A Probabilistic‐Statistical Model of Change of Particle Size Distribution in Settlers and Tanks

A probabilistic and statistical model of changes in the particle size distribution of the dispersed phase of low‐concentrated suspensions has been developed. The applicability of the method is theoretically substantiated. It is demonstrated that changes in the particle size distribution, in particular in the field of gravity, can be described by the Fokker‐Planck‐Kolmogorov equation.     

Practical Application of the Probabilistic‐Statistical Model of the Suspension Separation in Hydrocyclones

An effective practical approach that allows not only a significant reduction in the scope of practical experiments in the course of studying suspension separation processes in hydrocyclones, but also makes it possible to assess the intensity of random components of the processes and define the interrelation between such components and hydrodynamics of flows in a hydrocyclone is presented. Within the frames of the developed probabilistic‐statistical model of suspension separation in hydrocyclones on the basis of statistical self‐similarity properties, a relationship was found between determined and random components of the processes. This allowed transitioning from three‐parameter probability density functions for suspension particles in hydrocyclones to two‐parameter functions; thus significantly improving the efficiency of practical application of the developed model.     

Bed Expansion and Particle Classification in Liquid Fluidized Beds with Structured Internals

The inclusion of a structured packing as internal in a liquid‐solid fluidized bed allows expansion of the liquid velocity operation range before elutriation, promoting the liquid solid contact and mixing. The bed expansion of liquid‐solid fluidized beds provided with structured packing as internals is examined, for solids denser than the liquid phase and within a wide range of operating conditions. A correlation to estimate the bed expansion in liquid‐solid fluidized beds using structured packing as internals is developed. In addition, the feasibility of employing structured packing as internals for favoring classification of different density particles is demonstrated by analyzing the mass elutriated from the column at different liquid velocities for single particles or binary mixtures.     

A Comparative Study on the Separation of Different‐Shape Particles Using a Mini‐Hydrocyclone

The separation efficiency from water of different‐shape particles was studied experimentally using a mini‐hydrocyclone. Spherical and flaky (plate‐like) aluminum particles with the same particle size distributions were employed. Also, the effects of the feed flow rate and the temperature on the separation performance were studied. The results were investigated in terms of slurry recovery, total efficiency, and partition curves. The separation efficiency of the spherical particles increased with increasing particle size, temperature, and feed flow rate, as expected. The fishhook effect, as a noticeable phenomenon, was observed for the spherical particles. In case of the flaky particles, the separation showed an unusual behavior: The separation efficiency decreased with increasing particle size in the largest particle fraction, which has so far not been reported and addressed in this way.     

Flow Patterns in Mini‐Hydrocyclones with Different Vortex Finder Depths

Two‐phase flow patterns in a mini‐hydrocyclone with different insertion depths of the vortex finder were measured by a phase Doppler particle analyzer. The distributions of velocity, concentration, root‐mean‐square velocity, and average diameter of particles were evaluated. A deeper insertion of the vortex finder led to smaller tangential velocity at the cross section near the column cone interface. When the vortex finder insertion depth did not reach the column cone interface, the vortex finder was inserted deeper and the line of zero velocity value migrated more distinctly inward. When the vortex finder insertion depth reached or exceeded the column cone interface, strong turbulence occurred near the vortex finder. The distributions of the axial velocities of particles and root‐mean‐square velocities indicated that circulation flow existed at the bottom part of the mini‐hydrocyclone.     

Design and Numerical Simulation Analysis of an Integrative Gas‐Liquid‐Solid Separation Hydrocyclone

Normally, a gas‐liquid‐solid separation includes both degassing and desanding processes, which means a relatively higher facility investment and larger energy consumption. Based on an inner‐cone hydrocyclone developed before, an integrative degassing and desanding hydrocyclone was designed. Its design idea and process are described in detail. By means of a hollow inner cone (IC), the separated liquid enters into the cone through holes on it and then flows to the liquid‐phase outlet. Due to integrative separation and tangential solid outlet, the separator has a more compact size. Simulation analysis of the effect of IC diameter and IC height on separation performance was carried out. Results indicate that with a larger IC diameter the gas content in the solid outlet decreases, while as the IC height rises, the gas content in the liquid outlet increases.     

