Page 152 - Pressure Swing Adsorption

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126 PRESSURE SWING ADSORPTION EQUILIBRIUM THEORY
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Pres.rnnzation. Extra pure light product 1s reomred to oressunze this I due to expansion of gas from the dead soace:
soace, though 1t 1s recovered during the feed step. I
Feed. No effect exceot to retam part of the oroduct gas. if ! ( 4.46)
breakthrough was prevented; if breakthrough had begun,
mixing m this region ctamoens the contammatlon of the I where 'Po= /3sVoP, which is nil if Vov, = 0, P' = (PL - PH)/tBD• and 'BD
In comparison, dead volume at the feed end of a PSA column has the I 1s the time allotted for blowctown. This can be rearranged to get tl1e distance
product stream leaving the column.
mto the bed (measured from the product end) that 1s completely purged,
following effects: I, . 'Po -B
Zo =zl,-o = p7(l - P ) ( 4.47)
I
Blmwlown. ·No effect except to retain part of the waste gas. l
Purge. Same as blowdown. A material baiance for the dead volume demands that
Pressunzation. Excess pure light component IS necessary to pressurize this ( 4.48)
space.
Feed. Feed gas mIXes with the pure light component, resulting m wJ1ere AP= V 0 vr/Vc and Ve= rrd~L/4 ts the_volume·ofthe adsorbent bed.
1
I purge that 1s attatned during blowdown 1s found.
a ' diffuse" front entermg the adsorbent bed. When this IS combined with the Preceding relations, the fraction of complete
Thus, there are several disadvantages to dead volume, and few advantages.
In fact, the oniy positive aspect 1s the possibility that the dead voiume at the I X = ~o = ApfJa (1 - p-B\ (4.49)
product end of the column may hold sufficient pure product to partially L E !
purge the bed dunng blowdown. That benefit 1s balanced by the fact that the The bed 1s assumed to have been saturated with feed at high pressure
gas will be less effectiv'e at purging the column than gas admitted dunng the during the preceding feed steo. If the feed-end dead volume 1s verv large,
purge step (at low pressure), because it needlessly exoels gas while desorp- however, the actual concentration of A may be iess. That oossible discrep-
tion is m progress. ancy is neglected here. Thus, as blowdown oroceeds, the residual gas be~
The followmg development is based on linear isotherms and the four-step comes ennched m component A and 1s pushed towards the outlet end. The
cycle described in Section 4.4.1. The cycle ts composed of pressunzat1on with composition shifts to _v 80 , as m Ea. 4.32, which yields:
proctuct, con$tant pressure feel1, countercurrent blowdown, and complete 1111
Yim 13-1'
purge. To the extent oossible, both feed-end and product-end dead volumes Yao=l-(J-yF) ( Ycp ) (4.50)
are considered. Again m this section, compositions are expressed in terms of
the heavy component, A. Some of the concepts to be presented have been The characteristic havmg this composition propagates according to Eo. 4.33,
exam med by Kolliopoulos. 23
which may be combined with a material baiance to obtain:
For- simplicity, the analysis begms with the blowdown step. This 1s because
the gas retained in the product-end dead volume and exhausted in that step X* = !_I (4.51)
L Yao
contributes to purging. It is presumed that the feed step stops at the oomt of
Immment breakthrough, so that the gas retained in that dead volume. having
1 + (fJ - l)Yrm (.
vo1ume = Vnv,, 1s not contammated (i.e., Yov, = 0). The approach taken 1s 1 + ( /3 - 1) YF
to determine the extent of ourging that occurs durmg blowctown, and then to
determme the additional amount needed during the purge step. The amount The dimensionless distance, X*, reached by the expanding feed gas 1s
of pure light component reqmred for pressurization 1s Increased by that measured from the product end. Thus, Eas. 4.49 and 4.5 I define the partially
needed to fill the dead volumes. Under these assumptions, tile feed step 1s purged region between completely purged and expanded feect.
not directly affected by product-end dead volume, but only by the feed-end Before proceeding, 1t may be enlightenmg to consider the potential imoact
dead volume.
of dead volume at both ends of the column, and the vanety of possibilities
To predict the composition profile at the conclusion of blowdown, one that arise. For examole, the adsorbent seiect1vJty, feed composltmn, pressure
mllst follow characteristiCs representing different initial compositions and ratio, and size of the product-end dead volume all affect the uitil11ate position
axrnl positions. The characteristics velocttv is given by Ea. 4.35. Perhaps the Of the partially purged region. So, assummg that there 1s dead volume at the
most important charactenstic 1s the one that identifies the extent of ourgmg feed end, the contents of this space may be: unaffe'cted, partly affected, or