Bubbles in fluidized beds

Hydrody namical ly, fluidized beds are considered to be stable when they are not bubbling and unstable when they are bubbling. Several researchers (Knowlton, 1977 Hoffman and Yates, 1986 Guedes de Carvalho et al., 1978) have reported that fluidized beds become smoother at elevated pressures (i.e., have smaller bubbles) and, therefore, are more stable at high pressures. There are generally two approaches as to what causes instability in fluidized beds. Rietema and co-workers (Rietema et al. 1993) forwarded the theory that the stability of the bed depends on the level of interparticle forces in the bed. However, Foscolo and Gibilaro (1984) have proposed that hydrodynamics determines whether a fluidized bed is stable. 

With the Interparticle Force Theory, interparticle forces (van der Waals, etc.) are what cause the bed to be elastic. Bed elasticity is characterized by an Elasticity Modulus, M.. The criterion which determines when the fluidized bed starts to bubble is determined by the relative magnitudes of the two sides of Eq. (7). 

In this theory, increasing pressure causes gas to be absorbed onto the surface of the particles. This results in an increase in Mp and, by Eq. (7), an increase in the stability of the fluidized bed. 

The Hydrodynamic Theory of fluidized bed stability was proposed by Foscolo and Gibilaro who adapted the stability principle of Wallis. They postulated that a fluidized bed is composed of two interpenetrating fluids. One fluid is the gas phase, and the solids phase is also considered as a continuous fluid phase. In this theory, voidage disturbances in the bed propagate as dynamic and kinetic waves. The stability of the fluidized bed depends upon the relative velocities of these two waves. The velocities of the kinetic wave (ue) and the dynamic wave (nj are  

Equating ue and u and manipulating the resulting expression leads to the following stability criterion  

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In previous work, we have mainly used the DPM model to investigate the effects of the coefficient of normal restitution and the drag force on the formation of bubbles in fluidized beds (Hoomans et al., 1996 Li and Kuipers, 2003, 2005 Bokkers et al., 2004 Van der Floef et al., 2004), and not so much to obtain information on the constitutive relations that are used in the TFMs. In this section, however, we want to present some recent results from the DPM model on the excess compressibility of the solids phase, which is a key quantity in the constitutive equations as derived from the KTGF (see Section IV.D.). The excess compressibility y can be obtained from the simulation by use of the virial theorem (Allen and Tildesley, 1990). 

An advantage of this approach to model large-scale fluidized bed reactors is that the behavior of bubbles in fluidized beds can be readily incorporated in the force balance of the bubbles. In this respect, one can think of the rise velocity, and the tendency of rising bubbles to be drawn towards the center of the bed, from the mutual interaction of bubbles and from wall effects (Kobayashi et al., 2000). In Fig. 34, two preliminary calculations are shown for an industrial-scale gas-phase polymerization reactor, using the discrete bubble model. The geometry of the fluidized bed was 1.0 x 3.0 x 1.0 m (w x h x d). The emulsion phase has a density of 400kg/m3, and the apparent viscosity was set to 1.0 Pa s. The density of the bubble phase was 25 g/m3. The bubbles were injected via 49 nozzles positioned equally distributed in a square in the middle of the column. 

Bubbles, in fluidized beds, 11 805-806 Bubble size control, 11 805 in fluidized beds, 11 819, 821 Bubble size distribution, 12 14 in foams, 12 11 Bubble tear-offs, 20 229 Bubble tray absorbers, 1 27, 29 design, 1 83-86 Bubble-tube reactor, 25 194 Bubble tube viscometer, 21 739 Bubble two-phase theory of fluidization, 11 805-806... 

The cinephotographic method discussed above can be used only when the fluid in which the bubbles are formed is transparent. If the fluid is opaque, like some non-Newtonian fluids or fluidized beds, x-ray cinephotography has to be used. Rowe et al. (RIO, Rll) have used this technique for studying gas bubbles in fluidized beds. The column in which the bubbles are formed is placed between the x-ray tube and the cine camera (normally 35 mm). Photographs up to 50 frames per second have been obtained by Rowe and Partridge (RIO) with an exposure time per frame of the order of 0.01 sec. 

Baumgarten and Pigford (B2) have employed the y-ray method for their study of density fluctuations in fluidized beds. The method is laborious and time-consuming, and yields only approximate values based on a large number of bubbles. Because of this, the x-ray cinephotographic method is to be preferred for the study of the behavior of bubbles in fluidized beds. 

Similar initial motion occurs for bubbles in fluidized beds, where the final shape is attained after rising through a distance of the order of the initial radius (CIO, Ml 4). 

Impaction of water drops on solid surfaces has been studied (G3), and under some circumstances smaller drops are detached and leave the surface. Impingement of drops on thin liquid films may also cause breakup (K3, S5). Breakup of bubbles in fluidized beds due to impingement on fixed horizontal cylinders has also been observed (G4). Sound waves may lead to instability of bubbles in liquids (S2I). 

To describe the particle and gas flows around the bubble in fluidized beds, the pioneering model of Davidson and Harrison (1963) is particularly noteworthy because of its fundamental importance and relative simplicity. On the basis of some salient features of this model, a number of other models were developed [e.g., Collins, 1965 Stewart, 1968 Jackson, 1971]. The material introduced later follows Davidson and Harrison s approach. 

