Model-Based Scale-Up Predictions: From Micro- to Millireactors Using

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Model-based Scale-up Predictions: From Microto Millireactors using Inline FT-IR Spectroscopy Verena Fath, Stefanie Szmais, Philipp Lau, Norbert Kockmann, and Thorsten Röder Org. Process Res. Dev., Just Accepted Manuscript • DOI: 10.1021/acs.oprd.9b00265 • Publication Date (Web): 07 Aug 2019 Downloaded from pubs.acs.org on August 11, 2019

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Organic Process Research & Development

Model-based Scale-up Predictions: From Micro- to Millireactors using Inline FT-IR Spectroscopy Verena Fath1,2, Stefanie Szmais3, Philipp Lau3, Norbert Kockmann1, Thorsten Röder2* 1

Department of Biochemical and Chemical Engineering, Equipment Design, TU Dortmund

University, Emil-Figge-Str. 70, 44227 Dortmund/Germany 2

Institute of Chemical Process Engineering, Mannheim University of Applied Sciences, Paul-

Wittsack-Str. 10, 68163 Mannheim/Germany 3

Merck KGaA, Frankfurter Str. 250, 64293 Darmstadt/Germany

ACS Paragon Plus Environment

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Organic Process Research & Development 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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ABSTRACT

Scale-up predictions from continuous flow micro- (lab) to milli- (pilot or production) scale are important, but not trivial. To overcome the necessity of time-consuming trials on pilot or production scale, this work presents a model-based approach that builds on prior lab experiments. However, it also improves the understanding of the involved chemical process. A complete process development for a highly exothermic organometallic reaction is conducted. Kinetic studies on labscale, using inline FT-IR measurements, constitute the basis for a systematic scale-up approach. Subsequently, the scale-up from microreactor (inner diameter 0.5 mm) to milli-scale pilot reactor (inner diameter of 2 mm) through increasing the channel diameter and flow rates is investigated. Model-based scale-up predictions are presented, including heat and mass balances.

KEYWORDS Model-based scale-up – Scale-up predictions – Inline FT-IR spectroscopy – Microstructured devices – Organolithium compounds


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INTRODUCTION As flow chemistry offers many benefits over batch chemistry, the use of micro-structured devices within organic syntheses is of high interest.1–6 Especially in the case of strong exothermic organometallic reactions, continuous flow microreactors permit safe handling due to short residence times and very efficient heat and mass transfer.7–17 However, unintended decomposition reactions of intermediates can be minimized, and processes can be carried out in a controllable manner even at higher temperatures.18, 19 In addition, better yields and improved selectivity can be accomplished.20–26 By using microreactors within experiments on laboratory scale, well-defined reaction conditions are established. These allow for assuming nearly-optimal conditions close to ideal plug flow reactor behavior. While many works report on the utilization of microreactors in organometallic syntheses in lab context,7,

21, 27–44

the scale-up of these challenging reactions is described less often.45–51

Nevertheless, scale-up from lab to pilot or production scale is an important step in process development. It can be critical since mixing, residence time distribution, and heat removal strongly depend on reactor dimensions. Increasing the reactor’s inner channel diameter from micro- to millimeters, ideal conditions can no longer be assumed. Instead, real reactor characteristics have to be studied in detail. Hence, transfer to larger equipment scale requires good knowledge of mass and heat transport, and of the kinetic model itself. This work’s objective is to predict the scale-up of a highly exothermic organometallic model reaction from lab to pilot scale. In preliminary experiments, the industry-relevant synthesis of a lithiated intermediate through the deprotonation of a CH-acidic hydrocarbon compound was investigated.52–55 The reaction was carried out in a coiled capillary stainless steel microreactor,


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aiming to obtain reliable kinetic data (see previous publication56). The lab-scale reactor characteristics justified the assumption of an ideal, nearly isothermal plug flow reactor behavior (effective mixing, high Bodenstein numbers, negligible hot spot generation at the entrance of the reactor). Hence, the kinetic parameters were obtained independent of complex physical processes, such as formation of hot spots and backmixing. During the kinetic studies, an in-situ reaction monitoring through inline FT-IR spectroscopy was used within the microreactor setup,57–62 as the analysis of highly reactive, non-isolable lithiated components poses several challenges. Based on turnover-residence time curves at different reaction temperatures, an appropriate kinetic model was derived, illuminating the reaction mechanism. This article advances the prior work by investigating the scale-up from micro-scaled reactor to milli-scale pilot reactor. In the latter setup, efficiency in heat transfer and formation of hot spots have to be considered. Moreover, mixing performance and residence time distribution are strongly influenced by increasing the reactor dimensions. Ideal conditions can no longer be assumed due to deviations in mixing, residence time distribution, and heat transfer. Simulations based on the combination of those parameters with the derived kinetic model enable the prediction of product yield in the pilot reactor. In a final step, experiments at pilot conditions are performed in order to verify the model-based scale-up approach. A complete process development for the transfer of an industry-relevant organometallic reaction from lab to pilot scale is presented based on the detailed understanding of the reactor characteristics, including heat and mass balances as well as kinetic studies.


