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Ind. Eng. Chem. Res. 2005, 44, 2046-2057
Axial Mixing in Monolith Reactors: Effect of Channel Size Archis A. Yawalkar,*,† Rajat Sood,‡ Michiel T. Kreutzer,† Freek Kapteijn,† and Jacob A. Moulijn† Reactor and Catalysis Engineering, DelftChemTech, Delft University of Technology, Julianalaan 136, 2628 BL, Delft, The Netherlands, and Chemical Engineering Department, Indian Institute of Technology, Hauz Khas, NewDelhi-110016, India
The size of the channels in a monolith reactor is an important geometric factor which affects gas and liquid (G-L) distribution in monolith channels significantly and therefore axial-mixing behavior. In the present work the axial-mixing behavior of the liquid phase in cocurrent down flow square channel monoliths of different sizes (200, 400, and 600 cells per square inch or cpsi) has been studied by analyzing the residence time distribution (RTD) of the injected tracer pulse. Simultaneous pressure drop measurements were used to estimate the average liquid slug length. The liquid hold-up in all monoliths was found to be in reasonable agreement (within 30%) with that of a Taylor flow in a single capillary. Axial dispersion and liquid slug length were observed to decrease with increase in cpsi. When intermonolith G-L redistribution occurred between stacked monolith pieces, the axial dispersion decreased further. The ratio of gas bubble length to total slug length (βG), the total G-L velocity, and the liquid slug length affected the degree of axial mixing in a monolith with βG having a strong negative impact. The liquid corner flow in the square channels appeared to be the main cause of axial mixing and not a liquid film between a gas bubble and a channel wall. Overall axial mixing in the monolith could also be partly attributed to maldistribution of the G-L phases at the monolith entrance. A dimensionless correlation is proposed to estimate the overall flow Peclet number. Introduction Recently, monolith reactors are emerging as potential candidates for multiphase reactions of industrial importance. More specifically, this holds for gas-liquid reactions with catalyst as a solid phase coated on the wall of the reactor.1 Some of their major advantages over other conventional reactors (such as stirred tank reactors) are as follows: (i) comparable or high surface-tovolume ratio,2 (ii) high gas-liquid and liquid-solid mass transfer rates,3,4 (iii) the use of a fixed catalyst which avoids catalyst filtration problems encountered in slurry systems, (iv) the low diffusional path which prevents internal diffusion resistance, (v) a very low pressure drop (low energy consumption), and (vi) a regular Taylor flow pattern in all the channels and therefore ease in scale-up. (vii) Further, a recent study of the residence time distribution (RTD) of Taylor flow in a single capillary showed that the axial back mixing within the liquid phase is significantly lower than single phase laminar liquid flow through a capillary.5 The work of Bakker6 on the RTD behavior of a 400 cpsi down-flow monolith operating under the Taylor flow regime showed that the same plug flow behavior can be obtained in hundreds of parallel monolith channels. Thus, another important advantage that the multiphase monolith reactor offers is low axial mixing. Monolith reactors are strong contenders for carrying out fast catalytic reactions such as hydrogenation on an industrial scale,7 which require higher mass transfer rates. Axial mixing is detrimental to the performance of multiphase reactors in the case of positive order * To whom correspondence should be addressed. Fax: +3115-278-5006. E-mail:
[email protected]. † Delft University of Technology. ‡ Indian Institute of Technology.
