Velocity bubble phase

Knowing the bubble rise velocity, the bed expansion can be predicted from a material balance on the bubble phase gas. Thus, total gas flow through the bubble phase equals absolute bubble velocity times the volume fraction E of bubbles in the bed. 

The simulation results on bubble velocities, bubble shapes, and their fluctuation shown in Fig. 3 are consistent with the existing correlations (Fan and Tsuchiya, 1990) and experimental results obtained in this study. Bubble rise experiments were conducted in a 4 cm x 4 cm Plexiglas bubble column under the same operating conditions as those of the simulations. Air and tap water were used as the gas and liquid phases, respectively. Gas is introduced through a 6 mm nozzle. Note that water contamination would alter the bubble-rise properties in the surface tension dominated regime. In ambient conditions, this regime covers the equivalent bubble diameters from 0.8 to 4mm (Fan and Tsuchiya, 1990). All the air-water experiments and simulations of this study are carried out under the condition where most equivalent bubble diameters exceed... 

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. 

The Eulerian gas velocity field required in both the mass balance and the above transport equation for nh is found by an approximate method first, the complete field of liquid velocities obtained with FLUENT is adapted downward because the power draw is smaller under gassed conditions next, in a very simple way of one-way coupling, the bubble velocity calculated from the above force balance is just added to this adapted liquid velocity field. This procedure makes a momentum balance for the bubble phase redundant this saves a lot of computational effort. 

Two-Phase Theory of Fluidization The two-phase theory of fluidization assumes that all gas in excess of the minimum bubbling velocity passes through the bed as bubbles [Toomey and Johnstone, Chem. Eng. Prog. 48 220 (1952)]. In this view of the fluidized bed, the gas flowing through the emulsion phase in the bed is at the minimum bubbling velocity, while the gas flow above U j, is in the bubble phase. This view of the bed is an approximation, but it is a helpful way... 

Thus, the bubbling region, which is an important feature of beds operating at gas velocities in excess of the minimum fluidising velocity, is usually characterised by two phases — a continuous emulsion phase with a voidage approximately equal to that of a bed at its minimum fluidising velocity, and a discontinous or bubble phase that accounts for most of the excess flow of gas. This is sometimes referred to as the two-phase theory of fluidisation. 

In practice, proportionately more gas flows infersfifially (i.e. between the particles) as the velocity is increased than at Umf- In addition, there is a limited interchange of gas between the bubble phase and the dense phase. As the gas velocity is increased further the very smallest particles are likely to be carried out of the bed in the exhaust stream. This is because at any realistic fluidizing gas velocify, fhe ferminal falling velocify of fhe very smallest particles will be exceeded. The loss of bed maferial in fhis way is known as elutriafion and will increase as u... 

As the gas flow rate increases beyond that at minimum fluidization, the bed may continue to expand and remain homogeneous for a time. At a fairly definite velocity, however, bubbles begin to form. Further increases in flow rate distribute themselves between the dense and bubble phases in some ways that are not well correlated. Extensive bubbling is undesirable when intimate contading between phases is desired, as in drying processes or solid catalytic reactions. In order to permit bubble formation, the... 

The equations for the two-phase fully mixed system are thus reduced to the equations for a single stirred tank by the physically motivated notion of only using the available fraction of the feed. This has been made possible by the uniformity of the dense phase and the linearity of the transfer process in the bubble. This allows us to see how the rather implausible assumption that the bubble phase is really well mixed can be made more realistic. Let us go to the other extreme, and suppose that the bubbles ascend with uniform velocity U. The surface area per unit length of reactor is SIH, where 5 is, as before, the total interphase area and H the height of the bed. If h is the transfer coefficient and z the height of a given point, a balance over the interval (z, z + dz) gives the equation for the concentration in the bubble phase b(z)... 

In the fluidized bed, the velocity of the particles is of a few cm s-1 and the critical thickness of the fused plastic is between 4 and 7 mm. A fact that should be taken into account is that, although gas velocity is increased, particle velocity hardly changes because most of the excess gas rises through the bed in the bubble phase. Nevertheless, in the conical spouted bed, particle velocity is increased by raising gas velocity up to the dilute spouted bed, in which bed voidage is uniform (between 0.9 and 0.99) and the particle descent velocity is almost equal to the ascent velocity [9]. 

The bubbling fluidization regime, as shown in Fig. 9.3(b), is reached with an increase in the gas velocity beyond (7mb. Bubbles form and induce vigorous motion of the particles. In the bubbling fluidization regime, bubble coalescence and breakup take place. With increasing gas velocity, the tendency of bubble coalescence is enhanced. Two distinct phases, i.e., the bubble phase and the emulsion phase, are present in this regime. 

The distribution of gas flow in the fluidized bed is important for the analysis of the fundamental characteristics of transport properties in the bed. One common method to estimate the gas flow division is based on the two-phase theory of fluidization, which divides the superficial gas flow in the bed into two subflows, i.e., bubble phase flow and emulsion phase flow, as shown in Fig. 9.14. According to the theory, the flow velocity can be generally expressed as... 

As a first approximation a convective term in the film region has been negleted, u is the superficial gas velocity and u f denotes the gas velocity at minimum fluidization conditions. Tne specific mass transfer area a(h) is based on unit volume of the expanded fluidized bed and e OO is the bubble gas hold-up at a height h above the bottom plate. Mathematical expressions for these two latter quantities may be found in detail in (20). The concentrations of the reactants in the bubble phase and in film and bulk of the suspension phase are denoted by c, c and c, respectively. The rate constant for the first order heterogeneous catalytic reaction of the component i to component j is denoted... 

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