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Ind. Eng. Chem. Res. 2005, 44, 4898-4913
Scaling-up Multiphase Monolith Reactors: Linking Residence Time Distribution and Feed Maldistribution Michiel T. Kreutzer,* Jasper J. W. Bakker, Freek Kapteijn, and Jacob A. Moulijn Reaction and Catalysis Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands
Peter J. T. Verheijen Process Systems Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands
The scale-up of Taylor flow from a single capillary channel to a monolith is a critical step for the industrial application of microchannel reactors in general and monolith catalyst supports in particular. Characteristics of pressure drop in capillaries were used to identify the conditions under which all channels in a monolith behave essentially identically. This eliminated upflow as unstable and posed a criterion for the minimal stable gas and liquid velocity in downflow. The assumption that the pressure drop over all channels is the same allowed the transformation of feed maldistribution into a residence time distribution. The residence time of the bubble train was rather insentitive to feed maldistribution. Experiments confirmed the limited impact of maldistribution on the RTD for different distributors. The E curves in monoliths were described by a piston-dispersion-exchange (PDE) model, where the dispersion term quantified the maldistribution. Industrially relevant observations on distributor design and monoliths blocks stacking are reported. The most important practical conclusion was that monoliths can indeed be scaled-up using physically sound criteria. 1. Introduction Honeycomb monoliths are catalyst support structures of small parallel channels. Monoliths are well-known for environmental gas-cleaning processes, where the monolith combines low pressure drop with sufficient geometric surface area. The best known examples are the catalytic car converter and DeNOx reactors. The past decade has seen a growing interest in the use of monoliths as catalyst supports for three-phase applications, i.e., heterogeneously catalyzed gas-liquid reactions.1-5 The main focus has been on fast hydrogenation reactions such as those of R-methylstyrene,6,7 nitroaromatics,8-10 phenylacetylene,11 and sorbitol12 and fat hardening.13 A commercial application of three-phase monolith reactors is the production of hydrogen peroxide in the anthraquinone process.14 At low to moderate velocities, the flow pattern of alternating elongated bubbles and slugs, which is depicted in Figure 1, occurs in the capillary channels. Some important characteristics of this flow pattern were first reported by Bretherton15 and Taylor,16 and now, it is commonly referred to as Bretherton’s problem or Taylor flow. This flow pattern has some interesting features for multiphase reactors. First, when a chemical reaction occurs on the wall of the capillary, the recirculation inside the liquid slug enhances the radial mass transfer to the film. This film is very thin, so very high masstransfer rates can be achieved.7 Second, the degree of backmixing, compared to homogeneous laminar flow, is * To whom correspondence should be addressed. Tel.: +31 15 278 90 84. Fax: +31 15 278 50 06. E-mail: kreutzer@ tnw.tudelft.nl.
Figure 1. Computed flow of a bubble in a capillary. A lubricating thin liquid layer (dark gray) persists on the wall. Liquid between the slugs (light gray) circulates. Here, Ca ) 0.01 and Re ) 100. Kreutzer18 has reported the numerical details.