reactions, especially at high conversion or for consecutive reaction schemes. Therefore, for the purpose of designing monolith reactors, knowledge of the degree of axial mixing is as important as knowledge of gasliquid and liquid-solid mass transfer rates. The present work deals with the axial-mixing behavior of monolith reactors. Residence time distribution (RTD) is a powerful tool to analyze the back-mixing and hydrodynamic behavior of the fluids in the reactor.8,9 The residence time of phases, phase velocities and, therefore, phase hold-ups and magnitude and cause of back mixing within the reactor can be determined. The variance of residence time distribution of the reactor indicates the deviation from ideal plug flow.8 Patrick et al.10 analyzed the RTD behavior of a monolith operated under up-flow conditions. They observed that in up-flow monoliths as the ratio of liquid flow rate to total flow rate increases (uL/uT > 0.1), the liquid volume fraction inside the reactor becomes significantly higher than expected from a single capillary study. In other words, the maldistribution of phases inside the up-flow monolith increases with an increase in liquid flow rate at constant gas flow rate. The work of Thulasidas et al.5 on Taylor flow in single capillary up-flow showed that axial mixing in Taylor flow depends on the following Taylor flow parameters: bubble length to total slug length, bubble velocity, and liquid slug length. While in single channels these parameters are easily determined by photography or visual observation, in monoliths these parameters may vary from channel to channel. In a monolith reactor, these Taylor flow parameters are to a greater extent determined by the gas-liquid distribution at the entrance. The gas-liquid distribution at the entrance of the monolith depends on
10.1021/ie049338i CCC: $30.25 © 2005 American Chemical Society Published on Web 02/25/2005
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Figure 1. Schematic representation of the effect of channel size on slug length in monolith channels.
different geometric and operating configurations such as shape and size of the channels, type of the gas-liquid distributor, type of the flow (up-flow or down-flow), gas and liquid input rates, and physical properties (viscosity, density, and surface tension) of the liquid phase.11 The size of the monolith channels is a crucial geometric factor. In monolith reactors, the terminology used for channel size is “cpsi” or “cells per square inch”.1,2 With an increase in cpsi, the channel size decreases and hence the resistance for the liquid droplets to enter into the monolith channels should be expected to increase. The effect of channel size is explained below as well as in Figure 1 schematically. Case 1: If a drop of liquid from the liquid feeding system is falling on the monolith channel, then (a) If the monolith channel size is comparable to the size of the drop, then the drop will enter the channel as a continuous element without breaking up into multiple slugs. (b) On the other hand, if the monolith channel size is significantly smaller than the diameter of the drop, then the drop cannot enter as a continuous element into the channel. In other words, the resistance for the droplet to enter in the channel is increased. Because of vertical shear it experiences at the monolith surface (or at the solid frontal faces of the walls of the channels at the monolith entrance), on falling, it breaks down into smaller fractions, which then enter the channels in the vicinity, giving relatively smaller slug length. Case 2: Cases 1a and 1b are very simplified cases to discuss the effect of channel size. On the monolith surface, there always exists a very thin layer of gasliquid dispersion. If the size of the channels is significantly smaller, then the dispersed elementseither gas or liquidswill have to break up against the frontal surfaces of the channel walls and then will have to enter in the channels, giving smaller liquid slug lengths, or it will have to rotate to align itself with the channel axis
and then deform to enter into a channel. The latter phenomenon seems to be very unlikely to occur. On the other hand, if the channel size is bigger, then the liquid slug length should also be increased (Figure 1). Case 3: For the monoliths used in this work, with a decrease in channel size, the wall thickness between the channels decreases and number of channels per unit cross-sectional area increases. Hence, the porosity of the monolith increases. Therefore, the residence time of gas and liquid elements in the gas-liquid dispersion at the entrance of the monolith decreases. Hence, the degree of agglomeration of the gas and liquid elements in the dispersion should also decrease, giving smaller slug lengths. Some of the possible events discussed above indicate that the monolith channel size is an important geometric factor, which can significantly affect the gas-liquid distribution at the entrance of the monolith channels and therefore the Taylor flow