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Software-guided microscale flow calorimeter for efficient acquisition of thermokinetic data

Software-guided microscale flow calorimeter for efficient acquisition of thermokinetic data Fast chemical process development is inevitably linked to an optimized determination of thermokinetic data of chemical reactions. A miniaturized flow calorimeter enables increased sensitivity when examining small amounts of reactants in a short time compared to traditional batch equipment. Therefore, a methodology to determine optimal reaction conditions for calori- metric measurement experiments was developed and is presented in this contribution. Within the methodology, short-cut calculations are supplemented by computational fluid dynamics (CFD) simulations for a better representation of the hydrody- namics within the microreactor. This approach leads to the effective design of experiments. Unfavourable experimental condi- tions for kinetics experiments are determined in advance and therefore, need not to be considered during design of experiments. The methodology is tested for an instantaneous acid-base reaction. Good agreement of simulations was obtained with experi- mental data. Thus, the prediction of the hydrodynamics is enabled and the first steps towards a digital twin of the calorimeter are performed. The flow rates proposed by the methodology are tested for the determination of reaction enthalpy and showed that reasonable experimental settings resulted. . . . . Keywords Continuous reaction calorimetry Flow chemistry CFD simulation Microreaction technology Design of experiments Digital twin Introduction development of continuous flow calorimeter increases con- stantly [5–8]. Moreover, the miniaturization of calorimetry Continuously operated processes feature higher yields and enables the investigation of fast and highly exothermic reac- selectivity, facilitate process automation, reduce the ecologi- tions under safe conditions due to the superior temperature cal footprint and offer shorter process development times controlwhencomparedtostandardbatchequipment[9]. [1–3]. For the development of accurate kinetic models that Traditionally, thermokinetic data is experimentally obtained assist chemical reactor development, design and optimization, during process development using mostly batch equipment. extensive knowledge of interaction between reaction kinetics These studies provide reliable information about the physical and hydrodynamics is essential [4]. Thus, the interest in the processes. Yet, only limited information is obtained about the dynamic behavior within the reactor performing those exper- iments. Efficiency and effectiveness of process development Highlights can be increased by digitalization of research and develop- � Development of a methodology for selecting suitable kinetics ment [10]. The systematical use of simulation tools such as experiments. � Good agreement of simulations with experimental data validates the computational fluid dynamics (CFD) is essential to overcome CFD model. challenges related to experimental measurements and to opti- � Number of possible experimental settings has been halved. mize real processes [10, 11]. Thus, information regarding tran- sient flow behavior, velocity, pressure and concentration * Timothy Aljoscha Frede fields is gained and can be used to reduce the number of Timothy.Frede@tu-dortmund.de experiments. Once the model has been validated, process per- formance can be predicted under different flow conditions, Department of Biochemical and Chemical Engineering, Laboratory reactant concentrations and reactor configurations [11, 12]. of Equipment Design, TU Dortmund University, Emil-Figge-Straße The efficient combination of CFD and experiments for 68, 44227 Dortmund, Germany 322 J Flow Chem (2021) 11:321–332 evaluation of microreactor performance for fast and exother- previously used ones. The microreactor is made of glass and mic reactions has already been shown by Asano et al. [13]. features a Y-mixer to contact the incoming fluids and 19 chi- In this work, a methodology is developed for the selection cane mixers to improve mixing. The hydraulic diameter at the of experiments in a continuous flow calorimeter during chem- smallest cross-sectional area within the reactor is 1 mm, which ical process development aiming a time and cost-efficient ac- is used for the subsequent calculations. quisition of thermokinetic data. The methodology enables The technical data of the employed microreactor and sy- choosing the optimal reaction conditions out of the entire pos- ringe pumps is given in Table 1. sible range of experimental parameters of the calorimeter rath- er than performing full factorial design of experiment. Thus, Evaluation of optimal reaction conditions optimal designs of experiments are determined, which offer maximal information gain with minimal effort. Finally, the The methodology focusses on the evaluation of optimal reac- proposed experimental settings are tested for the determina- tion conditions, which are suited for continuous calorimetric tion of the reaction enthalpy of a test reaction. measurement experiments. The basis for this methodology is the approach of Krasberg et al. [16], who developed a meth- odology to select plug flow equipment for a modular and continuous small-scale plant. A schematic overview of the Materials and Methods stepwise methodology is shown in Fig. 2. The methodology includes CFD simulations complemented Calorimeter and experimental setup by short-cut methods. The methodology is a stepwise approach, in which the demand of data increases with the sequence of the The calorimeter’s setup and its peripheral equipment have steps. However, the possibility to restrict the experimental been described in previous works of Reichmann et al. [14, design space is also increasing. In the following, the available 15]. A central programmable logic controller (PLC) information is described with the individual steps of the (LabManager , HiTec Zang GmbH, Germany) has been methodology. added to the experimental setup to automate the execution of calibration and experiments. The current setup and the employed microreactor (type*-S, HTM series, Little Things Input data Factory GmbH, Germany) are displayed in Fig. 1.Compared to the setup in [15], only four Peltier elements are used here, The input data sets represent the basis for the subsequent steps. In whose projection area is about 4.5 times larger than the this study, reaction conditions are proposed based on the Fig. 1 a Experimental setup for continuous reaction calorimetry pump and thermostat for tempering the base plate. b Microreactor within ® 2 consisting of laboratory automation system (LabManager ), syringe the reaction calorimeter with four Peltier elements (15 × 15 mm ), which pumps for feeding, preheating thermostat, calorimeter itself with a gear are positioned on the base plate J Flow Chem (2021) 11:321–332 323 Table 1 Technical data of the device data type symbol unit value comment microreactor and the pumps used type*-S geometries V mL 0.10 d mm 1.00 d = d h h i ™ -1 SyrDos 2 possible flow rates V mL min 0.5 limited by min -1 V mL min 6.00 syringes used in max the pumps chemical reaction to be investigated and the used microreactor. Step 2: Pressure drop For the chemical reaction system, information regarding the physical properties of the reaction mixture in terms of The pressure drop represents a technical criterion. Among density, viscosity and diffusivity is required or has to be estimat- others, the reactor itself and the pumps limit the maximum ed. In addition, a rough classification of the reaction kinetics permissible pressure loss. The pressure is expected to be supports the methodology. The microreactors are defined regard- highest at the reactor inlet. The pressure drop can be calculated ing their geometries and allowed operation conditions. Since using generalized models, as shown in Eq. 2 [18]. commercially available microreactors are employed, this infor- mation is provided by the manufacturer. l ρ Δp ¼ λ þ !  w ð2Þ i i i i d 2 h;i Step 1: Residence time However, the friction factor λ and the influence of second- ary flow patterns ! have to be determined for each The residence time of fluids within microstructured devices is microreactor. For this purpose, microreactors are characterized in the order of seconds or less, which can be detrimental to slow using semi-empirical pressure drop modeling [19]. The Dean reactions [17]. Thus, the residence time is a crucial factor for number Dn is used to characterize the influence of secondary the successful investigation of chemical reactions in continu- flow profiles which are the result of centrifugal forces. In ously operated reactors. In case of insufficient residence time, Eq. 3,the channel’s curvature is expressed by d .