diminished by the presence of the bubbles, which effectively segregate the liquid phase into slugs that are isolated with respect to one another. In fact, the only mechanism for transfer of matter from one slug to the next is by diffusion from the slug to the film and subsequent diffusion from the film to the next slug. The combination of enhanced radial mass transfer (local mixing) and suppressed backmixing makes Taylor flow an ideal hydrodynamic regime for many gas-liquidsolid reactions. Although the extent of backmixing in a single channel is probably minimal, the same does not necessarily hold for a monolith column. If the distribution of gas and liquid into the monolith channels is not perfect, the velocity of the slugs and bubbles can vary from channel to channel. Note that there is no flow from channel to channel within a monolith block, so redistribution inside the packing is impossible. The extent of a velocity distribution can, in principle, be detected by comparing the residence time distribution (RTD) of Taylor flow in a single channel with the RTD of a monolith block. As redistribution inside the packing cannot flatten out a feed maldistribution, it is no surprise that previous studies, which will be reviewed shortly, have shown more severe backmixing in monolith reactors in comparison to trickle-bed reactors, and obtaining uniform stable Taylor flow has been marked as a critical requirement for the application of monoliths.17
10.1021/ie0492350 CCC: $30.25 © 2005 American Chemical Society Published on Web 01/06/2005
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This paper addresses the scaling-up of a single capillary to a bundle of capillaries and applies this to a monolith. The main question is whether variations between the channels can be ignored. We consider both dynamic variations (hydrodynamic instability) and steady-state variations (inlet liquid maldistribution). The analysis of the two-phase pressure drop of Taylor flow leads to insight into both phenomena and to criteria that set the conditions for minimal scaling effects. Experimentally, the residence time distribution in downflow monoliths is measured to investigate these scaling aspects. 2. Previous Work Single-Channel Taylor Flow. The low axial dispersion in Taylor flow has been studied extensively in single capillary channels. In so-called “continuous-flow analyzers”, samples are separated by bubbles that prevent mixing of samples prior to analysis. For these analyzers, Thiers et al.19 studied the interslug mass transfer in a capillary. Using sufficiently long liquid slugs, they made the reasonable assumption that the film and the slug have sufficient time to mix. This allowed them to model the dispersion in their apparatus using a model of tanks in series, connected by the film between the slugs. Pedersen and Horvath20 used a slightly different approach and modeled the film as tanks-in-series and the slugs as isolated tanks that communicated only with the film. A previously developed mass-transfer correlation21 was used to describe the rate of exchange between the film and the slugs. Thulasides et al.22,23 made several improvements. First, when the slugs are short, full mixing between slug and film can no longer be assumed, and the rate of exchange between the film and the slugs becomes sluglength-dependent.21,24,25 Second, for vertical capillaries, the film between the bubble and the wall becomes a falling film, for which the velocity can be calculated from the film thickness. For thick films or low slug velocities, the assumption that the film is stagnant no longer holds. This is especially important in noncircular channels, where the film is thicker in the corners. Thulasidas et al.23 used an infinite series solution for radial diffusion and took the gravity-driven flow in the film into account. The improved mathematical model described the experimental data accurately. In short, the experimental data and theoretical models in the open literature indicate that the residence time distribution in a single channel can be described by a model consisting of a dynamic zone (the slugs) that is in perfect plug flow and a stagnant or falling zone (the film) that exchanges matter with the dynamic zone. The main differences between these models are in the mathematical methods of determining the rate of exchange between the zones. An important characteristics of such piston-exchange (PE) models is that the broadening of the E curve is very asymmetrical, i.e., has a very sharp front and a long tail. This reflects the fact that tracer can only leak to slugs upstream and no tracer ever reaches a slug downstream. This is in sharp contrast to axial dispersion, in which random fluctuations around a mean lead to a (more) symmetric curve. The stability of Taylor flow was considered independently by Grolman et al.26 and Reinecke and Mewes,27 who both arrived at similar conclusions. If the pressure drop in a channel is dominated by friction, an increase in flow rate is accompanied by a increase in pressure
Figure 2. State of the art in monolith scale-up. The E(θ) curve for the monolith and the E(θ) curve for the single channel were taken from Thulasidas et al.23 The PE model curve is taken from Kreutzer.18
