Solids Dispersion Coefficient Research Articles

Solids dispersion in high density circulating fluidized beds

Transient local solid tracer concentration distributions were measured by a novel, simple and accurate measurement system with fast response to obtain axial solids dispersion in the riser of a circulating fluidized bed operated at solids fluxes up to 450 kg/m2s and gas velocities up to 8 m/s. Phosphorescent-coated FCC particles were used as the tracer which were activated by high intensity UV light and injected into the return leg of high-density circulating fluidized bed unit. A radially non-uniform axial dispersion model was utilized to determine axial solids dispersion coefficients, and the results were interpreted with the help of hydrodynamic data obtained in the same column. Comparison of the axial dispersion coefficients at different operating conditions revealed that dispersion decreases when solids circulation flux increases to 450 kg/m2s together with the increase in gas velocity to 8 m/s. Low solids dispersion coefficients (Daz < 0.1) at high solids circulation fluxes and high velocities resulted from the disappearance of the net downward flow of particles at the riser walls, signifying the existence of the dense suspension upflow regime.

Hydrodynamics of expanded bed adsorption studied through CFD-DEM

The hydrodynamics of the Expanded Bed Adsorption process is studied through simulations combining Computational Fluid Dynamics and the Discrete Element Method. A representative base case is defined, based on process design parameters commonly encountered in literature. Then, 19 other cases are defined, each representing a singular adjustment to the column design, material properties, or operating conditions. The parameters that are varied are the expansion factor, liquid viscosity, bed aspect ratio, mean particle density, width of the particle density distribution, width of the particle size distribution, column taper angle, and column alignment angle. The impact of each adjustment on the bed behaviour is discussed, using the local particle size distribution and solids dispersion coefficient as main indicators of bed stability. Optimal performance was found for an expansion factor of two to three, and the combination of particle size distribution and particle density distribution was found to greatly improve bed stability. The mixing process of the liquid and solid phases is concluded to be of highly complex nature, and cannot simply be predicted from the liquid flow velocity.

Optimal design of gas distributor in fluidized bed for synthesis of silicone monomer

The structure of the gas distributor is closely related to the production efficiency of organosilicon monomers. To improve the production efficiency of organosilicon monomers, this study uses Eulerian-Eulerian two fluid model and proposes a design formula for the gas distributor to optimize the gas distributor. It is proposed that the pressure drop of the gas distributor, the velocity nonuniformity coefficient, the relative standard deviation of the solid holdup, and the solid particle dispersion coefficient are used to evaluate the performance of the gas distributor. The results show that the performance of the gas distributor is significantly improved when the opening ratio Φ = 0.53% is optimized to Φ = 0.18%, in which the relative standard deviation of the solid holdup is reduced by 22%, and the solid particle dispersion coefficient is reduced by 40%. On this basis, this article studies the influence of different arrangements of vent holes on gas-solid fluidization characteristics. The results show that the circular arrangement of vent holes is helpful to the mixing of gas and solid.

A Study of the Solids Mixing in a Bubbling Fluidized Bed Using the TFM Method. Part II. Solids Dispersion Coefficient

A Study of the Solids Mixing in a Bubbling Fluidized Bed Using the TFM Method. Part II. Solids Dispersion Coefficient

Residence time distribution and solids mixing of sawdust in a horizontal pulsed fluidized bed

A prototype horizontal pulsed fluidized bed (HPFB) has been built for continuous biomass torrefaction in our lab. Solids residence time distribution (RTD) of hemlock sawdust in the HPFB reactor was measured to study particle transport and mixing using a pulse injection of particle tracer. Effects of weir height, gas pulsation frequency, solids feed rate and gas velocity were investigated. A modified axial dispersion model was adopted to fit the experimental RTD curves, where horizontal dispersion coefficients were obtained. It is found that horizontal dispersion coefficients were slightly higher in the deeper bed. In the shallow bed, horizontal dispersion coefficients increased with increasing solids feed rate. The solids mixing intensity also found to increase with increasing the gas velocity. Horizontal solids dispersion coefficients obtained in the HPFB were significantly smaller than values calculated by literature correlations. A correlation in the shallow HPFB was established based on our experimental data.

