Evaluation on the Dependence of Multiphase Flow and Reaction upon

Ind. Eng. Chem. Res. 2007, 46, 8459-8470

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Evaluation on the Dependence of Multiphase Flow and Reaction upon the Morphology of a Porous Media Network Zhen-Min Cheng,* Xiang-Chen Fang,† Zhi-Ming Zhou, Zi-Bin Huang, and Wei-Kang Yuan State Key Laboratory of Chemical Engineering, UNILAB Research Centre of Chemical Reaction Engineering, East China UniVersity of Science and Technology, Shanghai 200237, P. R. China

A fixed-bed reactor or a catalyst particle can be considered as a porous media network, which is characterized by the pellet size, void fraction, and connectivity of the network. In a fixed-bed reactor, the percolation threshold was calculated to be 0.13-0.17, while the porosity of a fixed bed is ∼0.38; therefore, there is no percolation problem and a fixed bed can be modeled as a continuum medium. In multiphase flow, the connectivity of the network is much reduced due to the attachment of liquid film on the particles and an analogy was made between a trickle bed and a Bethe tree. It shows from this work that radial velocity profile estimation in a fixed bed could be obtained from transforming the bed space into a tube of a certain equivalent diameter, and the trickling to pulsing flow transition could be explained from its analogy to a Bethe tree. Electrical capacity tomography was employed to measure the dynamic liquid holdup in pulsing flow. Two types of packing have been identified from their different flooding behavior, and a quadralobe extrude was specifically designed to obtain the high flooding velocity. When the catalyst was internally wetted, the reaction rate was found to decrease linearly with the catalyst wetting fraction, nevertheless, and no percolation threshold was encountered, and this strange result was explained from the egg shell-type distribution of Pd beneath the support surface of only 0.4 mm. Introduction A packed bed or a catalyst pellet is a porous media network that is composed of a mixture of solids and voids distributed discretely. The morphology of this network is the basis in understanding the transport and reaction behavior in a reactor or a catalyst, and a large amount of evidence have been found in the past decades to show the relationship between them. For the single-phase flow in a packed bed, the pressure drop is determined by the packing size and bed void fraction from the Ergun equation.1 For the gas-liquid two-phase flow, the pressure drop and liquid holdup are generally predicted by the Larkins equation,2 which is based on the Lockhart-Martinelli parameter and the single-phase pressure drop equation. The Ergun-type pressure drop model was developed by Specchia and Baldi;3 however, the two coefficients in the equation vary with both the particle shape and size. In two-phase flow, pressure drop not only represents the energy consumption of the reactor, which is a measure of the gas-liquid mass-transfer coefficient4 but also the catalyst wetting efficiency.5 In the trickle flow regime, liquid tends to flow in some preferred paths and the distribution is not always uniform. The liquid flow distribution is considered as resulting from the interactions between the fluids and the porous texture.6 Li et al.7 showed for both the beds packed with spherical particles and trilobe ones in the random structure, the distribution of liquid flow rate is relatively uniform. When the bed is packed with trilobe particles in a convex fashion, much liquid flows near the wall of the bed since the trilobe particles have an orientation in the direction toward the wall, while in the concave manner, much liquid is converged into the center of the bed. Li et al.8 also showed the liquid channeling flow with small hydrophilic particles of 1-3 mm in the trickle bed can be * To whom correspondence should be addressed. Phone: +86-2164253529. Fax: +86-21-64253528. E-mail: [email protected]. † Dr. Fang is with Fushun Research Institute of Petroleum and Petrochemicals (FRIPP-SINOPEC).

