Kinetic and scale-up investigations of a michael addition in microreactors

Article abstract of DOI:10.1021/op5002758

Microreactors are an efficient tool for process development and intensification. However, the scale-up from lab studies to small-scale commercial production is challenging, since a change in the channel dimensions requires good knowledge of heat and mass transfer phenomena. In this work, complete process development for an exothermic Michael addition is presented. In a systematic scale-up approach, kinetic studies and experimental characterization of the employed reactors provide key parameters for detailed reactor modelling. The residence time distribution, reactant mixing, and removal of reaction heat are taken into account. It is exemplarily shown how preliminary experiments can be the basis for the prediction of scale-up effects and the development of a continuous production process. Plug flow behavior and short mixing times could be confirmed for all investigated flow reactors. Furthermore, interactions of reaction kinetics and the formation of hot spots in the reactor channel were investigated. For the examined reaction, the simulations predicted the product yield under production conditions in good accuracy.

Full text of DOI:10.1021/op5002758

Article
pubs.acs.org/OPRD
Kinetic and Scale-up Investigations of a Michael Addition in
Microreactors
Sebastian Schwolow,† Birgit Heikenwalder,† Lahbib Abahmane,‡ Norbert Kockmann,§
̈
and Thorsten Roder*,†
̈
†Institute of Chemical Process Engineering, Mannheim University of Applied Sciences, Paul-Wittsack-Str. 10, 68163 Mannheim,
Germany
‡3M ESK Ceramics GmbH & Co. KG, Max-Schaidhauf-Str. 25, 87437 Kempten, Germany
§Biochemical and Chemical Engineering, Equipment Design, TU Dortmund, Emil-Figge-Straße 68, 44227 Dortmund, Germany
S
* Supporting Information
ABSTRACT: Microreactors are an efficient tool for process development and intensification. However, the scale-up from lab
studies to small-scale commercial production is challenging, since a change in the channel dimensions requires good knowledge
of heat and mass transfer phenomena. In this work, complete process development for an exothermic Michael addition is
presented. In a systematic scale-up approach, kinetic studies and experimental characterization of the employed reactors provide
key parameters for detailed reactor modelling. The residence time distribution, reactant mixing, and removal of reaction heat are
taken into account. It is exemplarily shown how preliminary experiments can be the basis for the prediction of scale-up effects
and the development of a continuous production process. Plug flow behavior and short mixing times could be confirmed for all
investigated flow reactors. Furthermore, interactions of reaction kinetics and the formation of hot spots in the reactor channel
were investigated. For the examined reaction, the simulations predicted the product yield under production conditions in good
accuracy.
reactors compared to the traditional batch process. Due to
superior heat removal in microreactors, the exothermic Michael
additions could be carried out without any solvent. In
consequence, the reaction time was decreased from 25 h in
semibatch operations to only a few minutes in microreactors.
This example clearly demonstrates the use of microreactors
enabling safe operation of fast exothermic solvent-free
reactions. The decrease in reaction time due to the enhanced
heat removal as well as the increasing interest in solvent-free
reactions as subject of green synthesis could be important
drivers to consider the application of a flow reactor in a small-
scale production process.8
In this paper, a general approach for process development is
proposed: First, kinetic data of the reaction are obtained by a
series of experiments using a microreactor with small internal
volume of a few microliters. Analysis of reactor characteristics
(Reactor Characteristics Section) allows for confirmation of the
assumption of an ideal, nearly isothermal plug flow reactor
behavior. On this basis, experimental data can be used for
fitting the results to a kinetic model. In a subsequent step, the
scale-up from the microscaled reactor to a production reactor
has to be considered. Increasing the channel diameter and
changing flow rates strongly influences the mixing performance,
residence time distribution, and the efficiency in heat transfer.
Reliable parameters for the calculation of these effects can be
obtained by experimental characterization of the production
INTRODUCTION
■
The main advantages of microreactors are rapid mixing and
excellent temperature control of chemical reactions.1,2 Both
processes strongly depend on the reactor dimensions. In
microchannels, efficient mixing results from a high local energy
dissipation rate and short diffusion paths.3 The speed of heat
removal in a microreactor not only benefits from the short
length scale for heat transfer, but also from a high heat transfer
coefficient in laminar flow at small channel diameters. During
scale-up to commercial production, the outstanding perform-
ance of microreactors is often maintained by numbering up
with massive parallelization. Since the scale-up by multiplication
results in high equipment costs and problems such as flow
maldistribution,4,5 this concept has low practical value.
Therefore, the scale-up considerations described in this paper
focus on the transfer to larger equipment scale, which requires
good investigation of the interaction of transport and kinetic
phenomena. In the case of a fast and exothermic reaction,
especially the temperature control is a crucial aspect, since
parametric sensitivity can cause problems in terms of reactor
stability. The scale-up can be critical since an increase of the
channel diameter of 1 order of magnitude can increase the
characteristic times for mixing and heat transfer to a much
larger extent.6 In this paper, we discuss different aspects of the
development of a continuous process for an exothermic
reaction, exemplarily demonstrated with the synthesis of 3-
piperidino propionic acid ethyl ester by a Michael addition.