Validation of CFD-DEM simulation of a liquid–solid fluidized bed by dynamic analysis of time series

Liquid–solid fluidized beds (LSFB) modeling validation is crucial for establishing design rules and monitoring tools. However, it generally relies on comparing global variables, which overlook dynamic features that influence reaction outputs. This work aims to implement time series analysis tools to compare Radioactive Particle Tracking data with a simulation consisting of Computational Fluid Dynamics coupled with Discrete-Element Method. Experiments have been performed in a pilot-scale LSFB of calcium alginate spheres fluidized with a calcium chloride solution. The Diks’ test indicates that the simulation can capture the LSFB behavior. It also allows diagnosing flow regime transitions from the simulation. Trends of solid dispersion coefficients and mixing times predicted by the simulation are in good agreement with the experiments.

Mixing and dispersion behaviours of ellipsoid particles in a bubbling fluidized bed

Fluidization of non-spherical particles is widely practised in chemical engineering processes. In this work, the mixing and dispersion behaviours of non-spherical particles in a bubbling fluidized bed (BFB) are explored by a computational fluid dynamics-discrete element method (CFD-DEM) featuring a super-quadric model to describe particle morphology. After model validation, the general flow patterns, solid mixing, and solid dispersion of ellipsoid particles are studied, together with the discussion of the effect of aspect ratio (AR) on fluidization behaviours. The results show that minimum fluidization velocity increases with the aspect ratio. Bed permeability depends on bed porosity and particle shape. Bubbles place a significant role in determining flow patterns, which induce a double-recirculation pattern where particles mainly move from the wall region to the central region in the lower bed and oppositely in the upper bed. Ellipsoid particles with higher sphericity (e.g., AR = 0.75 and 1.5) show a smaller mixing index in the bed. The magnitudes of solid dispersion coefficients in x, y, and z directions are about ~10−3 m2/s, ~10−5 m2/s, and ~ 10−2 m2/s, respectively. Ellipsoid particles with higher sphericity show larger solid dispersion intensity. These findings shed light on the fundamental understanding of the particle shape on fluidization dynamics.

Particle behaviours of biomass gasification in a bubbling fluidized bed

Biomass gasification in a bubbling fluidized bed (BFB) reactor is numerically studied based on a particle-scale computational fluid dynamics-discrete element method (CFD-DEM), with thermochemical and polydispersity effects featuring. After model validation, the particle-scale information (e.g., particle motions, particle mixing, solid dispersion, and heat transfer contribution) are thoroughly explored with the discussion of the effects of several critical operating parameters on particle behaviours. The results show that the middle dense region has the highest biomass pyrolysis reaction rate due to the vigorous particle motion. Sand and biomass particles show synchronous horizontal motions, and the solid vertical dispersion coefficients are much higher than the solid horizontal ones, denoting that the vertically introduced gas flow dominates bed hydrodynamics. A higher operating temperature causes a higher solid dispersion coefficient. Elevating temperature and steam to biomass ratio (S/B) first increases and then decreases the particle mixing index. Convection plays a dominant role during the biomass gasification process, followed by the radiation and heat of reaction. The conduction accounts for the smallest proportion and can be neglected. Increasing operating temperature promotes chemical reactions, biomass temperature, and all heat transfer modes. Increasing S/B promotes biomass motions and gasification reactions, leading to more heat consumed and biomass temperature decrease. Decreasing biomass temperature results in a larger temperature difference between biomass particles and bed material, which enhances the conduction, convection, and radiation.

