction Open-celled foams are three-dimensional (3D) cellular materials made of interconnected solid struts, forming a network.1 The unit cell in a foam resembles a polyhedron with pentagonal or hexagonal faces that limit a spherical-like inner space. Each cell, defined by the hollow volume of the polyhedron, constitutes a pore. The cell size is commonly expressed in terms of pores per linear inch (PPI): the overall range of variation in cell size goes from 5 PPI to 100 PPI. Typical porosity values range from 80% to 97%.2 Many properties make foams attractive for use as catalyst supports, because their low density and high mechanical strength permit the design of light, stiff components. When loading a fixed-bed reactor with a foam cartridge rather than with packed particles, the high foam porosity would result in much lower pressure drops,3 whereas the use of preformed structures can simplify loading and unloading operations. Furthermore, tortuous flow paths through the porous matrix are expected to enhance gas/solid heat- and masstransfer rates, and high surface-to-volume ratios would yield high activity per unit reactor volume. Examples of applications where metallic or ceramic foams have been used or proposed for use in heterogeneous catalysis include the catalytic combustion of * To whom correspondence should be addressed. Tel.: ++3902-2399 3264. Fax: ++39-02-7063 8173. E-mail: [email protected].

methane (CH4),4 the production of hydrogen gas (H2) via water-gas shift reaction,5 the purification of exhaust gases from automotive engines,6 the oxidation of ammonia for the production of nitric acid,7 the partial oxidation of methanol,8 the deep oxidation of hydrocarbons,9 carbon dioxide reforming,10 and the FischerTropsch synthesis.11 With respect to more-common ceramic reticulated materials, the use of metal foams is expected to minimize the occurrence of hot spots in the catalyst when highly exothermic reactions are performed, while avoiding mechanical-strength and thermal-shock limitations. Moreover, the spongelike properties of these supports allow convenient sealing in a reaction chamber via mechanical contact, while a closely matched thermal expansion between the metal foam and the housing chamber can be used to minimize gas channelling around the porous support at higher reaction temperatures.12 In this work, we focus on the application of metal foams to gas-solid catalytic processes with short contact times and high reaction rates, which are typically controlled by diffusional limitations. Many examples of such processes can be found in the field of environmental catalysis, including, e.g., catalytic combustion, selective catalytic reduction of NOx by NH3 (the SCR-DeNOx process), and automotive exhaust gas after-treatment. Our goal is to estimate mass-transfer coefficients in foams of different cell sizes, and to derive a generalized engineering correlation for their prediction.

10.1021/ie0490886 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/09/2005

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the structure (see Figure 2), it is possible to conclude that the struts of the tested foams are not massive but, instead, are hollow. However, the void volume in the hollow struts must not be taken into consideration when calculating the open-void fraction, because it is hardly accessible either for the reactants or for the catalytic washcoat. As shown in eq 1, the open-volume fraction () can be expressed in terms of densities:

)1Figure 1. Foam structure and pore identification.

Figure 2. Hollow struts in the foam.

In a previous work, Richardson and co-workers determined mass- and heat-transfer properties for a single 30-PPI R-alumina ceramic foam.13 Herein, we address metal foams instead of ceramic foams and extend the analysis by taking into consideration the influence of foam cell size. For this purpose, mass-transfer coefficients were determined by performing oxidation of carbon monoxide (CO) over various foams washcoated with palladium/γ-alumina under external diffusioncontrolled conditions.14 This work reports also pressure drop measurements across the tested metal foams, because pressure drop constraints may be quite relevant in environmental catalytic processes. Eventually, foams are compared with other catalyst supports of current use in environmental catalysis on the basis of a merit index pondering mass transfer and pressure drop performances. 2. Experimental Section 2.1. Metal Foams. The foam samples investigated in this work were supplied by Porvair as panels of different nominal cell size (10 PPI, 20 PPI, and 40 PPI) and 5% nominal relative density. Samples were made of Fecralloy with a composition of 73% iron, 20% chromium, 5% aluminum, and 2% yttrium. This alloy material was chosen because of the possibility to modify its surface by thermal oxidation: the process involves the formation of a dense and adherent alumina layer that protects the underlying matrix against further degradation,15 which is also useful as an anchor for the washcoat that must be applied to make the foam catalytically active. 2.2. Geometrical Characterization. Foam samples were characterized by measuring their pore diameters and open void fractions. Micrographs were taken of each panel, to identify pores situated at the same depth and measure their diameters, as shown in Figure 1. To make the value statistically representative, 40 pore diameter measurements were averaged for each foam sample. The open-void fraction in a cellular solid is defined as the ratio between the accessible empty volume and the total volume. From the microscopic observation of

