Page 133 - Pressure Swing Adsorption

108 PRESSURE SWING ADSORPTION EQUILIBRIUM THEORY 109

The moles of the oure, light product withdrawn during the feed step may
be determined from Eqs. 4.10 and 4.22, as follows
1.0
( 4.24)
where 8 A has the same value as m Eqs. 4.20 and 4.22. R o.5
The pressunzation with product step m this cycle follows the purge step;
so the bed 1s presumed to contain only the pure, light component. Thus, Eq.
4.17 yields 0
0
( 4.25)
Consequently, the rate of pressunzauon ts immaterial; only the initial and
final pressllres matter.
The definition of recouery of the light component for this four•step cycle,
with pressurization by product 1s: (a)
.-
_ :0::tlF - Q;;;tlPR - O:tlru
R ( 4.26)
Qiu'IFY8F
Thus, by combining Eas. 4.22 through 4.26 and rearrangmg, one obtains:

0.1
( 4.27)
R o.o5
where/;= 1/[1 + (gPHYF/3A.,)/(1 - /3 )] is a factor that deviates from umty
0
only for nonlinear isotherms. For · examole, when component A follows a
auadratic isotherm, qA = KAcA + MAc~ and component B follows a linear 0
isotherm, q = K»c , one gets
8 8 0
l - e MA
t= -,-R
Some specific results of Ea. 4.27 are shown m Figure 4.4 for the case of '-o '
linear isotherms (MA = 0 and { = 1). This figure illustrates the effects of
feed composition and pressure ratio on product recovery, for two adsorbent (b)
selectivities, -{3 = 0.1 and 0.9. These selectivities span the range of very easy
Figure 4.4 The effeci on recovery of feed composition and pressure ratio, for ~
(e.g., hydrogen purificatmn) to qmte difficult (e.g., separation of argon from
(a) = 0.1 and (b) 0.9, for pressurizatton with product. 13
oxygen), respectively. The resuits are shown as three-dimensional surfaces
that nave qmte similar shapes, despite the large difference m selectiviues.
Both surfaces approach an asymotote at high oressure ratios and, to a lesser
extent, as the oercentage of the heavy component m the feed approaches
zero. Conversely, recovery of the light comoonent always decreases as the
amount of the heavy component m the feed mcreases. Later, m Secllon 4.6,
additional comparisons are made that focus on the effect of isotherm curva-
ture.
Another measure of overall PSA performance is the ennchment of the
byproduct, EA = Y AwlYAF- This may be of interest when the more strongly
adsorbed component 1s valuable. If that component is very valuable, the