reduced by addition of large-size particles of 6-20 mm. The statistical liquid flow in the trickle bed has been described by means of the concept of percolation by the group of Crine, Marchot, and L’Homme.9,10 Nevertheless, the influence of the geometry and size of the packing on the flow regime transition is confusing. For example, Standish and Drinkwater11 found the particle shape has a significant effect on flooding rates in packed columns, and they introduced the packing sphericity into the Sherwood standard ordinate. However, Charpentier and Favier12 found the spheres of 3 mm and cylindrical particles of 1.8 × 6 mm and 1.4 × 5 mm occupy the same flow regime transition profile. Weekman and Myers13 measured the trickling to pulsing flow transition line with TCC beads of 3.8 mm, glass spheres of 4.7 mm, and alumina spheres of 6.5 mm in diameter and found there was no difference among them. However, they found the packing size can influence the pulsing frequency, the 3.8-mm TCC beads has a value of 6.5 Hz, while that of 6.5mm alumina spheres has only 3.7 Hz. The pulse velocity also depends on the particle size, which was found to defer by 2-fold for the 3- and 6-mm particles.14 The particle size effect on trickling-to-pulsing flow transition was observed by Blok et al.;15 they noticed for each system and type of packing pulsing flow always occurred at a same real liquid velocity and used uLt/b(dp1/2) as the abscissa, where dp is from 2 to 12 mm. As to the catalyst pellet, the effective diffusivity has been conventionally written as

Deff ) (p/τ)DAB

(1)

where Deff is the effective diffusion coefficient of the particle, DAB is the molecular diffusion coefficient, p is the porosity of the particle, and τ is the tortuosity factor. From Monte Carlo simulation, both Abbasi et al.16and Zalc et al.17 found τ = 1/p, then eq 1 is equivalent toDeff ) p2DAB, which means Deff will not become zero only if p > 0. However,

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this conclusion conflicts with the experimental findings in catalyst deactivation18-20 and supported liquid-phase catalysis21-23 studies, where the diffusivity was found to approach zero if the porosity was decreased by 70% due to blocking by coking or liquid loading, and this can only be explained from the percolation theory. Percolation Analysis on the Fixed-Bed Reactor Although porous media are not completely random, they are sufficiently disordered that the percolation theory will give an accurate qualitative description of the fluid dynamics. A porous medium is expressed as a collection of sites (nodes) and bonds (branches) with each end of a bond being attached to a site, and the coordination number z is the number of bonds connected to a site.24-27 Regular lattices and Bethe trees are known to capture the important topological feature of porous media, and by an appropriate choice of a regular tree or a lattice with a coordination number, the porous media of interest will be well characterized. However, there is a little difference between the two ideal networks; the high genus internal structure of porous media, i.e., the highly interconnected pore space, can only be represented by lattices since they have a high connectedness, but not by the Bethe trees. In this sense, lattices are better models of porous media than trees. Nevertheless, the simplicity of the Bethe tree makes its topological properties mathematically tractable.28 Broadbent and Hammersley24 showed rigorously that no mass transport was possible if the porosity is smaller than a nonzero threshold value called φc. For the 2-D and 3-D regular lattice, the bond percolation threshold φc(b) is expressed as26

zφc(b) = d/(d - 1)

z ) 22.47 - 39.39b

for

0.259 e b e 0.5

(4)

Another correlation in calculating the number of contact points for each sphere was written as30

z ) 22(1 - b)2

(5)

The coordination numbers predicted from eqs 4 and 5 are shown in Figure 2, and it shows the value of z is between 7 and 9. It is seen from Figure 1 that the percolation threshold φc of a fixed bed is 0.13-0.17, and the bed void fraction in gas flow is 0.37-0.39, which is much higher than φc; therefore, the fixed bed can be considered as a continuum system, and it is not needed to discriminate the sites and bonds for gas flow.

(2)

where d is the dimension; thus, zφc(b) ) 1.5 for a 3-D lattice and zφc(b) ) 2.0 for a 2-D lattice. The percolation threshold for a Bethe tree is given by Fisher and Essam:25

φc ) 1/(z - 1)

Fixed-Bed Reactor with Gas Flow. A fixed-bed reactor has an average void fraction from 0.35 to 0.44 depending on how the solids are packed. In the common industrial practice, a bulk mean voidage b varies from 0.375 to 0.391. In percolation theory, the coordination number for regular packings of equalsized spheres has been evaluated and was found to vary between 6 and 12 corresponding to the cubic packing group with b equaling 0.4764 and rhombohedral packing group with b of 0.2595, and the points of contact in a random packing group were found between 7 and 9 with respect to loose and compact packings.29 The average coordination number given by Haughey and Beveridge29 is a function of bulk mean voidage:

(3)

In Figure 1, the relationship between φc and z from the two prediction methods by eqs 2 and 3 are shown, and only a little difference was found between them.

