Properties of ceramic foam catalyst supports: pressure drop

Applied Catalysis A: General 204 (2000) 19–32

Properties of ceramic foam catalyst supports: pressure drop J.T. Richardson∗ , Y. Peng, D. Remue Department of Chemical Engineering, University of Houston, Houston, TX 77204-4792, USA Received 24 November 1999; received in revised form 21 February 2000; accepted 25 February 2000

Abstract Ceramic foams are prepared as positive images of corresponding plastic structures and exhibit bed porosities as high as 80–90%. This makes them attractive as catalyst supports in processes where high pressure drop in the reactor tube is a problem. In this research, pressure drop relationships were examined for 10, 30, 45 and 65 pores per inch (PPI) ceramic foam samples made from 92.0 and 99.5% ␣-Al2 O3 and from ZrO2 stabilized with Mg, Ca, and La2 O3 . Pore distributions were determined with imaging analysis, using digital techniques. Pressure drop measurements confirmed that ceramic foams follow the Forscheimer relationship and may be interpreted with the Ergun model, in which the pressure drop is the sum of viscous and inertial terms. The Ergun parameters, α and β, are not constant, α decreases from 8.05 to 2.88 and β increases from 0.0338 to 0.111 as the pore density increases from 10 to 65 PPI. Empirical equations were developed for these parameters in terms of the mean pore size and the bed porosity, and these indicated a dependence on the media properties. Calculated pressure drop from these equations were within 15% of measured values. Up to 15 wt.% ␥-Al2 O3 washcoat was added to 30 PPI samples of ␣-Al2 O3 foams. Nitrogen BET surface areas increased from about 2 m2 g−1 in the unwashcoated samples to almost 15 m2 g−1 at the highest loading. Both α and β increase linearly with the BET surface area, α by only about 50% but β by a factor of 8. This suggests that roughness introduced by the washcoat plays a dominant role in the turbulent resistance. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Ceramic foams; Catalyst supports; Transport properties

1. Introduction Reticulated ceramic foams [1] have properties that make them attractive as catalyst supports [2,3]. They exhibit extremely high porosities (85–90%), formed by megapores 0.04–1.5 mm in diameter, with spherical-like cells connected through windows [1]. The pore structure of a typical commercial product, shown in Fig. 1, has a high degree of interconnectivity. The most characteristic parameter is the mean ∗ Corresponding author. Tel.: +1-713-743-4324; fax: +1-713-743-4323. E-mail address: [email protected] (J.T. Richardson).

pore diameter, dp , which is measured in several ways and correlates with the pore density (the number of pores per inch, PPI). Ceramic foams were first used as filters for molten metals [4–6] and catalytic combustion devices [7–8] but have recently been applied to catalysis (Table 1). The high bed porosity is the most significant property, resulting in a much lower pressure drop in a reactor filled with a foam ‘cartridge’ rather than packed particles. This is desirable not only for long narrow reactor tubes (e.g. in highly endothermic and exothermic processes) but also for reactions with low contact times (e.g. selective partial oxidation). These characteristics are also found in monolithic structures with uniform,

0926-860X/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 6 - 8 6 0 X ( 0 0 ) 0 0 5 0 8 - 1

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J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

Fig. 1. Pore structure of a 30 PPI, 99.5 wt.% ␣-Al2 O3 ceramic foam.

parallel channels [39]. However, honeycomb monoliths have laminar flow patterns with no lateral mixing between cells, whereas foams have extensive pore tortuosity that enhances turbulence, mixing and transport. These features suggest significant advantages for catalytic processes limited by mass or heat transfer. The first step in the preparation of ceramic foams (Fig. 2) is the selection of a polymer foam with Table 1 Reported examples of catalytic applications

Fig. 2. Preparation steps for ceramic foams.

Reaction

Features

References

Ammonia oxidation

800–1100◦ C

[9]

Selective Less Pt No hot spots Catalytic combustion

Hydrocarbons Preformed shapes

[10–14]

Partial oxidation

Hydrocarbons Selective Low contact times

[15–18]

Steam reforming

Foam particles Pressure drop 25% lower Heat transfer 10% higher

[19]

Auto and diesel

Three-way auto catalysts

[20–31]

Exhaust

Diesel particulate traps Vibration a problem

Solar processes

Preformed shapes CAESAR project CO2 –CH4 reforming

[32–36]

the same pore density [20,37–40]. This is usually polyurethane, but other organic polymers are equally suitable. The pores of the foamed polymer are filled with an aqueous slurry of ceramic (␣-Al2 O3 , ZrO2 , etc.) comprising 0.1–10 ␮m diameter particles in water, together with appropriate amounts of wetting agents, dispersion stabilizers and viscosity modifiers. When relatively low viscosity suspensions are used, excess slurry is removed by blowing air through the foam or by squeezing and kneading. The wet foam is dried and calcined in air at temperatures above 1000◦ C. The plastic vaporizes or burns and the ceramic particles sinter. A ceramic replica or positive image of the plastic is formed. Bulk densities are low and porosities high, but mechanical strength is relatively low. In another approach, the viscosity of the slurry is increased by adding thickening agents [41]. Excess slurry is removed only at the external surface of the

