Modeling axial distributions of adsorbent particle size and local voidage in expanded bed

Axial distribution of adsorbent particle as well as local voidage variation is very important and fundamental for the predicting and understanding of adsorptive performance in expanded bed adsorption. Based on the analysis of bed expansion and fluid hydrodynamic behaviors, a model was developed to predict the mean particle size and local voidage variations with the axial bed height under various operation conditions in expanded bed. Experimental measurements of particle size and local voidage changes with bed height were conducted in a modified glass column of inner diameter with sampling ports. Experimental data obtained in this work and in the literature with Streamline SP, Streamline Phenyl and Streamline quartz base matrix particles in the columns of inner diameters 20-, were used to verify the model prediction. The results were in good agreement with the experimental data.     

A 3-zone model for protein adsorption kinetics in expanded beds

The adsorption behavior of expanded beds is more complex than that of fixed beds, since the adsorbent particle size, local bed voidage and liquid axial dispersion will vary axially with expanded height. Models applicable to fixed beds maybe not adequately describe the hydrodynamic and adsorption behavior in expanded beds. In this paper, a 3-zone model is developed, in which the model equations are written for the bottom zone, middle zone, and top zone of the column, respectively, and the model parameters, such as the adsorbent particle diameter, bed voidage and liquid axial dispersion coefficient, are zonal values. In-bed breakthrough curves are predicted by the 3-zone model, and tested against literature data for lysozyme adsorption on Streamline SP in an expanded bed.Model parametric sensitivity is analyzed. The effects of film mass transfer resistance, liquid axial dispersion and adsorbent axial dispersion on the breakthrough curves are weaker than that of protein intraparticle diffusion resistance for stable expanded beds. Adsorbent particle size axial distribution and bed voidage axial variation significantly affect in-bed breakthrough curves, therefore, model parameters should not be assigned uniform values over the whole column; instead the model should account for the adsorbent particle size axial distribution and bed voidage axial variation.     

酵母悬浮液进料时膨胀床空隙率和粒径分布的动态变化

引言 膨胀床吸附技术可以直接从细胞破碎液(未澄清液)中提取目标产物[1-3],而无需预先进行固液分离操作,具有快速、高效和集成化的特点.在实际应用中,料液中细胞(碎片)的存在将会影响到膨胀床的床层稳定性和操作性能[4-6].     

Numerical Simulation of a Spouted Bed Using Computational Fluid Dynamics (CFD)

In this article, computational fluid dynamics (CFD) technology is used to model a spouted bed(SB). The multifluid Eulerian-Eulerian approach based on kinetic theory of granular flows and Gidaspow's drag model for the interaction between gas and particles are applied in the modeling. The effects of the SB properties—that is, cone angle, particle size, cylinder diameter, and static bed height of particles—on its dynamics performance are investigated. The simulated results—that is, flow pattern of particles, fountain height, voidage, and particle velocity of the spout zone—are presented. It is shown that periodic fluctuation of spouting appears in an SB with conical angle of 30° and inlet velocity at 16.6 m/s. When the SB cylinder diameter becomes 0.52 m, periodic fluctuation appears, too. The stable spouting of the SB with a 90° cone angle could be obtained at an inlet air velocity of 24.3 m/s. The fountain height of particles decreased with an increase in particle size and the static bed height of particles. It is kept at about 0.19 m when different SB cylinder diameters in the range of 0.36 to 0.48 m are used. In the spouting region, the voidage decreased with static particle height in bed, but the particle velocity increased. For a certain particle size, the voidage decreased with an increase in particle height, but the velocity of the particles increased. It was also found that the cylinder diameter did not affect the volume fraction of particles except for the cylinder diameter 0.52 m and the change in particle velocity was minimal in the spout zone. With the different static bed height of particles used, the voidage and particle velocity did not change much at the same level of spout zone.     

