solid mass transfer in metallic filters as supports for micro-structured catalysts

Chemical Engineering Science 65 (2010) 392 -- 397

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Experimental and theoretical study of gas/solid mass transfer in metallic filters as supports for micro-structured catalysts G. Groppi a , E. Tronconi a, ∗ , G. Bozzano b , M. Dente b a b

Dipartimento di Energia, Laboratorio di Catalisi e Processi Catalitici, Politecnico di Milano, 20133 Milano, Italy Dipartimento di Chimica Materiali e Ingegneria Chimica “G. Natta”, Politecnico di Milano, 20133 Milano, Italy

A R T I C L E

I N F O

Article history: Received 8 July 2008 Received in revised form 3 June 2009 Accepted 10 June 2009 Available online 18 June 2009 Keywords: Structured catalysts Metallic fibers Metallic filters CO oxidation Gas/solid mass transfer

A B S T R A C T

Commercial sintered metallic micro-fibers have been investigated in view of their adoption as enhanced catalyst carriers. The material herein studied has high porosity (86%) and very high interfacial area (22 400 m2 /m3 ), thus appearing promising for application in fast, mass-transfer limited catalytic processes. It was catalytically activated by calcination and impregnation with Pt, and tested in the model reaction of CO oxidation. The observed activity was very high: at T > 500 ◦ C, under diffusional control, CO conversions in excess of 90% were achieved at space velocities in the order of 106 h− 1. Dimensionless mass transfer coefficients extracted from these data, accounting also for axial dispersion, exhibited. However, negative deviations from those expected either for a single infinite cylinder or from extrapolation of previous correlations for open-celled foams at higher Reynolds numbers. According to an original and unifying theoretical approach herein proposed, such deviations are quantitatively explained by accounting for the limitations to boundary layer development due to the proximity of other fibers in the densely packed system. The key point is to assume a pseudo ordered locally parallel assembly of cylinders with average distance related to the fiber diameter and to the void fraction. © 2009 Elsevier Ltd. All rights reserved.

1. Introduction Structured carriers offer additional degrees of freedom for engineering of catalyst design (Cybulski and Moulijn, 2006). As an important example, the fast mass-transfer controlled gas/solid processes of environmental catalysis (e.g. lean NOx aftertreatment, catalytic combustion of methane, CPO of hydrocarbons for syngas and H2 production) could largely benefit from micro-structured catalyst supports with high porosities, low thermal mass, large surface areas and enhanced mass and heat transfer characteristics. In this perspective we have investigated the transport properties of metallic and ceramic open-celled foams, as well as those of sintered metallic micro-fibers. Particularly for the latter case, engineering correlations for the prediction of external mass transfer rates are lacking. De Greef et al. (2005) presented flow mixing and mass transfer data collected in a catalytic stirrer containing catalyst coated porous micro-fiber elements: their data were correlated by the following equation

Sh = 0.47Re0.5 Sc0.33 Such results however apply to a liquid/solid system. ∗ Corresponding author. Tel.: +39 02 2399 3264; fax: +39 02 2399 3318. E-mail address: [email protected] (E. Tronconi). 0009-2509/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2009.06.038

(1)

Other relevant data can be traced in the literature concerning mass transfer in contacting devices based on hollow fibers. Cussler and coworkers (Yang and Cussler, 1986; Wickramasinghe et al., 1992; Wang and Cussler, 1993) published mass transfer correlations applicable to the shell side of such contactors at low Reynolds numbers (1 < Re < 10), which suggest lower mass transfer coefficients, with a more marked dependence on the Reynolds number than expected from the analysis of mass transfer to a single fiber, due to non uniform distribution of the fluid flow within the fibers (Wickramasinghe et al., 1992): Sh = 0.15Re0.80 Sc0.33

Re > 2.5

(2a)

Sh = 0.12Re1.00 Sc0.33

Re < 2.5

(2b)

