Development of a Membrane-Assisted Fluidized Bed Reactor. 1. Gas

Ind. Eng. Chem. Res. 2005, 44, 5955-5965

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Development of a Membrane-Assisted Fluidized Bed Reactor. 1. Gas Phase Back-Mixing and Bubble-to-Emulsion Phase Mass Transfer Using Tracer Injection and Ultrasound Experiments S. A. R. K. Deshmukh, J. A. Laverman, A. H. G. Cents, M. van Sint Annaland,* and J. A. M. Kuipers Department of Science and Technology, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands

A small laboratory-scale membrane-assisted fluidized bed reactor (MAFBR) was constructed in order to experimentally demonstrate the benefits of this reactor concept, especially the enhanced bubble-to-emulsion phase mass transfer and the reduced overall axial gas phase back-mixing, due to the presence of the membranes and permeation of gas through the membranes. With steady-state tracer gas injection experiments, it was demonstrated that the experimental reactor exhibited approximately plug flow behavior for all the operating conditions investigated in this work as a result of the elimination of macroscale circulation patterns due to the presence of the membranes and, even more importantly, the permeation of gas through the membranes. With an ultrasound technique, the gas residence time distribution (RTD) of the MAFBR was measured over a wide range of fluidization velocities for two different bed heights. Interpretation of the RTD measurements with a phenomenological two-phase reactor model extending the bubble assemblage model proposed by Kato and Wen (Kato, K.; Wen, C. Chem. Eng. Sci. 1969, 24, 1351) showed that the average bubble diameter is significantly decreased for higher ratios of gas permeated through the membranes relative to the total gas flow rate. 1. Introduction Fluidized beds employing fine powders are finding increased application in the chemical and petrochemical industries because of their excellent mass and heat transfer characteristics. However, in fluidized bed chemical reactors axial gas back-mixing can strongly decrease the conversion and selectivity. By insertion of membranes in fluidized beds, large improvements in conversion and selectivity can be achieved, first by optimizing axial concentration profiles via distributive feeding of one of the reactants or selective withdrawal of one of the products, and second, by decreasing the effective axial dispersion via compartmentalization of the fluidized bed. Moreover, insertion of membrane bundles in a suitable configuration impedes bubble growth, thereby reducing reactant bypass via rapidly rising large bubbles. In this work these advantages of a membrane-assisted fluidized bed reactor (MAFBR) are quantified. In this paper, first, the influence of the presence of horizontal membrane bundles and especially the effect of gas addition via the membranes on the effective axial and lateral gas dispersion are studied experimentally using steady-state tracer gas injection experiments. Second, with an ultrasound technique2 the gas phase residence time distribution (RTD) of the MAFBR was measured over a wide range of fluidization velocities and for two different bed heights, where the relative amount of gas fed via the membranes compared with the amount fed via the bottom distributor was varied from 0 to 40%. In Deshmukh et al.3 it was already shown that the operating conditions in the fluidized bed do not affect * To whom correspondence should be addressed. Tel.: 0031-53-4894478. Fax: 0031-53-4892882. E-mail: [email protected].

the membrane permeation fluxes. A one-dimensional two-phase phenomenological reactor model is developed on the basis of the bubble assemblage model, proposed by Kato and Wen.1 The bubble assemblage model is extended to account for gas addition via the membranes. With this extended model, the experimental RTD curves are interpreted in order to quantify the effects of the presence of the membrane bundles and the ratio of gas fed via the membranes relative to the gas fed via the bottom distributor on the bubble-to-emulsion phase mass transfer rate. First the experimental setup, the experimental techniques, and experimental procedures used to measure the gas back-mixing and gas residence time distribution in the MAFBR are described in the next section. Subsequently, the hydrodynamic behavior of the MAFBR, i.e., the extent of axial gas back-mixing and the bubble-to-emulsion phase mass transfer rates, is studied as a function of the superficial gas velocity and the ratio of gas fed via the membranes relative to the gas fed via the bottom distributor. A two-phase phenomenological model is developed to analyze the measured RTD curves in order to quantify the effects of the operating conditions on the bubble-to-emulsion phase mass transfer. In part 2 this experimental and modeling study is continued to include chemical reactions, focusing on the industrially interesting partial oxidation of methanol to formaldehyde. 2. Experimental Section This section starts with a description of the MAFBR, followed by a description of experimental setups and experimental techniques used to measure the extent of gas-phase back-mixing and the gas residence time distribution in the MAFBR.

10.1021/ie049102e CCC: $30.25 © 2005 American Chemical Society Published on Web 02/23/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005

Figure 1. Schematic representation of the MAFBR.