drop. As a result, the dynamic response to a perturbation of the velocity will dampen out to the equilibrium situation. If other contributions to the pressure drop, such as a hydrostatic contribution, become important, an increase in flow rate can cause a decrease in pressure drop. Then the system becomes unstable, and for such conditions an oscillating behavior was observed and accurately modeled by Reinecke and Mewes.27 Multichannel Taylor Flow. Comparison of the single-channel RTD to that of an array of channels, i.e., a monolith, was performed in the group of R. L. Cerro.22,23,28 The results showed that the monolith was almost completely backmixed, and the single-channel data did not agree at all with the monolith data. Although the experiments in single channels all resulted in very narrow curves [Thulasidas et al.23 reported variances of the dimensionless E(θ) curves σθ2 in the range 0.0001-0.01], upflow in the bundle of capillaries gave E(θ) curves similar to those of one or two tanks in series. This day-and-night difference is illustrated by Figure 2. Clearly, in the description of the RTD of the capillary bundle, the small amount of piston-exchange backmixing caused by leakage to slugs upstream could be ignored. Most experimental data on residence time distributions in monoliths are reported for upflow conditions. Recently, Winterbottom et al.29 demonstrated that downflow Taylor flow conditions resulted in a narrow RTD in comparison to laminar single-phase liquid flow through the same monolith. Further, the narrow RTD corresponded to a higher attainable selectivity in a consecutive reaction scheme, highlighting the importance of plug flow for such reactions. Recently, Gladden and co-workers30-32 visualized downflow in monoliths at low superficial velocities using MRI tomography. This powerful technique provides a full picture of Taylor flow in a monolith, including the time-dependent local velocity and holdup. To date, however, the method works only for relatively low velocities, although the progress in this field is very rapid. In most of the channels, the flow was indeed downward, but a wide range of velocities was found. Further, in some channels, the direction of flow was upward, resulting in recirculation over the monolith block. This recirculation behavior, combined with the wide spread in velocities, might explain the large extent of backmixing observed by Thulasidas et al.23 Although no systematic investigation of the transient behavior of
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the channels was presented, Mantle et al.30 did observe that the flow in the channels was far from stable. Edvinsson Albers et al.14 discussed the scale-up from the laboratory scale of a commercial monolith reactor. Only in downflow could an even distribution of the liquid over the monolith be achieved. At low velocities, downflow became unstable, as was predicted by Grolman et al.26 In upflow, channeling occurred for the bubbles, and a good distribution over the monolith could not be obtained. 3. Model Formulation The key to describing the dynamic behavior of a single capillary channel is understanding how the pressure drop varies with the gas and liquid flow rates, as has been described above. The key to understanding the steady-state behavior of multiple channels is very similar: the pressure drop from the top of the monolith block to the bottom of the block is the same for all channels, and the condition of equal pressure drop over all channels in the monolith block provides a condition that limits the possible combinations of gas and liquid flow rates in each channel. Although it is tempting to regard this as a rather special feature of monolith packings, trickle-bed reactors do not behave all that differently: Boyer et al.33 demonstrated that a maldistribution introduced at the top of a trickle bed propagates through the entire bed practically unchanged if cross-sectional pressure gradients are absent. Maldistribution is the nonhomogeneity of throughput of gas and liquid in the channels or, on a per-area basis, the nonhomogeneity of superficial velocities. The condition of equal pressure drops can be used to (1) calculate all possible combinations (uLs, uGs) of gas and liquid superficial velocities that can occur at a given pressure drop (∆p/L) and (2) calculate the (gas or liquid) residence time for a given combination (uLs, uGs) of gas and liquid superficial velocities. We consider both aspects first for a single channel. As the Taylor flow pattern is well-defined and regular, it is possible to accurately correlate pressure drop, superficial velocities, and residence time distribution with one another. The pressure drop model can then be used to predict the unstable operating conditions. Subsequently, we investigate the effects of liquid maldistribution. The resulting model is nonlinear, and we begin with a narrow distribution around a mean liquid superficial velocity. For such a narrow distribution, a linearization is allowed. Finally, we make some remarks about more severe liquid maldistribution for which the linearization approach is less appropriate. Pressure Drop. In Taylor flow, the bubbles travel slightly faster than the sum of the gas and liquid superficial velocities or two-phase velocity uTP
uTP ) uLs + uGs
(1)
