An Experimental Assessment of Model-Based Solvent Selection for

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Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

An Experimental Assessment of Model-Based Solvent Selection for Enhancing Reaction Kinetics Angeliki Tsichla,*,†,‡ Christian Severins,‡,§ Michael Gottfried,‡,§ and Wolfgang Marquardt† †

Aachener Verfahrenstechnik−Process Systems Engineering, RWTH Aachen University, Forckenbeckstraße 51, 52074 Aachen, Germany ‡ Bayer Technology Services GmbH, 51368 Leverkusen, Germany

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S Supporting Information *

ABSTRACT: Scientific advances in the fields of chemistry and engineering have established the critical impact of solvents on the rate of a wide array of chemical reactions. This has triggered the interest of academia and industry for the search of solvents that optimize reaction kinetics. Yet, there are only a few systematic approaches to guide such solvent selection currently. In this work, a methodology was developed to identify suitable solvents that will enhance the reaction rate of an industrial process at minimum experimental effort. For the rapid data generation and quantification, a modular continuous reactor coupled with real-time in situ analytics was set up. The data generation is guided by a computational method that consists of two steps: the formulation of a model identification problem based on the solvatochromic equation and the computer-aided screening of a solvent database that provides a list of the most promising solvents. The methodology is applied to the amination of ethyl trichloroacetate with liquefied ammonia, a reaction of industrial interest. Two of the predicted promising solvents are verified experimentally, demonstrating the predictive power of the methodology. Thus, a systematic model-based solvent selection methodology was demonstrated successfully to an industrially relevant reaction problem.

1. INTRODUCTION Organic solvents play a key role in all steps of synthetic processes in the chemical industry, including reaction, separation, purification, and formulation, and the selection of the optimal solvent per step or combination of steps is essential for the overall efficiency and viability of the process. Currently, the state of the art of solvent selection is driven by extraction and extractive distillation processes,1−4 crystallization5 problems, as well as screening of solvent alternatives based on technical or techno-economic criteria.6−8 Solvents however also have a dramatic effect on the rate and selectivity of chemical reactions,9 making the selection of the right reaction solvent crucial in process development. In this work, we focus on chemical reaction problems only. Several solvent selection guides that cover chemical reactions, among other applications, are available in the scientific community. The guidelines developed by GlaxoSmithKline,10,11 the American Chemical Society, Green Chemistry Institute Pharmaceutical Roundtable,12 the solvent guide from the Innovative Medicines Initiative project CHEM21,13 and Pfizer’s14 and Sanofi’s15 guidelines focus on environmental, health, and safety (EHS) considerations. Grundtvig et al.16 developed a solvent screening procedure for bioprocesses that includes both EHS and technical requirements. All above-mentioned contributions help guide © XXXX American Chemical Society

chemists and engineers toward solvents with the best EHS profiles or the identification of the best solvents as part of an optimization approach but neglect the impact of the solvent on the reaction rate. Riechert and his co-workers17 proposed a thermodynamic approach that considers the interactions between the reacting species and the different solvents via activity coefficients. The Perturbed-Chain Statistical Associating Fluid Theory (PCSAFT) has been used to predict the solvent effects on the esterification reaction of acetic acid and of propionic acid with ethanol at different reactant ratios and solvents, once the thermodynamic equilibrium constants were determined from experimental data for the solvent-free reaction equilibrium. Lemberg and Sadowski18 studied the reaction kinetics for the esterifications of acetic acid and propionic acid with ethanol at 303.15 K. The thermodynamic model PC-SAFT was applied to account for the interactions between the reacting species and the solvents via activity coefficients. This allowed the Special Issue: Dominique Bonvin Festschrift Received: Revised: Accepted: Published: A

February 22, 2019 June 14, 2019 June 16, 2019 June 16, 2019 DOI: 10.1021/acs.iecr.9b01040 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

applied to predict the solvent effect on the reaction rate. The methodology has been validated by means of a literature case study, where the most promising solvents for the solvolysis of tert-butyl chloride have been identified. The methodology proposed in this contribution extends the theoretical work of Wicaksono et al.36 to cover real experimental data for a specific reaction of interest. For fast data generation, a continuous modular reactor was designed and built. Inline and offline analytical methods were developed for process monitoring and data quantification. A rational approach, based on chemical diversity, is introduced to select a suitable set of candidate solvents based on chemical diversity. A thorough analysis has been performed to assess the impact of the experimental setup, which does not perfectly meet the assumptions of the theoretical screening framework.36 In particular, temperature and dispersion effects, neglected in the plug flow model of the reactor coil, were studied. Furthermore, structural identifiability was employed to make sure that the model parameters for the developed candidate reaction mechanisms can be identified from the available measurements to facilitate model and hence mechanism discrimination. The proposed experimental methodology can be applied to various types of chemical reactions, provided a suitable parametric model is available to describe the effect of the solvent on the reaction rate. In this study, the solvatochromic equation is employed, which has been shown to successfully predict the solvent effect for certain types of chemical reactions in homogeneous liquid phase, including solvolysis reactions,30−32 Diels−Alder reactions,32 or nucleophilic substitution reactions, like the Menschutkin reaction.34,35 To our knowledge, this is the first report of assessing the capability of a solvent selection methodology developed to accelerate reaction kinetics experimentally in an industrial environment for a commercially relevant reaction system. This paper summarizes the major findings of the doctoral thesis of the first author37 and is structured as follows: The proposed methodology is outlined in the following section. Afterward, a case study is presented: the reaction, the amination of esters, is introduced followed by the description of the experimental setup, the experimental procedure, and the investigation performed toward model discrimination. The implementation of the methodology for the prediction of the most promising solvents for the amination of esters is presented and discussed in the subsequent section. Finally, some conclusions are given.

identification of solvent-independent kinetic constants and the prediction of the solvent effect on reaction kinetics in agreement with experimental data. Gani and his co-workers6,19 developed a systematic methodology for solvent screening and generation of alternative solvents for the promotion of organic reactions that incorporates computer-aided molecular design (CAMD) tools for solvent design and properties estimation along with data available from industrial practice. The methodology is able to evaluate both generated molecules and known chemicals as potential solvents, producing a short list of candidates ranked in terms of their performance, which may vary depending on the specific solvent-selection problem. Though valuable for solvent screening and generation of alternative promising solvents, CAMD techniques do not account for the effect of the solvent on reaction kinetics. Stanescu and Achenie20 conducted a theoretical study and proposed a methodology that combines CAMD and quantum mechanics for the investigation of solvent effects on the Kolbe−Schmitt reaction. Zhou and co-workers21 developed a model-based methodology where solvent descriptors were determined from conductor-like screening model for real solvents (COSMO-RS) quantum chemical computations. The methodology was applied on selected SN1, SN2, and Diels− Alder reactions for the identification of the most suitable solvent candidates. The same group22,23 proposed a method where kinetic models are built by correlating experimental reaction rate constants with corresponding descriptors of the solvent determined from quantum chemical calculations in a small set of known solvents, and optimal solvents are identified from the solution of an optimization-based molecular design problem. A solvent design framework is proposed to identify solvents that possess the best reaction performance under model uncertainties, and the methodology is exemplified for a competitive Diels−Alder reaction. In 2016, a CAMD methodology based on a genetic algorithm (GA) was proposed by this research team24 for identifying optimal solvents for liquidphase reactions where the objective is to maximize the reaction equilibrium conversion. The quantum computational approaches, though promising enough, are computationally demanding. A simple and easily applicable approach for the identification of solvents for enhanced reaction rates is the use of correlation methods.25−29 The solvatochromic equation30 has been used to quantify solvent effects on solvolysis reactions30−32 and on Diels−Alder reactions.32 Folic et al.33 proposed a methodology for solvent design that enhances reaction rates using the solvatochromic equation to model the solvent effects on the reaction rates. Reaction rate data were gathered from published experimental data, and CAMD techniques were used to generate candidate solvents. Struebing and co-workers34,35 proposed an extension of the methodology of Folić et al.33 that identifies improved reaction solvents by combining quantum mechanical computations with CAMD. The methodology was tested on the Menschutkin reaction and led to the identification of a high-performance solvent from a large set of possible candidates. Wicaksono et al.36 developed a hybrid model-based and data-driven framework of the screening of promising solvents to optimize reaction rates. The developed methodology integrates model identification for the prediction of solvent effects on reaction rates from experimental data with the computer-aided screening of a large databank of solvents. As in Folić et al.33 the solvatochromic equation has been

2. METHODOLOGY The methodology proposed in the present contribution is depicted in Figure 1 and explained in the following sections in more detail. Ιnitial Solvent Database Σ0. As a starting point, an initial solvent database Σ0 is considered, which should cover the set of all conceivable solvents. Σ0 may consist of all known solvents, diverse in terms of functional groups, physical properties like boiling and melting points, polarity, acidity, and basicity, to mention but a few. Molecules not commonly used as solvents, designed with the aid of CAMD tools, can also be included in the database Σ0, as such solvent candidates may reveal new opportunities in chemical synthesis. To this end, the ProCAMD toolbox of the ICAS software can be used for the generation of relevant molecules and for the prediction of molecular properties applying group contribution methods.6,19 B

DOI: 10.1021/acs.iecr.9b01040 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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• the hydrogen-bond donor acidity, α, which refers to the solvent’s ability to donate a proton in a solvent-to-solute hydrogen bond.25 • the hydrogen-bond acceptor basicity, β, which refers to the solvent’s ability to donate an electron pair in a solvent-to-solute hydrogen bond.26 • the dipolarity/polarizability, π*, which refers to the solvent’s ability to stabilize a charge or a dipole by virtue of its dielectric effect.27 • the Hildebrand solubility parameter,38 δH, or the related cohesive energy density that measures the solvent− solvent interaction. log k0 is the reaction rate constant for a reference solvent, which might be available from initial investigations of the reaction of interest. Often, this rate constant is unknown; then, as in this work, it is estimated together with the other parameters a, b, sπ, and h in the solvatochromic equation (eq 1) from experimental data of the reaction rate constants log ks for the solvents of subset Σ2. The solvent properties α, β, π*, and δH can be taken from literature or need to be determined in separate experiments. The set of solvatochromic equations for n solvents can be represented in the compact form log ks(θ ) = A Σ2θ

