Page 154 - Separation process engineering

from the bottom operating line, since liquid of composition x is a passing stream to vapor of
N
composition y N+1 (compare Figures 4-2 and 4-7). We can continue alternating between the equilibrium

curve and the bottom operating line as long as we are in the stripping section.
Figure 4-7. Stepping off stages in stripping section

If we are stepping off stages down the column, at the feed stage f we switch from the top operating line to
the bottom operating line (refer to Figure 4-3, a schematic of the feed stage). Above the feed stage, we
calculate x from equilibrium and y from the top operating line. Since liquid and vapor leaving the feed
f−1
f
stage are assumed to be in equilibrium, we can determine x from the equilibrium curve at y = y and then
f
f
find y from the bottom operating line. This procedure is illustrated in Figure 4-8A, where stage 3 is the
f+1
feed stage. The separation shown in Figure 4-8A would require 5 equilibrium stages plus an equilibrium
partial reboiler, or 6 equilibrium contacts, when stage 3 is used as the feed stage. In this problem, stage 3
is the optimum feed stage. That is, a separation will require the fewest total number of stages when feed
stage 3 is used. Note in Figure 4-8B and 4-8C that if stage 2 or stage 5 is used, more total stages are
required. For binary distillation the optimum feed plate is easy to determine; it will always be the stage
where the step in the staircase includes the point of intersection of the two operating lines (compare
Figure 4-8A to Figures 4-8B and 4-8C). A mathematical analysis of the optimum feed plate location
suitable for computer calculation with the Lewis method is developed later.
Figure 4-8. McCabe-Thiele diagram for entire column; (A) optimum feed stage (stage 3); (B) feed

stage too high (stage 2); (C) feed stage too low (stage 5)