Heat Management in Microreactors for Fast Exothermic Organic

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Heat Management in Microreactors for Fast Exothermic Organic Syntheses – First Design Principles Thomas Westermann, and Leslaw Mleczko Org. Process Res. Dev., Just Accepted Manuscript • DOI: 10.1021/acs.oprd.5b00205 • Publication Date (Web): 21 Oct 2015 Downloaded from http://pubs.acs.org on October 24, 2015

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Organic Process Research & Development

Heat Management in Microreactors for Fast Exothermic Organic Syntheses – First Design Principles Thomas Westermann and Leslaw Mleczko* Bayer Technology Services GmbH

Corresponding Author * [email protected]

ACS Paragon Plus Environment

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Abstract

Microreactors permit continuous operation of various organic syntheses. Due to their excellent heat transfer characteristics, many authors assume isothermicity and ignore the issue of heat management. This assumption can lead to severe misinterpretations of experimental results if a hot spot in a microchannel remains undetected. A simple methodology is presented that permits a first assessment of heat management in microreactors for fast exothermic reactions. Several typical reaction classes in organic synthesis are subdivided into three categories according to their heat production potential (HPP, [kW/L]). Category 1 reactions (HPP > 100 kW/L) are unsuitable for industrial-scale continuous syntheses in single channel arrangements. Category 2 reactions (HPP > 10 kW/L) are critical, and careful selection of channel diameters is necessary. Category 3 reactions (HPP < 10 kW/L) are suitable for continuous synthesis up to the millimeter scale. Very fast reactions with half-lives of less than 1 s are often category 1. To properly remove heat without generating significant hot spots, channel diameters must be smaller than 500 µm. A short-cut approach is proposed for the simple assessment of maximum channel diameters permitting near-isothermal operation.

Keywords: microtechnology, scale-up, flow chemistry, temperature control, run-away


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Introduction

Microreaction technology (MRT) is one approach for process intensification. Because MRT enhances mass and heat transfer, novel process windows become available, and reactions that were not controllable or scalable in classical reactors can be operated in a stable manner1. MRT can be applied to both gas phase and liquid phase reactions. In gas-phase systems, microreactors are primarily used to improve heat management. Several studies have examined exothermic reactions that are difficult to control in multitubular reactors, such as selective oxidations, and endothermic reactions that are limited by heat supply, such as reforming reactions2. The accurate measurement and prediction of temperature profiles has therefore received extensive attention. For many of these systems, the kinetics are known, and a model-based reactor design is used as a standard approach. This approach is based on the optimal design of a reactor for a particular process and is well-established for the production of bulk chemicals. By contrast, most fine chemicals are synthesized in the liquid phase. Traditionally, standardized equipment such as stirred tank reactors is used to prepare various products in multipurpose plants. The development target is to determine the optimal recipes to perform the reaction in a given reactor. Strategies such as reagent dilution or the use of reagents in large stoichiometric excess are often applied to adapt the reaction progress to the reactor. Similar strategies are now employed in MRT for organic synthesis. Consequently, readily available equipment is selected based on availability or ease of handling rather than an assessment of reaction engineering parameters3. Over-engineering is discouraged, and thus it is not surprising that capillary reactors with channel diameters in the millimeter range dominate over those in the micrometer range because the former are more readily available and appear less susceptible to clogging. In many cases, large capillaries (e.g., diameter of 4 mm) are applied even for highly exothermic reactions4. Due to the mostly laminar flow regime, effective mixing is a major concern in MRT equipment selection. Therefore, a number of mixer types based on different mixing principles have been developed. The issue of heat management has attracted less attention, perhaps because it is very difficult to monitor temperature profiles in microreactors. The small size of the channels hinders the introduction of classic sensors for temperature measurements, and special reactor designs are required5. Temperature control is often based on measurements of outlet temperatures. If the