Schoner et al. (1998) presented similar data, and concluded that the reduced mass transfer performances could be due to channelling and bypass phenomena within the fibers. A more complex dependence of Sh on Re and on the ratio of the distance between fibers to their diameter has been recently proposed also by Li et al. (2005) based on their own data for mass transfer in fibers at low Reynolds numbers (10–200). Altogether, analysis of the literature points out no clear agreement on the mass transfer behavior of fibrous systems at low Reynolds, one possible reason being the dependence on the

G. Groppi et al. / Chemical Engineering Science 65 (2010) 392 -- 397

random spacing and orientation of the fibers, which apparently plays a significant role. In this respect, a parallel with gas/solid transport properties of open-celled foams, which have received more attention in recent years, could be eventually beneficial. We present herein an experimental and theoretical comparative analysis of gas/solid mass transfer in foams and in metallic fiber elements. As in previous projects with foam supports (Giani et al., 2005a,b; Groppi et al., 2007), an initial part of the activities has addressed the development of techniques for the catalytic activation of the supports. Activated supports have been then tested in CO oxidation, taken as a model reaction: reaction conditions were sought corresponding to a mass-transfer limited regime, so that estimates of mass-transfer coefficients could be obtained directly from the catalytic activity data. Finally, an original theory has been developed in an attempt to reconcile all of the experimental observations.

393

Reactants inlet

2. Experimental Materials: The structures investigated in this work included sintered FeCrAlloy䉸 fiber mats from Beckaert. A representative micrograph is displayed in Fig. 1. The mechanical strength of such commercial materials is adequate for typical industrial applications in the field of filtration. Pycnometric and microscopic measurements were used to estimate their porosity ( = 0.86) and their mean fiber diameter (df = 25 m), respectively. The geometric area (Sv = 22 400 m2 /m3 ) was estimated according to a simple analogy with infinite cylinders, SV =

4 (1 − ) df

oven

stainless steel tube

1st thermocouple non-catalytic foam catalytic filter

(3)

For comparison, additional data will be presented for the following open-celled foam materials: (i) FeCrAlloy䉸 foams from Porvair (porosity = 0.95, 10–40 ppi nominal) (Giani et al., 2005a); (ii) -Al2 O3 foam from Goodfellow (porosity = 0.84, 20 ppi nominal) (Groppi et al., 2007). For estimation of the interfacial area, a simple cubic cell geometry was assumed in the case of the foam structures: more details on the structural properties of the foam samples are to be found in Groppi et al. (2007). It is worth emphasizing that the estimated interfacial area of the foams sample with the highest cell density (40 ppi nominal) was 962 m2 /m3 , i.e. over 20 times less than SV of the micro-fiber sample.

Fig. 1. SE micrograph of the metallic micro-fiber elements herein investigated.

non-catalytic foam

2nd thermocouple

Fig. 2. Schematic diagram of the test microreactor.

Catalytic activation: In a first stage, the metallic fibers were washcoated with pd/ -Al2 O3 according to a procedure similar to one previously developed for the deposition onto metallic foams (Giani et al., 2006). It was soon realized however that the -Al2 O3 layer was likely responsible for blocking part of the pores in the fibrous structure; furthermore, it was difficult to deposit a uniform layer onto all the fibers. In general, the procedure resulted in a good catalytic activity of the washcoated samples, but the results were found hardly reproducible. Accordingly, a new procedure was developed based on direct impregnation of the metallic micro-fibrous samples with the catalytic material (Pt in this case), as described in the following. The micro-fiber samples were preliminarily washed in ethanol in an ultrasound bath to remove impurities, and dried at 110 ◦ C. They were then calcined in an oven with air recirculation for 10 h with the purpose of promoting the migration of -Al2 O3 from the FeCrAlloy matrix to the surface. The optimum calcination temperature was found to be 950 ◦ C. The amount of segregated -Al2 O3 as determined by the weight increment during calcination was about 5 %w/w. The samples were then impregnated with an aqueous solution of Pt(NO3 )2 in a jacketed stirred cell at constant temperature (60 ◦ C) for 3 h. The concentration of Pt(NO3 )2 in the solution was also optimized (3.8×10−4 M), resulting in a Pt/Al2 O3 ratio of about 0.12 w/w. The final treatment involved calcination of the filters at 500 ◦ C for 10 h to effect decomposition of the nitrates. Catalytic activity tests: The activated micro-fiber samples were tested in CO oxidation with air in a micro-flow tubular reactor

