Residence time distribution of solid particles in a continuous, high-aspect-ratio multiple-impeller stirred vessel

In this paper experimental information on the retention time distribution (RTD) of solid particles in a high-aspect-ratio vessel, stirred by three equally spaced Rushton turbines, is presented. The relevant data were obtained by a special technique named twin system approach (TSA) that greatly simplifies the handling of particle-laden streams and is therefore particularly suited for investigating particle RTD in flow systems. The technique fundamentals are first summarized, together with the data analysis procedure. This lastly requires a numerical deconvolution operation that is easily performed with the help of Z-transforms. Two different approaches for excluding the spurious contributions of the external piping required for the experimentation are tested and discussed.Particle tracing was performed by an effective particle-coating/optical-detection technique that allows particles recovery and reuse after each experimental run.The RTD data obtained indicate that a cascade of ideally mixed tanks with backflow results into very good agreement with experiment, with practically any number of tanks in series but one, provided that the backflow rate parameter is chosen accordingly. In all cases, the recirculation is large enough for the resulting flow model to be quite close to a single perfectly stirred vessel.     

Residence time distributions in a co‐kneader: A chemical engineering approach

In this article, we have studied the residence time distributions (RTD) in a modular co‐kneader. Several papers have already addressed the co‐kneader modeling and operating mode but there is still a lack of experimental data on RTD. To investigate the RTD, we have used a colored tracer dispersed in polypropylene (PP) that was injected in the flow during the compounding of neat PP. The effect of operating parameters such as temperature, feed rate, and screw configuration was investigated, focusing on the influence of mixing and conveying elements in a zone where the polymer is molten. As can be expected, results on various screw configurations show that increasing the number of kneading elements makes the RTD longer. More interestingly, for a defined set of elements, their position does not change the experimental RTD. A chemical engineering approach was used to model the RTD, with an equation derived from a cascade of continuous stirred tank reactors. The model allows to retrieve an elementary RTD for each section of a defined type of elements and to propose a law for their combination in good agreement with experiments. POLYM. ENG. SCI., 55:1237–1245, 2015. © 2015 Society of Plastics Engineers     

Gas Flow Behavior in a Two‐Phase Reactor Stirred with Triple Turbines

Gas behavior was studied in a gas‐liquid reactor stirred with multiple turbines. Triple PBTs pumping either down or up and BT‐6's were used. The behavior of coalescing (water) and non‐coalescing (sodium sulfate solution) systems was investigated. The gas phase behavior was characterized by means of the RTD and modeled with the axial dispersion model. This model was confirmed to interpret the experimental data well for water and satisfactorily for the coalescence‐inhibiting solutions. The influence of the operating conditions, turbine type and system coalescing behavior on the model parameters is discussed. Comparison is also made with similar data regarding Rushton turbines and high‐solidity ratio hydrofoils, as well as gas holdup.     

假塑性流体在双螺带桨搅拌釜内停留时间分布

采用电导率法研究了羧甲基纤维素水溶液假塑性流体在双螺带搅拌釜内的停留时间分布(RTD)情况,考察了物料黏度、流量、搅拌转速和转向对停留时间分布的影响.发现假塑性流体在釜内的停留时间分布类似于全混釜,但有一定的拖尾现象.物料黏度对平均停留时间和当量全混釜数影响不大;随着流量增大,平均停留时间减小,而当量全混釜数基本不变;...     

Modeling of a cokneader for the manufacturing of composite materials having absorbent properties at ultra‐high‐frequency waves. Part 1: Modeling of flow from residence time distribution investigations

The purpose of this study is to gain better understanding of flow patterns and mixing conditions in a particular single‐screw extruder: the Buss Cokneader. To this end, the residence time distribution (RTD) of the polymer was investigated experimentally for different combinations of the operating variables (i.e. feed rate, screw rotation speed). The measurement of RTD used a standard stimulus‐response technique. Two kinds of tracer were used: free anthracene and anthracene grafted on the polymer. It was shown that only the second could characterize the actual flow of the polymer in the extruder. It does not perturb the flow and has the same rheological behavior as the studied fluid. Thanks to the RTD data, a model of the extruder based on the combination of ideal reactors, such as continuous stirred tank reactors or plug flow reactors, was finally set up. The establishment of relationships between model parameters and extrusion conditions allowed the prediction of RTD with good agreement.     

