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Mixing and fast chemical reaction—IIDiffusion-reaction model for the CSTR
Abstract
The coupling of 1-naphthol with diazotised sulphanilic acid produces by competitive, consecutive reactions two dyestuffs, whose concentrations can readily be measured spectrophotometrically. The reaction kinetics have been measured using the stopped-flow method and the reaction mechanism is known. Using mild reaction conditions (room temperature, aqueous solution of pH = 10, concentrations of order 0.1 mol m−3), the product mixture always contained more disubstituted and therefore less monosubstituted dyestuff than would have been formed in the chemically controlled regime. (In these experiments the stoichiometric and volumetric ratios of the reagents were varied and the 0.063 m3 reactor was operated semi-continuously, as well as continuously using various turbine speeds). The reactions were fast enough to produce inhomogeneity at the molecular scale (segregation) and are shown to possess highly convenient properties for studying such segregation.
... To address this shortcoming, several research groups have provided laboratory chemistries that exhibit complex reaction behavior . Accordingly, previous works have used spectrometry alongside a "chemical ruler" in which the reaction for the desired product is mixing limited, and the reaction for the undesired side product is kinetically limited (Angst et al., 1982;Angst et al., 1984;Baldyga and Bourne, 1984;Belevi et al., 1981;Bolzern and Bourne, 1983;Bourne et al., 1981;Bolzern and Bourne, 1983;Bourne et al., 1981;Bourne and Rohani, 1983;Li and Toor, 1986). Poorer molecular mixing encourages the selectivity of the undesired product. ...
... To address this shortcoming, several research groups have provided laboratory chemistries that exhibit complex reaction behavior . Accordingly, previous works have used spectrometry alongside a "chemical ruler" in which the reaction for the desired product is mixing limited, and the reaction for the undesired side product is kinetically limited (Angst et al., 1982;Angst et al., 1984;Baldyga and Bourne, 1984;Belevi et al., 1981;Bolzern and Bourne, 1983;Bourne et al., 1981;Bolzern and Bourne, 1983;Bourne et al., 1981;Bourne and Rohani, 1983;Li and Toor, 1986). Poorer molecular mixing encourages the selectivity of the undesired product. ...
... One such chemical ruler is provided by the competitive consecutive reaction between 1-Naphthol (A) and Diazotized Sulfanilic acid (B) introduced by Bourne et al. (1981) This is a competitive consecutive reaction that produces two independent dyestuffs as products. In the first reaction that results in the desired product, B transfers one diazonium ion to A, producing R. ...
... The prediction of gas absorption fluxes from these 3-D models deserves special consideration and a complete modeling strategy is proposed. The results obtained from the models and strategy are compared with experimental data by Littel et al. (1994) The effect of the presence of a dispersed phase on (micro-)mixing in multiphase systems was studied experimentally in Chapter 7. In this study the parallel/consecutive diazo coupling reaction system of Bourne et al. (1981) was used as test-reaction. Gas bubbles, glass beads and liquid droplets were applied as dispersed phase. ...
... A second important issue is the interaction between mixing and mass transfer between the continuous liquid phase and the dispersed liquid phase in the zones neighboring the feedpoint. An experimental study investigating the extent of these influences, also at higher volume fractions dispersed phase, using a well known model reaction system, as the diazo coupling reaction proposed by Bourne et al. (1981), was considered suitable to study these (micro-)mixing phenomena. ...
... The micromixing process can be studied experimentally by using chemical test reactions. The diazo-coupling reaction of Bourne et al. (1981), for which the reaction kinetics are well established , is frequently used for this purpose. ...
... Another reaction modeling approach incorporates the methodology used to describe micromixing, or mixing on the smallest scales (Fox, 1998;Hannon, 1992;Bourne, et al., 1981). In the context of a CFD calculation, micromixing is on a scale that is smaller than a typical computational cell. ...
... This is the reaction system used by Bourne et al. (1981) and Middleton et al. (1986). The first reaction is much faster than the second reaction: K 1 = 7300 m 3 /mole-s vs. K 2 = 3.5 m 3 /mole-s. ...
This 154 page booklet covers many topics in the field of simulating mixing processes using CFD. A printed version of this booklet was published by Fluent Inc. The booklet starts with a great Foreword by Prof. J.M. Smith that discusses the progress of understanding of mixing throughout the ages. It continues with an easily understandable Introduction to CFD; an Introduction to Numerical Methods; a chapter on Stirred Tank Modeling Using Experimental Data; a section on Stirred Tank Modeling Using the Actual Impeller Geometry; an overview of Evaluating Mixing from Flow Field Results; a very nice suite of Application Examples; and Closing Remarks giving you useful modeling advice.
... The chemical probe method usually involves a competitive-consecutive or competitive-parallel reaction system. The representative example reaction systems are naphthol/sulphanilic acid [26] and iodide/iodate reaction system [23,27]. Such competitive reaction system usually includes a pair of competitive reaction. ...
... Bourne et al. [26] proposed a unique fast competitive-consecutive reacting system with naphthol (A), diazotised sulphanilic acid (B), 4-(4′-sulphophenylazo)-1-naphthol (P), and 2,4-bis(4′-sulphophenylazo)-1-naphthol (S), respectively. The reaction system comprises of two steps and the reaction kinetic can be described as follows: ...
In the fast reaction category, the turbulent reactive mixing strongly affects the reaction products yield and distribution. The present work adopts a high-efficiency vortex structure induced by a novel static mixer – hollow cross disk (HCD) to enhance the turbulent reactive mixing within the tubular turbulent flow. Specifically, the direct quadrature method of moments (DQMoM) coupled with the interaction-by-exchange-with-the-mean model (IEM) is utilized to simulate the consecutive competitive reactions system in this tubular turbulent flow. In order to quantitatively evaluate the enhanced mixing effect of the HCD, the turbulent reacting flows in the Kenics static mixer and coaxial jet mixer have also been studied. A combining analysis of turbulent flow field and the chemical species distribution indicates that the turbulent mixing enhancement mechanisms of these two static mixers. The simulation suggests that the sinusoidal wave structure in the HCD generate an important flow structure-counter vortex pairs (CVPs), which increases the momentum exchange between the near-wall region and the flow core. Moreover, the spatial distribution of the mixture fraction and reaction product concentration in these configurations agrees well with its turbulent flow field characteristics. The improved turbulent mixing initially is located at the jet periphery when at 0 < z/D < 2, which fits well with the HCD's longitudinal evolution of turbulent energy dissipation. Whereas at z/D > 2, CVPs of the HCD ameliorate the near-wall area's turbulent mixing and thus increase the reaction productivity and selectivity. Additionally, the effects of flow rate on segregation index are studied to suggest that the improvement of Xs for HCD is of about 35% relative to the original tubular flow.
... In this way, the reactants have begun to react in the case of non-uniform contact at the molecular scale, and the product distribution will be controlled by the micromixing. 4 A commonly used consecutive reaction is the diazo coupling of 1-naphthol, [5][6][7] and the products are conveniently analyzed by spectrophotometry. However, the diazo dyes for this system are unstable, thus the experimental procedure need to be completed quickly. ...
Micromixing in chemical reactors can be characterized through test reactions that are sensitive to mixing. A new pair of parallel competitive reactions, including acid–base neutralization and diethyl oxalate hydrolysis, is proposed in this work. It has clear principles and high sensitivity to micromixing with quantitative accuracy and operational simplicity. The measurement results obtained from stopped‐flow spectra show that the alkaline hydrolysis of diethyl oxalate follows second‐order kinetics, and the rate constant conforms to the Arrhenius equation k2 = 2.331 × 10⁸ exp(−26.92 × 10³/RT) (L/mol/s). The estimated half‐life of hydrolysis is approximately 3 × 10⁻⁴ s under the selected concentration combinations, which provides significant advantages for the micromixing assessment in the strong turbulent fluid environment. In the same stirred tank, the critical feed time of new test reaction is shorter than that of the Villermaux–Dushman reaction. Overall, this work provides practical ideas for screening other desired esters for fast hydrolysis to construct more test reactions for micromixing.