2.1. Membrane-Assisted Fluidized Bed Reactor. A square fluidized bed (0.05 m × 0.05 m × 1 m) was constructed from stainless steel and filled to a packed bed height of 0.1-0.30 m with a commercial iron molybdate catalyst, kindly provided by Perstorp and crushed and sieved to a diameter range of 75-150 µm (particle density of 1750 kg/m3). The bed was equipped with 21 horizontal stainless steel heat transfer tubes (2 mm i.d. and 3 mm o.d.) and 24 horizontal ceramic membrane tubes (1.5 mm i.d. and 2.5 mm o.d. with an average pore size of approximately 0.15 µm), through which gas could be fed to the bed, arranged in a staggered arrangement with a pitch (horizontal and vertical) of 16 mm. The heat transfer tubes were inserted in the bed to remove the reaction heat in case strongly exothermic reactions, like the partial oxidation of methanol to formaldehyde, are carried out in the bed, which is studied in part 2 of this work. In Figures 1 and 2a, a schematic front and side view of the membrane-assisted fluidized bed is given, showing the tube arrangement in more detail. Uniform fluidization was achieved with a porous plate distributor with a pore size of 10 µm. 2.2. Steady-State Tracer Injection Experiments To Measure Axial Gas Back-Mixing. Figure 2 depicts the details of the experimental setup used to measure the axial back-mixing in the MAFBR. Steady-state tracer gas point injection experiments were performed by subsequently injecting CO2 tracer gas by a traversing probe at two lateral locations, indicated with A (near the wall) and D (near the center). Steady-state backmixed tracer concentrations were measured with an IR analyzer at three axial positions and five lateral positions for each of the axial positions. In these studies, the freeboard tracer gas concentration was set to 1%. Fluidization was performed with nitrogen distributed via a porous plate distributor. The fluctuations in the signal from the IR analyzer were smoothened by time averaging the analyzer signal. A maximum averaging time of 16 min was used for the detection points near the wall, and a somewhat smaller averaging time was sufficient for other locations in the bed (typically 2-4 min). It was ensured that the selected averaging time was sufficiently long to yield reproducible results. 2.3. Ultrasound Technique To Measure the Gas Residence Time Distribution. The measurement principle of the ultrasound technique is based on the dependency of the speed of sound in a material on the bulk modulus (of elasticity) and the density of this medium. Thus, with the ultrasound technique the concentrations of a component in a gas stream can be measured continuously and with a high frequency, which allows the determination of the residence time distribution in systems with a very small average

residence time. Details about the technique have been discussed by Cents et al.2 Helium was selected as the tracer gas, first because of its pronounced difference in sound velocity compared to nitrogen (965 vs 353 m/s at 23 °C) and second because it does not adsorb on the catalyst surface. The experimental setup (see Figure 3) consists of an arbitrary waveform generator (AWG), which sends any desired electric signal to a piezoelectric transducer (T) with a center frequency of 800 kHz. The signal is amplified to a maximum of 44 dB with a variable power amplifier. The transmitting transducer converts the electric signal to a pressure wave that is received in another transducer (R). The converted electric signal is, after 31-dB amplification, acquired with a maximum sampling rate of 2 GS/s (2 × 109 samples per second) and with 8-bit resolution in a digital oscilloscope. At the same time as the AWG sends the electric signal, a trigger signal is transmitted both to the oscilloscope and to an electrically controlled valve to start tracer injection. In this way, in every measurement, the starting point, t ) 0, is well defined. Data from the oscilloscope are transferred to a computer using a GPIB interface bus. The overall sampling frequency in this experimental setup was limited by the data transfer rate to 33 Hz. The theoretical maximum sampling frequency is in the order of 10 000 Hz. Continuously a mixture of helium (9.1%) and nitrogen mixed in a union tee was fed to the reactor. At a given time the helium flow was stopped, i.e., a step-down in the helium tracer gas concentration. The helium concentration was measured continuously at the reactor outlet using the ultrasound technique. Thus, the residence time distribution of the tracer gas in the MAFBR could be determined very accurately, despite the small average gas residence times. 2.3.1. Validation of the Ultrasound Technique with Single-Phase Model Reactors. Before discussing the results of the RTD measurements in the MAFBR over a range of fluidization velocities with and without gas addition via the membranes, the ultrasound technique was tested for two different single-phase reactors: (a) a reactor vessel with a volume of 1.25 L equipped with a magnetic stirrer to ensure nearly ideal gas phase mixing (CISTR) and (b) two stainless steel tubular reactors with inner diameters of 20.0 and 18.4 mm and lengths of 2000 and 815 mm, respectively, to approximate plug flow behavior (Pe > 50). Figure 4 shows a typical step-down response for the stirred tank. It can be seen that the obtained mean residence time is in very good agreement with the holding time. Several RTD curves were obtained for different gas flow rates and the number of CISTRs (N) obtained varied between 1.0 and 1.3, indicating that the stirred tank reactor is indeed almost ideally mixed. Moreover, Figure 5 shows a typical measured stepdown response for one of the empty tubes used (PFR, plug flow reactor) and the best fit with the tanks in series model. Figure 6 shows the parity plot of the mean residence time calculated from this model and the actual holding time. As expected the empty tube shows approximately plug flow behavior. On the basis of the results described above, it was concluded that the ultrasound measurement technique was accurate and reliable. 2.3.2. Validation of the Ultrasound Technique for the MAFBR. The ultrasound technique was used

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Figure 2. Schematic of the experimental setup to measure gas back-mixing in the membrane-assisted fluidized bed reactor by steadystate tracer experiments: (a) detailed side view of the reactor; (b) simplified flow-sheet.