For the addition of secondary amines to α,β-unsaturated
Special Issue: Continuous Processes 14
Received: August 28, 2014
carbonyl compounds and nitriles, Lowe and Hessel7 showed a
significantly higher productivity in microstructured flow
̈
© XXXX American Chemical Society
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reactor (Scale-up of reactor concept Section). Simulations
based on the combination of these parameters together with
the kinetic model enable the prediction of product yield in the
production reactor. In a final step, lab experiments close to
production conditions should be performed in order to verify
the scale-up approach.
Reactants are preheated in 1/16 in. capillaries (inner
diameter 1000 μm, tube length 2 m) and mixed in a slit
interdigital mixer (SIMM-V2, Fraunhofer ICT-IMM, Mainz,
Germany). Temperature control of preheating, mixing, and
residence time modules was achieved in a bath thermostat. In
order to stop the reaction precisely after an adjusted residence
time, a T-junction (inner diameter 500 μm) was used to
quench the product continuously with acetic acid solution in a
volume ratio of 10:1. Quenched samples were collected with an
automatic sampler (Autosam, HiTec Zang GmbH, Germany)
in 5 mL vials. The continuous feed and quench streams are
supplied by three continuous syringe pumps (Syrdos 2, HiTec
Zang GmbH) with 1 mL glass syringes. By using a laboratory
automation system (LabBox and LabVision Software, HiTec
Zang GmbH), a series of experiments were realized with
automated procedures including sampling, temperature, and
flow rate settings. All samples were analyzed on an Agilent 7820
gas chromatograph equipped with a HP-5 column (30 m ×
0.32 mm × 0.25 μm, Agilent) and a flame ionization detector.
The inlet temperature was 275 °C, the inlet pressure, 50 kPa,
and the split ratio, 100:1. An injection volume of 0.5 μL was
used in the automatic liquid sampler. The oven temperature of
60 °C was kept constant for 2 min and then increased to 200
°C with a ramp of 20 K/min.
Determination of the Mixing Performance. To
characterize the mixing process, an experimental approach
with competitive reactions was taken. The chosen test reaction,
a diazo coupling, is one of several mixing sensitive test reactions
that were described by Baldyga, Bourne, and co-workers,9−11
often also called fourth Bourne test reaction. In a first, quasi-
instantaneous reaction of 1-naphthol (A) and diazotized
sulphanilic acid (B), isomeric monoazo dyes 2-[(4′-
sulphophenyl)azo]-1-naphthol (o-R) and 4-[(4′-
sulphophenyl)azo]-1-naphthol (p-R) are formed (1a−1b).
Subsequently, their secondary couplings produce one bisazo
dye (S), in a fast, but comparatively slower reaction (1c−1d).
MATERIALS AND METHODS
Reaction. The synthesis of 3-piperidinopropionic acid ethyl
ester by a Michael addition (Scheme 1) was realized with nearly
■
Scheme 1. Synthesis of 3-piperidinopropionic acid ethyl
ester
neat reactants at temperatures between 30 and 70 °C. However,
a defined amount of 1-hexanol (11.5 wt %), used as internal
standard for analytics, was added to the reactant ethyl acrylate.
The resulting initial concentration of ethyl acrylate in the
reactant mixture, including both reactant streams, had a final
concentration of 4 mol/L. Since the influence of water on the
reaction was examined, water was premixed with piperidine.
Additionally, 1-butanol was added as a second internal
standard. The amount of 1-butanol was chosen in order to
adjust the initial concentration of piperidine for experiments
with equal flow rates, e.g., 4.4 mol/L for a molar ratio of 1.1. An
effective quench of the reaction at the outlet of the reactors was
realized by mixing with a solution of acetic acid in methanol
(11 vol. %). Thus, the reaction is terminated at a specified
location, and the reaction time can be calculated by the flow
rate and internal reactor volume between quench and reactant
mixer.
Experimental Setup. For steady-state kinetic studies, lab
experiments have been performed with a flexible microreactor
setup (Figure 1). It was aimed to operate at low flow rates, but
in a wide range of mean residence times in order to cover the
whole reaction progress. Thus, different reaction channel
dimensions had to be chosen. For short reaction times, a 1/
16 in. stainless steel capillary reactor with an inner diameter of
250 μm (tube length 0.5 m) was used. Larger reactor volume
was realized with a 1/16 in. capillary of equal length and 750
μm inner diameter. Both residence time modules were
constructed as helical coils, with an alternating change in the
direction of curvature, which is repeated every two coils (Figure
1b).
(1a)
A + B → o‐R
A + B → p‐R
(1b)
(1c)
o‐R + B → S
p‐R + B → S
(1d)
For the detailed reaction scheme and kinetic aspects, see
Baldyga et al.11 and Bourne et al.9 This experimental approach
is focusing on the ratio of the characteristic times for mixing
and reaction. If the mixing time is significantly shorter than the
reaction time, it can be assumed that the reaction takes place in
Figure 1. Microreactor setup for kinetic experiments (a), employing a microreactor with a coiled stainless steel capillary, connected to a slit
interdigital micromixer (b).