(2)

where θ are the unknown parameters θ T = [log k 0 absπ h]

AΣ2 is the (n × 5) matrix of the solvatochromic parameters for n solvents taken from the set Σ2, and (log ks(θ))T are the experimental reaction rate constants determined for each of the n solvents. A subset of database Σ1 is preselected based on chemical knowledge with the objective to maximize the physicochemical diversity of the type of solvents and reduce the number of candidates for rigorous screening to a manageable level. This subset can be directly employed as the subset Σ2 in dedicated kinetic experiments to produce the data for model identification. Alternatively, the preselected set of solvents can further be reduced to comprise of solvents resulting in the lowest condition number of the (generalized) inverse of matrix AΣ2. The condition number measures diversity in the set with regard to multiple solvent properties,36 namely, the solvatochromic parameters α, β, and π* and the Hildebrand solubility parameter δH, as well as the reference reaction rate log k0. The diversity-based selection aims to avoid collinearity that affects the accuracy of the estimated model parameters. The algorithm used to generate the Σ2 subset is as follows: • Choose the number of solvents n. At least five solvents are needed to estimate the four parameters a, b, sπ, and h of the solvatochromic equation and the reference reaction rate log k0, though a larger number is preferable to improve the quality of the estimated parameters. • Identify n solvents with maximum diversity, either by chemical insight or by computer-aided screening.36 The latter method identifies those solvents that result in the lowest condition number of the (generalized inverse of) matrix AΣ2 to reduce the propagation of experimental error in the reaction rate constants log ks to the estimates of the solvatochromic parameters to a minimum.

Figure 1. Methodology for the prediction of the most promising solvents with optimal reaction rates.

Solvent Database Σ1: Link to a Specific Process. With Σ0 as a starting point, a restricted second solvent database Σ1 is derived by means of chemical heuristics to exclude those solvents that do not fulfill the process constraints of the reaction under study or do not meet EHS criteria. The use of CAMD techniques and the ICAS software19 can provide good support for this step. A search can be performed within the associated CAPEC database, selecting solvents that satisfy specified property constraints, such as boiling and melting points, Hansen solubility parameters, chemical families, and EHS properties. Solvent Subset Σ2: Targeted Experimentation. Next, the solvent subset is further restricted to a subset Σ2 to identify a group of solvents that can be used to properly identify a parametric model of the solvent effect on the reaction rate. Obviously, the type and number of solvents in this set depends on the type of model involved. The present study relies on the solvatochromic equation in the form suggested by Abraham et al.30 to model the solvent effects on the reaction rate constant: log

δ 2 k = log k − log k 0 = aα + bβ + sπ π * + h H k0 100

(3)

(1)

This equation correlates the reaction rate ratio k/k0 with the Kamlet−Taft parameters, more specifically, with C


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Industrial & Engineering Chemistry Research Data Generation for Solvents in Subset Σ2. After an appropriate subset Σ2 is defined, experimental data for each solvent are generated to be employed for kinetic modeling and for the identification of the model describing the solvent effects on reaction rate, that is, the solvatochromic equation in this study. To this end, we must make sure that both the reactor and the reaction models properly represent the experimental conditions. In particular, axial dispersion and temperature effects need to be negligible to justify the use of an isothermal plug flow model of the reactor. Likewise, the candidate reaction models need to reflect the conceivable reaction mechanisms derived from experimental and theoretical investigations. Finally, structural identifiability analysis is necessary to guarantee that the parameters can be estimated in principle from the available measurements. Computer-Aided Solvent Screening Process. The computational strategy of Wicaksono et al.36 handles the model identification problem along with a computer-aided screening problem in a nested way. The model identification problem refers to the estimation of the four parameters a, b, sπ, and h and the reference rate of reaction log k0 in eq 1. The resulting model is then used for the computer-aided screening of the database Σ1. As the two problems are coupled, the solution of the computer-aided screening problem s *̃ = arg max log ks(θ *̃ )

Uncertainty propagation and its effect on the selection of the most favorable solvent can be analyzed by Monte Carlo simulation.36 In some cases, a single best solvent might not be identifiable. Rather, a set of promising solvents should be considered in this case. Experimental Validation. As a final step, the best candidate solvent predicted is verified experimentally. That solvent should be superior in terms of maximizing the reaction rate compared to the other solvent candidates in the subset Σ2. Disagreement of the experimental results with the predicted solution could be attributed to uncertainty propagation at the final solution. In that case, the most favorable solvent could be hindered by inferior solvents,36 and analysis of uncertainty propagation using Monte Carlo simulations could be helpful for the identification of further solvents that should be validated experimentally.

3. CHOICE OF REACTION AND EXPERIMENTAL SETUP Amination of Esters. The developed methodology is applied for the prediction of the solvent(s) that enhance the rate of a reaction of industrial interest, the amination of esters, and more specifically the reaction of ethyl trichloroacetate with liquid ammonia (Figure 2). Ammonia was chosen to be in the

(4)

is constrained by the solution of the model identification problem θ *̃ = arg min ∑ (log ks(θ) − log ks̃ )2

Figure 2. Amination of ethyl trichloroacetate.

liquid state to increase the concentration of the nucleophilic species in solution. The current approach involves no use of catalysts or oxidative agents. Substitution at a carbonyl group most often proceeds via an SN2-like addition−elimination mechanism designated by IUPAC as AN+DN mechanism39 and also known as the tetrahedral mechanism (Figure 3). The key step (Step 1 in

(5)

where s denotes the solvent candidate, θ is the model parameters, and ks is the reaction rate constant for solvent s. θ̃* is the solution of the model identification problem, and s̃* is the solution of the computer-aided screening problem. The tilde indicates the uncertainty associated with a computed value, which is originating from the measured values of the rate constants log k̃s. Special attention is paid to the uncertainty that may propagate from the data in the solution of the two problems resulting in a significantly larger uncertainty in the final solution. An ill-conditioned system (eq 2) could lead to high sensitivity of the solution of the model identification problem (eq 5) and thus to the solution of the computer-aided screening problem (eq 4). Hence, conditioning of the system (eq 2) is necessary not only for a more targeted experimentation but also to ensure accurate solutions of the coupled problems (eqs 4 and 5). Tikhonov regularization constitutes a complementary approach to address the possible ill-conditioning of the model identification problem.36 θ̃* resulting from Equation 5 after Equation 2 is introduced, the matrix AΣ2, and the experimental reaction rate constants determined for each of the n solvents (log ks(θ))T reads as θ *̃ = (A TΣ2A Σ2)−1A TΣ2 log ks̃

Figure 3. Simplified illustration of the two steps of the tetrahedral mechanism.

Figure 3) is the addition of the nucleophile to the acyl carbon atom, which generates a tetra-coordinate carbon atom. Elimination of one of the groups from the tetrahedral intermediate (Step 2 in Figure 3) leads to the formation of the amide. Despite the great number of experimental studies on the mechanism of the amination of esters,40−49 the different mechanistic alternatives became clearer only after more recent computational studies50−58 and converge into three possible mechanisms: a concerted path, a stepwise path through zwitterionic intermediates, and an alternative stepwise path through neutral intermediates. The reaction often exhibits general base catalysis43−45,59−62 with a second amine molecule

(6)

A regularized solution of Equation 5 is given by the equation θR̃* = (A TΣ2A Σ2 + λΙ)−1A TΣ2 log ks̃

(7)

The regularization parameter λ is determined by means of generalized cross-validation.36 I is the identity matrix. D


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maintenance reasons. The purge line includes a shutoff valve, a metering valve, and a reverse-flow check valve. The residence time can be altered either by manipulating the flow rates or, in case this is not possible due to equipment limitation, by variation of the length or/and diameter of the coiled tube. For the minimum reactor volume that can be achieved (1.83 cm3), the lower residence time that can be reached is defined by the HPLC pump flow rate range and, more specifically, their maximum volumetric flow rates: 10 mL· min−1 for pump 1 and 5 mL·min−1 for pump 2. The calculated values residence times for the solvents studied vary in the range from 6 to 9 s, given the various values of the densities of the mixture of the solvent and the substrate A. This is considered as one of the limitations imposed by the setup for the study of fast reactions. To move to shorter residence times, the T-piece holding the IR probe head should be removed. Given however the benefit of in situ IR measurements (i.e., real-time process monitoring, fast data generation), the present study has relied on the setup as described. Analytics. The data were quantified using in situ Fourier transform (FT)-mid-IR/ATR spectroscopy (MATRIX-MF FT-IR spectrometer equipped with a liquid nitrogen-cooled MCT detector, Bruker, Germany). The infrared radiation was guided by silver halide fibers (1.5 m length and 1 mm diameter) from the spectrometer to the probe head (6 mm diameter, made of Hastelloy material, gold coated). The ATR element at the outer part of the probe head (2 × 45° reflection diamond prism) was connected through a T-piece connector (diameter drilled from 6 to 8 mm, stainless steel, Swagelok) to the output of the reactor and inserted into the reaction mixture. Calibration models were built using partial leastsquares (PLS) regression. The reaction mixtures were quantified in real time (OPUS/QUANT package software, Bruker Optics Inc.) during the experiments. Gas chromatography was performed for validation purposes (Agilent Technologies 7890A gas chromatograph equipped with a flame ionization detector and a Zebron ZB-1, Phenomenex (30 m × 0.25 mm i.d. × 0.25 μm) capillary column). To compensate for any potential sources of errors related to sample preparation or sample introduction, the internal standard method of calibration and nonweighted univariate inverse linear regression were used for the construction of the calibration curves. The development of the IR and GC calibration models and an example of the calibration curves are presented in the Supporting Information (Figures S1−S5, Tables S1−S5). Gas chromatography/mass spectroscopy (GC/MS) analysis was performed for the identification of the reaction species (Hewlett-Packard HP-6890 gas chromatograph, equipped with a Hewlett-Packard HP-5973 mass selective detector (MSD) for GC/MS and a Zebron ZB-1 column (coating film thickness 0.25 μm, 30 m,·0.25 mm i.d., Phenomenex. Analysis performed in Currenta GmbH & Co. OHG). The GC/MS conditions are given in Table S6 in the Supporting Information. Experimental Procedure. An offline IR background measurement was taken at the beginning of each working lab day. Figure 5 represents a three-dimensional (3D) region of the FTIR spectra of a reaction mixture. The different stages observed while monitoring the reaction are marked. The band shown corresponds to the carbon−oxygen double bond stretching of the carbonyl group of the substrate ethyl trichloroacetate.

