Solids behaviour in a gas-solid two-phase mixture flowing through a packed particle bed

This paper reports the solids behaviour in a dilute gas-solid two-phase mixture flowing through a packed bed. The positron emission particle tracking (PEPT) technique was used in the work, which allowed investigation of three-dimensional solids motion at the single suspended particle level. Processing of the data gave solids velocity, the residence time of suspended particles, bed tortuosity in terms of solids motion, as well as solids occupancy in the cross-section of the packed bed. The results suggest that the wall effect on the motion of suspended particles is limited to approximately one packed particle diameter under the conditions of this work. Both the average axial and radial velocities of suspended particles, normalised by the superficial gas velocity, change periodically with radial position, but the periodicity does not correspond exactly to the packed particle diameter. The peak and trough values of the average axial velocity of the suspended particles in the bulk region are, respectively, ∼25% and ∼15% of the superficial gas velocity under the conditions of this work and the superficial gas velocity shows little effect. The peak and trough values of the average radial velocity of the suspended particles in the bulk region are, respectively, +5% (positive) and -5% (negative) of the superficial gas velocity. The results of the residence time and tortuosity of the suspended particles show an approximately Gaussian distribution with the peak residence time and tortuosity increasing with decreasing superficial gas velocity. The occupancy data suggest that particles spend more time in an annular region close to the wall, indicating a non-uniform particle distribution across the packed bed cross-section.     

Intraparticle diffusion coefficients in packed columns: Measurement by arrested-flow gas chromatography

Arrested-flow chromatography was used to determine intraparticle diffusivities of large-pore particles packed in columns. Particle and column tortuosity factors were determined for helium tracer in nitrogen carrier gas at 40°C and atmospheric pressure. Semiempirical modifications of Maxwell's, Burger's, Jeffrey's, and Rayleigh's relations for the composite diffusivity of spherical particles in a stationary medium are proposed for the effective composite diffusion coefficient for a packed bed of porous particles. The equations, modified to represent accurately the extraparticle void diffusion based on measurements for beds of nonporous particles, are used to evaluate intraparticle diffusivities from experimental data obtained by arrested-flow chromatography.     

蓄热小球填充床的气体阻力特性

通过冷态实验研究蓄热小球填充床的气体阻力特性,考察了气体流速、小球直径、堆积球层高度、空隙率对阻力损失的影响,得到了修正的Ergun公式系数. 结果表明,填充床中气体的阻力损失随气体流速增大而增大,呈二次方关系;对阻力系数回归,得到修正的Ergun公式系数f1=331.9, f2=1.402,由此计算的单位压降与实验值最接近.     

拉西环填料塔体动持液量和面动持液量及其计算

首次提出填料塔动持液量不是均匀分布的，高径比是影响动持液量的一个重要参数。定义整个床层的平均动持液量为体动持液量；定义填料层中水平截面上微分薄层的平均动持液量为面动持液量。根据实验数据和优化计算方法，得出恒持液量区到泛点拉西环填料层体动持液量计算修正式和面动持液量计算式。     

Prediction of bed pressure drop and top packed bed formation in gas-liquid-solid semi-fluidized bed with irregular homogeneous binary mixtures

We studied the hydrodynamics of a gas-liquid-solid semi-fluidized bed relating to packed bed formation and bed pressure drop with irregular homogeneous binary mixtures in a 0.05 m internal diameter Perspex column, with water and air (secondary) as fluidizing medium at constant static bed height of 0.08 m. A homogeneous binary mixture has been taken for easy formation of a semi-fluidized bed. Air is supplied centrally below the bottom grid in radial direction with a special design air sparger after the bed is first fluidized by the liquid. Experimental parameters studied included superficial gas and liquid velocities, average particle size and density and the bed expansion ratio. Empirical and semi-empirical models were developed. The calculated values from predicted models were compared with the experimental values and fairly good agreement was obtained.     

Kinetic behaviour of packed and fluidised bed electrodes

For the reaction of electrochemical quinone reduction at packed and fluidised bed electrodes an experimental parameter analysis of macrokinetic bed cd was carried out showing the influence of electrode potential, flow velocity, bed depth parallel to current flow direction, and electrolyte conductivity. A macrokinetic model of three-dimensional electrodes is established by introducing overpotential distribution within the electrode into the microkinetic rate equation. Theoretical calculations of macrokinetic bed cds yield reliable values as is shown by comparison with the experimental results. Both for packed and for fluidised bed electrodes analytical expressions are derived for penetration depth of diffusion limiting cd into bed electrodes.     

