Separations analysis fundamentals - Principles of Chemical Separations with Environmental Applications - page 67

Equilibrium line

y 1

Operating
line

y

y 2

x 1 x 0

x

Figure 3.30 Graphical depiction of passing and exit streams for a single
equilibrium-limited stage.

This form can be used to linearize a portion of a non-linear equilibrium relation, such
as the one shown in Figure 3.30. By combining the mass balance with the equilibrium
relationship, one can derive an equation that relates flowrates, and entrance and exit
compositions to the number of equilibrium stages needed.
The mass balance around Stage 1 for the process shown in Figure 3.29 yields

L
V

y 2 = y 1 + ( x 1 −

.

x 0 ) (3.41)

Combining the equilibrium expression with this operating line gives

y 2 − y 1 L

mV . b =

(3.42)

y 1 − mx 0 −

A similar balance around Stage 2 is

y 3 − y 2 L

mV . y 1 =

(3.43)

y 2 −