J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

structure, and the ceramic slurry remains in the pores. After calcination and removal of the plastic, pores replace the original organic material, giving a negative image of the plastic. Pore diameters are smaller, bulk densities higher and porosities lower, but mechanical strength is higher. In a third method, an organic monomer is polymerized directly in the ceramic slurry [42], which stabilizes the structure and prevents the collapse of smaller pores. Pores sizes are smaller than those in replicates, even through porosities are just as high. Most commercial ceramic foams are prepared by the first method. A wide variety of preformed shapes and sizes, such as cylinders, rings, rods, or customdesigned configurations, are fabricated by machining the plastic either before or after soaking and drying. Catalytic agents are dispersed on the support using conventional methods, such as single or multiple impregnation of suitable salts or adsorption of ionic precursors from solution, followed by heat-treatment at moderate temperatures. Measured BET surface areas of the foams are low (1–2 m2 g−1 ) but these may be increased to above 30 m2 g−1 by adding washcoats, using identical procedures to those for monoliths [37]. Washcoated foams have been successfully loaded with metals and oxides [20], zeolites [43] and carbon [44] using conventional techniques. Chemical vapor deposition methods have also been suggested [45,46]. Megapores created by these techniques provide a tortuous path for internal gas flow, and tracer experiments have confirmed that radial flow is much higher than in particle beds [47]. This enhances turbulence and results in improved heat and mass transfer, features that are important in highly endothermic or exothermic processes. The pore density used by ceramic foam manufacturers is not a precise measure but merely reflects the range of pore sizes. The quoted PPI refers to the plastic material used to make the ceramic foam and is found from the average number of pore boundaries encountered per inch. In practice, there is a wide variation between the nominal pore diameter calculated from the pore density (e.g. 1/PPI) and the measured mean pore diameter, dp [48]. The latter is usually measured with an imaging technique. Multiple cross-sections of the sample are cut, and images analyzed to give either mean pore diameters or number distributions of equivalent areas that can be quite broad. For example,

21

Sweeting et al. reported a lognormal distribution for 30 PPI foam, with a dp of 0.759 mm and a range from 0.450 to 1.550 mm [48]. The distribution depends on factors such as type of ceramic, size of the specimen, soaking method, drying technique and calcination conditions. When washcoats are added, the distribution could change if the washcoat fills and blocks smaller pores. It is not surprising that attempts to characterize such simple properties as pressure drop have been frustrated by differences between commercial foams with the same pore density but from different or even the same manufacturers. Although the pressure drop for beds of ceramic foams have been reported in the literature, there have been few systematic investigations leading to acceptable correlations. In this paper, we report the results of pressure drop measurements on foamed ceramic pellets, together with correlations for estimating the pressure drop in foams of different pore densities. Since most catalytic applications require washcoating to enhance the surface area, we also investigated the effect of washcoat loading on the pressure drop. 2. Experimental 2.1. Ceramic foam supports The ceramic foam samples were fabricated by HiTech Ceramics, Alfred, NY as cylindrical pellets, 1.27 cm in diameter and 2.54 cm in length. Four groups of foam pellets were examined in this research: 1. 10–65 PPI, 99.5 wt.% ␣-Al2 O3 foams without washcoat, 2. 10–65 PPI, 92.0 wt.% (balance mullite) ␣-Al2 O3 foams without washcoat, 3. 30 PPI, 92.0 and 99.5 wt.% ␣-Al2 O3 foams with an increasing amount of washcoat up to 15 wt.%, 4. 30 PPI foams made from Mg-stabilized ZrO2 (PSZ), Ca-stabilized ZrO2 (FSZ) and Y2 O3 stabilized ZrO2 (YSZ). 2.2. Addition of the washcoat The washcoat was added to the ceramic foam pellets using a high-purity alumina (36 wt.% boehmite) slurry supplied by Hi-Tech Ceramics. The procedure was as follows:

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J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

1. A diluted slurry was prepared consisting of 140 g of the original washcoat slurry and 133 cm3 of distilled H2 O. To this was added 50 g of Al(NO3 )3 ·9H2 O (to serve as a binder to the ceramic foam surface), 4.2 g of La(NO3 )3 ·6H2 O (to give La2 O3 that prevents the transformation of ␥-Al2 O3 to ␣-Al2 O3 upon calcination at high temperature), and a small amount of starch or glycerol (to increase the viscosity). 2. The ceramic foam pellets were dried at 120◦ C for 1 h to remove moisture. 3. Dried foam pellets were weighed and immersed in the washcoat slurry for 1 h. 4. The pellets were taken from the slurry, drained and excess slurry removed by blowing gently with an air jet. 5. The pellets were heated in an oven from 120 to 800◦ C at a heating rate of 15◦ C min−1 and calcined at 800◦ C for 2 h. 6. The pellets were removed from the oven, cooled slowly in air and weighed to obtain the wt.% washcoat loading. 7. Steps (2)–(6) were repeated until the desired washcoat loading was achieved. This procedure resulted in uniform washcoat loading, as indicated by visual and microscopic examination.

