MODEL FOR PREDICTING THE LATERAL DISPERSION COEFFICIENT OF SOLIDS IN GAS-SOLIDS FLUIDIZED BEDS

The lateral mixing of solids in a gas-solids fluidized bed is very complicated.It can be caused by:(a)bubble movement through the bed,(b)bubble burst at the bed surface,and(c)gross particle circulation in thebed.However,experiments show that the major factors effected the lateral mixing of solids are the bubblemovement through the bed and the bubble burst at the bed surface.Thus a model with two mixing re-gions,i.e.mixing in bubble rising region and mixing in bubble breaking region,was proposed.Based on thismodel,an equation for predicting the lateral dispersion coefficient of solids in gas-solids fluidized beds wasderived without any adjustable parameter.The calculated values by this equation are well comparable withthe observed data including the present work and the other investigations.     

Fluidization Characteristics in Micro‐Fluidized Beds of Various Inner Diameters

The fluidization characteristics of quartz sand and fluid catalytic crack (FCC) catalyst particles in six micro‐fluidized beds with inner diameters of 4.3, 5.5, 10.5, 15.5, 20.5, and 25.5 mm were investigated. The effects of bed diameter (D_t), static bed height (H_s), particles and gas properties on the pressure drop and minimum fluidization velocity (u_mf) were examined. The results show that the theoretical pressure drops of micro‐fluidized beds deviated from the experimental values under different particles and gas properties. The possible reason is due to an increase in bed voidage under smaller bed diameters. The equations for conventional fluidized beds did not fit for micro‐fluidized beds. u_mf increased with decreasing D_t. When the ratio of H_s to D_t ranged from 1:1 to 3:1, u_mf was characterized by a linear equation with H_s, while the slope of the equation u_mf versus H_s decreased with increasing D_t. In this paper, D_t/d_p and H_s/d_p were defined as dimensionless variables and a new equation was developed to predict u_mf in micro‐fluidized beds under the present experimental conditions.     

Electrochemical wall mass transfer in liquid particulate systems

Ionic mass transfer coefficients between the wall of a 2.081 inch tube and liquid fluidized beds of lead glass, soda glass and lucite spheres have been measured using the diffusion-controlled reduction of ferricyanide ion at a nickel cathode for porosities 0.90 to 0.45 and Schmidt numbers 580 to 2100. The developed fluidization mass transfer coefficient for 41 < D_T/d_p < 105 were correlated by i_D E = 0.274 Re_H^?0.38 for 10 < Re_H <1600 and by J_D E = 0.455 Re_H^?0.44 for 16.7 < D_T/d_p < 27 and 50 < Re_H < 3500. Re_H is the hydraulic Reynolds number = d_H up/μ_E and d_H is D_T E/[1 + (3/2) ((1–E)) (D_T/d_p)). The distinct effect of D_T/d_p ratio is attributed to wall effects and the non-particulate behaviour of the fluidized bed for D_T/d_p < 27. Measurements in the open pipe and packed bed agreed very well with literature values. The packed bed gives highest mass transfer coefficients at given Re_H.     

Ion exchange with irreversible reaction in deep fluidized beds

The exchange of CI^? ion between dilute aqueous solutions of hydrochloric acid and the ion exchange resin IRA-425 in fluidized beds was studied in a laboratory size column. Analysis of the experimental data showed that axial mixing of particles in deep beds was incomplete and also that packed and fluidized bed break-through curves were similar. A model is proposed describing the bed as a series of mixing stages for solids with axially dispersed flow of liquid. Data are presented in support of such a concept. An empirical method is proposed for prediction of the break-through curves at various operating conditions, requiring only a very limited amount of experimentation.     

Evaluation of wall boundary condition parameters for gas–solids fluidized bed simulations

Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas–solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas–solids flow. A model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (Li and Benyahia, AIChE J. 2012;58:2058–2068) is implemented in the open‐source CFD code‐MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial‐slip boundary conditions for the solids phase. Through a series of two‐dimensional numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient. Published 2013 American Institute of Chemical Engineers AIChE J, 59: 3624–3632, 2013     