B
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a homogeneous concentration field. In this case, selectivity is
determined only by chemical kinetics. The limiting reactant B is
consumed by the faster primary coupling, and the yield of
product S approaches zero. In contrast, if the reaction is fast
compared to mixing, the reaction takes place at the interfacial
region of segregated fluid lamellae. After the immediate
reaction of A and B, this region contains an excess of species
o-R/p-R. Subsequently, reactants o-R and p-R continue to
diffuse toward the region with a local overconcentration of
reactant B, where (in the absence of species A) the slower
reaction can proceed. As a result, a detectable yield of product S
will be achieved, depending on the degree of segregation. Based
on a closed material balance and no further byproduct
formation, the yield of the bisazo dye S in relation to the
initial concentration of B (cB,0) can be defined as
F-curve given by Danckwerts14 for open boundary conditions
(i.e., no dispersion discontinuity) can be expressed as
⎡
⎢
⎣
⎤
⎥
⎦
⎛
⎞
(1 − θ)
4θ
1
2
F(θ) =
1 − erf Bo
⎜
⎟
⎠
⎝
(4)
For determination of the Bo number, a least-square fit for the
measured response signal curve was performed.
Scale-up Experiments. The experimental setup of the
microreactor experiments was adapted for the use of a ceramic
production reactor (Figure 2a, 3 M ESK Ceramics GmbH &
2cS
cB,0
2cS
YS =
=
co‐R + cp‐R + 2cS
(2)
where co‑R, cp‑R, and cS are the concentrations of the products o-
R, p-R, and S. The initial solution containing the diazonium salt
was prepared by diazotization of 3 mol/m3 sulphanilic acid with
sodium nitrite and hydrochloric acid. Excess nitrite was
eliminated by adding sulphamic acid. 3.6 mol/m3 of 1-naphthol
was dissolved in water by stirring and heating the solution. This
stream was buffered using 222.2 mol/m3 each of sodium
carbonate and bicarbonate in order to obtain a pH of 9.9 and an
ionic strength μ = 444.4 mol/m3 in the mixed product solution.
Due to the limited stability of the reactants, both solutions were
prepared directly before starting the experiments. After
collecting the samples, the product mixture was diluted with
buffer solution. The absorption of each sample was measured at
a wavelength range of 400−700 nm. In order to determine the
concentration of the different dyes, multilinear regression
analysis was performed for the measured absorption spectra.
The calculations with multilinear spectra are based on the
molar extinction coefficients for each single substance given by
Bourne and co-workers. Since the absorption spectra of the
monoazo dyes are very similar, their concentrations were
determined in sum (co‑R + cp‑R).
Figure 2. ESK ceramic production reactor (3M, Kempten) in the
experimental setup (a) and plate design of the mixing module (b).
Co KG, Germany) made from silicon carbide (SiC). Flow rates
of 50 mL/min could be obtained with the same syringe pumps
by using 25 mL syringes. In order to keep the reactor plates at
constant temperature, a dynamic temperature control system
(Tango, Huber GmbH, Germany) was employed. Temperature
measurement at the reactor outlet was realized by using a T-
junction in order to insert a Pt100 resistance thermometer
(TMH GmbH, Germany) into the fluid channel (Figure 3).
Residence Time Distribution. Residence time behavior in
the reactors was characterized by stimulus-response experi-
ments. A step function in the tracer concentration was induced,
while the outlet concentration profile was recorded using online
UV−vis spectroscopy. Two feed streams, pure water and a 33
mg/L riboflavin tracer solution, were mixed at the reactor inlet.
An automated procedure switches the flow ratio of both
streams from 9:1 to 1:9 (and respectively vice versa). In order
to determine possible adsorption of tracer molecules at the
reactor wall, both step-up and step-down experiments were
compared. The resulting F-curves appeared to be identical in
very good approximation. Therefore, a possible retention and
accumulation of tracer material in the reactor is negligible.
The dispersion model12,13 was used for describing the
residence time behavior in flow channels. Herein, the degree of
back-mixing is expressed by the dimensionless Bodenstein
number
Figure 3. Temperature measurement in a capillary tube (inner
diameter 2.4 mm) with a Pt100 sensor at the reactor outlet.
Thus, fluid flow encloses the entire measurement tip. Three
different reactor modules, manufactured from silicon carbide,
were used. A mixer module, including preheating channels, T-
mixer, and a reaction channel (reaction volume, 2.9 mL), was
combined with two residence time modules of 16.8 and 33.6
mL. The reaction channel with a square cross section (2.0 mm
× 2.0 mm) is arranged in recurring 90° redirections (Figure
2b).
Since a flow rate of 50 mL/min would require an extremely
high flow rate of quench solution, the quenching procedure had
to be modified in order to use only part of the product stream
for sampling and analysis. Therefore, a split-up of the product
stream was realized by using a T-junction and a control valve to
adjust the flow ratio. A Coriolis flow meter (mass flow meter
M53, Bronkhorst High-Tech BV, The Netherlands) was used
uL
Bo =
D
(3)
ax
with the dispersion coefficient Dax, which quantifies the effects
of axial backmixing in one parameter. Applying eq 3, the
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to determine the exact flow ratio between the main stream and
the smaller stream for sampling (approximately 5 mL/min).
Thus, the flow rate of quench solution could be adjusted to
obtain the correct quench flow ratio of 10:1.
caused by the laminar velocity profile. Therefore, in order to
obtain lower axial diffusion and a higher Bo number (see eq 3),
it is necessary to increase the time ratio τ/tD with the
hydrodynamic residence time τ and the characteristic time for
molecular diffusion tD = d2t /Dm. In other words, the shorter the
mean residence time in the reactor, the smaller is the required
diameter to obtain a high Bo number.
