Simulation of Barium Sulfate Precipitation using CFD and FM‐PDF Modeling in a Continuous Stirred Tank

A mixing‐precipitation model combining computational fluid dynamics (CFD), finite‐mode PDF (probability density function) model, population balance and kinetic modeling has been proposed to simulate the barium sulfate precipitation process in a continuous stirred tank agitated by a Rushton turbine. The effect of various operating conditions such as impeller speed, feed concentration, feed position and mean residence time on the barium sulfate precipitation process is clearly demonstrated. It is shown that the mean crystal size increases by increasing the impeller speed and mean residence time. However, when the feed concentration is increased, the mean crystal size decreases. The predictions are in reasonable agreement with the experimental data in the literature.     

Experimental determination and numerical simulation of mixing time in a gas-liquid stirred tank

In this work, mixing experiments and numerical simulations of flow and macro-mixing were carried out in a 0.24 m i.d. gas-liquid stirred tank agitated by a Rushton turbine. The conductivity technique was used to measure the mixing time. A two-phase CFD (computational fluid dynamics) model was developed to calculate the flow field, k and ε distributions and holdup. Comparison between the predictions and the reported experimental data [Lu, W.M., Ju, S.J., 1987. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chemical Engineering Journal 35 (1), 9-17] of flow field and holdup at same conditions were investigated and good agreements have been got. As the complexity of gas-liquid systems, there was still no report on the prediction of mixing time through CFD models in a gas-liquid stirred tank. In this paper, the two-phase CFD model was extended for the prediction of the mixing time in the gas-liquid stirred tank for the first time. The effects of operating parameters such as impeller speed, gas flow rate and feed position on the mixing time were compared. Good agreements between the simulations and experimental values of the mixing time have also been achieved.     

混合对丙烯腈连续水相沉淀共聚的影响：Ⅱ 丙烯腈共聚物的颗粒形态

用电子显微镜考察了丙烯腈共聚物颗粒的结构,探讨了颗粒的形成机理,研究了混合,单体进料浓度对共聚物颗粒形态的影响。结果表明,在共聚物内部存在着3种微粒:即P_1粒子,粒径为10~(-3)～10~(-2)μm;P_2粒子,粒径为0.1～0.5μm;P_3粒子,粒径为1～3μm,这3种微粒相互凝聚形成了粒径为10～50μm的共聚物粒子,提出了用平均粒径、方差、沉降值、比表面积和悬浮液流变特性来表征共聚物的颗粒形态,发现提高单体进料浓度和混合强度能显著地改善颗粒形态,而对产品的其他性能影响较小,认为单体进料浓度和混合强度是控制颗粒形态的关键因素。提高单体进料浓度,满足足够的混合强度,是改善颗粒形态的有效途径。     

Effet du diamètre de l'agitateur et de la largeur des chicanes sur le niveau d'agitation en régime continu et sur la puissance dissipée

The system studied is made of a vertical cylindrical tank with a coaxial turbine agitator and baffles. The feed is in the bottom of the tank, the outlet at the surface, and both are coaxial with the agitator. A model proposed by Cholette and Cloutier, in which the parameters m and n are involved, was used to evaluate the effect of different variables. At a given agitator speed, the level of mixing is decreased when baffles are present, proportionally to the width of the latter. A lowering of the short-circuit is also observed. The torque varies with the level of mixing; it increases when baffles are present, and more so for large agitator diameters. The authors propose a flow pattern to explain the experimental results.     

新型催化裂化提升管进料段内原料射流浓度分布的大型冷模实验研究

通过大型冷模实验研究了喷嘴射流与催化剂逆向接触的新型提升管进料段内喷嘴射流浓度沿径向的分布,考察了喷嘴气速、预提升气速的影响. 结果表明,喷嘴气速Uj=78.5 m/s和预提升气速Ur=4.1 m/s条件下可获得较好的油剂混合效果. 与传统形式相比,新型结构可促进油剂混合,在轴向距离H<0.7 m内完成油剂混合,油剂初始接触区域内喷嘴射流相浓度分布更均匀. 给出了新型进料段中不同区域喷嘴射流浓度沿径向分布的经验模型,计算值与实验值吻合较好.     

