The upper column of an air-separation system of the type shown in Exercise 7.40 contains 48 sieve trays and operates at a nominal pressure of 131.7 kPa. A feed at 80 K and 131.7 kPa enters the top plate at 1,349 lbmol/h with a composition of 97.868 mol% nitrogen, 0.365 mol% argon, and 1.767 mol% oxygen. A second feed enters Tray 12 from the top at 83 K and 131.7 kPa at 1,832 lbmol/h with a composition of 59.7 mol% nitrogen, 1.47 mol% argon, and 38.83 mol % oxygen. The column has no condenser, but has a partial reboiler.  Vapor distillate leaves the top plate at 2,487 lbmol/h, with remaining products leaving the reboiler as 50 mol% vapor and 50 mol% liquid. Assume ideal solutions. Determine the effect of flooding on the separation and the median EMV for oxygen, using a rate-based model.

Data From Exercise 7.40

O₂ and N₂ are obtained by distillation of air using the Linde double column, shown in Figure 7.45, which consists of a lower column at elevated pressure surmounted by an atmospheric-pressure column. The boiler of the upper column is also the reflux condenser for both columns. Gaseous air plus enough liquid to compensate for heat leak into the column (more liquid if liquid-oxygen product is withdrawn) enters the exchanger at the base of the lower column and condenses, giving up heat to the boiling liquid and thus supplying the column vapor flow. The liquid air enters an intermediate point in this column. The rising vapors are partially condensed to form the reflux, and the uncondensed vapor passes to an outer row of tubes and is totally condensed, the liquid nitrogen collecting in an annulus, as shown. By operating this column at 4 to 5 atm, the liquid oxygen boiling at 1 atm is cold enough to condense pure nitrogen. The liquid in the bottom of the lower column contains about 45 mol% O₂ and forms the feed for the upper column. This double column can produce very pure O₂ with high O2 recovery, and relatively pure N₂. On a single McCabe–Thiele diagram—using equilibrium lines, operating lines, q-lines, a 45° line, stepped-off stages, and other illustrative aids—show qualitatively how stage requirements can be computed.