CFD simulation of gas–liquid flow in a high-pressure bubble column with a modified population balance model

In this study,based on the Luo bubble coalescence model,a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term.Then,a coupled modified population balance model(PBM) with computational fluid dynamics(CFD) was used to simulate a high-pressure bubble column.The simulation results with and without C_e were compared with the experimental data.The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions.These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.

A Population Balance Model for Disperse Systems:Particle Size Distribution in Suspension Polymerization

On the basis of population balance a mathematical model is developed to describe the formation of polymer particle in styrene suspension polymerization. The characteristics of coalescence and breakage of droplets and the gel effect are analyzed in particular. Parameters of the models are estimated by experimental data on reaction conversion and particle size distribution. The results show that the model is suitable for predicting polymerization processes.

Batch-to-batch Optimization of Batch Crystallization Processes

It is the fact that several process parameters are either unknown or uncertain. Therefore, an optimal control, profile calculated with developed process models with respect to such process parameters may not give an optimal performance when implemented to real processes. This study proposes a batch-to-batch optimization strategy for the estimation of uncertain kinetic.par.ameters in a batch crystallization process of potassium sulfate production. The knowledge of a crystal size distribution of the product at the end of batch operation is used in the proposed methodology. The updated kinetic parameters are applied for determining an optimal operating temperature policy for the next batch run.

Numerical simulation of flocculation and settling behavior of whole-tailings particles in deep-cone thickener

Rapid dewatering and thickening of whole-tailings with ultrafine particles is one of the most important processes for the whole-tailings paste preparation. Deep-cone thickener, a kind of such process for the flocculation and settling of whole-tailings, is particularly necessary to study. However, there exist many problems in observing the flocculation and settling process of whole-tailings, as well as the particle size distribution(PSD) of whole-tailings floccules in deep-cone thickener. Population balance model(PBM) is applied to predict the PSD in deep-cone thickener, and LUO model and GHADIRI model are employed to study the aggregation and fragmentation mechanism of the whole-tailings particles, respectively. Through three-dimensional numerical simulation on the whole-tailings flocculation and settling in deep-cone thickener using computational fluid dynamics(CFD)-PBM, the distribution of density and turbulent kinetic energy in deep-cone thickener were obtained, at the same time the spatio-temporal changes of whole-tailings floccules particle size distribution are analyzed. Finally, the major flocculation position in deep-cone thickener is found and the flocculation settling rules of whole-tailings are achieved.

CFD-PBE simulation of gas-phase hydrodynamics in a gas-liquid-solid combined loop reactor

The computational fluid dynamics （CFD）-population balance equations （PBE） coupled model is employed to investigate the hydrodynamics in a gas-slurry internal loop reactor with external slurry circulation. The predicted radial profiles of local gas holdup and bubble diameter are in good agreement with the corresponding experimental data. The spatio-temporal velocity profile of the gas phase reveals that the upward movement of gas is slowed down and the residence time of gas is prolonged by the downward momentum of the slurry, introduction of the external slurry can greatly improve the uniformity of gas holdup distribution in the reactor, especially in the downcomer-tube action region. Moreover, the interaction between the downward slurry and upward gas can lead to small bubble size and high interfacial area as well as good mass and heat transfer. The above results suggest the function of external slurry circulation for the internal loop reactor and would be helpful for optimizing the design and scale up of reactors.

Simulation of a semi-industrial pilot plant thickener using CFD approach

Thickeners are important units for water recovery in various industries. In this study, a semi-industrial pilot plant thickener similar to the tailing thickener of the Sarcheshmeh Copper Mine was simulated by CFD modeling. The population balance was used to describe the particle aggregation and breakup. In this population balance, 15 particle sizes categories were considered. The Eulerian-Eulerian approach with standard k-e turbulence model was applied to describe two phases of slurry flow in the thickener under steady-state condition. The simulation results have been compared with the experimental measurements to validate the accuracy of the CFD modeling. After checking the numerical results, the effect of important parameters such as, feed flow rate, solid percentage in the feed, and solid particle size on the thickener performance was studied. The thickener residence time distribution were obtained by the modeling and also compared with the experimental data. Finally, the effects of feedwell feeding on the average diameter of aggregate and turbulent intensity were evaluated.

