Velocity emulsion phase

Reynolds number based on velocity emulsion phase... 

Analysis of a method of maximizing the usefiilness of smaH pilot units in achieving similitude is described in Reference 67. The pilot unit should be designed to produce fully developed large bubbles or slugs as rapidly as possible above the inlet. UsuaHy, the basic reaction conditions of feed composition, temperature, pressure, and catalyst activity are kept constant. Constant catalyst activity usuaHy requires use of the same particle size distribution and therefore constant minimum fluidization velocity which is usuaHy much less than the superficial gas velocity. Mass transport from the bubble by diffusion may be less than by convective exchange between the bubble and the surrounding emulsion phase. 

The flow pattern of gas within the emulsion phase surrounding a bubble depends on whether the bubble velocity Ug is less than or greater than minimum fluidization velocity U . For Ubflow lines. For Ub> U , the much different case of Figure 4(B) results. Here a gas element which leaves the bubble eap rises much more slowly than the bubble, and as the bubble passes, it remms to the base of the bubble. Thus, a cloud of captive gas surrounds a bubble as it rises. The ratio of eloud diameter to bubble diameter may be written... 

The axial velocity profiles, calculated on the basis of Tollmien similarity and experimental measurement in Yang and Kcaims (1980) were integrated across the jet cross-section at different elevations to obtain the total jet flow across the respective jet cross-sections. The total jet flows at different jet cross-sections are compared with the original jet nozzle flow, as shown in Fig. 31. Up to about 50% of the original jet flow can be entrained from the emulsion phase at the lower part of the jet close to the jet nozzle. This distance can extend up to about 4 times the nozzle diameter. The gas is then expelled from the jet along the jet height. 

The first term, (1 - ty) /(I - z), corrects for the voidage difference between that in thejet and that in the emulsion phase. The second term, ( - z) /(I - z), takes into account the fact that only a fraction of the particles having the entrainment velocity Ve will be entrained, the remainder rebounding back to thejet wall due to collisions with the particles already in thejet. Substituting Eq. (63) into Eq. (62), we have... 

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. 

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. 

As in the fluidized beds analysis (Section 3.8.3), a similar simplification has been made in Kunii-Levenspiel model for the material balances in the emulsion phase, where again the corresponding derivatives have been omitted (eqs. (3.529) and (3.530)). As in the case of liquid flow in trickle beds, the flow of the gas in the emulsion phase is considered too small and so the superficial velocities can be neglected. Thus, in trickle beds, from eq. (3.367),... 

The emulsion phase stays at minimum fluidizing conditions. Thus, the relative velocity of the gas and solid remains unchanged. 

The concentration of solids in the wake is the same as the concentration of solids in the emulsion phase, and therefore, the gaseous void fraction in the wake is also the same as in the emulsion phase. Because the emulsion phase is at the minimum fluidizing condition, the void fraction in the wake is equal to film. The wake, however, is quite turbulent, and the average velocities of both the solid and gas in the wake are assumed to be the same and equal to the upward velocity of the bubbles. 

The only model that takes into consideration the fraction of the gas that flows through the emulsion phase is the Orcutt-Davidson-Pigford one and for the specific superficial velocity of 0.1 m/s, /bub = 0.86. The results of the models are close due to the fact that the flow... 

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. 

Consider a bubble rising in a fluidized bed. It is assumed that the bubble is solids-free, is spherical, and has a constant internal pressure. Moreover, the emulsion phase is assumed to be a pseudocontinuum, incompressible, and inviscid single fluid with an apparent density of pp(l — amf) + pamf. It should be noted that the assumption of incompressibility of the mixture is not strictly valid as voidage in the vicinity of the bubble is higher than that in the emulsion phase [Jackson, 1963 Yates et al., 1994]. With these assumptions, the velocity and pressure distributions of the fluid in a uniform potential flow field around a bubble, as portrayed by Fig. 9.10, can be given as [Davidson and Harrison, 1963]... 

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 discussed in Chapter 9, dense-phase fluidization other than particulate fluidization is characterized by the presence of an emulsion phase and a discrete gas bubble/void phase. At relatively low gas velocities in dense-phase fluidization, the upper surface of the bed is distinguishable. As the gas velocity increases, the bubble/void phase gradually becomes indistinguishable from the emulsion phase. The bubble/void phase eventually disappears and the gas evolves into the continuous phase with further increasing gas velocities. In a dense-phase fluidized bed, the particle entrainment rate is low and increases with increasing gas velocity. As the gas flow rate increases beyond the point corresponding to the disappearance of the bubble/void phase, a drastic increase in the entrainment rate of the particles occurs such that a continuous feeding of particles into the fluidized bed is required to maintain a steady solids flow. Fluidization at this state, in contrast to dense-phase fluidization, is denoted lean-phase fluidization. 

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