Page 123 - Pressure Swing Adsorption

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98 PRESSURE SWING ADSORPTION EQUILIBRIUM THEORY 99

PRESSURIZATION FEED SLOWDOWN PURGE
assumed mdeoendent m the adsorbed ohase:
aPy avPv ) aq.
( e Tt + az" + RT( l - e) a/ - O ( 4.1)
i
•I The subscript , refers to component A or B. Shendalrnan and Mitchell2
i 3
and Chan et al. considered the case of a trace amount of component A
bemg adsorbed from a earner, B. Shcndalman and Mitchell took the earner
to be nonactsorbing, while Chan et al. accounted for adsorotmn of the earner.
In both cases, the mterst1tiai veioc1ty, v, was taken to be independent of
composition (and of both time and axial position at constant pressure)_ As 1t
1s written, however, Ea. 4.1 applies to bulk separations as well as removal of
a dilute contaminant.
An important detail is the definition of the void fraction e. If the adsorbed
Y•D y .. 0
phase concentratwns are expressed on a particle volume basis (i.e., including
mtraparticle porosity), then e 1s simply the extra-particle or interstitial bed
Feed voidage. Such a defimtron JS Jog1cal where mass tran~fer rates are finite and
1.0
End when the mass transfer resistance JS associateO with external film diffusion,
- 0.8 l rnacropore diffusion, or solid-side mass transfer resistance at the part1cie
_J
surface. With this definition, the bed density (p ), particle density (pp), and
8
N
{ the solid or m1crooarhcle density (pc), and the corresponding void fractions
C
0 0.6 [ are related by:
:e '
(/)
0
Cl. 0.4
When m1cropore resistance 1s dommant, or mcteed under the assumption of
al
·x local equilibrium on which this chapter 1s based, it is' more logical to regard
<( the external void fraction as the sum of the particle macroooros1ty and the
bed voidage (i.e., all gas space outside the m1cropores). The dens1t1es and
Product
End void fraction are then related by:
Pressun- Feed
zation
Pc corresponds to the density determmed with a Huid that penetrates the
Figure 4.1 Steps in a convcnt1onal PSA cycje; onentatlon of column ~~d streams.
(Top) Flows and compositions associated with each step. (Bottom) Pos1tmns-versus- external voidage and the macropores but not the m1cropores. Since these
iimc representation of each step. Shaded regions depict pcnetratmn of heavy comoo- definitions affect the magnitude of the isotherm parameters, it is essential to
nent. maintam consistency when equilibrium data are incorporated into a PSA
model.
The balance equations are modified by subst1tut1ng adsorption isotherm
expresstons for each component in the form,
( 4.2)
Examples are given in Chapter 2. Following assumption 6 above, the temper-
ature is fixed, so the second term of Eq. 4.1 can be detenmned from Ea. 4.2.
as:
aq. 1
Tt = RTf'(PY;) ( 4.3)