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process outlet temperature and the cooling media outlet temperature remain nearly constant at varying flow rates, isothermal conditions are assumed. High heat transfer coefficients > 10000 W/m²K reported in the literature encourage the neglect of the energy balance and lead to the conclusion that isothermal operation is possible. Various authors have claimed to have conducted stable and isothermal operations for very fast (i.e., residence times between milliseconds and seconds) and highly exothermic reactions such as lithiations or diazomethane syntheses1,6. However, some studies have demonstrated that the process outlet temperature and the outlet cooling medium temperature can differ at varying flow rates and depend on the residence time7,8. In a study of the synthesis of ionic liquids characterized by instantaneous kinetics (tr = 0.012 s), a quasi-adiabatic temperature increase was predicted9. The low selectivity of the dibal-H reduction of methyl butyrate to butyraldehyde10 and the plugging of channels due to decomposition of intermediates in a two-stage synthesis of difluorotoluene8 were attributed to unidentified temperature peaks in the microreactors. Simulation studies of fast reactions such as the acetoacetylation of an aromatic amine with diketene11,12 or Michael additions13 predicted hot spots of up to 90°C or 55°C, respectively. These results demonstrate that microreactors do not guarantee isothermal operation. Multi-injection microreactors have been suggested for reactions that require heat management 9,12,14,15. Recognizing the importance of heat management remains challenging. Classic reactionengineering tools, such as stability criteria, are available.16 The applicability of these criteria to microreactors has been studied thoroughly, confirming that temperature control of reactors is a concern and that the issue of a run-away cannot be dismissed9,17. The failure to adopt this approach more widely is attributable to differences in workflows for the product development of bulk and fine chemicals. Furthermore, many organic chemists have not been trained to apply chemical engineering tools. Thus, general guidelines would be useful. A suitable “first approach” has been proposed by Roberge et al.11,18. Based on an analysis of various reactions in the fine chemical and pharmaceutical industries, three classes of reactions have been identified: types A, B and C. Type A reactions are very fast, with reaction half-lives of less than 1 s. These reactions occur mainly in the mixing zone and are controlled by the mixing process (i.e., micro-mixing domain). The flow rate and mixer type play important roles. Type B reactions are rapid, with reaction times ranging between 1 s and 10 min. They are controlled


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predominantly by kinetics instead of mixing. These reactions benefit from a microstructured reactor to effectively control reaction temperatures. Type B reactions can in principle also be performed in conventional equipment, but non-isothermal operations result in lower yields. Type C reactions are slow (> 10 min) and can be performed using classic equipment. However, a continuous process may be advantageous with respect to safety or product quality for Type C reactions. This classification is very helpful and a good first step for an assessment of the application of MRT to organic synthesis. The classification system generates a “positive list” that serves as an indicator of whether MRT would be beneficial or unnecessary. The disadvantage of this classification system is that it does not account for reaction enthalpies. Loewe et al.7 introduced an alternative categorization method by defining the following four groups of reactions: (I) slow reactions with negligible heat release; (II) fast reactions with moderate heat release; (III) very fast reactions with high heat release; and (IV) instantaneous reactions with high heat release. Loewe et al. used example reactions to study the effects of reaction rates and exothermicity and concluded that the extremely fast reactions required immediate and efficient cooling. Unfortunately, the distinctions among the different reaction classes were not quantitatively defined. Therefore, this classification cannot be used as a direct guideline. This paper readdresses the issue of heat control in micro- and milli-reactors. An overview of the interaction between reaction rate and enthalpy and the consequences of thermal management in microreactors is provided, including a rough classification of reaction classes. Simple reaction engineering simulations are used to illustrate the dependence among kinetics, reaction enthalpies, channel sizes and temperature profiles. The simulation results are compared with the indicators obtained from the stability criteria. Finally, a short-cut approach is proposed for the identification of the maximum channel diameter ensuring quasi-isothermal operation. Although this analysis focuses on channel diameter as the most effective means of addressing temperature increases, the results can also be used as a guideline for the selection of suitable microreactor systems.


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Methodology Reaction Engineering Model