Solids mixing behavior in a nano-agglomerate fluidized bed

The nano-particles mixing behavior in a nano-agglomerate fluidized bed (NAFB) using R972, a kind of nano-SiO₂ powder, was investigated by the nano-particle coated phosphors tracer method. The axial and radial solids dispersion coefficients in this system were two orders of magnitude lower than those in fluid catalytic cracking (FCC) catalyst systems. The axial solids dispersion coefficient increased with increasing superficial gas velocities, and ranged between 9.1 × 10^− 4 and 2.6 × 10^− 3 m²/s. There was a step increase in the axial solids dispersion coefficient between the particulate fluidization regime and bubbling and turbulent fluidization regimes. As the superficial gas velocity increased, the radial solids dispersion coefficient increased gradually, from 1.2 × 10^− 4 to 4.5 × 10^− 4 m²/s. The much smaller D_a and D_r, compared to regular fluidized systems, is mainly due to the reduced density difference between the fluidized particles and fluidizing medium. To validate this, the solids dispersion coefficients in the NABF were compared with literature values for liquid-solid particulate systems in the particulate fluidization regime and FCC systems in the bubbling and turbulent fluidization regimes. The density difference between the fluidized particles and fluidizing medium and kinetic viscosity of the fluidizing medium, and other hydrodynamic factors like the superficial velocity of the fluidizing medium and the average diameters of the fluidized particles, were the key factors in the solids mixing in the fluidized beds. Empirical correlations are given to describe the results.     

Solids mixing in a down-flow circulating fluidized bed of 0.418-m in diameter

The axial and lateral solids mixing in a down-flow circulating fluidized bed of 0.418-m diameter was investigated by a pneumatic injection phosphor tracer technique (PIPTT). The axial and lateral solids dispersion were determined by measuring the solids RTD at same axial but different lateral positions using point sources for tracer injection. A two-dimensional dispersion model described the measured RTD curves satisfactorily. The results were compared to those obtained in the small scale downers and the scale-up effect was investigated. The axial solids Peclet number Pe_a is around 110 and invariable with changing U_g, G_s and ?_s, while the lateral solids Peclet number Pe_r is linearly increasing with ?_s. And Pe_r is found to decrease with the square root of inner diameter (ID) in comparison with the results obtained in small ID downers. Correlation of Pe_r, Pe_r = (15 + 70.7 ?_s)D^− 0.5, is proposed.     

Convective solids transport in large diameter gas fluidized beds

It is demonstrated that the convective solids transport occurring in large diameter gas fluidized beds can be predicted quantitatively on the basis of measured properties of the bubble phase. Based on the fundamental findings of Rowe and co-workers [5], who have shown the solids mixing in gas fluidized beds for particle diameters greater than 100 μm to be caused solely by the action of rising bubbles, an equation has been derive from extensive measurements of the bubble development in a 1 m diam. fluidized bed of quartz sand which relates the convective solids mass flow due to solids transport in the bubble wakes to easily determinable parameters. The predictions of this relationship are found to bein good agreement with direct measurements of the convective solids transport carried out by Schmalfeld [21] on a pilot scale in a semicylindrical bed of 0.8 m diam.     

Experimental methods in chemical engineering: Reactors—fluidized beds

Industry relies on fluidized beds to synthesize chemicals (acrylonitrile, maleic anhydride, titanium dioxide, vinyl chloride), combust coal, dry powders, and treat waste. Fluidized bed folklore declares that they are hard to scale‐up and the gas phase is backmixed. Commercial failures that disregard standard design criteria around powder management, gas/solids injection, and mixing reinforce this belief. However, engineers select fluidized beds for processes that are impractical with conventional technologies to achieve economies of scale for highly exothermic, endothermic, or explosive reactions, for catalysts that deactivate in seconds (or minutes), and for chemistry that requires multiple dosing cycles. Failures are more frequent for these challenging applications. For this reason, researchers study reaction kinetics in fixed beds despite internal mass transfer limitations and axial and radial temperature and concentration gradients. Fluidized bed hydrodynamics vary with powder properties (particle diameter, size distribution, density, sphericity), operating conditions (gas density, viscosity, temperature, pressure), reactor geometry (diameter, height, mass, grid geometry). The minimum fluidization velocity (U_mf) is a property that identifies the transition from the fixed bed regime to the fluidized bed regime and equals the gas velocity at which the upward drag force equals the weight of the powder. At the experimental scale, fluidized beds operate isothermally, solids are completely backmixed, and the gas phase is close to plug flow (). Here, we describe the relationship between powder properties and fluidization quality, list experimental techniques, describe recent applications, and gas phase hydrodynamics and uncertainties.     

SORPTION DRYING OF SOYBEAN SEEDS WITH SILICA GEL. I. HYDRODYNAMICS OF A FLUIDIZED BED DRYER

ABSTRACT

Fluidization technology has been employed to mix soybean seeds and silica gel particles in aim of sorption drying of particulate agricultural products. The characteristic fluidization velocities, mixing mechanisms and fluidization quality have been studied in a 180 mm I.D. fluidized bed. Two sizes of silica gel particles (SG2 and SG3) were selected, with the mass fractions in the range of 0.33–0.75 to form a static bed with height from 100 to 280 mm (H/D = 0.56–1.56). The results show that the dispersion rate of soybean seeds is increased with addition of either SG2 or SG3, and that the frequency and the span of pressure fluctuations within the bed are increased. It is inferred that the gas–solids contacting is improved with addition of small particles in the bed of large particles. In addition, for practical design and operation of such a fluidized bed of binary mixtures, empirical correlations for characteristic fluidization velocities were developed with a wide application.     

