Mixing In Beds Research Articles

Teetering

Before 1940, when the term “fluidization” was coined to describe a gas–solids contacting process, liquid-fluidized beds of granular solids had long been used for classification of minerals by size (sizing) or density (sorting), and were referred to in the ore dressing literature as “teeter columns” or as being in the “teeter condition”. Liquid fluidization or “teetering” has subsequently achieved several other applications, in recent years most notably as extended electrodes for electrowinning metals from dilute solutions, as self-cleaning heat exchangers and as bio-catalytic reactors. Since several important applications, in addition to classification per se, involve particle stratification by size and/or density, the main focus of this paper is on the current understanding of particle segregation and mixing in liquid-fluidized beds.

Temperature Stratification and Mixing Dynamics in a Shallow Lake With Submersed Macrophytes

ABSTRACT This paper describes an investigation of temperature stratification and vertical mixing in lacustrine macrophyte beds. Field measurements in a shallow lake show pronounced diel temperature dynamics, driven by surface heat transfer. The temperature stratification data also indicate a significant dependence of vertical mixing characteristics on macrophyte stand height. While natural convective mixing during night-time cooling was rather uniform between measurement sites, wind-driven mixing during the day was significantly attenuated in dense, full-depth macrophyte beds, resulting in increased stratification and higher maximum surface temperatures. An unsteady, one-dimensional heat transfer model has been formulated to simulate temperature dynamics in shallow lakes with submersed macrophytes. Surface mixed layer dynamics are successfully modeled at time scales down to 1 hour, using an integral energy model formulated to include the effect of light attenuation and turbulent kineuc energy dissipation by submersed macrophytes. The results of this study have implications for the management of water quality and ecology of shallow lakes, as variation of thermal stratification and mixing likely has corresponding effects on the transport of dissolved oxygen and nutrients.

Effect of vertical baffles on particle mixing and drying in fluidized beds of group D particles

This study reports the effect of vertical baffles on the group D powder mixing and drying characteristics in a batch fluidized bed dryer. Results obtained in this study showed that operating the fluidized bed dryer with vertical baffles gave better particle mixing. This is due to the fact that the vertical baffles acted to limit the growth of small bubbles into large bubbles and the small bubbles caused more vigorous mixing in the bed of particles before finally erupting at the bed surface. Thus, insertion of vertical baffles is a useful way to process group D particles in a fluidized bed, especially when the fluidized bed is large.

The use of two different models to describe the axial mixing of solids in fluidised beds

Two widely used models to describe axial solid mixing in fluidised beds (the dispersion model and the countercurrent backmixing (CCBM) model) are evaluated against identical sets of experimental data. Experimental work has been obtained at different conditions (gas velocity, particle properties and two column diameters) using an image analysis technique. Previously published data by other authors are also compiled to enlarge the experimental database for model development and validation. It is shown that both models are capable to fit the majority of experiments well, in agreement with a well-known relation between the models in some extreme conditions. This relation is further explored by incorporating independent measurements of the tracer rise velocities during the mixing experiments. It is concluded that, although a simple correlation for the solid dispersion coefficients compiled in this work is useful, the CCBM model is a much more reliable idealisation in describing and scaling up axial solid mixing in fluidised beds.

An extended version of the countercurrent backmixing model suitable for solid mixing in two-dimensional fluidised beds

In this work, a new mathematical model to describe axial and lateral mixing in fluidised beds is presented. The model is an extension of previous versions of the countercurrent backmixing model (CCBM) that were restricted to axial mixing only. The fluidised bed is divided into parallel ‘mixing columns’, which are convective currents induced by the bubbles. Each mixing column has a central upflowing stream of solids and two adjacent moving downwards. The practical application of the model requires a minimum knowledge of the bubble properties and the definition of one empirical parameter: the exchange coefficient between countercurrent phases, K w. The model can be rapidly solved with the proposed algorithm and reproduces semi-quantitatively the main features observed in mixing experiments carried out in a bidimensional fluidised bed of coal and PVC as tracer.

