Mixing In Beds Research Articles

On the Kennedy and Bretton model for mixing and segregation in liquid fluidized beds

The foundations and applications of the Kennedy and Bretton model for mixing and segregation in liquid fluidized beds containing two sizes of equal density particles are critically examined. A direct method of solution that avoids all the difficulties and pitfalls of previous methods is presented.

Segregation and mixing in liquid fluidized beds

Segregation and mixing were studied in beds of binary mixtures of lead glass spherical particles (2 mm with 3 mm; and 2 mm with 4 mm diameter) fluidize by paraffin oil. Concentration profiles were obtained both by measuring pressure gradients in the bed and by sampling. A model for solid mixing, based on the combined effects of diffusive and convective mechanisms, has been used in conjunction with the experimental resu

Mixing and circulation in fluidized beds of flour

The mixing and bulk circulation characteristics of a fluidized bed of wheat flour having a relatively high aspect ratio were determined with a 6 in. diam. column fitted with a slowly revolving paddle just above the gas distributor. In this system the bulk of the solids moved down the column in stick-slip flow which was readily observed because of the appearance of relatively stable horizontal cracks in the bed. At lower gas velocities the behavior of the system was characterized by zone fluidization which led to erratic and unreproducible mixing performance. Operation at greater than twice the minimum fluidization velocity overcame this problem and provided consistent mixing. An increase in gas velocity increased the bulk circulation rate and reduced the batch mixing time. The solids next to the wall of the column seemed to move at the same rate as the core of the bed, at least at lower gas velocities. The downward velocity of these solids was directly proportional to gas velocity and to bed height and a complex function of flour moisture content. The velocity also depended on vertical position but not on the speed of the rotating paddle. Adding an anti-agglomerant promoted smooth fluidization and reduced the minimum fluidization velocity, and for the same relative gas velocity it increased the bulk circulation rate and reduced the batch mixing time.

A comprehensive interpretation of solid layer inversion in liquid fluidised beds

Solid mixing and segregation in liquid fluidised beds containing binary mixtures of spherical particles of different density and size has been studied for a range of liquid velocities, bulk bed compositions and particle properties. It was shown that a bed of denser particles expands with liquid velocity independently of the presence of the lighter particles. When the bulk volume fraction of the lighter particles is high and the liquid velocity is relatively low, the bed forms two layers, i.e. the upper layer consisting almost entirely of the lighter and the lower mixed layer consisting of both components in which the volume of the lighter increases with liquid velocity. A completely mixed bed is obtained at a certain velocity and then a further increase of the velocity causes “layer inversion”. The liquid velocity at which complete mixing occurs depends on the bulk bed composition, and at that velocity the volume fraction of the lighter in the lower mixed layer is constant regardless of the bulk bed composition. It is shown that layer inversion occurs for a given particle mixture when the liquid velocity passes through a value at which the volume fraction of the lighter in the lower layer becomes equal to the bulk bed composition; or for a given velocity, when the bulk bed composition becomes equal to the fraction of the lighter component which exists in the lower layer. The dependency of the fraction on the liquid velocity and the particle properties is examined to some extent.

Investigation of gas mixing and gas distributor performance in fluidized beds

The transverse concentration profiles of a tracer from a stationary point source and the distribution of residence times (DRT) of the gas flow were measured in bench and pilot plant scale fluidized beds for four different gas distributor types. For three of them DRTs with two maxima were found. These DRTs were evaluated by assuming the presence of two regions with different properties in the bed. By applying a two-phase longitudinal dispersion model the effective linear velocities and the dispersion coefficients were evaluated for these two so-called bubble-rich and bubble-lean phases. An extension of the bubble model of Kunii and Levenspiel by two dispersion terms gave good agreement between the calculated and measured moments of the DRT. A relation is proposed to assess the quality of the gas distribution. The DRTs of the gas flow were measured in fluidized beds of sand particles with bed diameters of 350 and 500 mm and for four different gas distributor types by means of mass spectrometry. For all gas distributors except the porous plate, DRTs with two maxima were found for a fluidization index u + = 1-2.5. The DRTs were evaluated by assuming two regions with significantly different properties in the bed, the so-called bubble-rich and bubble-lean phases, and by applying the longitudinal dispersion model for both these phases, which are coupled by an exchange process. The effective linear velocity u S in the bubble-lean regions is independent of the system parameters and is nearly equal to the effective velocity of minimum fluidization. The effective linear velocity u B of the bubble-rich regions increases with increasing u + and depends on the system parameters. The coefficient D B of effective longitudinal mixing in the bubble-rich regions is significantly greater than the coefficient D S in the bubble-lean regions. The properties of the bubble-lean regions must be close to the properties of the lean suspension (emulsion) phase and the properties of the bubble-rich regions close to those of the bubble + wake phase. A two-phase model gives a good description of these systems. However, the relative volume of the bubble phase cannot be calculated by eqn. (6a) and the volumetric exchange coefficients k are much smaller than those for a true two-phase system. The original bubble model of Kunii and Levenspiel cannot be applied. The extension of this model by including dispersion terms and a coefficient of interphase mass transfer improves the agreement between the calculated and measured moments of the DRT considerably. The ratio S* = u B/ u S is very sensitive to the efficiency of the gas distributor. A relation has been proposed to assess the gas distributors.