化学吸收法测定多级离心雾化旋转填料床有效相界面积及体积传质系数

对多级离心雾化旋转填料床的有效相界表面积及体积传质系数,用化学吸收法做了实验测量。实验结果表明：多级离心雾化旋转填料床不仅具有超低气阻,而且可产生良好的喷雾扩展相界面积的作用,体积传质系数比传统填料塔提高一个数量级,接近气液逆流型旋转填料床。多级离心雾化旋转填料床开拓了新的气液传热传质途径。     

EFFECT OF NATURAL CONVECTION ON MASS TRANSFER BETWEEN SOLID PARTICLES AND FLOWING FLUIDS IN PACKED BEDS

Mass transfer between solid particles in a packed bed and a flowing fluid in laminar flow region, where both forced and natural convection are important, was analyzed theoretically. The diffusion equation based on the free surface model proposed by Happel was solved and an approximate solution relating the average Sherwood number to the Peclet number, the Rayleigh number and the void fraction of a packed bed was obtained. The published experimental mass transfer data in packed beds were found to agree well with the theoretical predictions.     

Transfert de matière entre un electrolyte et une paroi cylindrique immergée dans un lit fixe ou fluidisé de grains isolants

Electrochemical mass transfer rates have been measured between a liquid and a surface immersed axially in a fluidised or packed bed of inert particles. The influence of different parameters on the mass transfer (Fluid Schmidt number, particle diameter and electrode length in the flow direction) leads to the conclusion that for a given flowrate the mass transfer rate is higher when the bed is maintained fixed. Moreover, the fluidised bed is intermediate between the fixed bed and the column without particles. An unsteady boundary layer model is in good agreement with the experimental results obtained in the packed bed.     

Low peclet number particle-to-fluid heat and mass transfer in packed beds

For low Peclet numbers most of the experimentally obtained particle-to-fluid heat and mass transfer coefficients in packed beds were found to be some orders of magnitude below the values predicted for a single sphere in cross flow.From theoretical considerations one should expect the transfer coefficients in packed beds to exceed the single sphere predictions as they actually do for higher Peclet numbers.The obvious discrepancy between theory and experiment can be cxplained by a simple model accounting for a nonuniform distribution of the void fraction. The model consists of a packed bed of uniformly sized particles with an average void fraction ψ, where a small part ? of the total cross-sectional area f is assumed to have a larger void fraction ψ₂. Since the same pressure drop applies to both parts of the bed, the superficial velocity will be much larger in the section with the larger void fraction, especially in the range of low Reynolds numbers.Even though in both parts of the packed bed the individual transfer coefficients are taken from a correlation which is based on the single sphere predictions (as it is valid in the range of high Peclet numbers), the apparent overall transfer coefficients for the nonuniform system become much lower, and show the same characteristic variation with Peclet number and the ratio of particle diameter to bed height as the majority of the experimental data.     

生物膜填料床内含有生化反应的多相传输模型

废气处理生物膜滴滤塔的多孔填料床内是带有气液两相流动、有机污染物扩散、生物膜内生化反应的复杂生化反应体系.在平行平板理论模型基础上,建立了生物膜多孔填料床内含生化反应的多元多相流动及传输特性的多相混合模型,获得了废气处理生物膜滴滤塔净化效率的理论计算方法.模型的理论预测值与生物膜滴滤塔净化低浓度甲苯废气的实验结果基本吻合.     

