MICROMIXING EFFECTS ON BARIUM SULFATE PRECIPITATION IN A DOUBLE-JET SEMI BATCH REACTOR

The effects of turbulent mixing on barium sulfate precipitation in an imperfectly mixed double jet semi batch reactor were investigated experimentally and theoretically. When two feed solutions in separate streams were fed into the semi batch reactor, the precipitation was significantly altered by the impeller speed and the feeding time. Generally, in the range of low impeller speed (below 400 rpm), the suspension was segregated vertically in the reactor and the average particle size increased with increasing impeller speed. However, in the range of high impeller speed (above 400 rpm) the suspension was homogeneously dispersed in the reactor, but the trend of the turbulent mixing effect on the precipitation was opposite to that in range of the low impeller speed. The precipitation in the semi batch reactor was controlled by particle mass transfer and micromixing of the feed streams, both of which were promoted by increasing the impeller speed. At low impeller speed the influence of the mass transfer was dominant so that the particle size increased with increasing impeller speed, but at high impeller speed it was surpassed by the influence of micromixing so that the trend was reversed because enhanced micromixing generates a large number of small particles in the reactor.

To model our hypothesis for the effects of imperfect mixing on the reaction precipitation in the semi batch reactor, a micromixing-limited plug flow-ideal semi batch series reactor model was developed. The model predicts that enhanced micromixing created high supersaturation levels in the premixing region (plug flow reactor) which reduces the average particle size. The model also predicts the effect of feeding time on the precipitation in the semi batch reactor. These predictions are in excellent agreement with the experimental data. An interesting prediction of our model is that micromixing in the premixing region plays an important role in the overall reaction precipitation and its effect is greatly intensified as the turbulent mixing intensity is increased, which is opposite to our common sense.     

Simulation of fine particle formation by precipitation using computational fluid dynamics

The 4‐environment generalized micromixing (4‐EGM) model is applied to describe turbulent mixing and precipitation of barium sulfate in a tubular reactor. The model is implemented in the commercial computational fluid dynamics (CFD) software Fluent. The CFD code is first used to solve for the hydrodynamic fields (velocity, turbulence kinetic energy, turbulent energy dissipation). The species concentrations and moments of the crystal size distribution (CSD) are then computed using user‐defined transport equations. CFD simulations are performed for the tubular reactor used in an earlier experimental study of barium sulfate precipitation. The 4‐EGM CFD results are shown to compare favourably to CFD results found using the presumed beta PDF model. The latter has previously been shown to yield good agreement with experimental data for the mean crystal size at the outlet of the tubular reactor.     

EFFECT OF PVA AND GELATIN ADDITIVES ON BARIUM SULFATE PRECIPITATION IN AN MSMPR REACTOR

The effect of high molecular weight additives (PVA and gelatin) on barium sulfate precipitation in an MSMPR reactor is investigated. The impeller speed is varied from 0 to 1200 rpm and the additive concentration in the bulk solution is increased up to 5.0 g/1. As the additive concentration is increased, the particle growth rate decreases and the nucleation rate increases. However, the particle morphology is not changed by the additives. The experimental results are explained qualitatively by supposing that the additive is adsorbed on the particle surface and inhibits the mass transfer to the surface.

To explain the additive effect quantitatively a diffusion limitation model is developed. The diffusion limitation model predicts the effects of additives over the entire range of additive concentrations and impeller speeds set in the experiments. The model predicts very high supersaturation levels in the reactor which is consistent with a mass transfer controlled particle growth. Furthermore, the model results are consistent with simple theories of polymer adsorption and diffusion in polymer solutions     

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.     

Predictive simulation of nanoparticle precipitation based on the population balance equation

Nanoparticle precipitation is an interesting process to generate particles with tailored properties. In this study we investigate the impact of various process steps such as solid formation, mixing and agglomeration on the resulting particle size distribution (PSD) as representative property using barium sulfate as exemplary material. Besides the experimental investigation, process simulations were carried out by solving the full 1D population balance equation coupled to a model describing the micromixing kinetics based on a finite-element Galerkin h-p-method. This combination of population balance and micromixing model was applied successfully to predict the influence of mixing on mean sizes (good quantitative agreement between experimental data and simulation results are obtained) and gain insights into nanoparticle precipitation: The interfacial energy was identified to be a critical parameter in predicting the particle size, poor mixing results in larger particles and the impact of agglomeration was found to increase with supersaturation due to larger particle numbers. Shear-induced agglomeration was found to be controllable through the residence time in turbulent regions and the intensity of turbulence, necessary for intense mixing but undesired due to agglomeration. By this approach, however, the distribution width is underestimated which is attributed to the large spectrum of mixing histories of fluid elements on their way through the mixer. Therefore, an improved computational fluid dynamics-based approach using direct numerical simulation with a Lagrangian particle tracking strategy is applied in combination with the coupled population balance-micromixing approach. We found that the full DNS-approach, coupled to the population balance and micromixing model is capable of predicting not only the mean sizes but the full PSD in nanoparticle precipitation.     