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EXPERIMENTAL SECTION Reaction The deprotonation reaction of a CH-acidic compound 1 in tetrahydrofuran THF (anhydrous max. 0.005 % H2O) with n-butyllithium 2 leads to a non-isolable, unstable, lithiated intermediate compound 3 (Scheme 1). The synthesis was investigated at temperatures between F35 °C and F 5 °C as well as between F+* °C and F,5 °C on lab and pilot scale (continuous flow reactors), respectively. The starting material n-butyllithium was chosen from Sigma Aldrich, Germany, with a concentration of 1.6 mol LF in n-hexanea. Initial concentration of the CH-acidic compound was 0.8 mol LF . Varying stoichiometric ratios at F35 °C (0.9:1, 0.7:1, 0.5:1; n-butyllithium in proportion to CH-acidic compound) with CH-acidic compound as excess component were studied.

R2 O

Li

+

deprotonation

O

Li

-

R1

1

R2

R1

2

3

Scheme 1. Synthesis of lithiated intermediate. 1 CH-acidic compound J 2 n-butyllithium J 3 lithiated intermediate

a

Within certain limits, the concentration of organometallic reagents might be subject to minor variation. However, pretests described in supplementary information section A.1 indicate that this limitation had only a negligible effect on the study’s findings.


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Right after inline measurement of the reaction progress, the highly reactive lithiated intermediate was quenched with excess of isopropyl alcohol to prevent thermal decomposition.

Lab Experiments Lab experiments were performed using a flexible microreactor setup consisting of coiled 1/16 in. stainless steel capillaries with varying inner diameters (0.5 to 1 mm) and reactor lengths (7 to 12 m), see previous publication for details.56 Dosage of starting materials within 1 mL glass syringes was accomplished by continuous working syringe pumps (SyrDos2, HiTec Zang GmbH, Germany). Temperature and flow rates were controlled by a laboratory automation system (HiTec Zang GmbH, Germany). Use of an inline FT-IR spectrometer (Bruker ALPHA, United States) allowed for real-time reaction tracing. All experiments were run under steady-state conditions. Every measurement was repeated 5 times from which mean values were calculated.

Scale-up Experiments Scale-up experiments are obtained in a flexible milli-reactor set-up, where the length of the reactor can be adjusted considering different residence times in the process. The set-up contains two gear pumps (P1 and P2) and two precooling loops á 3 m (ID 2 mm) for cooling down the CH-acidic compound and n-BuLi. After mixing the two reagents using an inline static mixer (Kenics, Ismatec, Germany), the reaction takes place in a reactor (ID 2 mm) depending on residence time with a length of 3 m and 25.5 m, respectively. Due to this, the length of the static mixer used is 7 % and 1 % of the total reactor length. For controlling temperature in the process, the temperature is


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directly measured within the reaction stream behind the precooling loop and the static mixer. The loops for precooling and reaction are cooled down with a cryostatic system. After obtaining a defined residence time, the reaction solution is analysed by inline FT-IR using the FlowIR (Mettler Toledo, United States). With this set-up, residence times of 0.3 to 10 minutes can be adjusted considering temperatures of –25 °C to F+* °C. Experiments were performed under steady-state conditions.

inline FT-IR

PIR

deprotonation

1

CH-acidic compound 1

TIR 2

P1 PIR

Lithiated compound 3

M R

2

n-BuLi 2

M = 0.3 to 10 min P2

T = F40 °C to F25 °C

TIR 1

TIR 3

Figure 1. Setup of pilot millireactors for scale-up experiments. Legend: M – inline Kenics static mixer, TIR1 – temperature measurement behind precooling, TIR2 – temperature measurement after mixer.

In contrast to the lab experiments, inline FT-IR measurements were conducted by use of a FlowIR (Mettler Toledo, United States). This also allowed real-time reaction tracing of the deprotonation reaction, with a time delay < 1 s. A short stainless steel capillary of 40 mm with an inner diameter of 2 mm connected the reactor outlet with the spectrometer’s flow cell (inner volume of 50 µL).


