Transverse mixing and heat transfer in horizontal rotary drum reactors

The transverse mixing of quartz sand (mean particle sizes 157, 323, 794 and 1038 μm) and sodium carbonate (soda) (mean particle size 137 μm) has been investigated in a laboratory rotary drum reactor of 300 mm length and 310 mm diam. Solid movement in the drum was observed by means of colored tracers and successive exposures as well as by means of hot tracers and recording the local temperature in the bulk of particles. Three different types of the particles and bulk behaviour could be observed for stickly particles. The time constant of the mixing was estimated as a function of the rotational speed of the drum. The “cooling-down” curves of the bulk of particles were measured in a laboratory oven of 250 mm diam. and 600 mm length. The temperature variation as a function of the time can be described by the Newtonian cooling law, from which the heat transfer coefficient at the wall α_w was estimated.The absolute value of α_w's and their dependence on the contact time and particle diameter cannot be calculated by the heat penetration model, which disregards the film resistance at the bulk/wall contact. By taking into account this resistance a good quality of fitting can be achieved.     

A Model for Residence Time Distribution of Solids in a Rotary Kiln

A five‐parameter model for residence time distribution of low‐density particles in a bed of high‐density particles in a rotary kiln is derived based on combinations of flow regimes in several sub‐regions. The parameters of the model are the number of turnover stages, the cascade volume fraction, the Peclet number, the dead volume fraction in cascade region, and the cross‐flow ratio. The effect of feed rate of solids, rotational speed and inclination of the kiln on the model parameters is evaluated.     

Paste Residence Time in a Spouted Bed Dryer. II: Effect of Spout Operational Conditions

Residence time distributions for an aqueous solution of 10% sodium chloride in a spouted bed dryer of inert particles were determined using the stimulus-response technique. Glass and polyethylene beads with diameters 2.6 and 3.4 mm were used as inert bodies in a cylindrical column of 14.0 cm diameter and 60° conical base. The effects of inert bodies load, air, and paste flow rates on the mean residence times and RTD were determined following 2³ factorial designs. The RTD could be correlated to the perfect mixing cell model with R² varying from 0.8684 to 0.9815. The mean residence times in CSBD varied from 10.8 to 13.9 and 10.7 to 13.3 min for glass and polyethylene beads, respectively. For both inert particles, mean residence times increased with bed height and decreased with paste feed rates. Also, terms of interaction among the factors were significant in some cases, showing a complex behavior of paste residence times. Equations obtained by response surface regression could predict mean residence times on glass and polyethylene beads with deviations lower than ±10%.     

Paste Residence Time in a Spouted Bed Dryer. II: Effect of Spout Operational Conditions

Residence time distributions for an aqueous solution of 10% sodium chloride in a spouted bed dryer of inert particles were determined using the stimulus-response technique. Glass and polyethylene beads with diameters 2.6 and 3.4 mm were used as inert bodies in a cylindrical column of 14.0 cm diameter and 60° conical base. The effects of inert bodies load, air, and paste flow rates on the mean residence times and RTD were determined following 2³ factorial designs. The RTD could be correlated to the perfect mixing cell model with R² varying from 0.8684 to 0.9815. The mean residence times in CSBD varied from 10.8 to 13.9 and 10.7 to 13.3 min for glass and polyethylene beads, respectively. For both inert particles, mean residence times increased with bed height and decreased with paste feed rates. Also, terms of interaction among the factors were significant in some cases, showing a complex behavior of paste residence times. Equations obtained by response surface regression could predict mean residence times on glass and polyethylene beads with deviations lower than ±10%.     

一种旋转锥体床的颗粒混合与输运规律

采用带竖立环壁的旋转锥体床,并在环壁上设置溢流口,在锥体内设置固定搅拌器.研究颗粒在这种新型的旋转锥体内的混合和输运规律,探讨锥体旋转速率、颗粒给料速率、溢流口面积等参数对锥体内的颗粒混合、动态存料量以及停留时间的影响.结果表明,通过增设竖立环壁将大大延长颗粒在锥体的停留时间,而搅拌器的设置对于保证颗粒在锥体内的充分混合起着关键作用.在设置搅拌器的情况下,锥体内的动态存料量与给料速率成正比,而与锥体旋转速率成反比;停留时间与锥体旋转速率和给料速率成反比.增加溢流口面积,将缩短颗粒停留时间和降低锥体内的存料量.研究结果对于设计耦合旋转锥体床的煤热解气化炉具有一定的参考价值.     

