Comparative Modeling Study on the Performance of Solid Foam as a

Ind. Eng. Chem. Res. 2010, 49, 5353–5366

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Comparative Modeling Study on the Performance of Solid Foam as a Structured Catalyst Support in Multiphase Reactors Patrick W. A. M. Wenmakers, John van der Schaaf, Ben F. M. Kuster, and Jaap C. Schouten* Laboratory of Chemical Reactor Engineering, EindhoVen UniVersity of Technology, P.O. Box 513, 5600 MB EindhoVen, The Netherlands

In this paper, the performance of two types of advanced foam packings (viz., Hairy Foam and washcoated Solid Foam) is compared with that of a packed bed of porous spherical particles. The comparison is done for two different types of reactions (viz., the slow hydrogenation of cinnamaldehyde and the fast hydrogenation of 3-methyl-1-pentyn-3-ol) and under two flow conditions (viz., upflow and downflow), in terms of selectivity, conversion, pressure drop, and reactor height. Under similar operating conditions, the simulation results show that, for both reactions, the Hairy Foam and Solid Foam packings reach higher selectivities and conversions than the packed bed of particles. However, in the case of the slow reaction, the pressure drop for the Hairy and Solid Foam packings is significantly larger than that for the bed of particles. This is due to the lower solids holdup, and thus lower catalyst concentration, of the Hairy Foam and Solid Foam packings. Therefore, larger reactors are required for the hairy foam and solid foam packings, resulting in a higher total pressure drop. Introduction Generally, the chemical industry is striving toward the use of more-efficient chemical reactors. To achieve this, (structured) packings are often used as a catalyst support. These packings increase the gas-liquid and liquid-solid interfacial areas and increase local turbulence, thus enhancing mass-transfer rates. The use of structured packings can increase the conversion and selectivity, when compared to the more conventional packed bed (e.g., porous spherical particles or Berl saddles). Many different types of structured packings have already been discussed in the literature, i.e., monoliths,1 Sulzer Katapak elements,2,3 cloths,4 and fibers.5 An excellent review describing different aspects of structured packings (e.g., mass-transfer characteristics, pressure drop, residence time distribution) is given by Pangarkar et al.6 The use of a packing also overcomes the cumbersome step of catalyst separation often encountered in slurry reactors. Another type of structured packing is the Solid Foam packing. Solid Foam is a highly porous open-cell material. Its structure resembles the inverse of a packed bed of spherical particles.7 The average cell size is often expressed in pores per linear inch (PPI) and can vary from 5 to 100 PPI, with porosities from 80% to 97%. Solid Foams are available in a wide variety of materials, e.g., ceramics, metals, plastics, and carbon (Figure 1). Solid Foam exhibits a low pressure drop compared to that for the conventional packed bed.8-15 Stemmet et al.10 also observed high gas-liquid mass-transfer rates, with values of kglagl of up to 0.6 ml3 mr-3 s-1 are reported. These mass-transfer rates are high because of the high interfacial surface area of the Solid Foam. However, the absence of micropores in carbon and metal foams results in a low surface area for catalyst deposition.7 The surface area of the Solid Foam can be increased by washcoating or by immobilization of a carbon nanofiber (CNF) layer.7,16-18 The combination of CNFs and Solid Foam resembles the inverse of a packed bed of spherical particles and is called Hairy Foam. The solid and void spaces of the porous packed bed are exchanged, which results in an open structure * To whom correspondence should be addressed. E-mail: [email protected]. Web site: www.chem.tue.nl/scr.

with a high external surface area. Instead of depositing the catalyst in the pores of the porous spherical particles, it can now be deposited on the external surface of the CNFs. The open structure of the fibers allows for liquid flow through the fibers, thus preventing diffusion limitation and increasing the liquid-solid mass-transfer rate.19 This work presents the modeling of multiphase reactors equipped with fixed-bed packings, such as the Solid and Hairy Foams. The reactor is modeled using the mixers-in-series approach. Gas-liquid mass transfer, liquid-solid mass transfer, and simultaneous diffusion and reaction in a porous support (without resorting to effectiveness factors) have been taken into account in the model. The work presents the strategy followed to solve the linked equations for the mole balances of the reactor (viz. convection and mass transfer) and the catalyst support (viz. diffusion and kinetics). The modeling results have been used to study the performance of the Hairy Foam catalyst support in comparison to a washcoated Solid Foam and to a packed bed of porous spherical particles. For this comparison, two different gas-liquid-solid reactions have been used: the slow hydrogenation of cinnamaldehyde described by Toebes et al.20 and the fast hydrogenation

Figure 1. Detail of a 10 PPI solid carbon foam with a porosity of 97% (ERG Materials and Aerospace Corp. Duocel). The detail shows the reticulated network of struts.

10.1021/ie900644e  2010 American Chemical Society Published on Web 04/30/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 11, 2010

r2 )

k2Cs,CALDKCALD 1+

∑C

s,jKj

k3Cs,HALDKHALD

r3 )

1+

r4 )

∑

Cs,jKj

k4Cs,CALCKCALC 1+

∑C

s,jKj

√Cs,H KH 1 + √Cs,H KH

(2)


(3)


(4)

2

2

2

2

2

2

with

∑CK

j j

Figure 2. Hydrogenation of (a) cinnamaldehyde as described by Toebes et al.20 and (b) 3-methyl-1-pentyn-3-ol as described by Nijhuis et al.21 Cinnamyl alcohol and the alkene compound have been chosen as the desired products.

of 2-methyl-1-pentyn-3-ol described by Nijhuis et al.21 The hydrogenation of cinnamaldehyde shows an activity of approximately 0.002 mmol gcat-1 s-1 under the studied conditions (a hydrogen partial pressure of 48 bar and a concentration of the reactants of 103 mol m-3, similar to those of Toebes et al.20). The hydrogenation of 3-methyl-1-pentyn-3-ol shows an activity of 5.5 mmol gcat-1 s-1.21 The intrinsic reaction rate of the fast hydrogenation of 3-methyl-1-pentyn-3-ol is thus approximately 2750 times higher than that of the slow hydrogenation of cinnamaldehyde. The performance of the packings is examined in terms of selectivity, conversion, pressure drop, and reactor height. Packings of different grades have been studied: 20, 45, and 60 PPI and 1, 3, and 5.6 mm for foam packing and spherical packings, respectively.

