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Continuous diameter increase reactor – a reactor concept for maximizing productivity by a controlled diameter extension

Continuous diameter increase reactor – a reactor concept for maximizing productivity by a... This paper presents a novel theoretical approach for maximizing productivity in microreactors by a controlled extension of the tube diameter. A one-dimensional numeric model was developed where the tube diameter increases based on the reaction heat to achieve a constant temperature throughout the reactor length. Through this approach, a basic plug flow reactor model for mass and heat transfer was used with an integrated algorithm for a controlled diameter extension. A parametric study was performed to ensure safe operating conditions concerning thermal runaway. The results show an increase in productivity of approximately 42% for the fictional second-order test reaction. . . . . . Keywords Microstructured reactors Tubular reactor Process intensification Process control Model-based scale-up Numerical evaluation Introduction tightly on the bottom plate to seal the microreactor channels [7]. The coiled tube, on the other hand, can be wound in Flow chemistry in microreactors offers many benefits over different configurations to increase the effect of Dean flow. conventional batch chemistry. The high surface-to-volume ra- A common approach is to change the direction of the winding tio provides high heat transfer coefficients, which are the key every couple of turns, as shown by the examples in [6]. to temperature control [1–3]. Improved temperature control The continuous improvement of additive manufacturing also translates into higher productivity, as an overall higher (3D printing) of metals, especially the reduced surface rough- process temperature can be achieved safely. In some in- ness, has allowed the printing of microstructured reactors with stances, increased selectivity can be achieved [4]. shapes and sizes previously unimaginable. Internal diameters Furthermore, this approach also allows process intensifica- of 0.6 mm are achievable using selective laser melting (SLM) tions and still guarantees a safe and controlled operation due [8, 9]. As a result of this study, a reactor shape is proposed that to minor hold-ups [1, 2, 5]. The small dimensions allow for could be easily achieved using modern additive manufactur- short diffusion paths and thus result in fast mixing [1, 3, 6]. ing techniques. Traditionally, microreactors were constructed either as a Inherently, tubular microreactors are not well suited for coiled tube or were milled from a plate of metal or glass. As very long reaction times. While the reaction rate is very high shown by several authors in [6, 7], several different micro- in the beginning due to the high concentration of the reactants, structures can be milled from a metal plate. For example, these it slows down rapidly toward the end as the concentration of microstructures include temporary diameter constrictions or the reactants decreases. This results in a rapid increase in con- baffles to improve mixing. To complete the construction of a version, high heat production for exothermic reactions and a microreactor, a second top plate is then pressed and screwed temperature rise at the beginning and a slow increase in con- version, decreasing heat production and a temperature de- crease toward the end. Additionally, the high surface-to- volume ratio of microstructures further benefits heat removal. * Thorsten Roeder t.roeder@hs-mannheim.de The Arrhenius law predicts slower reaction rates at lower tem- peratures, which inevitably results in changing process condi- Institute of Chemical Process Engineering, Mannheim University of tions along the reactor. In addition to the tendency of clog- Applied Sciences, Paul-Wittsack-Straße 10, ging, the most significant limiting factor of microstructured 68163 Mannheim, Germany 248 Journal of Flow Chemistry (2022) 12:247–254 reactors is the high pressure drop accompanying high volu- the approach can be seen in Fig. 1. In theory, this approach metric flow rates [2, 6]. should increase productivity while providing a constant tem- There are several approaches to choose from to overcome perature throughout the reactor. This temperature control is this weakness and provide more constant process conditions. especially beneficial for producing temperature-sensitive These approaches can either influence the concentration of the products such as nitroaromatic compounds, which are reactants or influence the temperature at which the reaction is temperature-sensitive and degrade exothermically. An in- taking place. A widespread way to manipulate the concentra- creased diameter also positively affects the pressure drop tion is by using a multi-injection solution, where the concen- and reduces the tendency of clogging. The presented approach tration of the reactant is increased successively at specific is not restricted to just one constant temperature profile. lengths of the reactor by injecting fresh reactants, thus increas- Additionally, any conceivable temperature profile can be em- ing the reaction rate. To influence the temperature at which the ployed to perform further optimizations, such as selectivity. reaction takes place, the reactor can be separated into different As presented in this paper, a numeric model was built for zones, each in a different temperature zone than the previous obtaining a tubular wall profile of the proposed continuous zone. For example, a coiled tube is immersed in different diameter increase reactor (CoDIR) introduced in Fig. 1.This cooling baths, each with a higher temperature than the previ- reactor shape was optimized for a specific exothermic reaction ous bath. based on specific system conditions with the goal of keeping The second option for optimizing the temperature profile in the temperature constant throughout the reactor. Afterward, the case of highly exothermic reactions is a stepwise increase we investigated this system for parametric sensitivity by sys- in the tube diameter at specific reactor lengths. As shown in tematically sweeping sensitive