Study of mixing in gas-fluidized beds using a DEM model

This paper examines the usefulness of a discrete element method simulation in studying solids mixing in gas-fluidized beds. At steady state, a part of the solids were tagged with a dark colour and the rest were tagged with a light colour. The state of mixing of bed solids was studied by analysing the variation of the proportions of the marked particles with time and position in the bed. This was achieved by scanning the bed using a sampling box. The variance of mixture composition based on the samples was incorporated into a mixing index which describes the degree of mixing of the particles at a particular time. This method enables assessment of the overall mixing behaviour in terms of the rate of mixing (through estimation of the time required for the mixing index to increase from zero to a certain value), together with the degree of mixing at the mixing equilibrium. Illustrative examples show that gas velocity and particle properties are important parameters influencing solids mixing in bubbling fluidized 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.

The diffusion model of longitudinal mixing in beds of finite length. Numerical values: H. Brenner, Chem. Engng Sci.17: 229–243, 1962

Accurate numerical values are tabulated pertaining to the solution of the partial differential equation governing miscible fluid displacement dispersion phenomena in finite beds. Nondimensional results are furnished for the instantaneous exit solute concentration and average solute concentration remaining. Various asymptotic cases are discussed.

Lateral solid mixing measurements in circulating fluidized beds

A thermal technique has been developed for measurement of solid mixing in fluidized beds. A batch of bed particles is preheated and then injected into the bed. An array of thermistor probes measures the spread of the tracer. A series of experiments has been done in the upper core region of a 7 m tall, 0.20 m diameter test circulating fluidized bed (CFB). The experiments involved one type of particle, having 180 μm diameter and 2350 kg/m 3 density. Models for the spread of tracer particles, transfer of heat from tracer particles to surrounding gas and particles, and for heat transfer to the thermistors were used to make estimates of the radial particle diffusivity in the core region. The diffusivity was on the order of 10 cm 2/s for the range of velocities and solid concentrations tested. A second set of preliminary solid mixing experiments has been done in the bottom of a 1.8 m tall, 0.16 m square CFB using 55 μm FCC (fluid cracking catalyst) particles. The mixing in this region, although not representative of a strictly diffusional process, appears to be somewhat more vigorous than the core mixing in the upper region of the bed.

Experimental study of sawdust and coal particle mixing in sand or catalyst fluidized beds

AbstractThis paper presents an experimental study in order to establish mixing and segregation conditions of wood sawdust and coal particles in a fluidized bed of sand or alumina particles. Experiments were performed at room temperature under atmospheric pressure. Simple equipment was used to divide the bed into layers and useful results could be obtained in a short period of time. The influence of fluidization velocity, time of an experiment, size and concentration of sawdust or coal particles was investigated.Uniformity of mixing was found to increase with an increase in the fluidization velocity. For u/umf less than 2.5, strong segregation occurred between sawdust and sand particles.Determination of good mixing conditions will be useful in gasification studies of sawdust and coal.

Particle mixing and solids flowability in granular beds stirred by paddle-type blades

Proper selection, design and scale-up of mechanically stirred vessels handling granular solids require an understanding of the flow dynamics of the sol

Computer simulation of isothermal fluidization in large‐scale laboratory rigs

AbstractFinite‐difference computer models have been used by several investigators to predict hydrodynamic mixing in fluidized beds. In the present study the finite‐difference model CHEMFLUB is used to simulate cold, isothermal mixing in axisymmetric fluidized beds. The bed geometries and the operating conditions are based upon those of two large‐scale laboratory cold flow rigs. The finite‐difference model is an iterative, implicit formulation to solve continuum equations describing the gas and particle dynamics of fluidization. Comparisons with experimental data are presented. It is shown that the model provides a good prediction of jet penetration height, bubble frequency, and bubble velocity.

FCC Regenerator flow model

Catalyst flow patterns in FCC cross-flow and swirl-type dense-bed regenerators affect regenerator efficiency. A two-dimensional, pseudo-homogeneous flow model describing such flow patterns is developed. The predicted catalyst flow patterns for swirl regenerators indicate catalyst bypassing and recirculating zones. More severe bypassing is predicted for cross-flow regenerators, the severity of bypassing increases with increasing Reynolds number. The calculated flow patterns are combined with a radial mixing-cell model to account for radial mixing in fluidized beds. Radial mixing rates in commercial size regenerators counteract somewhat the effect of bypassing. Model calculations coupling coke burning kinetics with the flow model, however, show that bypassing leads to non-uniform coke levels and oxygen breakthrough. This modeling technology is used to optimize FCC regenerator operation.

