Page 135 - Pressure Swing Adsorption

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110 PRESSURE SWING ADSORPTION EQUILIBRIUM THEORY Ill

present four-step cycle (with complete purge) may not be the best ch01ce. Removmg the restrictions on feed comoos1t10n and including tile impact of
More will be said about alternatives later in this chapter. Nevertheless, a sorotlon on the mtcrstitial gas velocitv ieads to a more widely applicable and
simple matenal baiance can he used to determine this parameter, regardless accurate model for mosi PSA systems. That approach was followed hy
of the oncrating conditions. The following reiatwn applies for any cycle thai Knaebel and Hill1.1 for a system havmg linear isotherms. Their relation to
splits a binary mixture in which the light component ts obtained as a pure predict recovery of the light component, also restncted to the case of
product, and the only other effluent stream 1s the byproduct: complete purge 1s:
R- P0-1
1 ( 4.30)
EA=J-y R (4.28) n- Ye,[ton + /3(AP- 1)1
B_, B
In this equation the parameter, fl ( = H m the ongmai paper), 1.s determined
by ,mtegrat,on via Runge-K~tta or a simiiar approach,- and 1s somewhat
4.4.2 Four-Step PSA Cycle: Pressurization with Feed mvolved. In general, ,0 o: JJ y " when /3 - 0 (e.g., 0.1 ). while for larger
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values of /3, n 1s somewhat largei than that product. Since n 1s not a simple
Wh~t may seem to be the simnlest modification of the four-steo cycle
function of feed compositton, adsorheni setect1v1ty, or operating pressures,
outlmed previously 1s to pressurize with feed rather than the light product.
one might expect that the dependence of recovery would he equally complex.
This arrangement was actually the cycle proposed by Skarstrom.'' It seems
mtuit1vely possible, if not probable, that pressunzmg with feed rather than The discrepancies between the models, due to differences m their mherent
assumptions, are discussed in Section 4.6. In addition, some of the subtleties
product could produce more net product (i:e., have a higher recovery). That
of the pressunzat1on steo are discussed in Section 4.9.
is, on physical grounds 1t IS easy (but deceptive) to regard oressunzatton as a
"parasitic" step, since no product evolves. At first giance, the basic mathe- As m the previous section, specific results caicu:Jated from Eq. 4.30 are
shown in Figure 4.5, for the case of linear isotherms. That figure illustrates
m.ittcs would secni to confirm these expectations. For example, m the case_ of
the effects of feed composition and pressure ratJO 'On product recovery for
pressunzat1on with feed, NPR• the moles consumed for pressunzat1on. ap-
pears m the ·ctenommator of the defimtion of recovery, as shown m Ea. 4.29. two adsorbent select1v1ties, f3 = 0.1 and 0.9, which span the range of very
For the counterpart cycle (pressunzat1on with product), NPR appeai:s as a easy to Quite difficult PSA applications. The results, agam are shown as
three-dimensional surfaces that in this case have ou1te different shaoes. due
negative term m the definition of recovery, Ea. 4.26. Thus, in both cases 1t
to the difference m selectivities. As for pressunzation with product, recovery
would appear th~t pressunzatjon 1s detenmental to performance. Following
that notion, it might be cteducCd that the relatively less valuable feed should ' of the light component always decreases as the amount of the heavy compo-
be employed for this puroose, as opposed to the pure product. ' I nent m the feed increases. In addition, both surfaces approach an asvmptote
Followmg this reasonmg, 1t is useful to examine oressunzatwn with feed as I at high pressure ratios, but, for the low-selectiv1ty case (/3 = 0.9), there 1s a
an alternative to oressurization with product, pnmarily in order to better l ridge representmg maximum recovery at low pressure rat.ios.
understand the PSA cycle, and secondarily to gain insight mto the develop- Another relevant issue is the mherent differences between the pressunza-
ment of eo_uilibnum models. As ment10ned earlier, both Shenctaiman and tmn methods discussed. Thougf1 there may he differences m mcchanicai
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Mitchell and Chan et al. ignored the effect of the heavy component on the complextty and other details, the most significant difference 1~, more than
likely, between the recoveries of the light product. To expand on that pomt,
molar flows and velocities. As a result, their models cto not distinguish
between the amount of gas reauirecJ for pressurization with feed versus Figure 4.6 shows the mcremental improvement in recovery for pressurization
product. Their predicted recovery of the light component. restricted to the by product versus pressunzation by feed as affected 'by feed composition and
case of cornpiete purge, is: pressure ratio, again for (3 = 0.1 and 0.9. The como'anson is again limited to
systems havmg linear isotherms. As can be seen, regardless of the conditions
and parameters, the recovery of the iight component that 1s attamable by
pressunzatton with product is generally suoenor to, that obtainable by ores-
Yn,[to'-B + /3(to- !)] ( 4.29) sunzation with feed. The oercentage difference is small for systems with high
selecttvities, but grows larger as select1v1ty ctroos. Perhaps surpnsmgly, the
Note that Yns--+ 1 was assumed by both Shendalman and Mitchell and Chan
difference mcreases as the pressure rat10 (.¢7) increases.
et al., so 1t would be superfluous m the denominator on the nght-hanct side m
This result underscores the fallacies of the previous mtuitive arguments in
their versmns. It is mcludect here only for completeness. In addition, favor of oressunzatmn by feed, and shows that it is a m1sconceotmn to view
Shenctalman and Mitchell assumed that f3 = f3A , and {3 = 1, while Chan pressunzat10n as a "parasitic" step. The pnmary underlymg prmc1pie 1s that,
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et al. assumed {3 = {3A /(3 . 11
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