A multi-dimensional population balance model approach to continuous powder mixing processes

This study is concerned with the development of a novel population balance model (PBM) framework that can qualitatively capture the dynamics of a continuous powder mixing process. For the first time, a PBM has been developed to model powder mixing and it accounts for key design and process parameters such as mixer RPM, processing angle in terms of powder fluxes, along with the effect of number of axial and radial compartments. Via this approach, results clearly show the qualitative validity of the PBM as a tool to capture the dynamics of the process that affect API composition, RSD and RTD. The model also demonstrates the use of the PBM as an overall multi-scale modeling tool to combine micro-level models such as DEM in a hybrid framework. Due to the relative computational simplicity of solving the PBM (as compared to DEM), the developed model can be used effectively in control and optimization of the mixing process.     

An extended cell-average technique for a multi-dimensional population balance of granulation describing aggregation and breakage

This paper focuses on obtaining the numerical solution to a three-dimensional population balance model (PBM) of granulation using the cell-average technique first proposed by [22]. Conventionally, linear grids are used for the solution of PBMs, but the ability to incorporate non-linear grids would be more advantageous given that a larger size range can be covered using fewer number of grids, thus reducing computational overhead. Furthermore, the use of linear representation of grids in PBMs to represent industrial granulation processes that span a wide granule size range is computationally prohibitive and results show that a non-linear grid representation is computationally more efficient with comparable accuracy. Parallelization of the PBM via a multi-core strategy has also been incorporated in order to reduce the simulation time of the model. Incorporating the cell average technique along with parallelization of the overall model lends credence to the overall use of the model for effective granulation process design and analysis.     

A compartment based population balance model for the prediction of steady and induction granule growth behavior in high shear wet granulation

This paper presents a predictive modeling approach of the high shear wet granulation process, quantifying the difference between the steady and induction granule growth behavior. The spatial heterogeneity in liquid binder distribution and shear rate is simulated using a compartmental population balance model. The granulator is divided into two compartments based on particle motion, which consists of a circulation compartment, and an impeller compartment. In the circulation compartment, a viscous dissipation dependent coalescence kernel is adapted for the aggregation process. In the impeller compartment a shear rate dependent aggregation kernel is implemented. The model was calibrated and validated using the dynamic evolution of granule mean size (d₅₀). The granulation dynamics are studied with respect to change in impeller speed, liquid to solid ratio, wet massing time, initial porosity, and binder viscosity. The transition from induction growth to steady growth regime with changing process conditions is demonstrated using the model. It is observed that the model captures the effect of process parameters and spatial heterogeneity on the dynamic evolution of d₅₀.     

Population balance modeling applied to the milling of pharmaceutical extrudate for use in scale-up

This study modeled the particle size distribution (PSD) of pharmaceutical extrudates after milling by developing a so-called time-discrete population balance model (PBM). The PBM, which models size reduction as a series of breakage events, was formulated so that the model parameters separate the effect of material properties and milling process conditions. Because of this novel aspect, the PBM should have excellent predictive capability with specific applications in technology transfer and scale-up. To investigate this application, copovidone extrudate produced by the hot-melt extrusion process was milled using a lab-scale continuous impact mill (Fitz Mill). The effect of impeller speed and classification screen size on PSD of the extrudate was investigated. The PBM with parameters obtained by fitting lab-scale PSD data was then applied to model the PSD of the extrudate following milling by a pilot-scale continuous impact mill (Hosokawa mill). The study found that the parameters determined at the lab-scale can be used to model PSDs at the pilot-scale and may be generally applied to similar classification-type impact mills. Since technology transfer and scale-up can be material and time consuming, this approach may offer significant benefits to the pharmaceutical industry for the development of milling processes.     

集成过程分析技术和群体粒数衡算模拟的药物材料造粒过程决策支持系统

通过集成在线近红外光谱仪、实时图像采集与处理系统和群体粒数衡算模型,开发了高剪切湿法造粒过程的决策支持系统(Decision support system,DSS)。利用近红外光谱仪和图像系统实时测量多个过程变量和产品质量指标,包括粉体混合均匀度、颗粒粘合剂含量、粒径分布以及团聚、破裂行为等,能够快速确定过程操作空间。同时,由过程分析平台得到的信息经分析处理后输入工艺过程模型模块,用于估算和校准群体粒数衡算模型中的团聚和破裂速率常数,以此持续提高模型精度。另一方面,模型可以指导实验体系寻找最优操作空间。该决策支持系统成功应用到了以微晶纤维素和甘露醇为原料,3%聚乙烯吡咯烷酮水溶液为粘合剂的高剪切湿法造粒过程中,对两个粘合剂喷淋速率下的造粒过程进行监测。DSS认定粘合剂喷淋过程分为四个阶段:润湿期、成核期、快速生长期和慢速生长期。不同阶段之间的分界点与粘合剂喷淋速率有关。在较高喷淋速率下,颗粒进入成核期和快速生长期所需粘合剂较少,但是对颗粒最终粒径无明显影响。此外,通过近红外光谱测定混合均匀度,确定了粉体的混合终点。该DSS系统将基于过程分析技术的高效实验和过程模拟结合,可以快速确定操作空间以及颗粒的生长行为,实时提供大量数据用于持续提高模型精确度和稳健性,提高造粒过程的优化效率。     