FFOAM FHS

(1)

where FFOAM is the foam density and FHS is the density of the hollow struts. The foam density was estimated by dividing the weight of the foam panels by the total measured volume, whereas the density of the hollow struts was determined using a standard pycnometry method that is based on the measurement of the buoyancy of the samples in ethanol (balance Sartorius YDK 01). Pure ethanol was used for the measurements, because water was unable to access the entire void volume inside the foam, leaving air bubbles attached to the structure, because of surface tension effects. The procedure was validated using pure metal standards. 2.3. Washcoating of the Foams. Foam samples were cleaned with ethanol in an ultrasonic bath, to remove any organic substance, and calcined at 900 °C for 10 h, to promote the migration of R-alumina from the FeCr alloy matrix to the surface. Palladium oxide supported on γ-alumina was chosen to catalyze the reaction of CO oxidation, because of its high activity and thermal stability. A sol-gel of pseudo-bohemite was used as a precursor of the γ-alumina. The composition of the sol-gel was determined, to make it sufficiently fluid to permeate through the entire foam structure when filling the pores by percolation. On the other hand, a correct level of viscosity is required to leave a uniform film that, after drying, would result in an adequate amount of alumina coating deposited on the foam. Optimal rheological characteristics were obtained by dispersing the sol-gel of pseudo-bohemite in an aqueous solution of nitric acid and suitably adjusting both the powder content and the nitric acid concentration.16 Pores in the foam were filled by percolation of the solgel through the structure. The excess was flushed away from the pores with an air jet, leaving a thin film around the foam struts. After that, foams were dried for 30 min at 110 °C and calcined for 10 h at 700 °C to promote the transition from pseudo-bohemite to γ-alumina of higher surface area. Typical washcoat loadings on the foams of 5% (w/w) have been obtained after calcination. Coated foams were impregnated with palladium, using a wet impregnation technique that consists of the immersion of the samples in a Pd(NO3)2 diluted aqueous solution.17 The concentration of palladium in the solution was calculated to obtain 3% (w/w) palladium over γ-alumina. The impregnation cell was stirred continuously and thermostatically set at 80 °C. The duration of the wet impregnation process was 3.5 h. Impregnated foams were calcined for 10 h at 500 °C to eliminate nitrates and form the catalytically active PdO species. Further details on the washcoating procedure are reported elsewhere.16

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Figure 4. Pressure drop test rig. Figure 3. Layout of the test microreactor.

2.4. Catalytic Activity Tests. Cylinders with diameters of 9 mm and heights between 6 mm and 25 mm were cut from the metal foam panels by electroerosion, thus producing a precise cut with no damage for the structure, while ensuring a perfect seal with the reactor tube wall. After washcoat deposition, foams were loaded in a 9-mm inner diameter (i.d.) tubular microreactor, which is schematically depicted in Figure 3. Air and CO were fed to the reactor through independent lines and massflow controllers, mixed, and preheated to a set temperature before entering the reactor. Compositions of reactants and products were analyzed on-line with a gas chromatograph (Agilent Technologies model 6890N) that was equipped with two thermal conductivity detectors and two packed columns: one column was filled with Molecular Sieve 5A 80/100 mesh, suitable to separate O2, N2, and CO, and the other column was filled with Porapak Q 80/100, to separate CO2. Foams were loaded inside the reactor in pairs: the upper one was washcoated while the lower, uncoated one was placed at the end of the reactor tube to secure an even flow distribution through the catalytic foam. The temperature of the catalytic foam was measured with a thermocouple placed in contact with the inlet foam cross section (marked as thermocouple 1, as shown in Figure 3). Another thermocouple that was located at the outlet section of the uncoated foam (thermocouple 2 in Figure 3) measured the temperature of the exiting gas stream. Activity tests were performed over different catalyzed foam samples at feed flow rates in the range of 300010000 cm3/min STP, which corresponds to gas hourly space velocity (GHSV) values of 2 × 107-1.5 × 108 h-1 and to superficial velocities of 0.8-2.6 m/s. Note that GHSV values are based on the weight of the deposited γ-alumina washcoat, which was in the range of 6-18 mg for the tested foam samples, leading to such extremely high GHSV values. The CO feed concentration was varied from 1% to 5% (v/v) of CO in air (STP). During each test, the inlet temperature was increased stepwise, and, for each temperature level, the CO conversion was determined by gas chromatography (GC) analysis after steady-state conditions were achieved. Complete (100%) CO conversions were observed at very low flow rates (1000 cm3/min STP), so that bypass