Figure 5. Typical response of one of the PFRs subjected to a stepdown input (xg,He ) mole fraction of helium in the outlet gas). Experimental data and tanks in series model are plotted.

Figure 3. Schematic of the experimental setup used to measure the gas residence time distribution in the membrane-assisted fluidized bed reactor by an ultrasound technique.

Figure 6. Parity plot of the measured mean residence time and the holding time of the PFR. Figure 4. Typical response of a stirred tank reactor to a stepdown input (xg,He ) mole fraction of helium in the outlet gas). Experimental data and the best-fit line (CISTRs in series model) are plotted for 5% helium concentration in the feed.

to measure the gas phase RTD in the membraneassisted fluidized bed reactor in order to study the effect of the ratio of gas fed via the membranes relative to the

gas fed via the bottom distributor. First, the ultrasound technique was used to measure the residence time and the residence time distribution of the tubing between the tracer gas injection valve and the distributor and between the freeboard region and the measurement cell. This external tubing indeed showed PFR characteristics, so that the mean residence time of this external tubing can simply be subtracted from the measured RTD to

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Figure 7. Parity plot of the mean residence time (calculated by the model) and the holding time of the MAFBR over a wide range of fluidization velocities and membrane permeation ratios for a static bed height of 0.25 m.

obtain the RTD for the membrane-assisted fluidized bed (see Figure 7). In the next section the experimental results to investigate the extent of gas back-mixing in the MAFBR using the steady-state tracer gas injection experiments are described and discussed. Subsequently, a phenomenological two-phase reactor model is developed with which the tracer response experiments using the ultrasound technique will be interpreted in order to quantify the effect of the presence of and the permeation of gas through the membranes in the MAFBR. 3. Gas Back-Mixing in a MAFBR To investigate the mixing behavior in our lab-scale membrane-assisted fluidized bed reactor equipped with horizontal membranes, tracer gas injection experiments were performed. Steady-state lateral concentration profiles (normalized with the freeboard concentration) were determined at three different axial locations in the bed with consecutive tracer injection at two different positions (near the wall (injection A) and near the center (injection D) of the bed) for three different fluidization velocities. The results of these experiments without permeation via the membranes are shown in Figure 8. The most important observations obtained from these experiments are as follows: 1. For the tracer gas injection near the wall at 8umf and 10umf, very low relative tracer concentrations are detected at points below the injection point for all of the three probes, which indicates that down-flow near the wall is not significant at these fluidization velocities and that the near-wall circulation pattern does not extend over the entire bed. When the fluidization velocity is increased to 12umf, the extent of down-flow near the wall increases but still does not extend over the entire height of the reactor (see Figure 8, injection A). 2. With the tracer gas injection located at the center of the bed, the relative tracer gas concentrations detected just below the injection point were very small for all of the three detection probes at all fluidization velocities studied (see Figure 8, injection D). This pinpoints the strong up-flow in the center of the bed. The slightly higher concentrations at the wall observed at all axial positions and gas velocities applied are attributed to a weak near-wall down-flow. The observed phenomena correspond very well to the experimental results presented in Deshmukh.4 For the lab-scale MAFBR, the extent of back-mixing is even smaller and the down-flow near the wall becomes

