Differentiation criteria study for continuous stirred tank reactor and plug flow reactor

All reactors in reality are not ideal plug flow reactor (PFR) or ideal continuous stirred tank reactor (CSTR). They are difficult to differentiate. This study was to investigate the reactor analysis of PFR and CSTR through tracer response curves, residence time distributions (RTD) and several hydraulic performance indexes. We set up the differentiated value of each index. The tracer response curve showed that our lab-scale CSTR was close to ideal CSTR and got 99.9% recovery. In the RTD curves, the results could significantly recognize the PFR nature of high rate pond (HRP). With hydraulic performance indexes study, every selected index demonstrated that the studied HRP was closer to PFR than the studied CSTR. Based on the lab-scale study results, this study established the cutting point between the PFR and CSTR in each index; we were looking through the different types of reactors in literature and we confirmed the criteria with all literature reactors with the “graphic method”. The method helped us to establish those important values to help us to differentiate the reactor types in practice and to understand the designs better.     

The bifurcation behavior of a polyurethane continuous stirred tank reactor

In this work the open-loop nonlinear bifurcation analysis of a continuous stirred tank reactor where polyurethane polymerization reactions take place is carried out. The effect of potential manipulated, disturbance and design variables on the reactor nonlinear behavior is addressed. Moreover, the impact of cascade feedback control on the steady-state multiplicity pattern is also discussed. It is shown that cascade control introduces new nonlinearity patterns increasing closed-loop sensitivity.     

Calcium carbonate precipitation in a continuous stirred tank reactor

The precipitation of calcium carbonate, brought about by mixing aqueous solutions of calcium nitrate and sodium carbonate in a continuous reactor, has been studied. The pH (8.5-10.0), reagent concentration (0.25-1.7 N), temperature (15-60°C), residence time (1-3 min), and mixing speed (100-500 rpm) were chosen so that the effects of agglomeration could be examined The presence of agglomerates was confirmed by microscopy. Precipitate size distributions were log normal, and the geometric mean diameters, ranging from 5 to 13 p.m, were extremely sensitive to pH. Large precipitates were obtained under conditions favouring a high agglomeration rate; namely high temperatures, concentrations, and mixing speeds. The effect of residence time was minimal. The geometric standard deviation increased with the mean size of the precipitate. The solids recovery decreased with increasing temperature, but was not significantly affected by the other parameters     

Age distribution and the degree of mixing in continuous flow stirred tank reactors

New development of mean age theory is discussed for quantitative analysis of mixing and age distribution in steady continuous flow stirred tank reactors. A new relationship between the moments of age and the moments of residence time are derived. With this new relationship the variance of residence time distribution can be computed much more efficiently and accurately. The relationships of three existing variances of age are described and a new set of variances and the degree of mixing are defined. The theory is used to characterize mixing performance in a CFSTR with different layouts of an inlet and an outlet. Mean age and higher moments of age in the reactors are obtained from CFD solutions of their steady transport equations. The spatial distribution of mean age reveals details of the spatial non-uniformity in mixing. Variances of age and the degree of mixing discussed by Danckwerts and Zwietering are computed for the first time in the literature for non-ideal stirred tank reactors. It is found that although these measures are useful, certain key features in non-uniform mixing are not reflected accurately. Results show that the new set of variances and the degree of mixing more accurately characterize the non-uniform mixing in the reactors.     

Scale-up of continuous flow stirred tank reactors

A model of a continuous flow stirred tank reactor based on laboratory experiments successfully describes the behavior of a pilot plant reactor. This model simulates the pilot plant performance over the full range of operating conditions: at high impeller speeds where performance approaches that of a perfectly mixed reactor and at low impeller speeds where performance significantly differs from perfect mixing. The micro-mixed feed model divides the continuous flow stirred tank reactor into a small micro-mixed impeller zone and a large macro-mixer.     

