Modeling of multi-solid liquid fluidized bed

A dynamic model of the liquid fluidized bed containing two or more solid particle species of different size and density is presented. The model incorporates the particle mass transport mechanisms of the convection and the dispersion. The movement of the upper interface of the bed subject to a change in the liquid velocity is specified using the mass balance constraint. The particle velocities and dispersion coefficients are evaluated using correlations. The model is capable of describing the bed expansion, concentration profiles of the individual particle species, the bulk density profile, and the occurrence of layer inversion.     

DISPERSION AND FLUCTUATION OF FLUIDIZED PARTICLES IN A LIQUID-SOLID FLUIDIZED BED

Axial dispersion coefficient and fluctuating frequency of fluidized particles have been determined in a liquid-solid fluidized bed by resorting to the relaxation method from the histograms of pressure fluctuation in the bed. Dependence of the axial dispersion coefficient and fluctuating frequency of fluidized particles on the liquid flow rate and particle size, and further on the bed porosity has been discussed. The axial dispersion coefficient and fluctuating frequency of particles have attained their maxima with increasing liquid flow rate and bed porosity, and those values increase with an increase in particle size under fully fluidized concitions. It also has been found that the axial dispersion coefficient shows its maximum at the liquid flow rate where the fluctuating frequency of particles reaches its maximum point.     

Phase holdup and liquid dispersion in gas-liquid-solid circulating fluidized beds

Axial and radial profiles of gas and solids holdups have been studied in agas-liquid-solid circulating fluidized bed at 140mm i.d..Experimental results indicate that the axialand radial profiles of gas and solids holdups are more uniform than those in a conventionalfluidized bed.Axial and radial liquid dispersion coefficients in the gas-liquid-solid circulating fluidizedbed are investigated for the first time.It is found that axial and radial liquid dispersioncoefficients increases with increaes in gas velocity and solids holdup.The liquid velocity has littleinfluence on the axial liquid dispersion coefficient,but would adversely affect the redial liquiddispersion coefficient.It can be concluded that the gas-liquid-solid circulating fluidized bed hasadvantages such as better interphase contact and lower liquid dispersion along the axial directionover the expanded bed.     

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.     

Axial dispersion characteristics in three phase fluidized beds

Axial dispersion coefficients in three-phase fluidized beds have been measured in a 0.152 m-ID x 1.8 m high column by the two points measuring technique with the axially dispersed plug flow model. The effects of liquid velocity (0.05–0.13 m/s), gas velocity (0.02–0.16 m/s) and particle size (3-8 mm) on the axial dispersion coefficient at the different axial positions (0.06–0.46 m) in the bed have been determined. The axial dispersion coefficient increases with increasing gas velocity but it decreases with an increase in particle size and exhibits a maximum value with an increase in the axial position from the distributor. The axial dispersion coefficients in terms of the Peclet number have been correlated in terms of the ratio of fluid velocities, the ratio of the panicle size to column diameter, and the dimensionless axial position in the bed based on the isotropic turbulence theory.     

Does the fluid elasticity influence the dispersion in packed beds?

Reasons are given why the axial dispersion in a gas flowing through a packed bed may be influenced by the elasticity - or compressibility - of the fluid. To support this hypothesis, experiments have been done in a packed column at pressures from 0.13 to 2.0 MPa. The elasticity E of a gas is proportional to the pressure P and the compressibility to 1/P. The axial dispersion coefficients as determined were found to be a function of the pressure in the packed bed in the turbulent flow region of 3 < Re_p < 150 if the Bodenstein number is plotted as a function of the particle Reynolds number. This is shown to be an artifact. The pressure influence is eliminated, if Bo_{m, ax} is plotted versus the ratio of the kinetic forces over the elastic forces ?u²/E. Regrettably, Bo_{m, ax} seems to be independent of ?u²/E. For the moment we only can conclude that Bo_{m, ax} in the turbulent region is a unique function of the velocity of the gas which flows through the packed bed. Although the fact that a constant Bo value is obtained when plotted against ?u²/E, the experimental results are so intriguing we wanted to make them public already now. The experimental work proceeds.     

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.     