Simulation of bubble column reactors using CFD coupled with a population balance model

Bubble columns are widely used in chemical and biochemical processes due to their excellent mass and heat transfer characteristics and simple construction.However,their fundamental hydrodynamic behaviors,which are essential for reactor scale-up and design,are still not fully understood.To develop design tools for engineering purposes,much research has been carried out in the area of computationalfluid dynamics(CFD)modeling and simulation of gas-liquidflows.Due to the importance of the bubble behavior,the bubble size distribution must be considered in the CFD models.The population balance model(PBM)is an effective approach to predict the bubble size distribution,and great efforts have been made in recent years to couple the PBM into CFD simulations.This article gives a selective review of the modeling and simulation of bubble column reactors using CFD coupled with PBM.Bubble breakup and coalescence models due to different mechanisms are discussed.It is shown that the CFD-PBM coupled model with proper bubble breakup and coalescence models and interphase force formulations has the ability of predicting the complex hydrodynamics in differentflow regimes and,thus,provides a unified description of both the homo-geneous and heterogeneous regimes.Further study is needed to improve the models of bubble coalescence and breakup,turbulence modification in high gas holdup,and interphase forces of bubble swarms.

Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation

In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.

Prediction of aggregation behavior of submicron-sized particles of praseodymium-doped zirconium silicate in aqueous suspension by population balance model

The aggregation behavior of submicron-sized particles of praseodymium-doped zirconium silicate, a ceramic pigment, in aqueous suspension was predicted by a modified population balance model, In the model, the collision frequencies were selected to describe evolution of the particle size distribution of the suspension. The collision efficiency was estimated as a function of interaction potential between particles based on Derjaguin-Landau-Verwey-Overbeek theory. The population balance model was modified to predict the stable state of the aggregation by introducing the volume mean size of aggregate to stability ratio. In addition, aggregation of the particles in aqueous suspension in the presence of sodium dodecyl benzene sulfonate or potassium chloride was experimentally investigated. The predicted data （i.e., the final aggregate size, aggregation rate, and particle size distribution） were similar to the experimentalresults.

Numerical simulation of granular silicon growth and silicon fines formation process in polysilicon fluidized bed

Operating conditions strongly affect the yield and quality of polysilicon in a polysilicon fluidized bed.In this study,a new model of polysilicon fluidized bed was established using the Euler-Euler model coupled with population balance model(PBM),which was combined with fluid flow,heat,and mass transfer models,while considering the scavenging effect of silicon fines.The effects of different operating conditions on the deposition and formation rates of silicon fines were investigated.Results show that the model can correctly describe the particle growth process in the fluidized bed of polysilicon.The silicon fines and the interphase velocity difference show"N"-and"M"-shaped distributions along the axial direction,respectively.The particle temperature and concentration near the wall are higher than those in the central region.The decomposition of silane in the bottom region of the bed is dominated by het-erogeneous deposition.The scavenging of silicon fines occurs in the dilute-phase region.The effects of operating conditions,i.e.inlet gas temperature,silane composition,and gas velocity,on the reactor performance were also explored comprehensively.Increasing the inlet gas composition and velocity enhances the formation rates of solid silicon and fines.Increasing the inlet gas temperature promotes the growth of solid silicon and inhibits the formation of silicon fines.High fluidization ratio,low inlet silane concentration,and high inlet gas temperature enhance the selectivity of silicon growth.

