Page 324 - Pressure Swing Adsorption

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MEMBRANE PROCESSES 301
PRESSURE SWING ADSORPTION
300
_ BOr-----------------=--c,-7
"
where a'(x) s given by Eq. 8.10. For any soecified feed comoositi~n (xr) and ,_,
1
pressure ratm (.9') the mtegration yields directly the relat1onsh1p between
the fractional recovery and punty of the raffinate product. 0
~ 60
8.3.3 Counter Current Flow I "' w
6
u
For the countercurrent flow case ·the integration is slightly !es~ _straightfor• 1 w /
4
er
ward, smcc it ,s necessary to allow for the variation m compos1t1on on both I oi. / Mixed Flow
sides of the membrane. A differential balance for each comoonent across the § / o( =10
I
membrane [Figure 8.6(a)] yields: I ~ I
(8.18) )t I
-dLA = d( Lx) = "TTA dA ( P11 - PLy) "- , I
-dL = -d[L(l-x)] =1T dA[PH(l-xJ-Pc{l-y)] (8.19) ,
8 8 I
(8.20) 0 '---'--L--L-..L_.L.__,_,c_,_-1._-L_..L~
d(Lx)=d(I.:y); dL=dI.:
0 2 4 6 B 10
Dividing Eas. 8.18 and 8.19: •1. 01 1n RAFFINATE
-Ldx - xdL L + xdL/dx (8.21) Figure 8.8 Rccovcry--puritv profile for production of nitrogen from air hy membrane
Ldx-(1-x)dL ( 1 - x) dL/dx - L and PSA processes. :i
a(PHx - PLY)
PH(l -x) -PL(J -y) With, a, P, and x 2 specified, the recovery may now be calcuiated by
2
1 dL 1 (8.22) integration starting from the raffinate product end at which ! = i .0, x is
- L d.x = fixed, and y ,s known from Eq. 8.27.
2
Jn order to integrate this ex;oression, we must express y in ter~s of x. This 1s
8.3.4 Comparison of Recovery - Punty Profiles
accomolished by a mass balance over the dotted section in Figure 8.?a.
The results of such caJcuJat1om, for a pressure ratio 5.0 and permeability
(8.23) rat10s of 5 and 10 are shown m Figure 8.8. These values are typical of the
current membrane processes for recovery of nitrogen from a1r m which the
To avoid the need for a trial and error solution, 1t is easier to change the nitrogen is the less permeable species. The strong effects of both permeabil-
variable and integrate from the raffinate end: 1ty ratio and flow pattern on performance are 1mmediately apparent. These
effects become most pronounced in the high-ounty region, which 1s generally
. L Lx-x 2 (8.24)
!=-,-, y= l-1' ! = 1.0, l - X = X2 the reg10n of oract1cal interest.
L2
p I dL _ 1 (8.25)
- , di - x+«/[(1-«) + (1-P)/(xP-y)] 8.4 Cascades for Membrane Processes

At the raffinate end y 2 1s given by: Where a pure product is required 1t 1s often advantageous to use ITiore than
one membrane element connected m senes as a "cascade." The best ar-
NA Y, l. Px, - Y, \ (8.26) rangement depends on several factors, .the most impOrtant being whether the
Nn = l -y, =a P(l -x ) - (1-y,)) primary requirement 1s for a pure raffinate (rctentate) product or for a pure
2
permeate. If the requirement 1s for a pure raffinate product a countercurrent
which is a s1mpie quadratic equatwn:
flow system is the hest arrangement. If idcai countercurrcnt flow could be
Yi(l - i/a) - y [(1 - 1/a)(l + Px,) +IV/a]+ Px 2 = 0 (8.27) achieved within a membrane eiement, there would be no advantage to be
2