Page 186 - Separation process engineering

the operation is feasible.
To be specific, consider the situation where the known variables are F, z, q, x , T reflux (saturated liquid),
D
p, Q = 0, N actual , N feed actual , diameter, L /D, the overall efficiency E , and CMO. This column is
col
o
0
illustrated in Figure 4-28A. The engineer wishes to determine the bottoms composition, x .
B
Figure 4-28. Simulation problems; (A) existing column, (B) McCabe-Thiele diagram

We start by deriving the top and bottom operating equations. These are the familiar forms,

and

The feed line equation is also unchanged

Since the reflux is a saturated liquid and the external reflux ratio, L /D, is known, we calculate L/V and
0
plot the top operating line (Figure 4-28B). The feed line can also be plotted. The intersection of the top
operating line and the feed line gives one point on the bottom operating line. Unfortunately, the bottom

operating line cannot be plotted because neither / nor x is known (why won’t external balances give
B
one of these variables?).
To proceed we must use the three items of information that have not been used yet. These are N actual , N feed

, and E . We can estimate the equilibrium number of stages as
actual o

(4-60)

The feed location in equilibrium stages, N , must be estimated as an integer, but the total number of
F
equilibrium stages, N, could be a fractional number. Now we can step off equilibrium stages on the top
operating line until we reach the feed stage N . At this point we need to switch to the bottom operating
F
line, which is not known. To use the final bit of information, the value N, we must guess x , plot the
B
bottom operating line, and check to see if the separation is achieved with N + 1 (the +1 includes the
partial reboiler) equilibrium contacts. Thus, the simulation problem is one of trial and error when a stage-
by-stage computation procedure is used. This procedure is illustrated in Figure 4-28B. Note that the
actual feed stage may not be (and probably is not) optimum.
Once x has been determined the external balances can be completed, and we can determine B, D, Q ,
c
B