acting as the catalyst. Several computational studies in literature50,53,54,63 point to the concerted and stepwise path involving neutral intermediates as the most possible ones for the amination of aliphatic esters, with a preference on stepwise mechanism in the case of catalyzed amination. In the present study, the stepwise path through neutral intermediates is considered as the most likely one, and three concrete reaction mechanisms are examined: (i) a noncatalyzed mechanism, (ii) a catalyzed one where a second ammonia molecule has a catalytic role, and (iii) a third one where the two abovementioned mechanisms take place in parallel. Experimental Setup. For the kinetic investigation of the reaction system under study, the setup presented in Figure 4

Figure 4. Basic configuration of the reactor setup developed and built at BTS.

was designed and built. A stream of the substrate A dissolved in the solvent and a stream of liquefied ammonia B are supplied at constant flow by two high-performance liquid chromatography (HPLC) pumps, indicated as (1) delivering A (JASCO PU-2080 Intelligent pump, JASCO Labor and Datentechnik GmbH Deutschland) and (2) delivering B (JASCO PU-2080-CO2 Supercritical Carbon Dioxide Pump, JASCO Labor- and Datentechnik GmbH Deutschland) and mixed in a static cascade mixer (3) (Ehrfeld Mikrotechnik BTS GmbH). The mixture then flows through a stainless steel (material no. 1.4571) capillary coil (4) that serves as a residence time unit. An IR attenuated total reflectance (ATR) probe head (5) is connected at the output of the reactor into the reaction mixture for real-time IR measurements. After the reactor, a back-pressure control device (6, BP-2080 Back Pressure Regulator, JASCO Labor and Datentechnik GmbH Deutschland) suitable for high-pressure applications and a phase separator (7) are placed. Samples from the liquid phase are analyzed offline by gas chromatography. A gas-washing system (8) is attached to the phase separator for the neutralization of the excess of ammonia. The pump outputs, the mixers, and the reactor are all inserted in a cooling/heating bath. Thermocouples are placed in the bath, at the output of the residence time unit, and after the T-piece, where the IR probe is inserted. All operating equipment, that is, the pumps, the back-pressure regulator, and the oil bath, were controlled by a process control system (MSR-Manager/Labmanager, HiTec Zang). The values of the flow rates, temperature, and pressure are adjusted either manually or via the HiTec Zang’s process control software. Finally, a purge line is added for feeding nitrogen to remove air before initiating an experiment and for cleaning ammonia off the pump at the end of a run for E


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On the basis of the acetonitrile data, the solvent search problem was formulated in ProCAMD as follows: the generated candidate solvents should be in liquid state at operating temperature (298 K) and pressure (1 bar). The substrate ethyl trichloroacetate and the products, namely, 2,2,2-trichloroacetamide and ethanol, should be soluble in the generated candidate solvent. Esters and amines were excluded from structure generation, as they may act as reagents in the specific reaction (Figure 2), as well as phenols and organic halogen compounds given the toxicity of these compounds. The normal boiling point should vary from 330 to 360 K, the normal melting point should vary from 140 to 210 K, the total solubility parameter should vary from 15 to 25, and the log P (octanol/water) should vary from −0.5 to 4. For the mixture calculations, the UNIPAR-Original UNIFAC (VLE) model was employed. The ProPred toolbox of the same software65 was then employed for the estimation of the component properties. The search with ProCAMD resulted in 25 additional solvents (Supporting Information, Table S8). Even though interesting results could be expected, none of these solvents has been added to Σ0, because most of them are not commercially available in the kilogram scale. Candidate Solvent Database Σ1Requirements of the Specific Process. At the experimental conditions (25 °C, 20 bar), the reaction takes place in the liquid phase; the solvent should therefore also be liquid. The components of the set Σ0 that do not fulfill this criterion were ruled out. Solvents that may participate in the reaction were also eliminated from the list of possible candidates. Esters and amines were excluded, as these compounds may act as reagents parallel to the main reagents (ethyl trichloroacetate and ammonia). Carboxylic acids may also react with ammonia in a nucleophilic substitution reaction and therefore were excluded. Addition of ammonia to aldehydes and ketones is expected to lead to the formation of hemiaminals;66 therefore, these compounds were ruled out. Alcohols may also participate in a transesterificaton reaction with the substrate and the alcohol. Preliminary experimental runs with alcohols used as solvents revealed formation of the transesterification reaction products just in traces.37 This is the reason why alcohols were included in the list of candidate solvents. Water was not included in the candidate solvent list to avoid possible hydrolysis of the substrate.67 Certain solvents (i.e., phenols) were also not considered due to their toxicity. Another factor considered is the solubility of the reaction species in the various solvents. Precipitation of the product in the reaction mixture can lead to clogging of the tubular reactor and must be avoided. To that end, the solubility of the reaction species in several solvents was either calculated based on literature data or tested experimentally. Solvents with low solubility of the product were excluded from the list of possible solvent candidates. The finally resulting database Σ1 consists of 86 solvents and is presented in the Supporting Information, Table S9. Solvent Subset Σ2. On the basis of chemical knowledge, six solvents were selected from the database Σ1: tetrahydrofuran, acetonitrile, dimethyl sulfoxide, 2-propanol, ethanol, and methanol. The selection was made with regard to highly diverse solvatochromic properties. The solvatochromic equation is a multiparameter linear relationship. Similarity of the solvent molecules can lead to collinearity between the Kamlet−Taft parameters and a linear relationship between

Figure 5. 3D representation of a wavenumber region of the FTIR spectra of a reaction mixture.

A mixture of defined concentration of the substrate diluted in the solvent under study was prepared by weighing the required amount of substrate and solvent. The feed mixture was pumped through the reactor ((i) in Figure 5) and, after a plateau of intensity had been reached ((ii) in Figure 5), at least 10 IR spectra were acquired. The average of the concentration values was used as the initial concentration for the kinetic modeling. A stream of ammonia was then supplied simultaneously to the feed stream ((iii) in Figure 5). The two flows were first mixed in the static cascade mixer and then passed through the capillary coil. Preliminary tests showed that the reaction needs a minimum of six residence times to reach a steady state. The steady state was also indicated by a second plateau of the intensity value ((iv) in Figure 5). The acquired data were quantified, and a minimum number of 10 values on the concentration plateau was averaged. The average value per reaction species was treated as one data point (corresponding to a specific residence time) for kinetic modeling. The same procedure was applied for all other reaction species, that is, the products and side products.

4. SOLVENT SELECTION FOR THE AMINATION OF ESTERS Initial Solvent Database Σ0. An initial list of candidate solvents was compiled to form the solvent database Σ0, consisting of 184 compounds that have been reported for their use as solvents before. The chemical families accounted for in the set are listed in Table S7 in the Supporting Information. The database could further be extended by the addition of substances not yet commonly employed as solvents to expand the selection beyond the conventional candidates. For this purpose, the ProCAMD toolbox of the ICAS software was used64 to generate feasible chemical structures, and the ProPred toolbox of the same software65 was used for the estimation of the component properties. The objective was the generation of structures with physical properties (melting point, boiling point, Hansen solubility parameter) similar to those of acetonitrile, a solvent that was shown in literature to promote the reaction of interest by substantially lowering all energy barriers.54 A basic search was initially performed in the CAPEC database to search for the properties of acetonitrile. F


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where υij is the stoichiometric coefficient of species i, and r0j (mol·m−3·s−1) is the rate of reaction j in which species i takes part. This model (i.e., eqs 10 and 11) can be applied for the interpretation of the experimental data of this study as long as temperature and dispersion effects are negligible. These effects are examined in the following paragraphs. Temperature Effect. If the reactor is adiabatic, then all the heat generated will be absorbed by the liquid medium, and its temperature will increase. The heat of reaction Q (W) absorbed by the liquid can be calculated from

the estimated parameters thus a severe problem in the precision of the estimated parameters. To tackle the issue of collinearity, the six solvents were selected so as to be diverse in terms of α, β, π, and δH parameters. A condition analysis of this six-solvent set can be performed to generate the subset Σ2 comprising the minimum of five solvents that provides the highest information content and results in lowest error amplification.36 The condition numbers of the (generalized inverse of) matrix AΣ2 for the six-solvent and all six five-solvent sets are shown in Table S10 of the Supporting Information. All but one of the condition numbers are of O(102). The condition number for the six-solvent set (620) is slightly higher than the smallest condition number of the five-solvent sets (576) and lower than all others. On the basis of this analysis, it was decided to use the data of all six solvents in the set Σ2 for parameter identification to reduce the risk of overfitting at least to some extent. Note, the small number of six solvents has been chosen pragmatically to reduce the (already high) experimental effort to its minimum. This choice obviously reduces the reliability of the prediction quality in solvent screening. The solvatochromic properties for all six solvents are retrieved from literature and are given in Table S11 in the Supporting Information. Experimental Kinetic Data. The experiments for all six solvents in Σ2 were performed at 25 °C, 20 bar, inlet concentration of substrate (ethyl trichloroacetate, denoted as A) of 1 mol·dm−3, and an ammonia (denoted as B) to substrate ratio of 5 (B/A = 5). Analysis by FT-IR spectroscopy in combination with a multivariate statistical method (PLS regression) was used for multivariate calibration to quantify the reaction species concentrations (Figures S1−S5 and Tables S1−S5, Supporting Information). The experimental data were determined by the first author and are reported in her doctoral thesis.37 Reactor Modeling. The residence time unit employed in the experiments is a tubular coiled reactor. The material balance for species i at steady state is given as −q

dCi + ri = 0 dV

−Q = ṁ ·Cp̅ ·(Tout − Tin) −1

dCi d

() V q

+ ri = −

(8) Figure 6. Temperature difference (ΔT) between the inlet and outlet of the reactor vs the substrate molar flow rate ṅ.