[20] complete conversion cannot be guaranteed, which reduces the sffiffiffiffiffi quality of the information gained during calorimetric measure- Dn ¼ Re ð3Þ ment. Otherwise, excessive residence times and broad resi- dence time distributions promote side or subsequent reactions, which negatively influence the selectivity and yield. The hy- In order to improve the determination of the pressure drop and draulic residence time  is calculated dividing the reaction later the mixing performance, the microreactor’s hydrodynamics volume V by the volumetric flow rate V, shown in Eq. 1. including the pressure drop are estimated using CFD simulations. Steady state CFD simulations are carried out for incompressible, ¼ ð1Þ single-phase flow through the microreactor using the open source software OpenFOAM. The solver icoFoam is used to investigate The range of possible volumetric flow rates is determined the hydrodynamics, which is completed by a passive scalar for by the pumps used in the experimental setup. The reactor solute transport. The data obtained is analyzed regarding the pressure drop as a function of volumetric flow rate. volume is obtained from the microreactor’sgeometry. Fig. 2 Methodology to evaluate optimal reaction conditions for efficient acquisition of kinetic data, where the experimental design space is limited by the stepwise determination of important time scales based on specified input data 324 J Flow Chem (2021) 11:321–332 Step 3: Time scales ˙ ˙ V V 1 2 2 σ ðÞ c ¼ ðÞ c  c ð9Þ ˙ 1 2 V;max Besides the residence time, mixing of reactants and its corre- ˙ ˙ V þ V 1 2 sponding time scale are decisive during chemical transforma- tion [21, 22]. Thus, the determination of mixing time scales is i t ¼ ð10Þ mix;CFD of great interest, especially in different microreactors. w Theoretically, laminar flow prevails in microreactors, Besides the mixing time scale, the characteristic reaction since Re < 2300 [23]. However, secondary flow patterns time is an important quantity in process engineering [28]. The such as Dean flow and engulfment are found in bend reaction time can be estimated using the reaction order m,the channels for Re > 100, which greatly enhance mixing [9, 24, starting concentration of the limiting component c and the A0 25]. A theoretical mixing time can be estimated roughly using reaction rate constant k, which is influenced by temperature, a short-cut method considering micromixing by engulfment shown in Eq. 11. [26]. For this purpose, a power law relationship between energy dissipation rate and mixing time was presented by t ¼ ð11Þ m1 Falk and Commenge [27]. The mixing time depends on the kTðÞ c A0 mean kinematic viscosity of the reaction medium, the energy dissipation rate  and a pre-factor matching the engulfment Since kinetic data is not available at this point, an educated guess based on similar reactions or heuristics for classification theory, shown in Eq. 5. The energy dissipation rate is defined of the reaction can be used to estimate the reaction rate con- in Eq. 6 with volumetric flow rateV , pressure drop Δp ,the tot i stant. A classification of the reaction according to Roberge mean fluid’sdensity ρ and the dissipation volume V .The [29] and Kashid et al. [9] allows for roughly estimating the pressure drop for these calculations is obtained from CFD reaction time. However, the educatedguess based experience simulations in step 2. and intuition play an eminent role at this stage of process d w development. In this case, the methodology has to be started Re ¼ ð4Þ with the operator assuming certain kinetic data. Since the goal 1=2 of the method is initially only to stake out the experimental t ¼ 17:3 ð5Þ mix;i design space, a rough estimate is sufficient for now. Based on this data, short test trials must be performed to check whether Δp V complete conversion is achieved in the reactor. If this is not ¼ ð6Þ ρV the case, the constraint for the reaction time must be adjusted iteratively. The exact kinetic data will then be determined by Besides the estimation using the short-cut method, the the experiments and subsequently, CFD simulations can be mixing performance of the microreactor is characterized using performed with the experimentally determined data to validate the CFD model. Therefore, the variance of the concentration the model for future applications. For optimal reaction condi- profile of the solute is evaluated at several cross sections of the tions and consequently optimal results, the three characteristic mixing channel. Since the flow velocity varies over the cross times of residence  ,mixing t and reaction t have to be i mix;i R section, the velocity-weighted mixing quality  is used for a V designed properly. Complete conversion within the microreactor better representation of the flow situation, shown in Eq. 7.In can be assumed, if both the mixing and reaction time are faster Eq. 8, the concentration c at a grid point is weighted with the than the mean residence time. Furthermore, two regimes can be velocity w at this grid point, and the mean velocity w with the distinguished. In a reaction-dominated regime, mixing time is cross section A . Based on the position of complete mixing, faster than reaction time, while in a mixing-dominated regime, the corresponding channel length l and the mixing time it is opposite. Experimental settings are rated as suitable if the t can be determined by dividing the obtained channel mix;CFD arrangement of the characteristic times follows the proposed length with the mean velocity, shown in Eq. 10.[28] sequence. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ ðÞ c ¼ 1  ð7Þ ˙ Experimental settings σ ðÞ c V;max The resulting constraints regarding the reaction and flow con- c w dA 1 i i 2 M ditions are visualized within a parameter plot to determine σ ðÞ c ¼ c  wdA ð8Þ ˙ i A w w dA M A i M suitable experimental settings, which is shown exemplarily in Fig. 3 J Flow Chem (2021) 11:321–332 325 hydroxide (NaOH) - is used to demonstrate the functionality of the presented methodology. Sen et al. [30] also investigated this model reaction for calorimetry using CFD for the devel- opment of a microfluidic reaction calorimeter. The thermokinetic parameters, which were determined experimen- tally, are given in Table 2. For nearly equimolar conditions, the neutralization reaction follows a second-order kinetics. [31] þ  þ  þ H Cl þ Na OH ! H O þ Na Cl ð12Þ Since aqueous solutions of HCl and NaOH with concen- trations of 1.0 M and 1.1 M respectively are used in this study, the physical properties of water are used in the short-cut cal- culations and in the advanced CFD calculations. The binary diffusion coefficient D is obtained from Dortmund Data Bank –10 2 -1 with a value of 9.6∙10 m s . Fig. 3 Qualitative representation of the experimental design space to evaluate suitable experimental settings for calorimetric measurements as function of temperature and volumetric flow rate. The constraints result Results and discussion from the steps of the presented methodology. In this section, the results of the performance of the individual Three conditions are essential to span the experimental de- steps are presented to determine suitable experimental settings sign space: for the investigation of the neutralization reaction. Subsequently, the obtained reaction conditions are tested and & ranges and discrete step sizes of the experimental the CFD model is validated using this experimental data. parameters & values for operating constraints & values of the constraints as a function of the experimental Case study, step 1: Residence time parameters At first, the possible range of residence time is checked for the Consequently, suitable experimental settings are located investigated reactor and syringe pumps used in the experimen- inside the constraints. The resulting settings are translated into tal setup. According to Eq. 1 and Table 1, the combination of control commands for the calorimeter, e.g. into settings of the microreactor and pumps provides a residence time between pumping system to adjust the volumetric flow rate to achieve a =0.5 sand  =6.0 s. min max specific residence time. Therefore, the experimental settings are transferred via Open Platform Communications (OPC) Case study, step 2: Pressure drop Unified Architecture (UA) to the PLC, which controls the whole experimental setup. The hydrodynamics in the reactor, and thus the pressure drop, too, are calculated on the basis of CFD simulations. Pressure Determination of thermokinetic data drops within the microreactor are displayed in Fig. 4 for vary- ing volumetric flow rates. In this step, the control commands for the calorimeter are In general, the pressure drop increases for higher volumet- executed automatically using the PLC and subsequently, the ric flow rates. A second-order polynomial, as described by the measured values are evaluated. Currently, the calorimeter is Darcy-Weisbach equation, matches the data according to operated in isoperibolic mode. The calorimetric measurement Eq. 2 with the highest coefficient of determination of R =1. method has been described by Reichmann et al. [14]and is used here to determine the reaction enthalpy. Table 2 Kinetic data of neutralization reaction of hydrochloric acid and sodium hydroxide. [31] Case Study -1 -1 -1 -1 k [L mol s]E [J kmol ] Δh [kJ mol]m[-] 0 A r 11 6 A well-known, exothermic reaction from the literature - acid- 1.69∙10 3.33∙10 -57.6 2 base reaction of hydrochloric acid (HCl) and sodium 326 J Flow Chem (2021) 11:321–332 Fig. 4 Simulated values for pressure drop over volumetric flow rates for Fig. 5 Energy dissipation rates over volumetric flow rates based on CFD the type*-S microreactor (HTM series, Little Things Factory GmbH) results for the type* -S microreactor (HTM series, Little Things Factory GmbH) The pressure drop ranges from 0.07 to 15.78 mbar, corre- −1 sponding to volumetric flow rates of 1–12 mL min ,flow The energy dissipation rate increases with higher flow −1 velocities of 21.22 to 254.65 mm s and Reynolds numbers rates. For higher flow rates, the cubic relationship between of 23 to 285, respectively. Pressure loss caused by piping, energy dissipation and volumetric flow rate becomes appar- which was not considered within the CFD simulations, was ent, as the velocity enters Eq. 6 to the power of three. estimated using Hagen-Poiseuille equation and resulted in a Subsequently, the velocity-weighted mixing quality is deter- maximum loss of 0.2 mbar for the highest possible flow rate. mined at various cross sections within the microreactor for the Hence, this pressure loss is negligible compared to the loss respective flow rates, shown in