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.     

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.     

A study of local liquid/solid mass transfer in packed beds under trickling and induced pulsing flow

Induced pulsing flow (by cyclic liquid feeding) in packed beds, operated in the trickling flow regime, is studied as a method of overall improvement of catalytic reactor operation. In this paper results are reported of experiments aimed at determining local and global liquid/solid mass transfer rates, mainly for the so-called fast mode of ON-OFF periodic liquid feeding, with frequencies of order 0.1 Hz. Such mass transfer data for the fast mode of induced pulsing are not available in the literature. Uniform 6 mm glass spheres and alumina cylindrical extrudates, of 1.5 mm diameter and a narrow distribution of lengths, are employed in the tests. For completeness, results are also reported for single-phase (liquid) and trickling flow through the same packed beds. A well-known electrochemical technique is employed to measure instantaneous local mass transfer coefficients by means of quite a few probes distributed throughout the bed. The hydrodynamic characteristics under the above conditions, reported in companion papers, are helpful in interpreting the new mass transfer data.There is a wide spread of the time-averaged local mass transfer rates, in all cases tested, apparently due to packing and flow non-uniformities. This spread is much smaller in the case of packed uniform spheres. In general, the benefits of cyclic liquid feeding are more evident in the packed bed of spheres than in that of cylindrical extrudates; for instance, with increasing mean liquid rate, induced pulsing tends to reduce the spread of local mass transfer coefficients, which suggests that more uniform fluids distribution is promoted. The imposed liquid pulses are reflected in the observed periodic variation of local mass transfer coefficients; the latter appear to decay along the bed in the same manner as the liquid pulses. Other trends of local mass transfer rates are identified and discussed in relation to measured variation of liquid holdup, under the same conditions. For packed spheres, the measured global mass transfer rates are in fair agreement with literature correlations obtained for the trickling flow regime, unlike the case of packed extrudates where significant deviation is observed.     

循环流化床气固传质实验研究

This study is devoted to gas-solid mass transfer behavior in heterogeneous two-phase flow. Experiments were carried out in a cold circulating fluidized bed of 3.0m in height and 72mm in diameter with naphthalene particles. Axial and radial distributions of sublimated naphthalene concentration in air were measured with an online concentration monitoring system HP GC-MS. Mass transfer coefficients were obtained under various operating condition, showing that heterogeneous flow structure strongly influences the axial and radial profiles of mass transfer coefficients. In the bottom dense region, mass transfer rate is high due to intensive dynamic behavior and higher relative slip velocity between gas and clusters. In the middle transition region and the upper diluter region, as a result of low mass transfer driving force and the influence of flow structure, mass transfer rate distribution becomes non-uniform. In conclusion, among the operating parameters influencing mass transfer coefficients, the superficial gas velocity is the most important factor and the solid circulation rate should be also taken into account.     

Gas‐Liquid Mass Transfer in a Bench‐Scale Trickle Bed Reactor used for Benzene Hydrogenation

The gas‐liquid mass transfer coefficients (MTCs) of a trickle bed reactor used for the study of benzene hydrogenation were investigated. The Ni/Al₂O₃ catalyst bed was diluted with a coarse‐grained inert carborundum (SiC) particle catalyst. Gas‐liquid mass transfer coefficients were estimated by using a heterogeneous model for reactor simulation, incorporating reaction kinetics, vapor‐liquid equilibrium, and catalyst particle internal mass transfer apart from gas‐liquid interface mass transfer. The effects of liquid axial dispersion and the catalyst wetting efficiency are shown to be negligible. Partial external mass transfer coefficients are correlated with gas superficial velocity, and comparison between them and those obtained from experiments conducted on a bed diluted with fine particles is also presented. On both sides of the gas‐liquid interface the hydrogen mass transfer coefficient is higher than the corresponding benzene one and both increase significantly with gas velocity. The gas‐side mass transfer limitations appear to be higher in the case of dilution with fine particles. On the liquid side, the mass transfer resistances are higher in the case of dilution with coarse inerts for gas velocities up to 3 · 10^–2 cm/sec, while for higher gas velocities this was inversed and higher mass transfer limitations were obtained for the beds diluted with fine inerts.     