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The chosen setup enabled extremely fast measurement times smaller than 2 ms, preventing the lithiated intermediate from decomposition. Infrared spectra were collected in the range of 500 to 1700 cmF , with an optical wavelength resolution of 8 cmF , through single reflection ATR (diamond crystal). The CH-acidic compound 1 was identified by means of a characteristic IR bond at )2,F)55 cmF . This bond results from a C-H deformation vibration out of plane of the aromatic ring 9Q9"F7: ( ( (:$ amounting to three adjacent hydrogen atoms. Over the course of the reaction, the bond is decreasing, since one H atom is replaced by a Li atom during lithiation. A quantitative analysis was carried out using a previously determined calibration curve. Hence, concentration profiles could be calculated based on the decreasing IR bond at )2,F)55 cmF (see details on analytical method in supporting information A.2). Conversion was determined with regard to the CH-acidic compound as excess component (as the amount of n-butyllithium in the reaction mixture is the limiting factor for the maximum conversion of 1). Each experimental data point was established by five repeated measurements with every measurement consisting of 94 scans. This resulted in a measuring time of 30 s. Standard deviations were calculated for all data points and sum up to an value of 1%, averaged across data points (standard deviations for all experimental data points displayed in detail in supporting information A.3). From a practical point of view, both FT-IR spectrometer, Bruker ALPHA (used during lab experiments) and FlowIR Mettler Toledo (used during scale-up experiments), deliver similar performance.


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REACTION KINETICS Kinetic data of the deprotonation reaction with n-butyllithium were determined in a microreactor (inner diameter 0.5 mm) under nearly ideal conditions. The experimental lab setup satisfied all requirements for assuming a nearly isothermal plug flow reactor behavior, including negligible hot spot formation, highly efficient mixing, and Bo numbers > 100, accounting for narrow residence time distribution. It was demonstrated that the reaction involves a complex reaction mechanism, as indicated by broken reaction orders (Table 1).63, 64 Several kinetic approaches were studied in detail, and a possible mechanism based on the formation of butyllithium aggregates in tetrahydrofuran was postulated (see previous publication for details56). Hence, a mechanistic modeling describing the whole synthesis as elementary reaction steps could not be accomplished through the lab experiments. Nevertheless, the derived kinetic model (Table 1), including broken reaction orders, describes the reaction adequately within the investigated parameter ranges, and can be used for scale-up predictions. R1 = - k J cn1 J cm 2

(1)

[ ( )]

(2)

k(T) = kref J exp -

EA R

J

1 1 T Tref

at Tref = - 30 °C

Table 1. Calculated kinetic data of deprotonation reaction with n-butyllithium.56 Concentration (CH-acidic compound 1)

0.8 mol LF

Reaction order n (CH-acidic compound 1)

1.3

Reaction order m (n-butyllithium 2)

0.3

Reaction rate coefficient kref (confidence level 95 %, at Tref F3* °C) [m1.8 molF*(1 sF ]

3.38 10F+ (± 2.5 %)

Activation energy EA (confidence level 95 %) [kJ molF ]

29 (± 6.6 %)


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SCALE-UP PREDICTIONS High mixing efficiency, narrow residence time distribution, and nearly isothermal reaction control are preconditions for determining reliable kinetic data. Therefore, reactor characteristics need to be taken into consideration. In the case of an ideal plug flow reactor behavior with fast mixing, it can be assumed that the reaction rate is neither affected by broad residence time distribution nor by imperfect mixing performance. Moreover, hot spot generation at the reactor entrance has to be avoided, requiring fast heat removal. When performing a scale-up by increasing the inner channel diameter and the flow rates, it must be noted that all mentioned criteria are affected. Specifically, the handling of much higher flow rates could require a more efficient mixing principle with greater energy input. A larger channel diameter might lead to back mixing due to broader residence time distribution. Further differences include a lower surface-to-volume ratio and a lower heat transfer coefficient in laminar flow. This reduces heat removal, which is especially crucial in the case of a highly exothermic reaction.65–67 In case of the presented scale-up from micro-lab to milli-pilot scale, it was necessary to study reactor characteristics in detail (regarding mixing efficiency, residence time distribution, and heat transfer). This can be done through an experimental investigation of the scale-up setup. However, this is a rather time-consuming procedure. Thus, based on previous lab experiments and on a literature review, we present a model-based approach that renders scale-ups significantly more efficient.


