Packed beds 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... 

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. 

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. 

Generally, stacked-membrane devices have a large diameter length ratio, while the opposite is true for packed beds. However, there is no fundamental reason why packed beds of similar aspect ratios as current stacked membrane devices cannot be formed. 

Multiphase packed-bed or trickle-bed microreactor [29, 30] Standard porous catalysts are incorporated in silicon-glass microfabricated reactors consisting of a microfluidic distribution manifold, a single micro-channel reactor or a microchannel array and a 25-pm microfllter. The fluid streams come into contact via a series of interleaved high aspect ratio inlet chaimels. Perpendicular to these chaimels, a 400-pm wide channel is used to deliver catalysts as a slurry to the reaction chaimel and contains two ports to allow cross-flow of the slurry. High maldistribution, pressure drop and large heat losses may occur... 

Chigada PI. Characterisation of flow and heat transfer patterns in low aspect ratio packed beds by a 3D network-of-voids model. Chemical Engineering Research and Design 2011 89 230-238. 

In principle, the concentration of the adsorbate in the effluent stream is zero before breakthrough, at least if we have no by-pass effects induced by very narrow packed beds with an aspect ratio of less than... 

Figure 4.10.70 Effective radial conductivity of a packed bed of spherical particles for different aspect ratios c/r/c/p, gases (Pr = 0.7), and high Rgp values (Rgp = Usdp/v) lines correlation given in VDI (2002), see Eq. (4.10.194), for a value of the static contribution A,bed/ fiuid 4 area range of literature data (Yagi and Kunii, 1960 Yagi and Wakao, 1959 Calderbank and Pogorski, 1957 Demirel, Sharma, and Al-Ali, 2000 Dixon, 1985 Li and Finlayson,...

The principles outlined for fiber-sphere and sphere-sphere interactions in pastes can be applied to platelet-sphere systems. Figure 17 shows the relationship for mica (J)-alumina composite [33], where it can be seen that the paste data follow the water absorption data for the packed bed. A difficulty which remains with platelets is that the contribution the diameter and aspect ratio play to packing is unclear. In this example, the powder and the plate have similar diameters, but the aspect ratio of the plate is only 0.1. 

The aspect ratio of the bed (height/diameter) determines the fluid velocity through the packed bed according to the equation ... 

Cross-sectional area and is adjusted so that the magnitude of fluid mechanical forces (proportional to the aspect ratio) within the bed is below damaging levels (Fig. 13). Fluidized beds differ from packed beds in that the perfusing fluid motion maintains the microcarriers in suspension. Packed-bed systems have been shown to support cell densities exceeding 10 cells/mL when using microporous microcarriers (500 to 850 lvc in diameter). In addition, packed beads (1.5-mm diameter) have been used to entrap aggregates of hepatocytes. The latter application was shown to maintain a relatively stable level of albumin secretion (a liver-specific product) for up to 3 weeks. 

The other type of decision variable is an equipment characteristic. The reactor volume and the number of stages are examples. Each specification that must be made before ordering a piece of equipment is a decision variable. Thus, the area of a heat exchanger and the aspect ratio of a packed-bed reactor are decision variables. 

Figure 12 shows the variation of bed ETC with aspect ratio. It can be observed that with the deviation of aspect ratio from 1.0, the bed ETC increases significantly, especially for a high particle thermal conductivity. Spheres have the lowest ETC. Such a feature can be explained by the difference of packing structures. For example, with particles being more... 

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