Residence time distribution of a pharmaceutical grade polymer melt in a single screw extrusion process

The residence time distribution (RTD) of a flowing polymer through a single screw extruder was studied. This extruder allows injecting supercritical carbon dioxide (scCO₂) used as physical foaming agent. The tested material is Eudragit E100, a pharmaceutical polymer. RTD was measured at various operating conditions and a model describing RTD has been developed. High screw speed or high temperature implies short residence time, but these parameters do not have the same effect on polymer flow. In the flow rate range studied, scCO₂ has no significant influence. A mathematical model consisting of a plug flow reactor in series with a continuous stirred tank reactor (CSTR) cross-flowing with a dead volume fitted well the experimental data.     

Residence Time Distribution Models Derived from Non‐Ideal Laminar Velocity Profiles in Tubes

The theoretical E‐curve for the laminar flow of non‐Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks‐in‐series models of residence time distribution (RTD). In this work, four RTD models derived from non‐ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.     

撞击流气化炉内颗粒停留时间分布的随机模拟

根据多喷嘴对置式气化炉流场测试,将气化炉划分为若干区域,运用时间离散、状态离散的马尔可夫链随机模型,模拟了气化炉内颗粒相的停留时间分布(RTD)。当颗粒在撞击区和射流区间的回流比为0.5,向下撞击流股区和管流区为平推流模型,其他区域按全混流模型处理时,模拟值与实验值吻合较好。随着进料流量的增大,平均停留时间减小,量纲1方差减小;随着回流比的增加,平均停留时间增大;气固两相平均停留时间接近,但RTD存在一定差异。     

Application of residence time distribution technique to the study of the hydrodynamic behaviour of a full‐scale wastewater treatment plant plug‐flow bioreactor

The hydrodynamic behaviour of a full‐scale wastewater treatment plant (WWTP) bioreactor treating municipal wastewater, situated in Granollers (Barcelona, Spain), has been studied by means of a residence time distribution (RTD) technique using lithium (chloride) as tracer. The bioreactor studied is designed to work as a plug‐flow reactor and it is divided into two independent lanes (1 and 2), each one composed of four compartments in series resulting in a total volume of 3970 m³ per lane. During the RTD experiments, working flow was 1000 m³ h^?1 per lane, which implied an ideal mean residence time of 3.97 h. When a lithium chloride tracer was injected in the bioreactor, both lanes showed a similar highly non‐ideal hydrodynamic behaviour, which had an important effect on the reactor's performance. This global RTD was complemented by means of local RTDs in different locations of the bioreactor in order to determine qualitatively the reactor's mixing regime. Different non‐ideal models (namely axial dispersion, tanks‐in‐series and some simple compartment models) have been tested for the modelling of the experimental RTD. The best model fitting RTD data for Lanes 1 and 2 was a configuration consisting of four mixed tanks in series. The RTD study proposed in this work will permit improvement of the reactor's mixing performance, which is of special interest in future projects including simultaneous removal of carbon, nitrogen and phosphorus. Copyright © 2005 Society of Chemical Industry     

连续进出料鼓泡流化床颗粒停留时间分布

针对双流化床气化或双床热解气化工艺中鼓泡床反应器的设计,采用脉冲法研究了Geldart B类固体颗粒在连续颗粒进料和出料的矩形流化床内的停留时间分布(RTD),考察了气速、床料高度、粒径、物料流率等操作参数对RTD的影响. 结果表明,物料流率、床料高度、粒径是影响颗粒RTD的主要因素,而气速则是次要因素. 随物料流率和粒径增加,鼓泡床内颗粒流动向平推流靠近;随床料高度增加,物料在床内的混合更加充分,颗粒流动向全混流靠近. 根据实验结果,推荐采用比理想平推流时间低9%~18%计算平均颗粒停留时间.     

