In the case of a continuous distillation column (see Figure 5-8) a method used to determine the number of ideal stages is the McCabe-Thiele.

Figure 5-8: Schematic of continuous distillation column. Section above feed is enriching or rectifying; below feed is stripping section. (Reproduced with permission from reference 38. Copyright 1997 American Chemical Society.)

The stages in a distillation column can be of various configurations. Two systems are shown in Figure 5-9.

Figure 5-9: Bubble cap ( a and b) and sieve plate ( c). Adapted from 36, 37.

The enthalpy balance for the McCabe-Thiele in the rectifying section essentially reduces to the vapor streams entering and leaving a stage V _in moles/time and ?, the enthalpy of vaporization.

(5-13)

For chemically similar materials,

(5-14)

and

(5-15)

This gives a condition known as constant molal overflow (i.e., all the V's in the rectifying section including V _a are equal; the same holds true for all the L's including L _a). The same condition holds for the stripping section (all vapor streams including V _b are equal and all L streams are equal to each other).

A mass balance for the rectifying section gives

(5-16)

or

(5-17)

Likewise, the mass balance for the stripping section is

(5-18)

or

(5-19)

Equations 5-16 through 5-19 are straight lines because of constant molal overflow.

The junction of the rectifying and stripping mass balances is fixed by the feed...