rate ṅ for the experiments conducted with dimethyl sulfoxide, ethanol, methanol, 2-propanol, and tetrahydrofuran as solvent. The temperature at the inlet was 25 °C, the inlet concentration of the substrate ∼1 mol·dm−3, and the ratio of ammonia to substrate concentration was 5. An increase of the substrate flow rate results in an increase of the generated heat of reaction Q and consequently of ΔT because of the increased converted amount in the coil (cf. Figure 6, Supporting Information, Table S12). Though the temperature is varying in the laboratory reactor, the lack of temperature data along the reactor does not allow for the consideration of the non-isothermal behavior of the reactor. Furthermore, the temperature difference ΔT is less than 3 °C for the majority of the experimental runs. Therefore, the reactor coil is pragmatically modeled as an isothermal (plug) flow reactor at steady state. Dispersion Effect. To analyze the flow regime, the Reynolds number Re

dCi + ri = 0 d(τ ) (9)

with τ (s) being the hydrodynamic residence time, leading to the final equation dCi = ri , dτ

Ci(τ ) = Ci,in

(10)

with ri =

∑ υijr0j j

−1

with ṁ (g·s ) the total mass flow rate, Cp (J·g ·K ) the heat capacity of the liquid, and Tout and Tin (K) the temperature recorded at the outlet and inlet of the reactor, respectively. The heat capacity of the mixture was computed as the mass fraction average of the heat capacities of the pure species at 25 °C, hence neglecting the heat of mixing. Given the absence of data for ethyl trichloroacetate, the heat capacity of ethyl acetate was used instead, as both molecules have similar molecular structure. The results are presented in the Supporting Information, Table S12. Figure 6 depicts the temperature difference ΔT between the inlet and outlet of the reactor versus the substrate molar flow

if plug flow is assumed. V (m3) relates to the volume coordinate along the flow direction, q (m3·s) is the volumetric flow rate, Ci (mol·m−3) is the volumetric concentration of species i, and ri (mol·m−3·s−1) is the reaction rate of species i. The volumetric flow rate is considered constant throughout the course of the reaction. Therefore, Equation 8 can be rewritten as −

(12) −1

(11) G


Article

Industrial & Engineering Chemistry Research Re =

uL v

this end, the system was initially considered as a mixture of the solvent employed and ammonia.76,77 The diffusivity of the mixture was estimated with the Perkins and Geankoplis method71,78

(13)

must be computed; u is the mean velocity of the fluid based on the actual cross section area of the tube (m·s−1), L is the tube length (m), and v is the kinematic viscosity (m2·s−1) of the mixture. The density and viscosity of the mixture were estimated by the Rackett method68 as modified by Spencer and Danner69 in combination with Li’s mixing rules70 for the estimation of the density of mixtures.71 Expected uncertainty of this method is ∼7% on average.71 The viscosity of the mixtures was estimated using Refutas’ equation.72 The required properties of the pure compounds were retrieved from literature and were based either on measured data or on predictive methods in case these properties were not available.37 The employed methods are considered sufficient for the purposes of this study, and therefore property prediction based on group contribution methods (i.e., by means of the ICAS software) was not performed. As seen in Figure 7, the Re value is always below the critical value of 2100, which indicates that the flow is in the laminar regime.73

n o DAm ηm0.8 =

where is the effective diffusion coefficient (cm ·s ) for a dilute solute A into the mixture, DoAj is infinite dilution binary diffusion coefficient (cm2·s−1) of solute A into solvent j, xj is mole fraction of jth solvent, and ηm is mixture viscosity (cP). The binary diffusion coefficient of the substrate in the lowest concentration (ethyl trichloroacetate) in ammonia and the solvent separately was estimated by the Wilke−Chang estimation method method79 o DAB =

dz 2

y u 2d t 2 ij ud jjfor 1 < R e = t < 2000zzz j z 192Dmol k v {

ηBVA 0.6

(17)

uL Dax

(18)

was computed as a measure of the deviation from plug flow behavior. In all cases, the Bo value is higher than 100 (Supporting Information, Table S12); hence, plug flow behavior can be safely assumed.80,81 The coiled geometry of a tube has been reported in literature to result in an even lower axial dispersion compared to a straight tube due to secondary flows induced in the radial direction.82−89 The Dean number, defined as iry Dn = R ejjj zzz kR{

1/2

(19)

where r is the tube diameter, and R is the coil diameter, can serve as a measure for the strength of secondary flows induced by the coil geometry. The high values of the Dean number computed (Supporting Information, Table S13) with the only exception of two experimental runs of dimethyl sulfoxide that showed a Dean number of 12 and 14) indeed indicate a further decreased axial dispersion and efficient mass transfer.90 This confirms the validity of the plug flow assumption even for the case of the coiled tubular reactor used in the experimental setup. Conclusion. On the basis of the above analysis, both the temperature and axial dispersion effects are expected to be minor. Hence, neither an energy balance must be considered nor additional terms need to be added to the mass balance to study the reaction kinetics. Hence, the reactor model employed

(14)

where u is the linear velocity of the fluid along the z-axis. The value of Dax can be determined either experimentally or based on correlations. According to Aris74 and Taylor,75 Dax for laminar flow in empty tubes is given by Dax = Dmol +

7.4 × 10−8(ϕMB)1/2 T

where DoAB (cm2·s−1) is the mutual diffusion coefficient of solute A at very low concentrations in solvent B, MB (g·mol−1) is the molecular weight of solvent B, T (K) is the temperature, ηB (cP) is the viscosity of solvent B, VA (cm2·mol−1) is molar volume of solute A at its normal boiling point temperature, ϕ is association factor of solvent B. The value of ϕ according to Wilke and Chang79 must be 2.6 if the solvent is water, 1.9 if it is methanol, 1.5 for ethanol, and 1.0 if it is unassociated. The researchers have reported an average error of ∼10% when employing this method.79 The computed axial dispersion coefficient Dax for each experimental run is given in the Supporting Information, Table S13. The Bodenstein number (Bo), defined as

Furthermore, the axially dispersed flow model was used to inspect the deviation from an ideal plug flow reactor. This model applies to straight tubes. Nevertheless, it was used to evaluate the coiled tube of the setup employed to get a first assessment. The influence of the coil will be considered afterward. An axial dispersion coefficient, Dax (m2·s−1), is introduced for the description of the nonconvective contributions, and the material balance is extended as Dax

(16) 2 −1

DoAm

Figure 7. Reynolds number, computed for experimental runs at 25 °C, grouped per solvent.

dC − u i = ri dz

xjDAojηj0.8

j ≠ Aj = 1

Bo =

d2Ci

∑

(15)

with the diameter of the tube dt and the molecular diffusion coefficient Dmol of a single solute in a solvent. For the estimation of the axial dispersion coefficient, the molecular diffusion coefficient Dmol must be first estimated. To H


Article


side reaction between the substrate and trichloromethane (Figure 9). On the basis of these findings, a reaction network consisting of three parallel reactions shown in Figure 9 is suggested. Considering the mechanisms reported in literature52,54 and the reaction network described above, the reaction mechanisms in Table 1 are suggested, where A refers to ethyl trichloroacetate, B to ammonia, C to 2,2,2-trichloroacetamide, D to ethanol, E to trichloromethane, F to urethane, G to tetrachloromethane, H to 2,2-dichloroacetate, I to intermediate, and Cat Complex to a catalytic complex. GC analysis of several reaction mixtures showed formation of the side products tetrachloromethane (G) and 2,2dichloroacetate (H) just in traces, if any. Therefore, these data cannot be used for fitting purposes, and the second side reaction cannot be considered in kinetic modeling. Moreover, the intermediate I and the catalytic complex are assumed to be at quasi-steady state.91 The main reaction is reversible; however, the experimental data showed high conversions for all solvents, such that the products govern the reaction mixture. As the reaction goes to completion, the forward main reaction dominates. Therefore, we reasoned that the reverse reaction can be ignored. Indeed, this hypothesis was confirmed experimentally by parameter estimation of the models amended to include the reverse reaction.37 The suggested irreversible candidate models that will be applied for the evaluation of the experimental results are presented in Table 2. Identifiability AnalysisTaylor Expansion Series. Prior to model application and parameter estimation, a study of the structural identifiability applying the Taylor expansion series method is performed to ensure that the parameter estimates can be reliable.92,93 The Taylor expansion of each measured model output was developed in the symbolic toolbox of MATLAB up to fifth order, as no additional information was added for higher-order derivatives, at t = 0, and for given initial conditions. Available measurement data for three compounds (substrate A, product C, and side-product E) were assumed, in accordance to the real lab situation. The inlet experimental values of A and B were [Α]0 = 1 mol·dm−3 and [B]0 = 5 mol· dm−3. The concentration of the product C and side-product E were expected to be negligible at the beginning of the reaction. To proceed with the calculations, [C]0 and [E]0 were set to a value of 1 × 10−5 mol·dm−3. The analysis showed that all parameters are structurally identifiable for all three models.37 Parameter EstimationWeighted Nonlinear Regression. For the determination of parameters of the suggested models, weighted least-squares nonlinear regression is applied.94 The generated experimental data were used to obtain parameter values by fitting each of the kinetic models to the data.37 The calculations were performed within the MATLAB environment. The estimated rate constants and 95% confidence intervals are given in the Supporting Information, Table S14. It is worth mentioning that the confidence intervals for the estimated parameters when employing Models 1 and 2 are reasonably small; this, however, is not the case for Model 3 (Table S14, Supporting Information). Most likely, this is due to the higher number of parameters of Model 3: the number of experimental data and the measurement precision may not be sufficient for the precise estimation of the three parameters knoncat, kcat, and kside. The experimental and simulated data are depicted in Figure 10. The rate constants knoncat and kside are expressed in dm3·s−1· mol−1 and kcat in dm6·s−1·mol−2. When acetonitrile and

for the analysis of the experimental data consists of Equations 10 and (11). Candidate Kinetic Models. To identify the species present in the reaction mixture, a GC/MS analysis was conducted (Currenta GmbH & Co. OHG). The GC-MS parameters are presented in Table S6 in the Supporting Information. The GC-MS fragmentation analysis of an experimental reaction mixture with acetonitrile employed as solvent (at 25 °C, 20 bar, inlet concentration of substrate 1.5 mol·dm−3, ammonia to substrate ratio 1, and residence time 300 s) confirmed the formation of 2,2,2-trichloroacetamide and ethanol as products (Figure 8). Formation of trichloromethane