On the influence of mixing on crystal precipitation processes—application of the segregated feed model

The segregated feed model (SFM), a compartmental mixing model, is used to predict the influence of mixing on crystal precipitation. In this method, the population balance is solved simultaneously with the mass balances using crystallisation kinetic, solubility and computational fluid dynamics (CFD) mixing data. Mean properties are calculated for the three different zones of the reactor (two feed zones and bulk zone). It is predicted that during continuous operation, the product particle size exhibits oscillating behaviour before reaching steady state after about ten residence times. In contrast, the second moment (surface area) sharply increases during the first residence time and remains constant thereafter.Different mixing conditions are modelled by varying the mesomixing and micromixing times, which can be regarded as convective and diffusive exchange parameters between the compartments of the reactor. The overall nucleation rate is found to strongly depend on the mixing conditions, as it depends in a highly non-linear manner on the level of supersaturation. In consequence, the nucleation rate varies over three orders of magnitude between ‘good’ and ‘poor’ mixing conditions. Using the SFM, the effect of different feed points, feed rates, feed tube diameters, energy dissipation rates, impeller types and vessel sizes on the nucleation rate and the particle size during crystal precipitation is illuminated. Predictions of the model compare favourably with batch and continuous experimental data for calcium oxalate.     

Macro‐ and Micromixing in a Taylor‐Couette Reactor with Axial Flow and their Influence on the Precipitation of Barium Sulfate

A new set‐up for precipitation experiments capable of independent adjustment of micromixing and macromixing conditions is presented. The setup consists of a Taylor‐Couette (TC) reactor serving as the reaction zone and an external loop where the slower stages of precipitation processes take place. Micromixing in the TC reactor has been investigated with a chemical reaction system and with PIV‐measurements. Micromixing times range between 6·10^–3 and 8·10^–2 s. Tracer experiments reveal the macromixing performance of the whole set‐up which has been compared with the behavior of ideal reactors. Precipitation experiments with barium sulfate show some influence of micromixing intensity on the particle size and of macromixing on particle morphology.     

Experimental study of continuous ultrasonic reactors for mixing and precipitation of nanoparticles

Nanoparticles can be synthesized by precipitation. State-of-the-art is the precipitation of nanoparticles in stirred tanks or high-pressure T-mixers. The study presents two new reactor concepts for continuous precipitation of nanoparticles. Both of them utilize ultrasonic sound as a mixing accelerator. The first reactor has a conical chamber (10 mL), which is used to study the micromixing quality, the cavitation intensity and the precipitation of barium sulfate nanoparticles. The second reactor has a so-called cavitational chamber (2.5 mL), which is an optimized conical reactor. Both reactors are compared with each other with respect to the properties of the products. Additionally, the influence of the ultrasonic output from the transducer to the liquid and the feed rate are demonstrated.     

The use of a new model of micromixing for determination of crystal size in precipitation

The course of the precipitation process and the size distribution of the solid particles obtained depend significantly on the intensity of mixing in the crystallizer. The authors have used a new model of micromixing, based on the spectral interpretation of mixing in the isotropic, homogeneous turbulent field to evaluate the influence of the intensity of mixing on the rate of precipitation and on the particle size of the product obtained in a stirred vessel with ideal macromixingThe results obtained from the model are in good agreement with the experimental results obtained for the precipitation of BaSO₄.     

Micromixing limits in an MSMPR crystallizer

The effect of micromixing limits on a process of crystallization in an MSMPR crystallizer is studied with respect to power law growth and nucleation kinetics. Three limiting cases corresponding to maximum mixedness and complete segregation in an MSMPR crystallizer and plug flow configuration were analyzed for processes in which supersaturation is generated by conventional techniques. The sensitivity of these three limiting cases to the supersaturation generation term in each mode of operation was investigated using several numerical examples. The study demonstrates the effects of mixing on the overall crystallizer performance and, in particular, the enormous micromixing influence at high supersaturation generation rates. The difference in the product CSD arise from the variations of supersaturation profiles experienced by the elementary volumes throughout their sojourn. Characterization of mixing in a real crystallizer at some intermediate levels is emphasized with the aid of relevant industrial examples.     