... Consecutive reactions Diazo coupling between 1-naphthol and diazotized sulfanilic acid 11,12 Simultaneous diazo coupling between 1-and 2-naphthol and diazotized sulfanilic acid 13 Parallel reactions Villermaux-Dushman reaction 14 Acid-base neutralization and alkaline hydrolysis of ethyl chloroacetate 15 Acid-base neutralization and alkaline hydrolysis of other esters 15,16 Acid-catalyzed hydrolysis of 2,2-dimethoxypropane (DMP) 17,18 Precipitation ...
Micromixing in reactors is typically characterized by chemical test reactions. A novel image‐based measurement system of engulfment vortex (IMEV system) is developed to assess the micromixing efficiency. Over 2000 vortices were recognized from images captured under various experimental cases, and key frames for their formation, engulfment and dissipation were identified. Inspired by the engulfment model (i.e., E model), this work quantified the micromixing time and local turbulent energy dissipation rate with the vortex lifetimes. The micromixing time obtained through the IMEV method is comparable to its value estimated by the micromixing model and segregation index of the test reaction, with a deviation of less than 20%. In turbulent gas–liquid systems, bubbles play a dual role on the local micromixing due to frequent disturbance and phase interface limitation. To summarize, this work offers an alternative approach for micromixing studies and provides valuable insights into dispersed phase effects on the micromixing efficiency.
... A high concentration of the by-product serves as an indicator for poor micromixing [27]. The consecutive competing reaction scheme developed by Bourne et al. [28] is widely used as such a probe by setting two chemical reactions with great difference in reaction rate [6,29]. Due to the stable reactants and the easy Bachelor length scale, m detection method of product concentration, such a reaction system is employed in current work, as follows, ...
Mixing performance for a consecutive competing reaction system has been investigated in a swirling vortex flow reactor (SVFR). The direct quadrature method of moments combined with the interaction by exchange with the mean (DQMOM-IEM) method was employed to model such reacting flows. This type of reactors is able to generate a strong swirling flow with a great shear gradient in the radial direction. Firstly, mixing at both macroscale and microscale was assessed by mean mixture fraction and its variance, respectively. It is found that macromixing can be rapidly achieved throughout the whole reactor chamber due to its swirling feature. However, micromixing estimated by Bachelor length scale is sensitive to turbulence. Moreover, the additional introduction of ultrasound irradiation can significantly improve the mixing uniformity, namely, free of any stagnant zone presented in the reactor chamber on a macroscale, and little variance deviating from the mean environment value can be observed on a microscale. Secondly, reaction progress variable and the reactant conversion serve as indicators for the occurrence of side reaction. It is found that strong turbulence and a relatively fast micromixing process compared to chemical reaction can greatly reduce the presence of by-product, which will then provide homogenous environment for particle precipitation. Moreover, due to the generation of cavitation bubbles and their subsequent collapse, ultrasound irradiation can further intensify turbulence, creating rather even environment for chemical reactions. Low conversion rate was observed and little by-products were generated consequently. Therefore, it is suggested that the SVFR especially intensified by ultrasound irradiation has the ability to provide efficient mixing performance for the fine-particle synthesis process.
... Not only does there exist turbulence but also the co-occurrence of parallel reactions in the current reacting turbulent flows. Suffice it to say that turbulence and competitive-consecutive reactions [1,30,31,32] when combined herein pose a great challenge in reactive flows. Since the reactions take place in dilute species concentrations, the effects of chemistry on the flow field and the variation of the local viscosity due to the generation of the chemical products are not considered in this study. ...
... So the selectivity of Z can be used to assess mixing efficiency of the reactor. A typical consecutive-competitive reaction system is the coupling reactions of 1-naphthol and diazotized sulphanilic acid proposed by Bourne et al. 12 The representative of parallel competitive system is the Villermaux/Dushman reaction system, which is consisted of a neutralization reaction and a redox reaction about iodide. 13 Furthermore, the test reactions coupling of acid-base neutralization and alkaline hydrolysis of halogenated ester are also a widely used parallel competitive reaction system. ...
Here, the consecutive‐competitive reaction system about aspirin and sodium hydroxide was proposed as a unified chemical probe to characterize the homogenous and heterogeneous liquid–liquid mixing. The kinetics of the reaction system was clearly studied. Then the mixing efficiencies were assessed in a standard stirred tank with this chemical probe and the obtained segregation index (XS) could well characterize the mixing performance. Based on the incorporation model, the estimation formula of micromixing time was established as tm=13.956ν/ε0.5. The chemical probe could show the influence of stirring intensity, interphase resistance, and two‐phase ratio on the mixing efficiency sensitively when it was extended to heterogeneous mixing. Using this chemical probe, we found the mixing efficiencies of homogeneous and heterogeneous process tended to be the same at sufficiently high stirring intensity. The reason for this phenomenon was unveiled by investigating the dispersed phase size and calculating mass transfer time.
... The former employs an iodide-iodate compounds, whilst the latter uses azodyes. Both can be used to quantify micromixing by determining which product is made spectrophotometrically (Bourne et al. 1981;Guichardon & Falk 2000). ...
Valorisation of agricultural wastes, such as Sugar Beet Pulp (SBP), for production of biofuels and value-added chemicals, has garnered increasing interest in recent years. Through physicochemical means, lignocellulosic material can be pretreated to release monosacharides which can then be upgraded by fermentative and biocatalytic routes. Previous UCL-led research has examined many aspects of utilisation of waste streams from sugar refineries. Vinasse, a glycerol-rich waste product of bioethanol production, was used as a nutrient source for enzyme production. Sugars from SBP, such as D-glucose, L-arabinose and D-galacturonic acid and which make up approximately 25% w/w, 21% w/w, and 20% w/w of the total pulp weight, respectively, were solubilised through operations such as steam explosion pretreatment and depolymerisation of the released polysaccharides. These SBP monosaccharides were then employed in bioconversion reactions using thermostable enzymes. This Thesis aims to study SBP as a feedstock for the enzymatic production of value added chemicals. It also aims to translate key reactions in the valorisation process from batch mode into a continuous flow process in a scalable, 100 mL, Agitated Cell Reactor (ACR). Initial Residence Time Distribution characterisation of the ACR showed that it provided excellent plug flow properties, equivalent to 13 stirred reactors in series. The ACR was able to handle SBP slurries over a range of solids loadings (1% w/v – 5% w/v) and residence times (3.8 min – 19.0 min). The SBP suspension was shown to be shear thinning with measured viscosities in the range of 0.0011 Pa.s at 1% w/v and 0.0339 Pa.s at 10% w/v. A set of correlations was developed that enable prediction of the feed viscosity as a function of SBP concentration and shear rate. The SBP particle size distribution ranged from 15.0 μm (D10) to 446 μm (D90) with a median size of 128 μm. Studies on the particle flow through the ACR demonstrated that steady state could be achieved, but that larger particles had longer residence times than smaller particles through the ACR. Dilute acid pretreatment (DAP) of SBP was investigated as an alternative to previous work on steam explosion as it would be more compatible with continuous operation. DAP using sulfuric acid at concentrations up to 75 mM and 80 °C was performed. These conditions showed good release of polymeric L-arabinose, which increased with higher temperatures and acid concentrations (70% w/w at 75 mM and 80 °C). Cellulose, which is more heat- and acid-resistant than SBP pectin, was only slightly hydrolysed into D-glucose, creating the potential for selective sugar fractionation. When compared to steam explosion pretreatment, flow DAP in the ACR obtained similar throughputs (3.5 and 3.1 g(L-arabinose).hr⁻¹, respectively), but productivity (throughput in terms of reactor volume) was an order of magnitude higher (3.5 and 25.6 g(L-arabinose).L⁻¹.hr⁻¹). Monomerisation of the polymeric L-arabinose could be achieved in a continuous flow enzyme-membrane as in previously described work. Finally, valorisation of the L-arabinose monomers by a continuous-flow, two-step enzymatic process in the ACR was demonstrated. L-gluco-heptulose is a rare ketoheptose which has potential cancer and diabetes treatment applications. The one-pot two-step production of L-gluco-heptulose using a thermostable transaminase (TAm) and transketolase (TK) both isolated from Deinococcus geothermalis DSM11300 was also carried out in the ACR. The initial goal was to use immobilized TK and TAm enzymes in order to intensify the bioconversion process. While TK could be successfully immobilized on both Nickel-chelated beads and Epoxymethacrylate resin, the TAm immobilization proved challenging with only low levels of retained activity. Consequently, the flow studies were performed with soluble TK and TAm enzymes. ACR bioconversions compared favourably with well-mixed batch reactions yields using the same reaction time (2 hours). Initial studies demonstrated the conversion of model substrates L-arabinose, L-serine and α-ketoglutaric acid into L-gluco-heptulose. Subsequently it was shown that L-gluco-heptulose could be synthesised equally well using SBP-derived L-arabinose. Concentrations of the intermediate product hydroxypyruvic acid (HPA) and L-gluco-heptulose obtained in continuous mode were 2.62 mM and 0.60 mM, respectively using SBP derived L-arabinose and 1.21 mM and 0.31 mM, respectively, using model solutes. This was equivalent throughputs of 170.5 µM.hr⁻¹ and 39.0 µM.hr⁻¹ for the SBP derived L-arabinose and 81.0 µM.hr⁻¹ and 20.0 µM.hr⁻¹ for the model solutes. Higher final L-gluco-heptulose concentrations could be obtained by increasing starting L-arabinose concentrations. The continuous process demonstrated here has clear potential for use within a SBP biorefinery. Future work needs to focus on alternative methods of TAm immobilization to enable process intensification and scale-up to pilot scale in order to demonstrate robust commercial operation.