Fig. 6. The cross sections are induced by the reactor. located in the middle of the straight part behind the chicane mixer. Case study, step 3: Times scales In general, the mixing quality increases with increasing At first, the energy dissipation rates are calculated based on distance from the reactor inlet and with increasing flow rate. Additionally, three distinct regimes can be observed. For the CFD results and displayed for varying flow rates in Fig. 5. Fig. 6 a Allocated position of cross sections within the microreactor for the evaluation of the mixing quality. b Velocity- weighted mixing quality over al- located position of cross sections within the microreactor for vary- ing volumetric flow rates c Concentration profile of NaOH −1 for ˙V = 8 mL min in the type*- S microreactor (HTM series, Little Things Factory GmbH). Simulations using icoFoam, postprocessing in ParaView. J Flow Chem (2021) 11:321–332 327 Table 3 Positions and corresponding channel lengths of complete a limit must be set for the mixing quality at which the mixing derived from CFD simulations mixture is considered completely mixed for the -1 microreactor used in this work. As can be seen in Fig. 6b, ˙V [mL min ] Position [-] Channel length [mm] a plateau of the mixing quality is reached within the reactor <6 - - −1 −1 ˙ ˙ only for V  8mL min .For V  6mLmin , the mixing 814 52.98 quality continues to increase along the reactor channel and does 10 19 72.98 not reach an almost constant value. Based on this observation, 12 11 40.98 the limit for the mixing quality is set so that complete mixing is only assumed for the last three volume flows. Thus, complete - indicates no complete mixing within the reactor mixing within the reactor is assumed from the cross-sectional area at which a limiting value of   0.95 is reached. The ˙V − 1 ˙ positions and corresponding channel lengths of complete V  3mLmin , the mixing quality increases almost mixing are given in Table 3. The results presented are in good linearly along the reactor coordinate. In this regime, the agreement with the study of Khaydarov et al. [34]onareactor Reynolds and the corresponding Dean number are com- with the same mixing structure. Especially the presented flow paratively small (Re  75 and Dn  50) and mixing is regime could also be observed here at the investigated assumed to be dominated by diffusion. Hence, the maximum Reynolds numbers. achieved mixing quality  remains below 0.6. However, the Table 3 shows that the channel length, at which complete slope of the mixing quality increases significantly for 4 and 6 mixing is achieved, does not consistently decrease with in- −1 mL min . For these volumetric flow rates, the Dean number creasing volume flow. This observation is due to the flow takes values of 67 and 100 respectively. Thus, secondary flow behavior at different flow rates. Figure 7 illustrates the stream- patterns can be assumed, which lead to improved convective lines within the first nine chicane mixers. mixing. According to Ligrani [32], Dean vortices are expected According to Fig. 7, the vortex regime is observed for the to be fully developed and stable for Dn > 64 and thus, mixing displayed flow rates. However, a slightly different flow behav- is greatly enhanced. This can also be derived from the higher −1 − 1 ˙ ˙ ior is evident between V =8mL min and V =10mLmin . mechanical energy consumption, which can be seen in the −1 −1 ˙ For V = 8 mL min , the streamlines in the middle of the energy dissipation rate graph. ForV  8mLmin , the course channel are stronger, which can be seen in a darker coloring. of mixing quality is almost identical. Re and Dn are relatively Thus, mixing in this area is improved compared to the flow high with Re  190 and Dn  134. For Re > 150, the mixing − 1 behavior ofV =10mLmin . The renewed increase in mixing performance of chicane mixers is significantly enhanced due −1 to stable vortex generation and mixing quality increases no- quality forV =12mLmin is due to the stronger expression of ticeably [33]. Based on these results, complete mixing within the vortices within the recirculation zones. − 1 Figure 8 displays the mixing times plotted over the corre- the reactor is assumed for V  8mLmin . sponding energy dissipation rate using the short-cut method Subsequently, the mixing time is calculated based on and the CFD model. the results of the mixing performance. For this purpose, Fig. 7 Simulated streamlines for different volumetric flow rates of − 1 8, 10 and 12 mL min (Re=190, 237 and 285). Postprocessing in ParaView 328 J Flow Chem (2021) 11:321–332 Fig. 8 Mixing time scale plotted over energy dissipation rates with power Fig. 9 Residence and mixing time over volumetric flow rates law trend line that fits the data of the short-cut method and the CFD simulations Model validation In order to validate the CFD results, the data obtained is com- In general, mixing times decrease with increasing energy pared with experimental measurements. The pressure was dissipation rates. Furthermore, the values of both calculations measured at reactor inlet and outlet via a T-shaped fitting are in the same order of magnitude for the respective flow using pressure sensors (type A-10, WIKA Alexander rates. Using the short-cut method, the mixing times are be- Wiegand SE & Co. KG, Germany). In Fig. 10, the pressure tween 0.37 and 5.28 s and those of the CFD simulations be- drop is plotted over the volumetric flow rate. tween 0.16 and 0.34 s. For the CFD results, the coefficient of As observed, the pressure drop obtained with CFD is in determination shows a relative low value with 0.59 for the good agreement with the experimental pressure drop. data fitting power law trend line. Additionally, the exponent In a next step, the CFD and experimental mixing times are with a value ofn= 0.62 differs from the theoretical value ofn= compared. Experimental mixing times were determined optically 0.5 [27]. The deviations between the CFD simulations and the and from heat flux profiles by Reichmann et al. [15]. The mixing literature are probably due to the setting of the limiting value times for different volumetric flow rates are shown in Fig. 11. for complete mixing. Moreover, the need for a detailed char- In general, the mixing time obtained with CFD is in a acterization of the hydrodynamics is illustrated by the fact that relatively good agreement with the experimental mixing the short-cut calculates mixing times for each flow rate, time. However, a larger deviation of 0.16 s can be seen whereas the simulations show that complete mixing cannot −1 for V =10 mLmin , which has been discussed on the −1 be achieved for V  6mL min . Subsequently, the characteristic reaction time of the neutral- ization reaction is calculated. According to Eq. 11 and the ki- − 11 netic data from Table 2, the reaction time t is 2.6∙10 s. This is consistent with the literature, as the ion reaction of a proton and a hydroxide ion to form a water belongs to quasi- instantaneous reactions [35]. Since the reaction time will always be shorter than the mixing time in this case, a mixing- dominated regime prevails. If reaction time exceeded the resi- dence time, the selected reactor would not be suitable for the investigated reaction. In this case, another reactor needs to be selected from the database, which, depending on the limitation, either mixes faster or offers more residence time. Figure 9 dis- plays the mixing and residence time over volumetric flow rates. Figure 9 shows that the time scales are designed properly −1 only for V  8mLmin . Therefore, only with these settings, complete conversion can be expected and thus the Fig. 10 Comparison of CFD and experimental pressure drop over information content is at its maximum. volumetric flow rates J Flow Chem (2021) 11:321–332 329 Fig. 12 Comparison of CFD and experimental mixing time over energy Fig. 11 Comparison of CFD and experimental mixing time over dissipation rates with adjusted limit for complete mixing of   0:8: volumetric flow rates ˙V − 1 basis of the flow behavior. For V =6 mL min ,no com- By adjusting the limit, complete mixing is also achieved for − 1 plete mixing within the reactor is calculated by CFD. 4and6 mL min using CFD model. Since experimental and Moreover, complete mixing was also observed experi- CFD results are generally in good agreement, the CFD model −1 mentally for V = 1 mL min with a mixing time of a can be used to determine suitable experimental settings in the 3.57 s. Due to the low Reynolds number (Re=23), mixing is form of reasonable flow rates. Although the adjustment leads dominated by diffusion. However, diffusive mixing is sup- to a better description of the mixing, it can be observed that the ported by convective mixing as theoretical diffusion time is exponent with a value of 0.8 deviates strongly from the liter- 12.5 s [15]. The deviation can be attributed to the flow regime ature value. This indicates that matching is not essential to and the assumed diffusion coefficient. On the one hand, the derive mixing times from the numerical data that are suffi- streamlines between CFD and experiment may differ slightly, ciently accurate for subsequent experimental design and that resulting, for example, in different dead volumes and thus agree sufficiently well with theory. longer residence times than in the real reactor. On the other hand, the diffusion coefficient may be too low, since it was Case study: Experimental settings used for pure water. Although the aspects have only a minor influence on their own, the interaction of both can influence On the basis of the method used, optimal reaction con- the results. ditions are translated into experimental settings. Since this mixing time is not covered by the CFD model, it Therefore, the experimental