Heat transfer in three-phase fluidized beds

Heat transfer coefficients h have been measured in two-phase (water—air, water—glass beads) and three-phase (water—air—glass beads) fluidized beds. Experiments were performed over a wide range of liquid and gas flowrates in a 0.24 m diam. column fitted with an axially mounted cylindrical heater. Four solids were employed ranging in size from 0.5 to 5 mm.Typical maximum values of h in the three-phase, liquid—gas, liquid—solid and liquid beds were approximately 4800, 4300, 3800 and 1300 W/m²K respectively. In the three-phase beds h generally increased with liquid and gas velocity and with particle size. Correlations are presented to calculate h in the different beds.     

Gas-liquid mass transfer in three-phase fluidized beds with viscous pseudoplastic liquids

Liquid phase volumetric mass transfer coefficients for oxygen were determined in three-phase fluidized beds of 8 mm glass spheres fluidized by a cocurrent flow of air and pseudoplastic polysaccharide solutions (carboxymethyl cellulose, xanthan). A semi-theoretical relation for the effective shear rate was suggested. The mass transfer coefficients could be correlated, together with literature data for particle diameters of 3 mm and 5 mm in other liquids, using the terminal velocity as the particle-specific property.     

Mass transfer in two-and three-phase fluidized beds

The effects of liquid (0.03-0.12 m/s) and as (0.04-0.20 m/s) velocities, and particle size (0-8.0 mm) on the volumetric mass transfer coefficients at the grid zone have been determined in a 0.152 mI.D. x 1.8 m high Plexiglas column. The volumetric mass transfer coefficient in the grid zone increases with increasing gas velocity and particle size. However, the coefficient exhibits a maximum value at an optimum bed porosity condition. The volumetric mass transfer coefficients in terms of the Sherwood number in three-phase fluidized beds have been correlated with the Schmidt number and particle Reynolds number which is related to the energy dissipation rate in the beds based on the local isotropic turbulence theory. Also, the coefficient has been correlated with the experimental variables.     

The plug flow model for mass transfer in three-phase fluidized beds and bubble columns

The plug flow model (PFM), overwhelmingly used to describe mass transfer in bubble columns and three-phase fluidized beds, has never been critically tested. This study analyzes the PFM single parameter, K_La, to quantify mass transfer in the forementioned systems. Particular attention is paid to the mass transfer features of the zone near the distributor (grid zone) largely ignored until now. This study, carried out under the largest gas and liquid flow rates ever published, for similar types of systems, indicates the presence of two well defined mass transfer zones. These features invalidate, for design purposes, the use of the PFM. However, it still can be used as a qualitative mass transfer indicator. This has permitted a comparison between the mass transfer efficiency of bubble columns and three-phase fluidized beds with the conclusion that three-phase fluidized bed of 0.5 cm particles can compete successfully with bubble columns.     

Oxygen transfer and hydrodynamics in three-phase inverse fluidized beds

Experiments were performed at ambient temperature and pressure in a 152 mm inner diameter column with air, tap water or 0.5% wt. aqueous ethanol solution, and polypropylene particles. An increase in liquid velocity and solids loading, and the presence of a surfactant reduces the gas velocity required to reach full bed expansion, which is delimited by the gas sparger. With an increase in gas velocity, solids holdups remain constant after full bed expansion, liquid holdups increase to a maximum and then decrease and gas holdups continuously increase. The addition of ethanol greatly increases the gas holdups leading to significant reductions in liquid holdups. The volumetric gas-liquid mass transfer coefficient, k_La, increases with increasing gas velocity but does not change significantly with liquid velocity. There are complex interaction effects between solids loading and surfactants as the values of k_La in the aqueous ethanol solution were greater than those in water when particles were present and smaller without particles. k_La data in water were found to be proportional to gas holdup whereas for the ethanol solution this proportionality constant first decreased with increasing gas velocity to eventually stabilize at a value smaller than for water.     