Reactor Modeling Reaction Kinetics. The performance of the Hairy Foam in terms of conversion, selectivity, and pressure drop was compared with that of the washcoated Solid Foam and a packed bed of porous spherical particles. Reaction schemes of the studied reactions are shown in Figure 2. The hydrogenation of cinnamaldehyde consists of a system of consecutive and parallel reactions; the hydrogenation of 3-methyl-1-pentyn-3-ol is made up of two consecutive reactions. These reactions allow for an analysis in terms of selectivity, where cinnamylalcohol and the alkene component have been chosen as the desired products.

) Cs,CALDKCALD + Cs,HALDKHALD + Cs,CALCKCALC + Cs,HALCKHALC (5)

where rj is the volumetric reaction rate, ki is the reaction rate coefficient, Cs, j is the concentration of component j in the catalyst, and Kj is the adsorption coefficient. The reaction rate of the 3-methyl-1-pentyn-3-ol hydrogenation is described as follows:21 r5 )

r6 )

k5NsKYCs,YCs,H2 1 + KYCs,Y + KECs,E + KACs,A k6NsKECs,ECs,H2 1 + KYCs,Y + KECs,E + KACs,A

(6)

(7)

where Ns is the number of adsorption sites. Reactor Model. The following assumptions were made for the reactor modeling of the different packings and the two reactions: • The hydrodynamics of the foam and spherical packings are described by the plug-flow model. • The temperature is constant throughout the reactor. • The pressure is constant in the reactor, i.e. the solubility of the gasses does not change along the reactor coordinate. • The reactor is operated in steady state, i.e. transient effects are not taken into account. • The liquid is nonvolatile, i.e., gas to liquid mass transfer is only taken into account for the gaseous component. Using the plug-flow reactor model, eqs 1-7 were solved. The plug-flow reactor was modeled using a tanks-in-series model (see Figure 3). A minimum of 100 mixers were used to obtain plug-flow conditions; this corresponds to a Peclet number of at least 199. For some conditions, 200 mixers were

The reaction rate of the cinnamaldehyde hydrogenation is described as follows:20

r1 )

k1Cs,CALDKCALD 1+

∑C

s,jKj

√Cs,H KH 1 + √Cs,H KH 2

2

(1)

Figure 3. Schematic representation of the mixers-in-series model. The detail shows the individual transfer steps used in the modeling, i.e., gas-liquid mass transfer, liquid-solid mass transfer, and simultaneous diffusion and reaction in the porous catalyst support.


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Table 1. Model Conditions and Results for the Hydrogenation of Cinnamaldehyde N

klsalsg klsalsl kglagl τr [min] [ml3 mr-3 s-1] [ml3 mr-3 s-1] [ml3 mr-3 s-1] εl [ml3 mr-3] τrmax,C [min]

S

X

-dp|total [×105 Pa] hreactor [m] ηmin

Packed Up dp ) 5.6 mm 100 100 dp ) 3 mm 100 dp ) 1 mm

100 100 100

0.06 0.15 0.77

0.03 0.08 0.43

dp ) 5.6 mm 100 100 dp ) 3 mm 100 dp ) 1 mm

100 100 100

0.05 0.12 0.52

0.03 0.07 0.30

NPPI ) 20 NPPI ) 45 NPPI ) 60

200 200 200

500 500 500

0.56 1.20 1.58

0.31 0.67 0.89


100 100 100

500 500 500

0.19 0.41 0.53

0.11 0.23 0.30


200 200 100

500 500 500

4.70 1.41 1.64

3.05 0.92 1.07

0.20 0.32 0.72

0.18 0.19 0.21

19 13 8

0.09 0.90 0.10 0.94 0.11 0.98

20.6 30.1 84.9

45.6 31.2 19.2

0.19 0.33 0.67

0.09 0.12 0.18

20 13 8

0.09 0.91 0.10 0.93 0.11 0.97

0.8 0.6 0.5

4.8 3.1 1.9

0.20 0.34 0.68

0.24 0.28 0.32

267.5 120 90

0.11 0.99 0.11 0.99 0.11 0.99

642.0 288.0 216.0

122.1 55.3 45.1

0.99 0.99 0.99

Packed Down 0.01 0.02 0.03 Solid Foam Up 0.38 0.38 0.38 Solid Foam Down 0.01 0.01 0.01

0.07 0.11 0.13

260 1200 90

0.11 0.99 0.11 0.99 0.11 0.99

43.2 43.2 43.2

7.4 7.4 7.4

0.99 0.99 0.99

0.24 0.28 0.32

135 110 65

0.11 0.99 0.11 0.99 0.11 0.99

324.0 264.0 156.0

61.6 50.7 32.6

naa naa naa

0.07 0.11 0.13

110 110 65

0.11 0.99 0.11 0.99 0.11 0.99

26.4 26.4 15.6

4.5 4.5 2.7

naa naa naa

Hairy Foam Up 0.38 0.38 0.38 Hairy Foam Down NPPI ) 20 NPPI ) 45 NPPI ) 60

100 100 100

500 500 500

0.93 0.47 0.75

0.60 0.30 0.49

0.01 0.01 0.01

a na ) not applicable. For Hairy Foam, it is assumed that the CNFs are in direct contact with the flowing liquid. Therefore, there is no diffusion with simultaneous reaction taking place.

