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.     

In-situ monitoring of axial particle mixing in a rotating drum using bulk density measurements

A device is described for measuring changes in the local composition of particulate materials in a rotary mixer by continuously monitoring changes in the bulk density. The bulk density is measured using a small cup mounted to the mixer wall that fills with powder during rotation through the bed of particles in the lower part of the mixer. The mass of material in the cup is measured using a load cell during rotation of the cup above the free surface of the particles, and the cup empties before re-entering the particle bed. For mixing of materials with a difference in either particle density, or packing density, the localised bulk density measurement gives a good measure of mixing progress. The measurement device is demonstrated in a 1 m diameter horizontal rotating drum in which two materials are mixed along the axis of the drum. Measurements of the rate of dispersion along the axis are consistent with other work in inclined rotary kilns and can be fitted with a simple diffusion model for the axial mixing of the two species.     

大型液相色谱分离过程参数辨识新方法

本文提出大型液相色谱分离过程流体轴向扩散系数、吸附相平衡常数和总传质系数参数辨识模型,用惰性物为示踪剂扰动应答实验技术和色谱测量技术测定参数。结果表明:在轴向扩散中,涡流扩散占主导地位;轴向扩散系数随流体流速以及装填密度的增大而增大;相平衡常数比总传质系数有较高灵敏度;葡萄糖果糖的相平衡常数随温度的升高而降低,而总传质系数随流体流速和温度的增大而增大;得到理论流出曲线与实验流出曲线一致的结果。     

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.     

Study of dynamic multi-dimensional temperature and concentration distributions in liquid-sprayed fluidized beds

A physically based model was developed for heat and mass transfer processes in liquid-sprayed fluidized beds. Such fluidized beds are used for granulation, coating and agglomeration. The complex correlations of a number of microprocesses, spraying, wetting, drop deposition, heat transfer, drying and mass transfer were studied, and transient three-dimensional distributions of air humidity, air temperature, particle wetting efficiency, liquid film temperature, particle temperature, local liquid loading and local evaporation rate were calculated. For the evaluation of the model, the stationary spatial air temperature distributions were measured at a fluidized bed pilot plant of the institute. The fluidized bed of monodisperse wood- or glass beads was sprayed with clear water. Conclusions are drawn on the relevance of particle dispersion, spraying and drying to simulating temperature and concentrations distributions.     

Liquid Radial Dispersion in Liquid-solid Circulating Fluidized Beds with Viscous Liquid Medium

Liquid dispersion in the radial direction was investigated in the riser of a viscous liquid-solid fluidized bed 0.102 m in diameter and 3.5 m in height. Pressure fluctuations in the riser were also measured and analyzed to examine the behavior of fluidized particles. Effects of liquid velocity (0.15–0.45 m/s), solid circulation rate (2–8 kg/m²s), particle size (1–3 mm), and liquid viscosity (0.96–38 mPas) on pressure fluctuations and the liquid radial dispersion coefficient were determined. The infinite space model was employed to obtain the radial dispersion coefficient from the radial concentration profiles of the tracer. The pressure fluctuations were analyzed by means of autocorrelation coefficient as well as power spectral density function. The dominant frequency obtained from the autocorrelation coefficient or power spectral density function of pressure fluctuations decreases with increasing liquid viscosity or liquid velocity, but it increases with increasing particle size. The liquid radial dispersion coefficient decreases with increasing liquid velocity or viscosity, but it increases as the solid circulation rate or particle size increases. The liquid radial dispersion coefficient is related closely to the resultant behavior of fluidized particles. The radial dispersion coefficient has been well correlated with operating variables in terms of dimensionless groups.     