Numerical Simulation of Flow and Particle Collision in a Rotating‐Drum Bioreactor

Fluid flow and particle collision intensity in a rotating‐drum bioreactor are investigated by numerical simulation and a conventional stirred‐tank bioreactor is selected for comparison. Fluid flow is simulated by the computational fluid dynamics (CFD) software package FLUENT® whereas particle collision intensity is approached numerically through a hard‐sphere model. The dissipation rate of turbulent kinetic energy and the maximum particle collision intensity in the rotating‐drum bioreactor are about one order of magnitude smaller than those in the stirred‐tank bioreactor. The rotating‐drum bioreactor is likely to have a less severe impact on bioleaching microorganisms, and thus is expected to have great potential in the field of bioleaching processes.     

Validation of a Discrete Particle Model in a 2D Spout‐Fluid Bed Using Non‐Intrusive Optical Measuring Techniques

To gain insight into the hydrodynamics of spout‐fluid beds, an experimental and numerical study was carried out. Particle image velocimetry was successfully developed and applied to determine particle velocity profiles, whereas voidage profiles were determined by digital image analysis. A 3D hard‐sphere discrete particle model was used to simulate the flow in a spout‐fluid bed. The simulations and experiments showed a similar influence of the background fluidization velocity on the spout behaviour.     

Dynamic Optimization and Non‐linear Model Predictive Control to Achieve Targeted Particle Morphologies

An event‐driven approach based on dynamic optimization and nonlinear model predictive control (NMPC) is investigated together with inline Raman spectroscopy for process monitoring and control. The benefits and challenges in polymerization and morphology monitoring are presented, and an overview of the used mechanistic models and the details of the dynamic optimization and NMPC approach to achieve the relevant process objectives are provided. Finally, the implementation of the approach is discussed, and results from experiments in lab and pilot‐plant reactors are presented.     

A Stochastic Model for Liquid Dispersion in a Trickle‐Bed Reactor

A stochastic model was developed to describe the liquid radial dispersion in a trickle‐bed reactor, which has conventionally been modeled by the effective diffusion model. To establish the stochastic model, the column was divided into some layers of particles in the axial direction and several annulus rings in each layer in the radial direction. The liquid spreading was regarded as a fluid transport process and the matrix of transfer probability was derived based on the coordinates of the particle network in the cross‐section of the column. With this transfer probability matrix and the initial liquid distribution, the liquid distribution in the downstream was predicted. In order to evaluate the model parameters, experimental data of the liquid dispersion were obtained from electrical capacitance tomography images and tracer injection. Good agreement was obtained between the stochastic model and the experimental liquid distribution data.     

Behavior of Elongated Liquid Jets in Viscous Liquid‐Liquid‐Systems

The stability of jets in elongational flow is exploited to obtain thin threads before breakup. Fine drops can be generated in suitable geometries with comparably large ducts. The examination deals with the stability of liquid threads simultaneously extended with the continuous phase in convergent flow. Breakup limits and regimes are discussed.     

Effect of Silicone Carbide on the Elastic Properties of Starch‐Based Composites: A Three‐Phase Model

The effect of a rigid filler on the elastic properties of starch‐based composites is investigated. Thermomolding of the targeted composite is conducted using a starch matrix with varying silicone carbide content. Mechanical testing reveals that the composite's Young modulus cannot be rationalized using two‐phase analytical models. The effect of a weak interphase region is highlighted using a finite‐element model that assumes the generation of virtual microstructures. Numerical results are discussed by describing the influence of the structural and interphase parameters on the composite's elastic modulus. Identification of optimal interphase parameters quantitatively demonstrates the weak adhesion between intrinsic phases for all studied filler fractions.

     

Liquid‐Solid Mass Transfer Behavior of a New Stirred‐Tank Reactor with a Packed Bed Fixed to its Wall

Rates of liquid‐solid mass transfer at a packed bed of Raschig rings fixed to the wall of a stirred tank were measured by a technique which involves the diffusion‐controlled dissolution of copper in acidified dichromate. Variables studied were impeller rotation speed, impeller geometry, Raschig ring diameter, bed thickness, presence of baffles, physical properties of the solution, and effect of superimposed flow. Mass transfer data for the batch reactor were correlated by a dimensionless equation. For a given set of conditions, the radial‐flow impeller was found to produce higher rates of mass transfer than the axial‐flow impeller. The presence of baffles increased the rate of mass transfer inside the bed. Applications of the suggested reactor in conducting different diffusion‐controlled liquid‐solid reactions were evaluated.     