Figure 8. Mass spectra of the reaction mixture obtained by GC-MSEI. The chemical structures assigned to each peak are indicated in the figure.

and urethane was also revealed, probably products of a parallel haloform cleavage of the substrate (Figure 9). In addition, two more compounds, namely, tetrachloromethane and 2,2dichloroacetate, were identified, which can be attributed to a

Figure 9. Suggested reaction network, based on the GC/MS analysis results. I


Article

Industrial & Engineering Chemistry Research Table 1. Suggested Candidate Reaction Mechanisms noncatalyzed reversible mechanism

catalyzed reversible mechanism

combined noncatalyzed/catalyzed reversible mechanism

A+B⇌I→C+D A+B→E+F A+E→G+H

A+2B⇌Cat complex→ C+D+B A+B→E+F A+E→G+H

A+B⇌I→C+D A+2B⇌Cat complex→ C+D+B A+B→E+F A+E→G+H

Given the low sample size with respect to the number of estimated parameters, the second-order information criterion AICC97,98 was applied, defined as

Table 2. Suggested Candidate Models mass balance equation

i 2K (K + 1) yzz AICC = − 2jjjjlog likelihood + 2K + z (n − K − 1) z{ k

dCi = ri dτ ri =

∑ υijr0j j

model 1

model 2

model 3

noncatalyzed mechanism

catalyzed mechanism

combined noncatalyzed/catalyzed mechanism

A+B→C+D A+B→E+F

A+2B→ C+D+B A+B→E+F A+B→E+F reaction rate laws 1

rnoncat(1) = knoncat[A][B]

rcat(1) = kcat[A][B]

rside(2) = kside[A][B]

rside(2) = kside[A][B]

where n is the sample size. The analysis was performed for the data set obtained for each solvent separately. For model comparison, the following two measures were used: • the difference Δi,c of AIC values of model i and model c, the model with the minimum AIC95

A+B→C+D A+2B→ C+D+B

Δi = AICi − AICc rnoncat(1) = knoncat[A][B] rcat(2) = kcat[A][B]2 rside(3) = kside[A][B]

(22)

• the Akaike weights wi defined as Δ

wi =

dimethyl sulfoxide are used as solvents, the reaction reaches a plateau of conversion at a residence time of ∼140 and 18 s, respectively (Figure 10). Unfortunately, the data points that define the slope of the concentration curves and provide most of the kinetic information are limited in number (four and one, respectively) due to residence time restrictions of the experimental setup. The accuracy of the estimates for those solvents, resulting from a coarse fitting of models 1, 2, and 3 to the experimental data, is low. It could be improved if lower residence times could be realized in a modified experimental setup. The large confidence interval of the estimates when using methanol as solvent may also be explained by the lack of experimental points at low conversion. The reaction proceeds fast, and all the experimental data points used for the estimation of the rate constants are already at steady state. The estimated values are therefore just an approximation, and the reaction could be even faster in reality. Overall, the experimental data scattering (Figure 10) could be attributed to different reasons: (i) the experiments were performed on different days, and therefore the IR probe might not be at exactly the same position, affecting the measurements, (ii) fluctuation of the nitrogen streamflow in the feed solution could result in vaporization of the solvent and alteration of the inlet composition, (iii) pumps may not always deliver the desired flow rates. Model Discriminationthe Akaike’s Information Criterion. To select the model that best approximates reality given the available experimental data and following the principles of simplicity and parsimony,95 Akaike’s Information Criterion (AIC)96 was employed. AIC is defined as AIC = − 2(log likelihood) + 2K

(21)

( ) exp(− )

exp − 2i R

∑r = 1

Δr 2

(23)

The results of the analysis are provided in the Supporting Information, Table S15. In all cases, Model 3 is less likely to be better than Models 1 and 2. In addition, the large confidence intervals of the parameter estimates as described earlier indicate that this system, even though structurally identifiable, is practically unidentifiable. Therefore, Model 3 cannot describe the system with the available data and is excluded from the set of model candidates. Regarding Models 1 and 2, the result differs for the various data sets. Application of the criterion for the data sets of dimethyl sulfoxide, tetrahydrofuran, acetonitrile, and methanol points to Model 2 being the most likely model. On the contrary, when applying the criterion to the data sets of 2-propanol and ethanol, the results point to Model 1 as the most likely one. For all six data sets, there is a high level of uncertainty involved, and we cannot discriminate between the two models with confidence. On the basis of literature suggesting that the reaction often exhibits general base catalysis,43−45,59−62 we assume that the reaction under consideration follows a catalyzed mechanism. Model 2, which considers one main forward reaction catalyzed by a second ammonia molecule and a parallel side reaction, will be hence employed for the rest of the study. Prediction of the Most Promising Solvent. As a first step, identification of the parameters in the solvatochromic equation using the subset Σ2 was independently performed for the main and the side reactions. Equation 7, the estimator using Tikhonov regularization and generalized cross-validation for determination of the regularization parameter λ, was employed to improve the condition of the estimation problem. The results are presented in Table 3. The correlation coefficient R2 and the root-mean-square error RMSE (last two rows in Table 3) are calculated from the predicted and the measured logarithms of the reaction rate constants (details on the calculation of R2 andRMSE can be

(20)

where K is the number of the estimated parameters in the model. J


Article


Figure 10. Experimental data and fitted kinetic models for all solvents studied. The error bars represent the standard deviation from the mean value at steady state.

explained by factors such as the quality of experimental data, the low number of experimental data points, and the capability of the solvatochromic equation itself to achieve high reliability in the predictions. Next, the second step, the computer-aided screening of the set Σ1 for the best solvent, was performed (Equation 6). Two objectives were targeted independently: (i) the maximization of the rate constant of the main reaction and (ii) the minimization of the rate constant of the side reaction. The results are presented in Table 4 in a rank decreasing order for both cases. The 10 ranked solvents under the column named “max log kcat” are predicted to maximize the reaction rate constant of the main reaction, while the 10 ranked solvents under the column named “min log kside” are those that are predicted to minimize the side reaction.

Table 3. Parameters of the Solvatochromic Equation for the Main and Side Reaction of the Amination of Ethyl Trichloroacetate at 25°C and 20 bar log k0 a b s h R2 RMSE

main reaction

side reaction

−7.9933 0.1861 −0.4302 −0.9977 0.2886 0.4728 0.3858

−6.2328 −1.0453 0.3417 −0.3596 0.8128 0.3858 4.5056

found in the Supporting Information). The R2 values indicate a relatively low predictive capability of the model, which can be K


Article


solvents does not fully match with performance of the solvents found experimentally. This shortcoming is due to several factors: the small number of solvents studied experimentally, the likely coarse approximation of the solvatochromic model to describe the effect of the solvent on the reaction rate, as well as the limitations in quantity and quality of the data used for identification of the reaction constants from the kinetic experiments.

Table 4. Solution of Computer-Aided Screening for the Amination of Ethyl Trichloroacetate at 25°C and 20 bar rank

max log kcat

min log kside

1 2 3 4 5 6 7 8 9 10

methanol formamide trans-1,2-dichloroethylene 1,1,1-trichloroethane ethanol carbon disulfide trichloroethylene i-butanol 1,1-dichloroethane n-hexanol

i-pentanol 2-phenylethanol n-pentanol n-octanol n-decanol 3-phenylpropanol n-hexanol n-butanol benzyl alcohol chloroform

■

CONCLUSIONS This contribution is the first report of a solvent selection methodology for accelerated reaction kinetics at minimum experimental effort that has been applied and demonstrated in an industrial setting. The method relies on real experimental data, generated in a setup that consists of a continuous flow reactor coupled with in situ IR spectroscopy for accelerated reaction kinetics investigations. The data generation is guided by a computational method originally suggested by ref 36 consisting of two distinct steps, that is, model identification based on the solvatochromic equation followed by computeraided screening of a solvent database that returns a list of the most promising solvents. Chemical knowledge is involved from the very beginning to account for EHS as well as specific reaction and equipment constraints. The proposed methodology can be applied to homogeneous liquid-phase reactions where the solvatochromic equation can be successfully employed to model the effects of the solvent on the reaction rate. Despite our efforts to robustify the method against uncertainty and a lack of information content in the experimental data, the reliability of the method has shown to be limited, and the results need to be interpreted with care. This experimental study clearly shows that an improved experimental setup is necessary to improve the data quality for kinetic modeling and the identification of the parameters in the solvatochromic equation. Furthermore, the solvatochromic equation itself may not be sufficiently accurate to achieve high reliability in the predictions. The established methodology presented here can be used as a starting point for further improvement and to address additional research questions. In particular, and most importantly, the experimental approach for data generation must be further improved based on the experience collected in this work. It would be desirable to extend the methodology to allow for incremental improvement of the screening quality by adding solvents to the set Σ2. Currently, the methodology aims at the identification of the best solvent within a certain solvent database. The initial solvent database could be expanded with other types of (emerging) solvents, such as ionic liquids, supercritical fluids, as well as solvents generated using CAMD and quantum chemical calculations. That way, completely new promising solvent candidates may be revealed, opening new windows in chemical synthesis. Currently, the methodology deals with the enhancement of the rate of the reaction leading to the desired products and the reduction of the rate of the side reactions as two independent objectives, resulting in two independent solutions. As a next step, the two objectives should be treated as a unified problem, leading to the prediction of the solvent that maximizes the rate of a desired reaction while minimizing the rates of undesired ones. The methodology should also be amended to account for selectivity maximization in case of reaction networks and to consider mixtures of solvents rather than pure solvents only.