The model equations are summarized in Table 1. The model describes a homogeneous reaction that occurs in a continuous plug flow through a cylindrical channel (application of the model to complex channel geometries is discussed in the supporting information). The channel is cooled from the outside. Heat is removed from the reacting fluid through the wall to the cooling medium (Figure 1). Sufficient cooling capacity ensures that the temperature of the cooling medium remains constant. Furthermore, heat transfer resistance on the cooling (shell) side is negligible compared to inside the channel (tube side), an optimistic scenario. Therefore, the wall temperature is constant and equal to the temperature of the cooling medium and also corresponds to the inlet temperature of the reactants (Equation 2). Thus, heat transfer only occurs when the process side starts reacting and generates reaction enthalpy, as indicated by an increase in temperature. In plug flow, the radial velocity profiles and their implications for residence time distributions are neglected, and the microchannel can be described by a one-dimensional model using the average fluid velocity (Equation 1). Because the Reynolds number is proportional to the tube diameter, the small dimensions of microreactors typically result in a laminar flow profile (Equation 3). In this flow regime, the Nusselt number is roughly constant (Equation 4)17. For a hydraulic diameter of 100 µm and water as the process fluid, the heat transfer coefficient may be as high as 26000 W/m²K19. Most organic solvents have lower thermal conductivities than water (~ 0.6 W/m/K) by a factor of 3 to 4. Therefore, for an organic solvent with a thermal conductivity of 0.2 W/m/K in a channel with a 1 mm hydraulic diameter, the heat transfer coefficient is less than 1000 W/m²/K (Figure 2). Simple first-order kinetics with an Arrhenius term for temperature dependency were applied for the case studies (Equation 5). For the sake of simplicity, we assumed that the activation energy was 60 kJ/mol; a comparative study with a lower activation energy of 20 kJ/mol is presented in the supporting information. Mixing limitations were not explicitly considered. For very fast reactions, the mixing time of the reactants, which typically ranges between 1 and 100 ms20, is the same order of magnitude as the reaction time, resulting in reduced reaction rates. Although this limitation may be favorable


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in terms of heat generation, it often leads to undesired side reactions and should be avoided by appropriate mixer selection. For further discussion, two parameters must be defined: the heat production potential HPP (Equation 6) and the heat removal capacity HRC (Equation 7). The heat production potential, which has dimensions of power per volume (e.g., kW/L), refers to the product of the reaction enthalpy and the reaction rate at the reactor inlet. Heat removal is proportional to the driving force, which is the temperature difference between the reactants and the wall. Heat removal capacity HRC (kW/L/K) describes the constant ratio of heat removal and temperature difference (Figure 2). Short-Cut Approach A simple assessment of whether the reactor can be operated isothermally can be performed on the basis of the energy balance (Equation 2 in Table 1). This balance indicates that the temperature of the fluid will increase if the heat generated in the chemical reaction in the channel cannot be fully removed. The rate of heat generation is usually a function of the concentration of reactants (i.e., for reactions with a positive order, the rate is highest at the reactor entrance, neglecting, for the moment, the effect of temperature. The increasing temperature in the channel accelerates both the reaction rate and heat removal because the temperature difference between the fluid and the reactor wall is the driving force for heat exchange. As conversion progresses, the reactant concentrations decrease, and the reaction slows down, ultimately leading to decreasing temperatures along the channel length. Therefore, the temperature profile in the reaction channel exhibits a maximum, where the heat that is generated is equal to the heat removed across the channel wall. The energy balance in this hot spot can be simplified to Equation 9, which we call the isothermicity criterion. The heat removal capacity multiplied by an acceptable temperature increase (e.g., 10 K) corresponds to the heat production capacity multiplied by a safety factor F (Equation 10). This safety factor accounts for the acceleration of the reaction due to the temperature increase and is a function of the activation energy and inlet temperature. If these data are unavailable, we suggest using a factor of F = 2, which roughly corresponds to a typical increase in reaction rate for a temperature increase of 10 K. The same balance equation can also be rearranged into the simple reactor design guideline described by Equation 11, which allows the calculation of the maximum channel diameters


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permitting stable operation. The numerator of this equation describes heat removal, and the denominator describes the potential for heat generation. The maximum diameter of the channel is a function of the allowed temperature increase in the channel, thermal conductivity, heat exchange coefficient, reaction rate and enthalpy. Stability Criteria As a benchmark for the simulations performed in this work, previously reported stability criteria for microreactors9 based on well-established general stability criteria16 were applied (Equation 8). The stability parameter N’/S’ represents the ratio between heat removal and heat production. An analytical solution can be derived for a zero-order reaction, which represents the worst case in terms of reactor stability, because the reaction does not slow due to decreasing reactant concentrations. In this case, the criterion demands N’/S’ > 2.7 for stable reactor operation. For higher-order reactions, this value represents a conservative estimate. Suitable corrections are available and lead to lower boundary values for higher-order reactions9.