Figure 2. Coordination number prediction from bed average void fraction.

Fixed-Bed Reactor with Two-Phase Flow. When gas and liquid coexist in a fixed bed, the situation will be much different. The most characteristic phenomenon is the interaction between the two phases. To characterize the influence of liquid holdup to gas flow, Sa´ez and Carbonell31 derived a correlation between the gas-phase relative permeability κg and saturation of the gasphase Sg:

κg ) Sg4.80

Figure 1. Relation between coordination number and percolation threshold for a 3-D regular lattice and a Bethe tree.

(6)

In percolation theory, the gas-phase relative permeability corresponds to the conductivity, and the gas-phase saturation corresponds to the accessibility. A comparison can be made of the two parameters between a trickle bed and a Bethe tree, which is shown in Figure 3. It was found the trickle bed is equivalent to a Bethe tree at the percolation threshold of 0.33, and from eq 3, the coordination number is 4. This result is reasonable from the comparison with a study by Ahtchl-All and Pedersen,32 who described liquid flow in a trickle bed by a body-centered cubic lattice model and found the transition point for flow transition from rivulet to film flow was at a permeability of 0.25. Sicardi and Hofmann33 proposed a pulsing flow model; in their model, the liquid film thickness in trickle flow was

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assumed to be 1/6 of the channel diameter, which gives a gasphase saturation Sg of 0.44. Considering occlusion of the channel when pulsing flow is occurring, the Sg will be reduced to the percolation threshold of 0.33. Nevertheless, the difference between the gas permeability profile of a trickle bed and the conductivity a Bethe tree is obvious from Figure 3, and this could be explained from the geometrical difference between a Bethe tree and a trickle bed.

compare reasonably well with measurements. However, to predict the velocity distribution, it is necessary to determine the effective turbulent viscosity for a particular packed bed. In this work, the fixed bed is considered as a continuum medium from percolation analysis. Thus, the fluid flowing through the packing is analogous to that in an empty tube. To avoid the calculation of effective turbulent viscosity, the volumetric differential method was developed, which is able to predict the radial velocity profile from all the given parameters.40

Figure 4. Illustration of volumetric differential method of a packed bed.40

Figure 3. Gas relative permeability of a trickle bed in comparison with the conductivity of a Bethe tree.

Reactor Modeling Gas Flow in a Fixed-Bed Reactor. In prediction of the radial gas velocity distribution in a fixed bed, three categories of modeling work have been developed based on whether the fixed bed is treated as a continuum or a discrete medium. (1) The Discrete Model. Schnitzlein34 assumed the packed bed is composed of a group of parallel tubes with different hydraulic diameters determined by the local porosity and particle diameter and defined this model as the multicapillary tube model. The defect of this model is that at the wall there was a significant difference between experiment and model due to the fact that viscous effects at the container wall are not accounted for. Subagyo et al.35 and Di Felice and Gibliaro36 developed a two-zone model, which divides the bed into two regions with different modeling methods. In the middle region with voidage of 0.5 the continuous approach is used. McGready et al.37 developed a network model, which considered the packed bed as a network of pipes and nodes corresponding to the voidage of the bed. In their simulation, a 5 × 5 × 10 network of tubes was established. However, it is difficult to build a network that fully represents the geometry of a fixed bed. (2) The Lattice Boltzmann Approach. Freund et al.38 applied a CFD simulation on the microscopic level, which merely uses the physical property of the fluids and the packing geometry was generated by the Monte Carlo method. Thereby the dimensional information about the fluid dynamics was obtained. Although this approach requires no model, the computation expenditure should be remarkable, since a large number of grid points are needed to get a reliable radial velocity profile, and therefore, it virtually belongs to the discrete model. (3) The Pseudocontinuum Media Method. In this approach, the packed bed is considered as a continuum and the homogeneous fluid dynamic equations such as the Navier-Stokes equation and the Brinkman equation are applied. By employing the concept of effective turbulent viscosity as an adjusting variable, Bey and Eigenberger39 found the simulation results