EFFECT OF PARTICLE SIZE DISTRIBUTION ON LOCAL VOIDAGE IN A BENCH-SCALE CONICAL FLUIDIZED BED DRYER

The effect of particle size distribution (PSD) on local voidage has been investigated in a conical fluidized bed containing dried placebo pharmaceutical granule. For each of the five PSDs examined, the static bed height was varied between 0.12 and 0.17 m and the superficial gas velocity was varied between 0.05 and 0.75 m/s. The local voidage was measured using a twin-plane electrical capacitance tomography (ECT) system. A wide PSD containing 12 wt% solids with a diameter of 2 mm or larger resulted in two different types of gas flow: an annular gas flow up to a gas velocity of 0.50 m/s and a centrally concentrated gas flow above 0.50 m/s. The mixtures containing less coarse material exhibited a centrally concentrated gas flow surrounded by a dense phase at the walls of the bed over the entire range of gas velocities and bed heights examined. Consideration of previous work by other researchers suggests that the behavior of the wide PSD mixture is due to segregation at the lower velocities. The local voidage was sensitive to small changes in static bed height. For the wide PSD mixture at a fixed gas velocity, the gas tended to spread more uniformly over the bed cross-section as static bed height increased. The opposite was true of the other mixtures, i.e., the gas flow became more centralized with increasing bed height.     

EFFECT OF PARTICLE SIZE DISTRIBUTION ON LOCAL VOIDAGE IN A BENCH-SCALE CONICAL FLUIDIZED BED DRYER

ABSTRACT

The effect of particle size distribution (PSD) on local voidage has been investigated in a conical fluidized bed containing dried placebo pharmaceutical granule. For each of the five PSDs examined, the static bed height was varied between 0.12 and 0.17 m and the superficial gas velocity was varied between 0.05 and 0.75 m/s. The local voidage was measured using a twin-plane electrical capacitance tomography (ECT) system. A wide PSD containing 12 wt% solids with a diameter of 2 mm or larger resulted in two different types of gas flow: an annular gas flow up to a gas velocity of 0.50 m/s and a centrally concentrated gas flow above 0.50 m/s. The mixtures containing less coarse material exhibited a centrally concentrated gas flow surrounded by a dense phase at the walls of the bed over the entire range of gas velocities and bed heights examined. Consideration of previous work by other researchers suggests that the behavior of the wide PSD mixture is due to segregation at the lower velocities. The local voidage was sensitive to small changes in static bed height. For the wide PSD mixture at a fixed gas velocity, the gas tended to spread more uniformly over the bed cross-section as static bed height increased. The opposite was true of the other mixtures, i.e., the gas flow became more centralized with increasing bed height.     

Local porosity in conical spouted beds consisting of solids of varying density

Local bed voidage has been measured in conical spouted beds by means of an optical fibre, for different geometric factors of the contactor (angle and inlet diameter) and under different experimental conditions (height of the stagnant bed, particle diameter and air velocity). The study has been carried out with glass beads and materials of lower density (high- and low-density polyethylene, polypropylene and extruded and expanded polystyrene). From the results, a correlation has been proposed for calculation of the local bed voidage in the spout and annular zones. The effect of the experimental conditions on the bed voidage in the solid ascent (core) and descent (periphery) regions of the fountain has been studied and the fountain has been proven to be of greater importance in the design of conical spouted beds, as solid density and shape factor are lower.     

膨胀床应用中的高密度薄壳型琼脂糖凝胶介质、流体力学与固相分布

Two dense pellicular agarose-glass matrices of different sizes and densities, i.e., AG-S and AG-L, have been characterized for their bed expansion behavior, flow hydrodynamics and particle classifications in an expanded bed system. A 26 mm ID column with side ports was used for sampling the liquid-solid suspension during expanded bed operations. Measurements of the collected solid phase at different column positions yielded the particle size and density distribution data. It was found that the composite matrices showed particle size as well as density classifications along the column axis, i.e., both the size and density of each matrix decreased with increasing the axial bed height. Their axial classifications were expressed by a correlation related to both the particle size and density as a function of the dimensionless axial bed height. The correlation was found to fairly describe the solid phase classifications in the expanded bed system. Moreover, it can also be applied to other two commercial solid matrices designed for expanded bed applications.     

膨胀床应用中的高密度薄壳型琼脂糖凝胶介质、流体力学与固相分布

Two dense pellicular agarose-glass matrices of different sizes and densities, I.e., AG-S and AG-L, have been characterized for their bed expansion behavior, flow hydrodynamics and particle classifications in an expanded bed system. A 26 mm ID column with side ports was used for sampling the liquid-solid suspension during expanded bed operations. Measurements of the collected solid phase at different column positions yielded the particle size and density distribution data. It was found that the composite matrices showed particle size as well as density classifications along the column axis, I.e., both the size and density of each matrix decreased with increasing the axial bed height. Their axial classifications were expressed by a correlation related to both the particle size and density as a function of the dimensionless axial bed height. The correlation was found to fairly describe the solid phase classifications in the expanded bed system. Moreover, it can also be applied to other two commercial solid matrices designed for expanded bed applications.     