2.4. Pressure drop measurement The pressure drop was measured at different superficial air velocities using the apparatus shown in Fig. 3. Each pellet was wrapped with very thin paper to eliminate bypassing and positioned in a precision bore, 1.25 cm in diameter and long enough to accommodate one to three pellets. Two holes (0.2 cm in diameter, centered 0.6 cm away from the bottom and top of the pellet) were connected to a Differential Pressure Transducer, Model PX274 from Omega Technologies Company. Air flow through the cell was controlled and measured with mass flow controllers (Tylan Model FC-260 with Model RO-20A readout), calibrated with a bubble flow meter for up to 150 SLPM. The pressure transducer was connected to a PC computer equipped with a central acquisition system (Omega Technologies Co.) consisting of an eight-channel analog card, one terminal panel and the required software. Data analysis was preformed with LABTECH NOTEBOOK PC software and logged to a disk in a text format, which was convenient to retrieve with a spreadsheet program.

2.3. Image analysis of the foams Cylindrical foam pellets were cut with a diamond saw along the axial and radial dimensions into ∼3 mm thick slices. Images were then taken of each slice using a Sony MVC-FDT digital camera with an optical magnification of 4 and a 640×480 VGA image size. Each image (similar to Fig. 1) was analyzed with Jandel SigmaScan software, an image analysis program that detects individual pore areas. Only the windows were recorded, and care was taken to eliminate pores that were obviously combinations of more than one, possibly resulting from the cutting procedure. The area of each individual pore was converted to the diameter of an equivalent circle, and the data from all segments were combined to give a distribution representing approximately 1000 pores. The distribution was then fitted to distribution functions, from which the mean pore diameter, dp , was determined.

Fig. 3. Cell for the pressure drop measurements.

J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

2.5. Surface areas, densities and porosities Nitrogen BET surface areas of the pellets were measured with a Quantasorb (Quanta Chrome Corp.) surface area analyzer, using a large sample cell, 13 cm in diameter and with a volume of about 6 cm3 . This instrument measures the amount of adsorbed N2 in equilibrium with a specific N2 /He mixture by thermal desorption. The solid density (ds ) was measured with a He multipycnometer (QuantaChrome Corp.), designed for measurement of the true volume of solid materials using He displacement. The bulk density (dB ) was found from the volume of the pellet calculated from the dimensions and included the volume of any closed or accessible pores within the particle. The bed porosity or voidage, ε, was found from the two densities using Eq. (1): ε =1−

dB ds

(1)

3. Results and discussion 3.1. Image analysis Typical results for the image analysis are shown in Fig. 4. The sample, a 30 PPI, 92% ␣-Al2 O3 foam without washcoat exhibited a very broad distribution with pore diameters ranging from 0.45 to 1.15 mm. We fitted the distribution with two common functions-a

23

Gaussian normal (dp,mean =0.751 mm, goodness of fit r2 =0.937) and the log-normal (dp,mean =0.734 mm, r2 =0.963). Although the lognormal gives a slightly better fit, there was no significant statistical difference between the two. We found no consistent trends with the other samples, in some cases the normal distribution was better, in others the lognormal. For this reason, the normal distribution value of dp,mean was taken as the characteristic value for dp . Imaging techniques measure the size of the windows or ‘throats’ at various angles to the plane of the cut, resulting in local departures from ideal geometry. Nevertheless, the mean value of 0.751 mm (normal distribution) is an accurate representation of the pore diameter. The distribution in Fig. 4 is similar to that reported by Sweeting et al. for the same type of foam [48]. Values of dp determined in this manner are given in Table 2. 3.2. Characteristics of the foams Characteristic properties of foam samples studied here are given in Table 2. Solid densities (ds ) are very close to the theoretical density of Al2 O3 or the appropriate ZrO2 , indicating only minor amounts of inaccessible pore volume, e.g. closed, hollow spaces in the struts of the foam. Bulk densities and porosities are similar to those quoted by the manufacturer for the specific class of foams. The values in Table 2 were used in subsequent calculations discussed in the following sections. 3.3. Pressure drop data and analysis Typical pressure drop versus superficial velocity data for five different samples of a 30 PPI foam of 92.0 wt.% ␣-Al2 O3 containing 6.00 wt.% washcoat are shown in Fig. 5. There is some variation between samples, probably caused by individual pellet differences, but there is satisfactory precision in the measurements. The results follow the Forscheimer equation [49] dP = a0 V + a1 V 2 L

Fig. 4. Pore size distribution for a 30 PPI, 92.0 wt.% ␣-Al2 O3 foam without washcoat.

