## Tray efficiency calculation example

Example 7.1 For the column in Examples 2.4 (Sec. 2.3.1), 3.4 (Sec. 3.2.5), ani 6.1 (Sec. 6.5.2), find the tray efficiency.

solution The O'Connell correlation requires liquid viscosity and relative volatility at the average arithmetic temperature between the column top and bottom. From Table 6.10, the average temperature is (70 + 309)/2 = 190°F.This temperature is closest to stage 8. Table 6.10 gives a liquid viscosity of 0.133 cP for this stage, and shows little variation in liquid viscosity throughout the column. Also, from Example 3.1, relative volatility of the key components at the average temperature from the column is 1.945.

Alternatively, Fig. 7.5a gives Eoc = 70 percent, which agrees well with Lockett's equation form.

Allowing for a ± 10 percent error, an efficiency of 62 percent will be appropriate for design purposes. This can also be seen from Fig. 7.5a. The number of trays is therefore 18 stages/0.62 = 29 trays. In the rectifying section, there will be 29 x 'A» = 11, while in the stripping section there will be 29 x 'Vie = 18 trays.

It is worth it to compare this design efficiency against data listed in the Vital et al. tabulation (131). The tabulation contains no data for depropanizers, but there are data for two related systems: a 4.7-ft ID, 264-psia stabilizer Œmv = 100 percent) and a propane-butane separation (Eoc = 100 percent). The data suggest that the depropanizer design efficiency may be conservative. However, the data are too few and do not simulate the depropanizer closely enough to provide an adequate basis for designing for higher efficiency.