parameters. Fig. 1, this results in an abrupt decrease in heat removal ca- pacity, thus allowing the temperature to rise and the reaction rate to accelerate. This approach also reduces the equipment Methods needed to set up different temperature zones. With the goal of maintaining the process conditions, i.e., a constant tempera- To model the plug flow reactor (PFR), a fictional exothermic ture, the stepwise diameter increase could be applied in small organic liquid phase irreversible second-order reaction is cho- steps throughout the reactor length. A visual representation of sen. Fig. 1 Comparison between the stepwise tube diameter extension (top) and the continuous diameter increase reactor (CoDIR) (bottom) Journal of Flow Chemistry (2022) 12:247–254 249 Table 1 Material Properties A þ B− > C: Parameter Value Unit Furthermore, an ideal plug flow is assumed. This assump- R 8.314 J/(mol·K) tion is further discussed in the Results section. E 50.00 kJ/mol The mass balance is calculated as a change in concentration k (293.15 K) 2.00E-05 m /(mol·s) ref over a length. This formula is derived from the basic mass Δ H −150.0 kJ/mol balance formula found in [10]. ρ 786.4 kg/m dc r η 0.0023 Pa∙s ¼ ð1Þ dz u c 153.6 J/(kg·K) λ 0.1365 W/(m·K) The reactionratefor all componentsinthissystemis the same; it has a negative prefix for the starting materials as they are used up and a positive prefix for the product as it is initial conditions for slice n + 1. The very first slice is calcu- generated. lated with the chosen starting conditions. The solution con- The reaction rate r is calculated with the following equa- tinues until all slices are calculated. After that, the data are tions [10]: evaluated, and the reactor is cut after the slice where a 90% conversion rate is reached. r ¼ kc c ð2Þ A B 1 1 − − R T T i ref k ¼ k e ð3Þ ref Algorithm for the diameter extension calculation The temperature-dependent reaction rate is calculated by applying the Arrhenius law to the fictional reaction rate con- In the first step, the reaction system is solved for a regular PFR stant k at a temperature of 293.15 K. ref model with a constant diameter. The resulting maximum tem- The equation for the energy balance used here is modified perature is the benchmark temperature we aim to hold con- to use the density and mean flow velocity instead of the area in stant throughout the CoDIR. Therefore, we aim to achieve an the source part. The basic equation can be found in [10]. isothermal mode of operation for the model by increasing the dT rðÞ −ΔH k πdTðÞ −T R W W i diameter and thus decreasing the heat transfer coefficient due ¼ þ ð4Þ dz ρ u c to their reciprocal relationship. The temperature difference i p mc between the reference and the slice temperature is fed into a The flow inside the reactor is laminar with a very low PID controller, which subsequently calculates a new reactor Reynolds number; thus, a Nusselt number of 3.656, which shape for each slice. If the temperature of the slice is lower represents the edge case of laminar flow, is applied here. than the benchmark, then the output increases the diameter, This means that the heat transmittance k will be limited by W which leads to a temperature increase in the next slice. the heat transfer on the process side α , so the heat conduction i Alternatively, the slice diameter is calculated by solving Eq. through the tube wall and the heat transfer to the cooling liquid (4)with dT /dz = 0, as seen in the supporting material. In this can be neglected. publication, the PID approach is chosen because it opens the As shown in [11], the hydrodynamic and thermal entry opportunity to create even more complex temperature profiles, length can be estimated by the following Eqs. (5)and (6): such as several temperature zones along the reactor length. Furthermore, to avoid oscillations of the diameter, the diame- L ≈0:05  Re  d ð5Þ hyd: ter is changed only when the temperature decreases from slice L ≈0:05  Re  d  Pr ð6Þ n to slice n + 1 or does not change. Therefore, the diameter th: canonly remainconstantor increase. In the following table, the constants used for the second- Figure 2 shows a flow chart of the CoDIR algorithm steps. order kinetics and the material properties for the product side are shown (Table 1): Solving the differential equations for a finite length dz. is Results and discussion beneficial for our model because the reactor is discretized into thin slices of a given thickness dz. The mass and heat balances An implementation of the algorithm previously described in are then solved numerically inside the slice over its thickness. the Methods section was developed (MATLAB). The process The differential equations are solved for a slice n based on conditions used as base parameters for the simulation are the initial conditions in the model. The results of slice n are the listed in Table 2. The reactor wall is assumed to be at a 250 Journal of Flow Chemistry (2022) 12:247–254 Table 2 Reference process conditions Parameter Value Unit T 20 °C T 20 °C C 3500 mol/m A0 C 3500 mol/m B0 C 0 mol/m C0 0.1 ml/min d 0.5 mm resemble a typical setup for fast, highly exothermic aromatic nitration, according to Westermann et al. [12]. Highly exother- mic aromatic nitration reactions are one example of reactions that can be performed very efficiently in microreactors [13]. Thedatapresented in Fig. 3 through Fig. 7 show the reactor behavior up to a 90% conversion. Additionally, a comparison between the results of the regular PFR and CoDIR is carried out. Figures 3 and 4 show the resulting temperature and con- version profiles for both scenarios. The resulting PFR has a volume of V =0.207 ml, while the CoDIR has a volume PFR of V =0.146 ml. Since for both cases, a constant flow rate CoDIR ˙ ml of V ¼ 0:1 is assumed, the reaction inside the CoDIR re- min sults in an overall shorter residence time of τ =87.6 s CoDIR compared to the residence time τ =124.1 s of the PFR. PFR As expected, the PFR shows a sharp temperature peak at the start, followed by a decrease in the reactor temperature due to the slowing down of the reaction while maintaining a very high heat removal. On the other hand, the CoDIR holds the