The rise velocity of a single spherical cap bubble in an infinite liquid medium can be described by the Davies and Taylor equation [Davies and Taylor, 1950] (Problem 9.6). Experimental results indicate that the Davies and Taylor equation is valid for large bubbles (4oo > 0.02 m, in general) with bubble Reynolds numbers greater than 40, while for bubbles in fluidized beds, the bubble Reynolds numbers are typically on the order of 10 or less [Clift, 1986]. By analogy, the rise velocity of an isolated single spherical cap bubble in an infinite gas-solid medium can be expressed in terms of the volume bubble diameter by [Davidson and Harrison, 1963]... 

Rowe, P. N. and Partridge, B. A. (1965). An X-Ray Study of Bubbles in Fluidized Beds. Trans. Instn. Chem. Engrs., 43,157. 

Satija, S. and Fan, L.-S. (1985). Characteristics of the Slugging Regime and Transition to the Turbulent Regime for Fluidized Beds of Large Coarse Particles. AIChE J., 31, 1554. Stewart, P. S. B. (1968). Isolated Bubbles in Fluidized Beds Theory and Experiment. Trans. Instn. Chem. Engrs., 46, T60. 

Clift ct al. (C6), in their study of bubbles in fluidized beds, indicate that instead of having a discrete maximum stable bubble size we can expect bubble splitting to occur over a relatively broad and continuous range of bubble sizes. Whether or not a particular bubble splits will depend not only on size but also on angular position, wavelength, and amplitude of disturbances of the bubble interface. It seems likely that measured maximum stable bubble diameters correspond to mean diameters for systems in which dynamic equilibrium has been achieved between coalescence and splitting. 

Even though (10.7) is strictly valid in liquids, the formula is widely used for calculations of the ideal rise velocity of single bubbles in fluidized beds, when the ratio of bubble to bed diameters is dt,/dt < 0.125 [29, 82] ... 

This expression and the arguments for its use were first presented by Nicklin ]102] for gas-liquid systems determining the rise velocity of a single bubble in a cloud of gas bubbles rising through a stagnant liquid, and later used by Davidson and Harrison [29] (p 28) for bubbles in fluidized beds. 

Like bubbles in liquids, it might be expected that every rising bubble in fluidized beds has an associated wake of material rising behind it. The ratio of wake to bubble volume fw = Vw/Vb has to be determined by experiments, but the void fraction of the wake is frequently assumed to be that of the emulsion phase. 

Reh L (1971) Fluidized Bed Processing. Chem Eng Prog 67(2) 58-63 Rodes MJ, Laussmann P (1992) A Study of the Pressure Balance Around the Loop of a Circulating Fluidized Bed. Can J Chem Eng 70 625-630 Rowe PN, Partridge BA (1965) An X-ray Study of Bubbles in Fluidized Beds. Trans Instn Chem Engrs 43 T157-T175... 

Ubr 0 ideal rise velocity of a single bubble in fluidized bed (m/s)... 

Homsy, G. M., El-Kaissy, M. M. Didwania, A. 1980 Instability waves and the origin of bubbles in fluidized beds - II. Comparison with theory. International Journal of Multiphase Flow 6, 305-318. 

Homsy, G.M., El-Kaissy, M.M., and Didwania, A. (1980). Instability Waves and the Origin of Bubbles in Fluidized Beds—11 Comparison with Theory, Int. J. Multiphase Flow 6, pp. 305-318. 

A greater understanding of bubbles in fluidized beds has come from theoretical studies and pictures of bubbles in two-dimensional and three-dimensional beds [3,9]. If the bubble rise velocity is greater than the superficial velocity, gas leaving the top of the bubble is carried back to the bottom... 

Grace (1970) reviewed the literature available in this area in 1970 and concluded that the direct measurement techniques commonly used to determine the viscosity of newtonian liquids tended to alter the behavior of the bed, e.g., the regions underneath and above the probe tended to have high and low voidages. Thus the viscosity obtained by those methods may not be the true viscosity of a fluidized bed. He, in turn, proposed an indirect method based on the behavior of bubbles in fluidized beds. 

In 1961, Davidson developed a simple theory that was capable of explaining a lot of phenomena relating to bubbles in fluidized beds observed experimentally. His development involves the following assumptions. 

From the computer enhanced video images of rising bubbles in fluidized beds, Yates et al. (1994) observed that the bubbles are surrounded by a region of emulsion phase in which the solids concentration is lower than that in the emulsion phase far from the bubbles. This region of increasing voidage was called the shell by Yates et al. The volumetric gas in the bubble and in the shell can be correlated as... 

The bubbles in fluidized beds grow in size due primarily to three factors ... 

Roach PE. Differentiation between jetting and bubbling in fluidized beds. Int J Multiphase Flow 19 1159-1161,1993. 

Campos JBLM, Guedes de Carvalho JRF. Drag force on the particles at the upstream end of a packed bed and the stability of the roof of bubbles in fluidized beds. Chem Eng Sd 47 4057 062, 1992. 

Clift R, Grace JR, Weber ME. Stability of bubbles in fluidized beds. I E C Funds 13 45-51, 1974. 

Upson PC, Pyle DL. The stability of bubbles in fluidized beds. In Fluidization and Its Applications. Cepadues-Editions, Toulouse, 1973, pp 207-222. 

On the basis of an empirical investigation on the effects of the behavior of the bubbles in fluidized beds and different types of internals on the motions... 

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