design space is visualized is to be expected that the interaction of diffusive and convec- using a parameter plot with volumetric flow rate and tive mixing is not yet sufficiently described by the simula- temperature as experimental parameter. The discrete step -1 tions, especially for very small Reynolds numbers. On the size for the parameters is set to 1 mL min for the one hand, experimental mixing time is generally smaller than volumetric flow rate and to 10°C for the temperature. the simulated one and, on the other hand, no mixing time is The influence of temperature on the reaction time can −1 determined by the CFD simulations forV = 6 mL min .This be neglected, since the reaction is instantaneous and deviation can be attributed to inaccuracies in the generation of dominated by mixing. According to the presented meth- the CAD model of the mixing structure. These inaccuracies odology, which has been validated on the basis of ex- result in differences between the real and the modeled struc- perimental data, the experimental design space is located -1 ture, which can have a major impact on the flow behavior, between volumetric flow rates of 6 and 12 mL min . especially in micro process engineering. Additionally, it is The limitation of the temperature T = 90 °C is due to max assumed that the limit of the mixing quality was set too high fact that aqueous solutions are used which start to boil initially. Hence, the limit was adjusted to approximate CFD for higher temperatures. This is a limitation that can be and experimental results. Based on Fig. 6b, the limit was ad- overcome, for example using a back-pressure regulator, justed to 0.8 to meet both of the aforementioned criteria. but is certainly a limitation of the setup used in this Figure 12 displays the adjusted CFD and experimental mixing study. This step needs to contain information about the times over energy dissipation rates. currently used setup and suggestions to overcome arising 330 J Flow Chem (2021) 11:321–332 -1 For6 and8mLmin , a peak in the heat flux profile was observed indicating complete conversion of reac- tants. This is also confirmed by the good agreement of measured reaction enthalpy with the literature value. In contrast, no peak and thus no complete conversion was -1 observed for 4 mL min , which can also be seen from the deviating reaction enthalpy. This result confirms the assumptions made previously and the applicability of the methodology. Conclusion and outlook In this study, a stepwise methodology to minimize the ex- perimental effort for thermokinetic data acquisition was Fig. 13 Quantitative representation of the experimental design space for calorimetric measurements as function of temperature and volumetric presented and evaluated. Short-cut calculations and CFD flow rate simulations using the open source software OpenFOAM were carried out to determine the residence, mixing and reaction time of a neutralization reaction within a commer- limitations be changing parts of the setup. As can be cially available microreactor. Additionally, the pressure seen in Fig. 13, the experimental design space is halved drop as a technical criterion was determined. The results by the methodology. obtained showed good agreement with experimental re- sults of pressure drop and mixing time. Thus, the CFD model was validated. However, deviations were observed, Case study: Determination of thermokinetic data especially at low Reynolds numbers. Thus, an investiga- tion with greater attention to diffusion would be necessary. The reaction enthalpy of the neutralization reaction was The results of the methodology also enabled to minimize determined at the previously determined experimental the possible volumetric flow rate by half. Consequently, settings and compared to the literature value. According the design space of experiments is rigorously reduced. to Fig. 13, calorimetric measurements were performed at The reasonable restriction of the design space was demon- -1 flow ratesof6and8mLmin and at ambient strated by determination of reaction enthalpy, which result- temperature. In addition, a counter test with a flow rate ed in meaningful data only for the proposed settings. In -1 of 4 mL min was investigated to demonstrate the applicability future studies, the input data set is to be extended by fur- of the methodology. In Fig. 14, the heat flux profiles and the ther commercially available microreactors in order to se- experimentally determined reaction enthalpies are displayed for lect a suitable reactor depending on the chemical reaction varying volumetric flow rates. to be investigated. Hence, a tool for contributing expert Fig. 14 a Spatially-resolved specific heat flux signals for neutralization reaction of 1 M HCl and 1.1 M NaOH for varying volumetric flow rates. b Measured neutralization enthalpies for varying volumetric flow rates and comparison to literature value (dotted line at -1 57.6 kJ mol ) J Flow Chem (2021) 11:321–332 331 Open Access This article is licensed under a Creative Commons knowledge has to be created in the same step to reliably Attribution 4.0 International License, which permits use, sharing, adap- estimate the reaction time. Therefore, consistent ranges of tation, distribution and reproduction in any medium or format, as long as parameters have to be set based on initial assumptions. In you give appropriate credit to the original author(s) and the source, pro- addition, the experimental parameter plots are to be ex- vide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included tended by the concentration to counteract limitations by in the article's Creative Commons licence, unless indicated otherwise in a varying the inlet concentration of the reactants resulting credit line to the material. If material is not included in the article's in a three-dimensional design space. Besides modeling of Creative Commons licence and your intended use is not permitted by hydrodynamics, the methodology should be supplemented statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this via heat management to ensure suitable and safe reaction licence, visit http://creativecommons.org/licenses/by/4.0/. conditions. For this purpose, Westermann and Mleczko [36] proposed a short-cut approach that can be adapted to the presented methodology. References 1 McMullen JP, Stone MT, Buchwald SL, Jensen KF (2010) Angew Chem Int Ed 49(39):7076–7080. https://doi.org/10.1002/anie. Acknowledgements The German Federal Ministry of Economic Affairs and Energy (BMWi) is acknowledged for funding this research of the 2 Heitmann D (2016) Chem Eng Technol 39(11):1993–1995. https:// Industrielle Gemeinschaftsforschung (IGF, IGF project: 20819 N) which doi.org/10.1002/ceat.201600150 is organized by the Arbeitsgemeinschaft industrieller 3 Elvira KS, Casadevall i Solvas X, Wootton RCR, deMello AJ Forschungsvereinigung (AiF) and the Forschungs-Gesellschaft (2013) Nat Chem 5(11):905–915. https://doi.org/10.1038/nchem. Verfahrenstechnik e.V. (GVT). 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Furthermore, we acknowledge financial support by 5 Mortzfeld F, Polenk J, Guelat B, Venturoni F, Schenkel B, Filipponi German Research Foundation (DFG) and TU Dortmund University with- P (2020) Org Process Res Dev 24(10):2004–2016. https://doi.org/ in the funding program Open Access Publishing. 10.1021/acs.oprd.0c00117 6 Ładosz A, Kuhnle C, Jensen KF (2020) React Chem Eng 5(11): Funding Open Access funding enabled and organized by Projekt DEAL. 2115–2122. https://doi.org/10.1039/D0RE00304B 7 Hosoya M, Nishijima S, Kurose N (2020) Org Process Res Dev 24(6):1095–1103. https://doi.org/10.1021/acs.oprd.0c00109 Declarations The authors declare no competing financial interest. 8 Maier MC, Leitner M, Kappe CO, Gruber-Woelfler H (2020) React Chem Eng 5(8):1410–1420. https://doi.org/10.1039/D0RE00122H Conflicts of interest/competing interests Not applicable. 9 Kashid MN, Renken A, Kiwi-Minsker L (2015) Microstructured devices for chemical processing. Wiley-VCH, Weinheim Symbols A , cross section area [m ]; c , starting concentration of M A0 10 Asprion N, Böttcher R, Mairhofer J, Yliruka M, Höller J, -3 limiting component A [mol m ]; c , concentration at grid point i [mol Schwientek J, Vanaret C, Bortz M (2020) J Chem Eng Data -3 2 -1 m ]; D, diffusion coefficient [m s ]; d , diameter of curvature [m]; d , c h, i 65(3):1135–1145. https://doi.org/10.1021/acs.jced.9b00494 -1 hydraulic diameter [m]; E , activation energy [J mol ]; h , molar reaction A r 11 Yang L, Nieves-Remacha MJ, Jensen KF (2017) Chem Eng Sci -1 3 enthalpy [J mol ]; k(T ), rate constant [-]; k , pre-exponential factor [m R 0 169:106–116. https://doi.org/10.1016/j.ces.2016.12.003 -1 -1 mol s ]; l , channel length [m]; m, reaction order [-]; n,exponentof 12 de Sousa MR, Santana HS, Taranto OP (2020) Int J Multiph Flow power law trend line [-]; p, pressure [Pa]; R , coefficient of determination 132:103435. https://doi.org/10.1016/j.ijmultiphaseflow.2020. [-]; t , mixing time [s]; t , mixing time from simulation [s]; T, mix, i mix, CFD temperature [K]; T , maximum temperature [K]; T , reactor tempera- max R 13 Asano S, Yatabe S, Maki T, Mae K (2019) Org Process Res Dev 3 -1 3 ture [K]; ˙V , volumetric flow rate [m s ]; V , dissipation volume [m ]; 23(5):807–817. https://doi.org/10.1021/acs.oprd.8b00356 3 -1 -1 V , reactor volume [m ];w , averaged velocity [m s ]; w ,velocity[ms ] R i 14 Reichmann F, Millhoff S, Jirmann Y, Kockmann N (2017) Chem Eng Technol 40(11):2144–2154. https://doi.org/10.1002/ceat. Dimensionless numbers Dn, Dean number [-]; Re, Reynolds number [-] 15 Reichmann F, Vennemann K, Frede TA, Kockmann N (2019) Chem Ing Tech 91(5):622–631. https://doi.org/10.1002/cite. Greek symbols  , velocity-weighted mixing quality [-]; Δ, differ- ˙V 2 -3 ence [-]; ε, energy dissipation rate [m s ]; λ, friction factor [-];  , 16 Krasberg N, Hohmann L, Bieringer T, Bramsiepe C, Kockmann N 2 -1 -3 2 kinematic viscosity [m s ]; ρ , density [kg m ]; σ , variance at cross (2014) Processes 2(1):265–292. https://doi.org/10.3390/pr2010265 ˙V section [-];σ , maximum variance at inlet [-]; τ, residence time [s]; 17 Knösche CM (2005) Chem Ing Tech 77(11):1715–1722. https://doi. ˙V;max τ , minimum residence time [s]; τ , maximum residence time [s]; ω , min max i org/10.1002/cite.200500123 influence of secondary flow patterns [-] 18 Deen WM (2012) Analysis of transport phenomena, 2nd ed., Topics in chemical engineering. Oxford University Press, New York Abbreviations CFD, computational fluid dynamics; HCL, hydrochloric 19 Holvey CP, Roberge DM, Gottsponer M, Kockmann N, Macchi A acid; NaOH, sodium hydroxide; OPC UA, Open Platform (2011) Chem Eng Process 50(10):1069–1075. https://doi.org/10. Communications Unified Architecture; PLC, programmable logic 1016/j.cep.2011.05.016 controller 20 Dean WR (1928) Proc R Soc Lond A 121(787):402–420. https:// do i.org/10.1098/rspa.1928.0205 332 J Flow Chem (2021) 11:321–332 21 Hessel V, Löwe H, Schönfeld F (2005) Chem Eng Sci 60(8–9): 31 Lide DR (2004) CRC handbook of chemistry and physics: A ready- reference book of chemical and physical data, 85th edn. CRC Press 2479–2501. https://doi.org/10.1016/j.ces.2004.11.033 22 Microfluidics (2011) In: Lin B, Basuray S (eds) Technologies and Taylor & Francis, Boca Raton applications, Topics in current chemistry. Springer, Berlin 32 Ligrani PM (1994) A study of dean vortex development and struc- 23 Kockmann N (ed) (2006) Micro process engineering, vol 5. Wiley- ture in a curved rectangular channel with aspect ratio of 40 at dean VCH, Weinheim numbers up to 430. NASA Contractor Report 4607 24 Howell PB, Mott DR, Golden JP, Ligler FS (2004) Lab Chip 4(6): 33 Fischer M, Kockmann N (2012) In: Proc. of ASME 12th Int. 663–669. https://doi.org/10.1039/b407170k Conference on Nanochannels, Microchannels, and Minichannels – 25 Kumar V, Aggarwal M, Nigam K (2006) Chem Eng Sci 61(17): 2012, American Society of Mechanical Engineers, Puerto Rico 5742–5753. https://doi.org/10.1016/j.ces.2006.04.040 34 Khaydarov V, Borovinskaya E, Reschetilowski W (2018) Appl Sci 26 Bałdyga J, Bourne JR (1999) Turbulent mixing and chemical reac- 8(12):2458. https://doi.org/10.3390/app8122458 tions. Wiley-VCH, New York 35 Mortimer CE, Müller U (2020) Chemie: das basiswissen der 27 Falk L, Commenge J-M (2010) Chem Eng Sci 65(1):405–411. chemie. Georg Thieme Verlag, Stuttgart https://doi.org/10.1016/j.ces.2009.05.045 36 Westermann T, Mleczko L (2016) Org Process Res Dev 20(2):487– 28 Kockmann N (2008) Transport phenomena in micro process engi- 494. https://doi.org/10.1021/acs.oprd.5b00205 neering. Springer, Berlin 29 Roberge DM (2004) Org Process Res Dev 8(6):1049–1053. https:// Publisher’snote Springer Nature remains neutral with regard to jurisdic- doi.org/10.1021/op0400160 tional claims in published maps and institutional affiliations. 30 Sen MA, Kowalski GJ, Fiering J, Larson D (2015) Thermochim Acta 603:184–196. https://doi.org/10.1016/j.tca.2014.09.024 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Flow Chemistry Springer Journals

Software-guided microscale flow calorimeter for efficient acquisition of thermokinetic data

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Abstract

Fast chemical process development is inevitably linked to an optimized determination of thermokinetic data of chemical reactions. A miniaturized flow calorimeter enables increased sensitivity when examining small amounts of reactants in a short time compared to traditional batch equipment. Therefore, a methodology to determine optimal reaction conditions for calori- metric measurement experiments was developed and is presented in this contribution. Within the methodology, short-cut calculations are supplemented by computational fluid dynamics (CFD) simulations for a better representation of the hydrody- namics within the microreactor. This approach leads to the effective design of experiments. Unfavourable experimental condi- tions for kinetics experiments are determined in advance and therefore, need not to be considered during design of experiments. The methodology is tested for an instantaneous acid-base reaction. Good agreement of simulations was obtained with experi- mental data. Thus, the prediction of the hydrodynamics is enabled and the first steps towards a digital twin of the calorimeter are performed. The flow rates proposed by the methodology are tested for the determination of reaction enthalpy and showed that reasonable experimental settings resulted. . . . . Keywords Continuous reaction calorimetry Flow chemistry CFD simulation Microreaction technology Design of experiments Digital twin Introduction development of continuous flow calorimeter increases con- stantly [5–8]. Moreover, the miniaturization of calorimetry Continuously operated processes feature higher yields and enables the investigation of fast and highly exothermic reac- selectivity, facilitate process automation, reduce the ecologi- tions under safe conditions due to the superior temperature cal footprint and offer shorter process development times controlwhencomparedtostandardbatchequipment[9]. [1–3]. For the development of accurate kinetic models that Traditionally, thermokinetic data is experimentally obtained assist chemical reactor development, design and optimization, during process development using mostly batch equipment. extensive knowledge of interaction between reaction kinetics These studies provide reliable information about the physical and hydrodynamics is essential [4]. Thus, the interest in the processes. Yet, only limited information is obtained about the dynamic behavior within the reactor performing those exper- iments. Efficiency and effectiveness of process development Highlights can be increased by digitalization of research and develop- � Development of a methodology for selecting suitable kinetics ment [10]. The systematical use of simulation tools such as experiments. � Good agreement of simulations with experimental data validates the computational fluid dynamics (CFD) is essential to overcome CFD model. challenges related to experimental measurements and to opti- � Number of possible experimental settings has been halved. mize real processes [10, 11]. Thus, information regarding tran- sient flow behavior, velocity, pressure and concentration * Timothy Aljoscha Frede fields is gained and can be used to reduce the number of Timothy.Frede@tu-dortmund.de experiments. Once the model has been validated, process per- formance can be predicted under different flow conditions, Department of Biochemical and Chemical Engineering, Laboratory reactant concentrations and reactor configurations [11, 12]. of Equipment Design, TU Dortmund University, Emil-Figge-Straße The efficient combination of CFD and experiments for 68, 44227 Dortmund, Germany 322 J Flow Chem (2021) 11:321–332 evaluation of microreactor performance for fast and exother- previously used ones. The microreactor is made of glass and mic reactions has already been shown by Asano et al. [13]. features a Y-mixer to contact the incoming fluids and 19 chi- In this work, a methodology is developed for the selection cane mixers to improve mixing. The hydraulic diameter at the of experiments in a continuous flow calorimeter during chem- smallest cross-sectional area within the reactor is 1 mm, which ical process development aiming a time and cost-efficient ac- is used for the subsequent calculations. quisition of thermokinetic data. The methodology enables The technical data of the employed microreactor and sy- choosing the optimal reaction conditions out of the entire pos- ringe pumps is given in Table 1. sible range of experimental parameters of the calorimeter rath- er than performing full factorial design of experiment. Thus, Evaluation of optimal reaction conditions optimal designs of experiments are determined, which offer maximal information gain with minimal effort. Finally, the The methodology focusses on the evaluation of optimal reac- proposed experimental settings are tested for the determina- tion conditions, which are suited for continuous calorimetric tion of the reaction enthalpy of a test reaction. measurement experiments. The basis for this methodology is the approach of Krasberg et al. [16], who developed a meth- odology to select plug flow equipment for a modular and continuous small-scale plant. A schematic overview of the Materials and Methods stepwise methodology is shown in Fig. 2. The methodology includes CFD simulations complemented Calorimeter and experimental setup by short-cut methods. The methodology is a stepwise approach, in which the demand of data increases with the sequence of the The calorimeter’s setup and its peripheral equipment have steps. However, the possibility to restrict the experimental been described in previous works of Reichmann et al. [14, design space is also increasing. In the following, the available 15]. A central programmable logic controller (PLC) information is described with the individual steps of the (LabManager , HiTec Zang GmbH, Germany) has been methodology. added to the experimental setup to automate the execution of calibration and experiments. The current setup and the employed microreactor (type*-S, HTM series, Little Things Input data Factory GmbH, Germany) are displayed in Fig. 1.Compared to the setup in [15], only four Peltier elements are used here, The input data sets represent the basis for the subsequent steps. In whose projection area is about 4.5 times larger than the this study, reaction conditions are proposed based on the Fig. 1 a