The mixed-bed ion exchange performance at ultralow concentrations 1. Variable feed concentration and incomplete mixing of resins

Experimental data were obtained to evaluate the performance of mixed-bed ion exchange for the cases of variable feed concentration and incomplete mixing of anion and cation resins observed in large scale industrial units. For variable feed concentration, step changes in feed concentration were arbitrarily introduced into a test column. For incomplete mixing, only anion resin was loaded in the upper 20% of the column and more cation resin in the lower portion. Feed concentrations of 5.0× 10⁻⁵−2.0×10^-4 M NaCl were used for the experiments, with flow rates of 0.665-7.0 ml/sec. The effluent from the column was collected periodically and analyzed using on-line/off-line ion chromatography. The step changes in feed concentration affect the breakthrough times of sodium and chloride. Sodium breakthrough curve is more sensitive to the step changes than chloride breakthrough curve. With the same volumes of cation and anion resins, incomplete mixing of resins increases the cation exchange rate slightly and decreases the anion exchange rate slightly. As the cation resin volume increases, the effect of the incomplete mixing of resins decreases. The breakthrough curves of both ions, plotted as the ratio of effluent to the influent concentration versus run time in hour, give some detailed results about the effects of the conditions.     

Matched asymptotic solutions of the coalescence-redispersion model for unmixed feed stream plug flow reactors

Matched asymptotic expansions are given for the first moments of the concentration distribution function of Curl's coalescence-redispersion population balance model when mixing is faster than reaction. The physical situation considered is an unmixed feed stream tubular reactor with a plug flow residence time distribution in which the single reaction A + nB → P occurs. The asymptotic expansions lead to analytical expressions for species conversion in such reactors and thus obviate the need for numerically tedious Monte Carlo simulations. It is also demonstrated that the perturbation technique applies in a straightforward manner to situations with competing reactions and that the analytical calculations compare favourably with Monte Carlo simulations.     

喷嘴油气在提升管进料段的浓度径向分布及混合行为

在φ200 mm提升管冷态实验装置上,根据喷嘴油气在进料段4个轴向位置（H=0.375、0.675、1.075、1.375 m）及不同操作参数（U_r=2.25～4.30 m·s^-1,U_j=41.7～62.5 m·s^-1,M_j/M_r=0.29～4.21）的浓度径向分布形式,考察了喷嘴油气与预提升气体和颗粒在进料段内的混合过程。结果表明,喷嘴油气在进料段内存在6种浓度径向分布形式,反映了喷嘴油气与预提升气体和颗粒在进料段的不同混合行为,沿轴向由下至上分别为：未混合区（强M形分布）、混合区（弱M形分布、强三峰形分布、弱三峰形分布、单峰形分布）及完成混合区（环-核分布）。随着U_j的增加或U_r的减小,喷嘴油气与预提升气体和颗粒在进料段内的未混合区、混合区及完成混合区的轴向高度逐渐增加。采用喷嘴射流动量与预提升来流动量之比M_j/M_r考察了操作参数及装置结构尺寸等对喷嘴油气与预提升气体和颗粒在进料段内混合过程的综合影响。喷嘴油气与预提升气体和颗粒的未混合区、混合区及完成混合区的轴向位置在动量比M_j/M_r≤0.29时分别为：0～0.375 m、0.375～0.525 m、0.525～0.675 m;在动量比M_j/M_r=0.29～0.54时分别为：0～0.375 m、0.375～0.875 m、0.875～1.075 m;在动量比M_j/M_r=0.54～4.21时分别为：0～0.525 m、0.525～1.225 m、1.225～1.375 m。     