REACTOR CHARACTERISTICS
■
For kinetic studies, precise characterization of the reactor is
crucial. When it comes to experimentally determining kinetic
characteristics of a reaction, it is advantageous to keep
approximately isothermal conditions and to use a reactor with
low deviation from the ideal flow pattern, e.g., plug flow. Thus,
kinetic parameters can be extracted from experimental data
without taking into account complex physical processes such as
back-mixing or the formation of local hot spots. Those
deviations from the ideal isothermal plug flow behavior can
cause a significant difference in the reaction progress.
Therefore, preceding estimates should be performed in order
to ensure that the reaction rate is decreased neither by a broad
residence time distribution nor by reactant segregation due to
poor mixing performance. Depending on the heat release of the
reaction, heat removal in the reactor has to be fast enough to
avoid a local hot spot at the entrance of the flow reactor.
The same criteria are important for scale-up considerations
which are subject of this work. A scale-up toward higher flow
rates is usually combined with an increase in the channel
diameter. Residence time distribution strongly depends on the
channel diameter, but also on channel design elements such as
flow redirection, obstacles, or channel curvature. Mixing of
larger flow rates might be a different task that requires a
different mixing principle or higher energy input. A critical
factor in scaling-up an exothermic reaction is the heat transfer.
While microreactors have superior heat transfer characteristics,
an increase in channel diameter causes not only a lower surface-
to-volume ratio but also a lower heat transfer coefficient in the
laminar flow. The fundamental equations that are the basis for
choosing reactors and for the scale-up considerations in this
work are discussed in the following. Detailed reviews about the
design and characterization of microreactors can be found in
literature.15,16
As stated above, two different capillary reactors were chosen.
For short reaction times, a stainless steel capillary reactor
(MR1) with an inner diameter of 250 μm is used. For high
mean residence times in a 250 μm channel, either an extremely
low flow rate or an extremely long reactor channel is required,
which would cause a very high pressure drop. Both possibilities
are limited by the specifications of the employed syringe
pumps. Hence, higher residence times were realized in a second
capillary reactor (MR2) with a larger inner diameter of 750 μm.
Due to the longer residence times, similar Bo numbers can be
obtained for similar flow rates in both microreactors.
For a further increase of the Bo number, the capillary reactor
is helically coiled with a radius of curvature of 8 mm. The
centrifugal force causes a secondary flow in form of inversely
rotating vortices. A measure for the strength of these secondary
flows is the Dean number
Dn = Re(dt/2R)1/2
(7)
The work of Janssen on axial dispersion in coiled tubes19
showed that dispersion can be correlated by the dimensionless
parameter Dn2Sc, where the Schmidt number Sc is given by Sc
= η/(ρDm). A significant reduction of axial dispersion
compared to the Taylor−Aris prediction for a straight tube is
predicted for Dn2Sc > 200. In contrast to common helically
coiled reactors, the capillary is coiled with an alternating change
in the direction of curvature, which is repeated every two coils.
Preliminary experiments for the residence time showed a small
decrease in axial dispersion compared to a uniformly coiled
helix.
Table 1 compares both microreactors used for kinetic
investigation of the Michael addition. The dimensionless
Residence Time Distribution. In order to determine the
residence time distribution in a real flow reactor, the one-
dimensional dispersion model was used. The material balance
for a plug flow reactor in steady state is extended by an
additional term that describes axial dispersion with the
dispersion coefficient Dax. For a component j, it can be written
as
Table 1. Channel dimensions of the microreactors used for
the kinetic study and dimensionless parameters, calculated
for selected mean residence times
reactor
MR1
MR2
channel diameter
length
(mm)
(m)
0.25
0.50
0.025
5
0.75
0.50
0.221
60
inner volume
(mL)
(s)
∂2cj
∂cj
∂z
mean residence time
flow rate
D
− u
+ νr = 0
j
ax ∂z2
(mL/min)
(m/s)
0.29
0.10
21.6
2.70
15
0.22
0.008
5.4
(5)
flow velocity
The dispersion coefficient Dax combines the effects of
backmixing due to a radial velocity profile in laminar flow,
molecular diffusion, and the formation of secondary flow in one
parameter.
Re number
Dn number
1.17
21
Bo number (Taylor−Aris)
Bo number (Janssen)
51
58
For laminar flow in empty tubes with circular cross-section,
Dax can be determined as a function of the molecular diffusivity
Dm, using the correlation of Taylor17 and Aris:18
parameters Re, Dn, and Bo vary with the applied flow rate.
They were exemplarily calculated for aimed mean residence
times, chosen in order to obtain low conversions in reactor
MR1 and high conversions in reactor MR2. The Bo number
according to Janssen,19 taking into account the secondary flow,
is increased by a factor of about 3 in comparison with the
Taylor−Aris correlation for straight tubes. This is in good
agreement with our own experiments and recently published
u2dt2
192Dm
D = Dm +
ax
(6)
Low axial dispersion in straight microchannels with laminar
flow is only possible if there is enough time for a diffusive
compensation of the radial concentration differences, which are
D
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experimental data.20 For high Bo numbers, the dispersion term
in eq 5 can be neglected in good approximation. The common
threshold for the assumption of plug flow conditions is a value
of Bo > 100.13 However, this threshold is not a sharp boundary.