Numerical simulation and experimental validation of mixing performance of kneading discs in a twin screw extruder

This work aims at simulation by particle tracking the local residence time distributions (RTDs) of a co‐rotating twin‐screw extruder using computational fluid dynamics. Simulated results follow reasonably well the trend of experimental results obtained by an in‐line measuring instrument for different screw configurations and feed rates. To analyze the distributive mixing performance and overall efficiency of different types of kneading discs (KDs), mixing parameters such as area stretch ratio, instantaneous efficiency, and time‐average efficiency are calculated. Among KDs with stagger angles 45°, 60°, and 90°, the 90/10/64 with disc gaps is most efficient in terms of distributive mixing. The effects of the disc width and disc gap on the local RTD and distributive mixing are also discussed. This provides a numerical tool for assessing point‐by‐point information on the local RTD, flow, and mixing along the screw extruder. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Experimental study and modeling of residence time distribution in impinging stream reactor with GDB model

Residence time distribution (RTD) in an impinging streams reactor with two or four nozzles was investigated with KCl solution as a tracer. The results showed that the flow pattern in the reactor was close to that in a continuous stirred tank reactor (CSTR). Macromixing process in the reactor was improved obviously when the opposite nozzles were added. Based on the analysis of flow region in the reactor, gamma distribution model with bypass (GDB) was applied for study on the RTD of the reactor. It was found that RTD in the impinging streams reactor could be finely described by the model. Also the effects of experimental conditions on parameters of model were analyzed according to the correlated values of the model parameters.     

Stereo‐PIV experiments and large eddy simulations of flow fields in stirred tanks with Rushton and curved‐Blade turbines

The flow characteristics in pilot‐scale stirred tanks with Rushton and curved‐blade turbines were investigated by using stereoscopic particle image velocimetry (SPIV) experiments and large eddy simulation (LES) methods. The velocity and turbulent kinetic energy (TKE) in the impeller discharge regions were carefully resolved with a high resolution SPIV system, and the detailed phase‐resolved velocity and TKE profiles were used to validate the LES results. The effects of Reynolds number and blade shape on the flow characteristics were discussed. The LES results of velocity, TKE, and the evolution of trailing vortices were compared with the SPIV experimental data, and good agreement was obtained at various phase angles. The effects of subgrid scale model and hybrid grid with different mesh resolutions on the LES results were investigated. LES is a computationally affordable method for the accurate predictions of the complex flow fields in pilot‐scale stirred tanks is presented. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3986–4003, 2013     

Markov chain model of residence time distribution in a new type entrained-flow gasifier

A continuous-time Markov chain has been used to establish the residence time distribution (RTD) model in a new type entrained-flow gasifier, which is called entrained-flow gasifier with opposed multi-burner. According to the measurement results of the flow fields in the gasifier, the state transfer diagram of Markov chain formed in the case of the flow fields are simplified. The results show that this method is feasible in modeling the flow system which consists of ideal mixing cells and plug flow regions. The flow pattern of the gasifier is closed to continuous stirred tank reactor (CSTR). The simulation results are in good agreement with the experimental data. The established model has been applied to forecast the RTD in the industrial gasifier.     

Laboratory investigation of inversion of heavy oil emulsions

Laboratory investigations have been undertaken to assess the suitability of heavy oil‐in water emulsions for pipeline transportation. The emulsions contained 65% oil in water and were prepared using polyethoxy nonylphenol surfactants. Two methods were employed for simulating the shear process which accompanies pipeline flow: a bench scale stirred vessel and a rotated pipe toroid. The progress of the emulsions towards inversion, at which point the oil becomes the continuous phase, was followed by measuring the surfactant concentration in the aqueous phase using liquid chromatography. At inversion the surfactant concentration falls below the threshold level required to sustain an oil‐in‐water emulsion. The experiments showed that the lifetime of the emulsion depends upon the initial surfactant dosage, the solids content of the oil, the intensity of shear and the nature of the shear process. Laminar flow was found to be less desirable than turbulent flow.     