temperature peak throughout the whole reactor at approxi- mately ϑ =25.6 ° C, resulting in a much shorter residence max time due to increased productivity according to the Arrhenius Fig. 2 Algorithm flow chart constant temperature of T =20° C. Together with the Fig. 3 Temperature vs. residence time for the CoDIR and PFR material properties in Table 1, the parameters were selected to Journal of Flow Chemistry (2022) 12:247–254 251 Fig. 4 Conversion vs. residence time for the CoDIR and PFR Fig. 6 Tube diameter vs. residence time for the CoDIR and PFR law. The CoDIR provides a much higher mean temperature diameter occurs, which successively balances the decrease in ϑ ¼ 25:6°C compared to ϑ ¼ 20:5°C while reducing CoDIR PFR generated heat from the reaction with a decrease in heat remov- the overall temperature fluctuation represented by the standard al through the reactor wall. The heat removal and generation for deviation σ =0.66 K and σ =0.88 K. This benefits CoDIR PFR both reactors can be found in the supporting material. the productivity and prevents the buildup of side products due An overall comparison of the test scenarios described in the to more uniform reaction conditions. Additionally, the conver- Methods section is shown in Table 3. The calculated space- sion profile also shows increased productivity along the reac- time yield for the CoDIR increases by approximately 42% for tor with an increased slope compared to the PFR after hitting the fictitious test reaction compared to the PFR, while the the peak temperature. residence time decreases by approximately 30%. This shows Figure 5 shows the change in the reactor diameter along the the overall effectiveness of the proposed approach. reactor length, while Fig. 6 also shows the reactor diameter plotted against the residence time. The much shorter reactor length and higher slope result from the volume of each new Reactor stability analysis volume element drastically increasing due to the increased di- ameter. Over the length of the CoDIR, a ninefold increase in the As described in the introduction, there exists a risk, especially for highly exothermic, fast reactions with high activation en- ergy, that during the startup of the reaction, an uncontrolled generation of heat occurs (thermal runaway). In this case, the generated heat exceeds the removed heat, which leads to an uncontrolled acceleration of the reaction and starts a feedback loop. The effect of thermal runaway can hold inherent safety risks due to pressure buildup leading to violent explosions. Especially in the case of flammable and highly toxic compo- nents, this scenario must be avoided [14, 15]. Since the con- cept of the CoDIR decreases heat removal with progressing Table 3 Comparison of the CoDIR and PFR simulation results L V τ STY m ml s kg/(m ·h) PFR 1.05 0.207 124.1 10960 CoDIR 0.0885 0.146 87.6 15540 Fig. 5 Tube diameter vs. reactor length for the CoDIR and PFR 252 Journal of Flow Chemistry (2022) 12:247–254 reactor length to reach higher productivity, the risk of thermal runaway could be amplified, creating unstable reaction condi- tions. This scenario is of particular concern, and insurance of safe reaction conditions during diameter extension was thor- oughly tested. The simulation, as described in the Methods section, was used to cover a change in the parameters listed in Table 4. The parameters were chosen according to their critical influence on heat removal and generation. A particular focus is placed on the effect of the activation energy with its strong nonlinear dependency within the Arrhenius law. In each simulation, the extracted optimum wall profile for the base case of the reactor was used. The base case parameters were varied for a 10 and 20% increase/decrease in the given parameter. Graphs for all parameter pairs can be found in the supporting material. None of the parameter studies presented resulted in a ther- mal runaway of the process. Therefore, a general stability of Fig. 7 Activation energy sweep, conversion vs. residence time the process can be concluded. Figure 7 shows a change in the activation energy of the reaction. To better view the tempera- ture peak, the y-axis was rescaled to start at 24.5 °C, although should be discussed to what extent the model assumptions the reaction starts at 20 °C. are appropriate and which limitations exist. The base case for the given wall profile shows a nearly A critical parameter in our model is the Nusselt number. As constant temperature after hitting the peak temperature. As the Reynolds number for the initial diameter of 0.5 mm is 1.4, expected for higher activation energies, the reaction acceler- the laminar flow edge case for a Nusselt number of 3.656 can ates much faster, leading to heat generation exceeding the heat be assumed. This results in a heat transmittance of 998 W/ removal and resulting in a higher maximum temperature. This (m K) for the initial diameter. In the case of heat transfer in leads to a higher conversion early on, followed by a decreased laminar flow regions, heat transport only occurs by thermal reaction rate afterward, explaining the undershooting com- conduction. Therefore, the Nusselt number for a laminar sys- pared to the base case. In contrast, a lower activation energy tem is the lowest possible value. Throughout the reactor, the leads to a lower temperature peak and overshooting of the Reynolds number further decreases as the volumetric flow rate temperature with progressing residence time. It is also clear is held constant and the diameter increases. Thus, safe opera- that for a 20% increase in the activation energy, there is no tion as a result of the ninefold diameter increase is not expect- thermal runaway, and stable reaction conditions are ensured. ed. Furthermore, for a real reactor system, the Nusselt number can be easily enhanced by inducing secondary flow with in- ternals such as static mixers, chicanes, or zigzag channels. Assuming fully developed hydrodynamic and thermal pro- Discussion of assumptions and limitations files for the entire reactor is applicable if the hydrodynamic and thermal entry lengths are significantly smaller than the Since the diameter of the CoDIR