Comment on ‘Analytical solution of the equation for transport of reactive solutes through soils’ by H. M. Selim and R. S. Mansell

Water Resources ResearchVolume 13, Issue 3 p. 701-701 Free Access Comment on ‘Analytical solution of the equation for transport of reactive solutes through soils’ by H. M. Selim and R. S. Mansell J.-Y. Parlange, J.-Y. ParlangeSearch for more papers by this authorJ. L. Starr, J. L. StarrSearch for more papers by this author J.-Y. Parlange, J.-Y. ParlangeSearch for more papers by this authorJ. L. Starr, J. L. StarrSearch for more papers by this author First published: June 1977 https://doi.org/10.1029/WR013i003p00701AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. References Brenner, H., The diffusion model of longitudinal mixing in beds of finite length, Numerical values, Chem. Eng. Sci., 17, 229– 243, 1962. Carslaw, H. S., J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, New York, 1960. Parlange, J.-Y., J. L. Starr, Linear dispersion in finite columns, Soil Sci. Soc. Amer. Proc., 39, 817– 819, 1975. Parlange, J.-Y., J. L. Starr, First and zeroth order kinetics and influence of boundary conditions on linear dispersion in finite columns, Soil Sci. Soc. Amer. Proc., 1977. Selim, H. M., R. S. Mansell, Analytical solution of the equation for transport of reactive solutes through soils, Water Resour. Res., 123, 528– 532, 1976. Volume13, Issue3June 1977Pages 701-701 ReferencesRelatedInformation

Local structure of a binary finely dispersed fluidized bed

Results are given of calculations of the quantities characterizing the random pseudoturbulent motions of the phases in a homogeneous fluidized bed consisting of particles of two sorts, differing in size. The dependence of the coefficients of pseudoturbulent diffusion of the particles, the mean-square velocities of the pulsations, etc., on the partial concentrations of the particles, the ratio of their sizes, and other parameters is evaluated. For granular beds, fluidized by a gas or a drop-type liquid, intense chaotic fluctuations of both phases are characteristic; these determine to a considerable degree the observed macroscopic properties of the bed and affect its effectiveness as a working body in various types of heat exchangers and chemical reactors. Such random (“pseudoturbulent”) motions are particularly considerable for beds of small particles under homogeneous fluidization conditions, where mixing due to the rise of cavities in the bed, filled only with the fluidizing medium, is practically absent. A similar situation is encountered in reactor and regenerating units for catalytic cracking [1, 2], in beds with a drop-type liquid phase, in rarefied two-phase systems under the conditions of strong fluidization or of the transport of bulk materials in a dilute phase, etc. The characteristics of pseudoturbulence in locally homogeneous flows of monodisperse two-phase systems have been investigated, for example, in [3–5]. However, real fluidized beds are generally polydis-perse; the presence of particles of different sizes in the bed has a very considerable effect, on the intensity of the pulsations, the effective diffusion coefficients of the phases of the bed, the effective viscosities, etc. [1, 6]. In addition, the chaotic mixing in polydisperse beds determines some of the technological characteristics, specifically, the rate of entrainment of small particles by the flow of the fluidizing medium and the settling of large particles, the degree of separation of the fractions of the disperse phase, which is very important in determination of the limits of the existence of the fluidized state, and in the modeling of numerous processes of the separation of particles with respect to size or density [1, 6].

Frequency response in liquid fluidized systems Part I. Effect of particle density and size

AbstractFluid mixing in liquid fluidized beds has been characterized by a dynamic response technique using pulse inputs. Solid particles with a size range of 0.5 to 3.0 mm diameter and a density range from 1.28 to 7.02 gms/cc were fluidized with water at void fractions of 0.4 to 0.85 in a 2‐inch column. A dispersed plug flow model has been applied successfully, including a frequency response comparison, and dispersion coefficients have been calculated by the moments method. The results are related to correlations previously advanced, including the use of an eddy diffusivity and of the Bodenstein number, and a more recent refined correlation allowing for density differences.

