Page 197 - Separation process engineering

C2. Derive the bottom operating line for a column with a total reboiler. Show that this is the same
result as is obtained with a partial reboiler.

C3. Derive Eqs. (4-51) and (4-52).

C4. For a side stream below the feed:
a. Draw a sketch corresponding to Figure 4-22A.

b. Derive the operating equation and y = x intercept.
c. Sketch the McCabe-Thiele diagram.

C5. Derive the operating equations for the two middle operating sections when an intermediate
reboiler is used (see Figures 4-23A and 4-23B). Show that the operating line with slope of L′/V′
goes through the point y = x = x .
B
C6. Show that the total amount of cooling needed is the same for a column with one total condenser
(Q ) as for a column with a total condenser and an intermediate total condenser (Q + Q ). F, z, q,
c
c
I
x , x , and Q are constant for the two cases. Sketch a system with an intermediate condenser.
B
D
R
Derive the operating equations for the two middle operating lines, and sketch the McCabe-Thiele
diagram.
C7. For the stripping column shown in Figures 4-24A and 4-24C, show formally that the intersection
of the bottom operating line and the feed line is at y . In other words, solve for the intersection of
D
these two lines.
C8. Develop the McCabe-Thiele procedure for the enriching column shown in Figure 4-24B.

C9. For Example 4-3 prove that:
a. The top operating line and the y=x line intersect at y=x=x .
D
b. The bottom operating line and the y=x line intersect at y=x=x .
B
C10. For a continuous distillation column with a saturated liquid feed, a total condenser that produces
a saturated liquid reflux, and a partial reboiler, show that Q /D = (1 + L/D)λ if CMO is valid.
R
C11. The boilup ratio /B may be specified. Derive an expression for / as a function of /B for a
partial reboiler.

C12. Show how to determine ( /B) min . Derive an equation for calculation of ( /B) min from ( / ) max .
C13. Sketch the McCabe-Thiele diagram if the Murphree liquid efficiency is constant and E ML = 0.75.

C14. Derive the equations to calculate / when a superheated boilup is used.

C15. Derive the equations to calculate / when direct superheated steam is used.
C16. Part a. In a binary distillation column with two feeds, show that the intersection of the top and
bottom operating lines occurs at the feed line for fictitious feed F where F = F + F , z F =
T
T T
2
1
T
z F + z F , and h F = h F + h F .
F,2 2
2 2
1 1
F,1 1
F,T T
Suggestion: Draw the McCabe-Thiele diagram for the actual column with three operating lines
using both actual feed lines. On the same diagram draw the two operating lines for a column with
the single mixed feed F (they are unchanged from top and bottom operating lines of two-feed
T
column) and then determine the feed line for this mixed column.
b. Assuming that CMO is valid, show that q ≈ (F q + F q )/F
T 1 1 2 2 T
C17. Derive the operating equation for section 2 of Figure 4-17. Show that the equations are identical
whether the mass balance envelope is drawn around the top of the column or the bottom of the