(2)

where dP/L is the pressure drop per unit length, V the superficial velocity, and a0 and a1 are constants.

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Table 2 Properties of the ceramic foam supports dp (mm)

He density (g cm−3 )

Bulk density (g cm−3 )

Bulk porosity

(1) 99.5 wt.% ␣-Al2 O3 without washcoat 10 30 45 65

1.68 0.826 0.619 0.359

3.82 3.94 3.91 3.93

0.464 0.498 0.772 0.562

0.878 0.874 0.802 0.857

(2) 92.0 wt.% ␣-Al2 O3 without washcoat 10 30 45 65

1.52a 0.734a 0.420a 0.289a

3.87 3.88 3.96 3.88

0.569 0.660 0.827 0.450

0.853 0.830 0.791 0.884

(3) 99.5 wt.% ␣-Al2 O3 with washcoat 5.59 wt.% 30 8.46 wt.% 30 12.09 wt.% 30

0.810 0.800 0.780

3.94 3.94 3.94

0.526 0.546 0.558

0.866 0.861 0.858

92.0 wt.% ␣-Al2 O3 with washcoat 6.00 wt.% 30 6.56 wt.% 30 9.60 wt.% 30 15.0 wt.% 30

0.695 0.714 0.706 0.690

3.89 3.95 3.95 3.95

0.700 0.703 0.723 0.759

0.820 0.822 0.817 0.808

0.708 0.704 0.754 0.746 0.796

5.60 5.62 5.61 5.61 5.88

0.840 0.649 1.29 1.16 0.889

0.850 0.885 0.770 0.793 0.849

Group

(4) ZrO2 -based PSZ (Mg) FSZ (Ca) YSZ (La2 O3 ) a

Pore size (PPI)

30 30 30 30 30

From HiTech Ceramics, Inc.

The most widely accepted interpretation for the constants a0 and a1 when applied to flow through packed beds was given by Ergun and Orning [50]. In their model, a0 and a1 represent flow resistance from vis-

Fig. 5. Typical pressure drop data for five samples of 30 PPI, 92 wt.% ␣-Al2 O3 with 6.00 wt.% washcoat.

cous and inertial or turbulent contributions, respectively. These constants are given by αSv2 µ(1 − ε)2 (3) ε3 αSv ρ(1 − ε) (4) a1 = ε3 where Sv is the geometrical surface area per unit volume of solid, µ the viscosity, ρ the density of the fluid, α and β represent parameters that depend on the geometry and packing of the particles. Ergun and Orning studied a wide variety of particle shapes and found values of α and β ranging from 3.6 to 20 and 0.14 to 0.70, respectively, but recommended α=4.17 and β=0.292 as universal ‘constants’. Macdonald et al. confirmed these conclusions but preferred α=5.00 and β=0.300 for smooth and β=0.667 for rough particles [51]. Most authors agree that α and β are not ‘constants’ but parameters that depend on the medium. For example, a0 =

J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

Macdonald et al. concluded that α=10.6 is better for consolidated media and that α∝Sv (1−ε)ε−3.6 . The appropriate value of Sv must be known to determine values of α and β using Eqs. (2)–(4). Accurate estimates of Sv are only possible for uniform, regular-shaped particles. The situation is far from clear for irregular surfaces, such as foams, or for wide distributions of particles. The usual practice for particles with approximately spherical geometry is to assign α=5 and determine Sv from Eq. (3), using low velocity air permeametry measurements [52]. This may not be appropriate for foams, and models that give Sv are desirable. 3.4. Models for determining Sv

Sv =

4ε dp (1 − ε)

tial element of surface area dS. Consider an array of test lines parallel to an edge of the cubic sample (e.g. the z-axis) and distributed randomly over the cube face through which they emerge. The sample space consists of a continuum of points contained in the face of the cube perpendicular to the test lines. The fraction of uniformly distributed test lines intersecting dS is given by pr =

dA(θ, φ) L2

(5)

A second method (model 2), independent of pore shape assumptions, was discussed by Underwood in studies of quantitative metallography [54]. Fig. 6 shows a random, non-specified pore surface in space. Assume d A (θ, φ ) is the xy-projection of a differen-

(6)

where L2 is the total area of the sample space. For N test lines of length L, the number of intersections per unit length of test line is found from dNL =