The mixing criterion in crystallization by cooling

In processes where mass flows have to be mixed, and the formation of new phases has to be prevented, it is essential for the composition and enthalpy (J/kg) to be so adjusted to each other that, whatever the mixing ratio, the ultimate mixture will consist of one single phase under physical equilibrium conditions (temperature and pressure).The requirements imposed on the composition and enthalpy will be called the mixing criterion.The mixing criterion plays an important role in technical crystallization processes involving mixing — frequently under adiabatic conditions — of liquid flows differing in temperature and/or concentration.For a binary system and a ternary one, both containing one component that can be crystallized, the authors determined the conditions under which supersaturation and its consequences (scaling and undesired nucleation) can be avoided during adiabatic mixing of the feed and the mother liquor in a draft-tube baffled (D.T.B.)-crystallizer.The correctness of the theory is confirmed by the results of runs conducted with a ternary system in a 100 l. experimental crystallizer; compliance with the mixing criterion proved to prevent scaling, and to increase the average crystal size by a factor of 3·5.     

The axial mixing model applied to ball mills

The unsteady-state, one-dimensional convective mixing equation was solved with finite end boundary conditions for a pulse of tracer admitted into a steady flow, assuming a constant dimensionless mixing factor D*. Radiotracer tests were performed on two continuous wet overflow ball mills, a laboratory mill of 0.3 m i.d. and a pilot-scale mill of 0.91 m i.d. Counting through the mill case enabled the tracer concentration to be measured at L/3, 2L/3 and L for the small mill, and L/2 and L for the pilot-scale mill. The results were consistent with the mixing model with D* = 0.5 and 0.3, respectively, with D* constant along the mill. The mean residence time of water was about 0.85 that of the solid, showing the slurry density in a mill to be higher than that of the feed and product streams.     

Mixing and fast chemical reaction—IX: Comparison between models and experiments

Theoretical considerations given in earlier parts indicate that mixing on the molecular scale (micromixing) takes place by molecular diffusion into small, turbulence-free fluid elements, which are being gradually distorted by uniform shear. This mechanism, when applied to fast, consecutive, competitive chemical reactions, predicts that the product composition will be a function of the variables given in eqn (3). A pair of diazo coupling reactions has been employed to test these predictions. The additional experimental results contained in this part refer to three impeller types (Rushto turbine, marine propeller and axial flow turbine), nine feed locations and three volumetric feed ratios. Semi-batch operation was modelled by extending the earlier batch reactor model and also used experimentally. Taking reasonable estimates of the model parameters from the fluid mechanics literature, satisfactory predictions of the experimental results were obtained.     

Experimental investigation on the micronization of aqueous cefadroxil by supercritical fluid technology

The supercritical-assisted atomization (SAA) process is a novel technique proposed recently to prepare micro-particles with controlled particles size distribution suitable for aerosolizable delivery. It has shown a great potential in drug micronization especially for water-soluble drugs. Cefadroxil micro-particles were prepared successfully from water–ethanol mix-solvent by SAA process. The influence of the operation parameters, including the pressure and temperature in the mixing vessel, the solution concentration and the solution feed rate, on the particle morphology, size and size distribution was investigated in detail. The results show that the concave cefadroxil micro-particles suitable for pulmonary drug delivery could be prepared by SAA process in certain conditions. The pressure in the mixing vessel and the solution feed rate are two most effective parameters while the solution concentration is the next. The temperature in the mixing vessel has a little effect. The particle characteristics could be controlled by adjusting operation conditions. The optimal operation parameters for preparing cefadroxil micro-particles in the scope of this work are: the pressure of 10 MPa and the temperature of 60 °C in the mixing vessel, the solution feed rate of 3 ml/min, and the solution concentration of 4 mg/ml.     