394

G. Groppi et al. / Chemical Engineering Science 65 (2010) 392 -- 397

(id = 9 mm) placed in an oven with temperature control. The tested samples were in the shape of disks, with diameters of 9 mm and depth around 1 mm: they were loaded in the reactor between two bare metallic foams acting as flow distributors. A schematic diagram of the test reactor is displayed in Fig. 2. Air and CO were fed to the reactor through independent lines and mass flow controllers, mixed and preheated to a set temperature before entering the reactor. Outlet compositions of reactants and products were analyzed on line by a gas chromatograph (Agilent Technologies model 6890N) equipped with two TC detectors and two packed columns. Two thermocouples placed immediately upstream and downstream from the foams measured the temperatures of the inlet and outlet gas stream, respectively. Activity tests were performed over a number of catalyzed fiber samples at total feed flow rates in the range of 1000–5000 cm3 /min (STP), corresponding approximately to GHSV in the range of 1–5×106 h−1 (referred to the total sample volume). The CO feed concentration in air was varied between 1 and 3 %v/v. During each test, the reactor temperature was stepwise increased: at each temperature, the CO conversion at steady-state was recorded.

3. Results and discussion Light-off curves: CO conversions obtained over the catalyzed fiber sample under typical conditions are plotted versus temperature in Fig. 3. At 2000 cm3 /min (STP) CO conversion was negligible at low temperatures, but started to become significant above 375 ◦ C. It asymptotically approached a value of about 90 % after light-off, and remained constant on further increasing the temperature up to almost 600 ◦ C. On increasing the flow rate, the light-off was delayed to higher temperatures, and the asymptotic CO conversion was reduced, though to a limited extent. The behavior of the data in Fig. 3 is in line with previous studies on the oxidation of carbon monoxide over catalytic foams (Giani et al., 2005a): the asymptotic CO conversion achieved after ignition suggests the onset of full external mass transfer control. This was further confirmed by additional runs (not reported), which indicated that the asymptotic CO conversion is independent of the CO feed concentration, as expected for the pseudo first-order kinetics associated with a diffusion-controlled regime, and opposite to the negative kinetic order of CO observed in a chemical regime.

100 90

Similar tests were repeated over other samples, providing reproducible results. Notably, the focus of the present work is on the catalytic activity under diffusional control, which is by definition unaffected by the details of the catalytic mechanism and is sensitive to catalyst deactivation only to a limited extent. It is worth noticing that CO conversions as high as 90 % and more were measured on passing a CO–air stream at high flow rates over a catalyzed fiber sample just 1 mm thick: this seems quite promising in view of the application of catalyzed micro-fiber elements to the design of compact reaction devices. Mass transfer coefficients: Mass transfer coefficients km were estimated from the CO conversions measured under diffusion-controlled conditions. Due to the small thickness of the catalyst sample and the steepness of the concentration profile, it was necessary to account also for axial dispersion in evaluating mass transfer coefficients. The following steady-state 1D pseudo homogeneous axial dispersion model was considered for the experimental reactor: v·

d2 C dC = Deff · 2 − km · SV · C dz dz

with boundary conditions:  ⎧  dC  ⎪  ⎪ − D · = v · C0 v · C ⎨ eff 0 dz 0  dC  ⎪ ⎪ ⎩ =0 dz L

2000 cm /min (STP)

CO conversion [%]

(5) at z = L

 v · df Deff = DM +  2·

(6)

