Shallow beds

Full rate modeling Accurate description of transitions Appropriate for shallow beds, with incomplete wave development General numerical solutions by finite difference or collocation methods Various to few... 

Cycles Design methods for cycles rely on mathematical modeling (or empiricism) and often extensive pilot plant experiments. Many cycles can be easily analyzed using the methods described above apphed to the collection of steps. In some cycles, however, especially those operated with short cycle times or in shallow beds, transitions may not be very fully developed, even at a periodic state, and the complexity may be compounded by multiple sorbates. 

The name derives from the firebed produced by containing a mixture of silica sand and ash through which air is blown to maintain the particles in suspension. The beds are in three categories, shallow bed, deep bed and... 

The deep bed, as its name implies, is similar to the shallow bed but in this case may be up to 3 meters deep in its fluidized state, making it suitable only for large boilers. Similarly, the recirculating fluid bed is only applicable to large watertube boilers. 

Several applications of the shallow-bed system are available for industrial boilers the two most used being the open-bottom shell boiler and the composite boiler. With the open-bottom shell, the combustor is sited below the shell and the gases then pass through two banks of horizontal tubes. 

A pellet bed must be shallow to avoid a high pressure drop. Most designs have a depth of 1 to 2 in., representing 5 to 15 layers of pellets. This shallow bed differs considerably from industrial practices in petroleum and chemical plants where a depth of several hundred layers is the rule. The more open monolith and metallic screens offer a lower pressure drop per inch, so that a bed 6 in. deep is still acceptable. Two pellet beds in series would create very high pressure drops. 

Steady-state reactors with ideal flow pattern. In an ideal isothermal tubular pZi/g-yZovv reactor (PFR) there is no axial mixing and there are no radial concentration or velocity gradients (see also Section 5.4.3). The tubular PFR can be operated as an integral reactor or as a differential reactor. The terms integral and differential concern the observed conversions and yields. The differential mode of reactor operation can be achieved by using a shallow bed of catalyst particles. The mass-balance equation (see Table 5.4-3) can then be replaced with finite differences ... 

The flow pattern of fluids in gas-liquid-solid (catalyst) reactors is often far from ideal. Special care must be taken to avoid by-passing of the catalyst particles near the reactor walls, where the packing density of the catalyst pellets is lower than in the centre of the bed. By-passing becomes negligible if the ratio of reactor to particles diameter is larger than 10 a ratio of 20 is recommended. Flow maldistributions might be serious in the case of shallow beds. Special devices must be used to equalize the velocity over the cross-section of the reactor before reactants are introduced onto the catalyst bed. 

In many respects, the solutions to equations 12.7.38 and 12.7.47 do not provide sufficient additional information to warrant their use in design calculations. It has been clearly demonstrated that for the fluid velocities used in industrial practice, the influence of axial dispersion of both heat and mass on the conversion achieved is negligible provided that the packing depth is in excess of 100 pellet diameters (109). Such shallow beds are only employed as the first stage of multibed adiabatic reactors. There is some question as to whether or not such short beds can be adequately described by an effective transport model. Thus for most preliminary design calculations, the simplified one-dimensional model discussed earlier is preferred. The discrepancies between model simulations and actual reactor behavior are not resolved by the inclusion of longitudinal dispersion terms. Their effects are small compared to the influence of radial gradients in temperature and composition. Consequently, for more accurate simulations, we employ a two-dimensional model (Section 12.7.2.2). 

Bauer et al. (1981) measured the influence of bed diameter on the catalytic decomposition of ozone. Figure 6 shows the decrease of the conversion with bed diameter for Bauer s data. This figure also shows the influence of distributor design on conversion. In many small scale experiments, a porous plate is used which will give better performance than the distributors used in large shallow bed commercial designs. 

Figure 29 (Qin and Liu, 1982) shows the behavior of individual particles above the distributor recorded by video camera of small clusters of particles, coated with a fluorescent material and spot-illuminated by a pulse of ultra violet light from an optical fiber. The sequential images, of which Fig. 29 just represents exposures after stated time intervals, were reconstructed to form the track of motion of the particle cluster shown in Fig. 30. Neither this track nor visual observation of the shallow bed while fluidized, reveal any vestige of bubbles. Instead, the particles are thrown up by the high velocity jets issuing from the distributor orifices to several times their static bed height.

CAFB [Chemically active fluidized-bed] A coal-gasification process intended for producing gas for power generation. Coal particles are injected into a shallow bed of lime particles that trap the sulfur dioxide. The bed particles are regenerated in a second fluidized bed, releasing the sulfur dioxide. Developed in the 1970s by the Esso Petroleum Company, UK, but not commercialized. 

Why is the catalyst arranged in four shallow beds rather than in one deeper bed ... 

Pyrolysis of propane was accomplished by bubbling the gas through a shallow bed of molten lead at 1400 F and 4 psig (Fair et al, Chem Eng Prog 53 433, 1953). The vessel was assumed to have no gradients of temperature or... 

Kerr (7-9) has shown the critical role of the calcination environment and bed geometry in the formation of USY zeolites ("deep bed" vs."shallow bed"calcination). Ward (10) prepared USY zeolites by calcining ammonium Y zeolites in flowing steam. The work done by Kerr and Maher et al. (11) has clearly demonstrated that USY zeolites are formed as a result of aluminum expulsion from the framework at high temperatures in the presence of steam. The nature of the non-framework aluminum species has not been completely clarified. Obviously, their composition will be strongly affected by the preparation procedure of the USY zeolite. Table II shows different oxi-aluminum species assumed to be formed during thermal dealumination of the zeolite framework. 

One difficulty in making measurements of transfer coefficients is that equilibrium is rapidly attained between particles and fluidising medium. This has in some cases been obviated by the use of very shallow beds. In addition, in measurements of mass transfer, the methods of analysis have been inaccurate, and the particles used have frequently been of such a nature that it has not been possible to obtain fluidisation of good quality. 

A number of other workers have measured mass transfer rates. McCune and Wilhelm(124) studied transfer between naphthol particles and water in fixed and fluidised beds. Hsu and Molstad(127) absorbed carbon tetrachloride vapour on activated carbon particles in very shallow beds which were sometimes less than one particle diameter... 

A relatively new design of a high-rate DAF unit uses a shallow bed system (Supracell) with only 3 minutes of retention time and operated at an overflow rate of 140Lpm/sqm (3.5 gpm/sq ft) [42]. This unit has been used for industrial and municipal wastewater treatment and offers lower capital cost and headroom requirements. It was installed at a petrochemical complex in Texas as a secondary clarifier to improve the operation and the capacity of an existing activated sludge system [43]. In recent years, nitrogen has replaced air in covered DAF systems because of the potential for explosion. These systems are called dissolved nitrogen flotation (DNF) systems. The operations of DAF and DNF are similar. 

For a shallow bed, fhe pressure drop across fhe disfribufor should be of fhe same order as fhe bed pressure drop (Richardson, 1971). 

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