... To characterize micromixing efficiency, various chemical test reactions have been developed such as the azo-coupling of 1-naphthol with diazotized sulphuric acid (Bourne reaction) [10] or the iodide-iodate test reaction also known as the Villermaux-Dushman reaction [11] which is extensively applied to characterize batch and continuous reactors. The Villermaux-Dushman reaction was first developed for a stirred tank reactor but later has been transferred to continuous reactors. ...
For the first time, micromixing characterization for the Villermaux–Dushman reaction could be performed with a non-reactive viscous medium at viscosities up to 2 Pas. As viscous medium, sucrose solution was used with the benefit of being a Newtonian fluid with tuneable viscosity. Due to the higher viscosities in comparison to established media for micromixing investigations, a new protocol for the experimental implementation was developed. Micromixing experiments were conducted and the applicability of viscous sucrose solutions was proven in a stirred tank reactor. Major challenges in characterizing micromixing efficiency in high viscous solution were consolidated.
... The hypothesis on Damkhöler number: Da = (mixing time)/ (reaction time) ≫ 1 indicates a prevalent effect of turbulent mixing time with respect to the reaction time due to the speed of the combustion reactions [54][55][56]. This of turbulence assures uniformity of the main thermochemical properties. ...
In the annular burner of a 100 kWe micro gas turbine (MGT), combustion begins or is supported by pilot. flames appropriately located. These can be thought as partially stirred reactors in which reagents are considered immiscible at the molecular level and homogeneous in the spatial dimension. The survey reports of a numerical sensitivity analysis developed in two steps. The first on the pilot flame model, focusing on some of the most well-known kinetic schemas of hydrocarbon combustion simulation, has helped to extrapolate the optimal conditions of ignition. Performances of different gaseous biofuels, simulated via the kinetic model's methane 17, methane 30, and GRI Mech 3.0, to extrapolate, in a sort of principal component analysis to compute NOx production. Operational environment described by the fluid-dynamic parameter MIXT, that identifies the partially stirred conditions of the flame; temperature at ignition, Tinit; the best feeding ratio. GRI Mech 3.0 is the only model able to calculate NOx production and so it was considered at the optimal conditions, by induction, in a sort of extensive meta-analysis.
... Approaches based on competing reaction system are widely used owing to their universal applicability, such as the azo reaction system 29,30 and the acid-base neutralization and alkaline hydrolysis of ethyl monochloroacetate system. 31 In particular, the iodideiodate reaction system, also known as the Villermaux-Dushman protocol 32,33 is a commonly used chemical quantification method for micromixing. ...
The gas–liquid vortex reactor (GLVR) has substantial process intensification potential for multiphase processes. Essential in this respect is the micromixing efficiency, which is of great importance in fast reaction systems such as crystallization, polymerization, and synthesis of nanomaterials. By creating a vortex flow and taking advantage of the centrifugal force field, the liquid micromixing process can be intensified in the GLVR. Results show that introducing a liquid into a gas‐only vortex unit results in suppression of primary and secondary gas flow. The Villermaux–Dushman protocol is applied to study the effects of the gas flow rate, liquid flow rate, and liquid viscosity based on a segregation index. Based on the incorporation model and reaction kinetics, the micromixing time of the GLVR is determined to be in the range of 10⁻⁴ ~ 10⁻³ s, which is comparable to the highly efficient rotating packed bed and substantially better than a static mixer.
... Thus, Da 1 and Da 2 can be estimated using Equations (31) and (32). ...
Effect of hydrodynamic heterogeneity on micromixing intensification in a Taylor–Couette flow (TC) reactor with variable configurations of inner cylinder has been investigated by adoption of a parallel competing iodide‐iodate reaction system. Two types of inner cylinder, circular inner cylinder and lobed inner cylinder (CTC and LTC), were used to generate hydrodynamic heterogeneity, focusing on the effects of the Reynolds number, the acid concentration, and the feeding time on the micromixing performance. Segregation index (Xs) was employed to evaluate the micromixing efficiency. It is revealed that Xs decreases with the increase of Reynolds number and feeding time but increases with the increase of acid concentration for both the CTC and LTC. However, the LTC does present a better micromixing performance at various operating conditions than that of the CTC as affirmed by both the experimental and computational fluid dynamics simulation results.
... Due to the rigorous conditions imposed for the on-line analysis of the single reaction, the last two schemes are favoured and usually employed when measuring the final product quality. Bourne and his co-workers proposed several reaction systems based on the consecutive competing scheme, such as the bromination of 1,3,5-trimethoxybenzene (Bourne and Kozicki, 1977), the azocoupling of 1-naphthol with diazotised sulphanilic acid (Bourne et al. , 1981) and the selective iodination of l-tyrosine (Bourne and Rohani, 1983). However, these proposed systems and the experimental methods still have some disadvantages, especially with their toxic, volatile and unstable nature. ...
... In other words, well-micromixed bioreactors allow higher yields whereas poorly micromixed devices lead to lower yields and favor by-product formation. It is remarkable that these conclusions perfectly match the modern vision of the interaction between reaction and mixing developed by Bourne, Bałdyga and Villermaux, among others, in the 80s [4][5][6]. The basic explanation is that mixing precedes the reaction. ...
The law of Pirt indicates that the substrate into biomass yield is a function of the cell's specific growth rate. This law introduces the concept of maintenance. Using experimental data regarding cell cultivation in heterogeneous bioreactor, we could show that the maintenance coefficient was actually an increasing function of the concentration field variance. Thus, we could relate the degree of mixing in a bioreactor with the change in the cell physiological state. Since the only information needed is the variance of the concentration field, a 3D description of the flow inside the reactor is not requested. In contrast, a 0-D model for hydrodynamics coupled to a PDF description of the concentration distribution works equally well. In highly segregated systems, the PDF can be approximated by two Delta functions and a IEM mixing model could therefore be used to predict mixing effects on bioeractor performances at a very low computational cost. Our proposition of modification of the law of Pirt including mixing effects on maintenance provides a very simple and cheap way to account for substrate gradients in industrial bioreactors.
... Notably, it is reasonable to assume that the diazo coupling reactions occur isothermally at 298 K for that the solution is dilute and the thermal diffusivity is about two orders of magnitude greater than the mass diffusivity. 29,30 The solution for the velocity field was used as input to solve for the species concentration profiles in the next step. ...