Bubble breakage phenomena,phase holdups and mass transfer in three-phase fluidized beds with floating bubble breakers

The individual phase holdups and mass transfer characteristics in three-phase fluidized beds with different floating bubble breakers have been determined in a 2.0 m high Plexiglas column of inner diameter 0.142 m. The bubble breaking phenomena by the breakers have been studied via a photographic method in a two-dimensional Plexiglas column. The volumetric mass transfer coefficient k_La in three-phase fluidized beds with hexagonal-shaped breakers is up to 40% greater than that in beds without floating bubble breakers. The bed porosity ε_L + ε_g, gas-phase holdup ε_g, and volumetric mass transfer coefficient k_La increase with an increase in the volume ratio of floating bubble breakers to solid particles, V_f/V_s, up to around 0.15, and thereafter decrease with V_f/V_s in three-phase fluidized beds with floating bubble breakers. Also, k_La increases with increasing breaker density, projected area and contact angle between the floating bubble breakers and the water. The volumetric mass transfer coefficients in terms of the Sherwood number in three-phase fluidized beds with the various floating bubble breakers have been correlated with the volume ratio of floating bubble breakers to solid particles, the particle Reynolds number based on the local isotropic turbulence theory and the modified Weber number.     

Wall-to-bed heat transfer in three-phase fluidized beds of low density particles

Bed-to-wall heat transfer was measured in three-phase fluidized beds under conditions typical of biochemical process applications. The thermal resistance of the fluidized bed, which was significant in the absence of gas, became negligible when gas was introduced. Decreasing the particle density at constant gas and liquid velocity increased the bed-to-wall heat transfer coefficient. Previously published heat transfer correlations were used and gave poor predictions of our data. A new correlation was developed which predicted very well all the heat transfer coefficient results in this paper.     

Wall to liquid mass transfer in fluidized beds

The paper reports a study of the influence of particle motion on wall to liquid mass transfer in liquid fluidized beds. Results obtained in classical fluidized beds are compared with those observed with expanded fixed beds of the same particles and having the same mean porosity. It is shown that the particle motion has no measurable influence. The particles only act as obstacles to the fluid flow in the same way as if they were fixed in their mean statistical positions.     

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.     

Wake characteristics of three-phase fluidized beds

Wake volumes in three-phase fluidized beds hae been computed from phase holdup and bubble rising velocity data over a wide range of experimental conditions. The ratio of the wake to gas holdup k? increased with liquid velocity and decreased with gas velocity and surface tension. A correlation relating k? to these variables was derived. Both a stable wake and vortex shedding appeared to contribute to the measured wake volume.     

Dimensional hydrodynamic similitude in three-phase fluidized beds

This study tests the scaling approach for three-phase fluidized bed hydrodynamics proposed by Safoniuk, Grace, Hackman, & McKnight (Chem. Eng. Sci. 54 (1999) 4961) based on geometric and dynamic similitude with a limited number (5) of dimensionless groups. Experiments were carried out in two systems in which all five dimensionless groups were matched: an aqueous glycerol solution with glass beads (system 1) and silicone oil with porous alumina particles (system 2), with air as the gas in both cases. Although bed expansions were similar for the two systems, trends differed. Gas holdups were always slightly higher for system 1. The dimensionless transition velocities from dispersed to coalesced flow were similar. The minimum liquid fluidization velocity Reynolds number was slightly higher for system 1 without gas, but somewhat lower with gas present. Differences between the systems are statistically significant, but generally less than 12%, so the dimensional similitude approach gives a reasonable basis for estimating global hydrodynamic parameters under the present operating conditions. The differences between the two systems are attributed to the complex coalescence behavior of liquid mixtures, suggesting that additional dimensionless groups are needed to fully characterize the local dynamic bed behavior.     

Local bubble behavior in three-phase fluidized beds

Bubble behavior, including bubble Sauter diameter, bubble rise velocity, bubble frequency and local gas holdup in different radial and axial positions, was measured using a dual electro-conductivity probe in air-water-glass beads fluidization systems. It has been found that the bubble characteristics differ significantly in various flow regimes, depending on the operating conditions; the radial distribution of bubble parameters also changes from one flow regime to another. Thus, it is necessary to employ local bubble behavior in the modeling of three-phase fluidized beds.     