increases by a factor of total length of the reactor. Using Eq. (5), a hydrodynamic approximately 9 (from 0.5–4.6 mm) along the reactor, it entry length of 0.035 mm is calculated, and using Eq. (6), a Table 4 Overview of all parameters for the parametric sweeps E k Δ H V T C / C n a ref r W A,0 B,0 α 3 3 ml/s kJ/mol m /(mol·s) kJ/mol °C mol/m − −20% 40 1.60E-05 −120 0.08 16 2800 0.8 −10% 45 1.80E-05 −135 0.09 18 3150 0.9 base 50 2.00E-05 −150 0.1 20 3500 1 +10% 55 2.20E-05 −165 0.11 22 3850 1.1 +20% 60 2.40E-05 −180 0.12 24 4200 1.2 Journal of Flow Chemistry (2022) 12:247–254 253 thermal entry length of 1.6 mm is calculated. Both values are productivity increases while the occurrence of temperature several orders of magnitude smaller than the reactor length of peaks is reduced. Additionally, the proposed approach even approximately 89 mm [11]. With regard to heat transfer, com- offers the option to optimize the selectivity of complex reac- pared to the fully developed region, the thermal entrance re- tion systems. Different temperature zones could be created to gion shows an intensified heat transfer rate. inhibit specific side reactions based on deviating activation Notably, for a reactive system, the Nusselt number would energies. be higher than that predicted for the laminar edge case [3]. As The drawback is higher simulation efforts since the optimal a higher Nusselt number leads to a faster drop in temperature, reactor profile must be tailored to the dedicated reactions/pro- the risk of thermal runaway further decreases. cess. As a result, one becomes somewhat inflexible since Plug flow can only be assumed for tubular channels if small changes in the process require a new optimal wall pro- radial compared to axial diffusion is sufficiently high [16]. file to be simulated. Therefore, we propose a possible appli- In general, plug flow provides a good representation of the cation of the CoDIR in ongoing production processes to boost prevailing flow regime in microreactors due to small tube productivity while reducing temperature fluctuations. dimensions and therefore short radial diffusion paths com- Therefore, with technologies such as metal 3D printing, a pared to axial ones. The dispersion model describes the degree new flexible module can be derived. of local back mixing for laminar flow in circular microchannels [16]. Axial dispersion can be calculated ac- cording to Taylor & Aris as a function of the tube radius, the mean velocity, and the coefficient of molecular diffusion Conclusion [17–19]. As a result of the ninefold diameter increase through- out the CoDIR, the radial diffusion time increases by approx- A numeric one-dimensional model was developed based on imately a factor of 81 toward the end of the reactor [20]. the governing PFR equations, proposing an approach to in- Especially in the later stages of the CoDIR, plug flow behavior creasing the productivity of microreactors by a continuous can therefore probably only be achieved by enhancing radial diameter increase. The increase in diameter leads to an overall dispersion, e.g., by installing additional mixing elements such higher mean reaction temperature throughout the reactor while as static mixers [21, 22], chicanes [23], coiled flow inverters decreasing temperature fluctuations. The simulation results of [24, 25] or zigzag channels [26, 27]. the proposed CoDIR show an increase in space-time yield for Regarding mass transfer, the model assumes one ideally a fictitious reaction of approximately 42% compared to the mixed reactant phase. Therefore, the reaction rate is not lim- reference PFR. A parametric sensitivity study could confirm ited by mass transport and is only dependent on the intrinsic safe reaction conditions without thermal runaway, considering reaction kinetics. Since liquid phase nitration reactions often sensitive parameters in terms of heat generation and heat involve multiphase systems, mass transfer limitations affect removal. In conclusion, a reactor concept was proposed to the reaction kinetics and would have to be taken into account realize the full potential of microstructured devices in [13, 28]. terms of productivity. The complex shape of this Furthermore, a simplified fictitious second-order reaction microstructured device is easily achieved with today’s is used without side reactions taking place. The principle of 3D printing techniques or can be approximated with pipe the CoDIR can thus be illustrated in a manner that is segments of different diameters. decoupled from the chemistry. However, the improvements in productivity obtained in this way do not accurately repre- List of symbols c, concentration (mol/m ).; z, axial reactor coordinate sent the results obtained experimentally. A tendency toward (m).; r, radius (m).; u, velocity (m/s).; k, rate constant (m /(s mol)).; E , increased productivity, however, is also given in practice. activation energy (J/mol).; R, ideal gas constant (J/(mol K)).; T, temper- An independent parameter variation was performed to ature (K).; ρ, density (kg/m ).; Δ H, heat of reaction (J/mol).; c , heat r p evaluate the degree of parametric sensitivity. The results show capacity (J/(mol K)).; k , total heat transfer coefficient (W/(m K)).; d, diameter (m).; m , mass flow rate (kg/s).; L, length (m).; Re, Reynolds no thermal runaway among any of the tested variables. A number (−).; Pr, Prandtl number (−).; λ, heat conductivity (W/(m K)).; V sensitivity analysis, according to Semenov, Gray and , volumetric flow rate (m /s).; τ, residencetime(s).; σ, standard deviation Renken, is a widely accepted approach to quantify this partic- (−).; STY, space-time yield (kg/(h m )). ular problem [29, 30]. Because the traditional approach cannot Subscripts A, Substance A.; B, Substance B.; ref., Reference.; i, i-th represent the sensitivity of the CoDIR, an adapted approach slice.; W, Wall.; hyd., Hydrodynamic.; th., Thermal.; 0, initial value; CoDIR, Continuous diameter increase reactor.; PFR, Plug flow reactor. can be found in the supporting material. 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Continuous diameter increase reactor – a reactor concept for maximizing productivity by a controlled diameter extension