We present a 3D metal printing showerhead mixer to blend effectively two reagent streams into a confined mixing volume. Each stream is predistributed to multiple channels to increase the contact area in the mixing zone, which enables high mixing performance with smaller pressure drop. The showerhead mixer shows excellent mixing performance owing to its ability to intersperse rapidly the two streams as characterized by the diazo coupling reactions and computational fluid dynamics (CFD) simulations. Experimental results demonstrate superior performance of the showerhead mixer compared to two common commercial micro T‐mixers, especially in low Reynolds number regime. CFD results are employed to (a) help understand the mixing mechanism, (b) reproduce the experimental observations, and (c) inform the design specifications for optimal performance. Good agreement between experiments and simulations is achieved. The final design includes multiple side‐fed inlets for improved mixing performance of the showerhead mixer, as suggested by the validated CFD models.
... 4 This has therefore been acknowledged as one of the prime indicators to quantify the performance of reactors in recent years. In these years, some fast competitive chemical reaction systems [5][6][7] were developed and many researchers adopted them to measure the micromixing efficiency in conventional reactors 8,9 and novel reactors. [10][11][12] The most commonly used test systems are categorized into consecutive competitive reactions and parallel competitive reactions, 2 such as the iodide-iodate reaction, 5 the coupling of 1-naphthol with diazotized sulfanilic acid reaction 6 and the alkaline hydrolysis of ethyl chloroacetate reaction. ...
BACKGROUND
The rotating foam stirrer reactor (RFSR) has shown its high mass transfer efficiency. Nevertheless, its micromixing efficiency, which is one of the significant parameters, still needs more comprehensive study for its better application and optimization. This work therefore employed the iodide–iodate reaction system to analyze the micromixing efficiency in an RFSR, and the effects of reactor configuration and liquid viscosity on micromixing efficiency were investigated.
RESULTS
The results show that high micromixing efficiency can be achieved when the feed location is at the outer edge of the rotor. Solid foam with low pores per linear inch (ppi) and equipping baffles on the reactor wall can also considerably improve the micromixing efficiency. The results further reveal that the micromixing efficiency decreased with increasing liquid viscosity. Micromixing times in an RFSR with various configurations, estimated based on the incorporation model, ranged from 2.1 × 10⁻⁴ to 2.0 × 10⁻² s. The minimum value is smaller than that of many conventional reactors and is competitive with that of some novel reactors. In addition, a correlation to predict the micromixing time based on the average energy dissipation rate was developed, which agreed well with experimental values.
CONCLUSION
This study indicates that the RFSR has excellent micromixing efficiency and also provides fundamental information for optimization of the RFSR and its application in process industries. © 2019 Society of Chemical Industry
... Also the use of radioactive labelling techniques to follow the reaction rate was proposed (Domnesteanu 1973). Bourne et al. (1981) proposed the use of a competitive consecutive reaction (azo-coupling) and measurement of the product distribution. Even neutralization reactions have been studied (Bourne 1982). ...
... Habchi et al. [13] proposed a generic experimental procedure for the borate/iodide/iodate system to ensure better testing accuracy based on matching the reactor micromixing time with the optimal reagent concentrations. A typical serial competitive reaction system is the coupling of 1-naphthol with diazotized sulfanilic acid in dilute alkaline solution to produce two (monodiazo and bisazo) dyestuffs, developed by Bourne et al. [14]. ...
Micro-mixing is an important mechanism, which works simultaneously with macro-mixing in chemical reactors in process industries, for achieving the best selectivity with respect to desired products. In about a half century, a huge amount of data and knowledge has been accumulated from theoretical and experimental studies on micro-mixing. Nevertheless, those results are mostly composites of simplified theoretical and empirical models, and the true nature of interactions of flow inhomogeneity and micro-mixing with chemical reaction has not been fully unveiled. This article reviews the progress in micro-mixing study in chemical reactors to date. A few important topics related to the nature, experimental evaluation, and numerical simulation of micro-mixing are addressed. Some suggestions are given hopefully to motivate more chemical engineers to devote their efforts to better understanding of micro-mixing in chemical reactors.
... The reaction systems used to characterize micromixing characteristics of impeller mainly include competitive-consecutive reaction and parallel competing reaction. The coupling reaction between 1-naphthol with diazotized sulphanilic acid proposed by Bourne et al. [11] is the most common competitive-consecutive reaction. Parallel competing reaction systems typically involve the parallel competing reaction for sodium hydroxide between neutralization with hydrochloric acid and alkaline hydrolysis of ethyl monochloroacetate [12] , parallel competing reactions for the precipitation of cupric hydroxide and the alkaline hydrolysis of ethylchloroacetate [13] , iodide-iodate reaction [14][15][16][17] etc . ...
The novel large-double-blade impeller spans a wide range of industrial application areas owing to its obvious advantages in the rapid reactions. So it is indeed necessary to have a profound understanding of microrriixing characteristics about the novel large-double-blade impeller. This paper establishes a model to analyze the three main factors' effect on the segregation index through the numerical simulation which is used to research the performance of novel large-double-blade impeller. The three main factors are separately feed discretization number, feeding location and agitation speed. Through the analysis above, the turbulent energy dissipation rate and concentration distribution of H+, I-3(-) would be deduced. Meanwhile, it compared with the Fullzone (FZ) impeller and double ribbon (DHR) impeller. The results show that (1) when the feed discretization number is over 35, the segregation index would tend to be the fixed specific value. And only in that situation, the effect of macro mixture could be ignored. (2) The optimized feeding location is in the blade area with a vast, turbulent energy dissipation rate to achieve a better micromixing performance, which is demonstrate by the consumption curve of H+ and the generation contour of I3(-). (3) The main spot of the consumption of H+ and the generation of I-3- is on the one side of the feeding location. Besides, compared with FZ impeller and DHR impeller in the same scale and operating condition, novel large-double-blade impeller has a better micromixing performance.
... In the case k 1 k 2 , the selectivity of species R is sensitive to mixing (see Bourne and Rys, 1981) and this reaction is used as a test case on this basis later on. ...
This thesis investigates mean reaction rate closures for turbulent reacting flow. The closures model the mean rate of reaction in the flow and are applied to simulations of nanoparticle formation. The simulations couple detailed chemical reaction, particle population dynamics and turbulent flow, and offer the potential to improve the understanding of a range of industrial processes.
The numerical behaviour of a mean reaction rate closure based on the direct quadrature method of moments using the interaction by exchange with the mean micromixing model (DQMoM-IEM) is studied in detail. An analytic expression is presented for the source terms and a filter function introduced to address issues of boundedness and singularity. Analytic integrals are presented for special cases of specific terms. The implementation of the method in the Star-CD computational fluid dynamics code is described in detail and validated against a test problem.
The numerical performance of DQMoM-IEM is systematically compared to the stochastic fields (SF) turbulent reaction model. The methods share many similarities and are presented in a common mathematical framework for the first time. They differ in their treatment of key terms that make DQMoM-IEM numerically challenging. A variance reduction technique using antithetic sampling is introduced to increase the efficiency of the SF method. However, DQMoM-IEM is shown to remain competitive for the test problem considered.
A new methodology is presented to couple a detailed particle model to simulations of turbulent reacting flow. A projected fields (PF) method based on DQMoM-IEM is used to combine detailed chemistry and the method of moments with interpolative closure (MoMIC) population balance model in Star-CD. The method is applied to the example of the chloride process for the industrial synthesis of titania nanoparticles and includes full coupling between the flow, chemistry and particles undergoing simultaneous inception, coagulation and surface growth.
... To characterize mixing and the influence of flow rates and geometries, several experimental methods, either physical or chemical, have been developed: (1) injection of an electrolyte and use of a conductivity probe [14], (2) visualization of a dye along the mixing device [15], (3) use of reactions generating colored species or a color change [15], (4) use of two consecutive or parallel competitive reactions with different characteristic time and the determination of the concentration of the product obtained by the slowest reaction [16]. Nowadays, the system of parallel competitive reactions proposed by Guichardon et al. [17], the so called the Villermaux-Dushman reaction and the one proposed by Baldyga et al. [18] are widely used. ...
