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Determination of the Dispersion Characteristics of Miniaturized Coiled Reactors with Fiber-Optic Fourier Transform Mid-infrared Spectroscopy Clemens B. Minnich,† Frank Sipeer,†,‡ Lasse Greiner,†,§ and Marcel A. Liauw*,† Institut fu¨r Technische und Makromolekulare Chemie, RWTH Aachen UniVersity, Aachen, Germany
A miniaturized modularized tubular reactor setup designed for flexible small-scale experimentation under continuous flow conditions was investigated for its residence time behavior. Studies focused on the question of whether the coil shape of the tubular reactor segments beneficially affects the dispersion behavior of the system by inducing secondary flows in the dispersed plug flow pattern. In the studies, fiber-coupled sensors for the attenuated total reflectance technique were applied to measure concentration profiles of tracer substances by Fourier transform mid-infrared spectroscopy. Sensor flow cells with specifically structured flow geometries were designed in order to reduce the impact on the flow characteristics, and in this context they have proven to be superior to nonstructured flow cells. Quantitative evaluation of the measured spectra yielded goodquality time profiles of the tracer concentration that were subjected to a mathematical approximation with the well-established dispersion model by Taylor and Aris. In accordance with model predictions from literature, the axial dispersion coefficient is drastically reduced in coiled capillaries as compared to the coefficient in the Taylor-Aris case for straight tubes. Depending on the influence of the tube curvature and the flow properties, expressed by the product of the square Dean number and the Schmidt number, the reduction of the axial dispersion coefficient can be by up to a factor of 4. For chemical processes with critical requirements regarding selectivity, this can be of great advantage since the detrimental impact of axial back-mixing is effectively reduced. Introduction Recently microfluidic devices have become the objects of increased research interest because of their greater use in microprocess engineering and lab-on-a-chip concepts in analytical and bio-analytical applications. A reliable assessment of the performance of these small-scale structured devices in chemical process applications, for example, improved selectivity or yield, enhanced mass, and heat transfer, etc., requires substantial knowledge of the flow specifications present in this type of equipment. Flow patterns in geometries with short characteristic dimensions (e.g., below 1 mm) are typically in the laminar regime, making the flow pattern in general be predicted more easily and leading to extensive discussion in the literature.1 A crucial piece of information to the user of fluidic devices in chemical processes is the nature of the residence time distribution; however, straightforward methods for the measurement of residence time are still scarce. Careful design of the analytical equipment is mandatory in order to minimize detrimental impact on the flow pattern. In this contribution we report the adaptation of mid-infrared fiber optic sensors to a modular continuous-flow bench-scale chemical plant designed for process studies in early stages of process development, that is, in small reactor volumes. This reactor setup was designed at good mechanical stability for high pressure applications, low manufacturing and machining efforts, and easy handling. Fluidic sensor interfaces with an optimized fluid geometry have been designed and constructed to overcome limitations that are experienced with existing “micro” flow-cells in inline measurements.2 With this setup at hand, the dispersion * To whom correspondence should be addressed. E-mail: liauw@ itmc.rwth-aachen.de. † RWTH Aachen University. ‡ Current address: AkzoNobel Functional Chemicals, Cologne, Germany. § Current address: DECHEMA e.V. Karl-Winnacker-Institut, Frankfurt, Germany.
behavior of the tubular reactor modules can be assessed by classical stimulus-response tracer experiments, as demonstrated in step-change mode. Methodology Characterized Setup. For continuous lab experimentation and steady-state kinetic studies, a flexible and cost-effective modular reactor setup has been constructed. The central design criterion is the availability of a sufficiently large residence time in the hours range for preparatively relevant flow rates while maintaining well-defined flow characteristics. With regard to applications at elevated pressure, for example, for hydrogenation reactions or processes involving supercritical fluids, a design based on stainless steel capillaries was favored. The reactor modules have therefore been constructed from coils of 1/16 in. o.d. and 1.0 mm i.d. stainless steel (1.4571) capillary, inserted into a housing with connectors for a circulating thermostatting fluid (Figure 1). A set of modules with volumes of 0.25 mL (tube length, 318 mm), 0.5, 1.0, 2.0, and 4.0 mL (5093 mm), that is, up to a total reactor volume of 7.75 mL connecting all in series, allows a scale-up factor of 31. Two independently controlled feed streams
Figure 1. Cross-section (left) and photograph (right) of a 1 mL capillary reactor module.