due to leaking along the reactor tube wall can be ruled out. In a few dedicated diagnostic tests, a third bare foam sample was loaded in the reactor on top of the catalytic foam, to act as a flow distributor (notice that this configuration prevents measurement of the foam inlet temperature); because essentially no differences in CO conversion were detected, with respect to experiments run without the additional foam under identical conditions, we conclude that results of our catalytic activity tests were not affected by flow maldistribution problems. 2.5. Pressure Drop Measurements. Pressure drop measurements were performed in the test rig that is schematically shown in Figure 4. Foam samples used for these tests consisted of cylinders with a diameter of 75 mm and depths of 50-75 mm. They were placed inside the flow tube and the pressure drop generated by air flow across the sample was measured by a differential manometer. The air volumetric flow rate was measured with a rotameter and the mass flow was calculated for the temperature T1 and pressure P1 (see Figure 4). Temperature T2 and pressure P2 were used to calculate the air velocity before entering the sample. Temperature during the test was ∼25 °C. The air velocity was varied over a range of 1-16 m/s. 3. Results and Discussions 3.1. Geometrical Model of the Foam Structure. Different models describing the geometrical configuration of foam structures are reported in the literature. Lu, Stone, and Ashby18 have proposed a cubic cell model in which the foam struts are represented as slender cylinders, representing the edges of an uniformly distributed cubic structure, as illustrated in Figure 5. Reportedly, the model well-predicted the geometrical characteristics of aluminum foams with porosities of  ) 0.88-0.96. Cylinder diameters and specific areas calculated according to this model were observed to match those measured with a microcomputer tomography system reasonably.18 Dimension a in Figure 5 corresponds to the pore diameter and can be measured directly using optical measurements, as described previously. In the case of anisotropic foams, where the pore size differs when considering either a tangential section or a longitudinal section, the model can be easily modified to consider a prism instead of a cube, where the height of the prism corresponds to the pore size in the longitudinal section.

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Figure 5. Cubic cell model proposed by Lu, Stone, and Ashby.18

The strut diameter (dS) can be calculated for an isotropic foam as follows. Considering the cubic cell volume Vo, given as

Vo ) a3

(2)

the overall volume of the struts Vs can be expressed as a function of the foam void fraction  (eq 3):

Vs ) (1 - ) × Vo ) (1 - ) × a3

(3)

However, Vs also can be calculated as the overall volume of the cylinders included in the unit cell. Considering that each strut is shared among four cells,

( )

dS2 a Vs ) 3π 4

(4)

Combining eqs 3 and 4, one obtains an expression that relates the strut diameter dS to a and :

[3π4 (1 - )]

dS ) a

1/2

(5)

The specific area per unit cell volume is then computed as

SV )

4 (1 - ) dS

(6)

Considering eq 5, SV can be expressed as a function of the foam porosity  and the pore diameter a:

2 SV ) [3π(1 - )]1/2 a

(7)

Other models in the literature describe the unit cell as a dodecahedron structure,19 a tetrakaidecahedron,1,20-22 and a regular packing of various polyhedra.1,23 Through study of a ceramic foam, Richardson et al.3 have recommended the use of a model that is familiar in the catalysis field, being based on the analogy with a packed bed of particles. Pores are treated as uniform parallel hollow cylinders with a constant diameter equal to the pore diameter. The specific area is estimated by eq 8:

SV )

4 a

(8)

Although both expressions for the specific surface area (eqs 7 and 8) exhibit the same dependence on the pore diameter, they differ considerably for the dependence

Figure 6. Dimensionless specific area predicted by eqs 7 and 8 versus foam porosity. Table 1. Geometric Properties of the Metal Foam Samples Investigated in This Work sample

pore size, a (m)

 (%)

cell density (ppi)

dS (m)

SV (m2/m3)

A B C D E F

4.3 × 10-3 4.7 × 10-3 2.2 × 10-3 2.0 × 10-3 1.7 × 10-3 4.6 × 10-3

94.5 92.7 93.8 93.7 93.2 91.1

5.9 5.4 11.5 12.8 15.0 5.6

0.66 × 10-3 0.82 × 10-3 0.37 × 10-3 0.33 × 10-3 0.28 × 10-3 0.80 × 10-3

333 352 696 767 942 449

on the open-volume fraction . In Figure 6, we have plotted the dimensionless product SVa, which is estimated according to either eq 7 or eq 8, versus the  value of the foam. This permits the influence of the void fraction on the estimate of the surface area to be evaluated independently from the pore diameter. The two geometrical models give similar results in the porosity range that is typical of ceramic foams (0.75-0.80) but deviate quite significantly in the higherporosity range that is characteristic of metal foams. It is apparent that the selection of a valid geometrical model for foams with high porosities is not a trivial issue. Taking into consideration the appearance of the foam structure (see Figure 1), we feel that the analogy between the interconnected net of solid struts and a packed bed is weak. Geometrical models based on regular networks of cylinders, such as the tetrakaidecahedron model or the cubic cell model, seem to reflect the configuration of the foam better. Accordingly, the cubic cell model has been herein preferred for our purposes, because it combines simplicity, an acceptable level of accuracy in the estimation of the specific geometric surface area,18 and also the possibility of being easily modified to describe anisotropic foams. Thus, starting from measured values of a and , it is possible to estimate the basic geometric parameters of the foam according to eqs 5 and 7. Estimates of the geometrical parameters for the metal foam samples tested in this work are reported in Table 1. Pore sizes in the range of 1.7-4.6 mm have been observed. Notably, this widely differs from the range of nominal pore densities declared by the manufacturer. High open-void fractions (in the range of 91.1%94.5%) have been measured. Estimated strut diameters vary from 0.28 mm to 0.8 mm, which correlates well with values measured by microscopic imaging. The extremely high void fractions, together with the relatively low cell densities, result in moderate specific geometric areas (in the range of 336-942 m-1). All samples were made of FeCr alloy, except for sample F, which was made of copper and was only used

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Figure 8. Estimated mass-transfer coefficients versus flow rate for different foam samples and CO feed concentrations.

Figure 7. Measured CO conversion versus temperature for foam sample E at different CO feed concentrations and air flow rates: (a) 3000 cm3/min (STP) and (b) 6000 cm3/min (STP).

for pressure drop measurements. The unit cell for sample F is anisotropic: its pore size in the tangential direction is a ) 4.6 × 10-3 m, and the pore size in the longitudinal direction is b ) 3.3 × 10-3 m (defined with respect to flow). 3.2. Mass-Transfer Coefficients. Foam samples A-E in Table 1 were coated with Pd/γ-Al2O3 and tested in CO oxidation in the microreactor. As an example, CO conversions obtained for sample E at two different air flow rates (3000 and 6000 cm3/min (STP)) and different CO feed concentrations (3% and 5% (v/v)) are plotted versus the foam front temperature in Figure 7. As shown in Figure 7, CO conversion was negligible at low temperatures. However, when the temperature was increased, the reaction lighted off between 170 and 250 °C. Notably, light-off temperatures were lower for a 3% CO inlet concentration than for 5% CO in the feed: this behavior is in agreement with the negative intrinsic reaction order, with respect to CO reported in the literature, when CO oxidation is performed over precious metal catalysts.24 At a feed flow of 3000 cm3/ min (see Figure 7a), the conversion asymptotically reached a value of 96% after light-off and remained constant with further increases in the reaction temperature. When the flow rate was doubled to 6000 cm3/min (see Figure 7b), the asymptotic conversion decreased to 80%: this value seems still quite promising if evaluating the metal foam mass-transfer performances, considering that the depth of the tested sample (sample E) was only 6 mm. Figure 7 indicates that, upon ignition, CO conversion remained constant with increasing temperature: such an asymptotic behavior of CO conversion suggests the onset of full external mass-transfer control. Besides, it can be observed that the asymptotic CO conversion is independent of CO feed concentration, further confirm-