Mixing efficiency of three Hartridge-Roughton mixers with different geometries is characterized by a segregation index measured via the Villermaux/Dushman test reaction and by Computational Fluid Dynamics. The small values of the segregation index (always lower than 0.025 for the concentrations and the flow rate studied) confirm these vortex mixers achieve very good mixing performance. The use of the Turbulent Mixing Model indicates that mixing times are less than 5 ms for inlet flowrates faster than 5 L/h. Mixing performance is even better when these devices have a separate mixing chamber upstream of a narrower outlet pipe, whose diameter is half that of the chamber. Computational Fluid Dynamics shows the internal flow depends on the geometry of the mixer and has a direct influence on its efficiency. When no separate chamber is present, the flow has a double spiral structure. The two inlet fluids roll up together as they pass through the mixer, which slows down the mixing process. For precipitation reactions, we recommend the use of a mixer with conical narrowing which has a high mixing efficiency and a lower risk to be obstructed by the particle agglomeration.
... In the case k 1 k 2 , the selectivity of species R is sensitive to mixing (see Bourne and Rys, 1981) and this reaction is used as a test case on this basis later on. ...
This thesis investigates mean reaction rate closures for turbulent reacting flow. The closures model the mean rate of reaction in the flow and are applied to simulations of nanoparticle formation. The simulations couple detailed chemical reaction, particle population dynamics and turbulent flow, and offer the potential to improve the understanding of a range of industrial processes.
The numerical behaviour of a mean reaction rate closure based on the direct quadrature method of moments using the interaction by exchange with the mean micromixing model (DQMoM-IEM) is studied in detail. An analytic expression is presented for the source terms and a filter function introduced to address issues of boundedness and singularity. Analytic integrals are presented for special cases of specific terms. The implementation of the method in the Star-CD computational fluid dynamics code is described in detail and validated against a test problem.
The numerical performance of DQMoM-IEM is systematically compared to the stochastic fields (SF) turbulent reaction model. The methods share many similarities and are presented in a common mathematical framework for the first time. They differ in their treatment of key terms that make DQMoM-IEM numerically challenging. A variance reduction technique using antithetic sampling is introduced to increase the efficiency of the SF method. However, DQMoM-IEM is shown to remain competitive for the test problem considered.
A new methodology is presented to couple a detailed particle model to simulations of turbulent reacting flow. A projected fields (PF) method based on DQMoM-IEM is used to combine detailed chemistry and the method of moments with interpolative closure (MoMIC) population balance model in Star-CD. The method is applied to the example of the chloride process for the industrial synthesis of titania nanoparticles and includes full coupling between the flow, chemistry and particles undergoing simultaneous inception, coagulation and surface growth.
Optimal control over fast chemical processes hinges on the achievement of rapid and effective mixing. Impinging jet mixers are a unique class of passive mixing devices renowned for their exceptional ability to achieve rapid mixing at micro‐length scales, whilst offering the possibility of a high throughput. Comprising of two co‐linear jets flowing in opposite directions and colliding with each other within a small (usually confined) volume, these devices effectively intensify various mixing‐controlled processes in a reproducible manner. Impinging jet mixers find extensive use in both the chemical and pharmaceutical industry for a plethora of applications, such as reaction injection molding and precipitation processes. This review provides an overview of research related to impinging jet mixers, with an emphasis on the mixing characteristics and the influence of design and process parameters on the mixing performance. Lastly, specific applications for which these devices are exceptionally suited are discussed.
In the spotlight of successful breakthrough of the COVID-19 mRNA vaccines, lipid nanoparticles are becoming an important vehicle to deliver a variety of therapeutics. The encapsulation of mRNA using lipids is a self-organizing process that necessitates fast mixing to achieve uniform supersaturation. This is achieved in a confined impinging jet reactor (CIJR) where two input jets collide and fast mix in the mixing chamber. While CIJR is not a new mixing technology, it stands out for its capability to achieve mixing times below a millisecond. This study presents a critical review of major studies concerning CIJRs, starting with the CIJRs’ structures and flow characterization, through experimental and numerical studies, and closing with successful applications in a wide range of chemical/pharmaceutical processes. The detailed mixing principles, scaling-up, and mechanisms of making nanoparticles are discussed focusing mainly on the hydrodynamic aspect. The objective of the review is to supply essential information for the optimized design and operation of CIJRs, catering to both industry and academia.
Liquid-liquid mixing, including homogeneous and heterogeneous mixing, widely exists in the chemical industry. How to quantitatively characterize the mixing performance is important for reactor assessment and development. As a convenient and direct method for mixing characterization, the chemical probe method uses some special test reactions to characterize the mixing results. Here, the working principle and selection requirements of this method are introduced, and some common chemical probe systems for homogeneous and heterogeneous mixing processes are reviewed. The characteristics and applications of these systems are illustrated. Finally, the development of the new system is proposed.
A polyurethane reaction under different mixing rates and reaction rates are studied in an adiabatic batch reactor. Results are explained by using a slab model and dimensional analysis. Four characteristic times are used to describe the interactions of mixing, diffusion and chemical reaction, which may serve as conceptual guidelines in determining the proper reaction rate and mixing power for a specific reaction system.
An experimental investigation into the micromixing performance of coaxial mixers in a viscous system is reported, in which the iodide‐iodate reaction system is chosen to quantitatively characterize the product distributions. The effects of feeding time, feeding position, impeller speed, inner impeller configuration, and operation mode on the segregation index, Xs, are examined. It is revealed that the feeding near the inner impeller benefits micromixing and should be regarded as the preferred position. The presence of the rotating outer impeller causes the micromixing performance of the coaxial mixer to be significantly better than the single‐shaft mixer. While an increase in the outer impeller speed has a limited influence on micromixing, the inner impeller speed is the dominant influencing factor, that is, the Xs decreases obviously when the inner impeller speed is increased. On the other hand, the coaxial mixers with multiple and axial inner impellers have a better micromixing performance at the same specific power consumption, PV, than that with single and radial inner impellers. Among the configurations consisting of a Rushton impeller (RT), six‐straight‐blade turbine impeller (SBT), and six‐pitched (45o)‐blade turbine impeller (PBT), the Xs of the coaxial mixer is always the smallest at the same PV when the PBT + RT configuration is used as the inner impeller. In addition, it is found that the difference in Xs that results from various operation modes is small in terms of power consumption; however, the co‐rotation mode is still recommended for the micromixing of the coaxial mixer due to its excellent performance in general.
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In view of the significance, complexity and difficulty of micromixing in viscous system, coaxial mixers with wide adaptability to viscosity are first combined with the micromixing. The effects of feeding position, rotation mode and impeller type on the micromixing performance of coaxial mixers are investigated numerically with standard engulfment model and eddy dissipation concept model (EDC), and a dimensionless estimating correlation of segregation index Xs is established based on the Buckingham π theorem. The results show that feeding near the discharge zone of the impeller favors the micromixing and Rushton turbine impeller (RT) is better qualified as the impeller near feeding point compared with six-straight-blade turbine impeller (SBT) and six-pitched(45o)-blade turbine impeller (PBT). At the same specific power consumption, the coaxial mixer has better micromixing performance with PBT+RT as inner impeller than with SBT+RT, and the difference of segregation index resulting from the rotation mode is small. Moreover, the proposed correlation is validated to be suitable for qualitative evaluation of micromixing performance of coaxial mixer consisting of inner impeller combining PBT and RT and outer anchor.