Table 2. Model Conditions and Results for the Hydrogenation of 3-Methyl-1-pentyn-3-ol N

klsalsg klsalsl kglagl τr [min] [ml3 mr-3 s-1] [ml3 mr-3 s-1] [ml3 mr-3 s-1] εl [ml3 mr-3] τrmax,C [min]

S

X

-dp|total [×105 Pa] hreactor [m] ηmin

Packed Up dp ) 5.6 mm 100 100 dp ) 3 mm 100 dp ) 1 mm

30 30 10

0.03 0.07 0.38

0.02 0.04 0.22

0.18 0.29 0.65

dp ) 5.6 mm 100 200 dp ) 3 mm 200 dp ) 1 mm

30 30 30

0.02 0.05 0.21

0.01 0.03 0.12

0.01 0.02 0.03

0.26 0.27 0.30

2.7 1.2 0.4

0.67 0.76 0.68 0.73 0.66 0.81

2.2 2.2 3.4

6.5 2.9 1.0

0.01 0.01 0.04

0.12 0.17 0.22

4.8 2.9 1.2

0.82 0.81 0.84 0.86 0.87 0.90

0.2 0.1 0.1

1.2 0.7 0.3

0.01 0.02 0.05

0.28 0.31 0.37

0.9 0.5 0.4

0.76 0.88 0.75 0.89 0.75 0.88

0.3 0.2 0.2

2.2 1.2 1.0

0.11 0.13 0.14

0.08 0.12 0.13

12.0 11.4 11.4

0.92 0.95 0.92 0.96 0.92 0.97

0.4 0.4 0.4

2.9 2.7 2.7

0.07 0.07 0.07

0.28 0.31 0.37

0.2 0.3 0.2

0.89 0.94 0.87 0.92 0.85 0.91

0.1 0.1 0.1

0.5 0.6 0.5

naa naa naa

0.08 0.12 0.13

12.0 11.4 11.7

0.92 0.98 0.93 0.97 0.92 0.98

0.4 0.4 0.4

2.9 2.7 2.8

naa naa naa

Packed Down

Solid Foam Up NPPI ) 20 NPPI ) 45 NPPI ) 60

100 100 100

10 10 10

0.22 0.47 0.62

0.12 0.27 0.35


100 100 100

60 60 60

0.07 0.16 0.21

0.04 0.09 0.12


100 100 100

5 5 5

2.47 0.74 0.86

1.63 0.49 0.57

0.26 0.26 0.26 Solid Foam Down 0.002 0.002 0.002 Hairy Foam Up 0.26 0.26 0.26 Hairy Foam Down


100 100 100

60 30 30

0.49 0.25 0.40

0.32 0.16 0.26

0.002 0.002 0.002

a na ) not applicable. For Hairy Foam, it is assumed that the CNFs are in direct contact with the flowing liquid. Therefore, there is no diffusion with simultaneous reaction taking place.

needed to obtain convergence of the numerical solution (see Tables 1 and 2). Because the liquid was assumed to be

nonvolatile, the gas-to-liquid mass transfer was taken into account only for hydrogen. The liquid-to-solid mass transfer

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was considered for all components present in the liquid. This yields the following set of mole balances for the liquid phase in mixer n:

(

)

pg 1 n-1 n n n i,n - Cl,j )0 (Cl,j - Cl,j ) - klsals(Cl,j - Cs,j ) + ... + kglagl τm H gaseous component (8)

1 n-1 i,n (C - Cnl,j) - klsals(Cnl,j - Cs,j ))0 τm l,j liquid-phase component (9) where τm is the residence time of the liquid phase per mixer, Cl,n j the liquid-phase concentration of component j in mixer n, klsals the liquid-solid mass-transfer coefficient, Cs,i, nj the concentration of component j at the liquid-solid interface in mixer n, kglagl the gas-liquid mass-transfer coefficient, pg the partial pressure of the gaseous component in the gas phase, and H the Henry coefficient. The properties of pure hydrogen gas were used in the calculations; therefore, the partial pressure is not a function of the reactor coordinate. In the cases of the washcoated Solid Foam and the packedbed reactor, the reaction takes place in the porous catalyst layer. For these cases, the transient reaction-diffusion equations have been solved with the appropriate boundary conditions. The steady-state reaction-diffusion equations are boundary value problems that have multiple numerical solutions. To obtain the physically correct solution, the transient reaction-diffusion equations have been solved using a coarse time grid. The span of the time grid was long enough to obtain the steady-state solution, which was used for further calculations. The transient reaction-diffusion equations are given as follows:

(

)

∂Cs,j 1 ∂ 2 ∂Cs,j ) 2 2 θ De - Rs,j ∂t ∂θ ∂θ Rp θ

spherical particles

(10) ∂Cs,j De ∂2Cs,j ) 2 - Rs,j ∂t δ ∂θ2

(11)

washcoat

where Cs,j is the radial concentration of component j in the catalyst, t the time, Rp the particle radius, θ the dimensionless radial coordinate of the catalyst particle, De the effective diffusivity in the catalyst, Rs,j the reaction rate of component j, and δ the washcoat layer thickness. The effective diffusivity in the catalyst is approximated by22 De ) Dεp2

(12)

where D is the diffusivity in the liquid phase and εp is the porosity of the spherical particles or the washcoat. The boundary conditions for eq 10 are as follows: ∂C )0 ∂θ