AN EVALUATION OF MODELS OF MIXING AND CHEMICAL REACTION WITH A TURBULENCE ANALOGY

Five mechanistic models of mixing and chemical reaction having an analogy with isotropic turbulent mixing are evaluated. The turbulence analogies, based on matching variance decay laws of models and turbulence theory, provide a physical basis for the models and a means of estimating their micromixing parameters apriori. Experimental data for single second order liquid phase reactions provide strong support for the analogies. However, it is demonstrated that in spite of their success for single reactions, the models may predict grossly different selectivities in the case of competing reactions in a plug flow reactor. This emphasizes the importance of certain structural features of the models which are independent of the existence of a turbulence analogy, such as: (i) reacting regions which are rich in each of the reactants of a two feedstream reactor, and (ii) unmixed regions in the reaction mixture. The importance of obtaining data for competing reactions in a highly segregated plug flow reactor for the purpose of model discrimination is made apparent.     

Effect of impeller type on the mixing in torus reactors

Torus reactors are characterized by a homogeneous fluid circulation without dead zones. Torus reactors were used for applications in biotechnology, food processing, polymerization and liquid waste treatments. The relatively simple extrapolation of performances, due to the absence of dead volume, is one of the main advantages of this reactor, with low shear stresses and an effective radial mixing allowing efficient heat dissipation. This study is based on the mixing in order to analyse the fluid circulation, mainly in turbulent flow regime, and to characterize the torus reactor with the axial dispersion plug flow model. The objective of this study is to characterize the flow and the mixing in the torus reactors in batch and continuous modes. The mixing analysis was made according to the flow parameters and to the geometrical characteristics of the reactor and impeller. The mixing in the torus reactor can be characterized by the Péclet number, Pe_D, defined with torus diameter. A representative model based on plug flow with axial dispersion and partial recirculation was proposed.     

Multi-scale modeling of a mixing-precipitation process in a semibatch stirred tank

In this work the influence of turbulent mixing on the course of barium sulfate precipitation is investigated for a process carried out in a semibatch stirred tank reactor. A time-scale analysis for the controlling process mechanisms is presented to highlight the multi-scale nature of the process. A detailed CFD based process model is presented which accounts for all relevant phenomena from the micro- to the macro-scale and interactions between mechanisms on different scales. Computational results of the models for various operating conditions, i.e., different agitation rates, reactant concentrations and feed addition modes, are compared with experimental data and simulation results obtained using a simpler mechanistic model, thus highlighting the strengths of the complex model.     

Barium Sulphate Agglomeration in a Pipe – An Experimental Study and CFD Modeling

Agglomeration effects, observed during precipitation of barium sulphate in the unpremixed feed two‐dimensional tubular precipitator, are studied experimentally and interpreted theoretically. Effects of process parameters on precipitation–agglomeration phenomena are predicted using a CFD based model that describes micromixing (the multiple‐time‐scale turbulent mixer model is used) and precipitation (including nucleation, growth and agglomeration of crystals). Agglomeration rate is defined as a product of the collision frequency and the probability of agglomeration.     

旋转填充床内微观混合的数值模拟

旋转填充床作为新型的高效反应传质设备,广泛应用于快速反应过程,如制备纳米粉体材料.对旋转填充床内微观混合进行研究,有助于进一步认识旋转填充床内高度分散液体微元在填料丝网中的流动行为和分散混合机制,为旋转填充床内液液反应混合制备纳米材料提供理论基础.基于公开文献报道的实验观测结果,通过合理假设,建立了旋转填充床内微元流动的物理模型.在该物理模型的基础上,结合此前提出的湍流混合与反应模型,模拟计算了液体微元经过实验条件下50层丝网填料最终流出填料空间的浓度分布.由浓度分布得到的微观混合特征指数与实验值进行了对比,吻合良好.     

TAILORING PARTICLE SIZE THROUGH NANOPARTICLE PRECIPITATION

Precipitation of nanoscaled particles and the size-determining precipitation parameters are investigated experimentally as well as numerically using barium sulfate as a reference substance. The objective of this work is to successfully understand and predict precipitation kinetics. Optimization and tailoring of product properties to specific needs would then be possible without the need of extensive experimentation and its costs. Special attention is paid to the influences of mixing as well as stabilization on the formed PSD. To simulate particle formation the population balance equation, including the terms for nucleation, growth, and agglomeration, is coupled with an specially developed extended version for equi-volumetric mixing of the Engulfment-Deformation-Diffusion-model of micromixing of Baldyga and Bourne (1999). The proposed predictive model for nanoparticle precipitation is explained in detail and simulation results are presented, discussed, and compared to experimental results.     