Scale-up procedure of parameter estimation in selection and breakage functions for impact pin milling

This paper presents a scale-up procedure of parameter estimation in the selection function and breakage function from single particle impact breakage to inform the predictions at the process scale of an impact pin mill. The selection and breakage functions used in population balance model (PBM) for particle breakage in the literature are briefly reviewed. Single particle breakage tests are conducted in a vertical impact tester subject to varying impact velocities. The single particle breakage results further serve to provide the database for the parameter estimation in Vogel and Peukert model (Vogel and Peukert, 2005). The estimated parameters in the particle level are upscaled in an impact pin mill using the population balance model, which is implemented in the software gPROMS (Process Systems Enterprise, UK) (gPROMS® 4.1 Release Notes, 2016). The impact milling tests were carried out in an impact pin mill UPZ100 subject to four feed rates, providing the dataset for model validation. The sensitivity analysis of the PBM parameters was conducted to help identify their leverage on the particle size distribution. The scale-up procedure by specifying the parameters from single particle level to the process level of PBM demonstrates an approach to help predict the size reduction process subject to the prevailing mechanism in an impact pin mill and other milling processes alike.     

Twin-screw granulation: Mechanistic understanding of the effect of material properties on key granule quality attributes through the analysis of mixing dynamics and granulation rate mechanisms

This study focuses on understanding the effect of material properties on granule quality attributes through the analysis of mixing dynamics and granulation rate mechanisms. Powder wettability, binder viscosity, and liquid-to-solid (L/S) ratio were the factors that were investigated in this study. The mixing occurring inside the twin-screw granulator (TSG) was quantitatively assessed by obtaining the axial dispersion coefficient from the experimentally measured residence time distribution (RTD) curves. It was observed that the quality of the nuclei fed to the kneading zone significantly affected the mixing dynamics. The quality of nuclei was governed by nucleation kinetics, which in turn was principally affected by the liquid saturation of the nuclei and the ratio of drop penetration time and encounter time, which in turn were affected by the L/S ratio and binder viscosity respectively. The hydrophobicity of the blend mainly affected the extent of nucleation. The type of nuclei entering the kneading zone and mixing dynamics in the TSG also determined whether the granulation growth mechanism was “layering-dominant” or “viscous-dominant”. It was also shown that the resultant granule quality attributes were a reflection of the growth mechanisms. Ultimately, a mechanistic link between material properties, mixing dynamics, granulation rate mechanisms, and granule quality attributes was established.     

Modeling and simulation of carbon black synthesis in an aerosol flame reactor

Carbon black has diverse industrial applications such as a reinforcing agent in tires and as a black pigment in printing inks. Flame aerosol synthesis is the commonly employed route for large scale production of carbon black. A coupled flame dynamics – monodisperse population balance model for the synthesis of carbon black in an aerosol flame reactor is presented here. The population balance model was incorporated into the commercial computational fluid dynamics software CFX to simulate the effect of flame dynamics on particle synthesis. The model was tested with published experimental data for acetylene black synthesis through oxidative thermal decomposition of acetylene with oxygen in a premixed flame reactor. The predicted axial temperature profiles at different equivalence ratios (actual acetylene/oxidizer ratio divided by stoichiometric acetylene/oxidizer ratio) were reasonably close to experimental data. The effect of the equivalence ratio on process parameters like maximum temperature of the flame, specific surface area of particles and flame structure was investigated. It was observed that the maximum temperature of the flame and specific surface area of carbon black particles decrease upon increasing the equivalence ratio which is in agreement with published experimental studies. Simulation results are also presented for carbon black synthesis in a diffusion flame reactor with different burner designs.     

