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Find: Most probable cause for abnormal operation.
Recommended further tests.
If 90 mol% methanol distillate could be obtained by increasing the reflux ratio for a
constant vapor rate.
First determine whether the normal operation can be verified by the McCabe-Thiele
method. With L/D = R = 1, from Eq. (7-7), the slope of the rectifying operating line = L/V =
R/(1 + R) = 1/2 = 0.5. Also, xF = 0.5, xD = 0.90, and xB = 0.05.
What is not known is the phase condition of the feed. If a saturated liquid feed is
assumed, giving a vertical q-line as shown in the plot below, stepping stages up from the bottom,
with the feed stage to plate 3 from the bottom, less than 2 theoretical plates are needed in the
rectifying section, while 4 are present. The construction is shown on the next page.
Therefore, it appears that the feed is not a saturated liquid, but is partially vaporized. Exercise 7.19 (continued) Analysis: Normal Operation (continued) By trial and error, using q-lines of various slopes, the following McCabe-Thiele diagram is
consistent with the given data. It shows a q-line with a slope of -0.34. slope = q /(q − 1)
Therefore, q = slope/(slope-1)=-0.34/(-0.34-1.0)=0.25
From Eq. (7-19), molar fraction vaporized = 1 − q = 1 − 0.25 = 0.75 Exercise 7.19 (continued) Analysis: Normal operation (continued) The material balance for the normal operation is as follows, using the overall balances,
F = 100 = D + B and 0.5F = 0.5(100) = 50 = xDD + xBB = 0.90D + 0.05B. Stream
52.94 mol% methanol
90 Exercise 7.19 (continued) Analysis: Abnormal operation
For the abnormal operation, first check the overall total material balance using the given
data. F = 100 kmol/h. D + B = 53 + 62 = 115 kmol/h. Therefore, it appears that we have
115 - 100 = 15 kmol/h more flow out of the distillation system. Now check the methanol overall
material balance using the given data. Methanol flow rate in = 0.51(100) = 51 kmol/h. Methanol
flow rate out = 0.80(53) + 0.12(62) = 49.84 kmol/h. Therefore, the methanol balance is close,
with only about a 2% discrepancy. Now check the water overall material balance using the given
data. Water flow in = 0.49(100) = 49 kmol/h. Water flow out = 0.20(53) + 0.88(62) = 65.16
kmol/h. Therefore, we have 65.16 - 49 = 16.16 kmol/h more water out than in. This is a
significant discrepancy. It appears certain that water is leaking into the distillation system. Two
possibilities are: (1) leakage of condenser cooling water into the condensate, or (2) leakage of
reboiler steam into the boilup vapor. A reboiler steam leak may not be serious because the steam
might not get to the top of the column to dilute the methanol product. A condenser cooling water
leak could be very serious because part of it would end up in the distillate, thereby diluting the
methanol product. Because of the impure methanol distillate for the abnormal operation, it
appears that a condenser cooling water leak is the fault. Check thi...
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