θ ) 0;

θ ) 1;

-

|

n 12Deεs ∂Cs,j ∂θ θ)1 dp2

|

θ)1

n ) klsals(Cnl,j - Cs,j |θ)1) (14b)

(15)

where Rv,j is the reaction rate of component j per unit of reactor volume. The kinetics of Toebes et al.20 and Nijhuis et al.21 are based on the catalyst volume, whereas a reactor volume based reaction rate is required for eq 15. The reaction rate was converted to the reactor volume by scaling with respect to the volumetric specific surface area of the catalyst: RHF v,j ) Rv,j

SHF BETFHF ref Sref BETFcat

(16)

where RHF v,j is the volumetric reaction rate for the Hairy Foam per unit of reactor volume, Rv,j the volumetric reaction rate calculated according to eqs 1-7, SHF BET the Brunauer-EmmettTeller (BET) surface area of the Hairy Foam, FHF the density of the Hairy Foam, Sref BET the BET surface area of the reference catalyst used by Toebes et al.20 and Nijhuis et al.,21 and Fref cat the density of the reference catalyst. Model Solution Strategy. The balances shown in eqs 8 and 9 are connected to the boundary conditions described in eqs 13b and 14b. This does not allow for a direct solution of the concentration profiles. Equations 1-15 have been solved according to the algorithm presented in Figure 4. As a first n estimate, the liquid bulk concentration of one mixer, Cl,j , is set n-1 to the outlet concentration of the previous mixer, Cl,j . Subsequently, the liquid-solid interfacial concentration is calculated. For the washcoated Solid Foam and the packed bed, this is done by solving the transient diffusion-reaction equation shown in eqs 10 and 11. For the Hairy Foam, the liquid-solid interfacial concentration is obtained from eq 15. Next, the liquid concentrations are calculated by means of the mole balance of the particular mixer: pg 1 n-1 i Cl,j + klsalsCs,j + kglagl τ H m Cnl,j ) 1 + klsals + kglagl τm

gaseous component

(17) 1 n-1 i C + klsalsCs,j τm l,j ) 1 + klsals τm

liquid-phase component

(18)

The boundary conditions in the case of the washcoat are ∂C )0 ∂θ

n Deaf ∂Cs,j δ ∂θ

i klsals(Cl,j - Cs,j ) ) Rv,j

Cnl,j

) klsals(Cn,j - Cn,j | θ)1)

-

In the case of the Hairy Foam packing, it is assumed that there is convective flow through the CNFs, which prevents diffusion limitation.7,19 Model calculations using Darcy’s law for porous media show that velocities of 1 × 10-5-3 × 10-3 m s-1 can be induced in the CNF layer when it is exposed to an external flow.23 Because there is no diffusion limitation, the concentration is uniform throughout the CNF layer and the interface concentration for the Hairy Foam is obtained by solving the following mole balances:

(13a)

(13b)

θ ) 0;

θ ) 1;

(14a)

The calculated liquid-phase concentration is compared with the initial guess. If the relative deviation is larger than 10-4, the bulk liquid concentration obtained in this iteration is used as the initial guess for the next iteration. If the relative deviation is less than 10-4, the bulk liquid concentration and


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Figure 4. Flowchart of the algorithm used to calculate the concentration profiles in the reactors studied in this work.

the concentration profiles inside the particles are stored and the calculation proceeds with the next mixer. This procedure is repeated for all mixers. The model calculation time of the concentration profiles inside the particles was significantly reduced by using the concentration profile of the previous iteration as the initial conditions for eqs 10 and 11. In the case of the packed bed with 5.6-mm spherical particles under upflow conditions, the total calculation time was 83 times longer than when the concentration profile of the previous iteration was used as the initial condition. The liquid-solid and gas-liquid mass-transfer coefficients, the pressure drop, and the liquid holdup have been obtained from existing correlations in the literature. These correlations are presented in the Appendix. The values obtained from the correlations and used in the calculations are shown in Tables 1 and 2. The physical properties of the fluids and the inlet concentrations used in the calculations are shown in Table 3. For Hairy Foam, no data are available, with respect to the hydrodynamics of the gas-liquid flow through the Hairy Foam, i.e., holdup and pressure drop. Therefore, the correlations for the Solid Foam, as presented in the Appendix, were used for the calculation of the hydrodynamic parameters. This is considered to be justified because Edouard et al.24 have shown that SiC nanofibers on SiC foam did not have a significant influence on the pressure drop.

The kinetic data for the hydrogenation of cinnamaldehyde and 3-methyl-1-pentyn-3-ol have been obtained from Toebes et al.20 and Nijhuis et al.,21 respectively. Both authors have correlated their experimental data to a diffusion-reaction model and have validated that the external mass-transfer limitation was absent. Therefore, the kinetic data presented by the authors are the intrinsic kinetic data devoid of the diffusion limitation and external mass-transfer limitation. The parameters used in the kinetic models (eqs 1-7) are shown in Table 3. Equations 8-15 have been solved using Matlab software. The partial differential equations shown in eqs 10 and 11 have been solved using the pdepe solver of Matlab. For the case of the hydrogenation of cinnamaldehyde, an evenly spaced grid of 20 elements was sufficient to obtain a smooth solution, without oscillations, of the concentration profile inside the particles. For the case of the hydrogenation of 3-methyl-1-pentyn-3-ol, a spatial grid of 155 elements was needed. The spatial grid between θ ) 0.99 and 1 was exponentially spaced in order to obtain a high density of grid points near the liquid/solid interface. Between θ ) 0 and θ ) 0.9, the grid was evenly spaced. The reactor models have been solved for two hydrodynamic regimes: cocurrent upflow and cocurrent downflow of the gas and liquid. In the case of cocurrent upflow, a superficial liquid velocity, ul, of 0.04 ml3 mr-2 s-1 and a superficial gas velocity, ug, of 0.4 mg3 mr-2 s-1 were used. Packed beds are operated in the bubble-

