A basic population balance model for fluid bed spray granulation

A basic population balance approach is developed for a granulation process in a fluid bed spray granulator. The particle size distribution predicted by the model is confirmed by plant data. Hence this model is considered to be useful to describe and optimize an industrial process. The model depends on a limited number of parameters (most of these factors can be measured or are known): the spray volume flux, the nucleation fraction (the fraction of the spray volume flux which leads to new particles formed), the nucleation particle diameter, the product withdrawal threshold diameter, and the product withdrawal rate. Analysis of the model reveals a steady-state constraint; a steady state does not exist if the nucleation fraction is too large. For cases where the steady state does exist, the steady-state particle size distribution is solved analytically. A numerical implementation of the model is used to illustrate the transient evolution of the process. The steady-state solution appears to be stable for a constant nucleation fraction. However, if the nucleation fraction depends on the bed height the steady state can be unstable. Such a situation may occur if the spray inlet is near the height of the bed surface. Instead of convergence towards a steady state, the transient solution displays ongoing oscillatory behavior with an oscillation period of a number of hours. A linear stability analysis is performed to confirm the findings on the stability of the steady state.     

Identification of thermal zones and population balance modelling of fluidized bed spray granulation

Air temperature measurements in a fluidized bed of glass beads top sprayed with water showed that conditions for particles growth were fulfilled only in the cold wetting zone under the nozzle which size and shape depended on operating conditions (liquid spray rate, nozzle air pressure, air temperature, and particles load). Evolution of the particle size distribution during agglomeration was modelled using population balance and representing the fluidized bed as two perfectly mixed reactors exchanging particles with particle growth only in the one corresponding to the wetting zone. The model was applied to the agglomeration of non-soluble glass beads and soluble maltodextrin particles spraying respectively an acacia gum solution (binder) and water. Among the three adjustable parameters, identified from experimental particle size distributions evolution during glass beads agglomeration, only one describing the kinetics of the size distribution evolution depended on process variables. The model allowed satisfying simulation of the evolution of the particle size distribution during maltodextrin agglomeration.     

Modeling of the Spray Zone for Particle Wetting in a Fluidized Bed

In a spray agglomeration process the particle wetting influences the agglomerate growth and particle dynamics in the granulator. The mass of binder liquid that is deposited on single particles affects the amount of energy dissipation during particle contacts. For the agglomeration of colliding particles the whole impact energy has to be dissipated due to viscous and capillary adhesion forces in the liquid film and plastic deformation of the material. Therefore, a detailed knowledge of the particle wetting is necessary to model the agglomeration process. This contribution uses a coupled DEM‐CFD approach to describe the spray zone of a two‐fluid nozzle in a fluidized bed agglomerator. Droplets modeled as discrete elements showed the formation of a spray zone with a conical shape. Simulations of the spray zone and the wetting of single particles are in good agreement with experimental results.     

Foam granulation: Binder dispersion and nucleation in mixer-granulators

Traditional wet granulation method involves spraying of liquid binder onto a moving powder bed to granulate the powder particles in the granulator. A new alternative method of wet granulation has been developed where foam delivery of binder is used to granulate the powder particles.This study investigated binder distribution in wet granulation and focused on the nucleation stage, where nuclei are formed during the initial binder distribution. Nucleation experiments were used to study the formation of nuclei by the foam and spray delivery methods in a high shear mixer-granulator. The distribution of foams on a dynamic powder bed were also investigated by filming small portion of foams as they penetrated into moving powder beds under different powder flow conditions in a high shear mixer-granulator.Nucleation experiments in this study show that foam delivery tends to create a narrower nuclei size distribution during the early stage of wet granulation process compared to spray delivery at the same processing conditions, demonstrating the potential of foam granulation in achieving improved binder distribution. For foam delivery, the nuclei formation is influenced by the foam properties and powder flow conditions in the granulator. The experiments show that the narrowest nuclei size distribution is obtained by granulating with high-quality foam and intensive powder mixing conditions. Coarser nuclei are formed when low-quality foam is dispersed in a less intensively agitated powder. The interactions of foam quality and the powder flow pattern are discussed and two distinct wetting and nucleation mechanisms are proposed: (1) under bumping flow, a low-quality foam tends to induce localised wetting and nucleation. The wetting and nucleation is “foam drainage” controlled. (2) Under roping flow, foam will be dispersed by the motion of the agitated powder. The wetting and nucleation is “mechanical dispersion” controlled.     

