Separation Process Principles- 2n - Seader &amp; Henley - Solutions Manual

# 2 equilibrium stages in the rectifying section thus

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Unformatted text preview: iciency for distillation of a methanol-water mixture. Given: Performance data for a distillation column. Vapor-liquid equilibrium data. Assumptions: Partial reboiler is an equilibrium stage. Constant molar overflow. Find: (a) (b) (c) (d) Overall plate efficiency from performance data. Predicted plate efficiency from Drickamer-Bradford correlation. Predicted plate efficiency from O'Connell correlation. Predicted efficiency from Chan-Fair correlation. Analysis: (a) Convert the performance data for feed and product flow rates and compositions from mass units into mole units, molecular weights of 32.04 for methanol and 18.02 for water. The results are as follows: Component Methanol Water Total: Flow rate, lbmol/h: Feed Distillate Bottoms 709.1 702.7 6.4 1260.8 65.3 1195.5 1969.9 768.0 1201.9 Mole fraction: Feed Distillate 0.360 0.915 0.640 0.085 1.000 1.000 Bottoms 0.0053 0.9947 1.0000 Use the McCabe-Thiele method, based on methanol mole fractions, to find the number of equilibrium stages needed. The slope of the rectifying section operating line is given by Eq. (77). L/V = R/(R + 1)=0.947/(1.947)=0.486. This line intersects the 45o line at x = 0.915. The slope of the stripping section operating line is given by Eq. (7-12). L / V = VB + 1 / VB = (1.138 + 1)/1.138 = 1.88. This line intersects the 45oi line at x = 0.0056. The McCabe-Thiele diagram is given below in two parts to achieve accuracy. From the two parts of the diagram, it is observed that the two operating lines do not intersect on the q-line. This is probably because the assumption of constant molar overflow is not valid and the operating lines have some curvature. Assuming the feed stage in the actual column is near the optimal location, the questionable McCabe-Thiele diagram gives 5 equilibrium stages in the stripping section, one of which is the partial reboiler, and 4.2 equilibrium stages in the rectifying section. Thus, the total equilibrium stages in the column = Nt = 8.2 + the partial reboiler. The column contains 12 plates + the partial reboiler. From Eq. (6-21), the overall plate efficiency is, Eo = Nt /Na = 8.2/12 = 0.68 or 68%. The column contains 5 plates in the rectifying section. This is equivalent to a plate efficiency in that section of 4.2/5 = 0.84 or 84%. The stripping section contains 6 plates plus the feed plate. Analysis: (a) (continued) Exercise 7.41 (continued) Therefore, the efficiency in this section is 4/7 = 0.57 or 57%. Note these results are subject to degree of curvature of the operating lines and the placement of the feed in the McCabe-Thiele method. In the McCabe-Thiele method, if one more equilibrium stage is added to the stripping section, so as to give 5 stages plus the partial reboiler, then the rectifying section only needs 3.8 equilibrium stages. Then the overall plate efficiency is 73%, with 71% in the stripping section and 76% in the rectifying section. This still does not account for the effect of curvature of the operating lines. Analysis: (a) (contin...
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