The optimization of the photo-oxidation parameters to remediate wastewater from the textile dyeing industry in a continuous stirred tank reactor

The remediation of textile dying wastewater was carried out at ambient temperatures in a pilot-scale continuous stirred tank reactor by using the photo-Fenton oxidation process. The preliminary results suggest that the treatment system reached a steady state condition within 5–10 min after it was started up. By using a 2 ^k factorial design, the effects of various parameters on the removal efficiency of color, BOD and COD were identified under steady state conditions. The removal efficiencies of color and BOD were affected by the feed rate of H₂O₂ and Fe²⁺, whereas none of the parameters in the investigated ranges affected the removal efficiency of COD. Consequently, using univariate analysis to investigate higher parameter range values, the optimum conditions for treating textile wastewater were found to be 25 ml H₂O₂/min, 5 ml Fe²⁺/min and 90 W UV-A power for 20 min. In addition, the removal of all pollutants was enhanced within the acidic pH range. Approximately 69.2, 99.4 and 48.5% of color, BOD and COD were removed, respectively. However, the concentration of TDS increased slightly during the treatment period due to the formation of new species or intermediate oxidation products. Nevertheless, all values of pollutants in the treated wastewater except COD were in the range of the standard values permitted for discharge into the environment.     

On the optimal unsteady state operation of a continuous stirred tank reactor

Optimal modes of operation of a continuous stirred tank reactor in which consecutive-competing reactions are taking place are developed; the character of the optimal input control policies is found to depend critically on the number of control variables considered. For a single control variable (the inlet reactant concentrations constrained to vary in phase) the optimal policy depends on the mean residence time and is either periodic, switching between the maximum and minimum permissible levels, or constant at the maximum allowable level. In contrast, when two control variables are considered (the inlet reactant concentrations allowed to vary independently), an intermediate singular policy is obtained in all cases. A procedure for the determination of the singular policy is demonstrated and its optimality is confirmed by optimal control theory and steady state analysis.     

Modeling the continuous melt transesterification of bisphenol-A and diphenyl carbonate in a continuous stirred tank reactor

A model of continuous melt transesterification of bisphenol-A and diphenyl carbonate in a continuous stirred tank reactor is developed using phase equilibria assumption and the method of molecular weight moments. The model equations can be simplified into a polynomial system that has 17 equations and 17 unknowns. Solution of the polynomial system gives out almost every aspects of the continuous transesterification process. Molecular weight and polydispersity index, end group ratio of hydroxyl to phenyl carbonate, contents of molecular species, and lost diphenyl carbonate fractions are studied in different operation parameters.     

Time optimal control of an experimental continuous stirred tank reactor

In this paper the methods for applying Pontryagin's Maximum Principle to determine the time-optimal control policies for both a linearized and non-linear continuous stirred tank reactor system are presented. Both the time optimal control to a desired operating steady-state and to a specified region about this steady-state are considered. The paper also describes the successful simulation and control of the experimental system of the exothermic decomposition of hydrogen peroxide. The reaction is catalyzed by iodide ion which is introduced in a potassium iodide solution. The system is controlled by varying the water flow through an internal cooling coil.     

液体燃料合成浆态反应器内部过滤的研究

在液体燃料合成浆态搅拌反应器中设置了以金属烧结板为过滤介质的内过滤器,实现固液分离。研究了压降、温度、搅拌转速、固含率、过滤介质孔径及颗粒粒径对过滤速率的影响。实验结果表明:在浆态反应器中进行内过滤可以得到澄清稳定的滤液;随着操作进行,滤饼厚度达到动态平衡,过滤速率最终趋于稳定;过滤速率随着压降、温度、过滤介质孔径、颗粒粒径的增大及搅拌转速、固含率的减小而增大。应用因次分析法建立过滤模型,通过麦夸特算法对实验数据进行最优拟合得到模型的参数值,统计检验以及模型计算值与实验值的比较表明该模型可靠。     

Catalytic oxidation of benzene to maleic anhydride in a continuous stirred tank reactor

The kinetics of the vapor phase oxidation of benzene has been studied over an industrial catalyst in a continuous stirred tank reactor in the temperature range from 280 to 430°C and at atmospheric pressure. The products obtained are maleic anhydride, carbon oxides and water. The rate of the overall reaction (disappearance of benzene) is represented by the following expression based upon a steady state adsorption model The rate of formation of maleic anhydride is correlated by the equation which allows for a homogeneous depletion of maleic anhydride. The rate constants k_B, k_O, k_2(g) were found to follow Arrhenius behavior.      

Residence time distribution in continuous flow stirred tank reactors

Numerical values of the cumulative residence time distribution in a continuous flow stirred tank reactor are commonly required. It is shown in the paper that the above distribution is easily transformed into a Chi-squared distribution. This provides a fast easy way of obtaining the desired values from readily available statistical tables.     