parameters in a monolith reactor. In the present work the effect of monolith channel size (or cpsi) on the axial-mixing and hydrodynamic behavior of gas-liquid flow in a square channel monolith operating under the down-flow mode has been studied by analyzing the RTD behavior of the liquid phase. Simultaneous pressure drop measurements were also carried out to estimate average liquid slug length using the methodology proposed by Kreutzer et al.12 Redistribution or remixing of the phases between consecutive monolith pieces is expected to minimize the axial mixing in the reactor as a whole. Liquid elements of different residence times from different channels are mixed together in a very short gap between two monoliths and redistributed again in the lower monolith channels. Bakker6 and Kreutzer et al.11 noted that, instead of using a continuous large piece of monolith, if relatively smaller monolith pieces are stacked together with a small redistribution gap between successive pieces, axial mixing of monolith reactor as a whole goes down. To study the effect of redistribution further in detail, in this work the G-L distribution and liquid phase axialmixing behavior in a monolith just below the redistribution zone were analyzed in the context of different channel size monoliths. The majority of the experiments were carried out using a spray nozzle as a liquid distributor. Some experiments were also performed using a static mixer as a gas-liquid distributor to study the effect of distributor on axial mixing in the monolith channels. Experimental Section Experimental Setup. The experimental setup of the present work was similar to that used by Bakker6 and Kreutzer et al.11 A schematic diagram of the experimental setup is shown in Figure 2a. The liquid (tap water) was pumped with a screw pump (Monopumps, Ltd.) from the storage tank to the monolith and recycled back. Part of the liquid was bypassed to control the flow rate. The liquid from the pump was first filtered to remove any suspended particles and then fed to the column. A turbine flow sensor (Digi-flow, DFS 2, (1% full scale) was used to measure the input liquid flow rate to the monolith reactor. Gas was fed into the monolith column through a digital mass flow controller (Brooks). A pulse of tracer (Ecoline blue ink, Royal Talens) was applied via a special valve system to ensure the consis-
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Ind. Eng. Chem. Res., Vol. 44, No. 7, 2005 Table 2. Monolith Configurations Used in the Present Work RTD and pressure drop behavior measured for two monoliths in series one monolith redistribution effect nozzle distributor static mixer distributor
Figure 2. Experimental details. Table 1. Geometrical Properties of Monoliths Used in This Work2 cell density (cpsi)
200
400
600
porosity length (cm) channel diameter (mm) wall thickness (µm) geometrical area (m2/m3)
0.69 50 1.50 305 1850
0.74 50 1.09 178 2710
0.80 50 0.93 109 3450
tent injection of a fixed amount of tracer in all the runs. To achieve this, a prefilled dye injection volume was injected with process liquid using a fast response valve (Burkert, (15 ms). It was found that the maximum impact of injected volume flow on the liquid flow rate was 0.1) than expected from a single capillary study. This indicates the presence of many monolith channels filled predominantly with liquid and hence significant maldistribution of phases at the monolith entrance. In this work on down-flow monoliths, the same liquid hold-up criterion of Patrick et al.10 was used to study the gas-liquid phase distribution in monolith channels. In this work the maldistribution in a monolith was defined as
% maldistribution )
Figure 3. Raw experimental E curves.
ing the dimensional variance of the RTD curve value to the theory,8
σθ2 ) 2
( ) ( )
(1)
uLl De
(2)
1 1 +8 Pel Pel
2
The Peclet number is
Pel )
where l is the length of the column, De is the axial dispersion coefficient, and uL is the mean liquid velocity in the monolith reactor obtained from the mean residence time,
uL )
l tmean
(3)
Lmonolith - Lsingle channel Lsingle channel
× 100 (5)
where the experimentally determined hold-up in the monolith is compared to the hold-up in a single channel at the same gas and liquid superficial velocity. (a) Liquid Hold-Up in a Single Capillary in Taylor Flow. From their extensive experimental work on Taylor flow in single circular and square capillaries, Thulasidas et al.13 proposed an iterative scheme to predict gas bubble velocity in Taylor flow. From the analysis of their empirical data, Thulasidas et al.13 indicated that the ratio of bubble velocity (uB) to total velocity (uT ) uLs + uGs) can be correlated by a thirdorder polynomial in the logarithm of capillary number based on bubble velocity (CauB ) uBµ/σ). From their experimental data we have derived the following equations by regression:
For round capillaries, uB/uT ) 0.231(ln(CauB)) + 2.1486
(6)
which was based on experiments in the range 0.01 < CauB < 3. For CauB < 0.01, the ratio uB/uT is very close to unity.