As shown in Figure 4, fluid flow in the packed bed can be divided into two regions [R,r] and [R,r + ∆r], each of them can be transformed into an empty tube of a certain hydraulic diameter by considering the wall surface and the packing surface as the wetted area and the void volume as the wetted volume. Since these two imagined tubes possess the same pressure of the packed bed, the superficial velocity in each tube can be solved according to the Ergun equation.40 If the average superficial velocity in the region [R,r] is u1and that in the region [R,r + ∆r] is u2, the point superficial velocity in the region [r,r + ∆r] will be obtained by assuming a small width ∆r:

u(r) )

π(R2 - r2)u1 - π[R2 - (r + ∆r)2]u2 π(R2 - r2) - π[R2 - (r + ∆r)2]

(7)

In practice, ∆r is normally set as 0.01 dp. The effect of particle diameter on velocity distribution is illustrated in Figure 5. It shows all the velocity profiles exhibit a reduced oscillating behavior with a period of about one particle diameter. The influence of gas flow rate on velocity distribution is also analyzed; see Figure 6. It shows in the turbulence regime, e.g., Rep > 40, the velocity profiles are much similar.

Figure 5. Effect of particle diameter on the radial velocity distribution.

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stricted channel model is the closest approach to the real case. The physical basis for this model is that the channel diameter is not constant but is varied due to constriction by the particle surface exposed in the channel. Development of this model was initiated in 1978, which is illustrated in Figure 8.

Figure 6. Influence of gas flow rate on the radial velocity distribution.

Gas-Liquid Flow in a Fixed Bed. Although pulsing flow seldom appears in the laboratory-scale trickle-bed reactors, and induced pulsing flow has to be employed to improve the reactor performance. In industry, the mass flow rates of liquid and gas are large enough that the operation is always in the pulsing flow regime. To provide more evidence on this opinion, seven recent industrial hydrogenation operation data are listed in Table 1 and plotted in Figure 7 according to the flow pattern diagram constructed by Charpentier and Favier12 and Tosun.41 It is found these industrial reactors are all operating in the pulsing flow regime, even for the pyrolysis gasoline hydrogenation, which has a H2/oil ratio as low as 16.

Figure 8. Constricted channel model for two-phase flow in a trickle bed.

The model shown in Figure 8e by Cheng and Yuan49 is an improvement to the original work of Ng,47 in which work the liquid was considered stagnant and the friction between the gas and liquid film was ignored; therefore, the model prediction for pulsing flow velocity of the gas was only 1/4 of experimental, although the trend was satisfactory. For transition from trickling to pulsing flow, the most possible triggering position is at point 2 in Figure 8e, where the gas velocity is at the highest and the liquid film is most unstable. A constitutive equation for pulsing flow inception can be proposed:

(Vg - Vl) 1 L 1 FgVg12 + p1 ) FgVg22 + p2 + 4fi (8) Fg 2 2 Dg 2 2

p1 ) p2 +

Figure 7. Flow regime of some industrial hydrogenation processes in Table 1.