A dynamic two-zone model of continuous fluidized bed layering granulation with internal product classification

A dynamic two-zone model is proposed to address the formation of granulation and drying zones in fluidized bed layering granulation processes with internal product classification. The model assumes a constant volume for the granulation zone, but a variable overall volume for the fluidized bed to account for classified product removal. The model is used to study the effect of various process parameters on dynamics and process stability. Stability is shown to depend on the separation diameter of product removal and the flow rate of the injected liquid. A lower and upper range of separation diameters with stable process behavior are found. In an intermediate range instability in the form of self-sustained oscillations is observed. The lower stability boundary is in qualitative agreement with recent experimental observations （Schmidt, Bück, ＆ Tsotsas, 2015）; the upper boundary was reported in a theoretical paper by Vreman, Van Lare, and Hounslow （2009） based on a single zone model.

PRODUCTION OF PIGMENT NANOPARTICLES USING A WET STIRRED MILL WITH POLYMERIC MEDIA

Pigment nanoparticles with a size range of 10~100 nm were produced from large agglomerates via a stirred media mill operating in the wet-batch mode and using polymeric media. The effects of several operating variables such as the surfactant concentration, polystyrene media loading, and media size on the pigment size distribution of the product were studied. The process dynamics was also investigated. Dynamic light scattering and electron microscopy were used as the characterization techniques. The polymeric grinding media are found to be effective for the production of pigment nanoparticles. The experimental results suggest the existence of an optimum media size and surfactant concentration. A population balance model of the process reveals a transition from first-order breakage kinetics for rela-tively coarse particles to non-first-order kinetics, with a delay period, for the smaller particles. The model implies that large agglomerates split in a first-order fashion whereas the breakage of individual nanoparticles may depend on induced fatigue of the particles.

On the determination of particle impact breakage in selection function

This paper presents a thorough study of particle impact breakage in selection function with a unified breakage criterion.The impact mode and breakage pattern for particulate materials are classified based on a significant review of well-established impact testers.It was found that the lack of a unified breakage criterion to determine the breakage probability disables a direct comparison of particle breakage propensity from different impact loading testers.The literature breakage models to describe the breakage probability are reviewed where the advantage and drawback of these models are scrutinized.The sourced literature breakage models are compared with the zeolite breakage datasets in a unified breakage criterion to evaluate the model performance.A novel computational modelling workflow for a milling process is proposed to provide a guidance in implementing the digital twin in milling process prediction.The breakage probability models,i.e.the selection functions are comprehensively assessed in population balance model to examine the model serviceability.The model simplicity and fidelity in the model assessment are specifically discussed and the value of digital twin in substantially reducing the experimental trials is highlighted.

Simulation of aggregation effects on co-fired biomass-coal ash in an electrostatic precipitator

Aggregation of fine ash into larger particles benefits fly ash removal in an electrostatic precipitator.Thermal aggregation,turbulent aggregation,and electrical aggregation of fine ash (derived from co-firing of biomass fuel and anthracite coal) was simulated under different conditions in an electrostatic precipitator.A population balance model and user-defined function in Fluent were assumed to obtain aggregation kernel functions and calculate the aggregation effects on the co-combusted particles.The results show that electrical aggregation had an obvious effect on both micron-and submicron-sized particles.For submicron particles,the effect of thermal aggregation is about ten times greater than turbulent aggregation.Meanwhile,for micron-sized particles,turbulent aggregation is about seven times greater than thermal aggregation.Therefore,particle aggregation in the electrostatic precipitator mainly occurs because of electrical aggregation,supplemented by thermal aggregation and turbulent aggregation.When the flow velocity is 1.0 m/s,particle volume fraction is 1.4%,and biomass co-firing ratio is 10%,the effects of all three aggregation processes on ash particles are optimized.

From Single Droplet to Column Design

The technique state to design counter-current extraction columns is based on the performance of pilot plant experiments. The modelling is then either with the equilibrium or dispersion model, whereas in the latter the dispersion coefficient accounts for all hydrodynamic non-idealities. A new approach uses single droplet experiments to obtain the basic laws and functions governing droplet breakage, coalescence, relative velocity, and axial dispersion when using droplet populance balance models （DPBM）. The hydrodynamics simulation results show that the mean Sauter diameter, hold-up, and concentration profiles could be well predicted, which promotes the use of DPBM models for further applications in industrial scale.