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For square capillaries, For CauB e 0.01, uB/uT ) 0.0653(ln(CauB))2 + 0.8579(ln(CauB)) + 3.8908 (7) For CauB > 0.01, uB/uT ) 0.2336(ln(CauB)) + 2.2675
(8)
The experimental data of Kreutzer et al.11 on a single capillary were compared with the bubble velocity estimated from the iteration scheme of Thulasidas et al.13 in Figure 4. A good fit shows that the iteration scheme of Thulasidas et al.13 is reliable for predicting the gas bubble velocity in a Taylor flow in a single capillary. From uB, the fractional gas hold-up in Taylor flow can be obtained as14
G ) uGs/uB
(9)
Figure 4. Parity plot for the iterative-material balance scheme of Thulasidas et al.13 The predicted values of bubble velocities, uB, are compared with the single capillary data of Kreutzer et al.12 Legend: [, air-water system; 0, air-decane system; ×, airtetradecane system.
Therefore, the fractional liquid hold-up in a single capillary under Taylor flow is
L ) 1 - G
(10)
The above-described procedure was used to estimate the fractional liquid hold-up in a single capillary under Taylor flow for a given gas and liquid superficial velocity. This semiempirical single channel result was compared with the experimental liquid hold-up in the monolith to determine the extent of maldistribution of the phases. (b) Average Fractional Liquid Hold-Up in Monolith Channels from Mean Residence Time. From the analysis of concentration versus time data, the mean residence time of a liquid (tmean) in a monolith was obtained. From the volumetric liquid flow rate (VL), the volume of liquid in the monolith is
VLtmean
(11)
Therefore, the fractional liquid hold-up in the monolith is
Lmonolith ) VLtmean/vm
(12)
vm is the monolith volume available for gas-liquid flow, which is the product of porosity and the total volume of the monolith. Figure 5a shows a comparison between the actual fractional liquid hold-up in monoliths and the fractional liquid hold-up in a single capillary, for two monolith pieces stacked together, with a small redistribution space in between. The deviation from the diagonal line represents the percentage maldistribution in the monolith under given conditions. Most of the data points lie within 30% of the fractional liquid hold-up line of a single capillary. Data points for a 200 cpsi monolith, in comparison, deviate more from the diagonal line than data of 400 and 600 cpsi monoliths. This means that the gas-liquid distribution in 400 and 600 cpsi monoliths is significantly better than that in 200 cpsi monoliths. Many of the data points for all three monoliths lie above the single capillary line. The data points above the single capillary line indicate the presence of
Figure 5. Comparison of fractional liquid hold-up (L) between the down-flow monoliths observed in the present work and a single capillary operating under the Taylor flow regime. (a) Fractional liquid hold-up in two monoliths in series configuration. Legend: ], 200 cpsi; ×, 400 cpsi; 2, 600 cpsi. (b) Fractional liquid hold-up in lower monolith. Legend: ], 400 cpsi (nozzle distributor); ×, 600 cpsi (nozzle distributor); 2, 600 cpsi (static mixer distributor).
some channels preferentially filled with liquid. Data points below the single capillary line indicate the presence of some channels in which liquid content is significantly lower and/or the gas bubble lengths are substantially longer than in the rest of the channels. Figure 5b shows the fractional liquid hold-ups in the 400 and 600 cpsi lower monoliths of the stack in Figure 5a. Thus, Figure 5b shows the effect of redistribution.
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Redistribution data for 400 and 600 cpsi monoliths for nozzle and static mixer distributors lie within 15% of the single capillary liquid hold-up line. This deviation is comparatively less than that for the data for two monoliths in series for these two types of monoliths. From Figure 5 it can be seen that intermonolith redistribution results in better gas-liquid distribution in monolith channels. However, Figure 5b also indicates the presence of some monolith channels with high liquid holdup. Liquid Slug Length Estimation from Pressure Drop Measurement. Kreutzer et al.12 proposed that pressure drop in Taylor flow in a single round capillary can be modeled in the form
f)
(
( ))
a b Re c 1+ Re ψL Ca
(13)
where f is the friction factor and ψL is the dimensionless liquid slug length (LS/dC). The first term in the parentheses represents the frictional pressure drop of HagenPoiseuille flow, while the second term represents the effect of the presence of the gas bubble on the liquid flow, which is mostly due to a Laplace pressure term related to the shape of the bubble under flowing conditions and, to a lesser extent, related to the circulation within the liquid slug. The Reynolds number and capillary number are based on the velocity of the liquid in the liquid slug, uT. The friction factor f is obtained from the total pressure drop as
f)
(
)(
)
∆Pmonolith 1 dC 4 lLmonolith 1 F u 2 2 L L
Figure 6. Variance of monoliths observed in the present work. (a) Variance of monoliths of different cpsi for two monoliths in series configuration. Legend: [, 200 cpsi; +, 400 cpsi; 4, 600 cpsi. (b) Effect of G-L redistribution between the successive monoliths on the variance of the 600 cpsi monolith. Legend: [, upper monolith; 0, lower monolith.