The most promising solvent in terms of maximizing the rate of the main reaction is predicted to be methanol (Table 4). It is interesting to note that methanol is not among the top 10 solvent candidates that minimize the rate of the reaction clearly showing that there is an inherent tradeoff. Since the topranking solvent methanol is already included in the subset Σ2, no additional kinetic experiments need to be performed in the lab for verification. Comparison of the estimated parameters for the solvents of the subset Σ2 (Figure 11) indicates that the

Figure 11. Experimental rate constants for the four solvents of subset Σ2, the identified best solvent methanol, and the candidate solvent ethanol for validation.

use of methanol as a solvent indeed maximizes the rate of the main reaction as predicted by the proposed solvent selection methodology. Ethanol, which is ranked at position five in the screening, does perform significantly worse than the topranked methanol. This result is promising, because it shows that the suggested solvent selection methodology can even lead to useful results under significant uncertainty, which has been present in this study due to (i) the limited number of solvents studied experimentally, (ii) the experimental limitations posed by the setup for fast reactions, and (iii) the temperature effects that further limited the range of study. Nevertheless, the experimental results agree with the predicted solution pointing to methanol as the most promising solvent for the reaction under study. However, dimethyl sulfoxide, tetrahydrofuran, and 2-propanol, which are performing better than ethanol in the experimental study, have not been ranked among the top 10 solvents in the screening. Therefore, the ranking of the L


Article

Industrial & Engineering Chemistry Research Notes

The proposed methodology could potentially also be extended to enzymatic reactions in a homogeneous reaction mixture. This is especially interesting given the importance of the solvent system in enzyme stability, selectivity, and reaction yields of enzymatic reactions.99,100 Enzyme activity and stability have been shown to correlate with various solvent descriptors, such as dipole moment, dielectric constant, and Hildebrand solubility parameters.101,102 In their review, Zeuner and co-workers103 explored the use of group contribution activity coefficient model UNIFAC104−106 and quantum chemistry-based COSMO-RS107 for thermodynamic predictions and preliminary solvent screening and suggested a thermodynamically based solvent design for enzymatic saccharide acylation with hydroxycinnamic acids. Incorporation of such thermodynamic tools in the methodology proposed in the current contribution could potentially facilitate the solvent design process and expand our understanding of the enzymatic reaction systems. As far as heterogeneous systems are concerned, the selection of solvent is typically done empirically. The main points of interest while choosing a solvent are the solubility of the reaction species in the solvent and the boiling point of the solvent so that it will be recycled after separation. The methodology could be potentially applied to heterogeneous reactions, but this will require additional research.

■

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors express gratitude for the financial support provided by the Marie Curie Actions−Initial Training Network (ITN) funded through European Commission FP7 under the Grant No. 238013, namely, Multiscale Computational Modeling of Chemical and Biochemical Systems (MULTIMOD).

■

Abbreviations

AIC AICC AN+DN ATR CAMD CI COSMO COSMO-RS DFT DMSO EHS FTIR GC GC/MS I ICAS IR PLS ProCAMD ProPred SN2 THF TS

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications Web site. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b01040.

■

NOMENCLATURE

IR and GC calibration model development strategy and example, GC and GC/MS conditions, chemical families accounted for in the set Σ0, solvents generated with the use of ProCAMD toolbox, solvent database Σ1, solvents that compose the Σ2 subset and their solvatochromic properties, results of the condition analysis, calculated temperature difference (ΔT) between the inlet and outlet of the reactor and generated heat Q, computed Reynolds number (Re), axial dispersion coefficient (Dax), Bodenstein number (Bo) and Dean number (Dn) for all experimental runs, estimated parameter values and 95% confidence intervals, Akaike’s second-order information criterion (PDF)

Akaike’s information criterion Second-order information criterion Addition−elimination mechanism Attenuated total reflection Computer-aided molecular design Confidence interval Conductor-like Screening Model Conductor-like Screening Model for Real Solvents Density function theory Dimethyl sulfoxide Environmental, health and safety Fourier-transform infrared spectroscopy Gas chromatography Gas chromatography/mass spectroscopy Intermediate Integrated computer aided system software Infrared Partial least-squares Toolbox of the ICAS software Toolbox of the ICAS software Bimolecular nucleophilic substitution reaction Tetrahydrofuran Transition state

Symbols

[A] Bo Cp Dax Dmol Dn L ṅ Q q R r0 r0j

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Angeliki Tsichla: 0000-0001-7401-1093 Wolfgang Marquardt: 0000-0002-4455-8378

Re Tin

Present Address §

Bayer AG, Engineering & Technology, 51368 Leverkusen, Germany.

Tout

Author Contributions

u v vij

Designed research: A.T., C.S., M.G., W.M. Designed reactor: A.T., C.S. Performed experiments: A.T. Analyzed data: A.T., C.S., M.G., W.M. Wrote paper: A.T., W.M. All authors have given approval to the final version of the manuscript.

VR M

Molar concentration of species A (mol·dm−3) Bodenstein number Heat capacity of the liquid (J·g−1·K−1) Axial dispersion coefficient (m2·s−1) Molecular diffusion coefficient (m2·s−1) Dean number Characteristic length of the tube (m) Molar flow rate (mol·s−1) Calculated generated heat (J·s−1 or Watt) Volumetric flow rate (cm3·s−1) Coil diameter (cm) Inner tube radius (cm) Rate of reaction j in which species i takes part (mol·m−3· s−1) Reynolds number Temperature recorded at the inlet of the reactor (K or °C) Temperature recorded at the outlet of the reactor (K or °C) Mean velocity of the fluid (m·s−1) Kinematic viscosity (m2·s−1) Stoichiometric coefficient of species i taking part in reaction j Reactor volume (m3) DOI: 10.1021/acs.iecr.9b01040 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research wi

(13) Prat, D.; Wells, A.; Hayler, J.; Sneddon, H.; McElroy, C. R.; Abou-Shehada, S.; Dunn, P. J. CHEM21 Selection Guide of Classicaland Less Classical-Solvents. Green Chem. 2016, 18 (1), 288. (14) Alfonsi, K.; Colberg, J.; Dunn, P. J.; Fevig, T.; Jennings, S.; Johnson, T. A.; Kleine, H. P.; Knight, C.; Nagy, M. A.; Perry, D. A.; Stefaniak, M. Green Chemistry Tools to Influence a Medicinal Chemistry and Research Chemistry Based Organisation. Green Chem. 2008, 10 (1), 31. (15) Prat, D.; Pardigon, O.; Flemming, H.-W.; Letestu, S.; Ducandas, V.; Isnard, P.; Guntrum, E.; Senac, T.; Ruisseau, S.; Cruciani, P.; Hosek, P. Sanofi’s Solvent Selection Guide: A Step Toward More Sustainable Processes. Org. Process Res. Dev. 2013, 17 (12), 1517. (16) RosinhaGrundtvig, I. P.; Heintz, S.; Krühne, U.; Gernaey, K. V.; Adlercreutz, P.; Hayler, J. D.; Wells, A. S.; Woodley, J. M. Screening of Organic Solvents for Bioprocesses Using Aqueous-Organic TwoPhase Systems. Biotechnol. Adv. 2018, 36 (7), 1801. (17) Riechert, O.; Husham, M.; Sadowski, G.; Zeiner, T. Solvent Effects on Esterification Equilibria. AIChE J. 2015, 61 (9), 3000. (18) Lemberg, M.; Sadowski, G. Predicting the Solvent Effect on Esterification Kinetics. ChemPhysChem 2017, 18 (15), 1977. (19) Gani, R.; Gómez, P. A.; Folić, M.; Jiménez-González, C.; Constable, D. J. C. Solvents in Organic Synthesis: Replacement and Multi-Step Reaction Systems. Comput. Chem. Eng. 2008, 32 (10), 2420. (20) Stanescu, I.; Achenie, L. E. K. A Theoretical Study of Solvent Effects on Kolbe−Schmitt Reaction Kinetics. Chem. Eng. Sci. 2006, 61 (18), 6199. (21) Zhou, T.; Qi, Z.; Sundmacher, K. Model-Based Method for the Screening of Solvents for Chemical Reactions. Chem. Eng. Sci. 2014, 115, 177. (22) Zhou, T.; McBride, K.; Zhang, X.; Qi, Z.; Sundmacher, K. Integrated Solvent and Process Design Exemplified for a Diels−Alder Reaction. AIChE J. 2015, 61 (1), 147. (23) Zhou, T.; Lyu, Z.; Qi, Z.; Sundmacher, K. Robust Design of Optimal Solvents for Chemical Reactions. a Combined Experimental and Computational Strategy. Chem. Eng. Sci. 2015, 137, 613. (24) Zhou, T.; Wang, J.; McBride, K.; Sundmacher, K. Optimal Design of Solvents for Extractive Reaction Processes. AIChE J. 2016, 62 (9), 3238. (25) Taft, R. W.; Kamlet, M. J. The Solvatochromic Comparison Method. 2. the Alpha-Scale of Solvent Hydrogen-Bond Donor (HBD) Acidities. J. Am. Chem. Soc. 1976, 98 (10), 2886. (26) Kamlet, M. J.; Taft, R. W. The Solvatochromic Comparison Method. I. the Beta-Scale of Solvent Hydrogen-Bond Acceptor (HBA) Basicities. J. Am. Chem. Soc. 1976, 98 (2), 377. (27) Kamlet, M. J.; Abboud, J. L.; Taft, R. W. The Solvatochromic Comparison Method. 6. The. pi.* Scale of Solvent Polarities. J. Am. Chem. Soc. 1977, 99 (18), 6027. (28) Abraham, M. H.; Grellier, P. L.; Nasehzadeh, A.; Walker, R. A. C. Substitution at Saturated Carbon. Part 26. A Complete Analysis of Solvent Effects on Initial States and Transition States for the Solvolysis of the T-Butyl Halides in Terms of G, H, and S Using the Unified Method. J. Chem. Soc., Perkin Trans. 2 1988, (9), 1717 (29) Palm, V.; Palm, N. On the Total Number and List of Parameter Scales Significant for General Quantitative Description of Solvent Effects. In Organic Reactions 1993, 28, 125−150 (30) Abraham, M. H.; Doherty, R. M.; Kamlet, M. J.; Harris, J. M.; Taft, R. W. Linear Solvation Energy Relationships. Part 37. An Analysis of Contributions of Dipolarity−Polarisability, Nucleophilic Assistance, Electrophilic Assistance, and Cavity Terms to Solvent Effects on T-Butyl Halide Solvolysis Rates. J. Chem. Soc., Perkin Trans. 2 1987, 0 (7), 913. (31) Abraham, M. H.; Taft, R. W.; Kamlet, M. J. Linear Solvation Energy Relationships. 15. Heterolytic Decomposition of the TertButyl Halides. J. Org. Chem. 1981, 46 (15), 3053. (32) Abraham, M. H.; Doherty, R. M.; Kamlet, M. J.; Harris, J. M.; Taft, R. W. Linear Solvation Energy Relationships. Part 38. An Analysis of the Use of Solvent Parameters in the Correlation of Rate