The effect of the residence time distribution on the reaction
progress not only is a function of the Bo number, but also
depends on reaction kinetics and the conversion obtained in
the reactor. For Bo numbers less than 100, the influence of axial
dispersion can be calculated by applying eq 5. This approach
was performed for the conditions summarized in Table 1. With
the reaction kinetics of the Michael addition and Bo numbers in
the range of 50, a conversion decrease of less than 1% is the
result of the deviation from ideal plug flow behavior. Hence,
application of the plug flow assumption can be considered as
justified in good approximation. Further results and details of
the calculation can be found in the Supporting Information.
Mixing. For a kinetic study, the determined reaction rate
should not be influenced by the mixing process. Thus, the main
objective in mixing is to achieve short mixing times compared
to the time of chemical reaction. In every mixing process,
molecular diffusion is required as the final step, when it comes
to mixing reactants on a molecular scale. A suitable micromixer
is able to reduce the length scale of diffusion. For this purpose,
several types of micromixers exist. In a previous paper,21 an
experimental approach has been carried out to characterize
mixing performance with competitive reaction systems. For low
flow rates (< 10 mL/min), the best mixing performance was
found for a slit interdigital mixer (SIMM, Fraunhofer ICT-
IMM, Mainz, Germany). It can be assumed that this is due to
the formation of multilamellae flow smaller than 100 μm in
microstructures. Therefore, short diffusion paths are generated.
For the kinetic experiments at low flow rates, the SIMM was
chosen in combination with the reactor capillaries MR1 and
MR2. Considering a scale-up to higher reactor throughputs, this
mixer type is not transferable due to the high pressure drop in
the microstructured device. A different mixing principle has to
be found with comparable mixing performance at high flow
rates.
(th ≪ tR). Table 2 shows the heat transfer parameters for the
reactors MR1 and MR2. Due to the smaller channel diameter,
Table 2. Characteristic parameters for heat transfer in the
investigated microreactors
reactor
MR1
MR2
channel diameter
(mm)
0.25
0.75
5333
731
specific surface area
heat transfer coefficient α
transfer time th
(m2/m3)
(W/(m2K))
(s)
16 000
2194
0.030
0.273
the specific surface area and the heat transfer coefficient in MR1
are three times larger than in MR2. As a result, the
characteristic time for heat transfer differs by a factor of 9.
However, heat transfer parameters indicate very efficient heat
removal for both microreactors, even for fast exothermic
reactions (10 s < tR < 10 min).
If kinetic data are available, the temperature profile in a plug
flow reactor can be calculated by using the energy balance
dT
4
dt
ρuc
+ rΔHR + k (T − TW) = 0
p dz
(10)
With the reaction rate r as a function of the reactant
concentration, this equation is coupled with the material
balance (eq 5). It was assumed that the overall heat transfer
coefficient k is mainly is determined by the coefficient of heat
transfer α in the reaction channel. Heat transfer in the oil bath
and heat conduction in the wall of the stainless steel capillary is
considered to be very high in relation to the inner heat transfer.
REACTION KINETICS OF THE MICHAEL ADDITION
■
A lot of aza-Michael reactions with amines can be performed
easily at ambient temperature and without any catalyst.24 Some
of them seem to follow second-order kinetics based on the
concentrations of the nucleophile (amine) and the Michael
acceptor.25 However, in the case of the chosen reaction with
piperidine and ethyl acrylate, a simple second order mechanism
did fit the experimental data only by rough estimation. In
consequence, a more detailed kinetic model had to be chosen.
As shown in Scheme 2, a zwitterionic intermediate is formed by
the nucleophilic attack on the activated double bond.
Heat Removal. The objective to run the reaction at
approximately isothermal conditions can be achieved if heat
removal in the reactor is high in comparison with the
generation of heat by the reaction. While the released heat of
reaction changes due to concentration decrease as the reaction
progresses, heat removal depends on the local temperature of
the reaction mixture. For this reason, it is difficult to estimate
the temperature profile in a reactor without exact kinetic data.
However, for a rough estimation, the expected time for reaction
tR can be compared to the characteristic time for heat transfer.22
The precise mechanism of the subsequent proton transfer
towards the neutral product is unknown, but can be considered
as a bottleneck in the reaction mechanism. In literature, a direct
intramolecular transport is reported as well as a solvent or
reactant-assisted proton transfer.26 A publication about the
mechanism of the addition of amines to trans-(2-furyl)-
nitroethylene27 demonstrates that this reaction is catalyzed by
a second molecule of the amine reactant. For the aza-Michael
reaction, a recent publication describes significant rate
acceleration for the addition in the presence of water.28 Both
observations lead to the conclusion that a water molecule as
well as an amine molecule can act as shuttle for the proton and
therefore promotes the charge equalization of the zwitterionic
intermediate.
In the experimental work, these dependencies of reaction
rate could be confirmed for the current Michael addition. A
reaction kinetic that is second order in the piperidine and first
order in ethyl acrylate was suitable to describe the conversion as
reaction progresses with increasing residence time. Further-
more, a strong influence of water as catalyst could be observed.