Solid-liquid mass transfer in a gas-liquid-solid fluidized bed

Solid-liquid mass transfer in co-current two- and three-phase fluidized beds of water, air and benzoic acid pellets is studied. An axial dispersion model is used to describe the liquid flow when evaluating the solid-liquid mass transfer. The axial concentration profile of benzoic acid in the liquid is compared to that obtained experimentally and is found to be accurate. Three-phase fluidized bed solid-liquid mass-transfer coefficients are higher than the corresponding two-phase bed coefficients. The mass-transfer coefficient increases with increasing gas rate and is independent of liquid rate over the entire range studied. The mass-transfer coefficient also appears to be dependent on particle size, but only at high gas rates. At low or zero gas rates, k is nearly independent of particle size. A generalized correlation is developed which accurately and conveniently predicts the mass transfer in both two- and three-phase fluidized beds. Comparison to the solid-liquid mass-transfer characteristics of slurry bubble columns is also performed.     

Liquid Radial Dispersion in Liquid-solid Circulating Fluidized Beds with Viscous Liquid Medium

Liquid dispersion in the radial direction was investigated in the riser of a viscous liquid-solid fluidized bed 0.102 m in diameter and 3.5 m in height. Pressure fluctuations in the riser were also measured and analyzed to examine the behavior of fluidized particles. Effects of liquid velocity (0.15-0.45 m/s), solid circulation rate (2-8 kg/m²s), particle size (1-3 mm), and liquid viscosity (0.96-38 mPas) on pressure fluctuations and the liquid radial dispersion coefficient were determined. The infinite space model was employed to obtain the radial dispersion coefficient from the radial concentration profiles of the tracer. The pressure fluctuations were analyzed by means of autocorrelation coefficient as well as power spectral density function. The dominant frequency obtained from the autocorrelation coefficient or power spectral density function of pressure fluctuations decreases with increasing liquid viscosity or liquid velocity, but it increases with increasing particle size. The liquid radial dispersion coefficient decreases with increasing liquid velocity or viscosity, but it increases as the solid circulation rate or particle size increases. The liquid radial dispersion coefficient is related closely to the resultant behavior of fluidized particles. The radial dispersion coefficient has been well correlated with operating variables in terms of dimensionless groups.     

Prediction of Layer‐Inversion Behavior of Down‐Flow Binary Solid‐Liquid Fluidized Beds

The layer‐inversion behavior of down‐flow binary solid‐liquid fluidized beds is predicted using the property‐averaging approach. The binary pair in this case consists of a larger solid species which is also heavier than its smaller counterpart, while both are lighter than the fluidizing medium. The model is based on using the generalized Richardson‐Zaki correlation for evaluation of the bed void fraction wherein mean values of particle properties are used. However, unlike the maximum bulk density condition for the conventional up‐flow binary solid fluidized bed, the model is based on a minimum bulk density condition for occurrence of layer inversion. This is due to the fact that the volume contraction phenomenon associated with the mixing of unequal solid species leads to a decrease in bulk density of the bed. Model predictions are also compared using the limited data available in the literature. Predictions are consistent with the observed mixing behavior.     

Transient heating and cooling of cocurrent three-phase fluidized beds

The thermal transient behaviour of three-phase fluidized beds have been investigated for a liquid viscosity ranging from 35 to 75 mPa · s. For the operating conditions used in this study, a 6 mm glass particle bed was found to have a thermal response similar to that of a fixed bed. The transient responses, which were not significantly affected by gas sparging, were, however, faster for heating than for cooling. This result has been analyzed from a model assuming liquid plug flow through stationary particles using combined free and forced convection correlations for heat transfer around the particles. Different correlations are then proposed to predict the contribution of natural convection to the liquid-to-particle heat transfer in heating and cooling modes. The effect of gas sparging was found to strongly affect The 2.0 mm particle bed responses but only moderately the 3.9 mm bed responses. These responses were analyzed using axial dispersion models for the liquid and solid phases. For the 3.9 mm particle bed, the axial dispersion coefficient of the solids, E_ZS, was found to be of the same order of magnitude as that of the liquid coefficient, E_ZL. However, the value of E_zs for the 2 mm particle bed was found to be five times that of E_ZL.     