Hydrodynamic characteristics in an inverse internal-loop airlift-driven fibrous-bed bioreactor

An inverse internal loop airlift-driven fibrous bed bioreactor (ALFBB) was designed by combining the advantages of an internal loop airlift bioreactor and packed bed bioreactor into one column. This bioreactor, with a high degree of design flexibility, is expected to handle genetically engineered cells as well as fragile cells, which are shear-sensitive. The hydrodynamic characteristics of the combined system have been investigated. Woven cotton was set in the downcomer of the I-IL-ALB to represent the fibrous bed packed bed and the outcome results were compared with those of the polyurethane foam (PUF) packed system and the unpacked I-IL-ALB system. The effects of the packing nature, packing height, packing top and bottom clearances, gaps between adjacent fiber surfaces, and superficial gas velocities were investigated. The hydrodynamic output variables included the gas holdup and liquid circulation velocity. Gas holdup for all packed systems continuously increased with increases in packing height, packing top clearance and superficial gas velocity. It was found highest in the downcomer of the cotton packed system than in the PUF counter part due to the roughness and hydrophilicity of the woven cotton fibrous material. Increased amounts of packing in the I-IL-ALB, whether in the form of cotton or PUF decreased the liquid circulation velocity in the bioreactor because of the increased frictional resistance and tortuosity. The reduction in liquid circulation velocity was significant for large packing with small gaps between fiber surfaces and increased bottom clearances of the cotton packed system. Empirical models based on packing properties are presented which accurately predict the gas holdup, whereas energy based model was proposed to predict liquid circulation velocities. The optimum hydrodynamic conditions were observed with cotton packing.     

单一尺寸圆柱颗粒填充床的阻力特性

通过直径为3、4 mm不同长度的圆柱颗粒填充床的阻力特性实验,研究了颗粒密度对填充床孔隙率的影响,结合文献孔隙率数据修正了孔隙率模型使其在高球形度时预测更准,分析了等效直径的计算方法对Ergun常数的影响,得到圆柱颗粒填充床的阻力特性并与Nemec和Wu的阻力预测模型进行对比,提出新的拟合方法对Ergun常数进行拟合。结果表明：颗粒密度在1156~7947 kg/m3范围内对填充床的孔隙率没有影响;结合文献数据得到圆柱颗粒填充床的孔隙率修正模型;文献中预测不同L/D的圆柱颗粒堆积床的阻力时结果相差较大,Nemec模型要比Wu模型预测准确度高,但也不适用所有L/D下的阻力预测;结合圆柱颗粒填充床孔隙率提出新的拟合方法,拟合Ergun常数时,采用d_ep作为等效直径的拟合优度最高;提出新的Ergun常数表达式,适用于圆柱直径3~4 mm,L/D=1~10的圆柱颗粒,相比于Nemec模型其R²更高,适用范围更明确,因此实用性更强。     

A macroscopic model for shear-thinning flow in packed beds based on network modeling

The flow of non-Newtonian fluids in packed beds and other porous media is important in several applications such as polymer processing, filtration, and enhanced oil recovery. Expressions for flowrate versus pressure gradient are desirable for a-priori prediction and for substitution into continuum models. In this work, physically representative network models are used to model the flow of shear-thinning fluids, including power-law and Ellis fluids. The networks are used to investigate the effects of fluid rheology and bed morphology on flow.A simple macroscopic model is developed for the flow of power-law and Ellis fluids in packed beds using results from the network model. The model has the same general functionality as those developed using the popular bundle-of-tubes approach. The constant β, which appears in these models, is often directly derived from the tortuosity and a simple representation of the porous media. It is shown here that this can lead to incorrect and ambiguous values of the constant. Furthermore, the constant is a weak function of the shear-thinning index, indicating that no single bundle-of-tubes could ever properly model flow for a wide variety of shear-thinning fluids.The macroscopic model is compared to experimental data for shear-thinning fluids available in the literature. The model fits the data well when β is treated as an experimental parameter. The best-fit values of β vary, which is expected because even the constant C in the Blake-Kozeny equation varies depending on the source consulted. Additionally, physical effects, such as adsorption and filtration, as well as rheological effects such as viscoelasticity may affect the value of β. We believe that in the absence of these effects, β equals approximately 1.46 for packed beds of uniform spheres at relatively moderate values of the shear-thinning index (>0.3).     