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Mixing Mixing times should be short compared to the duration of a chemical reaction.68 Therefore, a suitable micromixer is necessary to ensure high mixing efficiency. To enhance mass transfer, a Kenics static mixer is incorporated within the pilot reactors. Mixing efficiency is increased due to its helical form with alternating right- and left-hand elements. This mixing unit causes velocity reversal, splitting, recombining, and directing the flow radially towards the tube wall and back to the center.69, 70 Nonetheless, resulting mixing times within the pilot reactors (with an incorporated Kenics static mixer) should be evaluated. Several approaches to calculate mixing time are reported in the extant literature.71–77 For example, Baldyga and Bourne78 indicate the total mixing time as the simultaneous contribution of diffusion time and shear stretching characteristic time. Mixing time of intertwined lamellae can be estimated, if the striation thickness and the shear rate in the reactor are known. Based on this concept, Falk and Commenge79 developed the stretching efficiency model applicable to laminar flow regimes. The theoretical mixing time tmixing,theoretical of intertwined lamellae (including molecular diffusion and shear in a tube in laminar flow) can be described as a function of Peclet number Pe.

(d 2/ Dm) tmixing, theoretical =

8 J Pe

ln(1.52 J Pe)

(3)

The theoretical mixing time in micro-structured devices can be very short. However, the presumed perfect mixing situation does not arise in reality, and real mixing times are much longer.69,

70

Therefore, Ottino et al.80 proposed the concept of mixing efficiency. To account for real mixing conditions, the model for the theoretical mixing time tmixing,theoretical is extended by the energetic efficiency of mixing '.79


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tmixing, real =

d ln(1.52 J Pe J ') 8 J u J '

Page 14 of 42

(4)

The value of energetic efficiency of mixing can be rather low. Baldyga et al.78 found the value to amount to 5 % in the semibatch reactor, and to 0.75 % in the twin-screw extruder. Especially for Kenics static mixers, Fang and Lee81 investigated the micromixing efficiency at varying Reynolds numbers Re, ranging from 66 to 1020. A parallel competing reaction scheme proposed by Villermaux et al.82 formed the basis of their examination. The authors demonstrated that, compared to an empty tube, Kenics static mixers enhance micromixing efficiency in both laminar and turbulent flow regimes. Based on a model by Fournier et al.83, Fang and Lee81 provided a correlation for the mixing time in Kenics static mixers, tmixing,Kenics, as function of Re (valid for Re > 150). Two approaches are included: an exponential model (with fitting parameter a1 = 2.21), and a linear model (with fitting parameter a2 = 1.69). The dimensionless parameter nKenics always amounts to 1.5. tmixing,Kenics = ai J Re

nKenics

(5)


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Table 2 summarizes mixing times that were calculated with the two approaches described by Falk and Commenge79 and by Fang and Lee81. They are indicated for two different Re numbers (lower and upper limit of scale-up experiments within validity of approaches). Table 2. Mixing times calculated from different approaches,79, 81 as function of Re. Re = 150

Re = 350

0.09

0.04

1.43

0.67

Mixing time in Kenics static mixer [s], linear model81

0.92

0.26

Mixing time in Kenics static mixer [s], exponential model81

1.15

0.32

Theoretical mixing time [s]79 Effective mixing time (' = 5 %)

[s]79

As described above, theoretical mixing times are much shorter than those occurring in reality. Hence, under real conditions, the concept of mixing efficiency should always be considered. However, compared to the mixing efficiency obtained in semibatch reactors (with ' = 5 %), even shorter mixing times can be achieved in Kenics static mixers. Yet, for rather low flow velocities (Re < 150), mixing times higher than 1 s cannot be ruled out. The scale-up approach presented in this work uses the linear correlation postulated by Fang and Lee81 to determine mixing time, as Kenics static mixers are incorporated within the reactor tube. This correlation was chosen, because Fang and Lee81 verified their model through several lab experiments and compared these results against established theoretical approaches that had already been reported in literature. Moreover, the scope of their correlation is applicable for the presented scale-up approach.


