# 5.17: Untitled Page 114

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## Chapter 5

*Figure 5.10a*. Graphical analysis

are *not sufficient* to produce the desired result, i.e., ( *y *) 0 010

*. *

, and

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1

one is forced to make a choice of adding a sixth stage or accepting a somewhat reduced separation.

If we reduce the water flow rate from 90 kmol/h to 70 kmol/h the slope of the operating line is reduced from 3.00 to 2.33, and the situation illustrated in Figure 5.10a changes to that illustrated in Figure 5.10b. An overall mole balance indicates that ( *x *) 0 00386

*. *

and the graphical

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construction indicates that slightly more than 18 equilibrium stages are required.

*Two‐Phase Systems* & *Equilibrium Stages *

209

*Figure 5.10b*. Influence of a reduction in the molar flow rate of water This means that we need 19 stages to accomplish the objective of reducing the mole fraction in the ‐phase to ( *y *) 0 001

*. *

. If the water flow rate is

*A * 1

further reduced to 67 kmol/h we see in Figure 5.10c that the equilibrium line and the operating line intersect at *x * 0 *. * 00337 . This is referred to as *A*

a *pinch point* within the cascade of equilibrium stages, and an infinite number of equilibrium stages are required to reach this point.

Consequently, it is impossible to reach the desired design specifications for the cascade, i.e., ( *y *)

0 *. * 010 and ( *x *) 0 *. * 403 .

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0

1

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210