Spectrophotometric analysis of disintegration mechanisms (abrasion and crushing) of agglomerates during the disc granulation of dolomite

The analysis of mechanisms which affect the formation of agglomerates and determine the granulation process in a broad sense encounters difficulties related to the many ways of the formation of granules. The aim of the study was to perform a qualitative and quantitative analysis of granulation mechanisms with special reference to agglomerates’ disintegration in the disc granulation process. This paper contains an analysis of disintegration mechanisms (abrasion and crushing) of agglomerates during the disc granulation of dolomite. The analysis of the mechanisms taking place during the process concerns the granulation stage after wetting. During the research, each time after the wetting stage, the size fraction 10–12.5 mm was substituted with an analogous fraction wetted by means of an aqueous solution of a coloring agent and the process was continued. After the specified time of granulation, the obtained product was sieved through laboratory sieves and then the content of the provided coloring agent in different size fractions was analyzed by means of a spectrophotometer. Measuring the absorbance of the analyzed samples and granulometric composition of the bed, the level and cause of the migration of material of the tested fraction into other size classes were determined, and at the same time, the occurring granulation mechanisms were analyzed. The proposed model and measurement method consisting of determining the absorbance of the tested granulometric fraction enable the qualitative and quantitative analysis of granulation mechanisms are encountered during the carrying-out of the process after wetting the bed.     

Evaluation and comparison of a moist granulation technique to conventional methods

In the moist granulation technique (MGT), a minimum amount of liquid is used to activate a binder in a planetary mixer. Then, any excess moisture is absorbed by the addition of a moisture-absorbing substance. In the experiments described below, acetaminophen (APAP) was the model drug; polyvinylpyrrolidone (PVP) and microcrystalline cellulose (MCC) served as the binder and moisture-absorbing material, respectively. Water was used as the granulating fluid. Comparison of the MGT with direct compression (DC) and wet granulation (WG) methods was accomplished by sieve analysis (particle size) and density measurements. Moist granulation yielded an increase in particle size compared to direct compression; these results are comparable to those from the traditional wet granulation after drying and screening. Based only on the particle size, moist granulation appears comparable to conventional wet granulation for this formula. The moist granulation technique appears to have potential for the development of controlled-release formulations.     

Comparing modeling approaches in simulating a continuous pilot-scale wet vertical stirred mill using PBM-DEM-CFD

Vertical stirred mills have become increasingly popular in size reduction operations in the fine and ultrafine range, being normally used in industry in continuous operation. The present work describes the application of a mechanistic mill modeling approach based on the population balance (PBM) to describe the performance of a pilot-scale gravity-induced continuous stirred mill using 6 mm steel grinding media. At first, DEM and coupled DEM-CFD were compared in simulation of the mill, clearly demonstrating the significant effect of incorporating explicitly the fluid flow in describing the motion of the grinding media. The work then uses data from the stirred mill grinding calcite in multiple passes for model calibration and validation, besides breakage parameters from previous studies. It shows that the population balance-based mechanistic mill model predictions vary depending on the number of mixers-in-series used to predict product size, but that are capable of describing very well the milling operation considering the mill as three perfectly mixed grinding zones in series.     

Continuous high-shear granulation: Mechanistic understanding of the influence of process parameters on critical quality attributes via elucidating the internal physical and chemical microstructure

Over the past decade, continuous wet granulation has been emerging as a promising technology in drug product development. In this paper, the continuous high-shear mixer granulator, Lӧdige CoriMix® CM5, was investigated using a low-dose formulation with acetaminophen as the model drug. Design of experiments was deployed in conjunction with multivariate data analysis to explore the granulator design space and comprehensively understand the interrelation between process parameters and critical attributes of granules and tablets. Moreover, several complementary imaging techniques were implemented to unveil the underlying mechanisms of physical and chemical microstructure in affecting the tablet performance. The results indicated that L/S ratio and impeller speed outweighed materials feeding rate in modifying the granule and tablet properties. Increasing the degree of liquid saturation and mechanical shear input in the granulation system principally produced granules of larger size, smaller porosity, improved flowability and enhanced sphericity, which after compression generated tablets with slower disintegration process and drug release kinetics due to highly consolidated physical microstructure. Besides, in comparison to batch mixing, continuous mixing integrated with a conical mill enabled better powder de-agglomeration effect, thus accelerating the drug dissolution with increased surface area.     

Effect of collision angle on particle-particle adhesion of colliding particles through liquid droplet

In wet granulation processes, a particle adhesion mediated by a liquid bridge is one of the quite important phenomena. In an actual process, the liquid bridge shows dynamic motion due to continuous motion of the particles. Therefore, understanding of the particle adhesion phenomenon by a dynamic liquid bridge is essential to adequately and precisely control wet granulation processes. This study presents a direct numerical simulation of the particle–particle adhesion by a dynamic liquid bridge. Collision of a dry particle and a wet particle was simulated at various collision angles. In particular, translational and rotational motions of the particle at different collision angles were discussed through comparison with a conventional static liquid bridge force model. As a result, it was found that both translational and rotational motions were largely different between simulation results of the direct numerical simulation and static liquid bridge force model, especially at the tangential collision. To understand these results, we focused on the rotational behavior of the particle and deformation of the liquid bridge. It was concluded that the non-slip behavior of the liquid bridge on the particle surface is a key phenomenon for the particle-particle adhesion by the dynamic liquid bridge at the tangential collision.     