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Residence Time Distribution Within a narrow empty tube with laminar flow, radial diffusion and the extent of axial dispersion play a crucial role in influencing the velocity profile, and the residence time distribution. To characterize these effects, the dispersion model is used for describing residence time behavior in flow channels.84, 85 The stronger the occurring axial dispersion is, the broader the residence time distribution within a flow channel becomes. In case of an ideal plug flow reactor (such as the micro-lab reactor), axial dispersion can be neglected. However, by increasing the inner channel diameter (scale-up to pilot millireactors), axial dispersion might increase considerably. This causes a broader residence time distribution and promotes backmixing. In order to assess the extent of axial dispersion within a flow channel, reactor characteristics have to be taken into account. Several dimensionless parameters can be calculated to describe the characteristics of a continuous flow reactor. For example, the dimensionless Bodenstein number Bo is utilized to characterize the degree of backmixing. As a rule of thumb, the threshold to assume nearly plug flow conditions (negligible axial dispersion) amounts to Bo > 100.85

Bo =

u J L Dax

(6)

In eq. 6, the dispersion coefficient Dax incorporates molecular diffusion, effects of backmixing due to radial velocity profile in laminar flow, and the development of secondary flows. For straight reactor tubes, Dax can be calculated through a correlation according to Taylor86 and Aris87. For coiled reactor tubes, Dax can be estimated according to Daskopoulos and Lenhoff 88. Table 3 compares the lab microreactor and the two pilot millireactors (used during scale-up experiments, considered as empty tubes) regarding Re, Dn, and Bo numbers (both for straight86, 87


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and for coiled capillary tubes88). Those dimensionless parameters depend on the flow rate and are provided for several residence times (lower and upper limits). Table 3. Comparison of lab reactor with pilot millireactors (as empty tubes): dimensions and calculated dimensionless parameters for selected residence times; stoichiometric ratio nBuLi:CH-acidic compound 0.9:1. Lab reactor

Pilot reactor 1

Pilot reactor 2

Channel diameter [mm]

0.5 + 0.75 b)

2

2

Length [m]

5 + 2 b)

3

25.5

Inner volume [mL]

1.87

9.42

80.11

Residence time (lowest – highest) [min]

0.5

6

0.3

2.5

2.5

10

]

3.73

0.31

31.34

3.77

32.04

8.01

Flow velocity (highest – lowest) [m sF ]

0.097

0.008

0.167

0.020

0.170

0.043

Re number

61

5

333

40

340

85

Dn number

12

1

2

0.3

2

0.6

Bo number c) (straight capillary reactor86, 87)

35

424

3

7

7

29

Bo number d) (coiled capillary reactor88)

184

960

13

20

25

39

minF

Flow rate (highest – lowest) [mL

b) Lab reactor: Consisting of two modular reactor pieces that are connected to each other. First capillary: inner diameter 0.5 mm; length 5 m. Second capillary: inner diameter 0.75 mm, length 2 m. c) Applicable Bo number when reactor is not coiled (theoretical consideration). d) Actual Bo number present in the experiments, given the coiled reactor design.

The actual Bo numbers present in the experiments are those obtained for coiled reactor designs, since secondary flows arise and, therefore, lower backmixing is expected. Comparing the microreactor with the millireactors, it can be assumed that the lab experiments were carried out under nearly ideal plug flow conditions, whereas high backmixing due to extremely low Bo numbers occurred in the pilot-scale experiments. Therefore, axial dispersion considerably affected the pilot reactors and cannot be neglected due to the larger inner diameter. More details on residence time distribution in empty flow channels and in flow channels containing Kenics static mixers are provided in the supporting information C.


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Heat Removal High heat removal during an exothermic reaction allows for running the latter at nearly isothermal conditions. This is the case when heat transfer within a reactor occurs extremely quickly (otherwise, hot spot formation could affect the reaction and safe handling becomes more difficult). However, heat transfer strongly depends on reactor dimensions and therefore is a crucial factor when scaling-up an exothermic reaction.89, 90 Heat transfer efficiency depends on reactor characteristics. The characteristic heat transfer timescale th can be used to assess the time that is required to remove the heat that is released during an exothermic reaction. Its value can be estimated as follows:91

th =

6 J cP J d

7 =

4 J 7 Nu J 8 d

(7) (8)

Eq 7 outlines that high heat transfer coefficients 7 and small inner diameters d lead to short transfer times. Heat transfer parameters (specific surface area, heat transfer coefficient, and heat transfer timescale) were calculated for the micro-lab and the pilot millireactors. In all cases, 7 was

X

by assuming fully developed laminar Y 8 heat transfer with Nu = 3.66 (constant wall temperature). Further assumptions include that heat transfer in the oil bath and heat conduction in the wall of the stainless steel capillary both are much higher than the inner heat transfer. Table 4 compares the lab microreactor and the two pilot millireactors regarding their heat transfer parameters.