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Table 3. Parameters Used in the Model Simulations cinnamaldehyde Fl [kg ml-3] µl [×10-3 Pa s] Fg [kg mg-3] µg [×10-6 Pa s] DH [×10-9 ml3 mi-1 s-1] DL [×10-9 ml3 mi-1 s-1] εb [mvoid3 mp-3] εf [mvoid3 mp-3]c H [×104 ml3 Pa mol-1] pg [×105 Pa] Cl0 [mol ml-3] k1 [mol mcat-3 s-1]f k2 [mol mcat-3 s-1]f k3 [mol mcat-3 s-1]f k4 [mol mcat-3 s-1]f KCALD [mcat3 mol-1]f KHALD [mcat3 mol-1]f KCALC [mcat3 mol-1]f KH [mcat3 mol-1]f k5 [mcat3 mol-1 s-1]g k6 [mcat3 mol-1 s-1]g KY [mcat3 mol-1]g KE [mcat3 mol-1]g KA [mcat3 mol-1]g Ns [mol mcat-3]h FHF [kg mr-3] Toebes Fref [kg mr-3]i Nijhuis Fref [kg mr-3] 20 PPI SBET [m2 kg-1] 45 PPI SBET [m2 kg-1] 60 PPI SBET [m2 kg-1]

705a 0.30a 5.8a 10.9a 4.25b 1.79b 0.6 0.97 3.08d 48 300 26.7 3.5 4.3 0.27 18 5.7 18 10

3-methyl-1-pentyn-3-ol 789 1.2 0.33a 9.12a 2.05b 0.895b 0.6 0.97 2.76e 4.053 32

4.78 × 105 4.78 × 105 0.31 0.0071 0.011 2.073 × 10-5 60 800 300 68 × 103 67 × 103 122 × 103

a

Determined using Aspen Plus software, with the SoaveRedlich-Kwong base method. b Determined by the estimation method of Wilke and Chang.29 c Porosity used for the simulation of Solid Foam and Hairy Foam packings. d Obtained from Brunner.30 e Obtained from Carius.31 f Obtained from Toebes et al.20 The kinetic data reported by Toebes et al. are presented in units of mol mcat-3 s-1; however, their data show that this should be mol mcat.-3 min-1. The kinetic data are reported for a reaction temperature of T ) 383 K. g Obtained from Nijhuis et al.21 The kinetic data are reported for a reaction temperature of T ) 298 K. h Calculated based on the data from Nijhuis et al.21 i Obtained from Lee et al.32

flow regime under these conditions.17 In the case of cocurrent downflow, a superficial liquid velocity of 0.004 ml3 mr-2 s-1 and a superficial gas velocity of 0.04 mg3 mr-2 s-1 were used. Packed beds (in the case of downflow, also called trickle beds) are operated in the trickle-flow regime under these conditions.25 Stemmet et al.10 have studied the gas-liquid mass transfer for foam packings at the superficial velocities used for both hydrodynamic cases. Typical particle diameters for packed beds are in the range of 1-10 mm.26 For this study, particle diameters of 1, 3, and 5.6 mm were used, where 5.6 mm corresponds to the cell size of a 20 PPI Solid Foam27 and has been chosen as the upper limit for the particle diameter. Wenmakers et al.19 have studied the liquid-solid mass transfer for Hairy Foams of 20, 45, and 60 PPI. Therefore, Solid Foams of 20, 45, and 60 PPI were used for the foam packing simulations. In the case of a washcoated Solid Foam, a washcoat thickness of 20 µm was used.11 The total residence time of the reactor (τr) was varied for the different simulations, to ensure that the reaction is close to completion and that the solution is smooth (see Tables 1 and 2 for the values of τr). The change in residence time of the reactor does not impede the plug flow assumption. The plug flow behavior is determined by the total number of mixers, rather than by the residence time per mixer, as can be seen from the relation Bo ) 2(nmixers - 1).28 Results A typical example of the liquid-phase concentration as a function of the reactor coordinate is shown in Figure 5a for a

packed bed of 5.6 mm spherical particles in the case of the hydrogenation of cinnamaldehyde. The graph shows the concentration profiles that are typical for consecutive reactions, showing a local maximum for the intermediate products (CALC and HALD) and reaching full conversion to the final product (HALC). For analysis of the reactor performance, the selectivity, conversion, pressure drop, and reactor height have been determined for the space time with the maximum concentration of the desired product. Figure 5b shows an example of a concentration profile inside a catalyst particle for the hydrogenation of cinnamaldehyde in the case of the packed bed of 5.6 mm spherical particles. The concentration profile is plotted for τr ) 19 min, which is the space time at which a maximum value for the CALC concentration is obtained for this case. The graph reveals the presence of significant concentration gradients within the catalyst particles, indicating that diffusion resistances are significant in this case. Hydrogenation of Cinnamaldehyde (Slow Reaction). To assess the efficiency of the catalyst, the effectiveness factor of the porous catalyst support was calculated. The effectiveness factor was calculated based on the reaction rate of hydrogen, according to

η)

Rp-3

∫

R 2

0

r Rs,H2 dr

Rs,H2 int

η)

δ-1

∫

δ

0

spherical particle

Rs,H2 dz

washcoat

Rs,H2 int

(19)

(20)