(14)
Here,
∆Pmonolith ) (P1 - P2) + ∆Pdist + ∆Pg
(15)
and P1 - P2 is the pressure drop measured using the pressure sensors (Figure 2). ∆Pdist is the pressure drop across the liquid distributor,15 and ∆Pg is the pressure drop from the gravity effects. Kreutzer et al.12 proposed that, from the relationship, eq 13, for a given pressure drop across a capillary operating under the Taylor flow regime, an average liquid slug length can be predicted. From their experimental data on a single round capillary, Kreutzer et al.12 found the constants in this correlation are a ) 16, b ) 0.17, and c ) 0.33. Kreutzer16 indicated that if the pressure drop across the distributor is corrected for, then the same relationship could be used to estimate the liquid slug length in a monolith reactor. In this work the simultaneous pressure drop measurements carried out during all the RTD experiments were used to estimate liquid slug lengths for a given pressure drop in monolith reactors from the correlation of Kreutzer et al.12 Variance. Figure 6a shows the variance of 200, 400, and 600 cpsi monoliths, for two monoliths in series configuration. With an increase in total G-L velocity (uT), the variance of all three monoliths decreases. The variance of the 600 cpsi monolith is lowest. Figure 6b compares the variance of the upper monolith with that of the lower monolith under the redistribution zone for a 600 cpsi monolith. The data points for the lower monoliths lie below the corresponding data points for the upper monolith, suggesting less axial mixing in the
Figure 7. Axial dispersion coefficient for monoliths used in the present work. (a) Axial dispersion coefficient in two monoliths in series configuration. Legend: [, 200 cpsi; ×, 400 cpsi; 4, 600 cpsi. (b) Comparison of axial dispersion coefficients in the lower monoliths under the redistribution zone. Legend: [, 600 cpsi (nozzle distributor); 0, 600 cpsi (static mixer distributor).
monoliths just under the redistribution zone. The same trend was observed for the 400 cpsi monolith. Axial Dispersion Coefficient. The axial dispersion coefficient data derived from the variance of the E curves for 200, 400, and 600 cpsi monolith stacks are shown in Figure 7a. The axial dispersion coefficients for 600 cpsi monoliths are lower than those for 200 and 400
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Figure 9. Effect of uT and uGs/uT (≈βG) on Pef in two 600 cpsi monoliths in series configuration. Legend: [, uGs ) 0.071 m/s; 0, uGs ) 0.108 m/s; 2, uGs ) 0.122 m/s; ×, uGs ) 0.131 m/s; 4, uGs ) 0.172 m/s.
Figure 8. Liquid slug length estimated from eq 13, in different monolith configurations. (a) Liquid slug length in two monoliths in series combination. Legend: ], 200 cpsi; ×, 400 cpsi; 2, 600 cpsi. (b) Liquid slug length in lower monoliths under the redistribution zone. Legend: [, 400 cpsi (nozzle distributor); 0, 600 cpsi (nozzle distributor); ×, 600 cpsi (static mixer distributor).