THE IMPORTANCE OF AXIAL DISPERSION IN LIQUID-PHASE FIXED-BED ADSORPTION OPERATIONS

Methods are given for computing concentration profiles and breakthrough curves in fixed bed adsorbers for Freundlich and Langmuir equilibria, for cases of zero and non-zero axial dispersion. The methods are limited to situations in which either particle diffusion or external film diffusion is the dominant mass transfer process. By considering parameter values typical of liquid phase systems, it is shown that the values of parameters representing the ratios of mass transfer resistances to the axial dispersion coefficient serve as indicators of whether or not axial dispersion effects are important. Axial dispersion can be significant whenever the particle size and/or flow rate is substantially smaller than usual.     

Influence of high density particles in reduction of axial dispersion in liquid fluidized bed with residence time distribution curve studies

iquid phase RTD curves were investigated in classical fixed and fluidized bed regimes with high density particles. The effect of liquid velocity was studied on bed hydrodynamics. Using an impulse tracer injection technique in a column of 5 cm inner diameter and 1.2 m height, liquid RTD, mean residence time (MRT), axial dispersion coefficient (ADC) and vessel dispersion number (N _D ) were determined. ADC increases with liquid superficial velocity. It varied from 4.63 to 20.7 cm²/s for the particle Reynolds number of 43 to 279, respectively. The experimental results show that the hight density particles cause less ADC than the low density particles at an identical Reynolds number.     

A simple correlation for solids holdup in a gas-liquid-solid fluidized bed

A simple empirical model was established which allows solids holdup in a gas-liquid-solid fluidized bed containing large and dense particles to be readily predicted based on the equation of Richardson and Zaki (1954, Trans. Inst. Chem. Engrs32, 35) for liquid-solid fluidized bed systems. The approach is applicable both to monocompnent particle systems and to binary mixtures of particles. For a monocomponent system, a correlation for model parameters was proposed which is expressed as a function of particle diameter, particle density, bed diameter and liquid density. For a binary mixture of particles, the averaging and serial approaches were shown to predict the solids holdup equally well within the range of the gas and liquid velocities considered. Experiments were also performed using eight solid particles for the monocomponent system and five binary mixtures of particles differing in diameter and/or density for the mixture system to substantiate the model.     

Mixing processes in liquid fluidized beds

The degree of mixing in the liquid phase of bench scale fluidized beds of 14 cm diameter was measured by means of a tracer technique and the Peclet numbers for transversal, longitudinal and back-mixing were evaluated using a two-dimensional dispersion model. They were investigated as functions of liquid flow rate, mean particle diameter and bed height for narrow and broad range of particle diameters and were interconnected by the Taylor—Aris relation.     

蛋白质的膨胀床吸附过程穿透模型分析

引　言膨胀床吸附技术是近十几年来出现的一种新型生物分离模式 .该技术集细胞碎片清除、料液浓缩和蛋白质纯化等步骤于一身 ,大大提高了目标产物收率 ,降低了纯化时间和费用 .自 1993年Streamline系列膨胀床吸附介质和装置问世以来 ,国外已有不少利用膨胀床吸附技术提取蛋白质的报道[1,2 ] .已有研究表明 ,料液特性、吸附剂粒径等对膨胀床的流体力学特性和蛋白质在膨胀床内的吸附行为有着不同程度的影响[3～ 5] .考察这些影响因素有助于加深对膨胀床层析行为的理解 ,指导膨胀床层析的优化设计 .然而 ,由于膨胀床层析过程的复杂性 ,众多因素相互作用 ,某一参数的改变往往引起操作参数的系统性变化 ,因此实验条件下考察单一参数的改变对膨胀床层析过程的影响是不现实的[5,6 ] .　　　前期研究表明 ,对不同黏度的缓冲液 ,穿透模型能够较准确的预测蛋白质的穿透行为 .因此 ,本研究在前期研究的基础上[4 ,7] ,利用穿透模型分析了膨胀床吸附过程的质量传递和流体力学特1　穿透模型该模型假设[4 ,5] :①吸附剂颗粒为球形 ,有均一的尺寸和密度 ,离子交换基团均匀地分布在颗粒内部 ;②床内径向不存在浓度梯度 ;...     