Semi‐Empirical Equations for the Residence Time Distributions in Disperse Systems – Part 1: Continuous Phase

Residence time distributions (RTD) are often described on the basis of the dispersion or the tanks in series models, whereby the fitting is not always good. In addition, the underlying ideas of these models only roughly characterize the real existing processes. Two semi‐empirical equations are presented based on characteristic parameters (mean, minimum, maximum residence time) and on an empirical exponent to permit better fitting. The determination of the parameters and their influence on the RTD are discussed. The usefulness of the models is shown in this first part for single‐phase systems and for the continuous phase of multiphase systems using data from literature for laminar and turbulent flows in different apparatuses. A comparison with the results of other models is also done.     

Stochastic Modeling of the Particle Residence Time Distribution in an Opposed Multi‐Burner Gasifier

The gasification technology of impinging streams has been extensively applied to chemical production and power generation. Particle residence time distribution (RTD) is an important parameter required for modeling, designing and optimization of an impinging stream gasifier. A stochastic mathematical model based on the Markov chains model is developed for the opposed multi‐burner gasifier (OMBG), which closely describes the behavior of the flow pattern and particle RTD in the gasification system. The model simulates the motion of single particle moving in the gasifier using the Markov chains. The predicted results give a reasonable fit to the experimental data. This shows that the flow process of particles in the gasifier has recirculation eddies, which have a downward flow direction near the downflow core and an upward flow direction near the wall, but no short‐circuit. Finally, the effect of particle flux rate on the RTD is predicted, and the contrast between gas and particles RTDs at a laboratory scale and in an industrial gasifier are presented.     

Characterization of the Residence Time Distribution in Spray Dryers

In this work it is presented a study on the residence time distribution (RTD) of particles in a co-current pilot-plant spray dryer operated with a rotary atomization system. A nuclear technique is applied to investigate the RTD responses of spray dryers. The methodology is based on the injection of a radioisotope tracer in the feed stream followed by the monitoring of its concentration at the outlet stream. The experiments were performed during the drying of aqueous suspensions of gadolinium oxide. The RTD responses obtained experimentally presented good reproducibility, indicating that the technique applied is well suited to investigating fluid-dynamics of spray dryers. In addition to the experimental investigation, a mathematical model was used to describe the RTD experimental curves.     

Modeling of the Residence Time Distribution and Application of the Continuous Two Impinging Streams Reactor in Liquid‐Liquid Reactions

The two‐phase monosulfonation of toluene, as an example of liquid‐liquid reactions, has been conducted in a continuous two impinging stream reactor (TISR). The extent of reaction under different operating conditions has been determined. A comparison has been made between the performance capability of the TISR and that of continuous stirred tank reactors (CSTR). Under identical conditions, including mean residence time, temperature, feed compositions and phase ratio, the impinging stream reactor has shown a higher efficiency. Finally, a stochastic model, based on Markov chain processes has been developed for the TISR, which describes the flow pattern and the residence time distribution (RTD) within the reaction system. The RTD model, combined with the kinetic expression, has been applied to calculate the conversion of toluene in the reactor. The predicted values for toluene conversion have been compared with those determined experimentally.     

Modeling and simulation of polypropylene particle size distribution in industrial horizontal stirred bed reactors

This work aims at developing a steady-state particle size distribution (PSD) model for predicting the size distribution of polypropylene particles in the outflow streams of propylene gas-phase horizontal stirred bed reactors (HSBR), on the one hand and investigating the effect of the catalyst residence time distribution (RTD) on the polymer PSD, on the other hand. The polymer multilayer model (PMLM) is used to describe the growth of a single particle. Knowing the PSD and RTD of a Ziegler–Natta type of catalyst and polymerization kinetics, this model allows calculating the polymer PSD of propylene polymerization in the HSBRs. The calculated polypropylene PSDs agree well with those obtained from the industrial reactors. The results reveal that both the PSD and the RTD of the catalyst affect the polymer PSD but in different manners. The effect of RTD on the PSD is less significant in the case of a nonuniform size catalyst feed. This model also allows investigating the effects of other process parameters on the polymer PSD under steady-state conditions, including intraparticle mass- and heat-transfer limitations, initial catalyst size, and polymer crystallinity. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012