cpsi monoliths. For monoliths under the redistribution zone (Figure 7b), almost all the data points for 600 cpsi monoliths with nozzle and static mixer distributors lie below the data for 400 cpsi monoliths. The axial dispersion coefficients in the lower monolith with a static mixer distributor are slightly lower than those with a nozzle as distributor. From Figure 7 it can be seen that the axial dispersion coefficients in the lower monolith under the redistribution zone are lower than those for two monoliths in series configuration, indicating clearly that the redistribution reduces the degree of back mixing in the monolith channels. Here, it should be noted that in monoliths under the redistribution zone the G-L maldistribution is also lower than that in two monoliths in series configuration (within 15% of the single capillary Taylor flow regime). Liquid Slug Length. Figure 8a shows liquid slug length data for monoliths of 200, 400, and 600 cpsi, estimated from the pressure drop measurement for two monoliths in series. The liquid slug length (LS) values in the monoliths show the trend LS(200 cpsi) > LS(400 cpsi) > LS(600 cpsi). From 200 to 600 cpsi, the channel size of monoliths decreases from 1.50 to 0.93 mm. As discussed in the Introduction, with a decrease in channel size the resistance for liquid droplets/elements to enter the monolith channel increases, resulting in a decrease in liquid slug length. The trend of slug length data with total velocity, uT, shows that the slug length for a given monolith is almost independent of total velocity. This indicates that the slug length is mainly dependent on the system geometry and not the operating conditions. The system geometry
includes the channel size of the monolith and the feeding system. Each feeding system has a different hydrodynamic behavior in the feeding section, and as a result, each distributor will have its own characteristic droplet size. Figure 8b shows liquid slug lengths in 400 and 600 cpsi monoliths under the redistribution zone. The liquid slug lengths in the 600 cpsi monolith are significantly lower than those in the 400 cpsi monolith. From Figure 8 it is seen that the liquid slug lengths in lower monoliths are somewhat lower than those in two monoliths in series configuration. This difference can be attributed to better G-L distribution in the lower monoliths as compared to the case of two monoliths in series configuration. Thus, it can be argued that if the number of redistribution zones in a monolith reactor is further increased, the behavior of such an assembly will be closer to that of a single capillary operating under a Taylor flow regime. Fluid Flow Peclet Number. The Pef data were analyzed on the basis of Taylor flow parameters. It was observed that the value of Pef increased with total velocity (uT) and decreased with an increase in the ratio of gas bubble length to total slug length (βG), which is approximately equal to the ratio uGs/uT.13 Figure 9 shows the variation of Pef with uGs/uT for different total velocities, uT, for a 600 cpsi monolith. Similar behavior was observed for all the monolith configurations studied in the present work. Transport of tracer from one liquid slug to the following takes place via the liquid film and the corner liquid flow between a gas bubble and a wall of the channel. On increasing βG at constant uT (i.e. constant residence time and liquid film thickness), the tracer from the liquid film and corner flow is transferred to a relatively lower number of liquid slugs in a given time and, therefore, the retention time of a tracer in this liquid fraction increases, increasing the axial dispersion. This phenomenon is schematically explained in Figure 10. To explain the effect of βG more clearly, the total velocity and liquid slug length are assumed to be constant. On increasing total velocity, uT, at constant βG, three factors affecting axial mixing in Taylor flow change; that is, (i) the liquid film thickness between a bubble and a channel wall increases, (ii) the internal circulation velocity within a liquid slug increases, and (iii) the residence time of a liquid in a channel decreases. Increasing the liquid film thickness implies that more tracer could be transferred from the tracer-containing
Ind. Eng. Chem. Res., Vol. 44, No. 7, 2005 2053
Figure 10. Schematic representation of the effect of βG, at constant uT and liquid slug length, on tracer transfer in the Taylor flow.
liquid slug to the following adjacent liquid slug. This would increase the axial dispersion. The increase in internal circulation velocity within a liquid slug should result in higher radial mass transfer to the film and corner liquid, giving higher axial mixing. On the other hand, since the residence time of the liquid phase goes down, the contact time between the tracer-containing slug and the liquid film and corner liquid flow decreases. Therefore, comparatively less tracer is transferred from the tracer-containing slug to the liquid slug behind it. This factor leads to a decrease in the axial dispersion coefficient and, hence, an increase in Pef. From the results obtained in this work, it can be concluded that under the prevailing experimental conditions in square channeled down-flow monoliths factor iii is dominating compared to factors i and ii. The insignificant effect of the increase in liquid film thickness on Pef can be attributed to a comparatively substantial amount of liquid in the corner liquid flow in square channels of the monolith. Thus, the corner liquid can be considered as a major source of transfer of tracer from one liquid slug to the following adjacent liquid slug. Figure 11 shows some smoothed experimental E(θ) curves for 200, 400, and 600 cpsi monoliths for two monoliths in series configuration. In these curves the dimensionless time, θ, is based on the mean residence time obtained from the first-order moment of the outlet Et(t). As can be seen on increasing βG at constant uT, the percent area under the tail increases, indicating an increase in the amount of tracer in the corner liquid and the liquid film (dead zone). This behavior can be explained on the basis of the reasons discussed above. When uT increases at constant βG, the tail decreases in intensity, due to the dominating effect of reduced residence time, as explained before. Figure 12 shows the area under the tail of the E(θ) curves for 200, 400, and 600 cpsi monoliths for two monoliths in series configuration. To determine the average tailing, a graphical method proposed by Kushalkar and Pangarkar17 was used. The figure indicates that the percent tail area decreases with an increase in cpsi or a decrease in the channel size of the monolith. This means, on increasing cpsi of the monolith, the corner liquid flow in monoliths with square channels decreases. Thus, from the results discussed, the lower axial dispersion in a 600 cpsi monolith can be attributed to
Figure 11. Some E curves for 200, 400, and 600 cpsi indicating the effect of variation of uT and βG.