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Case studies

Figure 4 summarizes typical reaction classes in the field of organic synthesis that are considered fast and exothermic. In this diagram, the range of reaction enthalpies and characteristic reaction half-lives (i.e., the time the reaction requires to achieve 50% conversion) are summarized. The diagram covers a wide range of reactions with half-lives between 0.1 and 100 s and reaction enthalpies between 50 and 600 kJ/mol. In our case studies, we fixed the residence times in the channels to five half-life times, which corresponds to a 97% conversion rate for isothermal operation. Lithium Chemistry in Flow Organolithium compounds serve as useful carbanion equivalents in chemical synthesis21. Organolithium-involved reactions are highly exothermic, with reaction enthalpies in the range of 300 kJ/mol. Assuming an inlet reactant concentration of 1 mol/L, density of 1 kg/L and heat capacity of 1 kJ/kg/K, this enthalpy corresponds to an adiabatic temperature increase in the range of 300 K. Thus, accurate temperature control is critical. Due to the high reactivity and instability of organolithium compounds, these reactions are usually performed under cryogenic conditions in a semi-batch operation with slow addition of one reactant. Because safety is critical with respect to organolithium-involved reactions, special measures are necessary to prevent runaways, e.g., hold-up must be minimized, which decreases capacity. Organolithium reactions are promising candidates for flow chemistry and MRT, and a number of studies of these types of reactions in flow chemistry have been reported6. Thus, analysis of this reaction class is interesting from both methodological and practical perspectives. The simulations were performed using a reaction rate constant estimated from a moderate halflife of 5 s. Please note that the assumed reactant concentration of 1 mol/L is a typical order of magnitude used in lab studies, albeit on the lower end. In other words, we examined an optimistic scenario. The effect of channel diameter on the temperature and conversion profiles is presented in Figure 4. For a channel diameter of 0.6 mm, reactor operation is close to isothermal, with a temperature increase of 5 K. In the 0.8-mm channel, the temperature increases by 17 K. This value may seem low but is attributable to the allowed operating temperature window (i.e., assuming that the decomposition temperature is -30 °C, the cooling temperature must be less


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than -47 °C). This temperature is similar to temperatures used in batch operations. A further increase in reactor diameter is critical; in a 1 mm diameter reactor, a hot spot exceeding 250 K would be generated, more than 80% of the adiabatic temperature increase. This hot spot would appear in the front-end section of the channel after a few seconds of residence time. The temperature would decrease quickly because heat no longer accumulates downstream of the hot spot due to a lower generation rate and the large temperature difference between the two sides of the channel. Therefore, the hot spot would not be detected by usual temperature measurements at the reactor outlet. Different temperature profiles have significant impacts on conversion, e.g. an increase in the hot spot temperature would result in complete conversion at shorter residence times because the reaction rate increases exponentially with temperature. The apparent spacetime-yield would increase in a similar manner. At first glance, the uncontrolled and undetected temperature increase may mislead investigators to believe that MRT automatically led to process intensification without realizing that a high-temperature phenomenon occurred in the reactor.

For comparison, the maximum channel diameter calculated using the short-cut method for a temperature increase not larger than 10 K is 0.7 mm. This value is consistent with the model predictions. Unstable operation in larger channels was also predicted by the stability analysis. When applying the stability criterion for a channel diameter of 1 mm, the value of N’/S’ = 1.22 is below the limits of 2.77 for zero-order reactions and 2.03 for first-order reactions according to Haber et al.9. This approach predicts stable operation at channel diameters smaller than 0.78 mm. In general, all methods applied in this analysis were consistent and confirmed that the studied reactions can only be operated stably in small channels. The frequently applied millimeter-sized capillaries would lead to unstable operation, and microfluidic-type reactors would be necessary to guarantee isothermal operation. Our results are not valid for all lithiation reactions. Figure 4 illustrates that reaction rates in this reaction class can vary significantly depending on the conditions and routes, with typical half-lives ranging between 0.5 and 50 s.