Scale-up predictions from continuous flow micro- (lab) to milli- (pilot or production) scale are important, but not trivial. To overcome the necessity of time-consuming trials on pilot or production scale, this work presents a model-based approach that builds on prior lab experiments. However, it also improves the understanding of the involved chemical process. A complete process development for a highly exothermic organometallic reaction is conducted. Kinetic studies on lab-scale, using inline FT-IR measurements, constitute the basis for a systematic scale-up approach. Subsequently, the scale-up from microreactor (inner diameter 0.5 mm) to milli-scale pilot reactor (inner diameter of 2 mm) through increasing the channel diameter and flow rates is investigated. Model-based scale-up predictions are presented, including heat and mass balances.
Use of a membrane within a bioreactor (MBR), either microbial or enzymatic, is a technology that has existed for 30 years to increase process productivity and/or facilitate the recovery and the purification of biomolecules. Currently, this technology is attracting increasing interest in speeding up the process and in better sustainability. In this work, we present the current status of MBR technologies. Fundamental aspects and process design are outlined and emerging applications are identified in both aspects of engineering, i.e., enzymatic and microorganism (bacteria, animal cells, and microalgae), including microscale aspects and wastewater treatment. Comparison of this integrated technology with classical batch or continuous bioreactors is made to highlight the performance of MBRs and identify factors limiting their performance and the different possibilities for their optimization.
This chapter deals with modeling and simulation issues specific to multiphase bioreactors. Characteristic times of mixing, mass transfer, and biological phenomena (growth and uptake) are calculated and used to provide a guide for the modeling of bioreactors at various scales. Depending on the ratio of these characteristic times, simplifying hypothesis, related to the degree of homogeneity within each phase, can be made. As far as the biological phase is concerned, heterogeneity appears to be constitutive but also partly induced by the fluctuating environment of the cell. A strong two-way coupling results and constitutes the specificity of bioreactors. The predictive unsteady simulation of a bioreactor requires a sounded combination of hydrodynamic, mass transfer, and metabolic models. The scale-up (20L to 20m³) proposed at the end of the chapter reveals that in addition to the concentration gradients, the exposure time to nutrient excess/limitation and the intrinsic biological dynamics are equally important.
This chapter deals with modelling and simulation issues specific to multiphase bioreactors. Characteristic times of mixing, mass transfer and biological phenomena (growth and uptake) are calculated and used to provide a guide for the modeling of bioreactors at various scales. Depending on the ratio of these characteristic times, simplifying hypothesis, related to the degree of homogeneity within each phase, can be made. As far as the biological phase is concerned, heterogeneity appears to be constitutive but also partly induced by the fluctuating environment of the cell. A strong two-way coupling results and constitutes the specificity of bioreactors. The predictive unsteady simulation of a bioreactor requires a sounded combination of hydrodynamic, mass transfer and metabolic models. The scale-up (20 L to 20 m3) proposed at the end of the chapter reveals that beside the concentration gradients, the exposure time to nutrient excess/limitation and the intrinsic biological dynamics are equally important.
Magnetic nanofluid actuation by rotating magnetic fields was proposed as a high-performance tool for liquid mixing with enhanced micromixing features. A comparative study was conducted to evaluate the mixing index in T-type mixers of magnetic and non-magnetic fluids subject to static (SMF), oscillating (OMF) and rotating (RMF) magnetic fields. RMF excitation unveiled superior mixing indices with strong dependences to magnetic field frequency and content of magnetic nanoparticles. The impact of magnetic field types on micromixing was further examined at low and moderate Re numbers using the Villermaux-Dushman reaction and IEM micromixing model. The IEM-inferred micromixing times were remarkably shorter by nearly 4 orders of magnitude in comparison with OMF and SMF excitations, and without magnetic field. The proposed mixing strategy is foreseen to complement innovative microfluidic devices with valuable mixing tools and methods for the diagnosis of the coupling between transport and intrinsic kinetics. This article is protected by copyright. All rights reserved.
Reactive flows in the liquid phase are of major interest for the chemical engineers, but also for the scientist from a theoretical point of view.
Attempts to describe mixing in chemical reactors is one of the most striking examples which show that Chemical Reaction Engineering is not a mere combination of chemistry and applied physics, but an original scientific discipline which has developed its own concepts .
Micromixing efficiency at larger Reynolds number(Re) conditions was investigated in a side tee mixer by using iodide-iodate test reaction as working system, which was characterised by a segregation index Xs. Experiments were conducted by considering the effects of Re, flow rate ratio, reactant concentration, viscosity and "branch" pipe diameter on micromixing efficiency. The results showed that the influence of micromixing to iodide-iodate test reaction was insignificant when Re was larger than 12 000. Based on the incorporation model, the micromixing time of the side tee mixer was estimated in the range of 3 × 10-5 to 3 × 10-4s, which indicated that side tee mixer is an attractive alternative to stirred tanks that the micromixing time was 0. 02-0. 2 s.
Numerical simulation of multiphase reactors with continuous liquid phase provides current research and findings in multiphase problems, which will assist researchers and engineers to advance this field. This is an ideal reference book for readers who are interested in design and scale-up of multiphase reactors and crystallizers, and using mathematical model and numerical simulation as tools. Yang and Mao's book focuses on modeling and numerical applications directly in the chemical, petrochemical, and hydrometallurgical industries, rather than theories of multiphase flow. The content will help you to solve reacting flow problems and/or system design/optimization problems. The fundamentals and principles of flow and mass transfer in multiphase reactors with continuous liquid phase are covered, which will aid the reader's understanding of multiphase reaction engineering. © 2014 Chemical Industry Press. Published by Elsevier Inc. All rights reserved.
Processes for micromixing of liq. streams with chem. reactions by continuous collision were briefly reviewed. A new apparatus based on 2 perpendicular jets was developed and used for the pptn. of dyes produced by coupling p-N2C6H4SO3H with 1-naphthol (test method). The process was recommended for pptn. of pharmaceutical products from reaction mixts. as fine crystals (1-5 μm).
The non-isothermal coalescence/redispersion micromixing model is presented and analysed using the population balance approach. Development of the model is based on the concept of diffusive mass and heat exchange interactions of the fluid elements identified as the Kolmogorov-scale eddies. The model is formulated as a non-linear, multidimensional population balance equation describing deterministic chemical reactions and temperature variations inside the fluid elements and stochastic mass and heat exchange processes between the fluid elements by their impacts. The population balance equation is solved by applying a hybrid continuous time/Monte Carlo method. The behaviour and properties of the model is analysed by numerical experimentation using an adiabatic continuous stirred tank coalescence/redispersion reactor model. Simulation results are presented for second order uni-molecular and quasi-linear consecutive-competitive chemical reactions. It is shown that non-isothermal micromixing in a reactor can be evaluated and characterized by applying appropriately chosen concentration and temperature configurations of partially premixed or segregated feeds measuring the mean concentrations and temperature of the reaction mixture both in dynamic and steady state processes. In well-designed conditions measurement of the mean temperature in itself provides satisfactory information on the mixing state of reactors at microscale.
Scale-up strategies and techniques including economic evaluations at any stage of process development are described in this chapter. Process development is a set of research, design, and engineering activities, accompanied by economic studies. Selection of the most advantageous methods of product isolation, purification, effluent treatment, the most suitable sequence of operations, and the best full-scale equipment are the essence of process development. Basic parts of process development are process design, process engineering, and scale-up procedures. Process design involves determination of all items necessary to construct a plant or to run the process including piping, instrumentation for process control, auxiliary operations, and equipment. Process engineering is a set of activities that leads to the specification of process equipment that is most suitable for processing mixtures with a predetermined composition. Process development must be planned well to anticipate changes. Process development entails laboratory studies, conceptual design, development of individual steps of the process, pilot plants and miniplants, environmental and safety aspects of process development, and process evaluation. Chemical reactors, classification of reactors, the most common industrial reactors, and reactor design, scale-up, and operation problems are presented in this chapter. Some guidelines for scale-up of these techniques and producing experimental data for scale-up are also provided.