Observer-based nonlinear control law for a continuous stirred tank reactor with recycle

This paper proposes new results concerning the problem of the control of a continuous stirred tank reactor with recycle. The novelty of the proposed results consists of a new nonlinear observer-based controller which is found by means of recent results of differential geometry for time-delay nonlinear systems, without using linear approximations of the model. Local convergence of the system state to the arbitrarily chosen operating point is theoretically proved. The significance of the proposed control law is shown by many simulations, which show high performances with any initial conditions, even at the start-up, and with critical cases of mismatched parameter values.     

Turbulence parameters in a stirred tank

Mean and fluctuating radial velocities have been measured in the inipeller stream of a baffled, turbine-agitated cylindrical tank. Auto-correlation functions, energy spectra and amplitude probabilitv density functions of the radial velocity fluctuations were also obtained. In the vicinity of the impeller, the motion is distinctly periodic, with a time scale corresponding to n_bN/60, where n_b is the number of turbine blades and N is the rpm. The amplitude of the periodic component was found to decrease with radial distance from the inipeller tip and was used to correct the measured turbulence intensities.     

搅拌反应器内气液两相流的CFD研究进展

搅拌式气液反应器因其操作灵活、适用性强等优点,在过程工业中应用广泛.综述了采用计算流体力学CFD技术对搅拌反应器内气液两相流动行为的数值模拟研究.Euler-Euler双流体模型作为主要方法用于描述气液两相流动,在其基础上耦合相对简单的气泡数密度函数模型或复杂的群体平衡模型,可较为准确地预测搅拌反应器内气泡尺寸和局部气含率及其分布规律.CFD模拟结果可用以分析和评价不同搅拌桨叶、搅拌桨组合和气体分布器的气液分散性能,对气液反应器的结构优化和过程强化提供了有效手段.     

Mixing and recycle for analysis of a continuous flow stirred tank

During the course of a study[9] on mixing in the impeller stream of a continuous flow stirred tank two pertinent points were uncovered. The first involves a relation between, and thus a clearer picture of, the idealized turbulent mixer theory of Corrsin and the turbulent mixing vessel approach of Rosensweig. The second point involves the necessity of modification of the definition of the Intensity of Segregation when recycle occurs. The original definition of this was restricted to mixing of two pure species and new defining equations were derived when one or both of the species are contaminated with the other.     

搅拌器内两相流动及混合过程的数值分析

以油和水2种液体作为模拟实例,搅拌器采用宽桨和窄桨2种叶轮的组合方式,应用计算流体力学技术对搅拌器中两相介质的混合过程进行模拟分析.结果表明, 搅拌的开始阶段,两相流体无论是流场分布或是流动范围均有较大的区别,随着搅拌时间的延长,叶轮抽吸结果使搅拌轴中心产生低压区;重相液体因叶轮离心力的作用一般集中在容器边壁;轻相液体则在上层叶轮的作用下首先向搅拌轴中心聚集,然后沿着搅拌轴向下移动,到达容器底部后在下层叶轮的作用下扩散到搅拌槽四周,最后两相流体的流场分布、流动范围逐渐趋近一致,达到均匀状态;下层叶轮的转矩及轴功率是上层叶轮的2倍以上,选取高效的下层叶轮对于提高搅拌装置的效率十分重要.     

Modeling and control of continuous stirred tank reactor for thermal copolymerization

A mathematical model is developed for solution copolymerization in a continuous stirred tank reactor. For the thermal copolymerization of styrene and acrylonitrile (SAN), the kinetic rate expression for thermal initiation is derived by applying the pseudo-steady-state hypothesis to the intermediates, and the kinetic parameters are estimated by experimental investigation. The moment equations of living and dead polymer concentrations are derived by applying the pseudokinetic rate constantmethod. The model is used to calculate the conversion, the copolymer composition, the weight-average molecular weight, and the polydispersity. It is demonstrated that this model can predict the industrial data very well under various operating conditions. The dynamic analysis of the reaction system enables us to determine the polymer properties against the changes in the operation parameters. It is noticed that the monomer conversion is controlled to some extent by the reaction temperature and the feed monomer fraction. The monomer conversion control of a solution copolymerization reactor is treated with different control algorithms. The fuzzy/proportional–integral–derivative controller shows satisfactory performances for both setpoint tracking and disturbance rejection and can be easily applied to continuous polymerization processes. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:921–931, 1998