significant at even higher fluidization velocities, which can be attributed to the larger aspect ratio of this reactor. To study the effect of gas addition via the membranes on the mixing behavior of the membrane-assisted fluidized bed reactor, tracer gas point injection experiments were performed at a superficial gas velocity of 12umf with the tracer injection again at position A (near the wall) and position D (near the center), where part of the fluidizing gas was fed via the membranes (25-50%), keeping the total flow rate corresponding to 12umf respectively (see Figure 9). The relative tracer concentrations detected near the wall (injection A) are substantially smaller than detected (for the same conditions) without membrane permeation. Furthermore, the concentrations detected near the wall decrease with an increase in the gas flow rate permeated through the membranes. This indicates that the local near-wall down-flow is effectively annihilated by gas permeation through the membranes. Moreover, the concentrations detected at the center (injection D) also decreased substantially in the case of gas addition via the membranes demonstrating the near plug flow behavior of the membrane-assisted fluidized bed with membrane permeation. 4. Two-Phase Reactor Model for the MAFBR A one-dimensional two-phase reactor model is developed for the MAFBR accounting for gas permeation through the membranes in order to interpret the RTD data obtained from the ultrasound experiments. This model will subsequently be used to describe the partial oxidation of methanol experiments in our MAFBR, discussed in part 2 of this work. The most common phenomenological description of the two-phase flow phenomena in fluidized bed reactors is based on the bubble assemblage model, originally proposed by Kato and Wen.1 In their model the fluidized bed is divided in the axial direction into a number of CISTRs for the bubble phase as well as for the emulsion phase, where the size of the CISTR was related to the local bubble size. The model presented here also divides the fluidized bed into a number of CISTRs, following Kato and Wen.1 However, in our model the CISTRs are assumed to be of equal volume for each phase and consequently their size is no longer directly related to the local bubble size, but to the extent of gas back-mixing in the MAFBR in each phase, as measured with independent tracer injection experiments. The model assumptions and model parameters are described in the following section. 4.1. Model Assumptions. Our model is based on the following main assumptions: (a) The fluidized bed consists of two phases, viz. the bubble and the emulsion phase. (b) In the axial direction each phase is divided into several compartments of equal size, where the height of each compartment is given by the total expanded bed height and the number of compartments for each phase. The number of compartments for each phase determines the extent of axial gas back-mixing and should be determined by separate experiments. (c) The gas flowing through each phase is considered to be completely mixed within each individual compartment (i.e., CISTR behavior). 4.1.1. Bubble Phase. The superficial bubble velocity (usb) is an important parameter in fluidized bed reactor modeling, since many other parameters such as the


Figure 8. Effect of the superficial gas velocity on the experimentally determined lateral relative tracer gas concentration profile with injection point near the wall (injection A) and at the center (injection D); the injection point was 0.168 m above the distributor.

volume fraction of each phase and the superficial gas velocities of the phases have been correlated as a function of the superficial bubble velocity. The earliest and most common postulate to compute usb, which is known as the two-phase theory of fluidization (Toomey and Johnstone5), suggests that the gas flow rate in the bubble phase is equal to the excess gas flow rate above what is required for minimum fluidization. This model assumes that usb remains constant throughout the bed. This observation is however contrary to what Werther6 has observed in his experiments. Werther’s6 data indicate that usb increases monotonically with the bed height. His data showed that a smaller diameter bed results in significantly higher usb compared to larger

diameter beds. Thus, when bubbles rise in a fluidized bed, the dense phase continues to transfer gas to the rising bubbles. This, in turn causes the bubbles to grow in size and ascend with higher velocities. Moreover, because of the wall effect, the bed diameter has a strong effect on the rate of gas withdrawal from the dense phase. Due to the relatively smaller wall effect in a larger-diameter bed, the withdrawal rate of the dense phase is less and, consequently, the bubble size as well as the bubble gas flow rate at a given height will be smaller in a large-diameter bed. Furthermore, bubbles are known to move laterally toward the center, which actually induces the microscale lateral mixing in the emulsion phase, which is assumed

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Figure 9. Effect of gas addition via the membranes on the experimentally determined lateral relative tracer gas concentration profile for a fluidization velocity of 12umf, with injection near the wall (injection A) and at the center (injection D); the injection point was 0.168 m above the distributor.

to be laterally perfectly mixed. However, a uniform distribution of the bubble phase is assumed. It is therefore assumed that the bubbles disperse uniformly in each CISTR. The following assumptions have been made for the bubble phase: (a) A laterally uniform bubble fraction is assumed and lateral concentration differences in the bubble phase are assumed to be negligibly small due to the assumed frequent bubble coalescence and breakup. (b) The bubble phase is considered to be free of catalytic particles, so that no catalytic reactions occur in the bubble phase. Alternatively, the reaction rates

are assumed to be relatively small, so that the extent of chemical conversions occurring in the bubble phase can be neglected. (c) The bubble phase gas is assumed to be in plug flow (i.e., large number of CISTRs). The number of CISTRs in the bubble phase has been fixed at 20 in this work. 4.1.2. Emulsion Phase. In a fluidized bed without internals, a macroscale circulation pattern prevails with down-flow of the emulsion phase near the wall and upflow at the center of the bed. However, as shown with tracer gas experiments in the bed with horizontal inserts the macroscopic circulation is effectively annihi-

Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 5961 Table 1. Mass Conservation Equations for the Bubble and Emulsion Phase for Compartment n Total Mass Balances s s s s 0 ) ub,n-1 AT - ub,n AT + ue,n-1 AT - ue,n AT +

utotATF Nb

where s AT ue,n

) ue,nAT(1 - δb,n),

usb,0AT ) (1 - F)utotATδb,0, use,0AT ) (1 - F)utotAT(1 - δb,0) Bubble Phase Component Mass Balances Vb,n

dCb,n,i utotATFCp,n,iδb,n s s ATCb,n-1,i - ub,n ATCb,n,i + + ) ub,n-1 dt Nb utotATF(1 - δb,n) s s (ue,n-1 AT - ue,n AT) + Ce,n,i Nb Kb,e,nVb,n(Cb,n,i - Ce,n,i)

[

]

for i ) 1...nc Cb,n,i(t ) 0) ) Cb,n,i,0 Emulsion Phase Component Mass Balances dCe,n,i s s Ve,n ATCe,n-1,i - ue,n ATCe,n,i + ) ue,n-1 dt utotATFCp,n,i(1 - δb,n) s s - [(ue,n-1 AT - ue,n AT) + Nb utotATF(1 - δb,n) Ce,n,i + Kb,e,nVb,n(Cb,n,i - Ce,n,i) Nb for i ) 1...nc Ce,n,i(t ) 0) ) Ce,n,i,0

lated, especially in the case of gas permeation through the membranes. The following assumptions have therefore been made regarding the emulsion phase: (a) The emulsion phase gas only flows upward. This is based on the fact that the reactor exhibits approximately plug flow behavior (large number of CISTRs), which improves even further with addition of gas via membranes. (b) A constant emulsion phase porosity is assumed, which remains at the minimum fluidization porosity. (c) The gas fed to the emulsion phase via membranes is assumed to be first perfectly mixed in the emulsion phase and subsequently instantaneously transferred to the bubble phase (because of the assumed constant emulsion phase velocity and porosity). 4.2. Model Equations and Model Parameters. On the basis of the aforementioned assumptions, the bubble and emulsion phase total and component mass conservation equations have been formulated for each compartment and are shown in Table 1, where the equations have been simplified assuming an equal number of compartments for both phases for clarity. For calculations where the number of CISTRs in the bubble phase is larger than the number of CISTRs in the emulsion phase, the number of compartments in the emulsion phase is kept equal to the number of compartments in the bubble phase, but additional mixing terms between neighboring emulsion phase compartments are incorporated in the emulsion phase component mass balances in order to simulate the larger back-mixing. For an explanation of the symbols used, the reader is referred to the symbol list at the end of the paper. The empirical correlations for the model parameters have been taken from the literature, although they were originally obtained for beds without internals (see Table 2). It is

assumed that these correlations can reasonably well describe the MAFBR. Since the bubble size is expected to grow well beyond the pitch length, the average bubble size is only mildly affected by the presence of the horizontal inserts (see Yates et al.7). Despite the fact that some experimental results have been reported in the literature on the effect of the presence of horizontal inserts on the local bubble size considering bubble growth and coalescence and breakup, no correlations have been found that account for the important effects of the membrane permeation and gas production due to the chemical reactions on the evolution of the bubble size. Since the tracer gas injection experiments have clearly demonstrated that the lab-scale MAFBR exhibits approximate plug flow behavior, a spread in the residence time is the result of mass transfer limitations between the bubble phase and the emulsion phase. Thus, the RTD experiments can be used to quantify the bubble-to-emulsion phase mass transfer rate. Assuming that the bubble growth as a function of height is undisturbed by the presence of and the permeation of gas through the membranes, but that simply the average bubble size is reduced by a constant factor, the RTD data can be used to quantify this factor as a function of the superficial gas velocity and the ratio of gas fed via permeation through the membranes and gas fed via the bottom distributor, which is discussed in the next section. 5. Bubble-to-Emulsion Phase Mass Transfer in a MAFBR The effect of fluidization conditions, viz. superficial fluidization velocity, ratio of gas addition via the membranes to gas fed via the bottom distributor, and the static bed height, on the bubble-to-emulsion phase mass transfer rate has been quantified in terms of a constant factor with which the bubble diameter decreases (or increases) as calculated with the Mori and Wen10 equation for fluidized beds without internals.

db ) fdb[db,max - (db,max - db,0)e(-0.3Z/DT)]

(1)

where the maximum bubble diameter db,max has been set to the column diameter. This factor fdb, referred to as the bubble diameter factor, was determined by minimizing the discrepancies between the RTD curve as measured with the ultrasound technique and calculated with the two-phase model. Figure 10 shows a typical measured step-down response curve for the membrane-assisted fluidized bed reactor and the best fit of the two-phase model with modified bubble diameter correlation, showing a good correspondence. 5.1. Parametric Sensitivity of the Model. 5.1.1. Number of CISTRs in the Emulsion Phase. Before discussing the effect of the superficial gas velocity and ratio of gas addition via the membranes relative to the gas fed via the bottom distributor on the bubble size in terms of the modified Mori and Wen10 correlation, the influence of the number of CISTRs in the emulsion phase on this bubble diameter factor was investigated. For a static bed height of 0.25 m, the variation of the bubble diameter factor with the variation in the number of CISTRs (3-40) in the emulsion phase was calculated. It was found that for cases with more than 3 CISTRs in the emulsion phase, there was no significant influ-