Figure 6 shows the minimum observed effectiveness factor for the Solid Foam, the trickle bed, and the packed bed for the hydrogenation of cinnamaldehyde. The effectiveness factor for the Solid Foam is approximately unity for all cases. In the case of the spherical particles (i.e., trickle bed and packed bed), the effectiveness factor is significantly lower than unity. This shows that diffusion resistances significantly reduce the reaction rate. The effectiveness factor increases as the particle diameter decreases, as expected. The high effectiveness for the Solid Foam can be attributed to the size of the washcoat, which is 20 µm. The particle size of the trickle bed and the packed bed is at least 50 times larger, resulting in diffusion limitation. The influence of the rates of gas-liquid and liquid-solid mass transfer on the reaction rate was examined for all reactor packings. The influence of gas-liquid mass transfer was examined based on the liquid concentration of hydrogen. In the case of gas-liquid mass-transfer limitations, the liquid concentration of hydrogen should be ∼0. For the hydrogenation of cinnamaldehyde, the liquid concentration of hydrogen was significantly larger than 0 for all reactor packings. In most cases, the liquid concentration was similar to the saturation concentration (which is defined as pg/H). This indicates that gas-liquid mass-transfer limitations are not present. The influence of the liquid-solid mass transfer was examined using the Mears criterion:

|

Rs,H2|bulk - Rs,H2|obs Rs,H2|bulk

|

< 0.05

(21)

where RH2|bulk is the reaction rate of hydrogen under bulk liquid conditions and RH2|obs is the actual observed reaction rate. The criterion is calculated for hydrogen, which is the component with the highest mass-transfer coefficient. The Mears criterion


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Figure 5. Concentration profiles for the hydrogenation of cinnamaldehyde in a cocurrent upflow packed-bed reactor with 5.6-mm-diameter particles. (a) Liquid-phase concentration profile along the reactor coordinate. The solid circle (b) indicates the location of the maximum concentration of cinnamyl alcohol, τr ) 19 min. (b) Concentration profile inside a catalyst particle at τr ) 19 min. The graph shows that concentration gradients are present within the particle, which illustrates that diffusion has a significant contribution to the reaction rate. The effectiveness factor for hydrogen for the packed bed with 5.6-mm-diameter particles at τr ) 19 min is η ) 0.202 (s).

Figure 6. Minimum effectiveness factor for the hydrogenation of cinnamaldehyde. The minimum effectiveness factor is determined between τ ) 0 min and the location of the maximum concentration of cinnamylalcohol. The effectiveness factor for the foam packings is approximately unity, showing that diffusion resistances are absent. For the packed bed and the trickle bed, significant diffusion resistances are present. Legend: FD ) Solid Foam downflow, TB ) trickle bed, FU ) Solid Foam upflow, PB ) packed bed upflow.

was calculated over the complete reactor coordinate. For all packings, except the Hairy Foam packing, the Mears criterion was not met, indicating that liquid-solid mass transfer significantly influences the reaction rate. The Hairy Foam packing showed no liquid-solid mass-transfer limitations whatsoever. Figure 7 shows the model simulation results obtained for the hydrogenation of cinnamaldehyde, with respect to selectivity, conversion, total pressure drop, and reactor height. Figure 7a shows that the selectivity for the Hairy Foam and the Solid Foam packings, SCALC ≈ 0.11, is slightly higher than that for the trickle bed and the packed bed (SCALC ≈ 0.097). The selectivity is approximately the same for all foam packings and does not vary significantly for different PPI numbers. The high selectivity for the Hairy Foam and the Solid Foam can be attributed to the absence of diffusion limitations. The selectivity in the trickle bed and in the packed bed increases as the particle diameter

decreases, which can be attributed to the increasing effectiveness factor with decreasing particle diameter. Figure 7b shows that the conversion of cinnamaldehyde is approximately the same for all foam packings (XCALD ≈ 0.99). The conversion is lower for the trickle bed and the packed bed (XCALD ≈ 0.94). The conversion for the trickle bed and packed bed increases as the particle diameter decreases, which is due to the reduced contribution of diffusion for decreasing particle diameter. Figure 7c shows the total pressure drop (static + frictional) for all packings. The graph shows that the pressure drop is significantly lower for the downflow configuration, up to ∆p ) 7.4 bar, than for the upflow configuration (up to ∆p ) 122 bar). Figure 7d shows that the reactor height required to obtain the maximum concentration of the desired product is also the lowest for the downflow configuration. This is due to a significant contribution of the kinetics to the reaction rate. Therefore, the total space time is approximately the same for the upflow and downflow configurations. However, the liquid velocity is higher for the upflow configuration. This results in larger reactors for the upflow configuration, and thus gives a higher pressure drop. The lowest pressure drop and reactor height, in the case of downflow, are obtained for the trickle bed. For the upflow configuration, the packed bed shows the lowest pressure drop and the lowest reactor height, except for particles 1 mm in size, which show a high pressure drop. The lower pressure drop and reactor height for the trickle bed and packed bed are due to the higher solids holdup. An estimation can be made for the amount of catalyst that is present in the reactor using the calculated reactor height of all packings. A weight percentage of 2 wt % catalyst and a solid density of 710 kg m-3 of the porous catalyst support (i.e., the density of the solid phase in the particle or washcoat) were obtained. The results of this analysis are shown in Figure 8. The graph shows that the Hairy Foam in downflow configuration requires the least amount of catalyst, whereas the packed bed requires the highest amount of catalyst. For all cases, it is seen that the foam packings require less catalyst than the packed and trickle beds. The required amount of catalyst is expressed in weight per projected area of the reactor. The required production