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Table 4. Heat transfer parameters calculated for lab microreactor and the two pilot millireactors. Lab reactor

Pilot reactor 1

Pilot reactor 2

Channel diameter [mm]

0.5

0.75

2

2

Length [m]

5

2

3

25.5

Specific surface area [m2 mF3]

8000

5334

2001

2000

Heat transfer coefficient [W mF, KF ]

979

653

245

245

Heat transfer timescale [s]

0.19

0.42

2.98

2.98

When increasing the inner channel diameter from 0.5 mm (microreactor) to 2 mm (pilot millireactors), the characteristic time needed for heat transfer increases by a factor of 16. Hence, efficient heat removal regarding the scale-up of the exothermic lithiation reaction can no longer be assumed, and a possible hot spot formation at the entrance of the reactor has to be considered. Actual kinetic data is required to estimate the temperature profile in a given reactor, as heat release depends on reaction rate. Therefore, if kinetic data is available, the temperature profile can be calculated using the energy and mass balance (see Table 6 for details on balance equations). Regarding the overall heat transfer, the limiting factor is the inner heat transfer due to small area and organic solvent. Therefore, heat transfer coefficient 7 was

X

by assuming fully

developed laminar Y 8 heat transfer with Nu = 3.66 =const. (constant wall temperature). The assumption that heat transfer in the oil bath and heat conduction in the wall of the stainless steel capillary are much higher than the inner heat transfer needs to be justified, however. A detailed calculation of the outside heat transfer depending on mean flow velocity within the cooling bath is provided in the supporting information D.3. There, it is demonstrated that a 20 % higher outside heat transfer coefficient is already achieved when the cooling oil has a mean flow velocity of 0.1 m sF . Since this is a rather small threshold given that silicon oil is pumped through the bath


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with high throughput, the outside heat removal can be expected to be fast enough for entire heat dissipation.

Scale-up Verification Conversion in the pilot millireactors can be predicted through scale-up simulations. First, an isothermal plug flow reactor was simulated as reference scale-up scenario. Then, two model-based scale-up approaches were tested with each including heat and mass balances as well as the kinetic model (that was derived in previous lab experiments). The first model-based approach describes a quick estimate consisting of a simplified model that is developed from a practical point of view and under idealized conditions. The second model-based approach represents a more detailed scale-up model. All scale-up scenarios were compared to experiments using the pilot millireactors in order to verify the scale-up considerations. Table 5 summarizes the parameters of the three scale-up scenarios regarding mixing, residence time distribution, and heat transfer.


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Table 5. Parameters of chosen scale-up scenarios regarding mixing, residence time distribution, and heat transfer.

isothermal plug flow reactor

quick estimate

detailed scale-up model

mixing

instant mixing

residence time distribution

plug flow

heat transfer

isothermal behavior

mixing

dosing process (tmixing = const.)


plug flow

heat transfer

Nu = 3.66 = const.

mixing

mixing time in Kenics static mixer as function of Re


dispersion model

heat transfer

Nu = 3.66 = const. including thermal dispersion

The resulting heat and mass balances of the three scale-up scenarios, when applying the parameters for mixing, residence time distribution and heat transfer, as described in Table 5, are listed in Table 6.


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Table 6. Balance equations of chosen scale-up scenarios (continuous flow tube under steadystate conditions). Zci Zt mass balance isothermal plug flow reactor

Zci

= - u

Zz

+

Ri = 0

with Ri = - k(T) J cn1 J cm 2

[

and k(T) = kref J exp -

heat balance

J

(

1 T

)]

1

- Tref

= 0

Zt mass balance

Zci

= - u

+

Zz

Ri = 0


quick estimate

[

and k(T) = kref J exp -

ZT heat balance ZT = - u Zt Zz

Zci Zt

detailed scale-up model

R

ZT ZT = - u Zt Zz Zci

mass balance

EA

Ri J 9HR

Zci

= - u

Zz

6 J cp

EA R

(

1 T

1

)]

- Tref

7 J (T - T0) J -

Z2ci

+ Dax

J

4 d

6 J cp

= 0

+ Ri = 0

Zz2


[

and k(T) = kref J exp 2

EA R

heat balance ZT ZT Z T Ri J 9HR = - u + Aax 2 Zt Zz 6 J cp Zz

J

(

1 T

1

)]