10.1021/ie901094q 2010 American Chemical Society Published on Web 05/11/2010
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Figure 2. Flowsheet for the automated residence time distribution measurements.
are supplied by continuously operated syringe pumps (MDSP3f, MicroMechatronic Technologies, Siegen, Germany). Mixing can be achieved either by a simple T- or Y-junction or in a static mixer or micromixer. Independent temperature control in the mixer and the feed streams is achieved by installation into individual thermostatted housings. By connecting the reactor modules to different circulating chillers or heaters, a temperature profile can be imposed onto the reactor at different stages of the process. The automation of the setup is realized in LabVIEW (National Instruments Inc., Austin, TX), including flow rate and temperature settings as well as the documentation of relevant process parameters in protocol files. A schematic overview of the setup is given in Figure 2. FTIR measurements are embedded into the setup and are triggered by OPC communication. Data handling and evaluation procedures are effectuated in inline mode and allow for realtime inspection of the experiments. Injection and Detection. Characterization of the residence time behavior was achieved with stimulus-response experiments, recording the inlet and outlet concentration profiles of a tracer compound. Fiber-optic-based mid-infrared spectroscopy, approved in numerous experimental studies,3 was chosen as a viable technology for automated time-resolved measurement, using 2-octanone as a tracer substance in n-octane (diluted to 20% for adjustment of the fluid properties). FTIR spectra were recorded in repetitive measurement loops at a sampling frequency of 0.3 Hz on a Bruker MATRIX-MF spectrometer equipped with fiber optical ATR probes. The probe heads carrying the optical element were inserted into specifically structured miniaturized flow cells4 assuring excellent reproducibility of the measurements. The obtained spectra were subjected to a PLS (partial least squares) model delivering the quantitative information. For the residence time characterization of channel geometries with high length-to-width ratio, step-change experiments are superior to pulse experiments due to the comparably higher tracer concentrations at the reactor outlet. These step-changes were effectuated by an automated switching procedure with switching times below one second and allowed for sufficiently sharp transitions between tracer and inert fluid. The use of static inlet check valves inhibited the upstream dilution of the tracer
and justifies the use of one-side open system boundaries for the selection of the correct RTD model.5 Residence Time Model. Flows in empty tubes or channels show back-mixing behavior closer to an ideal plug-flow reactor (PFR, no back-mixing) than to an idealized continuous stirredtank reactor (CSTR, perfect back-mixing) and are therefore better described with modified plug-flow models. The dispersion model introduced by Taylor and Aris6 has found wide application in characterizing flows through pipes and channels. Here, the material fluxes are expressed as the superposition of ideal plug flow with an axial dispersion, which is driven by the concentration gradients in the flow direction. In analogy to Fick’s second law of (molecular) diffusion, an axial dispersion coefficient Dax is introduced for the description of nonconvective contributions to the flow. For the flow geometries considered here, where a radially symmetric distribution of axial velocities is assumed and dispersion coefficients are considered to be constant, the description as a dispersed plug flow according to the fundamental classification by Levenspiel7 is most appropriate. The material balance of a compound in the flow reads ∂c ∂2c ∂c ) Dax 2 - ux ∂t ∂x ∂x
(1)
where ux is the linear velocity of the fluid along the x-axis. The dominating flow regime in channels of submillimeter dimensions is laminar, since the characteristic Reynolds numbers are far from reaching the threshold level of Re ) 2300 (kinematic viscosity 0.75 × 10-2 cm2 s-1, hence Re ) 20 for a typical linear velocity of 1.5 cm s-1). Sufficiently long residence times, however, allow for an equilibration of the radial concentration gradients by radial diffusion. This is set as a boundary condition to the application of the Taylor-Aris conditions and expressed with the Fourier number Fo, the ratio between the hydrodynamic residence time τ, and the characteristic time for diffusion τd in a channel of the characteristic dimension r: Fo ) τ/τD )
τDm r2
(2)
In the situation when Fo is significantly larger than 0.25 (and preferrably higher than 1), the measured concentration profiles
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from tracer experiments can be considered to be dominated by convection only.8,9 The absence of radial concentration gradients then also allows the consideration of through-the-wall10 measurements for the determination of residence time distributions. The hold-up volume of the inline check-valves used in the contactor is sufficiently small relating to the reactor volumes, which excludes upstream diffusion or dispersion of the tracer and sets the inlet axial dispersion coefficient Dax to zero. For that reason, open-closed boundary conditions are applied, which is in contrast to most available studies in microchannels where upstream diffusion is possible due to the injector geometries.11-14 The exit-age function of a fluid, flowing at a mean velocity u in a straight tube of length L which fulfills the open-closed condition,10,15 is available as E(θ) )
1 2
[
-(1 - θ)2uL uL exp πDax 4Dax
]
(3)