Parameterization for Atmospheric New-Particle Formation: Application to a System Involving Sulfuric Acid and Condensable Water-Soluble Organic Vapors

A new parameterization for atmospheric new-particle formation has been developed. The parameterization takes into account the early growth of nucleated clusters by condensation of sulfuric acid and water-soluble organic vapors, as well as the scavenging of the growing nuclei by coagulation into larger pre-existing particles. The main input parameters are the nucleation rate, the concentration of sulfuric acid and organic vapor(s) contributing to the nuclei growth, and the pre-existing particle size distribution. The resulting output quantity is the formation rate of particles at a desired size, typically a few nanometers of particle diameter. Comparisons to detailed numerical simulations demonstrated that the parameterization is relatively accurate when the nucleation rate, condensable vapor concentrations, and nuclei growth rate change sufficiently slowly with time, and when the nucleation rate is not very high. As such, the parameterization is most applicable to“regional nucleation events,”in which new-particle formation occurs over distances of tens to hundreds of kilometers. The main obstacle in applying the new parameterization is that organic vapors contributing to the early growth of nucleated clusters have not been identified so far. A couple of solutions to this problem are proposed.     

Experimental study and modeling of fluidized bed coating and agglomeration

This work deals with the fluidized bed coating and agglomeration of solid particles. The effect of particle size on coating criteria was investigated using sand particles as the coating support and aqueous solutions containing NaCl as coating liquid. The results showed that both growth rate and efficiency increase with decreasing the particle size. The growth was mainly governed by layering for particles larger than 200 μm, whereas for finer particles it occurred by agglomeration. As the particle size became less than 90 μm, the coating operation led to uncontrolled growth and bed quenching. However, the coating of the same particles was successfully achieved by adding some coarser particles. In addition, a mathematical model based on the population balance concept, taking into account the simultaneous growth by layering and agglomeration, was established to predict the time evolution of the particle size distribution. The comparison between experimental and calculated data permitted the establishment of a law for the size dependency of the agglomeration kernel.     

Modelling nucleation in wet granulation

Nucleation is the first stage in any granulation process where binder liquid first comes into contact with the powder. This paper investigates the nucleation process where binder liquid is added to a fine powder with a spray nozzle. The dimensionless spray flux approach of Hapgood et al. (Powder Technol. 141 (2004) 20) is extended to account for nonuniform spray patterns and allow for overlap of nuclei granules rather than spray drops. A dimensionless nuclei distribution function which describes the effects of the design and operating parameters of the nucleation process (binder spray characteristics, the nucleation area ratio between droplets and nuclei and the powder bed velocity) on the fractional surface area coverage of nuclei on a moving powder bed is developed. From this starting point, a Monte Carlo nucleation model that simulates full nuclei size distributions as a function of the design and operating parameters that were implemented in the dimensionless nuclei distribution function is developed. The nucleation model was then used to investigate the effects of the design and operating parameters on the formed nuclei size distributions and to correlate these effects to changes of the dimensionless nuclei distribution function. Model simulations also showed that it is possible to predict nuclei size distributions beyond the drop controlled nucleation regime in Hapgood's nucleation regime map. Qualitative comparison of model simulations and experimental nucleation data showed similar shapes of the nuclei size distributions. In its current form, the nucleation model can replace the nucleation term in one-dimensional population balance models describing wet granulation processes. Implementation of more sophisticated nucleation kinetics can make the model applicable to multi-dimensional population balance models.     

