Continuous ion exchange in fluidized beds

A mathematical model has been developed for prediction of the performance of a continuous ion-exchange column, comprising a series of fluidized beds of resin, operated with periodic flows of both phases. Simple small-scale tests provide the data required in calculations. Experimental work was carried out on uranium extraction from unfiltered ore leach pulps and clarified liquors.     

Mass transfer in liquid fluidized beds of ion exchange particles

Mass transfer rate data in a shallow liquid fluidized bed of ion exchange resin particles have been obtained in the range 2 < Re_s, < 25. At low voidage, ε < 0.55–0.60, the rate of mass transfer is reduced and it is inferred that a fluidized bed tends to maintain an ordered axial structure. This is lost at high voidage due to increased flow perturbation caused by the distributor plate. A generalised correlation is given for fluidized, fixed and distended beds in the range 2 < Re_s, < 25.     

On the superficial gas velocity in deep gas–solids fluidized beds

The superficial gas velocity is one of the key parameters used to determine the flow hydrodynamics in gas–solids fluidized beds. However, the superficial velocity varies with height in practice, and there is no consistent basis for its specification. Different approaches to determine the superficial gas velocity in a deep gas–solids system are shown to cause difficulties in developing models and in comparing predictions with experimental results. In addition, the reference conditions for superficial gas velocity are important in modeling of deep gas–solids systems where there is a considerable pressure drop.     

A model for collisional exchange in gas/liquid/solid fluidized beds

A new model is presented for numerical simulations of collisional transfer of mass, momentum and energy in gas/liquid/solid fluidized beds. The mathematical formulation uses a collision model similar to that of Bhatnagar, Gross, and Krook (BGK), in a particle distribution function transport equation, in order to approximate the rates at which collisions bring about local equilibration of particle velocities and the masses, compositions, and temperatures of liquid films on bed particles. The model is implemented in the framework of the computational-particle fluid dynamics (CPFD) numerical methodology, in which the particle phase is represented with computational parcels and the continuous phase is calculated on Eulerian finite-difference grid. Computational examples using the Barracuda^® code, a commercial CFD code owned by CPFD Software, LLC, show the ability of the model to calculate spray injection and subsequent liquid spreading in gas/solid flows.     

Grid leakage in fluidized beds

Solids leakage rates through different grids in two-dimensional and cylindrical beds of cracking catalyst fluidized with air have been measured. Single and multihole perforated plate grids and single nozzle grids were studied. Leakage fluxes were related to the average air velocity through the grid holes. The effects of superficial gas velocity and grid loading were also investigated. The decisive advantage of using nozzles to mini- mize solids leakage in fluidized beds has been observed.     

Elutriation from fluidized beds

Elutriation characteristics of widely different solids (density from 920 to 5900 kg/m³) were measured in fluidized beds (up to 0.9 m in size) having high freeboard (7.5 m), using gas velocities up to 4 m/s.The experimental findings were compared with previously reported results and all the variables were well correlated with a simple empirical expression     

Void characteristics in turbulent fluidized beds

Void properties (size, rising velocity) in the turbulent flow regime have been determined in a 0.1 m-ID X 3.0 m high Plexiglas column of glass beads (d_p = 0.362, mm) by using an optical fiber probe system. The bubble size increases with an increase in gas velocity in the slugging flow regime but it sharply decreases in the turbulent flow regime. The mean amplitude of pressure fluctuations is linearly related to the bubble or void size in the bed. The void rising velocity is almost constant in the turbulent flow regime. Uniform condition of the bed structure in the turbulent flow regime can be determined from the void distribution coefficient in the bed. In addition, the bed condition in the turbulent How regime has been evaluated from the variations of the void velocity coefficient and the propulsive power of a rising void with gas velocity.     