The absolute residence time is referenced to the mean residence time τ, which is either determined experimentally or calculated as the hydrodynamic residence time L/u, and transferred into a dimensionless number θ. Traditionally, the definition of the Bodenstein number, Bo ) uLDax-1, is introduced into the model eq 3 and used as a fit parameter for experimentally determined residence time distributions. When Dax is available, the molecular diffusion coefficient Dm is accessible as it has previously been suggested by Taylor,6 for example, for circular cross sections (the factor 1/192 accounts for the geometrical shape of the tube): Dax ) Dm +
u2dt2 192Dm
(4)
This basic structure of the one-dimensional axial dispersion model does not yet account for secondary fluxes in the radial section of the flow, as they are expected to occur in coiled or helical channels. These fluxes enhance radial diffusion and are considered as a cause for reduced axial dispersion compared to the Taylor-Aris base case for straight tubes. Descriptions by various authors are available from literature.16 The key geometrical parameter is the aspect ratio of tube diameter versus coil diameter, which multiplied with the Reynolds number gives the Dean number Dn ) Re(r/R)1/2 (sometimes De) as a dimensionless measure for the strength of secondary flows induced by the coil geometry. Flows at high Dn values are promising for applications requiring efficient heat and mass transfer17 and have been considered as a well-suited mixing strategy for the microscale.18 However, the discussion in these fields mainly concentrates on high Dn values,17 that is, high Re numbers and/or relatively high aspect ratios r/R. With the use of alternating planar coils, a regime of chaotic mixing with two countercurrent vortices on either side of the symmetry plane of the coil could even be reached.18 Whereas the quantitative description of the effects by Daskopoulos covers a wide range of flow conditions, Janssen16 focuses on low degrees of curvature (ratio of radii for tube crosssection and coil below 0.05) and accordingly low Dn values below 16. In the model, the ratio of Dax observed in a coiled reactor and Dax,TA in an equivalent straight tube (Taylor-Aris case) is expressed as a function of the dimensionless number Dn2Sc:16 Dax 96 ) Dax,TA A
c A [1 - 2( ar ) ] ReSc (a ∂c∂z ) dA ) f(Dn Sc) 2
2
(5)
Here, an integration of the predicted concentration profile is effectuated over the full coiled reaction tube (A, cross-sectional area; a, tube diameter; r/a, dimensionless radial coordinate; z/a, dimensionless axial coordinate) with Sc ) ν/Dm. Of the available models, this best represents the range of studied flow parameters. Results and Discussion Step-change experiments for the characterization of the residence time behavior were conducted with different sizes of coiled reactor modules, and the dispersion characteristics obtained from the fit of the model were compared to the equivalent straight tubes. Data Acquisition and Preparation. Response signals from applied step changes were obtained as concentration profiles from the chemometric model. The time resolution for all profiles was harmonized to ∆t ) 1 s by fitting Akima-type approximating splines to the data (performed with the integrated spline tool in DIAdem, National Instruments, Austin TX). Timedomain fitting to reduce data noise for the calculation of the derivatives has already been discussed, for example, by Boskovic.12 Depending on the available data points per step response, the approximation was performed with 2-5 nodes. In the resulting response profiles the interval between F ) 0.02 and F ) 0.98 was resolved in at least 60 data points (see Figure 3). Normalization of the F-curve and the transformation of the time axis show the excellent reproducibility of the experiment even for the highest applied flow rates. The deviation between the replicates is negligible at lower flow ranges (Figure 3). The relative standard deviation for the θ-value for F ) 0.5 is 1.2% at 120 mL h-1 and 0.2% at 12 mL h-1. From the individual step response profiles the E-curves were obtained by calculating the derivative and are compared for these two flow rates in Figure 4. The smoothness of the derivative curves and the accordance between the replicates is still high for the lower flow rate. At higher flow rates and a correspondingly lower time resolution of the E-curve, fluctuations are much more pronounced and significantly influence the quality of the subsequent fit of the dispersion model. Concerning the question of whether the ATR measurement with a typical optical path length inside the sample of a few micrometers is representative enough for the full cross section of the channel (300 µm), the shape of the presented exit-age distributions gives a good estimate. The fact that the exit-age distributions are with only minor deviations centered around the expected mean hydrodynamic residence time (i.e., around a dimensionless residence time value of 1) indicates that the observed step-change response at the probe head must be representative enough for the entire stream. A pronounced laminar concentration profile would in contrast lead to significantly higher observed mean values and to an asymmetric shape of the E-profile with pronounced tailing. Hence, the axial dispersion predicted by the Taylor-Aris approach and the radial dispersion induced by Dean flows in helical coils can be considered effective for the generation of plug-flow-type flow characteristics. Fit of the Dispersion Model. The calculated exit-age distributions (E-functions) were subjected to a least-squares fit according to eq 3 with the Bodenstein number Bo as the fit parameter. Fit results for the replicate experiments under identical conditions were averaged. From the obtained average Bo, the axial dispersion coefficient was calculated. An overview is given in Table 1 for the applied flow conditions. The listed experiments are classified in two groups in order to distinguish conditions with Fo > 1 (capitals) from those below Fo ) 1
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Figure 3. Data pretreatment at two different flow rates: (top) 120, (bottom) 12 mL h-1. (Left) experimental data and approximation; (right) profiles of replicate experiments.