Monte Carlo modeling of binder‐Less spray agglomeration in fluidized beds

Fluidized bed spray agglomeration is used in the industry to increase the particle size and to improve several properties, for example, bulk density, flowability, and dissolution behavior of particulate products. Usually, a binder liquid is sprayed on a particle bed. If amorphous materials are used, spraying of pure water may cause agglomeration due to glass transition at wet spots on the particle surface. As no process models covering binder‐less spray agglomeration currently exist, a model based on a Monte Carlo method is presented. In this method, the process is described by events and processes on the single particle scale. Additionally, agglomeration experiments in a lab‐scale fluidized bed using three different maltodextrins are presented. For each experiment, a simulation was performed. The simulation results are compared with the obtained experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3582–3594, 2018     

Kinetics of fluidized bed spray agglomeration for compact and porous particles

The effect of the primary particle porosity during the formation of agglomerates in spray fluidized beds is presented in this study. The method is based on the single micro-interactions occurring within the fluidized bed such as inter-particle collisions, droplet spread on the particle surface, aging of the deposited droplets and particle coalescence. The porous character of the particles is expected to directly affect the aging process of the deposited binder layer by penetration into the pores of the substrate. The droplet penetration process is experimentally analyzed by single droplet deposition on spherical, porous alumina particles. The results indicate that the penetration process is mainly governed by the viscosity of the liquid and that at relatively low viscosities, droplet penetration is fast. For highly viscous liquids, the penetration velocity slows down and an additional mechanism, namely drying becomes important. A combined imbibition–drying model is developed and included into a comprehensive stochastic agglomeration model that allows the simulation of agglomerate formation in a batch process. Lab-scale agglomeration experiments with porous and non-porous particles are carried out in an attempt to validate the general tendencies predicted by the main agglomeration model. The results show that the agglomeration rate for porous particles is significantly reduced due to the losses of deposited droplets into the pores of the primary particles; this tendency is much more pronounced at low binder viscosities.     

On the impact of accessible surface and surface energy on particle formation and growth from the vapour phase

This work investigates effects of reduced accessible surface area of aggregate particles and surface energy on titania particle formation and growth. It is taken into consideration that surface-related growth mechanisms, i.e. surface reaction and condensation, are limited to the fraction of the surface area of primary particles which is exposed to the collision with single molecules. Surface energy data determine the critical particle size with respect to evaporation and values are varied within the published range. This implies to develop a model which considers “surface shielding” and accounts for the formation of stable clusters from a supersaturated vapour due to nucleation and condensation besides considering the generation of monomers due to chemical reaction, growth due to surface reaction, agglomeration and sintering. Taking the accessible surface area into account is found out to be especially important if agglomerates contain a large number of primary particles or if agglomerate structure is rather compact. In this case, precursor consumption and primary particle growth turn out to be significantly retarded. Surface energy data are shown to be decisive with respect to the thermodynamic barrier to the formation of particles, thus to active particle formation and growth mechanisms, besides affecting sintering kinetics. Elevated surface energy data typically retard precursor consumption and favour primary particle growth.     

A new wavelet-based adaptive method for solving population balance equations

A new wavelet-based adaptive framework for solving population balance equations (PBEs) is proposed in this work. The technique is general, powerful and efficient without the need for prior assumptions about the characteristics of the processes. Because there are steeply varying number densities across a size range, a new strategy is developed to select the optimal order of resolution and the collocation points based on an interpolating wavelet transform (IWT). The proposed technique has been tested for size-independent agglomeration, agglomeration with a linear summation kernel and agglomeration with a nonlinear kernel. In all cases, the predicted and analytical particle size distributions (PSDs) are in excellent agreement. Further work on the solution of the general population balance equations with nucleation, growth and agglomeration and the solution of steady-state population balance equations will be presented in this framework.     