In this section we examine three models for calculating Sv . The first and most direct is to treat the pores as uniform, parallel cylinders, each with a constant diameter equal to dp . This ‘hydraulic diameter’ method was successfully used for packed beds by Kozeny, who applied it to a variety of particle shapes [53]. Using the simple assumption that the internal surface of the cylinder represents the surface of the idealized pore, geometrical considerations lead to

25

dA (θ, φ) L3

(7)

from which the number of intersections with an element of surface area of a randomly oriented test secant can be calculated. The average over the orientation is Z π Z 2π −dAsin φ dθ dφ (8) dNL = L3 4π 0 0 Substituting dA (θ , φ)=dS|cos φ| into Eq. (8) leads to Z π Z 2π −dS|cos φ|sin φ dθ dφ (9) dNL = L3 4π 0 0 from which Underwood [54] integrated dNL over the entire surface to obtain ZZ 2dS S = (10) NL = L3 2L3 For ceramic foams, each pore is formed by solid edges and each intersection of a pore equals two intersections with the solid phase, giving NL =

2 dp

(11)

from which we derive Sv =

Fig. 6. Random pore in space, model 2.

4 dp (1 − ε)

(12)

This method is valid for any system of surface in space with a uniform distribution of secants. Neither of these previous models takes into account the geometric structure of the foam. The original polyurethane foam is a network of approximately

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J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

spherical cells, each connected with neighboring cells through windows, with the structure defined by polymer struts that collectively form faces around the cells and edges around the windows. These struts are covered with slurry during formation of the ceramic foam. Ceramic replaces the original polymer struts when the material is calcined and the polyurethane burned away. These ceramic struts are approximately triangular in cross-section and sometimes hollow [1]. Since these struts form the ceramic surface, Sv may be calculated from the geometry of the structure. In their comprehensive review of cellular solids, Gibson and Ashby discussed models in which foam structures are treated as regular packing of various polyhedra, such as triangular prisms, rectangular prisms, hexagonal prisms, rhombic dodecahedra and tetrakaidecahedra [1]. According to these authors, tetrakaidecahedra are preferred since they give the most consistent agreement with observed properties. The unit tetrakaidecahedron is shown in Fig. 7a and the physical structure of the individual cell in Fig. 7b. Each cell consists of 14 faces or windows connected with neighboring cells to generate a three-dimensional structure throughout the foam. The windows (eight hexagonal and six square) are bordered by triangular struts of width ts (Fig. 7c). Gibson and Ashby derived geometric relationships for the tetrakaidecahedron unit cell, including the length of the edge of the hexagonal window, l, and these are listed in Table 3. In addition, Gibson and Ashby found that l and ts are related by l=

1.030ts (1 − ε)0.5

(13)

Table 3 Geometric constants for tetrakaidecahedra Property

Symbol

Formula

Pore diameter Solid porosity Hexagonal side Strut thickness Cell volume Surface area of the struts Surface area per unit volume (solid)

dp ε l ts Vc Ss

Measured Measured 0.5498dp /[1−0.971(1−ε)0.5 ] 0.971(1−ε)0.5 l 11.31l3 36ts l

Sv

Ss /[Vc (1−ε)]

when (1−ε) is small. Since dp is the diameter of a circle with an area equivalent to the hexagonal window, i.e. of six equilateral triangles of edge l−ts , we arrive at ts =

0.5338dp ( 1 − ε)0.5 1 − 0.971( 1 − ε)0.5

(14)

Using the expression for Sv in Table 3 leads to Sv =

12.979[1 − 0.971 (1 − ε)0.5 ] dp ( 1 − ε)0.5

(15)

Similar equations may be derived for other structures suggested for the foams. For example, we derived equations for the pentagonal dodecahedron, another favorite model, and found they were very close to those of the tetrakaidecahedron. Values of Sv calculated from these three models are listed in Table 4 for the 99.5 wt.% ␣-Al2 O3 foams without washcoat, using the measured results for dp given in Table 2. It is surprising that such widely differing models give results so close to each other. The averages are almost identical to those from the hydraulic diameter model. Although this is the most dubious of the three, it appears to be sufficient for the purpose. Since its use is also widely accepted for packed beds, Table 4 Values of Sv ×10−4 calculated from models 1, 2 and 3, m2 /m3 (solid)a

Fig. 7. The tetrakaidecahedron model.

PPI

Model 1

Model 2

Model 3

Average

10 30 45 65

1.72 3.36 2.55 6.68

1.95 3.84 3.18 7.79

1.46 2.90 2.60 6.05

1.71 3.37 2.78 6.84

a

99.5 wt.% ␣-Al2 O3 , without washcoat.