The model predictions qualitatively agree with experimental data. In the synthesis of 2,3difluorobenzaldehyde (DFBA) by a two-stage lithiation reaction, stable operation with regard to temperature control was achieved22. Measurements were performed in a commercial unit with a capacity of ca. 2 kg/h of DFBA consisting of six microstructured reactors in series. The overall


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residence time was ca. 4 min. There was no difference in temperature among the different modules. Of course, this result does not exclude the possibility that a temperature peak occurred in the first module. Slightly different results were obtained for the synthesis of 2,3difluorotoluene8. The overall residence time varied between 4 and 6 min, depending on conditions. However, temperature increases of approximately 10 K were measured after the first module. The residence time in this module was ca. 10 s. Furthermore, the reactor was very sensitive to the reaction rate, and a thermal runaway was observed for high reaction rates. Nagaki and Yoshida6 studied the effects of temperature and residence time on yield for the Br-Li exchange of bromonaphthalenes. The reactions were performed under a very wide range of reaction conditions, e.g., the residence times varied by two orders of magnitude between milliseconds and over 10 s. A temperature-residence time map was developed based on the experimental data. The highest yields were achieved at low temperatures and long residence times. At high temperatures, yields decreased dramatically even at very short (ms) residence times, indicating a lack of stabilization of unstable intermediates due to the temperature peaks. Therefore, it is advisable to operate reactions at low temperatures, particularly for mesoscale systems with diameters larger than 1 mm, such as commercial cryostatic flow reactors operating at -60 °C 23,24. Undetected hot spots in microchannel reactors can lead to space-time yields that correspond to much higher temperatures than those intended or measured at the reactor inlet and outlet. Thus, when experimenting with microchannel reactors, choosing the wrong diameter size could cause the reactor to fail, and smaller diameters may enable success. Diazomethane chemistry Diazomethane is a highly reactive agent with a wide range of applications in chemical syntheses25. However, diazomethane is a powerful carcinogen that is highly explosive and toxic. Its enthalpy amounts to ca. -5450 kJ/kg and is comparable with modern explosives. In spite of the good solubility of diazomethane in most solvents, dangerous gas mixtures can form due to its low boiling point. Therefore, safety remains a challenge and limits the mass production and wide industrial application of diazomethane. MRT thus seems to be ideally suited for the synthesis of diazomethane1. Ferstl et al.26 were the first to evaluate this concept experimentally. The advantages of microtechnology such as small hold-up or excellent temperature control perfectly


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suit the demands of diazomethane synthesis. Moreover, the small dimensions of the reactor, at least in the laboratory, allow the whole reactor to be immersed in a stopper solution as a safety measure to contain diazomethane leakage. Struempel et al.27 extended this concept by combining the continuous synthesis of diazomethane with its subsequent conversion in the same microreactor. In this approach, synthesized diazomethane is immediately consumed in a consecutive reaction step. Consequently, the hold-up of diazomethane is further reduced, which improves the reaction’s safety. Although the concept has thus been proven, scalability remains challenging. Therefore, it is an interesting example with practical importance. Temperature and conversion profiles simulated for diazomethane synthesis in channels with different diameters are presented in Figure 5. For a 1-mm-diameter channel, the temperature increase was nearly equivalent to that of the adiabatic reactor, with a temperature peak of 137 K. Due to the small heat exchange area, the temperature decreased quite slowly compared to the other simulated cases. Reducing the channel diameter to 400 µm was not sufficient to keep the temperature increase below 50 K. Only when the channel diameter was decreased to 200 µm could the reactor be considered near-isothermal, with a hot spot of 7 K. The short-cut assessment also suggests a channel diameter of 200 µm to keep the temperature increase below 10 K. This comparison again confirms that the two approaches are consistent with each other. Again, the comparison of the conversion profiles for the different channel sizes illustrates the strong impact of temperature peaks on conversion times. The data presented in Figure 5 also agree well with the results of the stability analysis. For a channel diameter of 1 mm, the stability criterion yielded a value of N’/S’ = 0.10, which was significantly lower than the stability threshold of 1.71. To achieve this value, the channel size would have to be reduced to 250 µm, corresponding to a temperature increase of 15 K. Rossi et al.28 studied the in situ generation of diazomethane in two reactors with different channel geometries. The channel dimensions differed by a factor of 10, and the cooling medium was maintained at the same temperature in both reactors. In general, the reactor with smaller channels produced significantly lower yields, even with longer residence times. Rossi et al. attributed the differences in yields to the different mixing efficiencies of the reactors and the critical impact of mixing efficiency on performance. However, mixing efficiencies should be expected to improve in smaller channels due to reduced diffusion distances. Therefore, it is much


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more probable that the higher yield of the larger channel was caused by an undetected hot spot inside the channel.