Deff ranges from 0.5 to 0.75 cm2 /s, while the order of magnitude of the vessel dispersion number Deff /vL is less than 0.1 for the present experiments. The total amount of converted CO is then obtained from:  L S ˙ V = km · V · C · dz (7) m L 0 The analytical solution of Eqs. (4)–(7) was used to evaluate km as a function of the reaction conditions and of the CO conversion  according to: 0 ·L· CCO A2 SV · V A1 [exp(1 L) − 1] − [exp(2 L) − 1]

Qeff

1

80

(8)

2

where

70

A1 = 

60

1−

50 40

A2 = −A1 ·

30 20

Deff v

· 1

C0





Deff 1 · 1− · 2 · exp[(1 − 2 ) · L] − v 2

1 · exp[(1 − 2 ) · L] 2

(9)

(10)

and

10 0 200

at z = 0

As usual two mechanisms contribute to axial dispersion, related to the molecular diffusion DM and to the variations of the fluid velocity v induced by the packing, respectively. Both contributions were considered, and corrected taking into account void fraction  and tortuosity  (set to 1.5) of the catalytic system, as follows:

km =

3

(4)

250

300

350 400 450 500 Reactor temperature [°C]

550

600

Fig. 3. Measured CO conversions versus temperature. Feed flow rate = 2000 cm3 /min (STP). CO feed concentration = 1% v/v.

1,2 =

v

2 · Deff

  ±

v

2 · Deff

2 +

km · SV

Deff

(11)

Fig. 4 illustrates the estimates of km obtained from the runs at 1000–4000 cm3 /min (STP) over three replicated catalyzed fiber samples. As expected, the mass transfer coefficients increase with flow

G. Groppi et al. / Chemical Engineering Science 65 (2010) 392 -- 397

where Sh and Remax are based on the diameter of the foam struts ds , and Remax includes the interstitial velocity umax . Eq. (13) closely resembles classical correlations for heat transfer to banks of tubes (Incropera and De Witt, 1996) and for heat transfer in catalytic gauzes (Satterfield and Cortez, 1970). It is also similar to the correlation for gas/solid heat transfer in metallic foams that some of us derived from independent transient cooling experiments (Giani et al., 2005b). Eq. (13) applies for 12 ⱕ Remax ⱕ 200 and for foam porosity  ⱖ 0.84. Due to very small fiber diameters, Remax becomes lower than unity in metallic filters. Correspondingly, the observed dimensionless mass transfer coefficients are far lower than expected on extrapolating Eq. (13), as apparent from Fig. 5. Furthermore, the data for the catalytic fibers exhibit a stronger dependence on Re than in Eq. (13):

km [cm/min]

Sample 1 Sample 2 Sample 3

1000 0.6 km = 2.78⋅Qeff

100

10000

1000

0.33 Sh = 0.089Re0.72 max Sc

Qeff [cm3/min] Fig. 4. Estimates of CO mass transfer coefficients versus effective flow rate for three replicated sets of catalytic activity runs.

Sh/Sc0.33

10

1

0.1 Ceramic & metallic foams Metallic fibers

0.01 0.1

1

10

100

Remax Fig. 5. Dimensionless correlations of mass transfer coefficients in metallic filters and in ceramic and metallic foams.

velocity: with reference to Fig. 4, such a dependence can be represented by 0.68 km = 2.78Qeff

(12)

In the Qeff range of interest (∼2000–7000 cm3 /min) the numerical predictions of Eq. (12) differ by less than 22% from those obtained for 0.80 ), thus suggesting a simple plug-flow reactor model (km = 0.87Qeff that the impact of axial dispersion is relatively modest under the adopted experimental conditions. Dimensionless representation and comparison with foams: Fig. 5 presents mean values of the mass transfer coefficients in Fig. 4 plotted according to the same dimensionless representation used in previous work to correlate mass transfer coefficients in metallic and ceramic foams. In the case of foams, all the estimates of the mass transfer coefficients could be fitted in fact by a single dimensionless correlation (Groppi et al., 2007), 0.33 Sh = 0.91Re0.43 max Sc