Figure 12. Percent area under tailing of E curves for two monoliths in series combination. Dotted lines represent conditions at approximately constant βG and uT. Legend: [, 200 cpsi; 9, 400 cpsi; 2, 600 cpsi.
(i) better gas-liquid distribution at the entrance of the monolith in terms of achieving Taylor flow approaching that of a single capillary for a given set of operating conditions (gas and liquid flow rates), (ii) shorter liquid slug lengths, and (iii) relatively less corner liquid flow. Actually, the smaller channel size in 600 cpsi monoliths is the main reason for these effects, indicating the importance of channel size for the performance of the monolith reactor. The major role of corner liquid flow in axial mixing in square channeled monoliths suggests the use of circular channel monoliths. If circular channeled monoliths are used instead of square channeled monoliths, then the axial-mixing behavior should decrease drastically. However, to date, high cpsi monoliths have been
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Figure 13. Comparison of vessel dispersion numbers of the downflow monoliths in two monoliths in series configuration observed in the present work with one phase laminar liquid flow in a capillary.8 Legend: 9, 200 cpsi; 4, 400 cpsi; ×, 600 cpsi.
made only in square channels for several reasons. Rectangular channels correspond with relatively easy manufacture and better-defined channel wall dimensions. Effect of Intermonolith Redistribution. The redistribution occurred in just a small gap of size between 3 and 4 mm between two monoliths. In this gap, liquid elements of different residence times from different channels of upper monoliths are mixed together. As discussed above, the corner liquid flow is one of the main causes of axial mixing in square channel monoliths. In the redistribution space, the liquid in the corner flow from different channels is also mixed with the bulk of the liquid in the slugs and redistributed again. Figure 5 shows that in the monolith under the redistribution zone the maximum maldistribution decreases from approximately 30% to 15% (i.e. maldistribution is decreased by 50%). Thus, the behavior of the monolith under the redistribution zone moves closer to the behavior of a single capillary. Hence, the axial mixing in a monolith under the redistribution zone should also decrease. Therefore, it can be concluded that when using a very short redistribution space between successive monoliths, the axial mixing decreases because of two phenomena: (1) remixing and redistribution of liquid elements of different residence times from different channels and (2) reduction in the maldistribution of phases. The important inference from this observation is that the monolith itself can act as an efficient gasliquid distributor for downstream monolith blocks. Comparison with Axial Dispersion in Single Phase Laminar Liquid Flow in a Single Capillary. Axial dispersion data of the present work are compared with axial dispersion in laminar liquid flow in a capillary (Figure 13). For laminar flow in a tube, many regimes may be identified, and here it is most appropriate to compare with the regime of significant radial diffusion and negligible axial diffusion, which may be described using the theory of Taylor and Aris.8 Figure 13 shows the vessel dispersion number data (1/Pef) for all three types of two monoliths in series configuration. It lies significantly below the liquid only flow line. This shows that a monolith operating in Taylor flow regime behaves closer to plug flow than one phase laminar liquid flow through the capillary. This behavior is in agreement with the single capillary Taylor flow study of Thulasidas et al.5 and RTD work of Bakker6 on 400 cpsi monoliths. In contrast, Patrick et al.10 from their study on up-flow monoliths found that vessel dispersion
