Residence Time Distribution Of Particles Research Articles

Impact of random packing on residence time distribution of particles in bubbling fluidized beds: Part 1–cross-current flow reactors

In this work, the influence of employing random packings on the residence time distribution in a bubbling fluidized bed is investigated. The bubbling fluidized bed cold-flow reactor setup allows for continuous cross-current flow of particles. Expanded clay aggregate (ECA) is employed in the packed-fluidized bed experiments as the packing. The effects of different parameters such as packing type (ECA or no packing), Fluidization number (4.4, 6.6, and 8.8), and solid throughflow rates (92, 133, and 164 g/s) are investigated. The axial dispersion and tank-in-series models are used to categorize flow patterns of particles in the packed-fluidized beds and compared to beds using no packing. Results show that the vessel’s dispersion number for solids decreases in the presence of ECA packings up to fourfold compared to unpacked beds. Furthermore, tank-in-series model shows that the number of tanks for experiments utilizing packing increases by up to threefold compared to unpacked beds. The experimental results are also compared to a model known as a hybrid model. The hybrid model considers a continuous-stirred-tank-reactor in series with a plug-flow-reactor. Comparison of the model to the measured data shows a clear shift of the relative size or residence time from the stirred tank reactor towards the plug flow reactor with axial dispersion in the packed-fluidized bed compared to a bed with no packing. Also the vessel dispersion number of the plug flow reactor model with axial dispersion is significantly decreased in the case of packed-fluidized bed.

An oxidation flow reactor for simulating and accelerating secondary aerosol formation in aerosol liquid water and cloud droplets

Abstract. Liquid water in cloud droplets and aqueous aerosols serves as an important reaction medium for the formation of secondary aerosol through aqueous-phase reactions (aqSA). Large uncertainties remain in estimates of the production and chemical evolution of aqSA in the dilute solutions found in cloud droplets and the concentrated solutions found in aerosol liquid water, which is partly due to the lack of available measurement tools and techniques. A new oxidation flow reactor (OFR), the Accelerated Production and Processing of Aerosols (APPA) reactor, was developed to measure secondary aerosol formed through gas- and aqueous-phase reactions, both for laboratory gas mixtures containing one or more precursors and for ambient air. For simulating in-cloud processes, ∼ 3.3 µm diameter droplets formed on monodisperse seed particles are introduced into the top of the reactor, and the relative humidity (RH) inside it is controlled to 100 %. Similar measurements made with the RH in the reactor < 100 % provide contrasts for aerosol formation with no liquid water and with varying amounts of aerosol liquid water. The reactor was characterized through a series of experiments and used to form secondary aerosol from known concentrations of an organic precursor and from ambient air. The residence time distributions of both gases and particles are narrow relative to other OFRs and lack the tails at long residence time expected with laminar flow. Initial cloud processing experiments focused on the well-studied oxidation of dissolved SO2 by O3, with the observed growth of seed particles resulting from the added sulfuric acid agreeing well with estimates based on the relevant set of aqueous-phase reactions. The OH exposure (OHexp) for low RH, high RH, and in-cloud conditions was determined experimentally from the loss of SO2 and benzene and simulated from the KinSim chemical kinetics solver with inputs of the measured 254 nm UV intensity profile through the reactor and loss of O3 due to photolysis. The aerosol yield for toluene at high OHexp ranged from 21.4 % at low RH with dry seed particles present in the reactor to 78.1 % with cloud droplets present. Measurement of the composition of the secondary aerosol formed from ambient air using an aerosol mass spectrometer showed that the oxygen-to-carbon ratio (O : C) of the organic component increased with increasing RH (and liquid water content).

Regulation characteristics and law of residence time distribution of polydisperse particles in numbered-up multiple-chamber fluidized bed reactors

How to simultaneously regulate the residence time of polydisperse particles and completely inhibit particle backmixing remains a challenge of fluidization technology. In this study, it is shown that adding elutriation pipes into multiple-chamber fluidized beds to strengthen particle elutriation and entrainment is an effective measure. Coarse-grained CFD-DEM simulation results show that the addition of the elutriation pipe can completely inhibit the particle back-mixing between adjacent chambers, and the mean residence time (MRT) ratio of coarse and fine particles can be regulated to be larger than their diameter ratio. Furthermore, a study on the numbered-up multiple-chamber fluidized beds find that (i) the MRT ratio of coarse and fine particles can be larger than the 1.5th power of their diameter ratio with full suppression of particle back-mixing between adjacent chambers; (ii) the MRT of each size of particles is a linear function of chamber number, whereas the MRT ratio approaches an asymptotic value. The results are of guiding significance for improving the overall conversion rate of polydisperse particles.

Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

Research on particle retention in continuous horizontal fluidized bed based on CFD-DEM method

Horizontal fluidized beds are widely used in continuous production lines due to their efficient heat and mass transfer mode. Continuous production goals require stabilized reaction systems, which can be achieved by controlling particle retention. But there is a lack of an effective means of controlling particle retention. In this paper, Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) method is applied to investigate the particle retention in different air inlet angles, which is characterized by the particle back-mixing degree, spatial and residence time distribution. The results show that at low air inlet angles, the system is effective in controlling particle retention. This is achieved through stronger particle back-mixing and more concentrated residence times, which are essential for maintaining reaction system stability. These findings provide guidance for controlling particle retention and enhancing continuous fluidization equipment efficiency.

Particle circulation and coating in a Wurster fluidized bed under different geometries

The performance of particle coating is essentially determined by the morphology and uniformity of coating shells, which significantly depend on particle circulation. In this study, the geometry of a Wurster fluidized bed is changed by regulating particle circulation port size and nozzle position, and their effects on particle circulation and coating properties are investigated by combining coating experiments and CFD – Discrete Element Model (DEM). By increasing the circulation port size, the particle circulation rate first increases then decreases slightly, accordingly, the uniformity of particle circulation increases then decreases, while the shell porosity decreases. By increasing the nozzle height, the particle circulation rate decreases slightly, accordingly, the uniformity of particle circulation increases then decreases, while the shell porosity decreases. At extremes with a too small circulation port size or too high nozzle position, particle residence and cycle time distribution are broader, and an obvious nonuniformity of particle growth is observed.

3D coarse-grained DPM simulation of the MIP reaction-regeneration loop

The reactor-regenerator loop is the core facility of the maximizing iso-paraffin (MIP) process. Although the discrete particle method (DPM) simulation can provide detailed information at the particle scale, it has been unable to simulate such a complex loop system due to limitations of coarse-grained (CG) models, computing software, and hardware. In this study, a newly proposed soft-shell CG-DPM model with a CG ratio of up to 800 is used to simulate a 3.5 Mt/a industrial-scale MIP reactor-regenerator loop. The solid fraction distribution obtained is found to agree well with in-situ measurements. Hydrodynamic properties including the distribution of solid fraction, gas and solid velocity, standard derivation of solid fraction with time, temporal distribution of the flow field, and particle residence time distribution are measured in the simulation, which are meaningful to better design and operate such systems in the future.

Numerical investigation of high-temperature rapid heating of coal gas in CFB heat exchanger via thermal carrier particles

High-temperature rapid heating technology of coal gas is a crucial issue that urgently needs to be addressed for the recycling of coal gas in the iron manufacturing. Drawing upon circulating fluidized bed principles, this study proposed a high-temperature rapid heating technology of coal gas with employing thermal carrier particles. Numerical simulation studies were conducted to evaluate the heating performance of this method. A 3D grid model was established and the Discrete Particle Model (DPM) was employed to simulate the gas-solid two-phase flow and heat transfer behaviors in the riser. The results demonstrate that the gas-solid flow within the circulating fluidized bed (CFB) heat exchanger is capable of achieving rapid heat transfer. The gas was effectively heated from an inlet temperature of 300 K to 1479 K within a height of 4.2 m and within 0.68 s. The CFB heat exchanger achieves rapid heat transfer under the designed industrial operating load conditions, with an average duration of heat exchange not exceeding 1.34 s. Moreover, the axial and radial particle size distribution was investigated during the gas-solid heat transfer process in the CFB heat exchanger and analyze the relationship between particle size distribution and the velocity and temperature of particles. To evaluate the operational flexibility of the riser, the gas-solid two-phase flow patterns, temperature distribution and particle residence time distribution were examined under different operating loads.