Dynamics of segregation and fluidization of binary mixtures in a cylindrical fluidized bed

Dynamics of segregation and fluidization of unary particles and binary mixtures in a cylindrical fluidized bed is investigated using temporally– and spatially–resolved measurements of solids volume fraction (α_s) performed using Electrical Capacitance Tomography (ECT). Through the comparison with high-speed imaging, we have shown that ECT can be used to measure the segregation behavior in cylindrical fluidized beds quantitatively. ECT measurements have been used further to quantify the effects of mixture composition, particle–diameter ratio, and superficial gas velocity on the bed segregation behavior. Dynamics of fluidization behavior is characterized using the time–evolution of local α_s fluctuations, corresponding frequency distribution, and bubble size distribution. Further, a relation between the measured variance of α_s fluctuations at different radial locations and corresponding flow structures under different fluidization conditions is established. The present work helps to understand dynamics of segregation and fluidization of binary mixtures and to provide a database for validation of Eulerian multifluid CFD models.     

Radial Gas Mixing in a Fluidized Bed with a Multi‐Horizontal Nozzle Distributor using Response Surface Methodology

The gas mixing in the radial direction within a fluidized bed equipped with a multi‐horizontal nozzle distributor was studied using response surface methodology (RSM), which enables the examination of parameters with a moderate number of experiments. All experiments were carried out in a circular fluidized bed of 0.29 m I.D. cold model fluidized bed. The distributor is placed beside twenty‐two horizontal nozzles that are arranged in three concentric circles with all existing discharge directed clockwise. The tracer gas (CO₂) was discharged into the bed as a tracer gas and the analysis was performed with a gas chromatograph. In order to compare the different internal circulations, the tracer gas was discharged in the center area or annular area of the bed. In RSM, the static bed height, superficial velocity and the open area ratio of the distributor are chosen as the research variables, and the standard deviation of the time averaged radial tracer concentration is used as the objection function. A mathematical model for the gas mixing as a function of the operating parameters was empirically proposed. The results show that the standard deviation of time averaged radial tracer concentration is well correlated with the operating and geometry parameters, (U – U_mf)/U_mf, H_s/D and ψ_d, and that the tracer gas injected to the center position has a better dispersion than when injected to the annular position. This model can be used for optimizing the design of fluidized bed reactors at a required performance level.     

Fictitious particle method: A numerical model for flows including dense solids with large size difference

Large solids coexist with small solids in a number of dense gas‐solid flow applications such as fluidized beds and pneumatic conveyers. A new numerical model that is based on the discrete element method–computational fluid dynamics mesoscopic model and extended by introducing an idea appearing in volume penalization method is presented. In computational cells including large and small solids, the amount of momentum exchange between the fluid and the solids is estimated by assuming that a large solid consist of small, dense fictitious particles. We describe the proposed model in detail and show the optimal model parameters found through a number of parameter‐dependency studies. Validation study is performed for the motion of a large sphere in a bubbling fluidized bed and good agreements are confirmed for floating and sinking motions of the sphere between the present model and the experiment. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1606–1620, 2014     

采用切圆射流及旋流布风板改进鼓泡床行为

用侧面切圆射流和旋流布风板造成了鼓泡流化床内气固流动的新流型。本文将改进鼓泡床与普通鼓泡床进行比较,在同样的空气量下,气泡尺寸减小,床面波动降低,加强了固体颗粒的横向混合,延长了颗粒床内停留时间。还研究了侧面切圆射流占总风量的份额、射流速度、喷入位置及角度对流化质量的影响。     

Bibliography of Literature on Fundamentals and Applications of Vibration in Particle Processing

This article describes the results of calculations of specific energy consumption, E _s , performed on a well-mixed fluidized bed dryer simulator. Exhaust air temperature–humidity loci required to yield a specified outlet moisture content were also determined. Most of the calculations related to solids whose drying rate was gas-film controlled. Six model drying curves were employed to examine the effects of drying rate and hygroscopicity in addition to the normal operating parameters. The results indicated that E _s was highest for slow-drying hygroscopic solids and lowest for fast-drying, non-hygroscopic solids. Specific energy consumption increased with decreasing bed temperature and outlet moisture content and with increasing heat loss but was independent of solids loading and airflow rate. For both the aforementioned solids and a much slower drying material (wheat), there was close agreement between the zero heat loss data and a single theoretical curve approximating the performance of an ideal adiabatic dryer. Distinct differences between the behavior of well-mixed and plug flow fluidized bed dryers are reported.     

