Liquid air is fed to the top of a perforated-tray reboiled stripper operated at substantially atmospheric pressure. Sixty percent of the oxygen in the feed is to be drawn off in the bottoms vapor product from the still. This product is to contain 0.2 mol% nitrogen. Based on the assumptions and data given below, calculate:
(a) The mole percent of nitrogen in the vapor leaving the top plate.
(b) The moles of vapor generated in the still per 100 mol of feed.
(c) The number of theoretical plates required.
SOLUTION:
Subject:
Separation of air in a reboiled stripper
Given:
Reboiled stripper with total reboiler operating at 1 atm. Liquid air (79.1 mol% N2 and 20.9 mol% O2) fed to top stage. 60% of O2 in the feed is drawn off in vapor product from the reboiler. Bottoms vapor product contains 0.2 mol% N2. Vapor-liquid equilibria data are given.
Assumptions:
Feed is a saturated liquid.
Find:
Mol% N2 in vapor from top stage.
Moles of vapor generated in reboiler per 100 moles of feed.
Number of equilibrium stages required.
Analysis:
(a)
Take a basis of F = 100 mol/h. Therefore, 79.1 mol/h of N2 and 20.9 mol/h of O2 in the feed. Bottoms product vapor contains 0.6(20.9) = 12.54 mol/h of O2 and (0.2/99.8)(12.54) = 0.025 mol/h N2. By material balance, the overhead vapor contains 20.9 - 12.54 = 8.36 mol/h O2 and 79.1 - 0.025 = 79.075 mol/h of N2. The mol% N2 in the overhead vapor = 79.075/(8.36 + 79.075) x 100% = 90.4 %.
(b)
Assume constant molar overflow. Then because the feed is assumed to be a saturated liquid, the moles of vapor generated in the reboiler per 100 moles of feed = mol/h of overhead vapor = 8.36 + 79.075 = 87.435 moles per 100 moles of feed.
(c)
Use a y-x diagram for N2 because it is the more volatile. The slope of the operating line is L/V = 100/87.435 = 1.14. At the top of the column, the operating line terminates at a (y-x) of (0.904, 0.791). At the bottom of the column, with a total reboiler, the operating line terminates at a (y-x) of (0.002, 0.002). To determine the number of equilibrium stages, it is convenient to use two diagrams, the usual one and a second one for just the very low mole fraction region so as to gain accuracy in the region of the lower end of the operating line. From the two diagrams, it is seen that just less than 8 equilibrium stages are required.