Maldistribution factor

This quantity characterizes the heterogeneity of the liquid flow it increases with the heterogeneity. 0 is very similar to the maldistribution factor defined by Berner et al.(l9T8). 

It is appropriate at this point to note that the maldistribution component of the bed effectiveness factor can be largely corrected, and the flow distribution improved by insertion in the bed of high-resistance gas redistributors. The maldistribution factor (p then becomes... 

Figure 6.4. Basic flow configurations in radial beds. On the left the two different axial profiles of the radial velocity for a maldistribution factor (p positive and negative.

Figure 6.5. Relationship between the maldistribution factor (p and the height-to-diameter ratio of the third catalyst bed of Fig. 6.2 in the tt- and Z-configuration. Operating conditions are as...

In Fig. 6.5 the maldistribution factor is shown as a function of the height-to-diameter radio for the previously considered (Fig. 6.2b) catalyst bed, in the tt- and Z-configuration, and for the sizing indicated in the sketch on the left of the same figure. The corresponding effectiveness factors of the full bed may be seen in Fig. 6.6. These values, of course, refer to a specific example, and the result may be considerably different in other cases. It should be kept in mind that, while the... 

Figure 6.6. Effect of the maldistribution factor (p on the conversion degree for the radial beds considered in Fig. 6.5. Operating conditions are as reported in Fig. 6.2b.

The data show that the maldistribution factor is practically not dependent on the liquid superficial velocity for Pall rings. For R hig Rings the effect of this parameter is very strong. The reason for this difference is not explained by the authors. 

In Table 1 the maldistribution factors of the liquid phase for different random and corrugated structured packings are presented. 

The form of Eq. (1) is us to describe also the maldistribution of the gas phase. Neverthel, up to now it is not possible to use this statistical fector for calculation of packed bed columns. It can be used only for comparison in cases when the number of the cells per column cross-section is constant. The rrason is that it is not demonstrated neither theoretically nor experimentally that the value of the maldistribution factor is not depending on die number of the collecting cells, i.e. on the experimenter choosing that number. Moreover, it is easy to prove that it depends on n. Nevertheless, the maldistribution factor is usefiil for determining the hei t of the packing after which the maldistribution remains constant. 

The maldistribution factor Jt for tire gas pha% is to characterize the divergence between the real flow and the id piston flow [30, 36, 38, 43, 44]. Usually it is defined the equation ... 

When straight or serrated segmental weirs are used in a column of circiilar cross secdion, a correction may be needed for the distorted pattern of flow at the ends of the weirs, depending on liquid flow rate. The correction factor F from Fig. 14-33 is used direcdly in Eq. (14-112) or Eq. (14-119). Even when circular downcomers are utilized, they are often fed by the overflow from a segmental weir. When the weir crest over a straight segmental weir is less than 6 mm V in), it is desirable to use a serrated (notched) weir to provide good liquid distribution. Inasmuch as fabrication standards permit the tray to be 3 mm Vh in) out of level, weir crests less than 6 mm V in) can result in maldistribution of hquid flow. 

The above results are based on data obtained for optimized designs and under ideal test conditions. To translate our findings to the real world, one must factor in liquid and vapor maldistribution, which is far more detrimental to the efficiency of packings than trays. In addition. one also must account for poor optimization or restrictive internals, which are far more detrimental to the capacity of trays than packings. We also have cited several other factors that need to be considered when translating the findings of our analysis to real-world towers. ... 

Vapor-Liquid Gravity Separator Design Fundamentals The critical factors in the performance of a horizontal separator are the vapor residence time and the settling rate of the liquid droplets. However, two other factors enter into the design—the vapor velocity must be limited to avoid liquid entrainment, and there must be sufficient freeboard within the vessel to allow for a feed distributor. For vertical separators, the design is based on a vapor velocity that must be less than the settling velocity of the smallest droplet that is to be collected, with due allowance for turbulence and maldistribution of the feed. The vapor residence time is a function of the vapor flow rate (mass), vapor density, and volume of vapor space in the separator, based on the following ... 

The effectiveness of a fixed-bed operation depends mainly on its hydraulic performance. Even if the physicochemical phenomena are well understood and their application in practice is simple, the operation will probably fail if the hydraulic behavior of the reactor is not adequate. One must be able to recognize the competitive effects of kinetics and fluid dynamics mixing, dead spaces, and bypasses that can completely alter the performance of the reactor when compared to the ideal presentation (Donati and Paludetto, 1997). The main factor of failure in liquid-phase operations is liquid maldistribution, which could be related to low liquid holdup in downflow operation, or other design problems. These effects could be critical not only in full-scale but also in pilot- or even in laboratory-scale reactors. 

Modeling and Prediction Maldistribution may drastically reduce packing efficiency. HETP may increase by a factor as high as 2 or 3 due to maldistribution. Shariat and Kunesh [lnd. Eng. Chem. Res., 34(4), 1273 (1995)] provide a good demonstration. 

Three factors appear to set the effect of maldistribution on efficiency ... 

A third factor is the nonuniformity of the flow profile through the packing (Sec. 9.2.4). This nonuniformity was ohserved as far back as 1935 (138) and first modeled fay Cihla and Schmidt (139). Hoek (140) combined this factor with the previous two for modeling the effect of maldistribution an packing efficiency. 

CF-tx is preferable for <1 and CP-7T is superior for <1. When maldistribution is absent, the effects of flow direction become evident, and for highly exothermic, irreversible Reaction, CPRF is preferred. Based on this argument, CP-lt would be the best flow configuration since it gives the best profile and also enjoys the advantageous effects of flow direction for highly exothermic reactions. In any case, the effects of all the factors at a certain reaction condition can be determined from the analysis presented here. 

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