- Tref

7 J (T - T0) J 6 J cp

4 d

= 0


22

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Both, conversion and temperature profiles, whilst simulating an isothermal plug reactor are provided in the supporting information E. The first model-based scale-up design, as a quick estimate, includes a constant mixing time. Mixing is thereby simulated as a dosing process by adding one starting material over a time of 1 s. Plug flow reactor behavior is assumed, with heat transfer being calculated using Nu = 3.66 = const. (assuming fully-developed laminar Y 8 heat transfer at constant wall temperature). Figure 3 compares the resulting simulated conversion-residence time curves (for various temperatures and stoichiometric ratios) with the scale-up experiments. Furthermore, the temperature profile as function of residence time is exemplarily depicted for a reaction temperature of F,5 °C. Simulated temperature profiles are illustrated as temperature differences between reaction mixture and coolant. Experimental values are calculated as temperature difference between precooling loop and mixer within the reaction channel. Actual temperature measurements during the scale-up experiments are provided in the supporting information D.1.


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In the second model-based scale-up design, as a more detailed model, the mixing time in a Kenics static mixer is incorporated as function of Re according to eq 5 (linear model). Plug flow reactor behavior is no longer assumed. Hence, balance equations for a plug flow reactor are extended by a term that describes axial dispersion. Heat transfer is once again calculated using Nu = 3.66 = const. (assuming that the inner heat transfer constitutes the limiting factor). In Figure 4, the scale-up experiments are compared to the resulting simulated conversion-residence time curves (when applying the detailed scale-up model). As an example, the temperature profile for a reaction temperature of F,5 °C is plotted against residence time.


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SCALE-UP DISCUSSION Comparing both model-based scale-up approaches, the detailed model is able to represent the scale-up experiments with higher accuracy (see comparison of conversion profiles at coolant temperature F,5 °C in Figure 5). In general, the quick estimate’s predictions for conversion are higher than the experimental values. This is in line with the rising impact of axial dispersion, when increasing the inner channel diameter from 0.5 mm (microreactor) to 2 mm (pilot millireactors). While the quick estimate assumes plug flow reactor behavior (narrow residence time distribution), the detailed reactor model includes a term describing axial dispersion. This axial dispersion causes backmixing, which in turn leads to a decrease in conversion. Despite this drawback, the quick estimate can nonetheless be applied for rough scale-up predictions in industrial contexts (errors are in the range of 5 to 12 %). Figure 5 further demonstrates that simulating an isothermal plug flow reactor (without applying any model-based approach) leads to a conversion profile resting between the two described modelbased approaches. Hence, conversion is not only affected by axial dispersion, but also by temperature profile, since concentration and temperature are interlinked as indicated in the Arrhenius relation. Due to a rather low activation energy of the investigated deprotonation reaction, differences within the concentration profiles are small. Although the ideal model of an isothermal plug flow reactor can predict conversion profiles with relatively high accuracy (and with even higher accuracy than the quick estimate), temperature profiles are fully neglected. However, hot spots released during the exothermic reaction may run up to 5 K. Neglecting this temperature release could lead to safety issues, when performing a scale-up based on an isothermal model. Therefore, model-based scale-up approaches should always consider the temperature profile, even if this results in inflated predictions of conversion.


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Regarding the simulated temperature profiles of both, the quick estimate and the detailed scale-up model (see Figure 3 and Figure 4), maximum temperature rise can be predicted with sufficient accuracy, but generally heat transfer is assessed too high. In reality, a slow mixing process could come along with slow hot spot decrease. However, this relation could not be implemented within the theoretical scale-up models as otherwise physical limits would be violated (Nu < 3.66, tmixing > 90 s). The resulting weighted sum of squared errors for concentration and temperature profiles are illustrated in Figure 5, both of the two model-based scale-up approaches and of the isothermal plug flow reactor. Comparing the quick estimate to the more detailed (but also more time consuming) scale-up model, it once again becomes apparent that the detailed model can predict conversion profiles with higher accuracy. While errors in predicting temperature profiles are similar for the quick estimate and the detailed scale-up model, in case of an isothermal plug flow reactor, the error is more than twice in magnitude, since temperature release during the exothermic reaction is fully neglected. Details on the frequency distribution of squared errors for all experimental data points for both model-based scale-up approaches are provided in the supporting information F.


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Finally, a sensitivity analysis of the individual scale-up variables in terms of conversion was conducted. The impact of variations in Nu, mixing time, Bo, and kinetic parameters (within their estimated confidence intervals) was measured. The results are provided in Table 7. Table 7. Sensitivity analysis of scale-up variables in terms of conversion (residence time 1.4 min, coolant temperature F,5 °C). value

e)

9;1, [%]

reference value

value

9;1, [%]

Nu

-

-

3.66 d)

34

F5(

mixing time [s]

0.5

+0.4

1

4

F*(5

Bo

10

F )(*

plug flow

40

F ,(6

kref [m1.8 molF*(1 sF ]

3.30E-04

F (*

3.38E-04

3.46E-04

+1.6

EA [kJ molF ]

27

+1.1

29

31

F*(3

reaction order m

1.17

F+*(5

1.3

1.43

+65.4

reaction order n

0.25

F 5(+

0.3

0.35

+15.3

Lowest value of Nu due to physical laws.