Numerical analysis on the transport properties and residence time distribution of ribbon biomass particles in a riser reactor based on CFD-DEM approach

A bended ribbon biomass particle model was developed to explore the dynamic transport properties inside a riser reactor. Residence time distribution (RTD) of the particles was analyzed by using the Eulerian-Lagrange method. The effects of sampling height, particle density, particle size and gas-to-solid mass ratio on RTD were investigated. The coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) model was verified firstly by experimental data on pressure drop and residence time distribution density function. The simulation results demonstrated that the ribbon biomass particles display a typical annular-core spatial distribution during transportation. The RTD of particles exhibit an approximate single-peaked normal distribution. The mean residence time (MRT) can reach up to 0.7 s when the particle density is 1200 kg/m3. Particle with higher density has longer mean residence time. The flow patterns are closer to plug flow if particle length over 12 mm. The particle flow pattern is not sensitive to changes in particle density and size, while the gas-to-material mass ratio has a significant impact on it.

Residence time distribution of ultrafine aerosol particles in a tube with transient and parabolic laminar flow

This paper presents a theoretical investigation concerning the residence time distribution (RTD) of ultrafine monodisperse aerosol particles flowing in a circular tube in laminar flow regime. If a fully developed, parabolic flow (PF) velocity profile is assumed for the whole tube length, the convection-diffusion process undergone by the aerosol particles can be described by means of two parameters, the dimensionless particle diffusion coefficient D and the tube aspect ratio a (radius/length). An additional parameter, the Reynolds number Re, must be taken into consideration when the flow develops starting from a given velocity profile at the tube entrance, which we have assumed to be a uniform (plug) flow. The latter situation is referred to as transient flow (TF). The RTD has been determined using two different variations of a Monte Carlo (MC) technique to simulate the particle trajectory within the tube. The difference between the two MC methods is the assumed distribution of Brownian random displacements of the particles; in both cases the distribution had zero mean and variance 2DΔt, but the distribution was uniform in one method and normal in the other. The simulation results obtained with the two methods were almost coincident. In either PF or TF, even for relatively small values of D the aerosol RTD is quite different from that of the fluid where the particles are suspended. In particular, the dimensionless mean particle residence time, which initially decreases with D, soon attains an asymptotic value of 0.65 for D ≥ 0.3 (the mean residence time of the fluid is 1) in PF; a similar asymptotic value is attained for TF but in this case it depends on the particular combination of a and Re considered. The relative influence of axial diffusion on the RTD is insignificant unless the tube ratio a is of the order of 0.5 (tube with a length equal to its diameter).

A new oxidation flow reactor for the measurements of secondary aerosol formation: Characterisation and a case study

Oxidation flow reactors (OFRs) have been extensively used to investigate secondary aerosol formation of the ambient air or emission sources such as biomass burning or vehicular emissions, and they can provide useful information on the mechanisms of secondary aerosol formation. Here we present the design and characteristics of a newly developed OFR, named the Rapid Aerosol Ageing Device (RAAD). The RAAD was specially designed to provide time-resolved and fast-response chemical evolution of aged aerosols and can be applied to investigate how oxidative stress levels change upon ageing. The characterisation experiments included optimisation of the flow rate, residence time distributions for gas and particles, transmission efficiencies of particles, OH exposures with varying O3 concentrations and relative humidity conditions. Results show that the RAAD has near-laminar flow conditions at a total flow rate of 45 slpm with a low surface-area-to-volume ratio of 26.52 m-1. Wall losses for particles with mobility diameters greater than 40 nm are negligible, and narrow residence time distributions of gas and particles were observed. These features allow a better response to the ageing of rapid-changing emission sources, and measurements can be taken directly for instruments demanding high flow rates without diluting the samples. Additionally, the performance of the RAAD was further evaluated by measuring the secondary aerosol formation of biomass burning emissions. The organic aerosol enhancement ratios were comparable with other ageing studies, with an average value of 1.31 ± 0.05. In addition, the absorption Ångström exponent (AAE) value decreased from 1.7 ± 0.05 (primary emissions) to 1.4 ± 0.06 upon ageing. Overall, the RAAD is suitable for studying the formation mechanisms of photochemically aged aerosols from emission sources, and future work will aim to provide more details on the secondary aerosol production from ambient air.