J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

we selected model 1 as a standard throughout this research, and we recommend it to other workers in the field. As the pore density increases and the value of dp decreases, there is an expected increase in Sv , with the exception of the 45 PPI sample. We have no explanation for this; other than to note that the value of dp in Table 2 did not decrease as much as reported by the manufacturer. The value of Sv for the 30 PPI sample in series 2 is 3.36×104 m2 m−3 (solid). This corresponds to a surface area of 0.0085 m2 g−1 , which is about 200 times smaller than the measured BET surface area of 1.91 m2 g−1 . Obviously, the surfaces of the struts are not smooth but are indented with meso and macro pores. 3.5. Effect of different pore densities

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Table 5 Parameters for the Forscheimer equationa PPI

a0 (Pa s m−2 )

a1 (Pa s2 m−3 )

α

β

10 30 45 65

949 3790 4610 7630

128 651 1070 2050

8.05 7.72 4.85 2.88

0.0338 0.0838 0.0872 0.111

a 99.5 wt.% ␣-Al O foams, without washcoat. σ =1.161 2 3 air kg m−3 ; µair =1.827×10−4 kg m−1 s−1 .

size. The Ergun parameters, however, show opposite effects; α decreases and β increases as dp decreases, with the effect on α being much more pronounced. Although the values of these parameters are within the range suggested by Ergun and Oring [50] and MacDonald et al. [51], β is less than predicted for particle beds. This systematic variation supports the argument that these parameters depend upon the characteristics of the medium. We fitted the data for α and β versus PPI-related properties with a number of empirical equations and found the best results with

Fig. 8 shows pressure drop results for 10, 30, 45, and 65 PPI, 99.5% ␣-Al2 O3 foams without washcoat. Pressure drop increases as pore density increases and dp decreases, even though the porosities remain approximately the same. Forscheimer parameters derived from the curves in Fig. 8 are given in Table 5, together with the values of α and β calculated using Eqs. (3) and (4). The constants a0 and a1 are inversely proportional to the viscous and inertial permeabilities, respectively. Both increase as dp decreases, a0 by a factor of about 8 and a1 by about 20, signifying a greater increase in the turbulent resistance as the flow channels decrease in

α = 9.73 × 102 dp 0.743 (1 − ε)−0.0982

(16)

β = 3.68 × 102 dp −0.7523 (1 − ε)0.07158

(17)

Fig. 8. Pressure drop vs. velocity for 99.5 wt.% ␣-Al2 O3 foams without washcoat.

Fig. 9. Comparison of experimental and calculated pressure drop at 7 m s−1 for ceramic foam samples.

with dp in meters. The agreement between values extrapolated at 7 m s−1 from the measured pressure drop versus velocity data and those calculated from Eqs. (2)-(4), (16) and (17) is shown in Fig. 9. With the exception of the FSZ samples, the non-washcoated 92 wt.% ␣-Al2 O3 , 99.5 wt.% ␣-Al2 O3 , PSZ and

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J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

Fig. 10. Pressure drop vs. velocity for samples of 30 PPI, 99.5 wt.% ␣-Al2 O3 foams with washcoat.

YSZ samples examined obey the empirical equations within ±12%. The FSZ samples appear to have characteristics that are not reflected in the parameters used in the correlation. We will discuss this in detail in following sections. 3.6. Effect of washcoat loading Since washcoats are required to increase the surface area of ceramic foam supports, it is important to investigate any effect of washcoat loading on pressure drop. Fig. 10 shows how pressure drop increases with the addition of increasing amounts of washcoat for 30 PPI, 99.5% ␣-Al2 O3 samples. Table 6 gives the corresponding values of α and β for these samples. As the washcoat loading increases up to 12.1 wt.%, α increases modestly by about one-third but β increases by a factor of about 3. Fig. 11 shows the cumulative pore size distributions for the catalysts in Fig. 10. The distributions for 0 and 5.59 wt.% are essentially identical, but there-

Fig. 11. Cumulative pore size distributions for samples of 30 PPI, 99.5 wt.% ␣-Al2 O3 foams with washcoat.

after dp decreases slightly as the washcoat loading increases and the range of diameters stays the same. Clearly, the differences in pore structure and porosity do not account for the pressure drop increase shown in Fig. 10. The increase in the BET surface area for the washcoated 30 PPI samples of 92.0 and 99.5 wt.% ␣-Al2 O3 foams are shown in Fig. 12. The surface area increases moderately with washcoat addition for the first 5–7.5 wt.% and then increases more rapidly thereafter. These surface areas are lower than previously reported by Sweeting et al. [48], but this is most likely due to the higher calcination temperature used in this work. Some insight into this has been given by Moates et al. with back electron imaging (BEI) studies of this same ceramic foam with 10 wt.% washcoat loading loaded

Table 6 Parameters for 30 PPIa Washcoat loading (wt.%)

a0 (Pa s m−2 ) a1 (Pa s2 m−3 ) α

β

0 5.59 8.46 13.5

3790 3720 4710 5820

0.0838 0.130 0.169 0.259

a

651 1050 1400 2210

99.5% ␣-Al2 O3 foams with washcoat.