(1) Pulsing Flow Inception in a Trickle Bed. To predict the condition for pulsing flow inception in a trickle bed, different models have been proposed,42-48 and among them, the con-

dp 2σ - Fl g r 2

(9)

where L is the distance between positions 1 and 2 and is equal to dp/2, Dg is the gas flowing channel diameter, Dc is whole channel diameter. Vg1 and Vg2 are interstitial gas velocities at points 1 and 2, fi is the gas-liquid interfacial friction factor, and r is the radius of the liquid film surrounding the packing at point 2. Prediction results of the trickling-to-pulsing flow transition is shown in Figure 9 at two different bed void fractions, and the result is found to be satisfactory in comparison with experimental data and other model predictions including the bed

Table 1. Operating Data of Some Recent Industrial Hydrogenation Reactions symbol 1 2 3 4 5 6 7

feedstock

process

diesel oil

hydrofining

reforming oil

pre-hydrogenation

kerosene light circulating oil pyrolysis gasoline

hydrofining hydro-upgrading hydrogenation

PH2/MPa

LHSV/h-1

H2/oil/v/v (STP)

G/λ

L/G λψ

3.0-6.0 3.0-6.0 1.0-2.0 1.0-2.0 1.6-3.6 6.0 2.6

1.0-1.8 2.0-3.5 1.5-4.0 8.0-12.0 3.0-4.0 0.52-2.0 10.9

400-600 180-350 150-250 80-100 150-300 600-900 16

0.287 0.326 0.266 0.319 0.319 0.478 0.023

45 83 180 246 112 38 1401


Figure 9. Pulsing flow prediction for the air-water system.

Figure 10. Flow pattern transition of a foaming system in a trickle-bed reactor.52

scale model by Grosser et al.43 This finding confirms to a large degree the validity of the constricted channel model. Model eqs 8 and 9 have also been verified to the foaming system by Liu et al.52 (shown in Figure 10), who used anthraquinone solution as the foaming system. They found the size of particle has a significant effect on the flow regime transition, and this effect was predicted well by the theoretical model of Cheng and Yuan49 and could not be accounted for by the empirical correlation of Bartelmus and Janecki53 since the particle size was not a factor in their model. In the pulsing flow regime, the liquid holdup will periodically change at a specific frequency, which cannot be measured online by on-off of the electric magnetic valve. In this work, it was detected by a set of electrical capacity tomography (ECT) produced by the Process Tomography Ltd. The ECT apparatus is a twin-plane system comprising PTL300E capacitance with 12-electrode sliding ECT sensor for use on a 15-cm-diameter plexiglass column and is installed with Tomoflow Flowan software for flow measurement analysis. Figure 11 shows the variation of liquid holdup within 0.5 s in the pulsing flow regime for the air-water system flowing over a fixed bed of glass spheres of 5-6 mm in diameter. It is found in pulsing flow that the liquid saturation in the void space of the reactor varies from 70 to 86%, which implies that the channel is not occluded by the liquid. Since the liquid pulse did not completely occupy the flow channel cross section, the channel occlusion mechanism46,48 seems questionable. Instead, the liquid film instability theory47,49 is reasonable, since it does not require the occlusion of the flowing channel. Recent work by Gladden et al.,54 Gunjal et al.,55 and Wilhite et al.56 have also claimed that pulsing flow is originated from film instabilities on the surface of catalyst pellets and the transition itself is best modeled by considering the pore-scale characteristics of the trickle-bed reactor.54 This view is also in agreement with the early research by Blok et al.,15 who defined a constant Froude number as the criterion, and by Holub et al.,44 who found the laminar film stability criterion of Kapitza is statistically valid for 80% of the experimental data in predicting the trickle-to-pulse flow transition. (2) Flooding Velocity Prediction in a Packed Column. It is known the flooding behavior of a packed column is primarily affected by the size and geometry of the packing; nevertheless, the packing’s influence has been only qualitatively recognized rather than quantitatively. To better understand the effect of packing’s geometry, Fang et al.57 have recently arrived at a

Figure 11. Liquid holdup and distribution under a constant gas flow rate within 0.5 s in the pulsing flow regime. Condition: ul ) 0.0099 m/s, ug ) 0.271 m/s, dp ) 5-6 mm. Colors in the ECT figure: red liquid, green gas/liquid, blue gas (not shown). The image at t ) 0.1-0.3 s corresponds to a transient liquid slug.