Discussion

Table 2 presents an overview of the heat production potentials and maximum channel diameters that are required to keep the temperature increase below 10 K. These calculations are based on average values for reaction half-life times and reaction enthalpies as represented by the points in Figure 4. The short-cut approach was also applied. These parameters strongly depend on the reaction enthalpies. A safety factor of F = 2, which roughly corresponds to an activation energy of 60 kJ/mol and a hot spot temperature of 10 K, was applied in these calculations. These predictions are conservative for lower activation energies; for higher activation energies, the channel diameters must be corrected downward. A reactant concentration of 1 mol/L and constant reaction rates for the first 50% of conversion were assumed; these conditions are consistent with near-isothermal reactor operations. The concentration may be too low for industrial applications. Figure 3 presents the correlation between the maximum acceptable channel diameter and the heat production potential, which clearly confirms that for reactions characterized by a high heat production potential, classic capillaries with diameters larger than 1 mm are not suitable. In these devices, hot spots or run-aways may be expected. For many fast and exothermic reactors channels, diameters in the range of 300 – 500 µm are necessary. For nitro- and azo-decompositions in channels with a diameter of 1 mm, hot spots of at least 100 K were estimated. Hot spot temperatures of more than 20 – 50 K indicate that the reaction is not controlled, and consequently, partial evaporation or thermal decomposition cannot be excluded. Most reaction systems that are of interest for flow chemistry have the potential for hot spot formation in inadequately designed micro channel reactors. The nitro- and diazo-decompositions presented in Table 2 are particularly critical. Hydrogenation of nitroaromates should be easier to handle because the reactions are usually performed catalytically and, consequently, the reaction rate can be moderated by the design of the catalyst.

The comparison of the two case studies (i.e., the metalorganic reaction with the diazomethane synthesis) demonstrates that knowledge of the reaction enthalpy or the corresponding adiabatic


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temperature increase is not sufficient to determine if the reaction can be performed in a microreactor in a stable manner under optimal quasi-isothermal conditions. For example, despite having a lower reaction enthalpy, the synthesis of diazomethane demands significantly lower channel diameters due to the reaction’s rapid kinetics. Therefore, both parameters (i.e., reaction rate and enthalpy) must be considered. The small channel sizes that are necessary for stable operation have strong implications for reactor capacity. If a 200-µm channel is operated at a velocity of 0.1 m/s, products would be produced at only 11 mL/h. Thus, a single-channel arrangement is not suitable for commercial applications, and despite literature reports to the contrary, the scale-up of the diazomethane synthesis using increased channel diameters would be challenging. The two case studies demonstrate that pronounced temperature profiles must be expected when fast exothermic reactions are operated under continuous flow. Heat management becomes critical when the reaction enthalpy is high and the half-life is short. As the reaction rate increases, the volume of the reactor required to obtain complete conversion decreases. The active heat exchange area in the microreactor consequently decreases, and the temperature difference between the reactor and coolant must increase to fulfill the energy balance. In other words, the system moves toward adiabatic operation. A slow, highly exothermic reaction can easily be handled in microreactors. For fast reactions with low reaction enthalpies, heat management is obviously not an issue, and a microreactor is not required. We thus suggest using the “heat production potential” parameter to assess the amount of effort required for thermal management during the selection and design of suitable microreactors. Based on this parameter, the following reaction classification can be proposed:

Category 1 reactions: 100 kW/L < HPP are not suitable for industrial-scale continuous syntheses. Consider dilution or split feed. Lab-scale production is possible with very small microchannels. Category 2 reactions: 10 kW/L < HPP < 100 kW/L are critical, and microreactors should be carefully selected based on the effective hydraulic diameter. Category 3 reactions HPP < 10 kW/L are suitable for continuous syntheses in most microreaction systems and roughly correspond to Roberge’s group B11.


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These three groups of reactions are also indicated in Figure 3. Returning to the case studies, the organolithium example had a heat production potential of 30 kW/L for the selected feed concentration of 1 mol/L. Therefore, this case is representative of reactions in category 2. The diazomethane reaction was less exothermic but significantly faster. A reaction enthalpy of 140 kJ/mol and a half-life of 0.2 s resulted in a heat production potential of 350 kW/L (again for 1 mol/L). Therefore, this case is representative of reactions in category 1.