395

15 < Remax < 200

(13)

0.25 < Remax < 1

(14)

This behavior reminds of the anomalously low heat and mass transfer coefficients measured in dense packed beds of fine particles or in fine wire packs at low Re ( < 10), which also exhibit approximately a first power dependence on Re (Kato and Wen, 1970; Nelson and Galloway, 1975). On the other hand, it appears also in line with the reduced external mass transfer rates reported by Cussler and coworkers in the case of hollow fibers at low Re, and attributed to bypass and channeling effects due to the random dispersion of fiber size and spacing. Notably, such a behavior significantly limits the enhancement of mass transfer rates in metallic fibrous mats expected from the orderof-magnitude increment of the surface area per unit volume SV with respect to foams discussed in the Experimental section. It should also be noted that Eq. (14) differs from Eq. (1) proposed in the literature for external mass transfer to catalyzed micro-fibers in a liquid/solid reacting system. Theoretical analysis: A predictive theory has been developed to explain the apparently different transport properties of foams and fibrous mats, based on an approach similar to the heuristic one used by Nelson and Galloway (1975), which relies on accounting for the influence of other surfaces when describing stagnant molecular diffusion to a dense assembly of spheres. On the contrary in the present case the geometry is represented by an assembly of cylinders, which however exhibit different internal geometrical organizations depending on the type of structure. In fact, foams are more ordered than fiber mats, and this results in a different exposure of the catalyst surface to flow. By analogy with the mentioned procedure, the starting equation is, in cylindrical coordinates:  1 * *c *c (15) DM r = r *r *r *t and the following boundary and initial conditions apply: ⎧ *c(R, t) ⎪ ⎪ =0 ⎨ *r c(r, t = 0) = c0 ⎪ ⎪ ⎩ c(r0 , t) = cS

(16)

where R = r0 /(1 − )1/2 . The physical significance of R is such that the void fraction of the fiber and its surrounding matches the void fraction of the system. By applying to Eq. (15) the Laplace transform and solving with respect to the conditions (16), the following expression can be derived: c¯ =

c K1 (qR)I0 (qr) + K0 (qr)I1 (qR) c0 + s s K1 (qR)I0 (qr0 ) + K0 (qr0 )I1 (qR)

(17)

Q2

G. Groppi et al. / Chemical Engineering Science 65 (2010) 392 -- 397

where q = s/ DM , I0 and I1 are modified Bessel functions of the first kind and order 0 and 1, respectively, while K0 and K1 are modified Bessel functions of the second kind and order 0 and 1, respectively. A similar solution can be found in Carslaw and Jaeger (2004) for the analogous problem of heat transfer inside an hollow cylinder. The time averaged mass transfer rate is of course defined as:   ¯ ¯J = −DM dc (18) dr r=r0

10 Ordered, χ = 1

The Sherwood number therefore is given by: Sh =

df · ¯J

DM · c

= df · q

K1 (qr0 )I1 (qR) − K1 (qR)I1 (qr0 ) K1 (qR)I0 (qr0 ) + K0 (qr0 )I1 (qR)

v 1 df Sc0.33

(19)

Ceramic & metallic foams Metallic filters

0.01 0.1

1

10 Remax

100

Fig. 6. Dimensionless correlation of mass transfer coefficients in metallic filters and in ceramic and metallic foams: solid lines are theoretical predictions from Eq. (22).