Microfluidic opposed mixing tees were tested with hydraulic diameters of 100 mu m, 177 mu m, and 254 mu m. Mixing performance was characterized by feeding one stream with hydrochloric acid and another stream with sodium hydroxide and dimethoxypropane. Under ideal mixing conditions, the instantaneous neutralization of sodium hydroxide with hydrochloric acid would prevent the catalytic hydrolysis of dimethoxypropane. Therefore, higher conversions of dimethoxypropane in this fast, competitive reaction is an indication of lower mixing performance. For a constant Reynolds Number, the mixing performance was increased by decreasing the channel dimensions. Ultrasound energy was externally applied to all three reactors and was found to increase mixing performance. Challenges in sealing the 100 mu m mixer precluded operation at comparable pressures achieved with the 177 and 254 mu m mixers. The highest mixing performance was observed with the 177 um diameter mixer using a combination of pump work and ultrasound energy. A combination of ultrasound energy and pump work was demonstrated to be the most efficient mode of providing mixing for the 254 mu m system. Therefore, externally applied ultrasound energy can be an effective and efficient means of improving the mixing performance of microfluidic systems.
Computational fluid dynamics (CFD) modeling of turbulent reacting flows has a variety of applications, including minimizing the amount of pollutants from internal combustion engines and maximizing the selectivity of a desired product in a chemical reactor. One goal of modeling these flows is to better understand how fluid mixing affects selectivity. A transport equation for the joint composition probability density function (PDF) can be used to model for this purpose (Fox, 2003). Here, the interaction-by-exchange-with-the-mean (IEM) model is used to close the micromixing term in the joint composition PDF transport equation. Both the Conditional Quadrature Method of Moments (CQMOM) (Yuan and Fox, 2011) and the Direct Quadrature Method of Moments (DQMOM) (Fox, 2003) are used in this study to solve the joint PDF transport equation. Compared to direct numerical simulations (DNS), these two methods reduce the computational cost significantly and are applicable to simulate large-scale systems by forcing lower-order moments of a presumed PDF to be exactly preserved (Fox, 2003). Despite reducing the computational cost, statistical methods like these introduce errors that deviate from exact solutions obtained from DNS. In the past, DQMOM has been studied and found comparable results to previous methods (Zucca et al., 2007), but DQMOM introduces correction terms to the transport equations. CQMOM does not introduce these correction terms, and the optimal moments (Fox, 2008) are transported directly rather than as weights and weighted abscissas. Here, a competitive-consecutive reaction system is modeled by the PDF transport equation and solved using DQMOM-IEM and CQMOM-IEM to compare the statistical errors and computational costs of each method. The CQMOM formulation results in a robust solution algorithm for the PDF transport equation with a similar computational cost by avoiding the potentially singular correction terms arising in DQMOM-IEM (Akroyd et al., 2010).
References
Akroyd, J., Smith, A.J., McGlashan, L.R., Kraft, M., 2010. Numerical investigation of DQMOM-IEM as a turbulent reaction closure. Chemical Engineering Science 65, 1915–1924.
Fox, R.O., 2003. Computational Models for Turbulent Reacting Flows. Cambridge University Press.
Fox, R.O., 2008. Optimal moment sets for multivariate direct quadrature method of moments. Industrial & Engineering Chemistry Research 48, 9686–9696.
Yuan, C., Fox, R.O., 2011. Conditional quadrature method of moments for kinetic equations. Journal of Computational Physics 230, 8216–8246.
Zucca, A., Marchisio, D.L., Vanni, M., Barresi, A.A., 2007. Validation of bivariate DQMOM for nanoparticle processes simulation. AIChE Journal 53, 918–931.
An improved impinging stream reactor (ISR) was developed to synthesize the cathode precursor ferric phosphate by performing the reaction between Fe(NO3)3.9H2O and H3PO4 with aqueous ammonia as the precipitating agent. The chemical formula for the synthesized product was identified to be FePO4.3H2O based on the powder X-ray diffraction (XRD), thermogravimetry and differential scanning calorimeter (TG-DSC), and Fourier transform infrared spectrophotometry (FT-IR) measurements. The FePO4.3H2O particles were amorphous and will change to pure crystalline phase of anhydrous FePO4 after heating treatment in air at 600 °C for 5 hours. The particle size distribution (PSD) and morphology were characterized by the laser particle size analyzer and scanning electron microscope (SEM), respectively. It was found that the FePO4.3H2O prepared by ISR particle size is much finer and PSD is much narrower than that by stirred tank reactor (STR). The flow behaviour of both ISR and STR were investigated by determining the residence time distributions (RTD) using an electroconductivity input-response technique with KCl solution as the tracer. Bourne reaction scheme was employed to investigate the micromixing effects in both ISR and STR. The results show that the degrees of backmixing in the two reactors are similar, but the micromixing effect in the former is much better than that in the latter, which accounts for the FePO4.3H2O produced by ISR possess finer size and narrower PSD. The cell performance test results indicate that the LiFePO4/C obtained from FePO4.3H2O produced by ISR can exhibit a better electrochemical property.
This chapter discusses the effects of mixing and related phenomena in typical industrial crystallization processes. Mixing determines the environment in which crystals nucleate and grow, and therefore, it is central to industrial crystallization. Mixing is the family of processes that link local microenvironment to the macroscopic scale of the crystallizer that affects the mass transfer between crystal and the larger environment and the dynamics of crystal suspension in the crystallizer. Mixing creates microcrystal environments to a large extent. Furthermore, it determines the homogeneity of the macroenvironment, both temporally and spatially. Inhomogeneity in the macroenvironment affects microenvironments that cause temporal variations as the crystals circulate from one zone to another inside the crystallizer. Understanding mixing is vital to understand and control the basic phenomena associated with industrial crystallization. Even though quantitative predictions are not available for crystallizers in general, the importance of good qualitative understanding of the mixing phenomena that occur in operating crystallizers should not be underestimated. Both laboratory and computational modeling can now gives qualitative insight into the mixing processes. There are also tools available to investigate specific details of the mixing processes, which are a great help in designing, operating, and troubleshooting.
Stirred tank reactors with a Pfaudler type impeller are frequently used in the production of fine chemicals, but information on the mixing performance of this type of impeller is limited. This information is required to predict selectivities of mixing sensitive processes. For low feed rates, which are often used in the production of fine chemicals, the mixing process is controlled by micromixing. To investigate the micromixing in stirred tank reactors with a Pfaudler type impeller the product distributions of mixing sensitive reaction sets are determined. These experiments show that in a large part of the reactor the product distribution is not a function of feed point position. With a micromixing model (E-model) using the average energy dissipation rate, the product distribution is calculated. The calculated product distributions are in reasonable agreement with the measured product distributions for partially baffled reactors with a Pfaudler type impeller for a broad range of process conditions.
The state of micromixing in a CSTR was experimentally investigated through its influence on the selectivity of consecutive competitive reactions A plus B equals R, R plus B equals S in the liquid phase. An experimental segregation index was defined. The influence of the following parameters was investigated: stirring, space time, viscosity, ultrasounds, concentrations, temperature, nature of the reaction and contacting of reactants. It is demonstrated that the usual assumption of maximum mixedness in the design and use of the CSTR for complex reactions may be quite erroneous. The CSTR is not well suited to kinetic studies of complex reactions unless experimental conditions ensuring a perfect micromixing are determined.
The aim of this study is to provide well established experimental data, and to propose a new and tentative interpretation of micromixing in stirred reactors, with the hope of bridging the gap between phenomenological models and classical results of the theory of turbulence. With this object, the authors have chosen experimental conditions in which micromixing effects were expected to be a maximum i. e. a continuous stirred reactor and a rapid liquid phase reaction close to zero order with unmixed feed of rectants. Experimental parameters were adjusted to such values that the space time, the reaction time and the micromixing time was of the same order of magnitude, ranging from 1 to 10 seconds. Micromixing effects were thus clearly and reliably observed. A new model is proposed which describes the first stages of mixing in stirred tanks. The initial size of segregated domains has been estimated. At low stirring speed, mechanical stirring is much more efficient than jet stirring but this relative efficiency strongly decreases as stirring speed is increased.