Impact of polydispersity on the flow dynamics in the riser of a circulating fluidized bed

Circulating fluidized bed (CFB) has been commonly operated with polydisperse particles with a wide particle size distribution (PSD), which significantly affects solid transportation and the resulting thermochemical performance. Dense gas-solid flows in a pilot-scale CFB riser are simulated via the multiphase particle-in-cell (MP-PIC) coupled with a heterogeneous drag model. Gas-solid hydrodynamics together with the particle-scale information with a wide PSD is discussed. The results show that in the riser, the non-uniformly spatial distribution of solid phase appears with the presence of a core-annulus structure and a dilute-upper dense-bottom profile. The wide PSD gives rise to the axial segregation phenomenon with the accumulation of large particles in the bottom region. Enlarging the superficial gas velocity and PSD width respectively decreases and increases the segregation intensity of solid phase. As compared with gas velocity, the PSD width performs limited impacts on solid concentration, particle-scale information along the axial direction, and solid residence time. The horizontal solid dispersion coefficient is at the scale of 10−3 m2/s, while the vertical dispersion is at the scale of 1 m2/s. For a wide PSD, particles with larger sizes have larger slip velocities but smaller dispersion coefficients in the riser.

A novel experimental method for determining lateral mixing of solids in fluidized beds – Quantification of the splash-zone contribution

An experimental method to investigate the lateral mixing of bulk solids in bubbling fluidized beds is presented. The method utilizes finite volume analysis of the measured temperature field over the bed surface, from which the solids dispersion coefficient is determined. The temperature field is measured with a thermographic camera, which in this work is applied to a fluid-dynamically down-scaled fluidized bed that resembles the conditions relevant for hot large-scale operation. The method is applied to investigate the effect of key parameters for the solids mixing process; fluidization velocity, particle size and pressure drop over the air distributor plate. The results showed up-scaled dispersion coefficients in the order of 10−3 m2/s for the conditions investigated. The lateral mixing of solids decreased with increasing particle size and increased with increases in the fluidization velocity and pressure drop over the air distributor. The method was also used to quantify the contribution of the splash zone to the total lateral solids mixing. When lateral solids mixing in the splash zone was blocked with a vertical baffle the lateral solids dispersion was reduced by some 90%.

Quantification of Solid Mixing in Bubbling Fluidized Beds via Two-Fluid Model Simulations

The influence of particle density and fluidization velocity on the mixing behavior of Geldart B particles was investigated in bubbling fluidized beds for various operating conditions using a two-fluid model approach. The simulation results proved that the predicted solid flow pattern for a wide range of Geldart B particles differs from particles of Geldart B/D classification at identical fluidization numbers. Quantitative analysis of the predicted solid velocity variances revealed that the solid axial dispersion rate is higher than the lateral one. In detail, a Peclet number of 1.54 and 3.92 was predicted for axial and lateral mixings, respectively. Also, the solid dispersion and diffusion coefficients were linearly correlated with the excess gas velocity for a range of particle properties. Finally, the characteristic global particle mixing times were computed. Thereby, the characteristic mixing time can be correlated with the particle Froude number, expanded bed height, and solid dispersion coefficient with high accuracy.

Influence of acoustic waves on the solids dispersion in a gas-solid CFB riser: Numerical analysis

Ultrasonic waves were applied to improve the gas-solid flow homogeneity in CFB risers. The aim of this study is to verify if applying ultrasound in the radial direction of a lab-scale CFB riser improves the solids distribution along its cross-section. The best geometrical configuration of an ultrasonic device with a frequency of 40kHz applied to a lab-scale CFB riser was defined with a design of experiments. Seven variables were manipulated: the number of transducer rows, transducers per row, transducer diameter, the axial position of the device in the riser, sound pressure level, gas velocity, and solids mass flux. Numerical simulations were performed using the URANS-k-epsilon-KTGF model. Ultrasonic waves propagation were described using a jet flow approximation. The best solids distribution was found with 20 transducers of 120dB and 16mm diameter, which reduced the solids dispersion coefficient in 50% and reduced the pressure drop and the solids inventory.