Convective Heat and Mass Transfer Modeling in Gas‐Fluidized Beds

This review examines selected mechanistic and empirical models reported in the literature to predict convective heat and mass transfer coefficients in gas‐fluidized beds. The role of hydrodynamics in heat and mass transfer is briefly outlined before embarking on the modeling approaches. Both bed to wall and interphase heat transfer, are considered. In bed to wall heat transfer, the main focus of the review is the modeling of particle convective components, based on surface renewal. The concepts of transient and local heat transfer models are also discussed briefly. In the case of mass transfer, only interphase transfer is considered. Emphasis is placed on models based on combustion where mass transfer is seen to occur from a few active particles contained in a fluidized bed of inert particles.     

催化蒸馏合成乙二醇乙醚的过程模拟

修正了非平衡级速率模型,使之能适用于催化蒸馏过程的模拟.此催化蒸馏塔的精馏段和提馏段为一般的填料塔结构,而反应段为CR＆L公司提出的特定结构的催化剂填充层.采用专门测定此特殊结构的催化剂填充层的气膜和液膜传质系数关联式来计算反应段中的传质速率,用Onda的关联式计算精馏段和提馏段填充层中的传质速率.结合在NKC-01分子筛催化剂上环氧乙烷与乙醇反应的动力学方程式,采用Newton-Raphson技术完成了催化蒸馏合成乙二醇乙醚过程的模拟,结果是令人满意的.     

Mass transfer between a drop or gas bubble and an isotropic turbulent flow

Theoretical formulas have been set up for calculating the coefficients of mass transfer between a drop or gas bubble and an isotropic turbulent flow for various Peclet and Reynolds numbers. The mass transfer coefficients depend mainly on the characteristics of the isotropic turbulent flow (energy dissipation, turbulence length scale, turbulence time scale), on the properties of the medium, and on the particle size. A number of practical formulas for calculating the mass transfer coefficients for turbulent flow are presented. The calculated data are compared with experimental data.     

The Soret and Dufour Effects in Non-thermal Equilibrium Packed Beds with Forced Convection and Endothermic Reactions

To study the influence of the Soret and Dufour effects on the reactive characteristics of a porous packed bed with endothermic reactions and forced convection, a two-dimensional mathematical model cons...     

非均匀气固两相系统中多尺度传质模型

建立了适用于气固循环流化床的多尺度传质模型 .从过程与尺度的角度出发 ,将非均匀气固两相流中的传质过程分解为静态与动态的过程 ,并将前者分解为稀相内、密相内以及稀密相间 3个尺度下的传质 ;在用多尺度能量最小 (EMMS)模型求解已知物系性质和操作条件的非均匀气固两相流体动力学参数的基础上 ,借助于前人的研究结果 ,利用相对滑移速度、空隙率等参数求解传质系数 ,求得轴向的浓度场分布 ,并讨论非均匀两相流动结构对传质效率的影响     

NUMERICAL STUDY OF THE EFFECT OF THE WALL ON THE DISTRIBUTION OF ISOTHERMAL TWO-PHASE FLOW IN THE BED OF A HYDRODESULFURIZATION REACTOR

Numerical simulations of the isothermal two-phase flow distribution in the packed bed of a reactor used for fuel hydrodesulfurization using the commercial software Fluent are reported. As a first step, the heat and mass transfer as well as the chemical reactions are not taken into account. The reactor considered has, above the bed, a distribution tray equipped with chimneys. A Eulerian three-phase model that considers the catalyst particles as a granular static phase was used following the Holub single-slit model for particle fluid interaction to compute the liquid-solid and gas-solid drag coefficients. Physical properties of the fluids are assumed to be constant. In the present study, the tendency of the liquid to move towards the wall of the reactor was studied in a bed 11 m in depth. The simulations predict that there is no suction effect on the flow caused by the wall. As the two-phase flow moves downward through the bed, a slow radial liquid spreading takes place. However, flow distribution is not completely uniform, at least at a distance of 11 m from the inlet.     