Residence Time of Particles in Continuous Fludized Bed with Elutriation of Fines

The residence time distribution of particles in the continuous fluidized bed with elutriation of fines was studied experimentally and compared with that developed from the simple mixing model.It is found that the values of constant fines concentration in beds obtained in the previous work are important for the mixing in beds and the zone below elutriation surface height may be mixed parfectly but the all system of fluidized bed with elutriation of fines is not regarded as a perfect mixing system.

The effect of molecular diffusion on mixing in fluidized beds

Gas mixing in a 6·5 in fluidized bed of sand was studied using frequency response techniques with He and CO 2 tracers. Samples taken in the bed, where the probe saw mainly dense phase gas, had a lower amplitude ratio than samples at the top of the bed where the bubble contribution predominated. The gas interchange coefficients showed a small dependence on the molecular diffusivity at about twice the minimum fluidization velocity but no effect of diffusivity at high velocities.

Fluid mixing in particulate fluidized beds

A hydrodynamic mathematical model is developed for particulate batch fluidization. Longitudinal dispersion in such systems is predicted analytically. It is governed by the particle wake: its size and shedding rate. The wake size is evaluated from photographs and the shedding rate is calculated from boundary layer flow. The predicted Peclet numbers compare very well with experimental data in the flow range of 40 < Re < 2300.

Hold-up and fluid mixing in gas-liquid fluidised beds

Axial mixing in the fluid phases of liquid and gas-liquid fluidised beds has been examined by the imperfect pulse method, using radioactive isotopes as tracers. The intensity of mixing is strongly dependent on the particle size of the ballotini and the flow rate of the fluid phases. In beds of 6 mm particles mixing may be neglected except at very high superficial gas velocities, whereas beds of 1 mm particles are characterised by a high degree of mixing in the liquid phase. A new method of data reduction possessing some advantages over the normally used method of moments is applied and discussed.

PARTICLE MOVEMENT IN A GAS-SOLID FLUIDIZED BED

The photographs of particle movement were taken in a two-dimensional fluidized bed and statistically analyzed. The circulation of the solid phase was proved to exist from the mean particle velocity and the scale of movement concerning space and time was obtained from the autocorrelation coefficient of particle velocity. These informations will be available for simulating the solid mixing in fluidized beds.

Mixing and contacting models for fluidized beds

AbstractParameters of the two‐phase model for mixing in fluidized beds were evaluated from a large amount of available literature data. The dense phase dispersion coefficients and the cross flow, or interphase transfer, coefficients, based on the consistent model calculations, were correlated with operating conditions. A strong effect of bed length‐to‐diameter ratio was found for the dense phase mixing but not for the cross flow. On the basis of the given kinetics information with the mathematical model parameter correlations, some chemical reactor conversions from the literature were predicted by a priori calculations.

Gas mixing in fluidized beds containing screen packings

AbstractGas mixing was studied in a fluidized bed containing hollow, open‐wall packings using a continuous injection of oxygen as a tracer.During bed expansion, the reciprocal of mixing length, u/E1, for a gas‐fiuidized bed containing packings of dimension less than 3‐in. was found to decrease and then increase with the expansion ratio, Δ, passing through a minimum, in contrast to an unpacked fluidized bed for which no minimum u/E1, was reported.The minimum u/E1, occurred always at Δ = 0.30, independent of column diameter, of the shape or of the size of the packing, and of the size of the fluidizing particle. Values of the minimum u/E1's for a fluidized bed packed with various screen cylinders depended upon the size of the packing, dn, and of the fluidized particle, d1,. An empirical correlation of (u/E1)mn, with d1, and dn is presented.

Briefs - "Radial Gas Mixing in Fluidized-Packed Beds"

Briefs - "Radial Gas Mixing in Fluidized-Packed Beds"

Radial Gas Mixing in Fluidized-Packed Beds

Radial Gas Mixing in Fluidized-Packed Beds

The diffusion model of longitudinal mixing in beds of finite length. Numerical values

Accurate numerical values are provided for the solution of the diffusion model of miscible fluid displacement in beds of finite length. The calculations presented here apply to the case in which a solute, uniformly distributed throughout the medium at the outset of the experiment, is displaced by a solvent which may itself contain some of the solute. Results are given in dimensionless form for (i) the instantaneous concentration of solute leaving the bed, and (ii) the average solute concentration in the bed at any instant. Various limiting cases are discussed.