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Figure 7. Selectivity, conversion, total pressure drop, and reactor height for different reactor packings used for the hydrogenation of 3-methyl-1-pentyn-3-ol. (a) The selectivities are approximately the same for the Hairy and Solid Foams in the case of downflow. The selectivity of the trickle bed is slightly lower than that of the Hairy and Solid Foams in the case of downflow. In the case of upflow, the selectivity of the Hairy Foam is higher than that of the Solid Foam and the packed beds. (b) The conversion is approximately the same for the Hairy and Solid Foams in the case of downflow. The conversion for the Hairy Foam is higher than that for the Solid Foam and the packed bed in the case of upflow. (c) The total pressure drop, in the case of downflow, is higher for the Hairy and Solid Foams than for the trickle bed. In the case of upflow, the Hairy Foam shows the lowest pressure drop. The packed bed shows a significantly higher pressure drop than the Hairy and Solid Foams. (d) The reactor height for the trickle bed is significantly lower than that for the Hairy and Solid Foams in the case of downflow. The Hairy Foam shows the lowest reactor height for the upflow configuration, and the packed beds of 5.6 and 3 mm particles show the highest reactor height. HD ) Hairy Foam downflow; FD ) Solid Foam downflow; TB ) trickle bed; HU ) Hairy Foam upflow; FU ) Solid Foam upflow; PB ) packed-bed upflow.

rate will determine the projected area and, hence, also the required amount of catalyst. Hydrogenation of 3-Methyl-1-pentyn-3-ol (Fast Reaction). Figure 9 shows the minimum observed effectiveness factor for the Solid Foam packing, the packed bed, and the trickle bed. The graph shows that in all cases significant diffusion limitations are present, η < 0.14. The Solid Foam packing shows a slightly lower diffusion limitation than the packed bed. The effectiveness factor for the packed and trickle beds increases with decreasing particle diameter, as expected. The effectiveness factor for the Solid Foam in downflow is not dependent on the PPI number, whereas for the Solid Foam in upflow, the effectiveness factor increases with increasing PPI number. The packed bed and the Solid and Hairy Foam packings in the upflow configuration do not show any significant influence of gas-liquid mass transfer. For the trickle bed, a significant drop in the hydrogen liquid concentration is observed. However, the concentration does not drop below

23% of the saturation concentration. The liquid concentration in the case of the Solid and Hairy Foam packings operated in downflow reaches values below 2% of the saturation concentration, except for the 20 PPI Solid Foam, which reaches 6% of the saturation concentration. This shows that gas-liquid mass-transfer limitation is present for the Hairy and Solid Foams in the case of the downflow configuration. All of the packings did not meet the Mears criterion shown in eq 21, indicating that, for all packings, liquid-solid mass transfer significantly influences the reaction rate. Figure 10 shows the model simulation results for the hydrogenation of 3-methyl-1-pentyn-3ol. Figure 10a shows that the selectivity in the case of the Foam packings is approximately the same (Salkene ≈ 0.9) for the downflow configuration. In the case of Hairy Foam, there is no diffusion limitation, resulting in the high selectivity. In the case of Solid Foam, the low liquid-solid mass-transfer rate limits the concentration of the reactants in the washcoat, thus limiting the production of the undesired product. The selectivity for the trickle bed is slightly


Figure 8. Amount of catalyst in the reactor for the hydrogenation of cinnamaldehyde. The amount of catalyst in the reactor is the lowest for the Hairy Foam in both the downflow and upflow configurations. Legend: FD ) Solid Foam downflow, TB ) trickle bed, FU ) Solid Foam upflow, and PB ) packed bed upflow.

Figure 9. Minimum effectiveness factor for the hydrogenation of 3-methyl1-pentyn-3-ol. The minimum effectiveness factor is determined between τ ) 0 min and the location of the maximum concentration of 3-methyl-1penten-3-ol. The effectiveness factor is much smaller than unity, showing that diffusion resistances are present for all cases.

lower, because of significant diffusion limitations. In the case of the upflow configuration, the highest selectivity is obtained for the Hairy Foam packing, Salkene ≈ 0.9, as a result of the absence of diffusion limitation. The packed bed shows the lowest selectivity, Salkene ≈ 0.67. No significant effect of PPI number on the selectivity is observed for the downflow configuration. The selectivity increases as the particle diameter decreases, in the case of the trickle bed. In case of the packed bed, no significant effect of particle diameter is observed. Figure 10b shows the conversion for all packings. The highest conversion is obtained using Hairy Foam and Solid Foam under downflow conditions (Xalkyne ≈ 0.97). This is due to the absence of diffusion limitations, in the case of the Hairy Foam. In case of the Solid Foam, the low liquid-solid mass-transfer rate limits the supply of reactants to the catalyst, preventing the formation of the undesired product. The conversion obtained with the trickle bed is lower, Xalkyne ) 0.81-0.9, which is due to severe diffusion limitations. In the case of the upflow condition, the highest conversion is obtained using 20 PPI Hairy Foam, Xalkyne ≈ 0.93. The conversion for the Solid Foam under the upflow condition is 0.88. The lowest conversion is obtained for the packed bed (Xalkyne ) 0.73-0.81). The severe diffusion limita-

