Page 139 - Pressure Swing Adsorption

114 PRESSURE SWING ADSORPTION EQUILIBRIUM THEORY 115

when lhe adsorht~nt is pressurized with feed, the adsorbent near the feed end
contacts the feed at essentially the lowest pressure m the cycle. This allows
the more strongly adsorbed comoonent to penetrate farther into the bed,
because less 1s adsorbed by that adsorbent than if the gas were fully
pressurized. As a result, that adsorbent is less than fully utilized. Thus,
desmte the fact that oressunzat1on does not contribute directly towards
production. 1t can diminish the useful capacity of the adsorbent.

4.4.3 Four-Step PSA Cycle: Incomplete Purging
Purge Pressur1zotlon Feed
The two cycles considered so far m this section are stmole, and relatively easy S1ep Step Step
to anaiyze. Unfortunately, however, they are not oarticularly efficient m Figure 4.7 Paths of characteristics m the purge, prcssunzat1on, and feed steps. for a
terms of their performance relative to power requirements. That 1s, they fractional extent of purge of X. Note: z' is measured from the bottom toward the top.
generally require high pressure ratios to attam high recovenes. For this and z 1s measured in the reverse direction. 7
section, we consider a simple modification of the four-step PSA cycle
described in Section 4.4.J. It will be seen that this modification, which simply
involves varymg the extent of purgmg, can ieact to remarkably higher recovery and parameter vaiues. Generally, reducmg the amount of purge always
at rclat1vely low pressure ratios. results tn mcreased recovery, but beyond some limit (described below) there
Incomplete purging has been common m industrial practice, as mentioned 1s no assurance that pure product can be obtained.
by Wagner 14 and Wankat. 15 Quantitative studies of the extent of purge have It may help to visualize the action of the steps in terms of wave move~
focused mainly on flow rate ratios, especially the purge-to-feed ratio. For ments, as m the discussion of Figure 4.1. A schematic diagram of the wave
example, the effects of the purge-to-feed ratio on light-product purity were movements m the relevant steps 1s given m Figure 4.7, aithough m this figure
1
studied by Yang and Doong, 16 Doong and Yang, 17 and YangY Their results the shading that represents the mflux of the heavy component has been
implied that it was not feasible to increase recovery by decreasing the omitted. The ourge step ts still characterized by a simple wave. This wave
purge-to-feed ratio and still mamtam high oroctuct purity. Kirkby and soreacts as 1t propagates over the iength of the coiumn, as shown on the
19
Kenney showed theoretically and exoenmentally that there is an ootimum left-hand side of the diagram.
extent of purgmg, for which product ounty and recove1y are maximized. The key feature of the extent of ourgmg 1s the fraction of the column X
Their cell model suggested that the optimum corresponded to complete that 1s completely purged. That 1s, X is the fraction of L over which y = 0 at
purge, but their expenments revealed tlrnt a lesser amount was oot1mal. An the end of the purge step, t L· Because they are linearly reiated, this 1s
7
equilibrium-based model was develooed by Matz and Knaebel to assess the identical to the fraction -of the amount of gas requJred to purge the bed
effect of ourge on PSA performance, based on systems having linear completeiyt via Eos. 4.21 and 4.23, as
isotherms. ahct that work is the basis of the following discussion. Recently, X = f3Avintlpu = Qtlru
9
Rousar und Ditl solved the same basic equilibrium-based eauat,ons analyt1- I ( 4.31)
cally to determine the optmmm ourge amount, and they examined ooerat1on i L Qtlru
in a regime that yields impure light product. where ,BAvintlru is the distance mto the bed that 1s fully purged and Qtliu 1s
By Its nature. mcomoiete purging ieaves a comoositton tail, or heei. at the J the number of moles required for complete purge.
feed end of the column, containmg some of the more strongly adsorbed An arbitrary characteristic m the s1mpk: wave is denoted by its compos1-
compom::nt. Subsequent pressurization with product (also countcrcurrent to tlon, y • The one that Just reaches the effluent end of the coiumn as the
0
the feed) oushes that residual material toward the feed end. More subtly, 1t ourge steo ends is socciai. Its mole fraction 1s called Yoi:-i.· An operat1onal
also reduces the gas-phase mole fraction of the more strongly adsorbed constraint is that this should be less than the "expanded" feed mole fraction,
component m that region, since the heavy component is preferentially taken or, if it is not, when 1t 1s reoressunzed 1t will s1mpiy revert to the feed
up as pressurization proceeds. The presence of the compressed t.1il reduces composition. In other words, if this constraint is not met, rcgencratmn will he
the quantities of both the feed admitted antl lhc gross product obrnmed mcomplete, and the effective length of the column will he reduced, lctiding to
durmg the feed step. The relative amounts consumed and/or produced premature breakthrough. Malhcmat,cally, this amounts to the following
during each step depend on the extent of ourge, as well as on the conditions meauality Ysl,-L < Ye· Generally, the value of Ys can be determmed from