Axial gas dispersion in a fluidized bed of polyethylene particles

Gas mixing behavior was investigated in a residence time distribution experiment in a bubbling fluidized bed of 0.07 m ID and 0.80 m high. Linear low density polyethylene (LLDPE) particles having a mean diameter of 772 Μm and a particle size range of 200-1,500 Μm were employed as the bed material. The stimulus-response technique with CO₂ as a tracer gas was performed for the RTD study. The effects of gas velocity, aspect ratio (H₀/D) and scale-up on the axial gas dispersion were determined from the unsteady-state dispersion model, and the residence time distributions of gas in the fluidized bed were compared with the ideal reactors. It was found that axial dispersion depends on the gas velocity and aspect ratio of the bed. The dimensionless dispersion coefficient was correlated with Reynolds number and aspect ratio.     

Axial dispersion of gas in a circulating fluidized bed

An axial dispersion of gas in a circulating fluidized bed was investigated in a fluidized bed of 4.0 cm I.D. and 279 cm in height. The axial dispersion coefficient of gas was determined by the stimulus-response method of trace gas of CO₂. The employed particles were 0.069 mm and 0.147 mm silica-sand. The results showed that axial dispersion coefficients were increased with gas velocity and solid circulation rates as well as suspension density. The experimentally determined axial dispersion coefficients in this study were in the range of 1.0-3.5 m²/s.     

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。     

Study of the Fixed‐Bed Adsorption Behavior of Phenylalanine on Solvent Impregnated Resins,Part III

Abstract

The implementation of the SIR technique for the amino acid separation from diluted aqueous solutions in a fixed‐bed column is presented and a mathematical model for the prediction of the adosrption behavior is developed. Independently determined equilibrium and kinetic parameters are used for the calculation of the breakthrough curves. Fixed‐bed parameters, such as axial dispersion and bed porosity, are determined experimently and compared with correlations. Analysis of the Biot and Bodenstein number reveal that the mass transfer through the film liquid around the particles, as well as the axial dispersion in the column, could be neglected at the studied experimental conditions. A simplified mathematical model was found to give the best prediction to the experimental breakthrough curves over a wide range of feed concentrations and flow rates.     

Preparation of polyacrylamide-based supermacroporous monolithic cryogel beds under freezing-temperature variation conditions

Continuous supermacroporous monolithic cryogel is a novel sponge-like chromatographic adsorbent for bioseparation in downstream process and it is always prepared under a constant freezing-temperature condition. In this work, polyacrylamide-based supermacroporous monolithic cryogel beds in different inner diameter glass columns (I.D. 10, 16 and 26 mm) have been prepared by radical cryogenic copolymerization process under the condition of freezing-temperature variation. The matrix microstructure morphologies of these cryogels were analyzed by scanning electron microscopy (SEM) and the axial liquid dispersion characteristics in these cryogel beds were also analyzed by measuring the residence time distributions (RTDs). The formation of cryogel bed under the present situation has been considered as a coinstantaneous process of solvent crystal growth and polymeric monomer copolymerization. Effects of freezing-temperature variation route, cooling rate and redox initiator concentration on the cryogel microstructure and the liquid dispersion characteristics were investigated experimentally to reveal the cooperative mechanisms of these two processes on the formation of cryogel bed. The results showed that the cryogel pore-structures and the axial liquid dispersion coefficients in the cryogel beds depended strongly on the cooling condition, which controls the solvent crystallization process, and the redox initiator concentration, which influences the monomer polymerization.     

Dynamic analysis of a trickle bed reactor by moment technique

The performance of a trickle bed reactor is investigated by the moment technique. Residence time distributions of SO₂ tracer in both gas (Helium) and liquid (distilled water) effluents are used to predict zero reduced and first absolute moments and these values are compared with the derived theoretical expressions. Correlations are suggested for gas-liquid mass transfer coefficient, liquid hold up, and extent of axial mixing in liquid phase.True adsorption equilibrium constant of the system is estimated as 0.378 from liquid full bed experiments and contacting efficiency of the trickle bed reactor is found as 0.987.Effect of axial dispersion is not significant on gas-liquid mass transfer coefficient since absorption factor is small, but is found to be quite important on the true estimation of adsorption factor.     

Dynamic analysis of a fluidized bed reactor for sucrose inversion catalyzed by immobilized invertase

Axial mixing characteristics and performance of a liquid fluidized bed reactor for the sucrose inversion reaction, which was catalyzed by immobilized invertase was studied. The invertase enzyme was immobilized in polyacrylamide gel by the bead polymerization technique. Well-defined spherical gel particles of five different sizes (0.29–3.16 mm) were prepared. Efficiency of the immobilization technique, the optimum working conditions and the kinetic parameters were determined in a batch system. It is shown that as the particle size increases the rate of inversion first increases due to decrease of enzyme loss by leaching and then decreases because of diffusional limitations after a maixmum is reached. The performance of the fluidized bed reactor was investigated dynamically by introducing a step input of substrate at the inlet and analyzing the response curves. These experiments were performed at the optimum temperature (55°C) and using the optimum particle size (2.15 mm). The axial dispersion coefficient was found to increase from 0.45 to 1.26 cm²/s by changing the liquid velocity from 0.32 to 0.58 cm/s.     