(20)

where  is a proportionality constant determined by Nelson and Galloway equal to 0.6. Sc0.33 is obtained from the ratio of the concentration and velocity boundary layer thicknesses as a well known result of boundary layer theory. The definition of s according to Eq. (20) allows also to avoid the inverse Laplace transform of ¯J. By rearranging Eq. (20):  s = df · q = Re0.5 Sc0.33 (21) df

DM

Under these assumptions Eq. (19) can be rearranged in: Sh = 2A1 A3 A1 = 0.3 · (Re)0.5 · Sc0.33

Random, χ = 1/3

0.1

The physical significance of s is that of a renewal frequency that, following Nelson and Galloway (1975), can be assumed proportional to the ratio of a characteristic velocity to a characteristic length. The latter is df whereas the velocity would be some characteristic velocity within the concentration boundary layer. Nelson and Galloway proposed therefore the following expression: s = 2

1

Sh/Sc0.33

396

A2 =

A1

(1 − )0.5 I1 (A2 ) · K1 (A1 ) − I1 (A1 ) · K1 (A2 ) A3 = I1 (A1 ) · K0 (A2 ) + I0 (A1 ) · K1 (A2 )

(22)

 is a geometrical order index ( = 1/3 for fibers and 1 for foams), taking into account the non-uniform orientation of the fiber in the direction of flow: probably most of the flow is parallel to the sections of fibers among their crosslinking. The comparison of this theory with experiments is illustrated in Fig. 6. It can be clearly observed that the developed theory covers both the problem of the prediction of the mass transfer coefficient for metallic and ceramic foams and that for metallic fibers. This original theoretical analysis explains the deviations of the mass transfer coefficients at low Reynolds numbers by accounting for the limitations to boundary layer development due to the proximity of other fibers in the densely packed system. 4. Conclusions Metallic fiber mats are interesting materials for catalyst supports in view of their high porosity, extremely high surface areas per unit volume and low thermal mass. As demonstrated in the present work, they can be made catalytically active by suitable coating/impregnation techniques, and can be advantageously applied to high-temperature processes with very fast chemical reaction rates, which are typically limited by mass transfer. Our data for CO oxidation are quite promising in view of such applications: conversions in excess of 90% have been in fact observed at very high space velocities of the order of 106 h−1 , corresponding to a catalytic bed depth of 1 mm only.

Nevertheless, based on the extrapolation of the mass transfer rates experimentally observed in open celled foams or theoretically predicted for a single fiber, one could actually expect even better performances. Indeed, we have shown that gas/solid mass transfer data for micro-fibers exhibit negative deviations from the behavior of foams, similar to those observed in packed beds of particles at very low Re numbers. A rationale is possibly to be sought in the influence of packing and sintering the fibers, which adversely affects the boundary layer development as compared to the ideal situation of a single fiber. A theory derived from this assumption, Eq. (22), has provided a successful predictive description of the experimental findings herein reported. Possible alternative explanations rely on the negative effects of flow channeling and bypass resulting from the random spacing and orientation of the fibers. Eqs. (13)–(22) are currently used to assess the relative merits of foams and fibrous mats as enhanced micro-structured catalyst supports for “fast” catalytic processes. Notation c c¯ c0 cs c = cs − c0 df

DM Deff

km L ˙V m Q Qeff r0 Re Remax s Sh Sc

concentration, kmol/m3 Laplace transformed concentration, kmol/m3 average fluid bulk concentration, kmol/m3 equilibrium interfacial concentration, kmol/m3 difference of concentration, kmol/m3 fiber diameter, m molecular diffusion, m2 /s effective dispersion coefficient, m2 /s mass transfer coefficient, m/s or cm/min filter thickness, m amount of converted CO, kmol/s volumetric flow rate (STP), m3 /s or cm3 /min volumetric flow rate at the operating conditions, m3 /s or cm3 /min = radius of the fiber ( = df /2), m v·d

Reynolds number  f v·d maximum Reynolds number ·f Laplace transform variable = renewal frequency, s−1 k d

m f Sherwood number D M  Schmidt number D M

G. Groppi et al. / Chemical Engineering Science 65 (2010) 392 -- 397

SV u v V

specific surface, m2 /m3 interstitial velocity superficial velocity reactor volume, m3

Greek letters

 1,2    

void fraction characteristic roots in Eq. (11) kinematic viscosity, m2 /s conversion tortuosity factor geometrical order index

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