半圆管曲面涡轮搅拌槽内混合特性的数值模拟

在商业化软件ANSYS CFX 10.0平台上,采用多重参考系法来解决挡板与桨叶之间的相对转动问题,由标准k-ε模型对半圆管曲面涡轮搅拌槽内流动和混合过程进行了详细的数值模拟,本模拟所得的功率准数和设计值以及相关文献值吻合良好。结果表明：当搅拌桨离底距离由搅拌槽直径的1/2处变为1/3处时,搅拌槽内的流型均为典型的“双循环流型”,而当搅拌桨离底距离由搅拌槽直径的1/3处降低至1/6处时,槽内流型由典型的“双循环流型”转变为“单循环流型”;通过对不同时刻不同桨叶离底距离下的示踪剂浓度分布图分析表明槽内的混合过程与流动场密切相关;加料点位置对于最终的流场混合效果有着显著影响,对于混合时间数据的采集应注意不同加料位置时监测点的选取。CFD模拟结果表明本文所采用的模型可以很好的预测半圆管曲面涡轮搅拌槽内的混合特性,为进一步改进和优化半圆管曲面涡轮的设计提供了一定的参考。     

Mixing and Crystallization Kinetics in Gas‐liquid Reactive Crystallization

A study of gas‐liquid reactive crystallization for CO₂‐BaCl₂‐H₂O system was performed in a continuous flow crystallizer. The influences of mixing on the crystallization kinetics of barium carbonate crystals were investigated. The mixing parameters are stirrer speed, feed concentration, gas‐flow rate, pH of solution, addition rate of NaOH solution, and mean residence time. Under pH‐stat operation, the crystallization mechanism can be assessed by the addition rate of NaOH solution, which acts as an indicator for the absorption rate of carbon dioxide. Assuming a size‐independent agglomeration mechanism, the nucleation rate, growth rate and agglomeration kernel can be obtained, simultaneously, at steady state, by the method of moments. Evidence shows that feed concentration, feed rate, gas‐flow rate, and stirrer speed have a significant influence on the nucleation rates and mean particle sizes. This shows the effect of micromixing. The crystallization mechanism tends to be reaction limited when the feed concentration of barium chloride solution is higher than 5 mM, while at lower stirrer speeds and feed concentrations, the mechanism tends to be both mixing and reaction controlled. The growth rate depends on the mean supersaturation value and the pH of the solution and the mass‐transfer resistance cannot be completely eliminated in this work. For a monodispersal collision model, in the viscous sub‐range of turbulence, the agglomeration kernel can be expressed as β ∝ d^{3 –1/4}, showing a low efficiency of collision. The result is also demonstrated by the agglomeration kernel expression. Comparison with a liquid‐liquid‐mixing reactive crystallization system is also discussed.     

Analysis of an LDPE compact autoclave reactor by two-cell model with backflow

A two-cell model with backflow and heat exchange is developed to analyze the dynamics of an LDPE compact autoclave reactor. The backflow exists between the two mixing cells and represents the degree of mixing within the reactor. The performance of the reactor and the physical properties of the product polymer such as the number average molecular weight and the polydispersity are investigated under various operating conditions, especially when the initiator feed concentration is varied. Bifurcation diagrams are constructed by taking the initiator feed concentration as the bifuracation parameter and the dynamic feature in the feasible parameter ranges for operation are carefully examined. Indeed, various dynamic characteristics are observed by performing numerical analysis of the nonadiabatic system with the internal cooling device. As the rate of heat transfer increases, various multiplicity patterns and oscillatory behavior such as the limit cycle and the focus are found. The reactor behavior even undergoes period doubling and gradually gives rise to a chaotic behavior in certain ranges of the initiator feed concentration when the coolant temperature becomes low. The existence of chaos is examined by the phase plane plot and Poincaré map. Apparently, the monomer concentration can be substantially increased with proper heat removal and initiator supplement scheme. For this, however, the complex dynamic features must be taken into account in the reactor design.     