In fact, eq 1 would be exactly correct if the bubbles spanned the entire cross section of the channel. In reality, a thin film separates the bubble from the wall, and for round capillaries we find from a simple volumetric continuity balance the excess bubble velocity
uB 4δ ≈1+ uTP d
(2)
in which δ is the film thickness. The dimensionless film thickness δ/d is O(Ca2/3), where Ca is the capillary number, Ca ) (µu/γ) (see, e.g., Bretherton15). The fractional error introduced by using the simple estimate of eq 1 is therefore also O(Ca2/3). For surface-tensiondominated flows of low-viscosity liquids at moderate flow rates in monoliths, where Ca ) O(10-3), the error made by ignoring the finite film thickness is of the order 5-10%. In square capillaries, a thicker film remains in the corners, and the approximation of zero velocity in the film is less appropriate. On the other hand, if the corners are significantly rounded (e.g., in the process of coating the channel), this film also becomes very thin in the corners. For the present study, we accept the error introduced by ignoring the film thickness and assume that the velocity of the bubble, uB, and the velocity of the slugs can be estimated by uTP
uB ) uS ) uTP ) uLs + uGs
(3)
The pressure drop in each channel consists of a frictional term, a hydrostatic term, and a Laplace term. The frictional losses due to the bubbles (or, more precisely, the falling film separating the elongated bubbles and the wall) can be ignored with respect to the frictional losses due to the liquid slugs. For the frictional losses in those slugs, the friction factor for developed laminar flow can be used with the Reynolds number based on the actual slug velocity
Re )
FuTPd η
(4)
Again ignoring the film, we estimate the fraction of the channel filled with liquid slugs, i.e., the liquid holdup, by
L )
uLs uLs + uGs
(5)
Now, the frictional losses from the slugs per meter of channel length are, assuming negligible gas-liquid interaction
(∆pL)
)-
16 1 4 F u 2 Re 2 L TP d L
(6)
)-
32η uLs d2
(7)
(fr)
(
)( )
where the holdup estimate from eq 5 was used to estimate the fractional height of the channel filled with slugs. This same estimate is used to calculate the hydrostatic pressure term
(∆pL)
(st)
) FgL
(8)
The third contribution to the pressure drop in Taylor flow is related to the gas-liquid interface. Curved interfaces give rise to a pressure term that is proportional to the surface tension (Laplace pressure terms). There is a difference in the curvature of the nose and rear of Taylor bubbles: even at low velocities, the nose is slightly smaller than the rear. At higher Re, inertial
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stresses significantly deform the bubble, which then attains a bullet shape: very flat at the rear and elongated at the nose. The difference in curvature translates into a pressure drop over each bubble. These contributions to the total pressure drop are frequently overlooked. Kreutzer et al.34 showed that they are, in fact, significant for the short slugs and bubbles found in monoliths. The bubble pressure drop can be incorporated by defining a length-averaged slug correction for the developed flow friction factor that vanishes for long slugs
f)
[
( )]
16 d η2 1+a Re LS Fdγ
b
(9)
in which a and b are constants and LS is the length of the slug. Kreutzer et al.34 determined a ) 0.17 and b ) -1/3 in a single-channel study and used eq 9 to estimate slug lengths in a particular monolith pilot reactor. The obtained correlation for slug length was a nonlinear fit versus holdup, with an asymptote to infinity for L f 1 and a relatively constant region around L ) 0.5. Heiszwolf et al.35 experimentally determined pressure drop in a downflow monolith to find f in the range between 18/Re and 90/Re, which demonstrates that the Laplace terms are significant. Here, we incorporate the effect of the interfacial contributions only by replacing the constant 16 in eq 9 by a constant F. Note that the slug lengths are largely determined by the feed hydrodynamics, which differ from one feed distributor to the next, and the use of experimental correlations obtained for one particular distributor should not be used for other systems or even other liquids. However, we realize that the estimate 16/ Re is a lower limit. Combining the above contributions to the pressure drop in Taylor flow, we obtain an expression for downflow and upflow
u (∆pL) ) 2Fη d 2
Ls
uLs - Fg uLs + uGs
(10)
in which a positive value for velocity indicates downflow and the pressure difference is defined as ∆p ) ptop pbottom. Solving eq 10 for uGs, we obtain
uGs ) uLs A)
2Fη d2
-AuLs + B + C AuLs - C
B ) Fg
C)
(∆pL)
(11) (12)
This equation gives the gas superficial velocity, uGs, as a function of the pressure drop, fluid properties, and channel diameter. In Figure 3, several plots of uGs are given for different values of the pressure drop per unit length, C. These plots are best referred to as isobars, as they show, on a map of uLs versus uGs, the contours of equal pressure drop. They are important for two reasons: (1) in any monolith block, the pressure drop is the same for all channels, and (2) the stability and the onset of oscillations in flow rate are determined by the pressure drop. The map in Figure 3 is based on several assumptions: (1) Taylor flow occurs throughout the entire domain. It is possible that, at very low flow rates (