Oxidative dehydrogenation of butenes over Bi‐Mo and Mo‐V based catalysts in a two‐zone fluidized bed reactor

The oxidative dehydrogenation of a 1‐butene/trans‐butene (1:1) mixture to 1,3‐butadiene was carried out in a two‐zone fluidized bed reactor using a Mo‐V‐MgO and a γ‐Bi₂MoO₆ catalyst. The significant operating conditions temperature, oxygen/butene molar ratio, butene inlet height, and flow velocity were varied to gain high 1,3‐butadiene selectivity and yield. Furthermore, axial concentration profiles were measured inside the fluidized bed to gain insight into the reaction network in the two zones. For optimized conditions and with a suitable catalyst, the two‐zone fluidized bed reactor makes catalyst regeneration and catalytic reaction possible in a single vessel. In the lower part of the fluidized bed, the oxidation of coke deposits on the catalyst as well as the filling of oxygen vacancies in the lattice can occur. The oxidative dehydrogenation reaction takes place in the upper zone. Thorough particle mixing inside fluidized beds causes permanent particle exchange between both zones. © 2016 American Institute of Chemical Engineers AIChE J, 63: 43–50, 2017     

Heat transfer in aggregative and particulate liquid-fluidized beds

Wall-to-bed heat transfer in liquid fluidized beds, particulately and aggregatively fluidized, was studied. Glass particles fluidized with water gave particulate fluidization and lead particles with water gave aggregative fluidization. Local heat transfer coefficients and bed temperature profiles were measured. Heat transfer coefficients were found to be strongly dependent on particle size and porosity and increased with increasing particle size, but were independent of the height of the heater surface from the grid. Any variations in local bed properties, such as porosity do not affect wall-to-bed heat transfer. The heat transfer coefficients show a characteristic, maximum at porosities near 0.7 for both systems. Bed temperature profiles deviate considerably from open-pipe values.A two-resistance model for the heat transfer resistance agrees well with the data. Bed resistance is modeled by a radial eddy diffusivity, which indicates the mixing effectiveness in the core of the bed. Glass beds (particulate) show a maximum mixing effectiveness at porosities near 0.7 and the mixing effectiveness increases with particle diameter. Lead beds (aggregative) show two maxima in mixing effectiveness, the first between porosities of 0.5 and 0.6, and the second between porosities of 0.7 and 0.8. Mixing is greatest at an intermediate particle size in the case of lead beds. In both systems the fraction of the total resistance in the bed core increases as porosity decreases towards packed bed conditions.     

Hydrodynamics of an inverse liquid–solid circulating conventional fluidized bed

An inverse liquid–solid circulating conventional fluidized bed (I-CCFB) is realized by injecting particles from the top of a conventional liquid–solid fluidized bed (0.076 m ID and 5.4 m height) that is operated in a newly developed circulating conventional fluidization regime located between the conventional and circulating fluidization regimes. The I-CCFB can achieve a higher solids holdup compared to both conventional and circulating liquid–solid fluidized beds. A new parameter, the bed intensification factor, is defined to quantify the increased solids holdup observed with external solids circulation. The Richardson–Zaki equation is shown to be applicable to the I-CCFB regime and can be used to correlate the slip velocity and solids holdup, both of which increase with the solids circulation rate. A new flow regime map is presented, including the I-CCFB and a variety of other liquid–solid fluidized beds.     

Measuring and modelling lateral solid mixing in a three-dimensional batch gas—solid fluidized bed reactor

A 0.27 m diameter fluidized bed reactor has been designed to allow experimental measurement of the axial and radial mixing behaviour of the solids. A unique method has been developed which permits the continuous determination of solid tracer concentration with time at different radial and axial positions within the fluidized bed. Solids mixing has been described by a model in which vertical mixing is instantaneous and lateral mixing occurs by dispersion. The lateral solids dispersion coefficients have been evaluated at various operating conditions from the experimental results of tracer concentration versus time. Based on the results, a modification of an existing correlation is proposed.     

Taylor dispersion in fluidized channel flow

Taylor dispersion coefficients (D_t) were determined as a function of flow velocity ?u for flow of fluidized solids in a rectangular-sectioned channel under various conditions. Log—log plots of (D_t ?l D) versus ?u were found to be linear, as is the case for liquids in both turbulent and laminar flow. The experimental plots were compared with calculated values, based on solutions of the differential equations governing transport and mixing in the wake and emulsion phases, respectively. The calculated values were found to be reasonably consistent with the experimental data. It was concluded that mixing due to spreading of bubble wakes at the surface of the fluidized solids was a relatively unimportant lateral mixing mechanism.