Numerical investigation of the back-mixing and non-uniform characteristics in the three-dimensional full-loop circulating fluidized bed combustor with six parallel cyclones

The design and operation of circulating fluidized bed (CFB), which offers excellent heat and mass transfer, remain challenging because of the lack of a comprehensive understanding. CFD-DEM is used here for the high-fidelity simulation of the three-dimensional full-loop CFB with six parallel cyclones. Detailed information on the particle-scale information (i.e., solid dispersion, particle rotational speed, fluid and collision forces, mass distribution, and backing-mixing intensity) throughout the CFB are presented for the first time. Interesting results include: (i) the solid dispersion behavior is significantly different among the three directions; (ii) the solid loading in the middle cyclone on one side of the riser is twice that of the two adjacent ones, and this non-uniform distribution underscores the need for full-loop simulation for the CFB with multiple cyclones; (iii) the solid dispersion coefficients in all three directions, fluid force, collision force and particle rotational speed are similar among the six cyclones and correspondingly the standpipes; and (iv) approximately 50% and 48% of the total material are distributed respectively in the riser and standpipes. The results obtained provide valuable insights regarding the mass loading, particle-scale characteristics and non-uniform distribution of the solid phase throughout the entire CFB.

Solid residence time distribution in a cross-flow dense fluidized bed with baffles

The residence time distribution (RTD) of particles in a gas-solid dense fluidized bed with a continuous solid flow operation and baffles needs much more focus for the purpose of the wide industrial applications. The available models of solid RTD are not adequate in this case due to the additional convective diffusion induced by the cross-flow of the solid feeding and the complex geometry caused by the baffles. To address this problem, this work applied a two-phase Eulerian-Eulerian model combined with the species transport equation to predict solid RTD in a dense fluidized bed. The effects of the continuous solid feeding and baffles were considered. The solid dispersion coefficient Ds in the species transport equation was calculated by an analytical solution from kinetic theory of granular flow. Ds only needs the value at a molecular level due to the fact that the computational fluid dynamics (CFD) model is able to reproduce the RTD procedure exactly same as the practical experiments. To validate the established CFD model, a series of 3D lab-scale cold flow experiments were conducted in the free and baffled beds for the bed material with various severe non-spherical shapes. The measurement included the solid hydrodynamic characteristics at the outlet of the outflow pipe and solid RTD of the system. The reasonable agreement between the CFD prediction and experimental data demonstrated the good performance of the CFD model. 1D plug flow with dispersion model and the tanks-in-series model were further used to fit the calculated RTD curves. The estimated lateral dispersion coefficient of solids locates in a rational range compared with the data collected extensively from the literature. The results showed that the lateral dispersion coefficient of solids decreases when the baffles are installed.

Dynamic modeling of manganese removal in a pyrolusite fluidized bed contactor

A novel pyrolusite fluidized bed (PFB) contactor, which we recently developed for dissolved manganese (Mn(II)) removal through surface adsorption and subsequent oxidation by free chlorine, was modeled in this study. The hydrodynamic behavior of the filter media and water in the fluidized bed was described by the axial dispersion model. The model incorporated the effects of axial mixing in the liquid and solid phases, mass transfer resistance in a laminar fluid boundary layer surrounding a media grain, and a second order oxidation rate expression. The experimental data from lab-scale and field pilot-scale contactors was adopted for the model development and its validation. For the former, the data was employed to estimate the oxidation rate constant, the mass transfer coefficient, and the axial solid phase dispersion coefficient for the model. The model simulations matched the experimental data with less than 20% error across a wide range of Mn(II) and free chlorine concentrations and hydraulic loading rates that might be encountered in a drinking water treatment plant. The sensitivity analysis showed that the time to breakthrough is most sensitive to the adsorption isotherm constants and the oxidation rate constant. These observations indicate that the alluded parameters mainly control the performance of the PFB contactor as well as the process stability. Finally, a sample application of the model to acquire operational inputs was illustrated by analyzing the effect of free chlorine concentration on Mn(II) removal performance and breakthrough time within a PFB contactor.