7.72 7.24 8.89 10.4

Fig. 12. BET surface area for washcoated samples of 30 PPI, 99.5 wt.% ␣-Al2 O3 foams.

J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

and calcined in the same way [55]. These authors observed cracks and pores in the ␣-Al2 O3 ceramic struts that account for the measured BET surface area of the non-washcoated material. Back electron imaging clearly showed the washcoat firmly adhering to the ␣-Al2 O3 with a thickness of about 50 ␮m, and the highly porous nature of the washcoat was apparent. Furthermore, the surface area of the washcoat material itself was 88.8 m2 g−1 (washcoat) after calcination at 800◦ C, whereas a 10 wt.% washcoated foam sample exhibited a BET surface area of 8.9 m2 g−1 . The following semi-qualitative model explains the nature of the results in Fig. 12. Originally, the non-washcoated ceramic foam has sufficient fissures, cracks and pores to generate a surface area of about 2 m2 g−1 , which is over 200 times greater than the geometric or external surface area of 0.0085 m2 g−1 . With washcoat addition, these fissures, etc. fill and form the basis for a strong adherence of the washcoat to the surface. The inherent surface area of the original surface disappears. The surface area exposed is a combination of the washcoat layer and any uncovered ceramic struts. Finally, the ceramic is covered and the surface area originates solely from the washcoat material, as determined by the thickness of the layer. Using the ‘hydraulic diameter’ model and the values of dp from Table 2, we estimated the washcoat layer thicknesses for the 5.59, 8.46 and 12.1 wt.% 99.5 wt.% ␣-Al2 O3 samples to be 10, 14 and 22 ␮m, respectively. Assuming the washcoat has a porosity of about 0.5 with a bulk density of 1.98 g cm−3 , covering the external surface area completely with the washcoat gives thicknesses of 4, 6 and 9 ␮m, respectively. These lower values could mean either that Sv is smaller by a factor of about two or that only 50% of the surface is covered. The assumptions of the model and the precision of the measurements do not justify further speculation. Initially, the washcoat is not efficient in developing surface area, possibly some of it disappears in the fissure, etc., so that loadings of greater than about 7 wt.% are required to produce any significant enhancement. At 15.0 wt.%, the full potential of the washcoat is realized. Fig. 10 clearly shows that washcoat loading increases the pressure drop, and the data in Table 6 suggest that the effect is due mostly to an increase in β and not to changes in porosity, pore diameter or distribution. Fig. 12 shows a large increase in surface area,

29

Fig. 13. Dependence of α and β on the BET surface area of 30 PPI, 99.5 wt.% ␣-Al2 O3 foams with washcoat.

i.e. the roughness of the surface. This roughness intensifies the turbulent resistance of the pore surface to flow, thus accounting for the increase in β. This same effect is well-noted in pressure drop correlations in rough pipes [57]. The small effect on α may be of similar origin or is possibly only apparent. Fig. 13 shows the dependence of α and β on the surface area of the washcoated samples, leading to the empirical relationships α = 6.23(1 + 0.0711SBET )

(18)

β = 0.0676(1 + 0.3018SBET )

(19)

Eqs. (18) and (19) were found from the 99.5 wt.% ␣-Al2 O3 samples, but the agreement between measured and calculated pressure drops at 7 m s−1 for all the washcoated samples was within 11%. These results confirm a linear relationship between α and β and the roughness of the surface, as evidenced by the BET surface area. Since ceramic foams have BET surface areas far greater than their external surface areas, even without added washcoat, it is not surprising that attempts to find consistencies in values of α and β among commercial samples have not been too successful. The amount of enhanced surface area or roughness found in foams varies from batch to batch as manufacturing parameters differ.

30

J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

3.7. Comparison between foams and packed beds For catalytic reactors, the surface area per unit volume of bed (SB ) is SB = Sv (1 − ε)

(20)

From which dp αSB 2 µV + βSB ρV 2 = L ε3

(21)

where the viscous energy term (αSB 2 µ/ε3 ) for the foam is about one-third of that for particles in the Ergun model, whereas the inertial term (βSB ρ/ε3 ) is about the same. The latter is the dominant factor in commercial reactors, where space velocities are high and the pressure drop is almost completely determined by the second term of the equation. In comparing reactors consisting of ceramic foam ‘cartridges’ and a packed bed of catalyst particles with the same external surface area per unit bed volume, the important difference is the porosity. For example, from Table 2, a 30 PPI foam has a porosity of 0.874 and an Sv of 3.36×104 m2 /m3 (solid), which is equivalent to SB of 0.423×104 m2 /m3 (bed). A spherical particle diameter of 0.70 mm, with a calculated bed porosity of 0.510 [56], is necessary to generate an equivalent SB . We measured the pressure drop for a bed of 0.5 mm diameter spherical beads made of smooth glass (ε=0.416) and compared it to the 30 PPI, 99.5 wt.% ␣-Al2 O3 foam without washcoat in Fig. 14. Measurements from two separate experiments are reported for the 0.5 mm spheres in Fig. 14. The fitted values