Akaike weights

Greek Letter Symbols

α β δH Δi,c

Hydrogen-bond donor acidity Hydrogen-bond acceptor basicity Hildebrand solubility parameter Difference of AIC values of model i and the model c with the minimum AIC π* Dipolarity/polarizability ρ Density Σ0 Ιnitial solvent database Σ1 Solvent database: link to a specific process Σ2 Solvent subset τ Hydrodynamic residence time (s) Reaction Species Nomenclature Adopted in the Present Work

A B C D E F G H

■

Ethyl trichloroacetate Ammonia 2,2,2-trichloroacetamide Ethanol Trichloromethane Urethane Tetrachloromethane 2,2-dichloroacetate

REFERENCES

(1) Gani, R.; Brignole, E. A. Molecular Design of Solvents for Liquid Extraction Based on UNIFAC. Fluid Phase Equilib. 1983, 13, 331. (2) Karunanithi, A. T.; Achenie, L. E. K.; Gani, R. A New Decomposition-Based Computer-Aided Molecular/Mixture Design Methodology for the Design of Optimal Solvents and Solvent Mixtures. Ind. Eng. Chem. Res. 2005, 44 (13), 4785. (3) Chen, B.; Lei, Z.; Li, Q.; Li, C. Application of CAMD in Separating Hydrocarbons by Extractive Distillation. AIChE J. 2005, 51 (12), 3114. (4) Gebreslassie, B. H.; Diwekar, U. M. Efficient Ant Colony Optimization for Computer Aided Molecular Design: Case Study Solvent Selection Problem. Comput. Chem. Eng. 2015, 78, 1. (5) Karunanithi, A. T.; Achenie, L. E. K.; Gani, R. A ComputerAided Molecular Design Framework for Crystallization Solvent Design. Chem. Eng. Sci. 2006, 61 (4), 1247. (6) Gani, R.; Jiménez-González, C.; Constable, D. J. C. Method for Selection of Solvents for Promotion of Organic Reactions. Comput. Chem. Eng. 2005, 29 (7), 1661. (7) Kim, D.; Guk, H.; Choi, S.-H.; Chung, D. H. Benchmarking of Computational Approaches for Fast Screening of Lithium Ion Battery Electrolyte Solvents. Chem. Phys. Lett. 2017, 681, 64. (8) Kruber, K. F.; Scheffczyk, J.; Leonhard, K.; Bardow, A.; Skiborowski, M. A Hierarchical Approach for Solvent Selection Based on Successive Model Refinement. Comput.-Aided Chem. Eng. 2018, 43, 325. (9) Reichardt, C.; Welton, T. Solvents and Solvent Effects in Organic Chemistry, 4th ed.; Wiley-VCH, 2011. (10) Henderson, R. K.; Jiménez-González, C.; Constable, D. J. C.; Alston, S. R.; Inglis, G. G. A.; Fisher, G.; Sherwood, J.; Binks, S. P.; Curzons, A. D. Expanding GSK’s Solvent Selection Guide− Embedding Sustainability into Solvent Selection Starting at Medicinal Chemistry. Green Chem. 2011, 13 (4), 854. (11) Alder, C. M.; Hayler, J. D.; Henderson, R. K.; Redman, A. M.; Shukla, L.; Shuster, L. E.; Sneddon, H. F. Updating and Further Expanding GSK’s Solvent Sustainability Guide. Green Chem. 2016, 18 (13), 3879. (12) ACS Green Chemistry Institute Pharmaceutical Roundtable Home Page. https://www.acs.org/content/acs/en/greenchemistry/ research-innovation/tools-for-green-chemistry.html (accessed Jan 2019). N


Article

Industrial & Engineering Chemistry Research Constants, with Special Reference to the Solvolysis of T-Butyl Chloride. J. Chem. Soc., Perkin Trans. 2 1987, 0 (8), 1097. (33) Folić, M.; Adjiman, C. S.; Pistikopoulos, E. N. Design of Solvents for Optimal Reaction Rate Constants. AIChE J. 2007, 53 (5), 1240. (34) Struebing, H.; Ganase, Z.; Karamertzanis, P. G.; Siougkrou, E.; Haycock, P.; Piccione, P. M.; Armstrong, A.; Galindo, A.; Adjiman, C. S. Computer-Aided Molecular Design of Solvents for Accelerated Reaction Kinetics. Nat. Chem. 2013, 5 (11), 952. (35) Struebing, H.; Obermeier, S.; Siougkrou, E.; Adjiman, C. S.; Galindo, A. A QM-CAMD Approach to Solvent Design for Optimal Reaction Rates. Chem. Eng. Sci. 2017, 159, 69. (36) Wicaksono, D. S.; Mhamdi, A.; Marquardt, W. ComputerAided Screening of Solvents for Optimal Reaction Rates. Chem. Eng. Sci. 2014, 115, 167. (37) Tsichla, A. An Experimental Assessment of Model-Based Solvent Selection for Enhancing Chemical Reactions. Ph.D. Dissertation, University of Aachen: Germany, 2018. (38) Kamlet, M. J.; Abboud, J. L. M.; Abraham, M. H.; Taft, R. W. Linear Solvation Energy Relationships. 23. a Comprehensive Collection of the Solvatochromic Parameters, Pi*, Alpha, and Beta, and Some Methods for Simplifying the Generalized Solvatochromic Equation. J. Org. Chem. 1983, 48 (17), 2877. (39) Smith, M. B.; March, J. March’s Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 6th ed.; Wiley: NJ, 2007. (40) Betts, R. L.; Hammett, L. P. A Kinetic Study of the Ammonolysis of Phenylacetic Esters in Methanol Solution 1. J. Am. Chem. Soc. 1937, 59 (8), 1568. (41) Jencks, W. P.; Carriuolo, J. Imidazole Catalysis. II. Acyl Transfer and the Reactions of Acetyl Imidazole with Water and Oxygen Anions. J. Biol. Chem. 1959, 234 (5), 1272. (42) Bruice, T. C.; Mayahi, M. F. The Influence of the Leaving Tendency of the Phenoxy Group on the Ammonolysis and Hydrolysis of Substituted Phenyl Acetates. J. Am. Chem. Soc. 1960, 82 (12), 3067. (43) Bunnett, J. F.; Davis, G. T. The Mechanism of Aminolysis of Esters 1,2. J. Am. Chem. Soc. 1960, 82 (3), 665. (44) Bruice, T. C.; Donzel, A.; Huffman, R. W.; Butler, A. R. Aminolysis of Phenyl Acetates in Aqueous Solutions. VII. 1Observations on the Influence of Salts, Amine Structure, and Base Strength. J. Am. Chem. Soc. 1967, 89 (9), 2106. (45) Blackburn, G. M.; Jencks, W. P. The Mechanism of the Aminolysis of Methyl Formate. J. Am. Chem. Soc. 1968, 90 (10), 2638. (46) Jencks, W. P.; Gilchrist, M. Nonlinear Structure-Reactivity Correlations. the Reactivity of Nucleophilic Reagents Toward Esters. J. Am. Chem. Soc. 1968, 90 (10), 2622. (47) Menger, F. M.; Smith, J. H. Mechanism of Ester Aminolyses in Aprotic Solvents. J. Am. Chem. Soc. 1972, 94 (11), 3824. (48) Satterthwait, A. C.; Jencks, W. P. Mechanism of the Aminolysis of Acetate Esters. J. Am. Chem. Soc. 1974, 96 (22), 7018. (49) Castro, E. A.; Ruiz, M. G.; Salinas, S.; Santos, J. G. Kinetics and Mechanism of the Aminolysis of Phenyl and 4-Nitrophenyl Chloroformates in Aqueous Solution. J. Org. Chem. 1999, 64 (13), 4817. (50) Wang, L.-H.; Zipse, H. Bifunctional Catalysis of Ester Aminolysis − A Computational and Experimental Study. Liebigs Annalen 1996, 1996 (10), 1501. (51) Zipse, H.; Wang, L.-H.; Houk, K. N. Polyether Catalysis of Ester Aminolysis − A Computational and Experimental Study. Liebigs Annalen 1996, 1996 (10), 1511. (52) Yang, W.; Drueckhammer, D. G. Computational Studies of the Aminolysis of Oxoesters and Thioesters in Aqueous Solution. Org. Lett. 2000, 2 (26), 4133. (53) Ilieva, S.; Galabov, B.; Musaev, D. G.; Morokuma, K. Computational Study of the Aminolysis of 2-Benzoxazolinone. J. Org. Chem. 2003, 68 (9), 3406. (54) Ilieva, S.; Galabov, B.; Musaev, D. G.; Morokuma, K.; Schaefer, H. F. Computational Study of the Aminolysis of Esters. the Reaction of Methylformate with Ammonia. J. Org. Chem. 2003, 68 (4), 1496.