Effects of Assistant Solvents and Mixing Intensity on the Bromination Process of Butyl Rubber

A slow bromination process of butyl rubber （IIR） suffers from low efficiency and low selectivity （S） of target-product. To obtain suitable approach to intensify the process, effects of assistant solvents and mixing inten-sity on the bromination process were systemically studied in this paper. The reaction process was found constantly accelerated with the increasing dosage and polarity of assistant solvent. Hexane with 30%（by volume） dichloro-methane was found as the suitable solvent component, where the stable conversion of 1,4-isoprene transferring to target product （xA1s） of 80.2%and the corresponding S of 91.2%were obtained in 5 min. The accelerated reaction process was demonstrated being remarkably affected by mixing intensity until the optimal stirring rate of 1100 r＆#183;min-1 in a stirred tank reactor. With better mixing condition, a further intensification of the process was achieved in a ro-tating packed bed （RPB） reactor, where xA1s of 82.6% and S of 91.9% were obtained in 2 min. The usage of the suitable solvent component and RPB has potential application in the industrial bromination process intensification.     

Applications of computational fluid dynamics in the chemical industry

In order to illustrate the use of CFD in providing an understanding of mixing processes, three examples, mixing in a pipe, homogenization with a static mixer and flow in a mixing vessel with a Rushton turbine, are discussed and compared with experimental results. Special attention is focussed on the resultant concentration distribution, which is closely linked to turbulent properties. A semi-empirical model is presented for a quantitative prediction of the initial turbulent conditions. Using special numerical techniques a mixing vessel with wall-separated baffles, which represents a problem generally regarded as beyond the capabilities of numerical analysis, can be simulated.     

Derivation of supersaturation and nucleation flux during precipitation from the mixing pattern of an inert tracer in the same device: case of unmixed feed streams

Inert liquid tracer concentrations in a continuous mixer are analyzed by planar laser induced fluorescence (PLIF). Special attention is paid to the two separated entering feed streams containing the tracer solution or pure solvent. From the instantaneous tracer concentration fields, the method proposed allows one to easily calculate the instantaneous supersaturation fields, which would be obtained in the same mixing device with reagents instead of an inert tracer solution and pure solvent. A typical mixing situation in a stirred tank with separated feed streams is investigated. Maps of averaged supersaturation and averaged nucleation flux are yielded with high spatial resolution of a few tens of micrometers for each pixel. The method gives interesting indications about the ability of a given precipitator geometry to generate coarse or fine particles. However, it cannot be extended straightforward to partially premixed feed streams without the use of a mixing model.     

CFD simulation of flow and mixing characteristics in a stirred tank agitated by improved disc turbines

To reduce the power consumption and improve the mixing performance in stirred tanks, two improved disc turbines namely swept-back parabolic disc turbine (SPDT) and staggered fan-shaped parabolic disc turbine (SFPDT) are developed. After validation of computational fluid dynamics (CFD) model with experimental results, CFD simulations are carried out to study the flow pattern, mean velocity, power consumption, pumping capacity and mixing efficiency of the improved and traditional impellers in a dished-bottom tank under turbulent flow conditions. The results indicate that compared with the commonly used parabolic disc turbine (PDT), the power number of proposed SPDT and SFPDT impellers is reduced by 43% and 12%, and the pumping efficiency is increased by 68% and 13%, respectively. Furthermore, under the same power consumption (0-700 W·m^-3), the mixing performance of both SPDT and SFPDT is also superior to that of Rushton turbine and PDT.     

THE EFFECT OF IMPERFECT MIXING ON POLYMER QUALITY IN LOW DENSITY POLYETHYLENE VESSEL REACTORS

A mathematical model is developed for the calculation of polymer quality in low density polyethylene vessel reactors, taking into account mixing limitations at the initiator feed point. Model predictions show that imperfect mixing in the reactor can produce considerable variations in polymer molecular weight distribution. The effect of the most important process conditions, input feed temperature, solvent concentration, monomer flow rate and initiator type, on the final polymer quality is analyzed. The advantages of the design solution which divides the reactor in more compartments in series are also discussed.