CFD modeling of radial spreading of flow in trickle-bed reactors due to mechanical and capillary dispersion

CFD simulations of trickle-bed reactors are presented with radial spreading of the liquid due to mechanical and capillary dispersion. Simulations are performed with various particle sizes and the significance of the dispersion mechanisms at the industrially relevant particle size range is analyzed. The effect of the bed porosity distribution and particle size to the simulation results is also discussed. The choice of the radial porosity profile is found to have a significant impact to the simulation results, especially when the column to particle diameter ratio, D/d_p, is small, in which case the wall flow is important. The dependence of the standard deviation of porosity on the sample size is determined experimentally. Introducing just random variation of porosity to the model is found to describe inadequately the dispersive flow behavior. The presented hydrodynamic model with proper capillary and mechanical dispersion terms succeeds in capturing the features of the two independent physical phenomena. Separate models are presented for each dispersion mechanisms and it is shown that they both can have a significant contribution to the overall dispersion of liquid flowing through a packed bed. The hydrodynamic model is validated against the experimental dispersion profiles from Herskowitz and Smith [1978. Liquid distribution in trickle-bed reactors. A.I.Ch.E Journal 24, 739-454], Boyer et al. [2005. Study of liquid spreading from a point source in trickle-bed via gamma-ray tomography and CFD simulation. Chemical Engineering Science 60, 6279-6288] and Ravindra et al. [1997. Liquid flow texture in trickle-bed reactors: an experimental study. Industrial & Engineering Chemistry Research, 36, 5133-5145]. The extent of liquid dispersion predicted by the presented hydrodynamic model is in excellent agreement with the experiments.     

Numerical simulations of the spread of point-source liquid spills in inclined and rolling rectangular packed beds

Liquid spreading in thin rectangular vertical/inclined and oscillating porous media was simulated using a two-fluid dynamic model as a preliminary step in the design of fixed-bed reactors dedicated to marine applications. The model assessed the influence of capillary pressure and mechanical dispersion forces arising from the spatial inhomogeneity of point-source liquid injections in packed beds with different particle sizes, liquid and gas flow rates, liquid viscosity, static bed tilts, and rolling amplitudes and periods. In mildly static inclined beds, the lateral gravity force component and the capillary pressure force were the main factors affecting the liquid spreading. However, at considerable bed inclinations, the liquid phase accumulation in the lowermost regions of the packed bed tended to shrink the liquid spreading. Dynamic oscillatory evolutions of the liquid spills in the rolling bed enlarged the liquid spreading length as compared to the static vertical bed due to combined lateral liquid flow and increased liquid residence time.     

Liquid phase mixing in turbulent bed contactor

Axial mixing of the liquid phase in turbulent bed contactor (TBC) is studied through residence time distribution (RTD) experiments over a large range of variables such as flow rate of gas and liquid phases, static bed heights, diameter and density of particles and number of stages in presence of downcomer using air water system. Since all the liquid exits only through the downcomer, it enables the correct estimation of exit concentration of the tracer. The experimental RTD curves are satisfactorily compared with the axial dispersion model. The Peclet numbers evaluated by axial dispersion model and the Peclet numbers reported in the literature are used to propose a unified correlation in terms of operating and geometric parameters. Correlation is also developed for predicting the axial dispersion coefficient. It was observed in the present study that almost plug flow conditions can be achieved in multistage TBC.     

Hydrodynamics and mass transfer in carbon-nanofiber/graphite-felt composite under two phase flow conditions

A carbon nanofiber (CNF)/graphite felt composite was synthesized by growing CNFs on the surface of graphite fibers and was used as the packing of a fixed bed reactor under two phase flow conditions. The pressure drop, axial dispersion and mass transfer in the liquid were studied by experiment and by piston dispersion exchange (PDE) model. It was shown that the pressure drop and total liquid up could be predicted by the slit model in an acceptable accuracy. The axial dispersion in the liquid phase in the composite and the mass transfer between the dynamic and static liquid are higher than in the packed bed of solid particles owing to the porous and fluffy CNF layer on the carbon felt fiber.