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Abstract

This paper presents a novel theoretical approach for maximizing productivity in microreactors by a controlled extension of the tube diameter. A one-dimensional numeric model was developed where the tube diameter increases based on the reaction heat to achieve a constant temperature throughout the reactor length. Through this approach, a basic plug flow reactor model for mass and heat transfer was used with an integrated algorithm for a controlled diameter extension. A parametric study was performed to ensure safe operating conditions concerning thermal runaway. The results show an increase in productivity of approximately 42% for the fictional second-order test reaction. . . . . . Keywords Microstructured reactors Tubular reactor Process intensification Process control Model-based scale-up Numerical evaluation Introduction tightly on the bottom plate to seal the microreactor channels [7]. The coiled tube, on the other hand, can be wound in Flow chemistry in microreactors offers many benefits over different configurations to increase the effect of Dean flow. conventional batch chemistry. The high surface-to-volume ra- A common approach is to change the direction of the winding tio provides high heat transfer coefficients, which are the key every couple of turns, as shown by the examples in [6]. to temperature control [1–3]. Improved temperature control The continuous improvement of additive manufacturing also translates into higher productivity, as an overall higher (3D printing) of metals, especially the reduced surface rough- process temperature can be achieved safely. In some in- ness, has allowed the printing of microstructured reactors with stances, increased selectivity can be achieved [4]. shapes and sizes previously unimaginable. Internal diameters Furthermore, this approach also allows process intensifica- of 0.6 mm are achievable using selective laser melting (SLM) tions and still guarantees a safe and controlled operation due [8, 9]. As a result of this study, a reactor shape is proposed that to minor hold-ups [1, 2, 5]. The small dimensions allow for could be easily achieved using modern additive manufactur- short diffusion paths and thus result in fast mixing [1, 3, 6]. ing techniques. Traditionally, microreactors were constructed either as a Inherently, tubular microreactors are not well suited for coiled tube or were milled from a plate of metal or glass. As very long reaction times. While the reaction rate is very high shown by several authors in [6, 7], several different micro- in the beginning due to the high concentration of the reactants, structures can be milled from a metal plate. For example, these it slows down rapidly toward the end as the concentration of microstructures include temporary diameter constrictions or the reactants decreases. This results in a rapid increase in con- baffles to improve mixing. To complete the construction of a version, high heat production for exothermic reactions and a microreactor, a second top plate is then pressed and screwed temperature rise at the beginning and a slow increase in con- version, decreasing heat production and a temperature de- crease toward the end. Additionally, the high surface-to- volume ratio of microstructures further benefits heat removal. * Thorsten Roeder t.roeder@hs-mannheim.de The Arrhenius law predicts slower reaction rates at lower tem- peratures, which inevitably results in changing process condi- Institute of Chemical Process Engineering, Mannheim University of tions along the reactor. In addition to the tendency of clog- Applied Sciences, Paul-Wittsack-Straße 10, ging, the most significant limiting factor of microstructured 68163 Mannheim, Germany 248 Journal of Flow Chemistry (2022) 12:247–254 reactors is the high pressure drop accompanying high volu- the approach can be seen in Fig. 1. In theory, this approach metric flow rates [2, 6]. should increase productivity while providing a constant tem- There are several approaches to choose from to overcome perature throughout the reactor. This temperature control is this weakness and provide more constant process conditions. especially beneficial for producing temperature-sensitive These approaches can either influence the concentration of the products such as nitroaromatic compounds, which are reactants or influence the temperature at which the reaction is temperature-sensitive and degrade exothermically. An in- taking place. A widespread way to manipulate the concentra- creased diameter also positively affects the pressure drop tion is by using a multi-injection solution, where the concen- and reduces the tendency of clogging. The presented approach tration of the reactant is increased successively at specific is not restricted to just one constant temperature profile. lengths of the reactor by injecting fresh reactants, thus increas- Additionally, any conceivable temperature profile can be em- ing the reaction rate. To influence the temperature at which the ployed to perform further optimizations, such as selectivity. reaction takes place, the reactor can be separated into different As presented in this paper, a numeric model was built for zones, each in a different temperature zone than the previous obtaining a tubular wall profile of the proposed continuous zone. For example, a coiled tube is immersed in different diameter increase reactor (CoDIR) introduced in Fig. 1.This cooling baths, each with a higher temperature than the previ- reactor shape was optimized for a specific exothermic reaction ous bath. based on specific system conditions with the goal of keeping The second option for optimizing the temperature profile in the temperature constant throughout the reactor. Afterward, the case of highly exothermic reactions is a stepwise increase we investigated this system for parametric sensitivity by sys- in the tube diameter at specific reactor lengths. As shown in tematically sweeping sensitive parameters. Fig. 1, this results in an abrupt decrease in heat removal ca- pacity, thus allowing the temperature to rise and the reaction rate to accelerate. This approach also reduces