An addition of 0.25 equiv of water doubles the reaction rate,
ρcpdt
th =
(8)
4α
With the assumption of a constant wall temperature, heat
transfer in laminar flow is characterized by the constant Nußelt
number23
αdt
λf
Nu =
= 3.66
(9)
Using eq 9 to calculate the heat transfer coefficient α shows
that an increase in the channel diameter dt by 1 order of
magnitude extends the characteristic time for heat exchange by
2 orders of magnitude. The reactor design for an exothermic
reaction should ensure a comparatively short time for cooling
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Scheme 2. Formation of a zwitterionic intermediate in the Michael addition
Scheme 3. Assumed reaction scheme for kinetic modelling
and a linear dependency between water addition and reaction
rate seems to exist. In order to describe all experimental data
with a kinetic model, Scheme 3 were used as a basis for a data
fitting with the software DynoChem (Scale-up Systems Ltd.,
Ireland). This model includes the unassisted, water-assisted,
and amine-assisted proton transfer.
Scheme 4 and the products k2Keq and k3Keq (Scheme 3) are
below 3%. For both mechanisms fittings are based on 120 data
points. Conversion curves were determined for different
temperatures (30−70 °C), different amounts of water addition
(0−1.05 equiv H2O), and different molar ratios of reactants
(1.01−1.22 equiv piperidine).
As a result of the fitting, the rate constant k1 tends to zero;
thus the unassisted pathway can be neglected at least in the case
of an undiluted reaction mixture. Assuming a rapid
equilibration towards the intermediate, the concentration of
the intermediate can be described as
All experimental data could be described in good
approximation by using the simplified reaction scheme. The
difference between the fitting based on Scheme 3 and Scheme 4
is shown in Figure 4 for different stoichiometric ratios.
Acceleration of the reaction by increasing the amine ratio is
obvious and in agreement with the considered mechanism.
Furthermore, the strong influence of water, as demonstrated in
Figure 5, can also be described well by the kinetic model.
cInt = KeqcPip EA
which leads to a total rate expression of
r = k3K c c c
+ k2KeqcP2ip EA
c
(11)
c
eq Pip EA H2O
(12)
Using the observed rate constants kobs,A = k2Keq and kobs,B
=
k3Keq, the reaction scheme can be simplified with two parallel
reactions (Scheme 4).
Scheme 4. Simpified reaction scheme for kinetic modelling
Figure 4 shows fitted curves for both considered mecha-
nisms. The deviations between the observed rate constants in
Figure 5. Kinetic model and experimental data for different amounts
of water addition (cEA,0 = 4 mol/L, T = 30 °C, M = 1.1 equiv).
In the simplified reaction scheme, fitting parameters are
reduced to the observed third order rate constants kobs,A and
kobs,B and the observed activation energies EA,obs,A and EA,obs,B
.
The temperature dependency of both observed rate constants
was surprisingly low; the activation energies EA,obs,A = 0 kJ/mol
and EA,obs,B = 14 kJ/mol resulted from the curve fitting (Figure
6). In general, activation energies that are close to zero often
indicate mass transfer limitations. Since reaction takes place in
an efficiently mixed, single-phase flow, mass transfer limitation
can be neglected. Furthermore, low temperature dependency
can be accounted for by the presence of an exothermic pre-
equilibrium step in the reaction mechanism, which again would
be in good agreement with the proposed mechanism in Scheme
3. In this case, the observed activation energy would be the sum
of the actual activation energy and the standard enthalpy of
Figure 4. Comparison of a curve fitting using both kinetic models
(cEA,0 = 4 mol/L, T = 30 °C, W = 0.25 equiv).
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Figure 6. Kinetic model and experimental data for different reactor
temperatures (cEA,0 = 4 mol/L, M = 1.1 equiv, W = 0.25 equiv).
Figure 7. Measured F-function and model fits for the ESK production
reactor at a total flow rate of 50 mL/min.
reaction, which describes the temperature dependency of the
equilibrium step.29
surprisingly low axial dispersion, and as a consequence, plug
flow behavior can be assumed in very good approximation.
Since a narrow residence time distribution was determined for
the considered length scales of all reactors, eq 5 can be
simplified by neglecting the dispersion term.
EA,obs = EA + ΔHR0
(13)
A derivation of this correlation can be found in the Supporting
Information.
The measurements in the ESK reactor demonstrate the fact
that 90° bends in the reactor channel can be considered as
efficient mixing elements, which induce secondary flow
structures. Faster fluid from the middle of the channel is
forced to the outer wall due to centrifugal forces. This effect
strongly depends on the Reynolds number Re. As described in
literature,15 the present Re number (Re ≈ 300 at a flow rate of
50 mL/min) is sufficiently high to induce a pronounced
secondary flow structure in each 90° bend (L-mixer).
Mixing. The mixing zone in the SiC reactor module of the
ESK production reactor is a T-mixer with 2 mm channel width.
Reactants are contacted and redirected with 90° into the
reaction channel. As described above, mixing sensitive test
reactions were used as a practical approach to estimate the
mixing performance. Figure 8 shows the results of the fourth
Bourne test reaction for different flow rates. A low yield of the
bisazo dye indicates a short mixing time that is below the
SCALE-UP OF REACTOR CONCEPT
■
Capillary reactors with specific length, inner diameter, and
curvature are very flexible and easy to implement in small-scale
microreactor setups for kinetic experiments. In order to
maintain flexibility in production scale reactors, modular plate
reactors provide a suitable reactor concept. Process and utility
channels in the reactor modules of the ESK production reactor
can be combined to achieve a reactor with the required inner
volume. The considered scale-up not only implies a transfer of
channel dimensions, but also a change of flow guidance,
channel cross-section, and mixing principle. Since a different
reactor behavior can be expected, mass and heat transfer
processes have to be characterized experimentally. A set of
preliminary experiments for characterization is proposed, and
the results are discussed in the following.