ing the onset of a diffusion-controlled regime associated with pseudo-first-order kinetics. The tests were repeated over all foam samples from A to E, providing reproducible results. Temperature differences between thermocouples in the inlet and outlet section of the foam never exceed 25 °C for all the samples and flow ranges investigated. Mass-transfer coefficients km (given in units of m/s) were estimated from the CO conversions (η) measured under diffusion-controlled conditions, according to eq 9, which represents the steady-state CO mass balance in the reactor, assuming isothermal plug flow behavior and irreversible reaction:

km ) -

ln(1 - η) SVVo/Q

(9)

where SV is the specific area (given in units of m2/m3), Vo is the reactor volume (given in units of m3), and Q is the volumetric flow (given in units of m3/s). Estimates of the mass-transfer coefficients are plotted versus the feed flow rate in Figure 8 for different tested foam samples. It is apparent from the inspection of Figure 8 that the smaller the pore size is, the higher the mass-transfer coefficient becomes, which also increases when the flow rate increases with a linear dependence, on a logarithmic scale. The relevant variables were then expressed in dimensionless form by calculating the Sherwood (Sh), Schmidt (Sc), and Reynolds (Re) numbers, as defined in the Nomenclature section, assuming the strut equivalent cylinder diameter (eq 5) as the foam characteristic dimension. Gas properties were evaluated at the mean temperature between the readings of thermocouple 1 and 2 (see Figure 3). As shown in Figure 9, the mass-transfer data obtained for all the tested foams could be fitted by a single correlation, represented by the following equation:

Sh ) 1.1Re0.43Sc1/3

(10)

It is worth emphasizing that this correlation closely resembles semitheoretical literature correlations for heat transfer in flow across banks of tubes at low Reynolds numbers,25 e.g., the Nusselt number is Nu ) 0.9 Re0.4Pr1/3 for 10 < Re < 100. (Pr denotes the Prandtl number.) Richardson et al.13 determined mass-transfer coefficients by performing CO oxidation experiments over a single 30-PPI ceramic foam with dp ) 0.695 mm and

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Figure 9. Correlation between the Sherwood number (Sh) and the Reynolds number (Re).

Figure 10. Comparison of mass-transfer correlations for foams D and E.

 ) 0.82. Their reported correlation is

jD ) 0.233ReS-0.416

(11)

where the Reynolds number is calculated according to eq 12,

ReS )

Fu S Vµ

(12)

and the specific area SV is calculated according to eq 8. In an attempt to compare our results with eq 11, mass-transfer coefficients were estimated for the foam samples tested herein, using both the former correlation (eq 11) and our proposed correlation (eq 10). To be independent of the different geometrical models, the comparison was based on the product kmSV, which is representative of the reactant conversion for given flow rate and foam volume, as shown by eq 9. Comparison results are plotted in Figure 10. Mass-transfer rates predicted by our correlation are as much as 50% greater than those predicted by the literature correlation. This deviation cannot be explained by the fact that different models were used to describe the foam geometry, because, as shown in Figure 6, extrapolation of the packed-bed-type model to the high void fractions of metal foams would result in a marked overestimation of SV, with respect to the values provided by the cubic cell model adopted herein. A possible explanation for the lower conversions in the experiments reported by Richardson et al.13 is that their data were still limited by kinetic control. They estimated their mass-transfer coefficients assuming diffusion-controlled conditions for the runs at 560 °C,

Figure 11. Pressure drop measurements.