the equipment Methods needed to set up different temperature zones. With the goal of maintaining the process conditions, i.e., a constant tempera- To model the plug flow reactor (PFR), a fictional exothermic ture, the stepwise diameter increase could be applied in small organic liquid phase irreversible second-order reaction is cho- steps throughout the reactor length. A visual representation of sen. Fig. 1 Comparison between the stepwise tube diameter extension (top) and the continuous diameter increase reactor (CoDIR) (bottom) Journal of Flow Chemistry (2022) 12:247–254 249 Table 1 Material Properties A þ B− > C: Parameter Value Unit Furthermore, an ideal plug flow is assumed. This assump- R 8.314 J/(mol·K) tion is further discussed in the Results section. E 50.00 kJ/mol The mass balance is calculated as a change in concentration k (293.15 K) 2.00E-05 m /(mol·s) ref over a length. This formula is derived from the basic mass Δ H −150.0 kJ/mol balance formula found in [10]. ρ 786.4 kg/m dc r η 0.0023 Pa∙s ¼ ð1Þ dz u c 153.6 J/(kg·K) λ 0.1365 W/(m·K) The reactionratefor all componentsinthissystemis the same; it has a negative prefix for the starting materials as they are used up and a positive prefix for the product as it is initial conditions for slice n + 1. The very first slice is calcu- generated. lated with the chosen starting conditions. The solution con- The reaction rate r is calculated with the following equa- tinues until all slices are calculated. After that, the data are tions [10]: evaluated, and the reactor is cut after the slice where a 90% conversion rate is reached. r ¼ kc c ð2Þ A B 1 1 − − R T T i ref k ¼ k e ð3Þ ref Algorithm for the diameter extension calculation The temperature-dependent reaction rate is calculated by applying the Arrhenius law to the fictional reaction rate con- In the first step, the reaction system is solved for a regular PFR stant k at a temperature of 293.15 K. ref model with a constant diameter. The resulting maximum tem- The equation for the energy balance used here is modified perature is the benchmark temperature we aim to hold con- to use the density and mean flow velocity instead of the area in stant throughout the CoDIR. Therefore, we aim to achieve an the source part. The basic equation can be found in [10]. isothermal mode of operation for the model by increasing the dT rðÞ −ΔH k πdTðÞ −T R W W i diameter and thus decreasing the heat transfer coefficient due ¼ þ ð4Þ dz ρ u c to their reciprocal relationship. The temperature difference i p mc between the reference and the slice temperature is fed into a The flow inside the reactor is laminar with a very low PID controller, which subsequently calculates a new reactor Reynolds number; thus, a Nusselt number of 3.656, which shape for each slice. If the temperature of the slice is lower represents the edge case of laminar flow, is applied here. than the benchmark, then the output increases the diameter, This means that the heat transmittance k will be limited by W which leads to a temperature increase in the next slice. the heat transfer on the process side α , so the heat conduction i Alternatively, the slice diameter is calculated by solving Eq. through the tube wall and the heat transfer to the cooling liquid (4)with dT /dz = 0, as seen in the supporting material. In this can be neglected. publication, the PID approach is chosen because it opens the As shown in [11], the hydrodynamic and thermal entry opportunity to create even more complex temperature profiles, length can be estimated by the following Eqs. (5)and (6): such as several temperature zones along the reactor length. Furthermore, to avoid oscillations of the diameter, the diame- L ≈0:05  Re  d ð5Þ hyd: ter is changed only when the temperature decreases from slice L ≈0:05  Re  d  Pr ð6Þ n to slice n + 1 or does not change. Therefore, the diameter th: canonly remainconstantor increase. In the following table, the constants used for the second- Figure 2 shows a flow chart of the CoDIR algorithm steps. order kinetics and the material properties for the product side are shown (Table 1): Solving the differential equations for a finite length dz. is Results and discussion beneficial for our model because the reactor is discretized into thin slices of a given thickness dz. The mass and heat balances An implementation of the algorithm previously described in are then solved numerically inside the slice over its thickness. the Methods section was developed (MATLAB). The process The differential equations are solved for a slice n based on conditions used as base parameters for the simulation are the initial conditions in the model. The results of slice n are the listed in Table 2. The reactor wall is assumed to be at a 250 Journal of Flow Chemistry (2022) 12:247–254 Table 2 Reference process conditions Parameter Value Unit T 20 °C T 20 °C C 3500 mol/m A0 C 3500 mol/m B0 C 0 mol/m C0 0.1 ml/min d 0.5 mm resemble a typical setup for fast, highly exothermic aromatic nitration, according to Westermann et al. [12]. Highly exother- mic aromatic nitration reactions are one example of reactions that can be performed very efficiently in microreactors [13]. Thedatapresented in Fig. 3 through Fig. 7 show the reactor behavior up to a 90% conversion. Additionally, a comparison between the results of the regular PFR and CoDIR is carried out. Figures 3 and 4 show the resulting temperature and con- version profiles for both scenarios. The resulting PFR has a volume of V =0.207 ml, while the CoDIR has a volume PFR of V =0.146 ml. Since for both cases, a constant flow rate CoDIR ˙ ml of V ¼ 0:1 is assumed, the reaction inside the CoDIR re- min sults in an overall shorter residence time of τ =87.6 s CoDIR compared to the residence time τ =124.1 s of the PFR. PFR As expected, the PFR shows a sharp temperature peak at the start, followed by a decrease in the reactor temperature due to the slowing down of the reaction while maintaining a very high heat removal. On the other hand, the CoDIR holds the temperature peak throughout the whole reactor at approxi- mately ϑ =25.6 ° C, resulting in a much shorter residence max time due to increased productivity according to the Arrhenius