Particle flow behavior in three-phase fluidized beds

Non-uniform flow behavior of fluidized solid particles in three-phase fluidized beds has been analyzed by adopting the stochastic method. More specifically, pressure fluctuation signals from three-phase fluidized beds (0.152 m ID x 2.5 m in height) have been analyzed by resorting to fractal and spectral analysis. Effects of gas flow rate (0.01-0.07 m/s), liquid flow rate (0.06-0.18 m/s) and particle size (0.001-0.006 m) on the characteristics of the Hurst exponent, spectral exponent and Shannon entropy of pressure fluctuations have been investigated. The Hurst exponent and spectral exponent of pressure fluctuations attained their local maxima with the variation of liquid flow rate. The Shannon entropy of pressure fluctuation data, however, attained its local minima with the variation of liquid flow rate. The flow transition of fluidized solid particles was detected conveniently by means of the variations of the Hurst exponent, spectral exponent and Shannon entropy of pressure fluctuations in the beds. The flow behavior resulting from multiphase contact in three-phase fluidized beds appeared to be persistent and can be characterized as a higher order deterministic chaos.     

Mathematical modeling of mass transfer in a three-phase fluidized system

An algorithm and a program for calculating the driving force of the process of mass transfer and the mass fluxes of gas and liquid phases are developed on the basis of the fundamental two-parameter equation of convective diffusion taking into account the amplitude-frequency characteristics of wave packets. The algorithm and the program of engineering calculation of the processes of physical absorption and chemisorption are written.     

A correlation for heat transfer in liquid fluidized beds

A relationship, of the Colburn j-factor type⁽⁹⁾, is derived for heat transfer in fluidized beds. This correlation (10) successfully accounts for the existence of the characteristic maximum heat transfer coefficient at a particular porosity. The derived relationship also predicts the experimentally observed variation of h with change of particle size and density. These variations are mainly a function of the hydrodynamics of the system.     

Local study of wall to liquid mass transfer in fluidized and packed beds. I. Mass transfer in fluidized beds

This paper deals with the local influence of particles on mass and momentum transfer at a surface immersed in a liquid fluidized bed. The experimental distributions of mass-transfer coefficients and shear stresses along the surface appear to be similar and suggest large hydrodynamic perturbations near the leading edge of the diffusional boundary layer. It is shown that the fluidized bed behaves as a turbulent pseudo-fluid and that the Chilton-Colburn analogy, expressing the equivalence between mass and momentum transfer applies locally. The results of the study lead to a qualitative explanation of the influence of the fluidization parameters on the overall surface to liquid mass transfer coefficient in fluidized beds.Nomenclature a coefficient in Equation 6 - D molecular diffusion coefficient - d _p particle diameter - d microelectrode diameter - J _M k/(u/)(Sc) ^2/3 Colburnj-factor - k local mass transfer coefficient - k local mass transfer coefficient defined by Equation 1 - k _c k mass transfer coefficient given by the Chilton-Colburn analogy - ¯k overall mass transfer coefficient - L length of the transfer surface - m, n, p exponents in Equations 6 and 7 - s V _x /y) _y=0 velocity gradient at the transfer surface - (Sc) /D Schmidt number - u liquid superficial velocity - u _max maximum fluidization velocity - V _x length velocity - x length coordinate - x ₀ length of the inactive part of electrode - y normal coordinate - bed porosity - _max porosity corresponding to the maximum ofk in a fluidized bed - _F fluid density - _S particle density - dynamic viscosity - kinematic viscosity - s shear stress at the wall     

Particle dispersion in viscous three-phase inverse fluidized beds

Dispersion characteristics of low density fluidized particles such as polyethylene and polypropylene were investigated by using the stochastic method in three-phase inverse fluidized beds with viscous liquid medium ( in height). To establish the relationship between the pressure drop variation and the particle dispersion in test section, the histogram of pressure drop fluctuations were also measured and analyzed. Effects of operating variables such as gas and liquid velocities, liquid viscosity and media particle kind (density) on the fluctuating frequency, dispersion coefficient and exiting rate of media particles from the test section were determined. The fluctuating frequency and dispersion coefficient of particles increased with increasing gas or liquid velocity, but decreased considerably with increasing liquid viscosity in three-phase inverse fluidized beds. The dispersion coefficient of media particles of relatively higher density exhibited a value higher than that of lower density particles. The dispersion coefficients of particles were well correlated with operating variables in terms of dimensionless groups.     

Criterion for initial contraction or expansion of three-phase fluidized beds

Some beds contract and others expand when gas bubbles are introduced into the bottom of a liquid-fluidized bed. A quantitative criterion for predicting which of these two events will occur in any particular case, derived in an earlier paper, is tested against experimental data from the literature and shown to predict all the observed trends with various process variables correctly.