i.e., the maximum temperature reached during the reported experiments. As a matter of fact, at lower temperatures, the measured conversions (indirectly plotted as the rate constant ko (given in units of s-1)) increased as the temperature increased, a clear indication that the system was still partially governed by chemical kinetics. Nevertheless, no further experiments at higher temperature were performed to check that CO conversion would actually become constant, as expected under full diffusion control. Moreover, according to our experience,16 also a poor quality of the catalytic washcoat may result in a lower active surface per unit volume and, consequently, in lower mass-transfer rates. Ceramic foams could also differ from metallic foams by other geometrical and structural features than simply the lower void fraction. Considering the fact that the literature correlation (eq 11) was obtained for a single foam with a void fraction of 0.82, further investigations are needed to check whether the mass-transfer properties of both metallic and ceramic foams can be unified by a single correlation. 3.3. Pressure Drop Measurements. Experimental results expressed as pressure drop per unit length measured over four different foam samples and different air flows are plotted in Figure 11. Flow velocities up to 16 m/s were achieved during the experiments, resulting in pressure drops from 38000 Pa/m to 160 000 Pa/m. The pressure drop per unit length markedly increased with gas velocity and decreased when the pore size of the foams was increased. Many authors have studied pressure drop across foam structures.19,21,27-30 In accordance with the approach adopted for mass transfer in this work, analysis of the pressure drop measurements was also based on the analogy with pressure drop across banks of tubes, as already proposed by Lu et al.18 Considering an array of cylinders, the pressure drop experienced by the cross flow is proportional to the number of tube rows (NT) and can be expressed as31

[ ( )]

∆P ) NTχf′ F

umax2 2

(13)

In the case of foams, the number of rows NT is approximately equal to the length of the structure L divided by the longitudinal size b, as observed in Figure 12. Note that, for isotropic foams, b ) a. The factor χ usually accounts for tube arrangements that are different from the square arrangement and is dependent on the Reynolds number Re, whereas the friction factor f ′ is reported to be dependent on the ratio

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using the relation

f′ ) 0.87 +

Figure 12. Model of the foam as a bank of tubes.

Figure 13. Friction factors for the tested foam samples.

between the longitudinal pitch and the tube diameter: this parameter is typically in the range of 1.25-2.5 for industrial applications in heat exchangers. Taking into account the cubic cell model and the foam samples studied, the ratio between the pitch (that corresponds to the pore size) and the strut diameter is ∼6, which is far outside of the reported range. This fact implies that the influence between tubes in adjacent rows is actually minimized: as an approximation, therefore, χ is herein included into the estimate of the friction factor f ′. Fluid velocity is expressed as the maximum mean velocity, which occurs in the smallest spacing between adjacent tubes when the flow enters the mesh. Considering this effect, and taking into account the cubic array model shown in Figure 12, umax can be estimated as

[

umax ) u

]

a2 (a - dS)2

(14)

Finally, by incorporating χ, the friction factor f ′ can be expressed as

(∆P/L)b (Fumax2/2)

(15)

Friction factors calculated according to eq 15 from experimental pressure drop measurements are plotted as a function of Re in Figure 13. Re was calculated using the superficial air velocity instead of umax, to be consistent with other correlations developed in this article. A Forchheimer-type equation26 has been used to correlate the pressure drop data based on the combination of one viscous asymptote and one inertial asymptote. The best data fit has been obtained

(16)

Considering the simplicity of the model, the differences among the foam samples, and the strong dependence of f ′ on the cell size estimate and on the regularity of the foam geometry, the correlation in Figure 13 is regarded as satisfactory: although the data points are not perfectly unified in a single curve, the agreement is sufficiently fair for our purposes. Equation 16 will be used in the next section to derive a criterion for evaluation of the foam performances, in comparison with other catalyst supports. 3.4. Comparison of Catalyst Supports: Mass Transfer versus Pressure Drop Tradeoff. After the mass-transport properties of foams have been assessed, it is interesting to compare metal foams with other structures that are traditionally used as catalyst supports for environmental applications, such as packed beds of pellets and honeycomb monoliths. In such applications, very high conversions must be typically achieved under diffusion-controlled conditions, to secure the required abatement efficiency while keeping the pressure drop as low as possible, to avoid undue energy losses. Accordingly, a tradeoff between mass transfer and pressure drop performances must be pursued. In the following section, we proceed to derive a merit index that accounts for such aspects, to compare different catalyst supports. As already represented by eq 9, considering an irreversible reaction at steady state in a tubular reactor operating in a diffusional regime, the integral reactant mass balance can be expressed as