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Table 2. Hydrodynamic Parameters Used in the Model (without the Effect of Internals) parameter Archimedes number

equation

reference 8

3

Ar )

dp Fg(Fp - Fg)g 2

µg

( )

minimum fluidization velocity

µg umf ) (x(27.2)2 + 0.0408Ar - 27.2) Fgdp

bed voidage at minimum fluidization velocity projected tube area for a square bed rise velocity of a single bubble velocity of rise of swarm of bubbles initial bubble diameter (porous plate distributor) maximum bubble diameter

mf ) 0.586Ar-0.029(Fg/Fp)0.021 AT ) DT2 ubr ) 0.711(gdb)1/2 ub ) u0 - umf + 0.711(gdb)1/2 db0 ) 0.376(u0 - umf)2 db,max ) DT

superficial bubble gas velocity maximum superficial bubble gas velocity initial superficial bubble gas velocity superficial emulsion gas velocity bubble phase fraction emulsion phase fraction height of bed expansion

(

s - usb ub,max

) exp -

s ub,max - usb,0

0.55z HmfDT

9 8 8 8

)

10

s ub,max ) u0 - umf s ub,0 ) ubr,0δb0 where δbo ) (1 - Hmf/Hf) use ) u0 - usb δb ) usb/ub δen ) 1 - δbn Hf ) Hmf[C1/(C1 - C2)] where ub0 0.275 C1 ) 1 exp ub,avg DT

(

C2 )

(

[

usb

1 - exp -

ub,avg

11 12 5 9 1 9

) )]

0.275 DT

average bubble rise velocity

ub,avg ) u0 - umf + 0.711(gdb,avg)1/2

gas exchange coefficient

Kbc ) 4.5

( ) (

volume of emulsion phase in the nth compartment volume of bubble in the nth compartment bubble diameter

ence on the value of the bubble diameter factor calculated for all of the fluidization velocities studied and for all of the ratios of gas addition via the membranes. Hence, recalling the overall approximate plug flow behavior of the MAFBR determined from the steadystate tracer gas experiments, for all subsequent calculations of the bubble diameter factor at various fluidization conditions, the number of CISTRs in the emulsion phase was fixed at 5. 5.1.2. Is gas fed via the membranes taken up only by the bubble phase or by both phases

Figure 10. Typical RTD curve of the membrane-assisted fluidized bed reactor as a response to a step-down input of the helium concentration. Experimental data and the best-fit line (two-phase model) are plotted for a static bed height of 0.25 m, Nb ) 20, Ne ) 5, and a superficial velocity of 10umf.

)

umf Dg1/2g1/4 + 5.85 db db5/4

Kce ) 6.77

(

)

Dgmfub 3

9

8

1/2

db 1/Kbe ) 1/Kbc + 1/Kce Ve,n ) AT(Hf/Nb) Vb,n ) AT(Hf/Nb)δb,n db ) db,max - (db,max - db,0)exp(-0.3z/DT)

1 1 10

according to their respective fractions? For the formulation of the reactor model, it is important to know whether the gas fed via the membranes is taken up only by the bubble phase or by both phases according to their respective phase fractions at that particular height. The computed bubble diameter factor fdb obtained for different superficial gas velocities and different fractions of gas fed to the membranes compared to the total gas fed are compared in Figure 11 for both scenarios. Figure 11 clearly shows that for the case where all gas added via the membranes is directly entering the

Figure 11. Variation of the bubble diameter factor as a function of the fluidization velocity at 0.25 m bed height and for two different assumptions concerning the gas distribution via the membranes.


branes, especially since the above holds for different bed heights. Furthermore, the bubble diameter factors decrease strongly for higher ratios of gas addition via the membranes, where this effect is more pronounced at higher bed heights. Obviously, the effect of gas addition via membranes on the bubble diameter factors cannot be observed at low ratios of gas addition via the membranes, because only in these cases still most of the gas is fed via the bottom distributor and hence no effect on the bubble size is to be expected. Moreover, for a static catalyst bed height of 0.15 m the bubble diameter factors did not change significantly with superficial gas velocity and remained close to unity, which can be attributed to the minor role of bed height on the bubble growth and the apparent small effect of the membranes on the bubble breakup. However, at higher bed heights the average bubble diameter has decreased with 20-40% at 40% permeation of the gas through the membranes. 6. Summary and Conclusions

Figure 12. Variation of the bubble diameter factor as a function of the fluidization velocity for different ratios of gas addition via the membranes and for two catalyst static bed heights.