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universal flooding velocity prediction formula, which includes not only the commonly used packing factor Φ but also the geometry parameter B:

()() () (

ug,f ) AΦ-0.5

µl µw

0.1

Fw Fl

-0.5

Fl Fg

)

u0.5 l,f g0.5 1 - BΦ0.25‚ 0.25 g

0.5

corresponding to a column of Raschig ring and that of Intalox saddle can be obtained consequently. The above equations are also compared with the classical Eckert correlation:58

2

(10)

where Φ ) 3b/a, B ) mA0.25, and m ) (λL/λG)1/4. The remaining parameters, ug,f and ul,f, denote the superficial velocities of gas and liquid at flooding, µl and µw are the viscosities of working liquid and water, Fl, Fg, and Fw are densities of working liquid, gas, and water, b is the bed porosity, a is the specific surface area of the packing, and λL and λG are the frictional coefficients for the liquid and gas. The values of A, B, and m should be determined experimentally. In Table 2, these three parameters are presented corresponding to Raschig rings and Intalox saddles. Table 2. Estimation Result of Model Parameters parameter

A

B

m

raschig ring intalox saddle

0.45 0.45

1.4 0.9

1.709 1.099

Since m indicates the ratio of liquid and gas friction coefficients, the data of m in Table 2 imply that the liquid in an Intalox saddle column encounters much less resistance. Since ((λL/λG)Raschig ring)/((λL/λG)Intalox saddle) ) (1.4/0.9)4 ) 5.85, the liquid flow resistance in a Raschig ring column will be 5.85 times that in an Intalox saddle column. By substituting the parameter values in Table 2 into eq 10, the flooding gas velocity

Figure 12. Flooding velocity prediction for the Raschig ring and sphere.

lg

[ () ]

() ()

ug,f a Fg 0.2 L µ ) 0.022 - 1.75 g 3 Fl l G b

1/4

Fg Fl

1/8

(11)

where L and G are the liquid and gas mass flow rates, kg/m2‚h. Four kinds of packing, namely, the Raschig ring, ceramic sphere, Pall ring, and Intalox saddle, were used as the packing material for evaluation of the flooding prediction equation, with the results shown in Figures 12 and 13. From Figures 12 and 13 is found that the flooding gas velocity for the Raschig ring is 20% lower than that of the Intalox saddle for the same packing size of 25 mm. The flooding velocity for the packing of the Raschig ring and ceramic sphere can be predicted by taking the parameter B of 1.4, and this kind of packing can be considered as the low-flux packing. On the other hand, the flooding velocity for the packing of the Pall ring and Intalox saddle can be predicted by taking the parameter B of 0.9, and this kind of packing can be considered as the high-flux packing. Therefore, B is related to the packing geometry and can be recognized as a geometrical parameter. The introduction of B has largely improved the flooding predicting precision, as compared with the Eckert formula, where the packing factor was the only parameter. Development of a Novel Catalyst Support with a High Flooding Velocity. Deep desulfurization of diesel fuel is subjected to the inhibiting effect of H2S to the catalyst, which is generated during hydrogenation, and removal of the resulting


Figure 13. Flooding velocity prediction for Intalox saddle and Paul ring.

H2S from the reacting system is required.59 It is obtained from the authors’ work60 that, under countercurrent operations at 6.0 MPa and 360 °C, sulfur could be reduced from 13841 to 5.7 µg‚g-1 with nitrogen from 457 to 1.8 µg‚g-1 and the total aromatics from 41.4 to 26 wt %. In the industry, hydrogenation catalysts are normally sphere, cylinder, and trilobe of no more than 3 mm in diameter, and flooding will occur at very low gas and liquid velocities. In solving this problem, monolithic catalysts have been developed for improving the operating velocity,61-63 but they are nevertheless too complicated to be used in a large industrial reactor in comparing with the traditional dumped catalyst. To explore whether the flooding velocity can be improved by mixing the catalyst with a percentage of packing having a large void fraction, a series of flooding experiments were carried out by mixing spheres with Raschig rings, yet it shows the improvement is not very obvious,64 and the reason could be explained since they have the same geometry parameter. Therefore, a novel quadralobe catalyst composed of four slots with particle nominal diameter of 2.1 mm and 12-18 mm in length as shown in Figure 14 was developed.65

Figure 15. Flooding velocity measurements in comparison with those of Raschig ring and spherical ceramics.

