Page 131 - Pressure Swing Adsorption

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PRESSURE SWING ADSORPTION EQUILIBRIUM THEORY 107
where the products of the average molar flow rates and time are:
4.4.1 Four-Step PSA Cycle: Pressurization with Product
The cycle covered in this sect10n is shown in Figure 4.1, and it is probably the
(4.15)
simplest PSA cycle, at ieast from a mathemat1cal v1ewpomt. One result of
that s1molicity 1s that 1t has been possible to extend the equilibrium theory, in
( 4.16) closed form, to systems exhibitmg noniinear isotherms.~ For the sake of
clarity, although generality 1s sacrificed, the discussion 1s given here m terms
Fot steps m which pressure 1s constant, the influent flow rate or effluent of a specific type of mixture, viz .• m which th·e light component has a linear
isotherm while the isotherm for the heavy component 1s nonlinear (e.g., a
flow rate can be set to complete the stcn within the allocated step time. No
Langmuir or quadratic isotherm). When both isotherms arc pract1callv linear,
matter which is spedfied, the other can be easily determined if both composi~
the equations presented here can be easily s1mplified, and when both are
lions are 'known, vra Eo. 4.5 or 4.10, cteoending on whether a shock front
nonlinear, the preceding equations can be adapted, although the resulting
exists in the column.
For steps m which oressure vanes, it 1s easier to specify the rate of expressions become somewhat more comolicated.
As mentioned previously, step times, veiocities, and molar flow rates are
pressure change, because the volumetric flow rate vanes as pressure changes.
Emoloying Ea. 4.5, Eo. 4.16 can be written as: mterrelated through matenal balances. Therefore; smce the mfluent and
effluent moles requued for a certain step are fixed by Eqs. 4.13 through 4.19,
Q - !Slt:p = f''"'Q dt (4.17) the choice of step time really only affects the mterstitial velocity. For some
dP dP
0 steps that ch01ce 1s cnt1cal. For example 1 during the feed step the flow rate
affects the apparent selecttv1ty, as suggested in Figure 4.3, as well as pressure
For some steps, it iS convement to determine the flows from the molar
ctroo. In contrast, the time allotted for the purge step 1s usually chosen m
contents of the coiumn, when the composition orofiles are known. For either order to synchronize steos occurrmg m parallel beds. Pressure drop and mass
A or B, the contents are:
transfer rates are normally of little importance while ourgmg. From a
mathematical viewpoint, the veloc1t1es m the feed and purge steps are
N, - JL[ee, + (1 - •Jf;(c;}IAcsdz ( 4.18) governed by the rates at which the shock and Stmole waves propagate
0
through the bed, as given by Eos. 4.5, 4.7, 4.9, and 4.10. These equations
where { 1s the isotherm function, given by Eu. 4.2. This relation 1s eqUJvaient reiatc the interstitial velocity, the length of the bed, the step time, and the
to the column tsotherm mentioned m Section 4.3. In the same vem, the total column isotherm, as follows:
column contents are obtained by summing the amounts of both components.
vin,IF = L/6A ( 4.20}
Vin!lpu = L/{3A (4.21)
NTOTAL- J"(ee + (I - •)lJA(cA) + f.(c.}l)Acsdz ( 4.19)
0 Note that the feed step 1s assumed to oroduce the :_pure light component at
high pressure, so in Ea. 4.20 BA= BiPu, y = 0, Yi.). Furthermore, since in
Now these balance equat10ns can be combined to predict the overall
Eo. 4.21 the purge gas 1s also presumed to be pure, /3 A = f3 .. ,.,• In this section,
oerformance of some PSA cycles. As discussed in Chapter 3, the simolest
PSA cycles emoloy four steps, so they will be considered first. The steps the light comoonent 1s assumed to have a linear isotherm, so m the followmg
8
comprise: oressunzation either by feed or product, feed at constant pressure treatment _f3 - {3 = 0 8 •
80
Accordmgly, the moles required for the feed and purge s,teos mav be
until breakthrough ts imminent, countercurrent blowdown, and complete
determmed from Eos. 4.13 through 4.21 as
purge (so that all of the heavy component 1s exhausted). The version
6
employing feed for pressurization 1s usually called the Skarstrom cycle, and Q,,tlF - ,j,.r,! Pf3A,,/0A ( 4.22)
1s discussed in Section 3.2. Several vanations of the Skarstrom cycie have
been analyzed via the local equilibrium theory, including steps with incom- Q,,tlru = <Pf3A,,lf3A = </>, (4.23)
1 9
plete purge, - simultaneous pressurization and feed and strnuitaneous feed
and cocurrent blowdown,w cocurrent blowdown, 11 rinse, 12 etc. As shown m
Sect10ns 4.4.i-6, the final results of those models are surpnsmgly simple.
Futhermore, experiments conducted over a wide range of conditions have
confirmed their validity, as shown m Section 4.5. and K; ts the Henry's law coefficient of component i.