bubble phase, the calculated bubble diameter factors are higher than that for the second assumption where the gas is added to both phases according to their respective local phase fraction. Obviously this is especially valid for cases with high ratios of gas fed via the membranes. As expected, assuming that the gas added via the membranes is added to both phases according to their phase fractions and thus mainly to the emulsion phase, an additional mixing step is introduced in the emulsion phase, which is then compensated by enhanced bubble-to-emulsion phase mass transfer via smaller bubbles. Thus, the RTD experiments cannot discriminate between effects on back-mixing or on bubble-toemulsion phase mass transfer rates in the fluidized bed. However, steady-state tracer gas experiments where the tracer gas was fed via the membranes (not included in this work) substantiated the assumption that the gas is added to both phases according to their respective local volumetric phase fractions.4 Moreover, with our reactor model discussed in part 2 of this work, methanol conversions were grossly underpredicted, when it was assumed that all permeated gas through the membranes is taken up directly by the bubble phase, because it creates additional mass transfer resistance, since the reactions take place in the emulsion phase. 5.2. Effect of Superficial Gas Velocity and Gas Addition via Membranes on the Bubble Diameter Factor in a MAFBR. Figure 12 shows the effect of the fluidization velocity on the bubble diameter factors for different ratios of gas added via the membranes and for two static catalyst bed heights. Remarkably, the bubble diameter factors approach unity for high fluidization velocities and low ratios of gas addition via the membranes. This clearly indicates the applicability of the constitutive equations and especially the Mori and Wen10 equation to describe the bubble diameter as a function of height, despite the presence of the mem-

A small laboratory-scale membrane-assisted fluidized bed reactor equipped with horizontal porous ceramic membranes and cooling tubes was constructed to demonstrate the reactor concept for the methanol partial oxidation to formaldehyde over an industrial Fe-Mo catalyst. In this part the effects of the presence of the membrane bundles and the gas permeation through the membranes on the gas-phase back-mixing and the bubble-to-emulsion phase mass transfer rates were investigated. First the extent of gas back-mixing in the experimental MAFBR was quantified. Gas back-mixing studies employing steady-state tracer injection experiments have demonstrated that for the experimental reactor effective compartmentalization of the fluidized bed is realized via the insertion of horizontal membranes and cooling tubes, especially in the case of gas permeation through the membranes. In a MAFBR the macroscale circulation patterns are effectively eliminated resulting in a close to plug flow behavior. The effect of the presence of and the permeation of gas through the membranes on the bubble-to-emulsion phase mass transfer rates has been quantified by measuring the gas residence time distribution over a wide range of fluidization velocities and ratios of gas fed via the membranes relative to the gas fed via the bottom distributor using an ultrasound technique. A one-dimensional two-phase reactor model has been developed considering the MAFBR as a series of ideally stirred tank reactors for both the bubble and the emulsion phase, where the addition of gas via the membranes has been accounted for. By minimizing the discrepancies between the predicted RTD curve by this model and the experimentally determined RTD curve, the effect of the fluidization conditions, viz. superficial fluidization velocity, ratio of gas addition via the membranes to gas fed via the bottom distributor, and the static bed height, on the bubble-to-emulsion phase mass transfer rate has been quantified in terms of a constant factor with which the bubble diameter decreases (or increases) as calculated with the Mori and Wen equation for fluidized beds without internals. It was found that these bubble diameter factors approach unity for high fluidization velocities and low ratios of gas addition via the membranes, which indicates the

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applicability of the Mori and Wen equation to describe the bubble diameter as a function of height, despite the presence of the membranes. Furthermore, the bubble diameter factors decrease strongly for higher ratios of gas addition via the membranes, where this effect is more pronounced (up to 40%) at higher bed heights (0.25 m). Concluding, the RTD measurements using an ultrasound technique provide valuable information about the bubble size as a function of the fluidization velocity and the addition of gas via the membranes. However, a direct measurement of the bubble size (distribution) using noninvasive electrical capacitance tomography (ECT) techniques or optical/capacitance probes is required to support the reported experimental findings. In part 2 of this paper, the study is continued for a MAFBR with chemical reactions. On basis of reactive experiments, the feasibility of the MAFBR for the partial oxidation of methanol to formaldehyde is studied. The experimental findings will be compared with the developed reactor model extended to include chemical reactions, using the obtained information about the bubble diameter factors as a function of the fluidization velocity and gas addition via the membranes. Acknowledgment This research is part of the research program carried out within the Center for Separation Technology, as a cooperation between the University of Twente and TNO, The Netherlands Organization for Applied Scientific Research. The authors thank Wim Leppink for the construction and maintenance of the setups. Notation Ar ) Archimedes number AT ) bed cross section, [m2] Cb,n,i ) concentration of component i in compartment n of the bubble phase, [mol‚m-3] Ce,n,i ) concentration of component i in compartment n of the emulsion phase, [mol‚m-3] C1,C2 ) constants dp ) particle diameter, [m] Dg ) gas diffusivity, [m2‚s-1] db ) bubble diameter, [m] db,0 ) initial bubble diameter, [m] DT ) bed diameter, [m] F ) permeation fraction, [-] f ) bubble diameter factor, [-] g ) gravitational acceleration, [m‚s-2] Hmf ) minimum fluidization bed height, [m] Hf ) actual fluidization bed height, [m] Kbc ) volumetric interchange coefficient between bubble and cloud phase, [s-1] Kbe ) volumetric interchange coefficient between bubble and emulsion phase, [s-1] Kce ) volumetric interchange coefficient between cloud and emulsion phase, [s-1] m ) mass of catalyst, [kg] nc ) number of components, [-] N ) number of CISTRs, [-] Nb ) number CISTRs in the bubble phase, [-] Ne ) number of CISTRs in the emulsion phase, [-] Pi ) partial pressure of component i, [atm] R ) gas constant, [)8.314 J mol-1 K-1] t ) time, [s] T ) temperature, [K] or [°C] u ) velocity, [m‚s-1] u0 ) superficial gas velocity to the reactor, [m‚s-1]