Spatial distributions of O 2, CO 2 and SO 2 in a pilot-scale fluidized bed combustor operated with different coals

Axial concentration profiles of O 2, CO 2 and SO 2 have been measured at different radial positions in a coal-fired fluidized bed combustor. The profiles show some spatial inhomogeneity in the bed, the degree of which depends on fluidizing velocity and amount of excess air. Comparison of SO 2- with CO 2-concentration profiles reveals that SO 2 is formed in proportion to CO 2 only with anthracite as fuel. With bituminous coals, SO 2 is preferentially formed near the coal feed point. These results are discussed with regard to characteristic times of mixing and chemical reaction in fluidized beds, and SO 2-formation characteristics of the employed coals obtained in a thermobalance.

Gas flow and mixing behavior in fine‐powder fluidized bed

The experiments discussed here have been carried out to investigate the mechanism of gas flow and mixing in fluidized beds. Two tracing techniques have been employed in this study. One is referred to as the fine-powder tracing technique, which was developed in the present investigation to observe characteristics of gas flow in a two-dimensional fluidized bed. In the other technique hydrogen was applied as tracer gas to obtain the residence time distribution (RTD) and values of dispersion efficiency of gas. A Dirac delta-function input signal of hydrogen was injected in the beds when the beds were stationary.

Mixing and segregation in binary-solid liquid fluidised beds

Force balance considerations enable 'solid concentration relationships' to be evaluated for binary-solid particulate fluidisation which define the set of solid component volumetric concentrations that can coexist at axial locations in the fluidised state; these relationships are verified experimentally and applied to the analysis of mixing and segregation in water fluidised beds.

Very large lattice model of liquid mixing in trickle beds

Utilisation d'un modele a tres grand reseau a trois dimensions, base sur la theorie de la percolation, pour analyser l'ecoulement du liquide dans les lits a ruissellement. La distribution du liquide est fonction d'un seul parametre, la permeabilite du lit. On derive des correlations pour l'epaisseur moyenne du film liquide et pour la retenue dynamique, que l'on compare aux valeurs de la litterature

Inviscid model for gross solid circulation and gas back mixing in fluidized beds

An inviscid model is developed to describe gross solid circulation and gas backmixing in axisymmetric fluidized beds. Two distinct cases are shown to arise: 1. interstitial gas moves upwards everywhere; and 2. interstitial gas circulates giving rise to loop formation in an annular region near the wall. It is shown that gas back-mixing is a highly local phenomenon which explains the anomalously high “apparent wake fractions” estimated in the literature. The model predictions as well as analysis of published observations indicate the “onset” of gas backmixing near the wall to occur just above the minimum fluidization (or minimum bubbling) plint. An analytical expression derived to estimate the fraction of bed area available for fresh gas movement upwards indicates that the “dead volume” of the bed is usually greater than 50% and at times can approach even 90%.

Radial particle mixing in gas-solids fluidized beds

Difficulties involved in experimentally determining the mixing coefficients of particles in a gas-solids fluidized bed are well known. From the theoretical point of view, the mechanism of particle mixing in such a fluidized bed is influenced profoundly by complicated and stochastic phenomena, such as jetting and bubbling. It appears that a sufficiently effective deterministic approach is not available to analyse the mechanism. In the present work, the particle mixing in the radial or lateral direction of a gas-solids fluidized bed was studied by using heated particles as the tracer particles. The transient concentration distribution of these particles in the lateral direction was obtained by means of an impulse response technique; sensitive thermocouples were used for measurement. The mixing coefficients of particles have been estimated from the distribution by a stochastic approach, and the resultant coefficients are compared with those obtained by other investigators.

The influence of particle mechanical properties on bubble characteristics and solid mixing in fluidized beds

To determine the influence of interparticle forces on the fluid mechanics of large particle fluidized beds, experiments were conducted using particles with different values of the friction coefficient and the coefficient of restitution. The bubble characteristics and particle dispersion within the bed were measured. The bed characteristics were found to be insignificantly influenced by changes in friction and coefficient of restitution, indicating that either interparticle mechanical forces due to direct contact are unimportant or that these forces are only influenced by the particle size, density and velocity. The wake fraction was found to be a strong function of particle size. The upward particle transit velocity is proportional to the mean bubble frequency. Downward transit velocity is proportional to the volumetric flow rate of bubbles and the wake fraction.