Differences in reaction orders of the derived kinetic model as well as differences in Bo number yield the highest impact on conversion. Therefore, deviations within the kinetic model should be regarded carefully. As demonstrated before, axial dispersion strongly affects the scale-up experiments. The large impact of Bo numbers on conversion proves this further: Lower Bo numbers lead to reduced conversion. It becomes evident that dispersion plays a major role, and that the detailed scale-up model should be used in order to predict concentration profiles with high precision.


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CONCLUSION This work discusses model-based scale-up predictions of a deprotonation reaction with nbutyllithium, which is of high industrial relevance. A complete process development for its transfer from lab to pilot scale is presented. Lab experiments, which were conducted within a microreactor, provide the basis for a systematic scale-up approach including heat and mass balance and kinetic studies. When increasing the inner channel diameter from 0.5 mm (lab microreactor) to 2 mm (pilot millireactors), it is essential to take reactor characteristics, such as mixing efficiency, residence time distribution and heat transfer, into consideration. Two different model-based scale-up approaches were successfully applied in order to represent experiments at pilot scale. For the conversion, a quick estimate (non-isothermal plug flow reactor with constant mixing time in Kenics static mixer) is entirely sufficient. Nevertheless, it was shown that axial dispersion affects the reaction progress. Especially in the case of low Bo numbers, as it is the case within the pilot millireactors, high backmixing is promoted, and the one-dimensional dispersion model should be included. A second, more detailed scale-up approach predicts conversion with greater accuracy. The influence of transport mechanisms on the reaction kinetics is characterized and the model includes a term for mixing time in Kenics static mixers as function of Re, and considers both the effect of strong axial dispersion and the potential formation of hot spots at the reactor entrance. The latter are particularly important for the highly exothermic lithiation reaction. Moreover, it was demonstrated that a model-based prediction is generally superior to simply assuming an isothermal model. Depending on the intended application, one of the two presented scale-up approaches should be applied.


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The scale-up from lab to pilot or production scale is of high industrial significance, but simultaneously an error-prone step in process development. By using a model-based scale-up approach as described in this work, the necessity of conducting time-consuming measurements on pilot or production scale vanishes, and an even better understanding of the involved chemical process can be accomplished. Especially regarding the scale-up of challenging lithiation reactions, only few examples are described in the extant literature. Nevertheless, transfer from lab to pilot or production scale is essential due to their high industrial relevance. By application of the presented model-based approach, efficient scale-up of those crucial organometallic syntheses can be realized.


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ASSOCIATED CONTENT Supporting Information. A closer look at the method for analysis and reactor characteristics, including mixing performance, residence time distribution, and heat transfer, is provided in the supporting information section. This material is available free of charge.

AUTHOR INFORMATION Corresponding Author * Email address of corresponding author: [email protected] (Telephone +49 621 292 6800)

ACKNOWLEDGMENT This work was funded by the German Federal Ministry of Education and Research (BMBF), programme FH Impuls - Partnership for Innovation M2Aind, project SM2all (grant No. 13FH8I01IA). The authors would like to thank Daniel Meier (Merck KGaA, Darmstadt) for great technical support, and Scale-up Systems Ltd. (Dublin 4, Ireland) for providing the software DynoChem, especially Dr. Wilfried Hoffmann and Steve Cropper.


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ABBREVIATIONS

1

[-]

CH-acidic compound

2

[-]

n-butyllithium

3

[-]

lithiated intermediate

ai

[-]

fitting parameter mixing time Kenics static mixer

Aax

[m2 sF ]

thermal dispersion coefficient

Bo

[-]

Bodenstein number

c0

[mol LF ]

initial concentration

ci

[mol LF ]

concentration of compound i

cP

[J kgF KF ]

specific heat capacity

d

[m]

inner capillary diameter

Dax

[m2 sF ]

axial dispersion coefficient

Dm

[m2 sF ]

molecular diffusion coefficient

Dn

[-]

Dean number

EA

[kJ molF ]

activation energy

%3

Model-Based Scale-Up Predictions: From Micro- to Millireactors Using

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