ub ) rise velocity of cloud of bubble in nth compartment, [m‚s-1] ubr ) rise velocity of single bubble in nth compartment, [m‚s-1] s ub ) superficial bubble velocity, [m‚s-1] usb,0 ) initial superficial bubble velocity, [m‚s-1] s ) maximum superficial bubble gas velocity, [m‚s-1] ub,max umf ) minimum fluidization velocity, [m‚s-1] Vi ) volume of the ith phase, [m3] z ) axial position in the bed, [m] Greek Letters δbo ) initial bubble phase fraction, [-] δb ) bubble phase fraction, [-] mf ) bed voidage at minimum fluidization conditions, [-] µg ) viscosity of gas, [Pa‚s] Fg ) density of gas, [kg‚m-3] Fp ) density of fluidizing particles, [kg‚m-3] Subscripts and Superscripts 0 ) initial avg ) average b ) bubble phase bc ) bubble to cloud be ) bubble to emulsion br ) bubble rise e ) emulsion phase exp ) experimental i ) component i in ) inlet max ) maximum mf ) minimum fluidization n ) compartment number p ) permeation r ) rise s ) superficial tot ) total

Literature Cited (1) Kato, K.; Wen, C. Bubble assemblage model for fluidized bed catalytic reactors. Chem. Eng. Sci. 1969, 24, 1351. (2) Cents, A. H. G.; Kersten, S. R. A.; Brilman, D. W. F. Gasphase RTD measurements in gas and gas-solid reactors using ultrasound. Ind. Eng. Chem. Res. 2003, 42, 5506-5515. (3) Deshmukh, S. A. R. K.; Van Sint Annaland, M.; Kuipers, J. A. M. Effect of fluidization conditions on the membrane permeation rate in a membrane assisted fluidised bed. Chem. Eng. J. 2003, 96, 125-131. (4) Deshmukh, S. A. R. K. Membrane Assisted Fluidized Bed Reactor: Experimental demonstration for partial oxidation of methanol. Ph.D. Thesis, University of Twente, Enschede, The Netherlands, 2004. (5) Toomey, R. D.; Johnstone, H. F. Gaseous fluidization of solid particles. Chem. Eng. Prog. 1952, 48, 220. (6) Werther, J. Influence of the bed diameter on the hydrodynamics of gas fluidized beds. AIChE Symp. Ser. 1974, 147 (70), 53. (7) Yates, J. G.; Ruiz-Martinez, R. S.; Cheesman, D. J. Prediction of bubble size in a fluidized bed containing horizontal tubes. Chem. Eng. Sci. 1990, 45, 1105. (8) Kunii, D.; Levenspiel, O. Fluidization Engineering; Wiley: New York, 1991. (9) Shiau, C.; Lin, C. An improved bubble assemblage model for fluidized bed catalytic reactors. Chem. Eng. Sci. 1993, 48, 1299. (10) Mori, S.; Wen, C. Y. Estimation of bubble diameter in gaseous fluidized beds. AIChE J. 1975, 21, 109.

Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 5965 (11) Pyle, D. L.; Harrison, D. An experimental investigation of the two-phase theory of fluidization. Chem. Eng. Sci. 1967, 22, 1199. (12) Shiau, C.; Lin, C. Equation for the superficial bubble-phase gas velocity in fluidized beds. AIChE J. 1991, 37, 953.

Received for review September 15, 2004 Revised manuscript received January 10, 2005 Accepted January 11, 2005 IE049102E

Development of a Membrane-Assisted Fluidized Bed Reactor. 1. Gas

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