Figure 14. Geometry of the quadralobe catalyst support.

The flooding velocity was compared with three kinds of packings, the short Raschig rings of 6 mm × 4 mm × 4 mm (o.d. × i. d. × h) with the bed porosity of 0.65, the ceramic sphere spheres of 4.47 mm diameter with the bed porosity of 0.42, and the quadrolobe with dimension defined above and bed porosity of 0.52. Figure 15 shows that the quadralobe particle has the same flooding velocity as the Raschig ring. More importantly, it is found at a liquid velocity of 1 cm/s; the gas velocity can reach 10 cm/s without causing flooding, which meets most industrially required flow rates. The flooding velocity of gas for the quadralobe packing is also compared with monolithic catalyst supports studied by Heibel et al.,66,67 and it shows from Figure 16 that the quadralobe particle is comparable with the monolith of 200 cells/in.2.

Figure 16. Comparison of quadrolobe particle with the monolith on flooding velocity.

To explain the high performance of quadralobe packing, three flooding prediction formula were compared with the experimental data. It is found from Figure 17 that eq 10 with B ) 0.9 best describes the behavior of this packing, and it can be classified as a high-flux packing.

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Figure 17. Identification of the type of quadralobe packing.

Reaction Rate of Catalysts under Partially Internal Wetting To study the reaction rate of a catalyst under partially internal wetting conditions, benzene hydrogenation to cyclohexane was selected as the working system in view of its industrial and academic importance.68-71 With the assistance of adsorption-

desorption isotherm measurements, the catalyst wetting fraction has been evaluated on the molecular level.72,73 The purpose of this work is to determine the influence of catalyst wetting degree on the reaction rate; therefore, the partial pressure of benzene in the gas phase was varied to produce different catalyst wetting degrees, and the reaction rate was measured correspondingly. By increasing and decreasing the partial pressure of benzene, corresponding to adsorption or desorption of the molecules on the catalyst, two wetting fractions at one benzene vapor pressure were obtained as shown in Figure 18. The relationship between reaction rate and the catalyst wetting fraction is shown in Figure 19. It is found the reaction rate is only affected by the catalyst wetting fraction, but is independent of how this wetting condition is attained. This finding is very useful, since in modeling the reaction rate, only the catalyst wetting fraction is required; therefore, the following reaction rate equation can be applied to a partially wetted catalyst:

rp ) r0(1 - fw) + r1fw

(12)

where rp, r0, and r1 are reaction rates when the catalyst is

Figure 18. Catalyst wetting fraction predicted at different partial vapor pressures of benzene.


Figure 19. Reaction rates measured at different wetting fractions of the catalyst from increasing (adsorption) or decreasing (desorption) the partial vapor pressure of benzene.

partially wetted, completely dry, and fully wetted. Since r0 . r1, only the values of r0 and fw are required in estimating the rate of rp. However, the anticipated percolation threshold was not observed, since all the reaction rates were observed to decrease linearly with the wetting fraction of the catalyst from 0 to 1 as shown in Figure 19. This could be explained from the structure of the catalyst. It is known that the catalyst support is 4 mm in diameter, while the active component Pd is impregnated only in a thickness of 0.4 mm over the outside shell from the SEM photo shown in Figure 20. When the catalyst is partially filled

with liquid, it has been measured by magnetic resonance image that the liquid tends to distribute in the central area of the catalyst;74 therefore, although the bond percolation problem in the current situation has been encountered, there is no reaction in the center of the support; the sharp decrease of reaction rate at the percolation threshold will not appear. Actually, partial wetting of the pore channels in the outside of the catalyst layer only makes the reaction rate decrease linearly, as illustrated in Figure 21.

Figure 21. Conductivity of the catalyst pore network under partial wetting condition.