Figure 4. Exit-age distributions for replicate experiments at two different flow rates: (left) 12, (right) 120 mL h-1.
(lower case). Strict application of the Fourier criterion for straight tubes affects the discussion according to the Taylor-Aris theory only below Fo ) 0.25; however, experiments with 0.25 < Fo < 1 are treated separately. For all experiments with Fo > 1, Bodenstein numbers exceed the value of 100, which is considered as a threshold for the assumption of plug flow conditions.9,10 The influence of the coiled tube geometry on the measured axial dispersion is expressed by referencing it to the expected axial dispersion for a straight tube of identical length. Unless the molecular diffusion coefficient for the tracer compound is known from literature, it is accessible from a dispersion experiment under Taylor-Aris conditions (cf. eq 4). It is therefore estimated from the experiments with the lowest available Dn value for the respective reactor module (Dm ) 2.18 and 2.77 × 10-5 cm2 s-1 for 2and 4-mL module, which is in the typical range of 10-5 to 10-4 cm2 s-1 for small organic molecules) and used for the calculation of Dax and Dn2Sc (see Table 2).
With increasing Dn2Sc the axial dispersion is significantly reduced compared to that of the Taylor-Aris prediction. The improvement is already observed at Dn2Sc ) 68.8, and the relative axial dispersion falls below 0.3 at Dn2Sc > 10.000. This observation is in line with the predictions from the cited models16 for the enhanced radial diffusion caused by secondary radial flows. Compared to these, the effect is overestimated below Dn2Sc e 500, whereas the predicted limit value of 0.2 for high Dn2Sc is not reached in the considered experiments. Interestingly, all listed experiments with Fo values below 1 are in line with those above 1 if the corresponding axial dispersion coefficient is referenced to the hypothetically predictable Dax from the Taylor-Aris model. Under these circumstances, the application of this model appears justifiable even in the case of Fo < 1. The enhanced radial mass transfer induced by the secondary flows leads to shorter characteristic times for the radial equilibration of the concentration profiles and hence to
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Figure 5. Experimentally determined relative axial dispersion compared to models from literature.16 Open circles refer to measurements with Fo < 1. Lines are a guide to the eye only.
Figure 6. Experimentally determined relative axial dispersion for step-down experiments. Representation equivalent to Figure 5. Table 1. Parameters for the Fit of the Dispersion Model to Experimentally Obtained E-Functions at Given Flow Conditions expt. no.
τ [s]
u [cm s-1]
Re
Fo
average Bo
Dax [cm2 s-1]
Module Volume ) 0.25 mL a b c d
90 45 45 18
0.4244 0.8488 0.8488 2.122
A e f g
153.0 76.5 43.7 30.6
0.4244 0.8488 1.485 2.122
B C D
2460 1230 615.0
0.1061 0.2122 0.4244
E F G H I K L
4794 2397 1199 599.3 342.4 239.7 119.9
0.1061 0.2122 0.4244 0.8488 1.485 2.122 4.244
5.66 11.3 11.3 28.3
0.79 0.39 0.39 0.16
71.5 ( 3.5 30.4 ( 1.6 30.8 ( 1.1 32.1 ( 1.7
0.227 1.07 1.05 2.53
Module Volume ) 0.5 mL 5.66 11.3 19.8 28.3
1.33 0.67 0.38 0.27
123 ( 7 74.3 ( 4.1 36.7 ( 1.6 59.7 ( 2.7
0.224 0.741 2.63 2.31
Table 2. Relative Axial Dispersion Coefficients Compared to Taylor-Aris Case expt. no.