Fig. 2 Algorithm flow chart constant temperature of T =20° C. Together with the Fig. 3 Temperature vs. residence time for the CoDIR and PFR material properties in Table 1, the parameters were selected to Journal of Flow Chemistry (2022) 12:247–254 251 Fig. 4 Conversion vs. residence time for the CoDIR and PFR Fig. 6 Tube diameter vs. residence time for the CoDIR and PFR law. The CoDIR provides a much higher mean temperature diameter occurs, which successively balances the decrease in ϑ ¼ 25:6°C compared to ϑ ¼ 20:5°C while reducing CoDIR PFR generated heat from the reaction with a decrease in heat remov- the overall temperature fluctuation represented by the standard al through the reactor wall. The heat removal and generation for deviation σ =0.66 K and σ =0.88 K. This benefits CoDIR PFR both reactors can be found in the supporting material. the productivity and prevents the buildup of side products due An overall comparison of the test scenarios described in the to more uniform reaction conditions. Additionally, the conver- Methods section is shown in Table 3. The calculated space- sion profile also shows increased productivity along the reac- time yield for the CoDIR increases by approximately 42% for tor with an increased slope compared to the PFR after hitting the fictitious test reaction compared to the PFR, while the the peak temperature. residence time decreases by approximately 30%. This shows Figure 5 shows the change in the reactor diameter along the the overall effectiveness of the proposed approach. reactor length, while Fig. 6 also shows the reactor diameter plotted against the residence time. The much shorter reactor length and higher slope result from the volume of each new Reactor stability analysis volume element drastically increasing due to the increased di- ameter. Over the length of the CoDIR, a ninefold increase in the As described in the introduction, there exists a risk, especially for highly exothermic, fast reactions with high activation en- ergy, that during the startup of the reaction, an uncontrolled generation of heat occurs (thermal runaway). In this case, the generated heat exceeds the removed heat, which leads to an uncontrolled acceleration of the reaction and starts a feedback loop. The effect of thermal runaway can hold inherent safety risks due to pressure buildup leading to violent explosions. Especially in the case of flammable and highly toxic compo- nents, this scenario must be avoided [14, 15]. Since the con- cept of the CoDIR decreases heat removal with progressing Table 3 Comparison of the CoDIR and PFR simulation results L V τ STY m ml s kg/(m ·h) PFR 1.05 0.207 124.1 10960 CoDIR 0.0885 0.146 87.6 15540 Fig. 5 Tube diameter vs. reactor length for the CoDIR and PFR 252 Journal of Flow Chemistry (2022) 12:247–254 reactor length to reach higher productivity, the risk of thermal runaway could be amplified, creating unstable reaction condi- tions. This scenario is of particular concern, and insurance of safe reaction conditions during diameter extension was thor- oughly tested. The simulation, as described in the Methods section, was used to cover a change in the parameters listed in Table 4. The parameters were chosen according to their critical influence on heat removal and generation. A particular focus is placed on the effect of the activation energy with its strong nonlinear dependency within the Arrhenius law. In each simulation, the extracted optimum wall profile for the base case of the reactor was used. The base case parameters were varied for a 10 and 20% increase/decrease in the given parameter. Graphs for all parameter pairs can be found in the supporting material. None of the parameter studies presented resulted in a ther- mal runaway of the process. Therefore, a general stability of Fig. 7 Activation energy sweep, conversion vs. residence time the process can be concluded. Figure 7 shows a change in the activation energy of the reaction. To better view the tempera- ture peak, the y-axis was rescaled to start at 24.5 °C, although should be discussed to what extent the model assumptions the reaction starts at 20 °C. are appropriate and which limitations exist. The base case for the given wall profile shows a nearly A critical parameter in our model is the Nusselt number. As constant temperature after hitting the peak temperature. As the Reynolds number for the initial diameter of 0.5 mm is 1.4, expected for higher activation energies, the reaction acceler- the laminar flow edge case for a Nusselt number of 3.656 can ates much faster, leading to heat generation exceeding the heat be assumed. This results in a heat transmittance of 998 W/ removal and resulting in a higher maximum temperature. This (m K) for the initial diameter. In the case of heat transfer in leads to a higher conversion early on, followed by a decreased laminar flow regions, heat transport only occurs by thermal reaction rate afterward, explaining the undershooting com- conduction. Therefore, the Nusselt number for a laminar sys- pared to the base case. In contrast, a lower activation energy tem is the lowest possible value. Throughout the reactor, the leads to a lower temperature peak and overshooting of the Reynolds number further decreases as the volumetric flow rate temperature with progressing residence time. It is also clear is held constant and the diameter increases. Thus, safe opera- that for a 20% increase in the activation energy, there is no tion as a result of the ninefold diameter increase is not expect- thermal runaway, and stable reaction conditions are ensured. ed. Furthermore, for a real reactor system, the Nusselt number can be easily enhanced by inducing secondary flow with in- ternals such as static mixers, chicanes, or zigzag channels. Assuming fully developed hydrodynamic and thermal pro- Discussion of assumptions and limitations files for the entire reactor is applicable if the hydrodynamic and thermal entry lengths are significantly smaller than the Since the diameter of the CoDIR increases by a factor of total length of the reactor. Using Eq. (5), a hydrodynamic approximately 9 (from 0.5–4.6 mm) along the reactor, it entry length of 0.035 mm is calculated, and