x. mote fraction benzene in liquid (a)

x, mole fraction benzene In liquid <b>

Figure 9.2 x-y diagrams for Example 9.1. (a) Column 1; (A) column 2.

x, mole fraction benzene In liquid <b>

Figure 9.2 x-y diagrams for Example 9.1. (a) Column 1; (A) column 2.

requires a procedure that knits a maldistribution model together with a stage calculation model. Minimum requirement is a shortcut expression for maldistribution interknitted with a shortcut stage model (e.g., an x-y diagram). Such a procedure will suffer from all the limitations of shortcut stage models (e.g., Sec. 2.2.2). For rigorous computations, a rigorous model for maldistribution must be interknitted with a rigorous stage model (Chap. 4). A proper model would be extremely complex and appears to be many years down the road.

9.2.3 Effect of lateral mixing

Comparison of Fig. 9.2a to b shows that maldistribution causes changes in composition along the column cross section. At the same height, the mole fraction of the lighter component is highest when the local L/V ratio is highest. For instance, in column 1 of Example 9.1 (55 percent of the liquid), half way up the rectifying section (stage 4) the liquid contains 82 percent benzene while in column 2 (45 percent of the liquid), at the same height, the liquid contains 53 percent benzene (see Fig. 9.2). Lateral mixing, both of vapor and liquid, acts to reduce this composition difference, thus counteracting the reduction of packing efficiency. This lateral mixing is caused by liquid and vapor flow Bideways around each packing element.

Huber and Hiltbrunner (135) showed that when the column to packing diameter ratio {DjJDp) is smaller than 10, the effect of lateral mixing is so large that only a strong maldistribution can decrease column efficiency (but note also that this range of DTiDp is uncommon in practice because of wall effects, Sec. 9.2,4). However, when Dt!Dp is greater than 30, the lateral mixing becomes too small to counteract the influence of maldistribution, and the effect of variations in LfV ratio dominates.

In large-diameter towers and long beds, a redistributor may help correct a maldistributed composition profile. For instance, remixing stage 4 liquid of the two columns in Example 9.1 would have alleviated the pinch. Good redistribution practices are discussed elsewhere (40).

In the presence of maldistribution, efficient becomes a function of the following parameters.

1. The LfV ratio

2. The Dip/Dp ratio

3. Feed and product compositions

4. Thermal state of the feed and feedpoint location

5. Packing height

6. Relative volatility

The effects of these variables on efficiency in the presence of maldistribution are complex and interactive, as can be expected from Example 9.1. For instance, it has been shown (116,137) that under some feed composition and reflux conditions, efficiency increases with feed composition; under other conditions, the converse occurs. It has also been shown that as LfV was reduced from total reflux, efficiency improved—at least in some cases. Note, however, that the reverse may occur in other columns.

9.2.4 Effect of liquid flow nonuniformfty

Early work on liquid flow in a packed bed used a "random-walk" probability model (139,141-144). The spread of liquid from a point source was described by the normal gaussian distribution. In the 1960s, Porter et al. (141-143) developed the rivulet model, postulating that liquid runs down the packing along "preferred paths" or rivulets. The preferred paths take a random route through the packings. Rivulets may be of different sizes, may coalesce (when the path of one runs into another) and may split. Most recent models (67,136,145,146) analyze liquid spread in terms of Albright's concept (145) of interconnected random cells. Liquid and vapor leaving each cell are distributed to the surrounding cells according to some splitting rules. Based on both modeling and experimentation, the following have been established:

1. Liquid profile unevenness is more severe at low liquid flow rates (140,142,147).

2. Liquid flows through the bed in a time-independent stable flow pattern (140,141,148).

3. Both preflooding and repacking the bed influence the stable flow pattern (66,140,141,149), Repackinghas a much greater effect than preflooding (141).

4. The liquid reaches a stable profile after a certain height from the top of the bed, assuming good initial liquid irrigation (66,131,140, 147,149).

5. Smaller packings tend to spread the liquid more uniformly than larger packings (140). The liquid spread depends on packing geometry, but not on packing material (140,141). Structured packings generally spread liquid very uniformly (66,140,146). Modern random packing spread the liquid somewhat less uniformly, but more uniformly than first-generation random packings (140).

6. The uniformity of liquid spread in structured packings strongly depends on (67,146) texture of surface, presence and sue of perforations, connection of packing elements in packing layers, and presence of wall wipers.

7. Below the loading point, gas velocity has little effect on liquid flow profile (66,67,140).

Hoek (140) measured packed-bed liquid distribution profiles. A typical profile is shown in Fig. 9.3. It shows variation of liquid flows throughout the bed, and a tendency of liquid to flow toward the wall.

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