The short-cut approach delivers valuable information on heat management and the selection of channel diameters. It is easy to apply this approach to perform assessments and sensitivity analyses without using simulation tools. Equation 9 offers a simple tool to assess the suitability of different types of microreactors for various reaction systems. It also clearly demonstrates the available reactor design measures. The easiest measure is to reduce reaction rates by reducing the concentration of the reactants by diluting them with solvents or employing multiport injection of reactants14. A microreactor should be selected on the basis of its heat removal properties. The easiest parameter with which to compare different modules is the hydraulic or effective channel diameter. As always, a number of assumptions must be made when simplifying multidimensional systems. The most critical issue is chemical kinetics. The operating conditions, such as reagent concentrations, are also important. Therefore, the absolute values presented in this paper only illustrate the importance of assessing heat balances in a microreactor. The kinetics of reactions or basic information on reaction rates can be obtained from simple differential measurements. Kinetics is also an appropriate means of assessing activation energies, which is very important for predicting temperature profiles. This basic approach is seldom used in MRT studies because complete conversion is usually reported and targeted. A simple homogeneous model can be used to predict temperature profiles. However, because simulation tools are not always available in synthetic laboratories, the simple short-cut approach proposed in this paper can provide valuable information on heat management in microreactors. For industrialization purposes, a full assessment including stability analysis should be performed. As shown in the case studies, all of these methods yield very consistent results.


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Summary

The purpose of this paper was to draw attention to heat management in microreactors. Microreactors do not automatically operate isothermally, although they may appear to do so. Although microstructures enhance heat transfer due to large surface to volume ratios and small heat transfer distances, many typical organic syntheses are too fast and exothermic to operate continuously under isothermal conditions. If applied to reactions with heat production potentials of 10 kW/L or higher, significant hot spots or thermal runaways may go unnoticed due to a lack of intermediate temperature measurements. These observations may occur in conjunction with surprisingly low selectivities or, in worse cases, evaporation or clogging. Undetected hot spots or thermal runaways may even explain observations of increased reaction rates compared to macroscale reactions, which may not be a result of “intensification” but rather a result of incorrect reaction temperatures. This paper suggests using the “heat production potential (HPP)” parameter to determine if isothermal operation in a microreactor is feasible. HPP values can be easily compared to the heat removal capacity of a reactor, which is a function of the channel diameter. Very fast reactions with half-lives of less than 1 s often generate HPP values higher than 100 kW/L. For proper heat removal without generating significant hot spots, capillary diameters must be smaller than 500 µm. Scale-up must retain the small hydraulic diameter by tailoring the reactor to the specific application.

Acknowledgment

The authors would like to thank Dr. V. Haverkamp and Dr. A. Sanchen for compiling the data presented in Figure 4. Supporing Information The SI includes a sensitivity study which shows that even for an optimistically low value of the activation energy of 20 kJ/mol pronounced temperature gradients have to be expected in oversized channels. Some remarks regarding scale-up of microchannel processes are followed by a step-by-step guideline for the appropriate determination of the maximum channel diameter for a given reaction.


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References

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Symbols and Abbreviations Symbol

Unit

W/m²/K

Heat transfer coefficient

kJ/mol

Enthalpy of reaction

Pas

W/m/K

Fluid thermal conductivity

kg/m³

Fluid density

mol/m³

Molar concentration

kJ/(kg K)

Fluid heat capacity

F

J/mol

kW/L/K

c

DFBA

HPP

HRC

-

m

Parameter

void fraction = fluid volume / channel volume Fluid viscosity

Hydraulic/effective channel diameter Difluorobenzaldehyde

kW/L

Activation energy Safety factor accounting for activation energy Heat production potential Heat removal capacity

L

1/s

Kinetic rate constant

MRT

m

Reactor/channel length

N'/S'

-

Number of parallel channels

p

-

Stability parameter

Pa

Absolute pressure

N Q

$%&'

r

R T

Microreaction technology

m³/s

Volumetric flow rate

kW/L

Specific heat removal rate

mol/(m³s)

Reaction rate

8.314 J/(mol K) Universal gas constant

)

°C

Fluid temperature

°C

Wall/inlet temperature

s

Reaction half-life time

V

m/s

Fluid velocity

m³

Reactor/channel volume

m

Axial dimension

*.,

u z


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Table 1: Balance equations for the channel reactor model