Mass transfer variation within a packed bed and its relation to liquid distribution

The limiting current method is applied to characterize the local mass transfer in the axial, radial and angular directions throughout a packed bed of Pall rings. This is expressed in terms of the particle-to-fluid mass transfer coefficient of ferricyanide ions obtained from the limiting currents measured during its reduction to ferrocyanide at different locations in the bed. Particular focus is placed on the variability of the mass transfer coefficient with position in terms of the quantity MT_VAR, equivalent to the normalized deviation of the function Sh/Sc^0.33. The results confirm those reported by other researchers using more traditional liquid collection and tracer methods. Mass transfer coefficients throughout the bed closely follow normal distributions for the range of Re values investigated. When a multipoint distributor is used, MT_VAR is already low at the lowest flow rate (Re=95) considered and remains unchanged with any further increase in flow rate. In the case of a single-point distributor, on the other hand, MT_VAR decreases with increasing flow rate, but always remains significantly higher than that observed with the multipoint distributor. Moreover, the MT_VAR value depends on whether irrigated or full flow conditions prevail and on the cross-sectional area of the sampling electrodes, suggesting that local mass transfer variations are caused by local liquid velocity variations once the Pall rings are sufficiently wetted.     

Evaluation of Mass Transfer Coefficients in Biotrickling Filters: Experimental Determination and Comparison to Correlations

Overall mass transfer coefficients (K_Ga and K_La) were determined experimentally for four different‐nature packing materials used in gas‐phase biotrickling filters. A simple methodology based on overall mass balances and following a standard procedure allowed to calculate the mass transfer coefficients under different operating conditions corresponding to usual biotrickling filtration situations. Results showed an increase of mass transfer resistance when increasing the empty bed residence time (EBRT) of the reactor for all packing materials. Experimental results were fitted to existing and well‐accepted correlations used in conventional biofilter or biotrickling filter modeling. The comparison of experimental and theoretical data showed huge discrepancies. Simple correlations for the experimental data obtained in this study were also suggested.     

Mass transfer in tube bundles with liquid fluidized particles

Experimental studies were conducted of overall and local tube-to-liquid mass transfer for bundles of horizontal tubes in staggered and in-line arrays in a liquid fluidized bed. The mass transfer coefficients are compared with those obtained using a fixed packing and those obtained without particles at the shell-side of the bundle.     

液固磁稳定床中固含率分布与液相返混特性

固含率分布和液相返混系数是液固磁稳定反应器放大与优化所必需的基础数据。采用床层膨胀高度法、光电法及瞬态点源示踪技术,研究了以SRNA-4催化剂为固相的液固磁稳定床中固含率分布和液相返混特性。试验结果表明,固含率轴向分布基本均匀,径向为“扁-陡曲线”分布。固含率随磁场强度和颗粒尺寸的增大而增大,随液体粘度和空塔液速的增大而减小。轴向液相返混系数随磁场强度和液体粘度的增大而减小,随空塔液速和颗粒尺寸的增大而增大。回归得到了固含率和轴向普朗特准数的关联式,预测值与试验值吻合良好。     

喷雾塔内雾粒粒径对传质行为的影响

本文研究了喷雾塔内的两相混合及雾粒粒径对传质行为的影响.建立了描述粒子群在塔内运动和传质规律的数学模型,这一模型既考虑了两相的返混,也考虑了粒径的影响,即所谓粒子群的向前混合.通过稳态浓度剖面法求解模型方程,得到了两相的返混准数Pe_x、Pe_y及粒子的真空传质系数K_(oco)用线性最小二乘法关联得到计算这些参数的经验方程.这些关联式可用于计算塔内的真实浓度剖面,并能适用于不同结构和尺寸的喷嘴.     

Estimation of liquid phase mixing due to solids in a turbulent bed contactor

The mixing in two-phase gas-liquid and three-phase gas-liquid-solid system (turbulent bed contactor) is evaluated through residence time distribution (RTD) studies in terms of Peclet number. RTD experiments are conducted for various gas and liquid velocities, and number of stages for two- and three-phase systems. Since the mean residence time is very short in both the systems, a mixed flow tank with exponential decay RTD is used in series. After deconvolution, the RTD of the system is obtained. The experimental RTD curves are satisfactorily compared with the axial dispersion model and Peclet numbers are evaluated for all the experiments. The axial dispersion coefficients are calculated from Peclet numbers. With this study, it is thought that liquid phase mixing may be controlled by changing the quantity of solid particles in the bed.     

固--固换热器传热特性研究

在自制的固—固套管式换热器中,以催化裂化催化剂为原料,对系统的循环特性、传热系数进行了实验研究。分析了床层密度、提升风量、床层温度、催化剂粒径等因素对传热过程的影响。实验结果表明,随着提升风量增加,表观气速增大,床层密度下降,传热系数下降;提高床层温度,减小催化剂的粒径,传热系数增加。