Filtration model for polydisperse aerosols in gas‐solid flow using granule‐resolved direct numerical simulation

An analytical framework for calculating the filtration efficiency of polydisperse aerosols in a granular bed is developed for cases where inertial impaction and interception are the principal filtration mechanisms. This framework is used to develop a model for the polydisperse single‐collector efficiency from monodisperse single‐collector efficiency correlations. Conceptually, the polydisperse model is developed by transforming the probability density of particle radius into a probability density of particle Stokes number that is then used to weight the monodisperse single‐collector efficiency at a given Stokes number. An extension of this polydisperse filtration concept results in an analytical solution for the axial variation of polydisperse particle flux in a random three‐dimensional granule configuration. In order to verify the analytical results for polydisperse particle filtration, a granule‐resolved direct numerical simulation approach is coupled with Lagrangian particle tracking to simulate filtration of polydisperse aerosols in a granular bed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3594–3606, 2015     

CFD Model of Particle Agglomeration in Spray Drying

A 3D CFD model of the agglomeration of droplets and particles in a counter-current spray-drying process was developed and verified. An original discrete phase model was elaborated, with an agglomeration module taking into account hydrodynamic segregation of particles, droplet coalescence, and droplet shrinkage for accurate calculations of mass balance of the discrete phase. The characteristic drying curves were applied to the model of particle moisture evaporation, which included the coupling of particle agglomeration with heat, mass, and momentum transfer between the discrete and continuous phases. Two agglomeration zones were observed in the tower: wet particle agglomeration in the atomization zone, and “dry agglomeration” above the air inlets, due to the intensive mixing of particle streams. A comparison of the calculated particle size distributions and experimental data obtained from particle dynamics analysis (PDA) measurements proves the accuracy of the developed methodology. The elaborated model allows the final PSD of the powder in the spray towers to be predicted.     

Thermal Effects During the Absorption of CO2 in Aqueous Solutions of 3‐Amino‐1‐Propanol

In this work, we study the process of CO₂ absorption, at high partial pressures, in aqueous solutions of 3‐amino‐1‐propanol (AP), with respect to the thermal effects of this operation. All of the experiments were performed in a stirred tank gas‐liquid reactor with a flat, known interface. The variables considered were the AP concentration in the range of 0.1 to 3.0 M and the temperature within the interval of 288–313 K. From the results, we deduce that the process takes place in the instantaneous nonisothermal regime, and we propose an equation which relates the experimental results of molar flux with the initial amine concentration. At the same time, we can evaluate the temperature increase at the gas‐liquid interface.     

Liquid‐Liquid Equilibrium and Interfacial Properties of the System Water + Hexylacetate + 1‐Hexanol

Experimental and theoretical investigations of the phase diagram and the interfacial tension are presented. The theoretical framework was able to predict the phase behavior and the interfacial tension with a high accuracy, where only binary experimental data enter the model parameter. The theory permits the calculation of the concentration profiles across the interface. The profiles show that 1‐hexanol will be enriched, which was expected. In same circumstances a competition between hexylacetate and 1‐hexanol was figured out leading to slight minima in the profile of 1‐hexanol.     

Power Consumption in Gas‐Liquid Contactors Agitated by Double‐Stage Rushton Turbines

The dependence of power consumption on impeller spacing in unaerated and aerated gas‐liquid contactors agitated by dual Rushton turbine systems was studied, and the gas flow rate and viscosity effects were measured in relation to these parameters. The experiments were carried out in a 0.19 m i.d. vessel stirred by two Rushton turbines with a diameter d = 0.10 m; with blade length and blade height 0.25 d and 0.2 d, respectively. In tap water the impellers acted independently for spacings greater than 1.65 d, while in glycerol solutions the two impellers already acted independently at an impeller spacing equal to 1.2 d. In aerated systems, a notable increase in the power consumption with increasing impeller spacing could be detected for small gas flow rates and low viscosities, while a decrease in the Newton number with increasing Froude number could be observed at constant impeller spacing. The Newton number was not affected by flow number at high viscosity values.     

Prediction of Particle Deposition Using a Simplified Particle Model in Fully Developed Channel Flow

In this study the Eulerian particle model was modified to predict the particle deposition rate in fully developed channel flow. The modified model is less complicated and has much lower computation time. The performance of the simplified model was examined by comparing the particle deposition rate in a vertical channel with the experimental data for fully developed channel flow available in the literature. The effects of turbophoretic force, thermophoretic force, electrostatic force, gravitational force, Brownian/turbulent diffusion, and the wall roughness on the particle deposition rate were examined. The predictions of the modified particle model were in agreement with the experimental data.