Separations analysis fundamentals - Principles of Chemical Separations with Environmental Applications - page 69

When the separation requirement is specified but N is unknown, the above equation can
be rearranged to solve for N :

ln [1 L )] ( y N + 1 − y 1 ) ( y 1 − y 1 ) + L )

− ( mV / ( mV /

N = . (3.51)

ln ( L / mV )

The above equations are limited to cases of constant flowrates and linear equilibrium
relationships. For situations where there are small deviations from linear phase equilib-
rium and/or changes in flow from stage to stage, the above equations can be applied
over sections of the cascade in series. For situations where this approach is not reason-
able, finite difference mathematical analysis can also be applied to equilibrium-stage
calculations.

Example 3.6: gas stream with H 2 S

Problem:
A waste-gas stream from a chemical processing facility contains 10% H 2 Sonadry
basis. The remainder is primarily N 2 . This stream cannot be discharged directly into
the environment. One approach to the removal of H 2 S prior to discharge of the gas is
to contact it with water in a staged column.
The target is 1% H 2 S in the exit gas stream. The entering gas stream is saturated
with water so there is no mass transfer of water to the gas phase. The solubility can be
described by:

y H 2 S = 500 x H 2 S .

Initially, the ratio L V is set to 750 to compensate for the low solubility of H 2 Sin

H 2 O (i.e., use more water so the total amount sorbed into the liquid phase is greater).
Decide:
(a) how many equilibrium stages are needed;
(b) could this analysis be used if the entering concentration of H 2 S was larger (50%,
for example)?
Solution:
The equilibrium relationship is given. The slope of the operating line is also given. To
use the McCabe-Thiele analysis, one point on the operating line is needed. The exit
gas composition is 1% of H 2 S( y

/

= 0.01) and the entering water does not contain any

H 2 S( x 0). Since the points represent passing streams on one end of the cascade,

they represent one point on the operating line.
The McCabe-Thiele plot is drawn on Figure 3.31. Note that the scales are different
on each axis, based on the equilibrium relationship and operating-line coordinates.
One can step off stages starting at either end of the cascade. From the plot, it can be
seen that four equilibrium stages are needed.

=