Multivariate curve resolution for kinetic modeling and scale-up prediction

An imine synthesis was investigated in a nearly isothermal oscillating segmented flow microreactor at different temperatures using non-invasive Raman spectroscopy. Multivariate curve resolution provided a calibration-free approach for obtaining kinetic parameters. The two different multivariate curve resolution approaches, soft and hard modeling, were applied and contrasted, leading to similar results. Taking heat and mass balance into account, the proposed kinetic model was applied for a model-based scale-up prediction. Finally, the reaction was performed in a 0.5 L semi-batch reactor, followed by in-line Raman spectroscopy and off-line gas chromatography analysis. The successful scale-up was demonstrated with a good agreement between measured and predicted concentration profiles. • Oscillation segmented flow reactor with inline Raman spectroscopy. • Multivariate Curve Resolution with hard and soft constraints. • High quality kinetic model for scale-up predictions. Graphical abstract


Introduction
The possibility to reliably scale up reactions is crucial for the chemical industry. Over the years, different scale-up approaches, including numbering up, sizing up, and the combination of both have been investigated [1]. Particularly, the fine-chemical industry, producing drug substances and active pharmaceutical ingredients (APIs), primarily relies on the traditional approach of scaling-up the batch size [2]. Each strategy has its benefits and limitations, where reliable kinetic and thermodynamic parameters are needed for precise scale-up predictions. Continuous-flow microreactors have been shown advantageous for studying chemical reactions, due to their nearly isothermal behaviour, sufficient mixing, narrow residence time distribution, and low feed material consumption [3]. On top of that, procedures can be easily automatized [4]. In order to obtain kinetic data from microreactors, reactions can be monitored with online and inline analysis tools [5]. Studies have been performed using Raman [6], MIR [7], NIR [8] and UV/Vis spectroscopy [9]. Non-invasive inline analysis tools are especially advantageous for monitoring small sample volumes. Therefore, non-invasive Raman spectroscopy was applied for kinetic investigations in this work. In order to perform kinetic modeling, concentration profiles over time are needed. However, continuous-flow microreactors are limited considering a wide range of residence times. Oscillating segmented flow reactors, as shown in Scheme 1, can solve this issue. A segmented flow is generated by separating the reactive phase by an inert phase (e.g. perfluorinated oil). The resulting droplets are moved in an oscillatory motion. This offers the possibility to perform and monitor reactions which require long, as well as short reaction times, while maintaining plug-flow residence time distribution, effective mixing, and high heat-and mass-transfer rates [10][11][12][13][14].
Online monitoring of the course of reaction enables fast and reliable kinetic modeling. However, obtaining calibration curves beforehand can be quite time-consuming. Therefore, multivariate curve resolution (MCR) is of great interest as a universally applicable analysis method. MCR offers a (nearly) calibration free, chemometric approach for analyzing multiple component reaction mixtures [7,[15][16][17][18][19][20]. Additionally, MCR offers the advantage that data analysis is not limited to distinct or individual bands, meaning that the full spectral information can be exploited [15]. The general procedure of MCR is schematically shown in Scheme 2. Concentration profiles and spectra of the involved components (matrices C and S T , respectively) are extracted from spectroscopic raw data (matrix D). Matrix E (E = D-CS T ) consists of residuals that cannot be explained by the resolved components and should be close to the spectroscopic error [16]. In MCR methods, it is important to distinguish between hard and soft modeling (see Scheme 2b) [18,21]. Hard modeling starts from a kinetic model whose parameters are fitted to reconstruct the data D as well as possible [22]. In soft modeling, the factors C and S are computed in terms of least square calculation and using regularization functions. The choice and weighting of the regularizations decisively determine the calculated solutions [23].
While there have been a lot of studies concerning the scaleup using continuous-flow [1] and batch reactors [24], scaling up reactions investigated in segmented flow reactors has only been subject to little research. However, kinetic investigations and screenings have been performed by many groups [11,[25][26][27][28][29]. Furthermore, segmented flow reactors have been successfully applied in nanomaterial synthesis [30,31]. Regarding the synthesis of powders, a "scale-out" concept was proposed, by increasing the number of tubes in parallel instead of increasing their sizes [32]. In the past years, a lot of photochemistry research has been done dealing with oscillating segmented flow reactors and scale-up concepts [33][34][35]. Recently, a catalysed cross-electrophile coupling was investigated in an automated segmented flow reactor at 15 µL scale and afterward scaled up to a 5 mL photo-continuous stirred tank reactor [36].
In this work we describe the investigation of an imine synthesis (Scheme 3) in an oscillating segmented flow microreactor by non-invasive Raman spectroscopy. Even though a univariate analysis is feasible, MCR is applied in order to show the universal capability of this approach. The resulting high quality kinetic model is used for a scale-up prediction. The novelty of this work is the combination of an oscillating segmented flow reactor setup with the calibration free MCR approach for a model-based scale-up.