Modeling and simulation of an industrial slurry phase ethylene polymerization reactor: effect of reactor operating variables

A hierarchical and computationally efficient mathematical model was developed to explain the polymerization of high-density polyethylene (HDPE) in an isothermal, industrial, continuous stirred tank slurry reactor (CSTR). A modified polymeric multi-grain model (PMGM) was used. Steady-state macroscopic mass balance equations were derived for all species (namely, monomer, solvent, catalyst and polymer) to obtain the final particle size and the required monomer and solvent input rates for a given catalyst input and the reactor residence time. The interphase mass transfer coefficients were calculated for the industrial CSTR using the operating data on the reactor. The present model was tuned with some data on an isothermal industrial reactor and the simulation results were compared with data on another set of industrial reactor. The comparison revealed that the present tuned model is capable of predicting the productivity and the polymer yield at various catalyst feed rates and the mean residence times. The effects of variation of two operating variables (catalyst feed rate and mean residence time) on the productivity, the polymer yield, the polydispersity index (PDI) and the operational safety were analyzed. The present study indicated that an optimal value of the reactor residence time (for maximum productivity per catalyst particle) exists at any catalyst feed rate.

     

Prediction of axial velocity profiles and solids hold-up in a rotary kiln

Axial bed depth profiles were experimentally measured in a rotary kiln containing ilmenite particles under steady state and transient conditions. The variables include feed rate of solids, inclination and rotational speed of the kiln. and dam height. The variation of the axial velocity with kiln axis was estimated. The semi-experimental model proposed by Perron and Bui (1990) was modified to include the effect of the variables of the present study. The mean residence time of solids was estimated from the fractional hold-up and expressed in terms of the process variables. The transients induced by a step change in any of the operating conditions were measured as variation of discharge rate of solids with time.     

Paste Residence Time in a Spouted Bed Dryer. IV: Effect of the Inert Particle Size Distribution

The residence time distribution and mean residence time of a 10% sodium bicarbonate solution that is dried in a conventional spouted bed with inert bodies were measured with the stimulus-response method. Methylene blue was used as a chemical tracer, and the effects of the paste feed mode, size distribution of the inert bodies, and mean particle size on the residence times and dried powder properties were investigated. The results showed that the residence time distributions could be best reproduced with the perfect mixing cell model or N = 1 for the continuous stirred tank reactor in a series model. The mean residence times ranged from 6.04 to 12.90 min and were significantly affected by the factors studied. Analysis of variance on the experimental data showed that mean residence times were affected by the mean diameter of the inert bodies at a significance level of 1% and by the size distribution at a level of 5%. Moreover, altering the paste feed from dripping to pneumatic atomization affected mean residence time at a 5% significance level. The dried powder characteristics proved to be adequate for further industrial manipulation, as demonstrated by the low moisture content, narrow range of particle size, and good flow properties. The results of this research are significant in the study of the drying of heat-sensitive materials because it shows that by simultaneously changing the size distribution and average size of the inert bodies, the mean residence times of a paste can be reduced by half, thus decreasing losses due to degradation.     

Cyclic variation of the liquid flow residence time in periodically operated trickle-bed reactors

The cyclic variation of the mean residence time of the liquid phase is investigated in a trickle-bed reactor operated with a liquid feed rate modulated in a periodic square wave pattern. Experiments made using a salt tracer method are compared to a residence time model, based on the concept of continuity shock waves. The model predicts accurately the mean residence times and their cyclic variation in case of a non-zero base liquid flow rate. A particular application of the model is the adjustment of the feed cycle parameters in order to obtain a constant residence time of the liquid, no matter the moment at which it enters the bed. This particular cycle duration depends, among others, on the feed rates, but also on the bed length.     

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.     

An impinging–Streams reactor with two pairs of tangential air feeds

The original two–impinging steams devices have proved useful for processes in gas–solid Systems. A modified form of the original two–impinging–streams reactor, with two additional air streams, was explored. All four air streams are fed tangentially to the reactor. The Performance characteristics included the determination of the pressure drop on the reactor, limits of the gas and solid particle mass flow rate, the mean residence time of the particles, and the drying heat transfer, as a function of air flow rates of the secondary and major air streams. The behaviour of the particles and their residence time distribution was investigated by applying a stochastic Markov chain model. It was found that the secondary air stream increases the pressure drop on the reactor and the mean residence time of the particles along with their recycling in the reactor. On the other hand, the secondary air stream decreases the critical mass flow rate of the particles, delays their exit from the reactor and reduces the heat transfer coefficient in drying wet particles.     

Measurement of solid particle residence time in a cyclone reactor: A comparison of four methods

This paper describes four simple methods for measuring short residence times (down to 0.1 s) of solid particles in a cyclone reactor: detection of a single particle by use of phototransistors; analysis of the impact of a pulse of particles on piezocrystal probes; study of the profile of the vertical component of the particle velocities by use of a camera; measurement of the space time of the particles by a hold-up method. These four approaches lead to similar results for two kinds of solids (wood sawdust and sand) in a 12.5 × 10⁻² m diameter cyclone reactor operating with carrier gas residence times ranging from 0.5 to 5 s. A simple relationship is proposed for calculating the mean residence time of the particles (which increases with the gas flow rate) as a linear function of their theoretical free fall time through the cyclone and of the gas Reynolds number at the reactor inlet.     