(55) Galabov, B.; Atanasov, Y.; Ilieva, S.; Schaefer, H. F. Mechanism of the Aminolysis of Methyl Benzoate: a Computational Study. J. Phys. Chem. A 2005, 109 (50), 11470. (56) Xia, X.; Zhang, C.; Xue, Y.; Kim, C. K.; Yan, G. DFT Study and Monte Carlo Simulation on the Aminolysis of XC(O)OCH 3(X = NH 2, H, and CF 3) with Monomeric and Dimeric Ammonias. J. Chem. Theory Comput. 2008, 4 (10), 1643. (57) Andrada, D. M.; Jimenez-Halla, J. O. C.; Solà, M. Mechanism of the Aminolysis of Fischer Alkoxy and Thiocarbene Complexes: A DFT Study. J. Org. Chem. 2010, 75 (17), 5821. (58) Jin, L.; Wu, Y.; Kim, C. K.; Xue, Y. Theoretical Study on the Aminolysis of Ester Catalyzed by TBD: Hydrogen Bonding or Covalent Bonding of the Catalyst? J. Mol. Struct.: THEOCHEM 2010, 942 (1−3), 137. (59) Jencks, W. P.; Carriuolo, J. General Base Catalysis of the Aminolysis of Phenyl Acetate 1. J. Am. Chem. Soc. 1960, 82 (3), 675. (60) Bruice, T. C.; Felton, S. M. Intramolecular Amine-Catalyzed Aminolysis of an Ester. J. Am. Chem. Soc. 1969, 91 (10), 2799. (61) Felton, S. M.; Bruice, T. C. Intramolecular General-BaseCatalyzed Hydrolysis and Aminolysis of the Ester Bond by Imidazole and Quinoline Bases. J. Am. Chem. Soc. 1969, 91 (24), 6721. (62) Nagy, O. B.; Reuliaux, V.; Bertrand, N.; van Der Mensbrugghe, A.; Leseul, J.; Nagy, J. B. Mechanism of Ester Aminolysis in Aprotic Media and Specific Solvent Effects. Bull. Soc. Chim. Belg. 1985, 94 (11−12), 1055. (63) Ooi, T.; Tayama, E.; Yamada, M.; Maruoka, K. Efficient Synthesis of Aromatic Sec-Amides From Esters: Synthetic Utility of Bislithium Amides. Synlett 1999, 1999 (6), 729. (64) DTU Chemical Engineering KT Consortium-roCAMD. http:// www.Capec.Kt.Dtu.Dk/ (accessed Jan 2019). (65) DTU Chemical Engineering KT Consortium-ProPred. http:// www.Capec.Kt.Dtu.Dk/ (accessed Jan 2019). (66) Chudek, J. A.; Foster, R.; Young, D. 13C Nuclear Magnetic Resonance Studies of the Products of Reaction of Acetaldehyde and of Simple Ketones in Liquid Ammonia, in Hydrazine Hydrate, and in Some Substituted Hydrazine Solutions. J. Chem. Soc., Perkin Trans. 2 1985, 0 (8), 1285. (67) Ingold, C. K. The Mechanism of, and Constitutional Factors Controlling the Hydrolysis of Carboxylic Esters. Part I. the Constitutional Significance of Hydrolytic Stability Maxima. J. Chem. Soc. 1930, 0 (0), 1032. (68) Rackett, H. G. Equation of State for Saturated Liquids. J. Chem. Eng. Data 1970, 15 (4), 514. (69) Spencer, C. F.; Danner, R. P. Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data 1972, 17 (2), 236. (70) Li, C. C. Critical Temperature Estimation for Simple Mixtures. Can. J. Chem. Eng. 1971, 49 (5), 709. (71) Poling, B. E.; Thomson, G. H.; Friend, D. G.; Rowley, R. L.; Wilding, W. V. Physical and Chemical Data. In Perry’s Chemical Engineers’ Handbook; McGraw-Hill Companies: United States, 2008; pp 506−507. (72) Maples, R. E. Petroleum Refinery Process Economics, 2nd ed.; PenWell Books, 2000. (73) Reynolds, O. On the Dynamical Theory of Incompressible Viscous Fluids and the Determination of the Criterion. Philos. Trans. R. Soc., A 1895, 186 (0), 123. (74) Aris, R. On the Dispersion of a Solute in a Fluid Flowing Through a Tube. Proc. R. Soc. London, Ser. A 1956, 235, 67−77. (75) Taylor, G. The Dispersion of Matter in Turbulent Flow Through a Pipe. Proc. R. Soc. London A 1954, 223 (1155), 446. (76) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids; McGraw-Hill: New York, p 41, 2001. (77) Hottel, H. C.; Noble, J. J.; Sarofilm, A. F.; Silcox, G. D.; Wankat, P. C.; Knaebel, K. S. Heat and Mass Transfer. In Perry’s Chemical Engineers’ Handbook; McGraw-Hill Companies: New York, 2008; pp 5−54. (78) Perkins, L. R.; Geankoplis, C. J. Molecular Diffusion in a Ternary Liquid System with the Diffusing Component Dilute. Chem. Eng. Sci. 1969, 24 (7), 1035. O


Article

Industrial & Engineering Chemistry Research (79) Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, 1 (2), 264. (80) Emig, G.; Klemm, E. Technische Chemie. Einführung in die chemische Reaktionstechnik, 5th ed.; Springer-Verlag, 2005. (81) Günther, A.; Jhunjhunwala, M.; Thalmann, M.; Schmidt, M. A.; Jensen, K. F. Micromixing of Miscible Liquids in Segmented GasLiquid Flow. Langmuir 2005, 21 (4), 1547. (82) Dean, W. R. LXXII. The Stream-line Motion of Fluid in a Curved Pipe (Second Paper). The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 1928, 5 (30), 673. (83) Janssen, L. A. M. Axial Dispersion in Laminar Flow Through Coiled Tubes. Chem. Eng. Sci. 1976, 31 (3), 215. (84) Nauman, E. B. The Residence Time Distribution for Laminar Flow in Helically Coiled Tubes. Chem. Eng. Sci. 1977, 32 (3), 287. (85) Van den Berg, J. H.; Deelder, R. S. Measurement of Axial Dispersion in Laminar Flow Through Coiled Capillary Tubes. Chem. Eng. Sci. 1979, 34 (11), 1345. (86) Johnson, M.; Kamm, R. D. Numerical Studies of Steady Flow Dispersion at Low Dean Number in a Gently Curving Tube. J. Fluid Mech. 1986, 172, 329. (87) Daskopoulos, P.; Lenhoff, A. M. Dispersion Coefficient for Laminar Flow in Curved Tubes. AIChE J. 1988, 34 (12), 2052. (88) Jiang, F.; Drese, K. S.; Hardt, S.; Küpper, M.; Schönfeld, F. Helical Flows and Chaotic Mixing in Curved Micro Channels. AIChE J. 2004, 50 (9), 2297. (89) Minnich, C. B.; Sipeer, F.; Greiner, L.; Liauw, M. A. Determination of the Dispersion Characteristics of Miniaturized Coiled Reactors with Fiber-Optic Fourier Transform Mid-Infrared Spectroscopy. Ind. Eng. Chem. Res. 2010, 49 (12), 5530. (90) Nigam, A.; Nauman, E. B. Two-Phase Flow of Partially Miscible Components in Submicron Channels. Chem. Eng. Res. Des. 2005, 83 (7), 777. (91) Marin, G.; Yablonsky, G. S. Kinetics of Chemical Reactions; John Wiley & Sons, 2011. (92) Pohjanpalo, H. System Identifiability Based on the Power Series Expansion of the Solution. Math. Biosci. 1978, 41 (1−2), 21. (93) Walter, E.; Pronzato, L. Identification of Parametric Models from Experimental Data; Springer: Berlin, Germany, 1997. (94) Aster, R. C.; Borchers, B.; Thurber, C. H. Parameter Estimation and Inverse Problems, 1st ed.; Elsevier Academic Press, 2004. (95) Burnham, K. P.; Anderson, D. R. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach., 2nd ed.; Springer-Verlag New York: New York, NY, 2002. (96) Akaike, H. Canonical Correlation Analysis of Time Series and the Use of an Information Criterion. In System Identification Advances and Case Studies; Mehra, R. K., Lainiotis, D. G., Eds.; Mathematics in Science and Engineering; Elsevier, 1976; Vol. 126, pp 27−96. (97) Hurvich, C. M.; Tsai, C.-L. Regression and Time Series Model Selection in Small Samples. Biometrika 1989, 76 (2), 297. (98) Sugiura, N. Further Analysts of the Data by Akaike’ S Information Criterion and the Finite Corrections. Commun. Stat. Theory Methods 1978, 7 (1), 13. (99) Yang, Z.; Robb, D. A. Partition Coefficients of Substrates and Products and Solvent Selection for Biocatalysis Under Nearly Anhydrous Conditions. Biotechnol. Bioeng. 1994, 43 (5), 365. (100) Ghaffari-Moghaddam, M.; Eslahi, H.; Aydin, Y. A.; Saloglu, D. Enzymatic Processes in Alternative Reaction Media: A Mini Review. J. Biol. Methods 2015, 2 (3), No. 25. (101) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents: Physical Properties and Methods of Purification, 4th ed.;John Wiley and Sons: New Jersey, 1986. (102) Carlson, R. Design and Optimization in Organic Synthesis; Elsevier Science, 1991; Vol. 8, 3rd ed. (103) Zeuner, B.; Kontogeorgis, G. M.; Riisager, A.; Meyer, A. S. Thermodynamically Based Solvent Design for Enzymatic Saccharide Acylation with Hydroxycinnamic Acids in Non-Conventional Media. New Biotechnol. 2012, 29 (3), 255.

(104) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. GroupContribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21 (6), 1086. (105) Gmehling, J. Potential of Thermodynamic Tools (Group Contribution Methods, Factual Data Banks) for the Development of Chemical Processes. Fluid Phase Equilib. 2003, 210 (2), 161. (106) Weidlich, U.; Gmehling, J. A Modified UNIFACModel. 1. Prediction of VLE, hE, and. gamma. infin. Ind. Eng. Chem. Res. 1987, 26 (7), 1372. (107) Klamt, A.; Schüürmann, G. COSMO: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and Its Gradient. J. Chem. Soc., Perkin Trans. 2 1993, 2 (5), 799.

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