Results and discussion
Obtaining kinetic data in an oscillating segmented flow reactor The investigated imine synthesis (see Scheme 3) has already been described to follow a second order mechanism [37], which can be described as follows: In order to proof this proposed mechanism, the imine synthesis was investigated at varying stoichiometric ratios (see SI). The results confirm the proposed mechanism.
Only benzaldehyde and n-benzylidenebenzylamine show strong Raman bands and can therefore be depicted as independent components during MCR. Therefore, nonstoichiometric ratios can only be modelled accurately using hard modeling, where non-absorbing or weak absorbing components can be included in the kinetic model (see SI for details).
The result set shown in Fig. 1 consists of the concentration profiles over time obtained by soft and hard modeling at three different temperatures (see Experimental for details). For clarity reasons, the fourth temperature is excluded, but can be found in the SI. Regarding soft modeling (Fig. 1a), concentration profiles (symbols) were obtained and afterwards fitted to the previously described kinetic model, in order to gain reaction rate coefficients at each temperature. The associated kinetic models are shown as dotted lines. For hard modeling Scheme 1 Schematic drawing of an oscillating segmented flow reactor ( Fig. 1b), the concentration profiles were fitted directly to a kinetic model, resulting in reaction rate coefficients at every temperature. The dotted lines show the underlying kinetic model, while the symbols refer to the concentrations obtained by matrix decomposition. For better understanding, the concentration profiles are coloured according to their chronological order. Black/grey concentration profiles were obtained first, resulting in orange/brown profiles.
The resulting kinetic parameters obtained by soft and hard modeling are shown in Table 1. Reaction rate coefficients k are fitted at each temperature T and then linearized using the re-parameterized Arrhenius Eq. (2), in order to obtain the reaction rate coefficient k ref and the activation energy E A at the reference temperature T ref (see SI for Arrhenius plots). The kinetic parameters k ref and E A obtained by soft and hard modeling nearly coincide.
Experiments were additionally conducted with another initial concentration of benzaldehyde and benzylamine, in order to proof the reliability and reproducibility of the procedure to obtain kinetic parameters. The results showed good agreement (see SI for details).

Scale-up
After obtaining a kinetic model, scale-up predictions were performed for a 0.5 L semi-batch process, taking the overall heat and mass balance into account. The reactor specific parameters, such as heat capacity and heat transfer coefficient, were obtained in independent experiments (see SI). The predicted kinetic model (dotted lines) and the experimental data (symbols) are shown in Fig. 2. Good agreement was observed between the estimated and measured concentration profiles. However, small deviations can be found shortly after dosing is completed. In this region the reaction is slower compared to the predicted course of reaction. This can be explained by the overestimated rise of temperature during the reaction in the simulation, compared to the measured temperature rise (see Scheme 2 a Generalized procedure of MCR b Flowchart contrasting soft and hard modeling Scheme 3 Imine synthesis: 1, benzaldehyde; 2, benzylamine; 3, nbenzylidenebenzylamine SI), leading to a faster predicted reaction. Comparing the simulated and by off-line gas chromatography (GC) obtained concentration profiles small differences can be recognized. Even though samples for GC were diluted and cooled to slow down the reaction rate, the reaction was not completely stopped, explaining the differences in the concentrations. Besides, there are differences in final concentration of both educts, due to deviations in starting concentration.
Additionally, a batch process was performed in a 0.5 L reactor. The predicted and measured concentration profiles   show good agreement. However, the temperature during reaction is overestimated again leading to a faster predicted course of reaction. Details can be found in the SI.