Mass transfer in trickle-bed reactors at low reynolds number

Mass transfer rates were determined in a 3.4 cm i.d. trickle-bed reactor in the absence of reaction by absorption measurements and in presence of reaction. Gas flow rates were varied from 0-100 l/h and liquid flow rates from 0-1.5 l/h. The catalyst particles were crushed to an average diameter of 0.054 and 0.09 cm. Mass transfer coefficients remained unaffected by change in gas flow rate but increased with liquid rate. The data from absorption measurements were evaluated with predictions based upon plug-flow and axial dispersion model. Mass transfer coefficients were found greater in case of axial dispersion model than that of plug-flow model specially at low Reynolds number (Re₁ < 1).Hydrogenation of α-methylstyrene to cumene using a Pd/Al₂O₃ catalyst was taken as a model reaction. Intrinsic kinetic studies were made in a laboratory-stirred-autoclave. Mass transfer coefficients were determined using these intrinsic kinetic data from the process kinetic measurements in trickle-bed reactor. Mass transfer coefficients under reaction conditions were found to be considerably higher than those obtained by absorption measurements.Correlations were suggested for predicting mass transfer coefficients at low Reynolds number.The gas to liquid mass transfer coefficients for lower gas and liquid flow rates were determined in a laboratory trickle-bed reactor. The effect of axial dispersion on mass transfer was considered in order to evaluate the experimental data. Three correlations were formulated to calculate the mass transfer coefficients, which included the effect of liquid loading, particle size and the properties of the reacting substances. The gas flow rate influences the gas to liquid mass transfer only in the region of low gas velocities. In the additional investigations of gas to liquid mass transfer without reaction in trickle-bed reactor, the mass transfer coefficients were determined under reaction conditions and the intrinsic kinetics was studied in a laboratory scale stirred autoclave with suspended catalyst. A few correlations are formulated for the mass transfer coefficients. A comparison with the gas-liquid mass transfer coefficient obtained by absorption measurements showed considerable deviations, which were illustrated phenomenologically.     

Axial liquid dispersion in a liquid–solid circulating fluidized bed

Although axial liquid dispersion has been studied extensively in particulate fluidized beds, no data has been reported previously in a liquid–solid circulating fluidized bed (LSCFb). In this work, the axial liquid dispersions at various radial positions were measured in an LSCFB of 76 mm in diameter and 3.0 m in height using a dual conductivity probe. The results reveal that the axial liquid dispersion is affected not only by the operating conditions but by the radial positions as well. A local axial dispersion model is proposed to describe the axial liquid dispersion at various radial positions. The local axial liquid dispersion coefficients determined by the proposed model are greater at the axis than near the wall region of the riser. This nonuniformity of axial liquid dispersion is believed to be caused by the radial nonuniform distribution of liquid velocity, and bed voidage in the LSCFB can significantly affect the axial liquid dispersion.     

RTD studies in trickle bed reactors packed with porous particles

The residence time distribution (RTD) for liquid phase in a trickle bed reactor (TBR) has been experimentally studied for air-water system. Experiments were performed in a 15.2 cm diameter column using commerical alumina extrudates with D/d_p ratio equal to 75 to eliminate the radial flow differences. The range of liquid and gas flow rates covered was 3.76 < Re_L < 9.3 and 0 < Re_G < 2.92. The axial dispersion model was used to compute axial dispersion coefficient. The effect of liquid and gas flow rates on total liquid holdup and axial dispersion was investigated. The total liquid holdup has been correlated to liquid and gas flow rates.     

Modeling and simulation of a horizontal pulsed sieve-plate extraction column using axial dispersion model

In this research, the impact of pulsation intensity and phase flow rates on the volumetric overall mass transfer coefficients based on the continuous phase (K_oca) and the axial dispersion coefficients of phases in a horizontal pulsed sieve-plate column has been investigated using axial dispersion model. The toluene-acetone-water and butyl acetate-acetone-water systems with acetone transfer in both directions were used. In this study, the flow regime transition from pseudo-dispersion regime to emulsion regime has been characterized. Two new correlations have been proposed for prediction of K_oca and E_c.     

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.     

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.