Material balance Energy balance

−4 =0

3 4 : ) 4 4 ⋅ 7− 8 − ⋅ 7) − ) 8 − ⋅ =0

; < 3 −1 ⋅

=> =

Reynolds number (flow regime)

A1 =

Nusselt number (heat transfer)

kinetics

[kW/L]

=N =

Heat removal capacity [kW/L/K]

Equation 4

G ⋅ H =)

II = $ %JK 7) 8 = 4 ⋅ 7− 8 ≈

7− 8 ⋅ 2 *.,

$%&' 4 4A1 = = ) − )

2.72 O P II Q R =)

Reactor stability criterion

Equation 2

Equation 3

= 3.66

4 = ⋅ >DE F−

First-order reaction

Heat production potential

1 < 1000

Equation 1

Equation 5

Equation 6

Equation 7

Equation 8

2.72 for worst-case zero-order reaction, lower limit for first-order Isothermicity criterion Safety factor for rate increase due to activation energy

Reactor design guideline

V=

=N ⋅ Δ) = V ⋅ II

47)8 ) = exp Y F1 − GZ ~2 47) 8 =) )

kJ for = 60 and ) − ) = 10 K mol

Equation 9

Equation 10

,'gh 7Δ)8 =i

4 ⋅ A1 ⋅ ⋅ Δ) 14.64 ⋅ ⋅ Δ) ⋅ *., ~i V ⋅ II ⋅ 7− 8

Equation 11


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Table 2: Estimates of heat production potentials and corresponding maximum channel

diameters for selected reaction classes. The selected parameters were λ = 0.2

k

'⋅l

, = 1

Reaction enthalpy

Half-life

Heat production potential

Max. channel diameter for 10 K hot spot

kJ/mol

s

kW/L

mm

Nitro-decomposition

-400

0.5

400

0.19

Diazo-decomposition

-140

0.2

350

0.20

Nitroaromates Hydrogenation

-550

1

275

0.23

Neutralization

-50

0.2

125

0.34

Metalorganic Reactions

-300

5

30

0.70

Nitration

-140

5

14

1.02

Polymerization

-100

100

0.5

>5

Amination

-120

200

0.3

>5

'Jm n


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In T = T0 c = c0

$%&' 7)8 =

4α ⋅ 7T − T 8 d

$ %JK 7)8 = 47)8 ⋅ Δ

Out d

Coolant / wall temperature T0=const L Figure 1: Schematic of the reactor model assumptions.

Figure 2: Heat transfer coefficient and corresponding heat removal capacity as functions of the channel diameter using Nu = 3.66 and λ = 0.2 W/m/K, corresponding to α (1 mm) = 730 W/m²/K).


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Figure 3: Channel diameter corresponding to a 10 K hot spot as a function of the heat production potential, HPP (for Nu = 3.66, F = 2 and λ = 0.2 W/m/K).


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Figure 4: Typical reaction classes for fast exothermic reactions and corresponding heat production potentials. At 10 kW/L, heat removal in capillaries becomes critical, with hot spots of approximately 10 K for a 1-mm diameter. Above 100 kW/L, diameters < 500 µm are required to keep the hot spots below 10 K but results in a pressure drop prohibitive for industrial production capacities.


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Figure 5: Temperature and conversion profiles for a typical metalorganic synthesis in channels with different diameters. First-order reaction, reaction enthalpy -300 kJ/mol, half-life 5 s, activation energy 60 kJ/mol, feed concentration 1 mol/L, fluid heat capacity 1 kJ/kg/K, fluid thermal conductivity 0.2 W/m/K, fluid density 1 kg/L, viscosity 1 mPas. The adiabatic temperature increase was 300 K.


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Figure 6: Temperature and conversion profiles for a typical diazo-decomposition reaction in channels with different diameters compared with isothermal operation. First-order reaction, reaction enthalpy -140 kJ/mol, half-life 0.2 s, activation energy 60 kJ/mol, feed concentration 1 mol/L, fluid heat capacity 1 kJ/kg/K, fluid thermal conductivity 0.2 W/m/K, fluid density 1 kg/L, viscosity 1 mPas.


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Heat Management in Microreactors for Fast Exothermic Organic

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