numbers in monoliths are much higher than those for only laminar liquid flow through a capillary, indicating a behavior far from plug flow. This contradicting result can be attributed to significant maldistribution in their monolith (Figure 13 of their paper). Their data show that the actual liquid hold-up in a monolith is 100350% higher than expected in a single capillary under Taylor flow. Thus, the liquid spends a significantly longer time in a reactor than expected in a Taylor flow, implying higher axial dispersion. In contrast, the liquid phase maldistribution observed in the present work on down-flow monoliths was within 30% (Figure 5). These results indicate that liquid phase maldistribution in Taylor flow in down-flow is significantly lower than that in up-flow. However, the validity of this observation should be checked by a detailed comparative study between up-flow and down-flow monoliths over a wide range of geometric and operating configurations. The ranges of vessel dispersion numbers observed in the studies of Thulasidas et al.,5 Patrick et al.,10 and this work are 1-18, 60-150, and 20-63, respectively. Even though the 1/Pef values observed in this work are significantly lower than those of Patrick et al.,10 they are higher than the single capillary values. The reason for this difference may be the liquid phase maldistribution at the entrance of the monolith even though it is less than 30% in this work. Correlation for Fluid Flow Peclet Number. Proper estimation of Peclet number is necessary for reliable design of multiphase reactors. For packed bed reactors, numerous studies are available in the literature proposing empirical correlations from their Peclet number data based on an axial dispersion model for different geometric and operating configurations.9 From the previous section it can be concluded that Pef in down-flow square channeled monoliths increases with a decrease in the ratio of gas bubble length to total slug length (βG ≈ uGs/uT) and a increase in total velocity (uT) and vice a versa. However, the specific trend of the dependence of Pef on liquid slug length could not be properly determined. This could be because of two reasons: (i) The dependence of Pef on liquid slug length is not so strong, and/or (ii) since for a given monolith the average liquid slug length varies with both the parameters βG and uT, therefore, it could not be controlled independently. Hence, its individual effect on Pef could not be observed, while in a single capillary study all three of these parameters can be varied independently.5 Therefore, to determine the dependence of Pef on all three Taylor flow parameters in this study, a linear regression of the data was done as Pef ) f(Re,βG,ψL). In this correlation form, the Reynolds number along with βG and ψL represents the flow dynamics with channel size, dC, as a length scale and total velocity, uT or uLs + uGs, as the average velocity of the liquid slug.13 The correlation obtained was
Pef ) (3.268 × 10-3)(Re)0.31(βG)-0.95(ψL)-0.23
(16)
Figure 14 shows a parity plot for eq 16. Most of the data points show satisfactory fit and lie within (30%. The standard error of eq 16 is 15%. The regression expression (eq 16) indicates that axial dispersion increases with an increase in βG and liquid slug length and a decrease in uT. The exponent of βG indicates a strong negative impact on axial dispersion. This inverse
Ind. Eng. Chem. Res., Vol. 44, No. 7, 2005 2055
Figure 14. Parity plot for eq 16. Legend: [, 200 cpsi (two stacked monoliths); 0, 400 cpsi (two stacked monoliths); 2, 600 cpsi (two stacked monoliths); ×, 400 cpsi (lower monolith); ], 600 cpsi (lower monolith, nozzle distributor); 4, 600 cpsi (lower monolith, static mixer distributor).
dependence of Pef on βG and ψL is in agreement with the observation of Thulasidas et al.5 in their single capillary study. The two exponents, 0.31 and -0.95, of the Reynolds number and βG, respectively, in the proposed correlations could be fixed to values usually found in the engineering correlations, 0.33 and -1, without influencing equation usefulness. The regression of the data is done accordingly, and the correlation obtained was
Pef ) (2.985 × 10-3)(Re)0.33(βG)-1.00(ψL)-0.24
(17)
Figure 14 indicates that even though the proposed correlation estimates Pef values reasonably well, the data points show some scatter around the correlating line. This can be partly attributed to liquid phase maldistribution at the entrance of the monolith (even though it is