Experimental setup for continuous reaction calorimetry pump and thermostat for tempering the base plate. b Microreactor within ® 2 consisting of laboratory automation system (LabManager ), syringe the reaction calorimeter with four Peltier elements (15 × 15 mm ), which pumps for feeding, preheating thermostat, calorimeter itself with a gear are positioned on the base plate J Flow Chem (2021) 11:321–332 323 Table 1 Technical data of the device data type symbol unit value comment microreactor and the pumps used type*-S geometries V mL 0.10 d mm 1.00 d = d h h i ™ -1 SyrDos 2 possible flow rates V mL min 0.5 limited by min -1 V mL min 6.00 syringes used in max the pumps chemical reaction to be investigated and the used microreactor. Step 2: Pressure drop For the chemical reaction system, information regarding the physical properties of the reaction mixture in terms of The pressure drop represents a technical criterion. Among density, viscosity and diffusivity is required or has to be estimat- others, the reactor itself and the pumps limit the maximum ed. In addition, a rough classification of the reaction kinetics permissible pressure loss. The pressure is expected to be supports the methodology. The microreactors are defined regard- highest at the reactor inlet. The pressure drop can be calculated ing their geometries and allowed operation conditions. Since using generalized models, as shown in Eq. 2 [18]. commercially available microreactors are employed, this infor- mation is provided by the manufacturer. l ρ Δp ¼ λ þ !  w ð2Þ i i i i d 2 h;i Step 1: Residence time However, the friction factor λ and the influence of second- ary flow patterns ! have to be determined for each The residence time of fluids within microstructured devices is microreactor. For this purpose, microreactors are characterized in the order of seconds or less, which can be detrimental to slow using semi-empirical pressure drop modeling [19]. The Dean reactions [17]. Thus, the residence time is a crucial factor for number Dn is used to characterize the influence of secondary the successful investigation of chemical reactions in continu- flow profiles which are the result of centrifugal forces. In ously operated reactors. In case of insufficient residence time, Eq. 3,the channel’s curvature is expressed by d .[20] complete conversion cannot be guaranteed, which reduces the sffiffiffiffiffi quality of the information gained during calorimetric measure- Dn ¼ Re ð3Þ ment. Otherwise, excessive residence times and broad resi- dence time distributions promote side or subsequent reactions, which negatively influence the selectivity and yield. The hy- In order to improve the determination of the pressure drop and draulic residence time  is calculated dividing the reaction later the mixing performance, the microreactor’s hydrodynamics volume V by the volumetric flow rate V, shown in Eq. 1. including the pressure drop are estimated using CFD simulations. Steady state CFD simulations are carried out for incompressible, ¼ ð1Þ single-phase flow through the microreactor using the open source software OpenFOAM. The solver icoFoam is used to investigate The range of possible volumetric flow rates is determined the hydrodynamics, which is completed by a passive scalar for by the pumps used in the experimental setup. The reactor solute transport. The data obtained is analyzed regarding the pressure drop as a function of volumetric flow rate. volume is obtained from the microreactor’sgeometry. Fig. 2 Methodology to evaluate optimal reaction conditions for efficient acquisition of kinetic data, where the experimental design space is limited by the stepwise determination of important time scales based on specified input data 324 J Flow Chem (2021) 11:321–332 Step 3: Time scales ˙ ˙ V V 1 2 2 σ ðÞ c ¼ ðÞ c  c ð9Þ ˙ 1 2 V;max Besides the residence time, mixing of reactants and its corre- ˙ ˙ V þ V 1 2 sponding time scale are decisive during chemical transforma- tion [21, 22]. Thus, the determination of mixing time scales is i t ¼ ð10Þ mix;CFD of great interest, especially in different microreactors. w Theoretically, laminar flow prevails in microreactors, Besides the mixing time scale, the characteristic reaction since Re < 2300 [23]. However, secondary flow patterns time is an important quantity in process engineering [28]. The such as Dean flow and engulfment are found in bend reaction time can be estimated using the reaction order m,the channels for Re > 100, which greatly enhance mixing [9, 24, starting concentration of the limiting component c and the A0 25]. A theoretical mixing time can be estimated roughly using reaction rate constant k, which is influenced by temperature, a short-cut method considering micromixing by engulfment shown in Eq. 11. [26]. For this purpose, a power law relationship between energy dissipation rate and mixing time was presented by t ¼ ð11Þ m1 Falk and Commenge [27]. The mixing time depends on the kTðÞ c A0 mean kinematic viscosity of the reaction medium, the energy dissipation rate  and a pre-factor matching the engulfment Since kinetic data is not available at this point, an educated guess based on similar reactions or heuristics for classification theory, shown in Eq. 5. The energy dissipation rate is defined of the reaction can be used to estimate the reaction rate con- in Eq. 6 with volumetric flow rateV , pressure drop Δp ,the tot i stant. A classification of the reaction according to Roberge mean fluid’sdensity ρ and the dissipation volume V .The [29] and Kashid et al. [9] allows for roughly estimating the pressure drop for these calculations is obtained from CFD reaction time. However, the educatedguess based experience simulations in step 2. and intuition play an eminent role at this stage of process d w development. In this case, the methodology has to be started Re ¼ ð4Þ with the operator assuming certain kinetic data. Since the goal 1=2 of the method is initially only to stake out the experimental t ¼ 17:3 ð5Þ mix;i design space, a rough estimate is sufficient for now. Based on this data, short test trials must be performed to check whether Δp V complete conversion is achieved in the reactor. If this is not ¼ ð6Þ ρV the case, the constraint for the reaction time must be adjusted iteratively. The exact kinetic data will then be determined by Besides the estimation using the short-cut method, the the experiments and subsequently, CFD simulations can be mixing performance of the microreactor is characterized using performed with the experimentally determined data to validate the CFD model. Therefore, the variance of the concentration the model for future applications. For optimal reaction condi- profile of the solute is evaluated at several cross sections of the tions and consequently optimal results, the three characteristic mixing channel. Since the flow velocity varies over the cross times of residence  ,mixing t and reaction t have to be i mix;i R section, the velocity-weighted mixing quality  is used for a V designed properly. Complete conversion within the microreactor better representation of the flow situation, shown in Eq. 7.In can be assumed, if both the mixing and reaction time are faster Eq. 8, the concentration c at a grid point is weighted with the than the mean residence time. Furthermore, two regimes can be velocity w at this grid point, and the mean velocity w with the distinguished. In a reaction-dominated regime, mixing time is cross section A . Based on the position of complete mixing, faster than reaction time, while in a mixing-dominated regime, the corresponding channel length l and the mixing time it is opposite. Experimental settings are rated as suitable if the t can be determined by dividing the obtained channel mix;CFD arrangement of the characteristic times follows the proposed length with the mean velocity, shown in Eq. 10.[28] sequence. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ ðÞ c ¼ 1  ð7Þ ˙ Experimental settings σ ðÞ c V;max The resulting constraints regarding the reaction and flow con- c w dA 1 i i 2 M ditions are visualized within a parameter plot to determine σ ðÞ c ¼ c  wdA ð8Þ ˙ i A w w dA M A i M suitable experimental settings, which is shown exemplarily in Fig. 3 J Flow Chem (2021) 11:321–332 325 hydroxide (NaOH) - is used to demonstrate the functionality of the presented methodology. Sen et al. [30] also investigated this model reaction for calorimetry using CFD for the devel- opment of a microfluidic reaction calorimeter. The thermokinetic parameters, which were determined experimen- tally, are given in Table 2. For nearly equimolar conditions, the neutralization reaction follows a second-order kinetics. [31] þ  þ  þ H Cl þ Na OH ! H O þ Na Cl ð12Þ Since aqueous solutions of HCl and NaOH with concen- trations of 1.0 M and 1.1 M respectively are used in this study, the physical properties of water are used in the short-cut cal- culations and in the advanced CFD calculations. The binary diffusion coefficient D is obtained from Dortmund Data Bank –10 2 -1 with a value of 9.6∙10 m s . Fig. 3 Qualitative representation of the experimental design space to evaluate suitable experimental settings for calorimetric measurements as function of temperature and volumetric flow rate. The constraints result Results and discussion from the steps of the presented methodology. In this section, the results of the performance of the individual Three conditions are essential to span the experimental de- steps are presented to determine suitable experimental settings sign space: for the investigation of the neutralization reaction. Subsequently, the obtained reaction conditions are tested and & ranges and discrete step sizes of the experimental the CFD model is validated using this experimental data. parameters & values for