Page 275 - Pressure Swing Adsorption

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252 PRE.5SURE SWING ADSORPTION PSA PROCE.5SE.5 253

The basic orinciole of a PSA "concentration process" may be understood In the limtt of Yo-> 0 and /3 -> 0 (high seiect1v1tv) these exoresstons reduce
from eouilibnum theory (see Section 4.2 and Figure 4.25). Consider an to:
adsorbent bed equilibrated at pressure P and mole fraction (of the more
O
strongly adsorbed species) y • If the euuilibna are linear: (6.12)
0
. p p
q~ ~ KAcA ~ KAy RT' q; ~ K 8c 8 ~ K 8 (1 - Y) RT (6.3)
I I \
By combining the differential mass balance exoress1ons for both components F =B!n\..0'.<>.J
- y
A
•
]
(Ea. 4.4), we obtam:
_!__ ap + {._!__ _ _!__) a(Py) + a(Pv) ~ ( .4)
/3 at \/3A [3 8 at · az 0 6
8
Figure 6.21 shows FA and F plotted agamst the pressure ratio for
and by elimmatmg the term av /az between Eqs. 4.4 and 6.3: 8
different values of y • The cmves are nonlinear, but, when the selecttv1ty 1s
0
ay) f3Av (ay) (/3-1)(1-y)y dlnP
( iii , + 1 + ( f3 - 1) y az , 1 + ( /3 - 1) y dt ( 6.5)
m which /J = BA/(3 8 and the total pressure differential anses from the
assumption of negligible pressure drop across the coiumn [P = P(t )]. Since
y ~ y(z, t), the left-hand side of Ea. 6.5 is s1moly the total lime derival!ve of
y, and the variatioff of comoosition during pressurization or blowdown steps
1s given by Ea. 4.8. It follows by direct mtegration that the vanat10n m ~ 0 0,0!
V 0.0!
0
composition during pressurization or blowdown will be given by: 0
l'... - (...:...=1'...)µ(.!!_)µ-, (6.6)
Yo - J - Yo _ Po
Eouations 4.4 and 6.4 yield:
_i ap + (/3 _ /(vPy) + a(vP) ~
f3a at 1 az az 0 (6.7)
Neglecting the axial variat10n of pressure leaves only the time dependence; so
the velocity durmg a pressurization or blowdown step can be found simply
0.8
mtegratmg from the closed end:
-z d In P
(6.8) 8
'' = f3n[I + (/3- l)y] dt 00 0.6
iii
The fraction of A desorbed durjng blowdown from pressure 1' to P is ~
0
given by: i':i
r
u 0. 4
<
F ~ f PB vyPdt (6.9) ~
~
A AZ)' p
P O O
0
and subsl!tutmg for v and y from Eqs. 6.8 and 6.6: 0.2
/3 (·l-yo\µ;cp-1) p y'l<P-1) . A y 0.0!
0
I
FA - l - 8 ~ t (1 - y/2"-ll/(p-1) dy ( 6.10) 0 ·,
0.8 0,S 0,4 0.2
Similarly, for the fraction of B desorbed:
PIP .
I ( Yo )1;<1-plf Po y(2-.B)/<.B-n
F =-.- -- ~---~dy ( 6.11)
8 I - /3 1 - Yo P ( 1 - y t1<a- 1l Figure 6.21 Fractional desorption durmg blowdown for differeni combinat1ons of Yo
and fl, calculated according to Eos. 6.10 anct 6.1).