for α and β are 5.93 and 0.0705, respectively. The value for α is within the normal range for the Ergun ‘constants’, but β is low. Fig. 14 clearly demonstrates the pressure drop advantage of the ceramic foam over the packed bed of spheres. At high flow velocities, the pressure drop of the foam is smaller by about a factor of 16. Two-thirds of this is due to the difference in porosity, the remainder results from lower values of α and β. The broken line in Fig. 14 is for the foam, using ‘smooth’ values of α and β derived from Eqs. (16) and (17), i.e. for a smooth ceramic surface close to the external area, and shows a further reduction in pressure drop. For ceramic foam supports loaded with washcoat, the advantages are reduced accordingly, but the difference is still significant. Such a decrease in pressure drop is a significant advantage for reactors with low diameter/length ratios used for processes with heat transfer limitations. 3.8. Practical considerations These studies have shown that, although systematic relationships may be developed for ceramic foams of a specific type (i.e. manufacture), they are only valid if pore size distributions and BET surface areas are available. Attempts to find general correlations for a wide range of ceramic foam types should include these parameters. If accurate pressure drop relationships are desired, it is recommended that they be found experimentally in the manner described. Otherwise, the correlations given in this work are useful for design purposes. For example, it is customary when estimating pressure drop in pipes or packed beds to deal with a dimensionless quantity dPdp = f (Rep ) Lρ V 2

(22)

where the ‘friction factor’, f (Rep ), given by   BRep (1 − ε)2 A+ f (Rep ) = 1−ε Rep ε3

(23)

is a function of the Reynolds number Fig. 14. Comparison of pressure drop for a bed of glass spheres and 30-PPI, 99.5 wt.% ␣-Al2 O3 without washcoat.

Rep =

ρVdp µ

(24)

J.T. Richardson et al. / Applied Catalysis A: General 204 (2000) 19–32

and the constants A and B. For the Ergun formulation, dp is the spherical equivalent of the particle diameter with A=150 and B=1.75. Eqs. (22)–(24) apply for ceramic foams, except that dp is the mean pore diameter and A=36α and B=6β. For the unwashcoated foams, α and β should be found from Eqs. (16) and (17). With washcoated foams, we adopt the procedures used in rough pipes in which the viscous term is unchanged but the inertial term depends on the ‘roughness’, defined as the ratio of the height of the protrusions on the inside of the pipe to the diameter of the pipe [57]. Accordingly, we define a roughness factor (RF) as the ratio of the enhanced washcoated surface area to that of the external surface area, i.e. for the 30 PPI foam RF = 3.95 × 106

SBET Sv

(25)

Eq. (19) becomes β = 0.0676(1 + 2.57 × 10−3 RF)

31

3. Pressure drop versus velocity data follow the Forscheimer equation and may be interpreted with the conventional Ergun model, except that the Ergun parameters, α and β, are not constants but depend on the properties of the media. 4. Empirical relationships for α and β in terms of the mean pore diameter and the foam porosity were developed and these predicted the pressure drop within ±15% for 10–65 PPI foams. 5. Washcoats added to the ceramic foam increase the total surface area with only very small decrease in the mean pore diameter and foam porosity. The pore size distributions of the washcoated foams are almost unchanged. However, the pressure drop is higher due to an increased roughness of the surface. This manifests itself mostly as an increase in β, and the effect is linear with the BET surface area. Correlations were developed for both α and β versus BET surface area, but only for 30 PPI foam.

(26)

We have shown that Eq. (26) applies to 30 PPI, 99.5 wt.% ␣-Al2 O3 foam. It may be applicable to 10–45 PPI foams from any ceramic, but this is yet to be verified. There could be difficulties in washcoating higher pore density foams in a uniform manner without blocking small pores.

4. Conclusions The main conclusions from this work are as follows: 1. Ceramic foams are excellent candidates for catalyst supports. In addition to being preformed into any desired shape, they can provide the same surface area per volume of catalyst bed while generating a pressure drop over 10 times smaller than corresponding particles. This point alone is attractive for reactions with very low contact times and for reactors with low diameter to length ratios, such as found in highly exothermic or endothermic processes. 2. The mean diameter of the megapores is easily determined with simple imaging analysis and may be used to characterize the external surface area of the ceramic. The simple hydraulic diameter model is preferred since it gives essentially identical results as more complex geometric models.

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