Subject-specific factors affecting particle residence time distribution of left atrial appendage in atrial fibrillation: A computational model-based study.

Atrial fibrillation (AF) is a prevalent arrhythmia, that causes thrombus formation, ordinarily in the left atrial appendage (LAA). The conventional metric of stroke risk stratification, CHA2DS2-VASc score, does not account for LAA morphology or hemodynamics. We showed in our previous study that residence time distribution (RTD) of blood-borne particles in the LAA and its associated calculated variables (i.e., mean residence time, tm , and asymptotic concentration, C ∞) have the potential to improve CHA2DS2-VASc score. The purpose of this research was to investigate the effects of the following potential confounding factors on LAA tm and C ∞: (1) pulmonary vein flow waveform pulsatility, (2) non-Newtonian blood rheology and hematocrit level, and (3) length of the simulation. Subject-Specific data including left atrial (LA) and LAA cardiac computed tomography, cardiac output (CO), heart rate, and hematocrit level were gathered from 25 AF subjects. We calculated LAA tm and C ∞ based on series of computational fluid dynamics (CFD) analyses. Both LAA tm and C ∞ are significantly affected by the CO, but not by temporal pattern of the inlet flow. Both LAA tm and C ∞ increase with increasing hematocrit level and both calculated indices are higher for non-Newtonian blood rheology for a given hematocrit level. Further, at least 20,000 s of CFD simulation is needed to calculate LAA tm and C ∞ values reliably. Subject-specific LA and LAA geometries, CO, and hematocrit level are essential to quantify the subject-specific proclivity of blood cell tarrying inside LAA in terms of the RTD function.

Detailed analysis of the particle residence time distribution in a pressurized drop‐tube reactor

AbstractSolid fuel conversion in a pressurized drop‐tube reactor is studied in detail using a three‐dimensional computational fluid dynamics (CFD) model. The main focus is on analyzing individual particle trajectories and residence times, as these data are crucial for the precise experimental estimation of heterogeneous reaction kinetics. The numerical results were substantiated by radioactive tracer measurements carried out in different operating conditions. The numerical results reveal a complex gas flow that is affected by buoyancy due to a non‐homogeneous temperature distribution, which has a strong affect on the trajectories of particular particle size fractions. In this case, empirical residence time correlations for particles, as commonly used for the evaluation of heterogeneous kinetic measurements, lose their validity since the assumption of a plug flow is no longer valid. It can be shown that if CFD‐assisted data evaluation is used, a significant improvement in the measured heterogeneous reaction kinetics is feasible.

Using Particle Residence Time Distributions as an Experimental Approach for Evaluating the Performance of Different Designs for a Pilot-Scale Spray Dryer

The performances of four different designs for a pilot-scale spray dryer have been evaluated and compared based on experimentally measured particle residence time distributions (RTD), recovery rates and physical properties of spray-dried fresh skim milk. The RTDs have been measured using a dye pulse injection method, and the measurements have been fitted to models using continuous stirred-tank reactors in series (CSTR-TIS) for quantitative performance evaluation and comparison. Conical drying chambers and a box connection design have been used in the latest dryer design to reduce the amount of wall deposition and provide a smoother gas flow pattern. The particle-to-gas mean residence time ratio for the latest design is significantly closer to unity (1.6 s/s to 1.0 s/s) compared with earlier designs (2.6 s/s to 1.5 s/s). The latest design has a wider spread of RTD (n = 5–8) compared with earlier designs (n = 13–18), which may be linked to the recirculation zone in the box connection. Although the latest design has a wider spread of RTD, the conical design has shown promising results compared with a cylindrical drying chamber in terms of overall wall deposition behaviours.