Dn
A B C D
0.895 0.224 0.447 0.895
E F G H I K L
0.224 0.447 0.895 1.79 3.13 4.47 8.95
Dax [cm2 s-1]
Dax/Dax,TA
275 17.2 68.8 275
0.224 0.0212 0.0587 0.194
0.522 1.000 0.693 0.572
17.2 68.8 275 1100 3370 6880 27500
0.0269 0.0948 0.267 0.863 2.51 3.86 11.9
1.000 0.881 0.620 0.501 0.476 0.359 0.277
Dn2Sc
Module Volume ) 2.0 mL 1.41 2.83 5.66
21.5 10.7 5.37
1305 ( 130 943 ( 9 572 ( 9
0.0212 0.0587 0.194
Module Volume ) 4.0 mL 1.41 2.83 5.66 11.3 19.8 28.3 56.6
41.8 20.9 10.5 5.23 2.99 2.09 1.05
2006 ( 158 1139 ( 19 810 ( 28 501 ( 13 301 ( 9 280 ( 19 181 ( 16
0.0269 0.0948 0.267 0.863 2.51 3.86 11.9
effectively higher Fo numbers, as compared with the Fo number reflecting diffusion only (eq 2). A validation of these findings is achievable by analyzing the inverse step-change experiments, that is, the displacement of the tracer solution by the pure solvent (“step down”, see Figure
6). In accordance with the step-up experiments, the reduction of the axial dispersion compared to the Taylor-Aris prediction is obvious and becomes significant for Dn2Sc > 200. The trend is comparable to the step-up experiment, although the improved dispersion behavior is less pronounced in the step-down experiments except for that under the Fo < 1 conditions. The limit of 0.2 for the relative axial dispersion coefficient is not reached even at high Dn2Sc. Judging from the properties of the two fluids involved, a higher polarity can be expected for the tracer solution containing 2-octanone, and hence the affinity to the stainless steel surface of the reactor capillaries is assumed to handicap the exchange of the fluids in the stepdown experiment. As a consequence, the broadening of the tracer concentration profile leads to relatively higher axial dispersion compared to the step-up experiment, where pure
Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010
n-octane is replaced by the tracer solution containing 2-octanone. Conclusions The influence of coiled geometries on the axial dispersion behavior in small-scale tubular reactors was studied with fibercoupled optic sensors for mid-infrared spectroscopy. Automated residence time experiments in step-change mode were performed using a tracer solution of 2-octanone in n-octane. Excellent reproducibility at a sufficiently high sampling rate was ensured by newly developed sensor cells with a precisely structured channel geometry. The beneficial influence of the secondary flows, induced by the coiled reactor shape, could be proven by comparison with the performance of straight tubular reactors of equivalent length. Qualitatively, the improved dispersion behavior can be predicted by reference models from literature. For the parameter range studied, a decrease of the axial dispersion by a factor of 4 was achieved. The experimental proof of the predicted benefit from induced secondary flows in coiled tubes gives rise to simple but effective design options for tubular reactors even at small-scale. Acknowledgment The work was mainly funded in the framework of the Integrated Project “IMPULSE” (funded under NMP2-CT-2005011816, http://www.impulse-project.net), within the 6th Framework Programme of the European Commission. A hardware investment grant by RWTH Aachen University Seed Fund is gratefully acknowledged. The authors thank Dr. Holger Lutz (BrukerOptics) for continued and immediate support, Willi Hempelmann (MicroMechatronic Technologies) for construction of the flow cells and fruitful technical discussions, Horst Kronenberg for construction of the reactor hardware, and Prof. Michael Kotter (Aachen University of Applied Sciences, Process Technology) for supervision of the diploma thesis of F.S. Literature Cited (1) Hessel, V.; Hardt, S.; Lo¨we, H. In Chemical Micro Process Engineering; I: Fundamentals, Modelling and Reactions; Wiley-VCH: Weinheim, Germany, 2004; Chapter 2.4, pp 169-181. (2) Hu¨bner, S.; Bentrup, U.; Budde, U.; Lovis, K.; Dietrich, T.; Freitag, A.; Ku¨pper, L.; Ja¨hnisch, K. An ozonolysis-reduction sequence for the synthesis of pharmaceutical intermediates in microstructured devices. Org. Process Res. DeV. 2009, 13, 952–960. (3) (a) Minnich, C. B.; Buskens, P.; Steffens, C.; Bäuerlein, P. S.; Butvina, L. N.; Küpper, L.; Leitner, W.; Liauw, M. A.; Greiner, L. Highly flexible fibre-optic ATR-IR probe for inline reaction monitoring. Org. Process Res. DeV. 2007, 11, 94–97. (b) Minnich, C. B.; Küpper, L.; Liauw, M. A.; Greiner, L. Combining reaction calorimetry and ATR-IR spectroscopy for the operando monitoring of ionic liquids synthesis. Catal. Today
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ReceiVed for reView July 7, 2009 ReVised manuscript receiVed March 19, 2010 Accepted April 11, 2010 IE901094Q