(Lu)

ln(1 - η) ) -kmSV

(17)

On the other hand, the pressure drop in foams, packed beds of pellets, or monoliths can be described by the following general equation, where f is a friction factor and d is the characteristic length, specific for each support:

2f 2 ∆P Fu ) L d

( )

(18)

Combining eqs 17 and 18, it is possible to define the following dimensionless tradeoff index, which reflects the overall performance of the catalyst support:

-ln(1 - η) 2

∆P/(Fu ) f′ )

13.56 Re

)

dSVkm dSVSh ) 2fu 2fReSc

(19)

Of course, the higher the index (eq 19), the better the support, because it grants higher conversions with smaller pressure drops. The merit index in eq 19 was calculated for each of the three investigated supports, using the expressions listed in Table 2. Classical literature expressions have been adopted for packed beds of spheres and honeycomb monoliths with square cells, whereas correlations derived in this work have been used for metal foams. Note that the tradeoff index (eq 19) is dependent neither on the characteristic size nor on the length of the catalyst bed; thus, the performance comparison is dependent

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Table 2. Expressions Adopted in the Calculation of the Tradeoff Index (See eq 19) pellets

foams

honeycombs

characteristic dimension

dp

dS

dh

relationship with SV and 

dpSV ) 6(1 - )

dSSV ) 4(1 - )

dhSV ) 4

friction factor

2f )

mass-transfer coefficient

Sh ) aRebSc1/3 c

1- 1- 1.75 + 150 Re 3

[

(

)]

a

(

f ) 0.87 +

)(

13.56 1 Re 1 - G()

)

4

Sh ) 1.1Re0.43Sc1/3 d

G() b 4

f)

14.23 Re

[

Sh ) 2.977 1 + 0.095

(Re )Sc(Ld)]

0.45 e

a From ref 32. b From this work. In this equation, G() ) 2[(1 - )/(3π)]1/2. c From ref 33. For 0.01 < Re < 50, a ) 0.91 and b ) 0.49; for 50 < Re < 1000, a ) 0.61 and b ) 0.59. d From this work. e From ref 34.

Figure 14. Conversion-pressure drop tradeoff index (as defined by eq 19) for different catalyst supports.

only on the support type (the type of correlation) and its void fraction. The results of tradeoff index calculations are plotted in Figure 14 as a function of Re. For the foams, the plot has been limited to the range of Re investigated in the mass-transfer measurements reported herein (10 < Re < 200). However, this is not a serious limitation to the general validity of the results, because, in view of the very small size of the characteristic dimension of the foams (i.e., the strut diameter), such a range covers most of the operating conditions of practical interest. According to Figure 14, because of their very high void fractions, metallic foams perform much better than packed beds of spheres, whose index is strongly penalized (lower by 1 order of magnitude) by the high pressure drop across the bed. On the other hand, the straightforward laminar flow in honeycomb monolith channels secures a superior tradeoff between mass transfer and pressure drop performances, especially at high flow rates (high Re) in metallic honeycombs with high void fractions. 3.5. Comparison of Catalyst Supports: Constraints on Reactor Size. Reactor size is another important feature to consider in the selection of catalyst supports, because many applications of environmental catalysis require lightweight and compact reactors. Accordingly, foams and honeycomb monoliths also have been compared, with respect to reactor size criteria only, with results shown in Figure 15: conversions predicted for both supports using eq 17 are plotted herein as a function of the ratio between reactor length and flow velocity (in an empty reactor). As shown in Figure 15a, for a gas velocity of 5 m/s, any given conversion is achieved in a more compact reactor using a 20-PPI metal foam than using a honeycomb monolith.

Figure 15. Calculated conversions in foams ( ) 0.95) and honeycombs ( ) 0.7) versus reactor length for two different feed flow velocities: (a) 5 m/s and (b) 20 m/s.