Interplay of Particle Suspension and Residence Time Distribution in a Taylor–Couette Crystallizer

In small-scale continuous crystallization, particle suspension and residence time distribution are critical factors determining operability and product quality. Here, the Taylor–Couette crystallizer stands out for its high flexibility. Its characteristic vortex structure intensifies local mixing, thus improving the suspension and simultaneously narrowing the residence time distribution, whereby these effects can be adjusted by operating and design parameters. However, the operating window is limited by the prerequisite of sufficient particle suspension. In this study, we investigated the suspension behavior and its impact on the attainable liquid phase residence time distribution and the flow regimes observed. For this purpose, the just-suspended rotation rate was visually determined for different design and operating parameters. A correlation was regressed from experimental data, showing that this rotation rate was mainly affected by the radius ratio of the rotor and stator. In addition, the liquid phase residence time distribution was measured by tracer experiments in regions of sufficient suspension, validating a correlation from the literature. With a combination of both correlations, the design parameters of the apparatus can thus be optimized according to the goal of, for example, a narrow residence time distribution in the suspended state.

Coarse-grained CFD-DEM simulation of coal and biomass co-gasification process in a fluidized bed reactor: Effects of particle size distribution and operating pressure

The co-gasification of coal and biomass through fluidized bed gasifier is a promising technology for the improvement of the utilization efficiency of fossil fuels and the development of renewable energy. In this work, a coarse-grained computational fluid dynamics-discrete element method (CFD-DEM) simulation is performed to investigate the co-gasification process in a bubbling fluidized bed gasifier. The effects of particle size distribution and operating pressure on the hydrodynamics, heat transfer, and co-gasification performance are analyzed. The results show that the increase of sand particle size distribution (PSD) width slightly affects the particle concentration distribution, particle residence time distribution, and co-gasification performance. The heat transfer rate of convection is an order of magnitude higher than those of conduction and radiation. At higher PSD width, the formation of the vertical solid temperature gradient at the bed bottom is attributed to the deteriorated solid mixing. As the operating pressure increases, the bed temperature decreases apparently. In addition, the variation of the convective heat transfer rate dominates the heat transfer efficiency as the operating pressure changes. The application of elevated operating pressure benefits to the thermal-chemical conversion of blend fuel since the char conversion reaction is accelerated.

An Interval-Simplex Approach to Determine Technological Parameters from Experimental Data

Statistical equations are widely used to describe the laws of various chemical technological processes. The values of constants and parameters included in these equations are determined by various methods. Methods that can determine the values of equation parameters using a limited amount of experimental data are of particular practical interest. In this manuscript, we propose a method to obtain simplex-interval equations. The proposed approach can be effectively used to control the values of technological process parameters. In this paper, we consider examples of chemical kinetics equation transformations and heterogeneous processes of solid particle dissolution. In addition, we describes mathematical model transformations, including equations for functions of the residence time distribution (RTD) of apparatus particles, the distribution of particles by size, etc. Finally, we apply the proposed approach to an example involving modeling of the calcination of coke in a tubular rotary kiln.

Elucidation of Compositional Inhomogeneities in LiNixCoyMnzO2 by Single Particle Laser Ablation-Inductive Coupled Plasma-Mass Spectrometry

Over the many years of cathode active material research for lithium-ion batteries, LiNixCoyMnzO2 (NCM, x+y+z = 1) have emerged as one of the most promising chemistries for mass application.[1] The exact NCM elemental composition is directly linked to the material properties which in turn influence energy density, durability, safety and cost of the final products.[2] The individual contributions of Ni, Mn and Co have been heavy investigated in both industry and academia to find the best trade-offs between all properties, nowadays settling for materials with Ni contents > 80 %.[3]The composition of NCM materials is determined in the precipitation step of the mixed transition metal hydroxide precursors.[4] At laboratory scale, precursor precipitation is typically operated in batch mode. However, the precipitation in continuous stirred tank (CSTR) reactors is industrially favourable due to the higher space-time-yield, thus reducing the overall production cost. In comparison to batch-type precursors that exhibit a homogeneous µm-sized spherical particle morphology, CSTR-type precursors can be distinguished by their broad particle size distribution due to the intrinsic residence time distribution of particles in the reactor setup. Although rarely discussed, this phenomenon is accompanied by a particle-size dependent elemental composition of the precursor particles, consequently impacting the battery performance.Besides inductive coupled plasma-optical emission spectroscopy (ICP-OES) or mass spectrometry (ICP-MS) that both determine the bulk elemental composition of NCMs and their precursors, scanning electron microscopy (SEM) or transmission electron microscopy (TEM) energy dispersive X-ray (EDX) analysis can access local elemental inhomogeneities. However, both methods are tedious in both acquisition and data evaluation.In this work, an alternative method to determine the elemental composition of individual µm sized particles is presented using a laser ablation (LA) system coupled to an ICP-MS. By the example of a Ni0.91Co0.045Mn0.045(OH)2 CSTR precursor, particle size dependent elemental inhomogeneities are demonstrated. An enrichment of Ni in larger particles with a concomitant enrichment of Co and Mn in smaller particles is identified, which persists after thermal lithiation of the precursors. The results of the LA-ICP-MS analysis are cross-validated with both SEM-EDX and TEM-EDX. Furthermore, the impact of the process conditions during precipitation on the elemental inhomogeneity are elaborated by the comparison of a series of Ni0.83Co0.12Mn0.05(OH)2 precursors precipitated at varying pH. Finally, future applications of the method are proposed. G. E. Blomgren, Journal of The Electrochemical Society, 164, A5019 (2017).H.-J. Noh, S. Youn, C. S. Yoon and Y.-K. Sun, Journal of Power Sources, 233, 121 (2013).W. Li, E. M. Erickson and A. Manthiram, Nature Energy, 5, 26 (2020).H. Dong and G. M. Koenig, CrystEngComm, 22, 1514 (2020).

