Page 170 - Separation process engineering

(4-43)

In Figure 4-16,

We need 4 + 0.9 = 4.9 equilibrium contacts.
E. Check. There are a series of internal consistency checks that can be made. Equilibrium should be a
smooth curve. This will pick up misplotted points. L/V < 1 (otherwise no distillate product), and
/ > 1 (otherwise no bottoms product). The feed line’s slope is in the correct direction for a two-
phase feed. A final check on the assumption of CMO would be advisable since the latent heats vary
by 15%.

This problem was also run on the Aspen Plus process simulator (see Problem 4.G1 and chapter
appendix). Aspen Plus does not assume CMO and with an appropriate vapor-liquid equilibrium
(VLE) correlation (the nonrandom two-liquid model was used) should be more accurate than the
McCabe-Thiele diagram, which assumes CMO. With 5 equilibrium stages and feed on stage 4 (the
optimum location), x = 0.9335 and x = 0.08365, which doesn’t meet the specifications. With 6
B
D
equilibrium stages and feed on stage 5 (the optimum), x = 0.9646 and x = 0.0768, which is slightly
D
B
better than the specifications. The differences in the McCabe-Thiele and process simulation results
are due to the error involved in assuming CMO and, to a lesser extent, differences in equilibrium.
Note that the McCabe-Thiele diagram is useful since it visually shows the effect of using open steam
heating.

F. Generalize. Note that the y = x line is not always useful. Don’t memorize locations of points. Learn
to derive what is needed. The total condenser does not change compositions and is not counted as
an equilibrium stage. The total condenser appears in Figure 4-16 as the single point y = x = x .
D
Think about why this is true. In general, all inputs to the column can change flow rates and hence
slopes inside the column. The purpose of the feed line is to help determine this effect. The reflux

stream and open steam are also inputs to the column. If they are not saturated streams the flow rates
are calculated differently; this is discussed later.
Note that the open steam can be treated as a feed with q = (L below − L above )/S = (B— )/S = 0. Thus, B
= . The slope of this feed line is q/(q − 1) = 0 and it intersects the y = x line at y = x = z = 0, which

means the feed line for saturated steam is the x-axis.

Ludwig (1997) states that one tray is used to replace the reboiler and 1/3 to one and possibly more trays
to offset the water dilution; however, since reboilers are typically much more expensive than trays (see
Chapter 11) this practice is economical. Open steam heating can be used even if water is not one of the
original components.

Note to Students: When you read the description of developing the bottom operating equation and plotting
the bottom operating line in Example 4-4, it probably appears a lot easier than doing the development by
yourself will prove to be. You need to practice deriving operating equations. Then practice simplifying
the operating equation, realizing that “pure steam” means y = 0 and that “saturated steam” means S = V
s
and thus B = L are nontrivial steps. How did we know that the bottom operating line could be plotted
using the point x = 0 (the y intercept)? We did not know this in advance, but tried it and it worked. You
will become better at solving these problems as you work additional problems. To aid in this, there are a
large number of problems at the end of this chapter.

4.8 General McCabe-Thiele Analysis Procedure