Conclusion Figure 20. SEM photo of the catalyst cross section showing the thickness of Pd layer.

It was shown in this work that the morphology of porous media has a large influence on multiphase reaction and

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multiphase flow on the reactor scale, the pellet scale, and the molecular scale, and the following points are worth mentioning: (1) The fixed-bed reactor has a void fraction larger than the percolation threshold; therefore, the fixed bed could be considered as a homogeneous medium without discriminating the solid and void phases, although they are discretely distributed in the space. This consideration leads to a concept on estimation of radial velocity distribution by differentiation of the reactor volume. (2) Comparing a trickle bed with the Bethe tree shows the reactor has a coordination number of 4 and a percolation threshold of 0.33. In this view, detailed information of the gas-liquid flow in a specific channel is important. The pulsing flow model has been discussed on the pellet scale, and the film instability analysis was shown to be the most reasonable mechanism in explaining the mechanism of pulsing flow. (3) An improved flooding prediction formula for gas-liquid countercurrent flow in a packed column was proposed by defining the packing geometry as a quantitative parameter, which was estimated to be 1.4 or 0.9, which characterizes the high-resistance and low-resistance packings. A quadralobe catalyst support of 2.1 mm in diameter has been developed based on morphology design and showed a remarkable flooding velocity. (4) The wetting fraction of a catalyst pellet was measured to be different under the same vapor pressure of the volatile component under different operation sequences. Although the liquid distribution in the pellet is different in the two cases, it gives the same reaction rate if the catalyst wetting fractions are equal. In current work, no percolation threshold was observed even if the catalyst pore was almost filled with liquid, since the active component Pd was deposited just on the outside surface layer of ∼0.4 mm.

V ) interstitial velocity, m/s z ) coordination number Greek Letters ) void fraction Φ ) packing factor, b3/a φA ) accessible porosity φc ) percolation threshold φE ) effective porosity λ ) flow parameter, [(Fg/Fair)(Fl/Fw)]1/2 λL ) frictional coefficients for the liquid λG ) frictional coefficients for the gas µ ) viscosity of working fluid, kg/m‚s F ) density, kg/m3 σ ) surface tension, N/m τ ) tortuosity factor ψ ) flow parameter, (σw/σl)[(µl/µw)(Fw/Fl)2]1/3 Subscripts 0 ) the initial value 1, 2 ) position b ) bed or bond f ) flooding g, G ) gas l, L ) liquid p ) particle or partial wetting t ) transition point w ) water Acknowledgment The authors are grateful to the supports of Natural Science Foundation of China (NSFC) under Grant 20106005 and the Chinese Education Ministry on the Program for New Century Excellent Talents in University under Grant NCET-04-0412. Literature Cited

Nomenclature a ) specific surface area of the packing, 1/m A ) model parameter in eq 10 B ) model parameter in eq 10 d ) diameter or dimension DAB ) molecular diffusion coefficient, m2/s Dc ) the whole channel diameter, m Deff ) effective diffusion coefficient, m2/s Dg ) gas flowing channel diameter, m dh ) hydraulic diameter, m fi ) gas-liquid interfacial friction factor fw ) internal wetting faction of a catalyst g ) gravitational acceleration, m/s2 G ) mass flow rate of gas, kg/m2‚s κg ) gas-phase relative permeability L ) length in m or mass flow rate of liquid in kg/m2‚s m ) model parameter in eq 10 p ) pressure, bar r ) radial position, m R ) radius, m r0 ) reaction rate of a dry catalyst, mol/g of cat‚s r1 ) reaction rate of a wetted catalyst, mol/g of cat‚s rB ) reaction rate of benzene, mol/g of cat‚s Rep ) Reynolds number rp ) reaction rate of a partially wetted catalyst, mol/g of cat‚s Sg ) saturation of the gas-phase u ) superficial velocity, m/s

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ReceiVed for reView April 28, 2007 ReVised manuscript receiVed August 19, 2007 Accepted August 28, 2007 IE0706055

Evaluation on the Dependence of Multiphase Flow and Reaction upon

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