声波与喷雾对于飞灰颗粒团聚的影响

为了研究声波团聚的影响因素,以燃煤飞灰细颗粒作为声波团聚的实验对象,使用光学颗粒物粒径谱仪测量颗粒的粒径分布与浓度,主要研究了声波频率与喷雾对声波团聚的影响。结果表明：在声波的作用下,细颗粒浓度显著减少,且声波团聚效果对频率较为敏感;无论在高声压还是低声压级下,1400Hz的频率下能获得最佳的团聚效果;在加入喷雾后,颗粒物浓度显著减小,且随着喷雾量增大,颗粒物浓度越小;分析了喷雾增强团聚效果的机理：在加入喷雾后,细颗粒间的相对运动增强;同时喷雾颗粒增大了颗粒浓度,增大了细颗粒碰撞概率;此外,喷雾改变燃煤飞灰细颗粒的表面特性,使颗粒的表面黏性增大,有助于团聚体形成。     

A novel nucleation apparatus for regime separated granulation

A novel nucleation apparatus is presented for the production of narrow sized nuclei from various powder and binder liquid combinations. Mono-sized binder liquid droplets are produced by a specially designed mono-disperse droplet generator. The droplet generator is positioned above a conveyor belt, transporting a powder bed through the spray zone of the droplet generator. By nucleating powder on a conveyer belt, the nucleation mechanism is completely separated from all other granulation mechanisms due to the lack of relative motion between primary particles and/or formed nuclei. Nucleation tests were performed using chalcopyrite and limestone powders with water as the binder liquid. At all operating conditions, the formed nuclei were found to originate from multiplicities of drops that merged on the powder bed surface. Investigation of the dynamics of nuclei formation showed that powder-binder liquid combinations with fast penetration dynamics result in less variation in the number of droplets from which nuclei originate. Smaller and more narrowly distributed nuclei were also achieved by increasing powder speed through the spray zone.     

The influence of additives on the primary particle nucleation and agglomeration in poly(vinyl-chloride)

The formation and agglomeration of PVC primary particles were studied in bulk polymerization experiments. In the absence of additives, the primary particles started to agglomerate at low conversions. The agglomeration conversion, as well as the size of the agglomerated particles, decreased when the agitation speed increased. At the highest speed tested, the agglomeration started already at 0.05 percent conversion. The primary particle size was about 0.16-0.18 μm, and seemed to be constant in the conversion interval studied (up to 5 percent). This indicated that the nucleation rate of primary particles was almost constant and that the growth rate of agglomerated particles was very low. The addition of sorbitan monolaurate produced a decrease in primary particle size. Polymeric additives such as PMMA, EVA, and PVAc stabilized primary particles against agglomeration but had no marked effect on the primary particle size. The monomer-soluble fraction of poly(vnyl alcohol-b-vinyl acetate) with high content acetate groups did not affect either the particle size or the agglomeration process.     

反应沉淀法制备亚微米粒子的粒度分布模拟与实验验证

采用基于粒数衡算方程及物料衡算方程的数值模拟方法模拟了包括反应、成核、生长及凝并的反应沉淀制备亚微米粒子的过程,其中颗粒间的凝并过程采用分级模型来模拟,产物颗粒的粒度分布（PSD）由离散化的粒数衡算方程求得.以BaSO₄的反应沉淀体系作为研究体系,将实验测量数据与数值模拟结果进行对比,验证了所构建的数学模型的正确性与适用性.应用此模型进行分析,发现沉淀时间、产物过饱和度及凝并对粒度及粒度分布有着显著的影响.在此基础上,提出了反应沉淀法制备亚微米粒子过程中颗粒粒度及粒度分布的控制方法.     

Coupled CFD-PBE Simulation of Nucleation in Fluidized Bed Spray Granulation

Fluidized bed spray granulation is used to produce porous granular particles from suspensions, solutions, and melts. It is the general aim of our work to provide a physics-based simulation tool for this process. For this the process-relevant mechanisms such as droplet deposition, dust integration, and drying are implemented using computational fluid dynamics (CFD) to generate growth kinetics of the granules and of the dust particles. The latter gives rise to the nucleation rate. This kinetics is applied to simulate the development of the particle size distribution of granules for a continuously operated fluidized bed spray granulation process using population balance equations of the granules.     

