Unformatted text preview: iciency for distillation of a
Given: Performance data for a distillation column. Vapor-liquid equilibrium data.
Assumptions: Partial reboiler is an equilibrium stage. Constant molar overflow.
(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:
Total: Flow rate, lbmol/h:
1201.9 Mole fraction:
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%,
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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