Conclusion
In this contribution, we have described the kinetic modeling of an imine synthesis in an oscillating segmented flow reactor. The reaction was investigated in a 7 µL droplet by noninvasive Raman spectroscopy. Performing MCR (soft and hard modeling approach) resulted in kinetic parameters, which were used to scale up the reaction which were used to scale up the reaction by a factor of 71,400. Since soft and hard modeling show similar, reproducible results, both approaches can be used for scale-up predictions. However, hard modeling is to be preferred, if the reaction includes non-or less-absorbing species, which cannot be modelled as independent components by MCR. The good agreement between the estimated and measured concentration profiles lead to the conclusion that a kinetic model with high quality for scale-up predictions was generated.

Oscillating segmented flow microreactor
The experimental setup for the oscillating segmented flow microreactor has already been described in detail (see Scheme 4a) and b) [25]. Benzaldehyde (2.0 M, for synthesis, > 99%, CHEMSOLUTE) and benzylamine (2.0 M, ReagentPlus, 99%, Sigma Aldrich) in methanol (for synthesis, > 99%, CHEMSOLUTE) were mixed in a micromixer at a total flow rate of 4.0 mL min -1 . The stoichiometric ratio amounted to 1.0. Slugs (4 mm) were generated by introducing FC-40 oil (> 99%, 3 M) using a T-junction at a flow rate of 1.5 mL min -1 . The total flow rate amounted to 5.5 mL min -1 . The superficial velocity of the moving slugs in the microreactor amounted to 1 mm s -1 . Further experimental details about the generation of the oscillating slugs and calculation of the slug volume can be found in the SI. The synthesis was investigated at temperatures between 15 and 45°C. Kinetic measurements were performed using the MultiSpec Raman system, produced by Tec5, with a 785 nm wavelength excitation laser. The output laser power amounts to a maximum of 500 mW. A contactless coaxial Raman focus probe with a fixed focal length of 25 mm is positioned over the reactor [25]. The integration time was set to 500 ms with a complete cycle time of 1000 ms.

Scale-up
The scale-up experiments were performed in a glass jacketed 0.5 L reactor with four baffles. Benzaldehyde Raman dip probe with a fixed working distance of 1 mm was directly inserted into the reactor. The integration time was set to 500 ms, while the cycle time amounted to 15 s. GC samples were taken over the course of reaction and immediately diluted by a factor of 10 with precooled methanol. The samples were stored cold and measured in a timely manner.

Data evaluation methods
The Raman spectra were processed as follows: FC-40 spectra were excluded (only necessary in oscillating segmented flow microreactor set-up); spectra were smoothed and first derivative was calculated using the savitzky-golay filter (polynomial order 2, frame length 7). Experimental data matrices (Raman spectra over time) were constructed. Concentration profiles were obtained directly by the MCR approach (soft and hard modeling). The MCR-ALS GUI 2.0 [16] was applied for soft modeling, while the FACPACK [22] software was used for hard modeling. Both work under MATLAB® environment. The following constraints relating to the row mode (concentration profiles) were defined for soft modeling: non-negativity, horizontal unimodality, mass balance closure and local rank information [17]. The constraints for hard modeling were defined by a kinetic model (see SI for details). Regarding soft modeling, the resulting concentration profiles were fitted to a kinetic model using DynoChem (Scale-up Systems Ltd., Ireland) to obtain kinetic parameters. In the case of hard modeling, concentration profiles and reaction constants were obtained directly. The re-parameterized Arrhenius equation was used to fit the rate constants k in order to obtain k ref and

Declarations
Conflict of interest The authors states that there is no conflict of interest.
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