Using Artificial Neural Network to Predict the Pressure Drop in a Rotating Packed Bed

Although rotating beds are good equipments for intensified separations and multiphase reactions, but the fundamentals of its hydrodynamics are still unknown. In the wide range of operating conditions, the pressure drop across an irrigated bed is significantly lower than dry bed. In this regard, an approach based on artificial intelligence, that is, artificial neural network (ANN) has been proposed for prediction of the pressure drop across the rotating packed beds (RPB). The experimental data sets used as input data (280 data points) were divided into training and testing subsets. The training data set has been used to develop the ANN model while the testing data set was used to validate the performance of the trained ANN model. The results of the predicted pressure drop values with the experimental values show a good agreement between the prediction and experimental results regarding to some statistical parameters, for example (AARD% = 4.70, MSE = 2.0 × 10^?5 and R² = 0.9994). The designed ANN model can estimate the pressure drop in the countercurrent flow rotating packed bed with unexpected phenomena for higher pressure drop in dry bed than in wet bed. Also, the designed ANN model has been able to predict the pressure drop in a wet bed with the good accuracy with experimental.     

The evaluation in time domain of mass transfer parameters from chromatographic peaks

Impulse response experiments have been carried out in packed beds in order to determine parameters as interstitial velocities, dispersion coefficients, internal diffusion coefficients and film transfer coefficients. The transfer function of the Kubín-Kucera model is solved in the Fourier domain. Two types of beds are considered, viz. long columns (about 6 m), packed with small particles and a short tube (1 m), packed with particles with a diameter in the order of the tube diameter. Moment analysis, Fourier analysis and fitting in the time domain are applied. It is shown that for Gaussian curves Fourier analysis has no advantage with respect to the method of moments. Moreover, for asymmetric curves a combination of Fourier analysis and time domain fitting is to be preferred. This is exemplified with a system where internal diffusion is the most important process. By applying Fourier analysis and fitting in the time domain, the interstitial velocity, axial dispersion coefficient and internal diffusion coefficient could be determined from a single experimental run with an accuracy better than 10 percent. For the experiments, performed in this work, the contribution of the film resistance compared with internal resistance proved to be negligible. The values obtained for the internal tortuosity factor and for the Péclet number agree with literature.     

Verification of a model for estimating the void fraction in a three-component randomly packed bed

The void fraction in a three-component randomly packed bed was calculated from the authors' model, and the calculated values were compared with published experimental data for spherical and irregularly shaped particles and with results from computer simulations. Results from the model were in good agreement with simulated and published experimental data.     

A plasticating model for single-screw extruders

By measuring the solid-bed transfer velocity, width and thickness under various conditions, die following results are obtained. As the result of melting, the solid bed decreases in width and thickness almost with the same rate, and the solid-bed transfer velocity is constant, while a melt layer exists between the solid bed and the screw root; also, when the phenomenon of dam-up occurs, caused by the combined effect of decreasing depth of the screw channel with tin insufficient decrease of solid-bed thickness, the transfer velocity increases proportional to the rate of decrease of channel depth. Consequently, the solid bed is considered to behave us loosely packed particles. A new plasticating model is developed by making the above results an assumption and adopting finite differential calculus with the Newton-Raphson method to obtain accurately the melting velocity, melt profile, and solid-bed temperature. Calculated values are in remarkably good agreement with the experimental values Solid-bed softening point, pressure, and screw torque are also successfully estimated.     

Experimental investigation of pressure drop in packed beds of irregular shaped wood particles

The knowledge of the pressure drop across a packed bed of irregular shaped wood particles is of great importance for achieving optimal control and maximum efficiency in many applications, such as wood drying, pyrolysis, gasification and combustion. In this work the effect of porosity, average particle size and main particle orientation on the pressure drop in a packed bed is investigated. To this end, particle size distributions and porosities are determined experimentally.Based on the experimental results obtained in this study, the form coefficient C and the permeability K of the Forcheimer equation are calculated for different packed beds. The Ergun equation requires an average equivalent particle diameter that is derived from the measured particle size distribution. This equivalent diameter and the corresponding bed porosity are used in the well known Ergun equation in order to derive adapted shape factors A and B.Since a change in bed porosity and particle size, caused by the degradation of the wood particles and gravity, can be expected in a reacting packed bed, a set of shape factors for use with the Ergun equation is determined that are independent of porosity and particle diameter and fit the experimental data very well.     

反应器内连续移热SO2转化系统(Ⅰ)深埋在颗粒填料中热管的传热性能

建立了气体横掠深埋在颗粒填料中的热管时的传热模型 ,并用数值方法进行求解 .此外 ,通过实验研究得到了传热的准数关联式 ,并对理论与实验结果进行了对比 ,为进一步进行SO₂ 连续换热的研究提供了基础