operating constraints & values of the constraints as a function of the experimental Case study, step 1: Residence time parameters At first, the possible range of residence time is checked for the Consequently, suitable experimental settings are located investigated reactor and syringe pumps used in the experimen- inside the constraints. The resulting settings are translated into tal setup. According to Eq. 1 and Table 1, the combination of control commands for the calorimeter, e.g. into settings of the microreactor and pumps provides a residence time between pumping system to adjust the volumetric flow rate to achieve a =0.5 sand  =6.0 s. min max specific residence time. Therefore, the experimental settings are transferred via Open Platform Communications (OPC) Case study, step 2: Pressure drop Unified Architecture (UA) to the PLC, which controls the whole experimental setup. The hydrodynamics in the reactor, and thus the pressure drop, too, are calculated on the basis of CFD simulations. Pressure Determination of thermokinetic data drops within the microreactor are displayed in Fig. 4 for vary- ing volumetric flow rates. In this step, the control commands for the calorimeter are In general, the pressure drop increases for higher volumet- executed automatically using the PLC and subsequently, the ric flow rates. A second-order polynomial, as described by the measured values are evaluated. Currently, the calorimeter is Darcy-Weisbach equation, matches the data according to operated in isoperibolic mode. The calorimetric measurement Eq. 2 with the highest coefficient of determination of R =1. method has been described by Reichmann et al. [14]and is used here to determine the reaction enthalpy. Table 2 Kinetic data of neutralization reaction of hydrochloric acid and sodium hydroxide. [31] Case Study -1 -1 -1 -1 k [L mol s]E [J kmol ] Δh [kJ mol]m[-] 0 A r 11 6 A well-known, exothermic reaction from the literature - acid- 1.69∙10 3.33∙10 -57.6 2 base reaction of hydrochloric acid (HCl) and sodium 326 J Flow Chem (2021) 11:321–332 Fig. 4 Simulated values for pressure drop over volumetric flow rates for Fig. 5 Energy dissipation rates over volumetric flow rates based on CFD the type*-S microreactor (HTM series, Little Things Factory GmbH) results for the type* -S microreactor (HTM series, Little Things Factory GmbH) The pressure drop ranges from 0.07 to 15.78 mbar, corre- −1 sponding to volumetric flow rates of 1–12 mL min ,flow The energy dissipation rate increases with higher flow −1 velocities of 21.22 to 254.65 mm s and Reynolds numbers rates. For higher flow rates, the cubic relationship between of 23 to 285, respectively. Pressure loss caused by piping, energy dissipation and volumetric flow rate becomes appar- which was not considered within the CFD simulations, was ent, as the velocity enters Eq. 6 to the power of three. estimated using Hagen-Poiseuille equation and resulted in a Subsequently, the velocity-weighted mixing quality is deter- maximum loss of 0.2 mbar for the highest possible flow rate. mined at various cross sections within the microreactor for the Hence, this pressure loss is negligible compared to the loss respective flow rates, shown in Fig. 6. The cross sections are induced by the reactor. located in the middle of the straight part behind the chicane mixer. Case study, step 3: Times scales In general, the mixing quality increases with increasing At first, the energy dissipation rates are calculated based on distance from the reactor inlet and with increasing flow rate. Additionally, three distinct regimes can be observed. For the CFD results and displayed for varying flow rates in Fig. 5. Fig. 6 a Allocated position of cross sections within the microreactor for the evaluation of the mixing quality. b Velocity- weighted mixing quality over al- located position of cross sections within the microreactor for vary- ing volumetric flow rates c Concentration profile of NaOH −1 for ˙V = 8 mL min in the type*- S microreactor (HTM series, Little Things Factory GmbH). Simulations using icoFoam, postprocessing in ParaView. J Flow Chem (2021) 11:321–332 327 Table 3 Positions and corresponding channel lengths of complete a limit must be set for the mixing quality at which the mixing derived from CFD simulations mixture is considered completely mixed for the -1 microreactor used in this work. As can be seen in Fig. 6b, ˙V [mL min ] Position [-] Channel length [mm] a plateau of the mixing quality is reached within the reactor <6 - - −1 −1 ˙ ˙ only for V  8mL min .For V  6mLmin , the mixing 814 52.98 quality continues to increase along the reactor channel and does 10 19 72.98 not reach an almost constant value. Based on this observation, 12 11 40.98 the limit for the mixing quality is set so that complete mixing is only assumed for the last three volume flows. Thus, complete - indicates no complete mixing within the reactor mixing within the reactor is assumed from the cross-sectional area at which a limiting value of   0.95 is reached. The ˙V − 1 ˙ positions and corresponding channel lengths of complete V  3mLmin , the mixing quality increases almost mixing are given in Table 3. The results presented are in good linearly along the reactor coordinate. In this regime, the agreement with the study of Khaydarov et al. [34]onareactor Reynolds and the corresponding Dean number are com- with the same mixing structure. Especially the presented flow paratively small (Re  75 and Dn  50) and mixing is regime could also be observed here at the investigated assumed to be dominated by diffusion. Hence, the maximum Reynolds numbers. achieved mixing quality  remains below 0.6. However, the Table 3 shows that the channel length, at which complete slope of the mixing quality increases significantly for 4 and 6 mixing is achieved, does not consistently decrease with in- −1 mL min . For these volumetric flow rates, the Dean number creasing volume flow. This observation is due to the flow takes values of 67 and 100 respectively. Thus, secondary flow behavior at different flow rates. Figure 7 illustrates the stream- patterns can be assumed, which lead to improved convective lines within the first nine chicane mixers. mixing. According to Ligrani [32], Dean vortices are expected According to Fig. 7, the vortex regime is observed for the to be fully developed and stable for Dn > 64 and thus, mixing displayed flow rates. However, a slightly different flow behav- is greatly enhanced. This can also be derived from the higher −1 − 1 ˙ ˙ ior is evident between V =8mL min and V =10mLmin . mechanical energy consumption, which can be seen in the −1 −1 ˙ For V = 8 mL min , the streamlines in the middle of the energy dissipation rate graph. ForV  8mLmin , the course channel are stronger, which can be seen in a darker coloring. of mixing quality is almost identical. Re and Dn are relatively Thus, mixing in this area is improved compared to the flow high with Re  190 and Dn  134. For Re > 150, the mixing − 1 behavior ofV =10mLmin . The renewed increase in mixing performance of chicane mixers is significantly enhanced due −1 to stable vortex generation and mixing quality increases no- quality forV =12mLmin is due to the stronger expression of ticeably [33]. Based on these results, complete mixing within the vortices within the recirculation zones. − 1 Figure 8 displays the mixing times plotted over the corre- the reactor is assumed for V  8mLmin . sponding energy dissipation rate using the short-cut method Subsequently, the mixing time is calculated based on and the CFD model. the results of the mixing performance. For this purpose, Fig. 7 Simulated streamlines for different volumetric flow rates of − 1 8, 10 and 12 mL min (Re=190, 237 and 285). Postprocessing in ParaView 328 J Flow Chem (2021) 11:321–332 Fig. 8 Mixing time scale plotted over energy dissipation rates with power Fig. 9 Residence and mixing time over volumetric flow rates law trend line that fits the data of the short-cut method and the CFD simulations Model validation In order to validate the CFD results, the data obtained is com- In general, mixing times decrease with increasing energy pared with experimental measurements. The pressure was dissipation rates. Furthermore, the values of both calculations measured at reactor inlet and outlet via a T-shaped fitting are in the same order of magnitude for the respective flow using pressure sensors (type A-10, WIKA Alexander rates. Using the short-cut method, the mixing times are be- Wiegand SE & Co. KG, Germany). In Fig. 10, the pressure tween 0.37 and 5.28 s and those of the CFD simulations be- drop is plotted over the volumetric flow rate. tween 0.16 and 0.34 s. For the CFD results, the coefficient of As observed, the pressure drop obtained with CFD is in determination shows a relative low value with 0.59 for the good agreement with the experimental pressure drop. data fitting power law trend line. Additionally, the exponent In a next step, the CFD and experimental mixing times are with a value ofn= 0.62 differs from the theoretical value ofn= compared. Experimental mixing times were determined optically 0.5 [27]. The deviations between the CFD simulations and the and from heat flux profiles by Reichmann et al. [15]. The mixing literature are probably due to the setting of the limiting value times for different volumetric flow rates are shown in Fig. 11. for complete mixing. Moreover, the need for a detailed char- In general, the mixing time obtained with CFD is in a acterization of the hydrodynamics is illustrated by the fact that relatively good agreement with the experimental mixing the short-cut calculates mixing times for each flow rate, time. However, a larger deviation of 0.16 s can be seen whereas the simulations show that complete mixing cannot −1 for V =10 mLmin , which has been discussed on the −1 be achieved for V  6mL min . Subsequently, the characteristic reaction time of the neutral- ization reaction is calculated. According to Eq. 11 and the ki- − 11 netic data from Table 2, the reaction time t is 2.6∙10 s. This is consistent with the literature, as the ion reaction of a proton and a hydroxide ion to form a water belongs to quasi- instantaneous reactions [35]. Since the reaction time will always be shorter than the mixing time in this case, a mixing- dominated regime prevails. If reaction time exceeded the resi- dence time, the selected reactor would not be suitable for the investigated reaction. In this case, another reactor needs to be selected from the database, which, depending on the limitation, either mixes faster or offers more residence time. Figure 9 dis- plays the mixing and residence time over volumetric flow rates. Figure 9 shows that the time scales are designed properly −1 only for V  8mLmin . Therefore, only with these settings, complete conversion can be expected and thus the Fig. 10 Comparison of CFD and experimental pressure drop over information content is at its maximum. volumetric flow rates J Flow Chem (2021) 11:321–332 329 Fig. 12 Comparison of CFD and experimental mixing time over energy Fig. 11 Comparison of CFD and experimental mixing time over dissipation rates with adjusted limit for complete mixing of   0:8: volumetric flow rates ˙V − 1 basis of the flow behavior. For V =6 mL min ,no com- By adjusting the limit, complete mixing is also achieved for − 1 plete mixing within the reactor is calculated by CFD. 4and6 mL min using CFD model. Since experimental and Moreover, complete mixing was also observed experi- CFD results are generally in good agreement, the CFD model −1 mentally for V = 1 mL min with a mixing time of a can be used to determine suitable experimental settings in the 3.57 s. Due to the low Reynolds number (Re=23), mixing is form of reasonable flow rates. Although the adjustment leads dominated by diffusion. However, diffusive mixing is sup- to a better description of the mixing, it can be observed that the ported by convective mixing as theoretical diffusion time is exponent with a value of 0.8 deviates strongly from the liter- 12.5 s [15]. The deviation can be attributed to the flow regime ature value. This indicates that matching is not essential to and the assumed diffusion coefficient. On the one hand, the derive mixing times from the numerical data that are suffi- streamlines between CFD and experiment may differ slightly, ciently accurate for subsequent experimental design and that resulting, for example, in different dead volumes and thus agree sufficiently well with theory. longer residence times than in the real reactor. On the other hand, the diffusion coefficient may be too low, since it was Case study: Experimental settings used for pure water. Although the aspects have only a minor influence on their own, the interaction of both can influence On the basis of the method used, optimal reaction con- the results. ditions are translated into experimental settings. Since this mixing time is not covered by the CFD model, it Therefore, the experimental design space is visualized is to be expected that the interaction of diffusive and convec- using a parameter plot with volumetric flow rate and tive mixing is not yet sufficiently described by the simula- temperature as experimental parameter. The discrete step -1 tions, especially for very small Reynolds numbers. On the size for the parameters is set to 1 mL min for the one hand, experimental mixing time is generally smaller than volumetric flow rate and to 10°C for the temperature. the simulated one and, on the other hand, no mixing time is The influence of temperature on the reaction time can −1 determined by the CFD simulations forV = 6 mL min .This be neglected, since the reaction is instantaneous and deviation can be attributed to inaccuracies in the generation of dominated by mixing. According to the presented meth- the CAD model of the mixing structure. These inaccuracies odology, which has been validated on the basis of ex- result in differences between the real and the modeled struc- perimental data, the experimental design space is located -1 ture, which can have a major impact on the flow behavior, between volumetric flow rates of 6 and 12 mL min . especially in micro process engineering. Additionally, it is The limitation of the temperature T = 90 °C is due to max assumed that the limit of the mixing quality was set too high fact that aqueous solutions are used which start to boil initially. Hence, the limit was adjusted to approximate CFD for higher temperatures. This is a limitation that can be and experimental results. Based on Fig. 6b, the limit was ad- overcome, for example using a back-pressure regulator, justed to 0.8 to meet both of the aforementioned criteria. but is certainly a limitation of the setup used in this Figure 12 displays the adjusted CFD and experimental mixing study. This step needs to contain information about the times over energy dissipation rates. currently used setup and suggestions to overcome arising 330 J Flow Chem (2021) 11:321–332 -1 For6 and8mLmin , a peak in the heat flux profile was observed indicating complete conversion of reac- tants. This is also confirmed by the good agreement of measured reaction enthalpy with the literature value. In contrast, no peak and thus no complete conversion was -1 observed for 4 mL min , which can also be seen from the deviating reaction enthalpy. This result confirms the assumptions made previously and the applicability of the methodology. Conclusion and outlook In this study, a stepwise methodology to minimize the ex- perimental effort for thermokinetic data acquisition was Fig. 13 Quantitative representation of the experimental design space for calorimetric measurements as function of temperature and volumetric presented and evaluated. Short-cut calculations and CFD flow rate simulations using the open source software OpenFOAM were carried out to determine the residence, mixing and reaction time of a neutralization reaction within a commer- limitations be changing parts of the setup. As can be cially available microreactor. Additionally, the pressure seen in Fig. 13, the experimental design space is halved drop as a technical criterion was determined. The results by the methodology. obtained showed good agreement with experimental re- sults of pressure drop and mixing time. Thus, the CFD model was validated. However, deviations were observed, Case study: Determination of thermokinetic data especially at low Reynolds numbers. Thus, an investiga- tion with greater attention to diffusion would be necessary. The reaction enthalpy of the neutralization reaction was The results of the methodology also enabled to minimize determined at the previously determined experimental the possible volumetric flow rate by half. Consequently, settings and compared to the literature value. According the design space of experiments is rigorously reduced. to Fig. 13, calorimetric measurements were performed at The reasonable restriction of the design space was demon- -1 flow ratesof6and8mLmin and at ambient strated by determination of reaction enthalpy, which result- temperature. In addition, a counter test with a flow rate ed in meaningful data only for the proposed settings. In -1 of 4 mL min was investigated to demonstrate the applicability future studies, the input data set is to be extended by fur- of the methodology. In Fig. 14, the heat flux profiles and the ther commercially available microreactors in order to se- experimentally determined reaction enthalpies are displayed for lect a suitable reactor depending on the chemical reaction varying volumetric flow rates. to be investigated. Hence, a tool for contributing expert Fig. 14 a Spatially-resolved specific heat flux signals for neutralization reaction of 1 M HCl and 1.1 M NaOH for varying volumetric flow rates. b Measured neutralization enthalpies for varying volumetric flow rates and comparison to literature value (dotted line at -1 57.6 kJ mol ) J Flow Chem (2021) 11:321–332 331 Open Access This article is licensed under a Creative Commons knowledge has to be created in the same step to reliably Attribution 4.0 International License, which permits use, sharing, adap- estimate the reaction time. Therefore, consistent ranges of tation, distribution and reproduction in any medium or format, as long as parameters have to be set based on initial assumptions. In you give appropriate credit to the original author(s) and the source, pro- addition, the experimental parameter plots are to be ex- vide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included tended by the concentration to counteract limitations by in the article's Creative Commons licence, unless indicated otherwise in a varying the inlet concentration of the reactants resulting credit line to the material. If material is not included in the article's in a three-dimensional design space. Besides modeling of Creative Commons licence and your intended use is not permitted by hydrodynamics, the methodology should be supplemented statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this via heat management to ensure suitable and safe reaction licence, visit http://creativecommons.org/licenses/by/4.0/. conditions. For this purpose, Westermann and Mleczko [36] proposed a short-cut approach that can be adapted to the presented methodology. 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Journal

Journal of Flow ChemistrySpringer Journals

Published: Sep 1, 2021

Keywords: Continuous reaction calorimetry; Flow chemistry; CFD simulation; Microreaction technology; Design of experiments; Digital twin

References