Page 143 - Pressure Swing Adsorption

ii,

118 PRESSURE SWING ADSORPTION EQUILIBRIUM THEORY 119

0.4 The interstitial flow rate can be found from the toUU matenal balance (i.e.,
the sum of Eq. 4.1 or 4.4 for both components). These equalions can be
0.3 integrated with boundary conditions (yF, t·i;:, specified at the feed end of the
"' bed) m order to evaluate the velocity and ~ompos1tion at other ppints in the
c
• 0.3 adsorbent bed. The individual component balance for component A, can
C
0 p = 4.0 then be solved, yielding results that are slightly more complicated character-
0.
E 0.2 1st1cs than those described by Eos. 4.7 and 4.8:
0
0
0.2 f3(,fro - P'z)
~ (4.35)
t P[l + (/3 - l)yA] 2
>- 0. i i
"' p = 2.0 I
w
> (/3 - 1)[1 + (/3 - !)y.4j(l - YA)Y;1
0 ( 4.36)
u O.i /3[( ,i, /P') - z l
w 0
"' I.
0.0 where P' - dP/dt - (,i, 0 - ,fr,)/L, and ,t, 0 - /3 v P[l + (/3 - I)y,10], in
11 0
' which the subscnot O refers to the outiet, and the subscript F refers to the
0.0 feed end of the packed bed. When pressure vanes lineariy with time, P' is
0.3 0.4 0.5 0.6 0.7 0.8 0.9 i .0 constant 1 as are the molar flow rates. A hypothetical: problem could arise if
' i imposing a pressure shift caused the shock wave to degrade into a diffuse
Extent of Complete Purge, X '
I
Figure 4.9 Effect of extent of purge on light product recovery for pressure ratios of front. The steo time would then have to be shortened to mamtam high
product purity, which would reduce recovery. On that oomt, Kavser and
2.0 and 4.0, for /3- 0.593 and y,-0.78. Knaebel 10 concluded via the entropy condition that unless the pressure shift
I causes a dramatic mcrcase in pressure drop or mass :transfer resistance, the
eauilibrium tendency should preserve the shock froni.
I
returns diminish. The only potential advantage foreseen for purging more When the pure, less strongly adsorbed comoonent, B, is used to pressurize
than the minimum amount is to compensate for any transport resistances or the column from PL to Pr:, and when the feed step iilvolves a pressure shift
dispersive effects that could cause contamination of the product. Such effects (e.g., partial oressunzation bv feed or oartrnl cocurrent blowdown) to PH, the
would be greater for faster cycling, so there is bound to be an optimum at I recovery of the oure,_less strongly adsorbed comoonent can be expressed as:
which oroduct ounty and recovery are balanced against adsorbent proctuct1v-
1ty and the vower reqmrement. I R- 1 + (/3P~-, - I )YA,, ( 4.37)
l P~(l - YA,)
4.4.4 Four-Step PSA Cycle: Pressure Vanation During Feed x[l _ 1//3 + (PF- 1) (P~[l + (: ~ l)YA,j _ Jl]
Modifications of certam PSA steos could lead to simolified equipment or 1 + (/3V,- - i)r .. ,, .
§J,,,-Ve
superior performance. For example, the simplest PSA cycie is a two-step
cycle that combines the oressunzation and feed steos, and the blowdown and where P, = PH/Pr, PF= PF/PL, and PH= PH/PL. Only two pressure ratios
ourge steos. This cycle reqmres the rnmimum number of valves and very of the three mentioned are mdeoenctent; the latter quantities are preferred
simple control logic. Conversely, a number of studies have shown that because they are constrained to be greater than un:1ty. Suh and Wankat 21
cocurrent blowdown can significantly increase the recovery of the light studied separate feed and cocurrent blowdown steps, and found that the
product. Therefore, 1t seems promising to combine the feed and blowctown distinct steps can yield better recovery than when combined.
(cocurrent) steps, even though domg so would involve some mechanical l Figure 4.10 shows predictions of product recovery as affected by the latter
como'Jications. The local' equilibnum theory ts a natural choice to study such pressure ratios. Three cases are shown involving ·separations that arc "dif~
cycies because tt can focus on the impact of major parameters and operating ficult," either because the feed is oredommately the heavy component, or
conditions, without the mtrus1on of extraneous effects which would involve because the adsorption selectivity 1s poor, or both. These are reoresented by:
adjustable parameters. f (a) /3 - 0.1 and Ye - 0.9; (b) /3 - 0.9 and Ye= 0.1; and (c) 8 - 0.9 and