Voidage profiles in magnetically fluidized beds

Voidage profiles in a fluidized bed of iron particles (230 μm) were investigated under the influence of an external uniform axial magnetic field. Passing a direct current through five solenoids generated uniform magnetic field. The five solenoids were arranged elaborately to get larger uniform magnetic space than that generated by Helmholtz electromagnet coils. A sensitive optical measuring system, based on detection of light reflected by particles, was used to measure local voidage in both dense and dilute phases.

Local voidage was measured as a function of superficial fluidizing air velocity, magnetic field intensity and the position in the bed. At a given magnetic field intensity and at the same position in the bed, the voidage was constant for a low air velocity range (in a fixed bed). The local voidage changed irregularly with increasing air velocity for an intermediate air velocity range (in a magnetically stabilized fluidized bed, MSFB). The local voidage changed linearly with increasing air velocity for a slightly high air velocity range (in a magnetized bubbling fluidized bed, MBFB). A general correlation was developed to predict the local solids fraction at the arbitrary position in the bed: (1−)=(1−)_c+[(1−)_w−(1−)_c](r/R)^B where (1−), (1−)_c and (1−)_w represent the local solids fraction at arbitrary position in the bed, at the bed center and on the bed wall; and B, (1−)_c and (1−)_w are the function of air velocity, distance from the distributor and magnetic field intensity.     

Flow regimes in circulating fluidized beds

Based on a comprehensive hydrodynamic analysis, a practical definition of the circulating fluidized bed (CFB) regime has been proposed. It was established that two flow regimes are involved in a CFB: fast fluidization and dense phase conveying. By demonstrating the variation of pressure gradient in both the lower and the upper section of the bed versus superficial gas velocity, the criteria for the determination of transition velocities have been obtained. Literature data which over wider operating conditions, particle properties and bed diameters from the basis of the obtained generalized correlations of transition velocities. A quantitative flow diagram is presented.     

Interfacial area in three-phase fluidized beds

On the basis of mass transfer models and the results of our previous investigations, Danckwerts' pseudo-first order reaction method was adapted for the determination of interfacial area in a three-phase fluidized bed. The results of our experimental investigations on the absorption of carbon dioxide in aqueous sodium hydroxide are presented. The works of other authors are analysed.     

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.     

微型流化床内气体返混

微型流化床基础和应用在近几年受到越来越多的关注。针对微型流化床对气固反应分析的应用要求,利用脉冲示踪法研究了内径10 mm和21 mm两种尺寸微型流化床中的气体返混特性,具体考察了管内径、颗粒静床高度、床料颗粒粒径和气体表观流速对气体返混程度的影响。结果表明:随着床内径、颗粒静床高度和表观气速的减小和床料颗粒粒径的增大,气体在床内的返混程度减小。使用粒径约270 μm粗颗粒时,两种床径的浅层微型流化床中的气体返混程度都较小,对应的Peclet数在27以上,证明了床内气体流动接近平推流,从而为利用微型流化床最小化气体返混对反应测试的影响,获得近本征反应动力学参数提供了流动特性的保障。     

Intraparticle ion exchange mass transfer accompanied by instantaneous irreversible reaction

A model is proposed for intraparticle mass transfer of ion exchange coupled with instantaneous irreversible reaction. The theoretical equations are der     

Periodic pressure fluctuations in fluidized beds

In shallow gas fluidized beds harmonic oscillations of the pressure around its equilibrium value can be observed. Three aspects of these vibrations have been analysed: the frequency, the critical bed height and the damping. The frequency decreases with the inverse of the square root of the bed height for values below the critical height.For bed heights larger than the critical height the fluctuations cease to be harmonic, the bed breaks up and voids are formed leading to the formation of bubbles or slugs. The critical bed height can be calculated from the frequency and the wave velocity. The maximum value of the critical bed height is a few hundred particle diameters, thus most beds will fluidize heterogeneously. Damping of the oscillations is governed by the ratio of the fluid- to solids-density; the lower this values the higher the damping. The damping is liquid fluidized beds is such that oscillations are prevented.