Lagrangian marker particle trajectory and microconductivity measurements in a mixing tank

Large regions of inhomogeneous mixing have been observed in industrial, bottom-sweeping impeller crystallizers. To investigate this phenomenon, we conducted experiments on a one-tenth volume model of this kind of mixing tank. Results are reported of Lagrangian marker particle (LMP) and microconductivity measurements using the model mixing tank with impeller tip Reynolds numbers of 25,000. Surprising structure is found in this high Reynolds number flow. Using the LMP trajectory data, we show the flow consists of a narrow region of rapidly moving, upward spiralling flow at the tank perimeter. This flow returns slowly through a vertical stack of tori and through a quiescent region centered on the impeller. These tori are concentric with the impeller and exist at loci of regions of shear found adjacent to the quiescent central region and the tank perimeter.Conditional analysis of the microconductivity signals reveals that large concentration fluctuations occur in the perimeter flow. In contrast, only small diffusive-like concentration fluctuations occur in the center of the tank. This segregation of regions of rapid transport in the perimeter flow from regions of micromixing in the quiescent region results in inhomogeneous mixing in the tank. The complexity of the flow is reflected in the large dynamical dimension (≈24) of the flow obtained from the calculation of the Kolmogorov entropy production rate. The return-time distribution was found to be composed of a superposition of two log-normal distributions. Period doubling phenomenon was also found in these distributions.     

NETmix®, a new type of static mixer: Modeling,simulation, macromixing,and micromixing characterization

NETmix® is a new technology for static mixing based on a network of chambers connected by channels. The NETmix® model is the basis of a flow simulator coupled with chemical reaction used to characterize macro and micromixing in structured porous media. The chambers are modeled as perfectly mixing zones and the channels as plug flow perfect segregation zones. A segregation parameter is introduced as the ratio between the channels volume and the whole network volume. Different kinetics and reactants injection schemes can be implemented. Results show that the number of rows in the flow direction and the segregation parameter control both macro and micromixing, but the degree of micromixing is also controlled by the reactants injection scheme. The NETmix® model enables the systematic study of micromixing and macromixing for different network structures and reaction schemes, enabling the design of network structures to ensure the desired yield and selectivity. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Application of in situ adaptive tabulation to CFD simulation of nano-particle formation by reactive precipitation

Reactive precipitation involves four fundamental processes: mixing-limited reaction, nucleation, growth, and aggregation. A novel algorithm, in situ adaptive tabulation (ISAT), has been implemented in a code for micromixing simulations, which is often applied together with computational fluid dynamics (CFD), using full probability density function (PDF) methods to incorporate these fundamental processes in the formation of nano-particles by reactive precipitation in a plug-flow reactor. The quadrature method of moments is applied to solve population balance equations for turbulent aggregation of the growing particles. The various performance issues (error control, accuracy, number of records, speed-up) for ISAT are discussed. Based on a large number of simulations, an error tolerance of 10⁻⁴-10⁻⁵ is found to be satisfactory for carrying out time-evolving full PDF simulations of nano-particle formation by reactive precipitation. Our results show that CFD simulation of reactive precipitation requires a much smaller computational effort when the ISAT algorithm is implemented than when direct integration is used. Finally, the effects of initial species concentrations, micromixing time, and turbulent shear rate on the reactive precipitation of barium sulfate are studied.     

Regulating the micromixing efficiency of a novel helical tube reactor by premixing behavior optimization

In this work, a novel helical tube reactor (HTR) was constructed, including a pre‐mixer for adjusting the premixing behavior of reactants and a helical tube as a further mixing unit. The pre‐mixer was modified to optimize the premixing behavior by using two methods, named as tangential‐feeding and insertion of a helical baffle. The premixing behaviors were investigated via computational fluid dynamics (CFD) simulation. Simulation results indicated that both methods can change the fluid flow, enhance the turbulence kinetic energy, and improve the premixing performance in the pre‐mixers. Based on the results of CFD simulation, it could be predicted that the micromixing efficiency of the HTR can be regulated by these methods accordingly. Then the predicated results were confirmed experimentally by a parallel competing reaction. Furthermore, the relationship between the premixing performance increasing and the corresponding micromixing efficiency increasing of the HTR was quantitatively analyzed. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2876–2887, 2017