PARTICLE GROWTH IN A CONTINUOUSLY OPERATED FLUIDIZED BED GRANULATOR

Fluidized bed spray granulation offers several advantages compared to commonly used drying processes as spray drying, e.g. free flowing dust free coarse particles with a narrow particle size distribution can be produced in a single processing step. Especially for large production units a continuous operation is desirable. Unfortunately, there is still a lack of understanding concerning the mechanisms of particle formation and growth leading to difficulties in planning and operating such continuous granulators. Hence, experiments were performed to investigate the influence of process parameters on the growth process in a continuously operated fluidized bed granulator. Furthermore, a model was developed taking into consideration the particle exchange between nozzle jet and fluidized bed as well as the wetting and drying processes. The processes inside the jet are modeled in analogy to a wet scrubber. This modeling approach predicts an increase of growth rate with particle size. The prediction is in good agreement with experimental findings.     

PARTICLE GROWTH IN A CONTINUOUSLY OPERATED FLUIDIZED BED GRANULATOR

Fluidized bed spray granulation offers several advantages compared to commonly used drying processes as spray drying, e.g. free flowing dust free coarse particles with a narrow particle size distribution can be produced in a single processing step. Especially for large production units a continuous operation is desirable. Unfortunately, there is still a lack of understanding concerning the mechanisms of particle formation and growth leading to difficulties in planning and operating such continuous granulators. Hence, experiments were performed to investigate the influence of process parameters on the growth process in a continuously operated fluidized bed granulator. Furthermore, a model was developed taking into consideration the particle exchange between nozzle jet and fluidized bed as well as the wetting and drying processes. The processes inside the jet are modeled in analogy to a wet scrubber. This modeling approach predicts an increase of growth rate with particle size. The prediction is in good agreement with experimental findings.     

Interaction of droplets with porous structures: Pore network simulation of wetting and drying

In fluidized bed spray agglomeration, the time evolution of a liquid droplet deposited on a porous particle is of paramount importance for the success of the process. The combination of droplet penetration into the pores and evaporation, either directly from the droplet surface or from the surrounding wet pores, determines how long free liquid remains on the particle surface so that other particles can bind via liquid bridges. In this work, a two-dimensional pore network model that combines the algorithms of liquid migration and drying is developed to track the full droplet evolution, from its deposition on network surface to complete evaporation of the liquid. The influence of the pore structure for mono-modal and bi-modal networks with different spatial correlation of the pore size on the evolution of the liquid droplet is investigated. The effect of the liquid viscosity on the evolution of the droplet in the pore network is studied. Moreover, pore network simulations with multiple depositions of liquid droplets on the same network are presented as a rough approximation of spray agglomeration process.     

Stochastic simulation of agglomerate formation in fluidized bed spray drying: A micro-scale approach

A stochastic model that describes agglomerate growth during fluidized bed spray agglomeration is presented and numerically solved by constant volume Monte Carlo method. The methodology overcomes the difficulties of solving multivariate population balance equations and includes continuous binder addition and drying. Agglomerate formation is treated as a complex combination of consecutive and parallel micro-mechanisms. Due to the discrete nature of the approach, the individual role of the micro-mechanisms on the agglomeration behavior can be analyzed.The results suggest that the droplet capture mechanism governs the agglomeration speed while the maximum agglomerate diameter is ruled by the equilibrium reached between coalescence, rebound and breakage. The mechanism of deposited binder drying is found to play a negligible role on agglomerate formation because of an extremely rapid droplet consumption. The main process variables affecting each micro-mechanism have been identified showing that the liquid spraying rate affects directly the droplet capture mechanism whereas binder properties influence mainly the agglomeration and rebound interactions.The model presented in this study is able to predict qualitatively the experimentally observed response of the system as well as the general shape of the agglomerate size distribution under the variation of several process parameters, demonstrating the potential of the discrete micro-level approach.