Study of Tire Particle Mixing in a Moving and Stirred Bed Vacuum Pyrolysis Reactor

The paper studies the motion of scrap tire shreds in a moving and stirred bed vacuum pyrolysis reactor. The reactor configuration is a novel concept. The pattern and the residence time distribution (RTD) of the particle motion in the reactor were investigated using tracers, for different feed rates and blade speeds. It was shown that the particle motion in the reactor is plug flow nature with intermediate dispersion (σ² = 0.02—0.055). The mean residence time is in the range of 7—23 min, depending on the speed of the blades and the feed rate. The ratio of mean particle speed and the speed of blades v_m/v_b varied between 0.03 and 0.07.     

Study on the wire electrochemical groove turning process

In this study a copper wire is proposed as a tool electrode in electrochemical groove turning process (WECGT). The working parameters, namely, radial feed rate, wire diameter, and rotational speed are investigated to study the performance criteria via MRR, groove width, and roundness error. An experimental study is presented through performing series of designed experiments. Key features of a WECGT setup that was designed and developed incorporating several unique features are also highlighted. The experimental results are statistically analyzed and mathematically modeled through response surface methodology (RSM). The mathematical model adequacies are checked using analysis of variance (ANOVA). Furthermore, optimal combination of working parameters has been evaluated to maximize MRR and minimize roundness error. The results reveal that using wire as an electrode in electrochemical turning instead of using a profiled tool proved its powerfulness to produce circular grooves. The results also demonstrate that the groove width has greatly increased by increasing the wire diameter, while it is decreased by increasing both the radial feed rate and rotational speed. Lower roundness errors are obtained by increasing both radial feed rate and wire diameter. The optimum combination of parameters setting is: radial feed rate of 0.08 mm min⁻1, wire diameter of 2.3 mm, and rotational speed of 578 rpm.     

基于能量等效的双转子连续混炼机混炼段相似放大研究探讨

根据双转子连续混炼机自身特性和等效平均停留时间、等价转子顶部剪切速率的原则,以能量等效为衡量混合效果的准则,提出双转子连续混炼机混炼段相似放大设计的流程及其理论模型。在该模型确定的转子转速和喂料速率下,利用Polyflow软件模拟了机筒内径分别为30 mm和100 mm的双转子连续混炼机混炼段和卸料段内的流场特征,以能量等效为指导准则,通过对流场特征和混合效果进行分析,对所提出的相似放大设计理论模型进行了验证。     

Dynamic simulation of propylene polymerization in continuous flow stirred tank reactors

The dynamic operation of an ideal continuous-flow stirred tank slurry reactor for propylene polymerization has been studied. A simple model is developed, which could be used for optimal computer control using advanced strategies. Step increases in input feed rates of propylene, solvent, and catalyst are used as the stimuli or forcing functions. It is assumed that the volume of the slurry in the reactor is maintained constant during the period. Responses of three output variables are studied, namely, monomer concentration in the liquid, volume-fraction of solids in the exiting slurry, and average mass fraction of catalyst in the exiting macroparticles. It is found that the transients last for about five times the mean residence time of the reactor. Competing effects of changes in the diffusional resistance, number density of catalyst particles, and washout and dilution effects lead to interesting dynamic results.     

Mixing performance comparison of milliscale continuous high‐shear mixers

Mixing performance of two continuous flow millilitre‐scale reactors (volumes 9.5 mL and 2.5 mL) equipped with rotor‐stator mixers was studied. Cumulative residence time distributions (RTD) were determined experimentally using a step response method. Distributions were measured for both reactors by varying impeller speed and feed flow rate. The mixing effect was determined by measured RTDs. Computational fluid dynamics (CFD) were used to verify that the residence time distribution in the measurement outlet agreed with the outlet flow. The mixing power of both reactors was determined using a calorimetric method. The reactor inlet flow rate was found to affect mixing performance at 1–13 s residence times but the effect of impeller speed could not be noted. Both milliscale reactors are close to an ideal continuous stirred‐tank reactor (CSTR) at the studied impeller speed and flow rate ranges. The specific interfacial area was found to depend on the reactor inlet flow rate at constant impeller speed for the case of copper solvent extraction.

     

Dynamic Characteristics of Solids Transportation in Rotary Dryers

An original method was proposed for the determination of the mean residence time in a continuous dryer, based on the step-change in the solids feed rate. The method has been validated through experiments performed in a pilot-scale rotary dryer. The effect of the solids flow rate, gas flow rate, dryer rotation speed, and dryer slope was quantified. Several design correlations to predict the residence time in rotary dryers were critically evaluated, and a new, more accurate correlation was derived.