The advantage of foams over honeycombs increases at higher gas velocities. At 20 m/s, the performance of a 10-PPI metallic foam is comparable to that of a 600 cpsi monolith (see Figure 15b). For this flow velocity, which is typical of an automotive gas exhaust aftertreatment system, the adoption of a 20-PPI foam instead of a 600 cpsi monolith can reduce the reactor length required to achieve conversions in excess of 90% by a factor of 2.5-3. Such a reduced size would also result in a lower thermal inertia of the catalytic reactor and, consequently, a faster transient response during start-ups and load variations, which are of key importance in mobile applications. However, recall that, as discussed in the previous paragraph, despite its reduced size, the foam monolith reactor would be still associated with significantly higher pressure drops than the honeycomb monolith. 4. Conclusions Measurements of mass-transfer coefficients in metal foams were performed by means of CO combustion tests, following deposition of a Pd/Al2O3 catalytic washcoat.

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The washcoated foams were active enough to successfully achieve mass-transfer-limited conditions in the temperature range of 300-450 °C, as confirmed both by the constant reactant conversion measured with increasing temperature and by the apparent first-order kinetics observed with respect to CO feed concentration. Using a simple cubic cell model to describe the foam network of connected struts and assuming the strut equivalent cylinder diameter as the foam characteristic length, all the mass-transfer data collected herein over foams with three different cell sizes were unified by a single correlation that covers a range of Reynolds numbers (Re ) 10-200). The estimated correlation shows a strong analogy with the literature expressions for heat transfer in tube bundles, which validates the concept of modeling the foam as a bank of tubes and confirms the goodness of the simple cubic cell model selected to describe the foam geometry. A tradeoff analysis between pressure drop and masstransfer performances indicates that metal foams exhibit marked advantages over packed beds but behave slightly worse than honeycomb monoliths as catalyst supports for fast reactions. On the other hand, in fast diffusion-limited processes, where pressure drop is of less concern, metallic foams can achieve conversions equivalent to honeycombs with significant reductions of the reactor size. In addition to measurements of mass-transfer rates and pressure drop, our work on the characterization of metal foams included also the determination of gassolid heat-transfer coefficients: related results will be presented in a forthcoming paper. Acknowledgment The authors gratefully acknowledge the help provided by Timothy Griffin and Regina Granacher from Alstom Power Technology Center, Baden-Da¨ttwill, Switzerland, where the pressure drop measurements were performed. Nomenclature a ) cubic cell dimension equal to the pore diameter (m) b ) cubic cell height for anisotropic foams (m) STP ) standard temperature (273 K) and pressure (1 atm) dS ) foam struts equivalent cylinder diameter in the cubic unit cell (m) DAB ) bulk diffusivity of species A in fluid B (m2/s) f ′ ) friction factor determined for the foams, eq 16 f ) friction factor G() ) function of the foam empty volume fraction in Table 2; G() ) dSa-1 i.d. ) reactor internal diameter (mm) jD ) Colburn factor k ) first-order rate constant (s-1) km ) mass-transfer coefficient (m/s) L ) reactor length (m) NT ) number of rows in a bank of tubes PPI ) foam pore density (pores per inch) Q ) gas flow rate (m3/s) Re ) Reynolds number based on strut equivalent cylinder diameter; Re ) FdSu/µ ReS ) Reynolds number based on the specific area; ReS ) FuSV-1µ-1 Sc ) Schmidt number; Sc ) µF-1DCO,air-1 Sh ) Sherwood number based on struts equivalent cylinder diameter; Sh ) kmdSDCO,air-1

SV ) external surface area per unit volume of bed (m2 m(bed)-3) u ) superficial flow velocity (m/s) umax ) maximum flow velocity inside the bank of tubes (m/ s) Vo ) bed volume (m3) Vs ) solid volume (m3) w/ ) weight percentage w Greek Letters  ) foam porosity or catalyst bed void fraction η ) conversion µ ) gas viscosity (kg m-1 s-1) F ) gas density (kg/m3) FFOAM ) density of the foam; FFOAM ) W/Vo (g/m3) FHS ) apparent density of the hollow struts; FHS ) W/Vs (g/m3) χ ) geometrical factor

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Received for review September 17, 2004 Revised manuscript received November 23, 2004 Accepted November 24, 2004 IE0490886