Bed aspect ratio

It may be that the extent of dispersion is to be determined from correlations rather than by direct experimental means. Suitable correlations based on large quantities of data exist for common reactor geometries, i.e. tubular reactors, both empty and packed, fluidised beds or bubble columns. Some of these are expressed in graphical form in, for instance, refs. 17, 21 and 26. Most forms of correlation give the intensity of dispersion D/ud as a function of Reynolds and/or Schmidt numbers if this intensity is multiplied by an aspect ratio, i.e. djL for a tubular reactor, then the dispersion number is obtained. 

There is no radial velocity, and the axial velocity across the radius of the packed bed is uniform. Schwartz and Smith (1953) found that the velocity across the diameter of a packed bed is not uniform for radial aspect ratios (tube-to-particle diameter) less than about 30, due to the significant effect of the increased void space near the wall where the particles are locally ordered. This result has been verified by Hoiberg et al. (1971) for a packed bed reactor with radial aspect ratio about 50. They considered a radial velocity variation suggested by experimental observations with a sharp peak about 15% greater than the mean fluid velocity situated close to the wall. Simulations using their model showed results virtually identical to those obtained with a uniform velocity profile.3... 

Preliminary residence time distribution studies should be conducted on the reactor to test this assumption. Although in many cases it may be desirable to increase the radial aspect ratio (possibly by crushing the catalyst), this may be difficult with highly exothermic solid-catalyzed reactions that can lead to excessive temperature excursions near the center of the bed. Carberry (1976) recommends reducing the radial aspect ratio to minimize these temperature gradients. If the velocity profile in the reactor is significantly nonuniform, the mathematical model developed here allows predictive equations such as those by Fahien and Stankovic (1979) to be easily incorporated. 

Bed moisture content Solution type and feed rate Bed temperature Fluidization velocity Aspect ratio Nozzle position and atomization Velocity Air distributor design Jet grinding... 

Fluidized-bed reactor (FLBR) The up-flow gas or liquid phase suspends the fine solid particles, which remain in the reactor (Figure 3.8). This reactor is of tubular shape with a relatively low aspect ratio of length to diameter. The most common application of FLBR is the classical FCC process. 

The catalyst beds are mounted in a single reactor vessel because it is more economical than using multiple vessels. The spacing between beds is set at 1 m. The length-to-diameter aspect ratio of the vessel is 10. Because a multibed reactor must have internal piping, flow distributors, and bed supports, a multi-bed reactor vessel is more expensive than a simple vessel. We assume that each additional bed increases reactor capital cost by about 25%, as shown in Table 5.2. 

Pressure Drop, Mass and Heat Transfer Pressure drop is more important in reactor design than in analysis or simulation. The size of the compressor is dictated by pressure drop across the reactor, especially in the case of gas recycle. Compressor costs can be significant and can influence the aspect ratio of a packed or trickle bed reactor. Pressure drop correlations often may depend on the geometry, the scale, and the fluids used in data generation. Prior to using literature correlations, it often is advisable to validate the correlation with measurements on a similar system at a relevant scale. 

To this end, experimental heat and mass transfer coefficients were determined in a fluidized bed. Nusselt and Sherwood numbers were obtained in terms of Reynolds number and aspect ratios dp/L and dp/D. The results are also analyzed in terms of the Kato and Wen(5) and Nelson and Galloway(6) models. 

If the flow rate is sufficiently high to create turbulent flow, then Pe is a constant and the magnitude of the right-hand side of the equation is determined by the aspect ratio, L/d. By solving Equation, (8.4.12) and comparing the results to the solutions of the PER [Equation (8.4.3)], it can be shown that for open tubes, L/d, > 20 is sufficient to produce PER behavior. Likewise, for packed beds, L/d, > 50 (isothermal) and L d, >150 (nonisothermal) are typically sufficient to provide PER characteristics. Thus, the effects of axial dispersion are minimized by turbulent flow in long reactors. 

In principle, the LFR is a fixed-bed reactor with a very low aspect ratio, i,e the ratio of bed height to bed diameter. Typically, the thickness of the catalyst layers is in the range of 15-75 mm. Hence, the reactor can be considered as a pancake reactor, in which the pancake has been folded for convenient accommodation in the reactor space. Because of the shallowness of the bed and its very large cross section, the pressure drop is much lower than in the case of a fixed bed of more conventional dimensions. 

An aspect ratio (bed length to pellet diameter) greater than 20 and preferably greater than 100 should be used to minimise axial mixing . 

Fig. 7a shows the analytical solution for probability of top seal leakage, which has been validated using Monte Carlo simulations. The maximum throw (Tjnax) needed for juxtaposition of leaky beds either side of a fault is calculated by considering the thickness of the thickest shale layer and the fault plane aspect ratio AR). The latter is included because the locus of Tmax may not coincide with the shale layer mid-point. A small correction to for the effect of the vertical gradient in displacement is described by... 

Powders do not readily transmit stress. In the case of columns, normal stress or weight of the bulk solid is held by wall friction. In addition, normal stress is not isotropic, with radial stress being only a fraction of normal stress. In fact, the end result is that stress in silos scales with diameter rather than bed height, a most obvious manifestation of this being the narrow aspect ratio of a corn silo. 

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