Modelling of continuous drying of heat-sensitive pharmaceutical granules in a horizontal fluidised bed dryer combined with a screw conveyor at steady state

• A novel FBD has been investigated for continuous drying of pharmaceutical granules. • A relatively simple and practical model has been developed to predict the continuous dryer operation. • This model contributes to facilitating process scaling up and gaining insight on process optimization strategies. • Usefulness of the work relies on the need of process intensification through continuous manufacturing in pharmaceutical industry. Continuous manufacturing improves productivity in terms of efficiency, flexibity and quality. However, the pharmaceutical industry still heavily relies on batch operations; extensive R&D work is required to convert the current processes into continuous ones. This work presents a phenomenologigcal modelling approach for continuous drying of pharmaceutical granules in a novel fluidised bed dryer (FBD) combined with a screw conveyor. A hybrid model methodology has been adopted to describe the drying kinetics of the target granules: (1) a phenomenological model for the constant-drying rate period and (2) an empirical one for the falling rate period. The model was first validated by batch drying results and then was extended to the corresponding continuous drying condition. The particle residence time distributions (RTDs) have been determined by the pulse-tracer injection method. Then, a dispersion model has been developed based on the RTD measurements and the drying kinetics that allows predicting the continuous drying results at a steady state. The solids flow has been considered as a plug flow moving from the inlet to outlet with moderate axial dispersion, and the back-mixing term has been expressed through an experimental dispersion coefficient. The influences of several parameters are studied towards process optimisation and scale-up. The increase of air temperature and velocity were efficient on reducing the final moisture content. The increase of the feeding rate enhanced the energy efficiency. And the increase of the internal rotation rate enhanced the process stability and reduced the overheating effect.

Residence Time Distribution of Non-Spherical Particles in a Continuous Rotary Drum

The motion of non-spherical particles with sharp edges, as they are commonly involved in practice, was characterized by residence time distribution (RTD) measurement in a continuous drum. Particles with two sizes, 6 and 10 mm, and two densities, 750 and 2085 kg/m3, were used in the experiments. The effects of rotation speed (3–11 rpm), incline angle (2–4°), feed rate, and mixture composition were investigated and compared to the results of other researchers on particles without sharp edges. We also fitted the RTD with an axial dispersion model to obtain a better insight into the flow behavior. MRT of non-spherical particles with sharp edges depends on ω−α similar to other shapes, while the value of alpha is higher for particles with sharp edges (0.9 < α < 1.24), especially at high incline angles. The MRT depends on incline angle, β−b, where b varies between 0.81 (at low ω) and 1.34 (at high ω), while it is close to 1 for other shapes. Feed rate has a slight effect on the MRT of particles with sharp edges and the effect of particle size diminishes when rotation speed increases. The MRT linearly increases with volume fraction of light particles in a mixture of light and heavy particles (from pure heavy to pure light particles).