Study of Axial Solid Concentration Distribution in Slurry Bubble Columns

The axial distribution of solid concentration was studied in semibatch slurry bubble columns. Tapered slurry bubble column (TSBC) and cylindrical slurry bubble column (CSBC) have been used in this study. Air, sodium chloride (NaCl) aqueous solution of concentration 0.15 M, and quartz sand, were represented gas, liquid and solid phases, respectively. The superficial velocity of gas was varied from 2.5 to 10 cm/s. Quartz sands with a mean diameter of 120 µm were used in the concentrations of 3,5,10 & 20 vol. %. Influences of gas velocity and solid loading on longitudinal profile of solid concentration were investigated. It was observed that the longitudinal distribution of solid concentration tends to be more uniform as superficial velocity of gas or solid loading increased. Under the same operation conditions, experimental results showed that TSBC offered more uniform distribution of solids along the column. The observed axial concentration distribution of solid particles in tapered slurry bubble column was analyzed on the basis of precipitation-dispersion model. The model successfully predicts the axial concentration distribution for narrow-sized range of solids systems in TSBC. Empirical correlation for the solid dispersion coefficient for solid particles in tapered slurry bubble column was proposed.

Features of the motion of gel particles in a three-phase bubble column under foaming and non-foaming conditions

Fil: Salierno, Gabriel Leonardo. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Industrias; Argentina

Residence time distribution of particles in circulating fluidized bed risers

Solids Residence Time Distribution (RTD) in Circulating Fluidized Bed (CFB) risers has received increasing attention due to its vital role in determining the operating condition, particle property, and reactor geometry in industrial CFB applications. In recent years, various solids RTD experimental techniques and theoretical models have been utilized and proposed to study CFB risers. Some controversial issues, however, also arose in the open publications. By means of exploring the advantages and disadvantages of each available RTD experimental technique and model when they are applied to particles in CFB risers, this study discussed the primary causes leading to the huge discrepancy in magnitude of solids dispersion coefficient and Peclet number, which can achieve 4 orders or span from 1 to 100. On the basis of the massive experiment data collected from the literature, the variations of average residence time, Peclet number and dispersion coefficient of solids with superficial gas velocity, solids mass flux and solids concentration were presented. By applying the transition of flow regime in CFB mode, we provided a helpful way to explain some existing contradictions in the reported effects of operating conditions on solids RTD. The possible reasons were also summarized to clarify why some researchers measured a double- or multi-peak solids RTD curve and the others could not in a similar situation.

Three-dimensional axial dispersion dynamics of granular flow in the rolling-regime rotating drum

The dispersion characteristics of the granular material frequently encountered in many chemical industries play an important role in the system operation since it is related to the solid residence time, and thus further influence the heat and mass transfer behavior of the whole process. To shed some light, the discrete element method (DEM) is employed here to study a three-dimensional rotating drum, with the key focus being the axial dispersion characteristics of the solid phase. Our results prove the natural existence of a preferential channel for axial dispersion spanning the entire drum length, which provides insights on the region where the most extensive axial segregation effects are expected. Furthermore, we show that the axial solid dispersion coefficients adhere to normal frequency distributions in the active region, passive region and the entire drum. Also, increasing the rotating speed enhances while increasing the fill level diminishes the axial dispersion intensity in the system. Collectively, the results here provide new and valuable insights on the axial dispersion characteristics in the rotating drum, which is useful for the further understanding and optimization of the system.

Solid motion in a three-phase bubble column examined with Radioactive Particle Tracking

Radioactive Particle Tracking (RPT) is a powerful advanced technique for studying the solid motion within industrial scale multiphase reactors. However, it is rather difficult to implement in actual industrial installations, mainly due to the required calibration stage under actual operating conditions. This work has the aim of comparing the motion of calcium alginate beads in a three-phase bubble column examined either with RPT or with an array of the same scintillation detectors used for RPT, but located vertically aligned beside the analyzed vessel. Liquid and solid used for the experiments were in batch mode and mixed by circulating air. The homogeneous and heterogeneous regimes have been explored. Results arising from both techniques, like axial tracer trajectories, axial profiles of tracer positions probabilities, solid axial mixing times and solid axial dispersion coefficients are compared, for highlighting the relevant information that can be extracted from the simplified method, validated by RPT. It is found that the simplified method fairly coincides with the classic technique for estimating several relevant parameters. Finally, the estimated flow regime transition inferred from the simplified method by symbolic analysis is compared with the one arising from chordal holdup trends determined by gamma densitometry, also with satisfactory agreement.