A survey of the development of chemical reaction engineering is followed by an account of the current state of knowledge of various types of reactors. The extent to which theoretical concepts have found favor in the design of reactors is examined critically. Determination of kinetic data and the development of mathematical models is examined.
The perceptibly slow conversion of p-nitrobenzenediazonium ion to the anti-diazotate with aqueous base and the reverse process in acid have been studied quantitatively. The syn-diazotate and the conjugate acid of the anti-diazotate have been detected as intermediates of significant life. The kinetics of the reactions and some equilibria have been investigated, all by spectrophotometric methods.
In contrast to many previous investigations, reaction conditions were found under which the nitration of durene (nitrating ratio of 1:1) gives predominantly, and in high yield, mononitrodurene rather than the usually formed dinitrodurene (plus unreacted durene). The method consists in nitrating by nitronium phosphorohexafluoride in nitromethane as solvent in presence of two equivalents of water.
With mixed acid (HNO3 + H2SO4) in nitromethane and in acetonitrile durene forms also monoand no dinitrodurene; but under most conditions by-products are formed. Some of the by-products were identified.
Some preliminary mechanistic results are reported: An addition complex of unknown structure is formed rapidly; 3, 6-dideuterodurene + D2O do not show a hydrogen isotope effect; the preferential formation of dinitrodurene under conventional conditions is due to the fact that the reaction occurs at encounter-controlled rate.
Nach einem kurzen Überblick über die geschichtliche Entwicklung der chemischen Reaktionstechnik wird der derzeitige Stand der Kenntnisse bei den verschiedenen Reaktortypen behandelt. Dabei wird auch kritisch untersucht, inwieweit die theoretischen Vorstellungen Eingang in die Praxis bei der Auslegung von Reaktoren gefunden haben. Es schließt sich ein Kapitel über die Ermittlung kinetischer Daten und die Entwicklung mathematischer Modelle an. Generell läßt sich sagen, daß außerordentlich viele theoretische Arbeiten von häufig zweifelhaftem Wert für die industrielle Praxis durchgeführt werden. Demgegenüber besteht zumindest auf manchen Gebieten ein kaum zu übersehender Mangel an experimentellen Ergebnissen. Die Erkenntnisse der chemischen Reaktionstechnik werden zur Auslegung von industriellen Reaktoren nur sehr zögernd übernommen. Besonders vielversprechend ist eine intensive Zusammenarbeit von Hochschulforschern mit Ingenieuren und Chemikern aus der Industrie, um die theoretischen Konzepte in der Praxis zu überprüfen.
The rate of a homogeneous reaction depends on rate of encounter between reactant molecules. When the reaction mixture consists of two reactant streams flowing into a continuous reactor, or of earlier and later parts of a single stream, the average rate of reaction is in general dependent on the degree of mixing on the molecular scale. It cannot generally be predicted simply from the distribution of residence times.The author analyses the concept of “mixing on the molecular scale”, gives it a quantitative definition, and shows how it can be measured.Some illustrations of practical interest are given.The problem of a generalised treatment of imperfectly mixed homogeneous reactors is tentatively discussed.
Polymer reaction engineering has the general goal of providing a polymerization environment optimum in time, temperature, composition, and shear. Various mixing phenomena play a major role in determining this environment, and the study of polymer reactors is in large part a study of these phenomena. The present work is primarily concerned with the time-composition environment in continuous polymerizers. This leads to a study of residence time distributions and the associated concepts of segregation and maximum mixedness. These concepts may be applied to polymer reactors in much the same way as in simpler chemical reactions. The theory can be applied either as a tool for prediction of performance or as a means for explanation of observed results. In polymer reactors, however, the scope of the prediction or explanation should include details of molecular weight and copolymer composition distributions as well as the overall yield of monomer to polymer.
The disguise of the intrinsic selectivity of competitive, consecutive reaction systems by the mixing process is demonstrated experimentally using the fast nitration of a number of aromatic compounds with nitronium salts in nitromethane. The measured product distributions were compared with the distributions predicted from our mixing-reaction model developed previously [2] [4]. This comparison enabled the relative intrinsic rate constants for the second nitration step of the aromatic compounds investigated to be determined.
The steady state behaviour of a continuous stirred tank reactor at a constant temperature of 30°C was studied using the saponification of ethylene glycol diacetate by sodium hydroxyde. The reactor studied was respectively fed by premixed and unmixed reactants. Experimental values of the level of segregation lay within the range of 0.15 to 0.5. The level of segregation has been correlated with the physicochemical dimensionless group k1C/β and we may conclude that the reactor would be in a state of maximum mixedness when the magnitude of this group is smaller than 10−4.
Le comportement d'un réacteur agité en régime continu et stable, maintenu à une température de 30°C, a été étudié à l'aide de la réaction de saponification du diacétate de glycol par la soude. Les réactifs ont été amenés au réacteur par alimentations prémélangée et séparée. Les valeurs expérimentales du niveau de ségrégation varient entre 0.15 et 0.50. Une corrélation du niveau de ségrégation en fonction du groupe physico-chimique adimensionnel k1C/β a été obtenue et permet de conclure que le réacteur étudié serait à l'état du mélange maximal lorsque l'ordre de grandeur de ce groupe est inférieur a 10−4.
The results of this study show that, for given initial and boundary conditions, four parameters are sufficient to describe the final product distribution of azo coupling reactions influenced by mixing. This is in agreement with the prediction of the mixing-reaction model developed previously [4] [5]. In order to explain the pH-dependence of the measured mixing-disguised product distribution, it is necessary to assume that a selectivity-determining, local pH-gradient exists even though the solution is macroscopically buffered.
Mixing effects for the homogeneous, liquid-phase, second-order, competitive-consecutive reaction of iodine (B) with L-tyrosine (A) to form 3-iodo-L-tyrosine (R) and 3,5-diiodo-L-tyrosine (S) were determined for the following conditions: vessel volume, 5 and 36 liters (baffled and unbaffled); turbine diameter (2 to 6 in.) and speed (95 to 1,600 r.p.m.); feed inlet locations (3), addition rate (0.25 to 18 min.), and distribution; temperature (11° to 43°C.); initial A concentration (0.1 to 0.4 g.-mole/liter); and kinematic viscosity (0.765 to 6.35 centistokes). A was initially charged to the reactor and an equimolar quantity of feed B was added over a time period. Yields of R are less than that expected for perfect mixing owing to local regions of excess B concentration that exist for time periods during which R over-reacts to S.
Agitation power for a given yield is less in unbaffled vessels without an air-liquid interface than for baffled vessels. The local fluctuating velocity u′ where feed is introduced correlates the mixing variables and predicts mixing requirements for maintaining yields of R on scale-up. Regions of excess B concentration are related to a concept of partial segregation. The extent of reaction occurring under this condition is correlated by the dimensionless group (k1bτ) (a0/b), where τ is a microtime scale of mixing related to u′ and the characteristic length of a microscale eddy. The magnitude of this group provides a criterion for predicting the importance of mixing effects on other reaction systems.
The product distribution from the bromination of resorcin (m-dihydroxybenzene) is influenced by mixing in an experimentally convenient range of concentration and mixing intensity at room temperature. The degree of bromination is insensitive to mixing, a fact which can be explained chemically. Similarly explicable is the high sensitivity of the composition of the isomeric dibromoresorcins; the % 2,4-dibromoresorcin formed has been used to characterise mixing in semi-continuous and continuous stirred tank reactor operation. In the latter case the influences of the concentration and flow rate of the feed, turbine speed and feed positions near the turbine were investigated. Although full reaction kinetics are not available, these reactions are fast and sensitive enough to study micromixing.
The systematic study of mixing processes requires a quantitative method of expressing “goodness of mixing”, based on conveniently-made
measurements. In this paper, mixtures of mutually soluble liquids, fine powders, or gases are considered. It is shown that
the important features of such mixtures can be expressed by two statistically-defined quantities, the scale and the intensity
of segregation, and methods of measuring these are suggested. The discussion also throws light on some of the factors which
affect the efficiency of mixing processes.
- Truong