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tions significantly reduce the reaction rate, in the case of the packed bed. Figure 10c shows the total pressure drop for all packings. The pressure drop for the packed bed is significantly higher than that for the other packings: ∆p ) 2.2-3.4 bar. This is due to the higher frictional pressure drop and the higher residence time. In the case of the downflow configuration, the lowest pressure drop is obtained using the trickle bed, which is due to the low residence time. The pressure drops of the Hairy Foam and the Solid Foam packings are approximately the same in the case of the downflow configuration, ∆p ≈ 0.42 bar. The lowest pressure drop is obtained using the Hairy Foam packing in the upflow configuration, ∆p ≈ 0.08 bar. Figure 10d shows the reactor height for all packings. The graph shows that the lowest reactor height is obtained for the Hairy Foam and for the trickle bed of 1 mm particles: hreactor ) 0.2-0.6 m. The Solid Foam in the upflow configuration shows a slightly higher reactor height, which decreases as the PPI number increases. The Hairy Foam and Solid Foam packings in the downflow configuration have approximately the same reactor height: hreactor ≈ 2.8 m. The reactor height of the packed bed significantly decreases as the particle diameter decreases: hreactor ) 0.96-6.5 m for particle diameters of 1-5.6 mm. Figure 11 shows the required weight of the catalyst for the different packings. The graph shows that the Hairy Foam and Solid Foam in the downflow configuration require the least amount of catalyst. For all cases, it is seen that the foam packings require less catalyst than the packed bed and trickle bed. Model Sensitivity. The results presented above for the hydrogenation of cinnamaldehyde and 3-methyl-1-pentyn3-ol are obtained by solving the equations presented in the reactor modeling section and the correlations shown in the Appendix. The validity of the modeling results depends on the accuracy of the correlations used to determine, e.g., the mass-transfer coefficients. Because almost no systems showed any gas-liquid mass-transfer limitations, the effect of the gas-liquid mass-transfer correlation on the results is minimal. In the case of the hydrogenation of 3-methyl-1-pentyn-3-ol for the downflow configuration of the Hairy Foam and the Solid Foam, gas-liquid mass-transfer limitations are observed. In this case, the accuracy of the gas-liquid masstransfer correlation directly reflects on the results obtained from the simulations. Especially, the required reactor lengthsand, hence, the pressure dropswill be directly influenced by a change in the gas-liquid mass-transfer rate. For almost all cases, a significant contribution of liquid-solid mass transfer to the overall reaction rate is observed. For all these cases, a change in the liquid-solid mass-transfer rate influences the required reactor length and the pressure drop. Also, some effect on the selectivity can be expected, because the liquid-solid mass transfer has significant influence on the liquid-solid interfacial concentration and, therefore, also on the diffusion-reaction phenomena. The accuracy of the pressure drop for all packings is directly related to the accuracy of the pressure drop correlations that were used and, for most cases, also to the accuracy of the liquid-solid masstransfer correlations. Conclusions Packing Comparison. In this paper, we have compared the performance of three types of reactor packings for two different types of reactions (viz., the slow hydrogenation of cinnamaldehyde and the fast hydrogenation of 3-methyl-1-pentyn-3-ol) and two flow conditions (viz., upflow and downflow). The results of this comparison are summarized below.

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Figure 10. Selectivity, conversion, total pressure drop, and reactor height for different reactor packings used for the hydrogenation of 3-methyl-1-pentyn3-ol. The selectivity (a) and the conversion (b) are approximately the same for the Hairy Foam and the Solid Foam in the case of downflow, and higher than for the trickle bed. In the case of upflow the selectivity and the conversion of the Hairy Foam is higher than of the Solid Foam and the packed beds. The total pressure drop (c) and reactor height (d), in the case of downflow, is higher for the Hairy Foam and the Solid Foam than for the trickle bed. In the case of upflow, the Hairy Foam shows the lowest pressure drop and reactor height. The packed bed shows a significantly higher pressure drop than the Hairy Foam and the Solid Foam. HD ) Hairy Foam downflow; FD ) Solid Foam downflow; TB ) trickle bed; HU ) Hairy Foam upflow; FU ) Solid Foam upflow; PB ) packed bed upflow.

Figure 11. Amount of catalyst present in the reactor for different reactor packings for the hydrogenation of 3-methyl-1-pentyn-3-ol. The Hairy Foam packing in the upflow configuration requires significantly less catalyst than the other packings.

Hydrogenation of cinnamaldehyde (slow reaction): (1) The selectivity and conversion are slightly higher for the Hairy Foam and the washcoated Solid Foam than for the packed bed and the trickle bed for both upflow and downflow. (2) The pressure drop is significantly lower for the downflow configuration than for the upflow configuration, with trickle beds showing the lowest pressure drop, ∆P ) 0.52-0.83 bar. In the case of upflow, the pressure drops for all packings overlap to a large extent, ∆P ) 20.5-122 bar. (3) The reactor height is significantly lower for the downflow configuration than for the upflow configuration, with trickle beds showing the lowest reactor height: 1.9-4.8 mr. In the case of upflow, packed beds show the lowest reactor height (19.2-45.6 mr), which is still unrealistically high. (4) The effectiveness factor for washcoated Solid Foam packings is close to unity for all cases, showing that diffusion does not significantly influence the reaction rate. The effectiveness factors for the packed and trickle beds range from 0.19 to 0.68, showing that, in this case, diffusion limitation does occur.


(5) The Hairy Foam packing operated in downflow requires the least amount of catalyst: 7.3-7.7 kg mr-2. The packed beds require the largest, unrealistic, amount of catalyst: 167-396 kg mr-2. (6) No gas-liquid mass-transfer limitations were observed for all reactor packings. (7) No liquid-solid mass-transfer limitations were observed for the Hairy Foam packings, in both upflow and downflow. For all other packings, the liquid-solid mass transfer has a significant contribution to the overall reaction rate. Hydrogenation of 3-methyl-1-pentyn-3-ol (fast reaction): (1) The selectivity and conversion are the highest for the Hairy and Solid Foams operated in the downflow configuration. The Hairy Foam shows the highest selectivity and conversion during upflow conditions. (2) The pressure drop is

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