Bubbling 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. 

Minchener el al. report that the bubble phase of atmospheric fluidised bed combustion has a pOi in the range 2 x 10 to 2 x 10 Combustion in the dense phase is sub-stoichiometric, with the /Oj as low as 10 and SO2 and SO3 present in the range 500-5 000ppm. Low Cr-Mo steels show heavy scaling in these conditions, whereas 9-12% Cr steels show good resistance to sulphidation up to 650°C. Roberts et however, report that for pressurised fluidised-bed combustion, ferritic steels at or below 9% Cr show heavy general corrosion above 540-560°C. 

In the first class, the particles form a fixed bed, and the fluid phases may be in either cocurrent or countercurrent flow. Two different flow patterns are of interest, trickle flow and bubble flow. In trickle-flow reactors, the liquid flows as a film over the particle surface, and the gas forms a continuous phase. In bubble-flow reactors, the liquid holdup is higher, and the gas forms a discontinuous, bubbling phase. 

The two models commonly used for the analysis of processes in which axial mixing is of importance are (1) the series of perfectly mixed stages and (2) the axial-dispersion model. The latter, which will be used in the following, is based on the assumption that a diffusion process in the flow direction is superimposed upon the net flow. This model has been widely used for the analysis of single-phase flow systems, and its use for a continuous phase in a two-phase system appears justified. For a dispersed phase (for example, a bubble phase) in a two-phase system, as discussed by Miyauchi and Vermeulen, the model is applicable if all of the dispersed phase at a given level in a column is at the same concentration. Such will be the case if the bubbles coalesce and break up rapidly. However, the model is probably a useful approximation even if this condition is not fulfilled. It is assumed in the following that the model is applicable for a continuous as well as for a dispersed phase in gas-liquid-particle operations. 

The emulsion phase approaches the performance of a CSTR with its inherent lower yield for most reactions. To make matters worse, mass transfer between the emulsion and bubble phases becomes limiting to the point that some of the entering gas completely bypasses the catalytic emulsion phase. The system behaves like the reactor in Example 11.5. 

Cross-sectional area associated with the bubble phase 11.46... 

Mass transfer coefficient between the emulsion and bubble phases in a gas fluidized bed 11.45... 

Because of the inadequacies of the aforementioned models, a number of papers in the 1950s and 1960s developed alternative mathematical descriptions of fluidized beds that explicitly divided the reactor contents into two phases, a bubble phase and an emulsion or dense phase. The bubble or lean phase is presumed to be essentially free of solids so that little, if any, reaction occurs in this portion of the bed. Reaction takes place within the dense phase, where virtually all of the solid catalyst particles are found. This phase may also be referred to as a particulate phase, an interstitial phase, or an emulsion phase by various authors. Figure 12.19 is a schematic representation of two phase models of fluidized beds. Some models also define a cloud phase as the region of space surrounding the bubble that acts as a source and a sink for gas exchange with the bubble. 

Figure 10. The flow pattern of the bubble phase in a bed of 200 mm diameter (uQ = 9 cm/sec, H= 50 cm). (From Werther, 1974.)...

Bubble Dynamics. To adequately describe the jet, the bubble size generated by the jet needs to be studied. A substantial amount of gas leaks from the bubble, to the emulsion phase during bubble formation stage, particularly when the bed is less than minimally fluidized. A model developed on the basis of this mechanism predicted the experimental bubble diameter well when the experimental bubble frequency was used as an input. The experimentally observed bubble frequency is smaller by a factor of 3 to 5 than that calculated from the Davidson and Harrison model (1963), which assumed no net gas interchange between the bubble and the emulsion phase. This discrepancy is due primarily to the extensive bubble coalescence above the jet nozzle and the assumption that no gas leaks from the bubble phase. 

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 the other form of fluidisation, aggregative fluidisation, two phases are present in the bed—a continuous or emulsion phase, and a discontinuous or bubble phase. This... 

Essentially aggregative fluidization is a two-phase system there is a dense phase (sometimes reterred to as the emulsion phase), which is continuous, and a discontinuous phase called the lean or bubble phase. The simplitied assumption that all the gas over and above that required tor minimum fluidization flows up through the bed in the form ot bubbles is known as the two-phase theory. It the total volumetric flow ot gas is Q then... 

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... 

Shear enhancement effects in foam formation can be understood through the modified cavity model. Shear force behaves as catalyst to reduce energy barrier to allow a quik path from stable gas cavity to unstable bubble phase. It can be concluded that both shear rate and viscosity contribute to foam nucleation in the continuous foam extrusion process. Therefore, proper die opening and process conditions will help to optimise the foam product. 11 refs. 

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