宽粒体系液固流态化随机理论数学模型

用快速切割流化床研究了宽粒级液固流态化的轴向混合和分离,测定了粒度分布、平均粒径和空隙度沿床高的变化.证实了颗粒的运动有随机性.用马尔柯夫过程建立了一个随机游走模型,描述了流化床中宽粒体系的混合和分级特性.对钛铁矿和石英砂(粒径0.04～0.40mm)进行了检验.结果表明,体系的初始流态化速度、膨胀性质、粒度分布以及平均粒径和空隙度沿床高的变化的测定结果,同模型的预测值很好符合.     

大孔树脂膨胀床的膨胀特性及液相轴向混合性能

以AB-8大孔树脂为固相,对膨胀床的膨胀特性及流体混合性能进行了研究。结果表明,不同直径范围的颗粒的膨胀性能可用Richardson-Zaki方程描述。在一定的膨胀比下,液含率随着轴向高度的增加而增加,存在较明显的不均匀分布。在一定的固定床高度下,液体轴向分散系数随着表观液速的增加而增加,轴向分散系数在0.5×10-5~5×10-5m2/s。     

60米高循环流化床内物料浓度分布的冷态试验

利用电厂循环流化床锅炉现有的结构和设备, 搭建提升管高度60m、内径400mm的超高循环流化床冷态实验台, 重点研究了流化风速和颗粒密度对提升管内轴向和径向空隙率分布的影响。实验结果表明:空隙率分布形式与流化风速和物料密度密切相关, 对于一定的床料高度, 在底部密相区一直有床料堆积的情况下, 随着流化风速的增加, 提升管底部密相区空隙率增大, 上部稀相区的空隙率减小并且其在径向的分布变得更加不均匀;在一定的流化风速下, 密度较小的物料将更多的被带入上部稀相区, 上部稀相区的空隙率减小, 其在径向分布将变得更加不均匀。     

Flow in the annulus of a bed of fine particles spouted with water

The flow in the annulus of a water spouted bed of glass particles (275 to 774 μm) was studied experimentally in a cylindrical half-column 50.8 mm in diameter. An axisymmetric model, which assumes Darcy flow in the annulus and uses the experimental spout pressure distribution, predicts the flow and pressure fields in the annulus. The substantial differences between this flowfield and that for coarse particle beds that are observed are caused by differences in the normalized interfacial pressure profile. The model predicts that both the fluid velocity and the normalized fluid velocity at the top of the annulus decrease as the particle size and bed height are reduced. Particles are observed to enter the spout primarily near the spout inlet in agreement with predictions of the axial spout voidage distribution. The residence time distribution of the fluid in the annulus is relatively broad and the measured residence times are about 25% higher than those calculated.     

Parametric study of fine particle fluidization under mechanical vibration

Investigations into the effects of vibration on fluidization of fine particles (4.8-216 μm average in size) show that the fluidization quality of fine particles can be enhanced under mechanical vibration, leading to larger bed pressure drops at low superficial gas velocities and lower values of u_mf. The effectiveness of vibration on improving fluidization is strongly dependent on the properties (Geldart particle type, size-distribution and shape) of the primary particles used and the vibration parameters (frequency, amplitude and angle) applied. The possible roles of mechanical vibration in fine particle fluidization have been studied with respect to bed voidage, pressure drop, agglomeration, and tensile strength of particle bed. Vibration is found to significantly reduce both the average size and the segregation of agglomerates in the bed, thus improving the fluidization quality of cohesive particles. Also, vibration can dramatically reduce the tensile strength of the particle bed. Obviously, vibration is an effective means to overcome the interparticle forces of fine powders in fluidization and enhance their fluidization quality.     

Effect of interparticle forces on the conical spouted bed behavior of wet particles with size distribution

This paper aims to analyze air-solid flow behavior in conical spouted beds composed of glass bead mixtures coated by glycerol. Four mixtures of glass beads are used as the solid phase. Although these mixtures have the same mean Sauter diameter, each one is characterized by a different size distribution function (mono-sized; flat, Gaussian or binary size distribution). When glycerol is added to the bed of these particles, which are spouted by air, the gas-solid flow characteristics are changed due to the growth of interparticle forces; however, the trends of these changes are affected by the glass bead mixture type as well as by the concentration of glycerol. For beds of mono-sized particles, the minimum spouting velocity is maintained almost unchanged as the glycerol concentration rises; while, for beds of inert particle mixtures, this velocity increases, becoming greater for flat and binary size distribution particles. Conversely, the minimum spouting pressure drop decreases as the glycerol concentration rises for all beds of particles used. Based on theoretical prediction of interparticle forces, it is shown that these changes in the minimum spouting conditions can be explained by the magnitude of these forces.     