using Eq. (6), a Table 4 Overview of all parameters for the parametric sweeps E k Δ H V T C / C n a ref r W A,0 B,0 α 3 3 ml/s kJ/mol m /(mol·s) kJ/mol °C mol/m − −20% 40 1.60E-05 −120 0.08 16 2800 0.8 −10% 45 1.80E-05 −135 0.09 18 3150 0.9 base 50 2.00E-05 −150 0.1 20 3500 1 +10% 55 2.20E-05 −165 0.11 22 3850 1.1 +20% 60 2.40E-05 −180 0.12 24 4200 1.2 Journal of Flow Chemistry (2022) 12:247–254 253 thermal entry length of 1.6 mm is calculated. Both values are productivity increases while the occurrence of temperature several orders of magnitude smaller than the reactor length of peaks is reduced. Additionally, the proposed approach even approximately 89 mm [11]. With regard to heat transfer, com- offers the option to optimize the selectivity of complex reac- pared to the fully developed region, the thermal entrance re- tion systems. Different temperature zones could be created to gion shows an intensified heat transfer rate. inhibit specific side reactions based on deviating activation Notably, for a reactive system, the Nusselt number would energies. be higher than that predicted for the laminar edge case [3]. As The drawback is higher simulation efforts since the optimal a higher Nusselt number leads to a faster drop in temperature, reactor profile must be tailored to the dedicated reactions/pro- the risk of thermal runaway further decreases. cess. As a result, one becomes somewhat inflexible since Plug flow can only be assumed for tubular channels if small changes in the process require a new optimal wall pro- radial compared to axial diffusion is sufficiently high [16]. file to be simulated. Therefore, we propose a possible appli- In general, plug flow provides a good representation of the cation of the CoDIR in ongoing production processes to boost prevailing flow regime in microreactors due to small tube productivity while reducing temperature fluctuations. dimensions and therefore short radial diffusion paths com- Therefore, with technologies such as metal 3D printing, a pared to axial ones. The dispersion model describes the degree new flexible module can be derived. of local back mixing for laminar flow in circular microchannels [16]. Axial dispersion can be calculated ac- cording to Taylor & Aris as a function of the tube radius, the mean velocity, and the coefficient of molecular diffusion Conclusion [17–19]. As a result of the ninefold diameter increase through- out the CoDIR, the radial diffusion time increases by approx- A numeric one-dimensional model was developed based on imately a factor of 81 toward the end of the reactor [20]. the governing PFR equations, proposing an approach to in- Especially in the later stages of the CoDIR, plug flow behavior creasing the productivity of microreactors by a continuous can therefore probably only be achieved by enhancing radial diameter increase. The increase in diameter leads to an overall dispersion, e.g., by installing additional mixing elements such higher mean reaction temperature throughout the reactor while as static mixers [21, 22], chicanes [23], coiled flow inverters decreasing temperature fluctuations. The simulation results of [24, 25] or zigzag channels [26, 27]. the proposed CoDIR show an increase in space-time yield for Regarding mass transfer, the model assumes one ideally a fictitious reaction of approximately 42% compared to the mixed reactant phase. Therefore, the reaction rate is not lim- reference PFR. A parametric sensitivity study could confirm ited by mass transport and is only dependent on the intrinsic safe reaction conditions without thermal runaway, considering reaction kinetics. Since liquid phase nitration reactions often sensitive parameters in terms of heat generation and heat involve multiphase systems, mass transfer limitations affect removal. In conclusion, a reactor concept was proposed to the reaction kinetics and would have to be taken into account realize the full potential of microstructured devices in [13, 28]. terms of productivity. The complex shape of this Furthermore, a simplified fictitious second-order reaction microstructured device is easily achieved with today’s is used without side reactions taking place. The principle of 3D printing techniques or can be approximated with pipe the CoDIR can thus be illustrated in a manner that is segments of different diameters. decoupled from the chemistry. However, the improvements in productivity obtained in this way do not accurately repre- List of symbols c, concentration (mol/m ).; z, axial reactor coordinate sent the results obtained experimentally. A tendency toward (m).; r, radius (m).; u, velocity (m/s).; k, rate constant (m /(s mol)).; E , increased productivity, however, is also given in practice. activation energy (J/mol).; R, ideal gas constant (J/(mol K)).; T, temper- An independent parameter variation was performed to ature (K).; ρ, density (kg/m ).; Δ H, heat of reaction (J/mol).; c , heat r p evaluate the degree of parametric sensitivity. The results show capacity (J/(mol K)).; k , total heat transfer coefficient (W/(m K)).; d, diameter (m).; m , mass flow rate (kg/s).; L, length (m).; Re, Reynolds no thermal runaway among any of the tested variables. A number (−).; Pr, Prandtl number (−).; λ, heat conductivity (W/(m K)).; V sensitivity analysis, according to Semenov, Gray and , volumetric flow rate (m /s).; τ, residencetime(s).; σ, standard deviation Renken, is a widely accepted approach to quantify this partic- (−).; STY, space-time yield (kg/(h m )). ular problem [29, 30]. Because the traditional approach cannot Subscripts A, Substance A.; B, Substance B.; ref., Reference.; i, i-th represent the sensitivity of the CoDIR, an adapted approach slice.; W, Wall.; hyd., Hydrodynamic.; th., Thermal.; 0, initial value; CoDIR, Continuous diameter increase reactor.; PFR, Plug flow reactor. can be found in the supporting material. 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Journal

Journal of Flow Chemistry – Springer Journals

Published: Sep 1, 2022

Keywords: Microstructured reactors; Tubular reactor; Process intensification; Process control; Model-based scale-up; Numerical evaluation

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