Residence Time Distribution. As discussed above, in
strictly laminar flow, back-mixing mainly depends on the mean
residence time in relation to the characteristic time for
molecular diffusion. Considering the scale-up to larger channel
dimensions in the ESK reactor, the time for molecular diffusion
would increase quadratically with the channel width. If radial
mass transport is only based on molecular diffusion, this would
result in a broad residence time distribution with an equivalent
decrease in the Bo number. However, the channel design of the
reactor can induce secondary flow structures which significantly
support the radial mass transport. In the ESK reactor, repeated
alternating 90°-redirections enhance the homogenization of the
radial concentration profile in the laminar flow. The resulting
residence time behavior was determined experimentally by
stimulus-response experiments.
Figure 7 shows the residence time function that is obtained
from the response signal of an automatically induced step
function of the tracer concentration. A numerical fit of the
dispersed plug flow model was performed, with Bo as the only
fitting parameter. The best fit for the dispersion model was
obtained with a Bo number of 1130. This result indicates
Figure 8. Experimental results of the fourth Bourne test reaction for
the investigated mixer types.
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Figure 9. Simulation of conversion and temperature in the reaction channel of the ESK flow reactor, compared with the microreactor MR2.
Figure 10. Kinetic model and experimentally determined yields in the microreactor and in the ESK ceramic production reactor.
reaction time of about 800 ms. Measurements with the ESK
reactor are compared to results of a previous study21 for the slit
interdigital mixer and a T-mixer with circular cross-section and
1.25 mm inner diameter.
tions for the heat transfer coefficient in straight laminar flow
(Table 2) demonstrated the general problem of the scale-up to
larger channel widths due to the quadratic dependency of the
heat transfer coefficient. However, it can be assumed that
secondary flow in the reaction channel enhances the heat
transfer. The calculated coefficient for straight laminar flow
would underestimate the actual value which is influenced by the
flow velocity and secondary flow formation. Therefore, the k-
value is an unknown parameter in eq 10.
A measurement of the temperature at the outlet of the first
reactor plate showed a temperature difference of 13 K
compared to the oil temperature in the reactor plate. This
measurement was used to perform a fitting of the temperature
profiles by adjusting the heat transfer coefficient (Figure 9).
While the calculation for straight laminar flow, based on eq 9,
results in a heat transfer coefficient of 274 W/(m2·K), the
fitting method leads to a result of 500 W/(m2·K). Thus, the
comparison indicates a significant enhancement in heat transfer
caused by the flow guidance in the reactor channel. However,
the hot spot is still about 5 times larger compared to the
micromixer, and a temperature rise of 25 degrees could be
critical for reaction control. In the case of the Michael addition,
the influence of the hot spot in the production reactor is
predicted to be extremely small. As can be seen in Figure 9,
only a slight acceleration of the reaction rate in the entrance
region of the reaction channel can be predicted compared to
the nearly isothermal microreactor. This result can be explained
by the exceptional low activation energy of the Michael
addition. As the kinetic experiments showed, no side reaction
should be expected in the overheated regions of the reactor.
Nevertheless, it is still important to estimate the hot spot for
In every micromixer, the final step in mixing is an
equalization of fluid lamellae by molecular diffusion. In the
slit interdigital mixer, these fluid lamellae are mainly created by
the multilamination mixing principle. In contrast, in a T-shaped
mixer convective mixing induces secondary flow structures with
small fluid lamellae. Therefore, a significantly higher flow
velocity is needed in the T-mixer in order to obtain similar
mixing times for both types of micromixer. Mixing behavior of
T-mixers is well-described in literature.15 Since the mixing
performance depends on the Re number, a larger channel
diameter has to be compensated by a higher flow rate. Figure 8
shows that, in the ESK production reactor, a minimum flow
rate of about 20 mL/min is required to ensure a mixing time
comparable to the mixing time in the SIMM at very low flow
rates. Hence, the convective mixing principle of a T-junction
provides a high efficiency in the employed reactor modules at
the aimed production rate of 50 mL/min. In contrast, however,
a T-mixer would not be suitable for the previously described
kinetic experiments in a small scale microreactor.
Heat Removal. In the bonded reactor plates of the ceramic
production reactor, it is not possible to measure temperatures
inside the reaction channel. For this reason, the location and
extent of the hot spot have to be estimated by simulations.
Assuming that the reaction rate as well as the heat transfer in
the reactor can be described with good accuracy, eq 10 allows
for calculation of the temperature profile in the reactors. Due to
the kinetic experiments, the reaction heat source is known as a
function of concentration and temperature. First approxima-
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the production scale reaction process, in order to avoid
decomposition or boiling of the reaction mixture.
similarity is not necessary in this scale-up approach, regarding
both mixer and channel design. Using the one-dimensional
dispersed plug-flow model, conversion and temperature profiles
can be simulated by correlating the reaction kinetics with
transport mechanisms. Applying this simplified reactor model,
based on results of lab experiments, is a suitable approach for
the prediction of scale-up effects. In the case of strong axial
dispersion (low Bo numbers) or uncontrollable hot spots, the
simulation would indicate the scale-up limitations. Application
of the systematic scale-up approach made it possible to perform
a valid transfer of the reaction to the ESK production reactor.