The bubbling behaviour of fine powders when fluidised

Narrow size cuts of particles in the range 40–260 μm have been examined by X-rays when fluidised by air. No discontinuity in behaviour was observed with decreasing particle size. The bubbles behave the same in all materials except that their velocity increases with decreasing particle size. The visible bubble flow is generally less than the excess over minimum fluidisation flow. Almost all flow occurs interstitially near the bottom of the bed but the proportion decreases with height to approach U_mf near the top of the bed. Appreciable changes in dense phase voidage occur with fine particles and this varies with bed height.     

Voidage characteristics and prediction of bed expansion in liquid-solid inverse fluidized bed

Studies on voidage fluctuations, axial voidage profile and bed expansion are carried out by measuring the local void fraction using particles of wide ranging characteristics in liquid-solid inverse fluidized bed. The quality of fluidization is elucidated by the local voidage fluctuations. The RMS voidage fluctuation depicts a maximum with respect to average bed void fraction and increases with increase in Archimedes number. The fluidization quality has been quantified using average normalized RMS voidage fluctuation in terms of Transition number. The axial void fraction is almost uniform throughout the bed except for particles with size distribution. All the literature and present experimental data on bed expansion are unified in terms of Richardson and Zaki equation using experimental terminal velocities. A new correlation is proposed for predicting the wall effect corrected experimental terminal velocities, as a substitute for standard drag equation. The bed expansion data are also predicted using the drift flux model.     

低密度循环流化床局部颗粒速度的轴径向分布的研究

在高8m,内径186mm的循环流化床中,利用光纤激光多普勒测速仪测量了FCC颗粒的局部速度沿轴径向的分布。实验结果表明:局部颗粒速度沿径向分布是不均匀的,床中心区域分布比较平坦,近壁环形区域分布较陡,颗粒沿轴向运动有较长的加速段。由实验数据回归得到预测低密度循环流化床局部颗粒速度的经验关联式。     

Measurement of voidage in the fountain of a spouted bed

A γ-ray technique is described for measuring the distribution of fractional voidage in the fountain of an air spouted bed. What appear to be the first experimental data on fountain voidage are presented. For the relatively shallow, 160 mm diameter, conical spouted bed studied, fountain fractional voidage is quite high, 0.88 and upwards. Generally voidage increases with height up the fountain, apart from a plateau or slight fall part way up. This trend differs from that proposed by Grace and Mathur in a theoretical model for a deeper cylindrical spouted bed. Fountain voidage is shown to depend on air flow rate and on particle size distribution.     

Particle fluctuations and dispersion in three-phase fluidized beds with viscous and low surface tension media

Particle fluctuations and dispersion were investigated in a three-phase (gas–liquid–solid) fluidized bed with an inside diameter of 0.102 m and height of 2.5 m. Effects of gas and liquid velocities, particle size (0.5–3.0 mm), viscosity (1.0–38×10⁻³ Pa s) and surface tension (52–72×10⁻³ N/m) of continuous liquid media on the fluctuating frequency and dispersion coefficient of fluidized particles were examined, by adopting the relaxation method base on the stochastic model. The fluctuations and dispersion of fluidized solid particles were successfully analyzed by means of the pressure drop variation with time, which was chosen as a state variable, based on the stochastic model. The fluctuating frequency and dispersion coefficient of particles increased with increasing gas velocity, due to the increase of bubbling phenomena and bed porosity in which particles could move, fluctuate and travel. The frequency and dispersion coefficient of particles showed local maximum values with a variation of liquid velocity. The two values of fluctuating frequency and dispersion coefficient of particles increased with increase in particle size, but decreased with increase in liquid viscosity due to the restricted movement and motion of particles in the viscous liquid medium. Both fluctuating frequency and dispersion coefficient of particles increased with decrease in surface tension of liquid phase, due to the increase of bubbling phenomena with decrease in σ_L. The values of obtained particle dispersion coefficient were well correlated in terms of dimensionless groups as well as operating variables.