Influence of Technological Factors on the Optimal Granulation Liquid Requirement Measured by Power Consumption

The optimal liquid requirement for wet granulation can be investigated by recording the power consumption of the mixer during liquid addition. In this work it was tried to use this technique on a small laboratory scale (one kg or less) for lactose wet granulation with water. The validity of the power consumption method could be confirmed by granule size analysis. Different factors were studied: kind of mixer, powder quantity, mixer speed, liquid addition speed, granulator screen size, mixing time.     

Mathematical modeling and distribution characteristics evaluation of fuel particles in iron ore sintering process

The distribution characteristics of fuel particles is a key factor affecting the thermal state of sintering. To find out the fuel distribution under different granulation conditions, a mathematical method based on the particle population balance and Lister’s model was established in this study. In combination with experiments including granulation and the fixed carbon and sulfur content of detection, the relative error of this model is within ±1.5. The proportion and particle size composition of fuel are selected to evaluate quantitatively the distribution characteristics. The result shows that the fuel distribution in granules mostly accumulates in the middle size granules. The increase of proportion and fine particles content of the fuel leads to the decline of the fuel content in +5 mm granules. With a higher ratio and higher content of fine particles in the fuel, the fuel distribution in the upper and middle of the sintering beds rises while that of the bottom layer is down, which is conducive to changing the nonuniform distribution of thermal. The fuel particle size composition has greater impact on fuel distribution than its proportion. To better investigation, further parameter simulation and optimization of granulation is necessary.     

Preliminary report of the discovery of a new pharmaceutical granulation process using foamed aqueous binders

Spray granulation is commonly used to improve the flow of drug formulation powders by adding liquid binders. We have discovered a new granulation process whereby liquid binders are added as aqueous foam. Initial experiments indicate that foam granulations require less binder than spray granulations, less water is added to the powder mass, rates of addition of foam can be greater than rates of addition of sprayed liquids, and foam can be added in a single batch to the surface of the powder mass for incorporation at some later stage in the process. This new process appears to have no detrimental effects on granulate, tablet, or in vitro drug dissolution properties. In addition, the elimination of spray addition reduces the complexity of the process and avoids the plugging problems associated with spray nozzles. Several formulations were successfully scaled up from laboratory scale (1.5 kg) to pilot scale (15 kg). Process control was good and there was no detrimental effect on tablet and drug dissolution properties. This paper also proposes a working hypothesis of the mechanism by which foam granulation operates.     

Influence of Technological Factors on the Optimal Granulation Liquid Requirement Measured by Power Consumption

Abstract

The optimal liquid requirement for wet granulation can be investigated by recording the power consumption of the mixer during liquid addition. In this work it was tried to use this technique on a small laboratory scale (one kg or less) for lactose wet granulation with water. The validity of the power consumption method could be confirmed by granule size analysis. Different factors were studied: kind of mixer, powder quantity, mixer speed, liquid addition speed, granulator screen size, mixing time.     

Experimental study and particle population modeling of coating in a jet-fluidized bed

The present work focuses on the study of a bottom-spray fluidized-bed coater in the absence of any liquid (solvent) evaporation. The main objective is to point out and model the effect of operating conditions on the coating efficiency and the coating mass content distribution of particles. A fluidized bed with a bottom-placed spraying nozzle situated in the middle of a perforated distributor plate was used. The experimental results showed that increasing the jet and fluidizing gas flow rates improve the quality of coating, but there is a limitation for the binder flow rate which is dependent on the bed size and jet gas flow rate. Based on the experimental results, an empirical function was derived to predict the coating efficiency in different operating conditions and this function was also used in the mathematical model. Furthermore, a mathematical model was derived based on the population balance equations for two different zones in the bed. The model could predict the coating mass content distribution and the effect of different operating conditions during the process.     

脉冲燃烧风洞测力天平动力学建模与分析

风洞试验在高超声速一体化飞行器研究过程中发挥着无法替代的作用,其中天平测力是风洞试验的关键技术。脉冲燃烧风洞试验的时间短、冲击载荷大。试验过程中,模型系统会产生强烈的振动,影响天平的测力精度,因而需对其进行动力性能的研究。由此,首先针对测力天平进行结构动力学建模,获得天平的动力学方程。通过仿真分析和锤击试验对测力天平的模态参数进行了计算和测定,然后将计算结果和试验结果进行对比分析,并解析两者的差异及产生的可能原因。理论和实验的全过程表明了测力天平的模态特性能够予以确认,同时也为试验模型系统结构动力学的进一步研究提供了有价值的依据。