Plug flow behavior as well as short mixing times compared to
reaction time could be obtained for all employed reactors. In
case of exothermic reactions, insufficient heat transfer has to be
considered as a crucial scale-up issue. Therefore, hot spots were
located by correlating reaction kinetics and heat transfer in the
reactor channel. It was shown that even though pronounced
hot spots occur in the ESK production reactor, they do not
affect the reaction control of the Michael addition with low
activation energy.
Scale-up Verification. The combination of preliminary
experiments and simulations made it possible to predict the
reaction yield in the examined production reactor under various
reaction conditions. Two types of experiment were performed
in order to verify the scale-up considerations. First, a reactor
setup with the mixing module (4 mL internal volume) and
without further residence time modules was used to examine
the reaction progress at short reaction times. The total flow rate
was kept constant at 50 mL/min and subsequently reduced
stepwise down to 20 mL/min in order to get four data points at
the steep beginning of the yield−time curve. A further decrease
of the flow rate would not be practical, since the mixing
efficiency in the T-mixer would decrease significantly (Figure
8). In a second experiment, the operation point was chosen in
order to reach a yield of about 90% in a long-term operation at
the aimed production rate of 50 mL/min. Steady state
conditions were obtained after about 20 min of operation. A
constant yield of 87% at the reactor outlet was determined by
GC analysis, which is slightly lower than the predicted yield
(90%). A limit in residence time is given by the total volume of
the three available reactor modules (54 mL). In order to reach
higher conversions, further residence time modules could be
added to the reactor setup. In Figure 10, the results of both
experiments are shown in comparison with the simulated curve.
Excellent agreement of the calculated and measured conversion
confirms the prediction that neither a broad residence time
distribution nor a bad mixing performance influences the
reaction progress significantly.
Results from the microreactor experiment with comparable
reaction conditions confirm the simulation results presented in
Figure 9: Despite the different temperature profiles, the
reaction rate is very similar in both reactors. No influence of
the pronounced hot spot in the production reactor was
observed, and the measured temperature and outlet concen-
trations prove stable reactor control. It must, however, be
emphasized that low temperature dependence is unusual for
chemical reactions and a specific characteristic of the examined
Michael addition. In contrast, assuming an arbitrary exothermic
reaction with higher activation energy, runaway behavior, and
parametric sensitivity can limit the operability of the reactor.
Scale-up considerations should then be extended by correla-
tions, which predict the limit of reaction runaway (e.g.,
Semenov model, Barkelew−Renken approach).30,31 As a
consequence, it could be necessary to consider alternative
reactor designs, e.g., multi-injection reactors32,33 or a successive
enlargement of the reaction channel in order to combine heat
control in the mixing zone with high-volume residence time
modules.34,35
ASSOCIATED CONTENT
* Supporting Information
■
S
A closer look at the influence of axial dispersion in the
microreactors that were used for the kinetic studies; derivation
of eq 13. This material is available free of charge via the Internet
at http://pubs.acs.org.
AUTHOR INFORMATION
Corresponding Author
* E-mail: t.roeder@hs-mannheim.de. Telephone: +49 621 292
6800.
■
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
This work was funded by the German Federal Ministry of
Education and Research (BMBF, funding code 03FH012I2).
■
The authors would like to thank Jurgen Sprinz and Andreas
̈
Zietsch (CHESS GmbH, D-68169 Mannheim, Germany) for
valuable discussions, and Scale-up Systems Ltd. (Dublin 4,
Ireland) for providing the software DynoChem.
NOTATIONS
■
Bo
cj
Bodenstein number
concentration of component j (mol m−3)
theoretical, initial concentration of component j in the
reaction mixture (mol m−3)
cj,0
cp
heat capacity (J kg−1 K−1)
dt
hydraulic channel/tube diameter (m)
axial dispersion coefficient (m2 s−1)
molecular diffusion coefficient (m2 s−1)
Dean number
Dax
Dm
Dn
EA,i
CONCLUSIONS
■
Several steps of process development in flow chemistry have
been discussed in this contribution, using the Michael addition
of piperidine to ethyl acrylate as an example. A systematic
approach for the transfer of lab experiments in microstructured
devices to the conditions of small-scale production processes is
proposed. Preliminary calculations, which focus on character-
istic times of transport phenomena, can be used in order to
ensure the operability of the production scale reactor. Further
experiments for reactor characterization provide additional
information to describe mixing, residence time distribution, and
heat transfer in the examined reactors. Therefore, geometric
activation energy of reaction i (J mol−1)
EA,obs,i observed activation energy of reaction i (J mol−1)
erf(x)
x −t2
(2/√π)∫ e dt
0
F(θ) dimensionless integral distribution function
ΔH0R standard enthalpy of reaction (J mol−1)
k
ki
overall heat transfer coefficient (W m−2 K−1)
rate constant of reaction i, n-th order (Ln−1 mol1−n s−1)
kobs,i observed rate constant of reaction i, n-th order (Ln−1
mol1−n s−1)
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L
M
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r
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characteristic time scale of heat transfer (s)
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