Page 122 - Pressure Swing Adsorption

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96 PRESSURE SWING ADSORPTION EQUILIBRIUM THEORY 97

Most PSA applications expio1t C(lllilihnum seiect1vfty, and systems are
l. Local equilibrium 1s achieved instantaneously between the adsorbent and
usually designed to m111im1ze the negative effecis of mass transfer resistance. adsorbates at each axial locat1on.
ln such cases. the trends and. frequently, even precise measures of PSA 2. The feed is a hinary mixture of ideai gases.
performance can he predicted accurately from iocal equilibrium models. In 3. Axial dispersion within the adsorhcnt hcd 1s ncgligihlc.
part1cu1ur, estimates of product recovery are often excellent, even when mass 4. Axial pressure gradients arc negligible.
transfer resistances are large, because mass conservation predominates over 5. There are no radial veioc,ty or comoositmn gradients.
diffusmn and heat effects. That such models can be accurate, without 6. Temperature ts constant.
requmng extensive experimental data, has made them valuable as a tool for
PSA simulation and design. Other advantages of equilibrium theories are: The second group links the eouatmns and condittons to a particular cycle
they help to identify proper comhinat1ons of operating conditions; under and geometry. The assumptions of a simple four-step cvcie and adsorption
certain conditions they reduce to very simple algebraic performance equa- system are listed, though they may be modified tff reflect other cycies or
tions relating the operating and design parameters; they clarify the underly- conditions without affecting the applicability of the eauilibnum theory.
mg links between steps, conditions, adsorbent properties, and oerformance;
7. All of the adsorbent is utilized dunng the feed and purge steps.
and as a result they may facilitate conception and optimization of novel
8. Pressure 1s constant dunng the feed and purge steps.
cycles.
9. The isotherms may be linear or nonlinear, but they arc uncoupled.
Another major advantage is th.at the model parameters may he obtained
dircctiy from equilibrium measurements; so 1t is not necessary to fit experi- 10. Dead volume at the adsorher entrance and exit is negligible.
mental PSA data. In the simplest case, that 1s, when isotherms are practically Actually, m the first group of assumptions. all ·but the first could be
linear, the adscirbent-adsorbate interactions can be Jumped together as a reiaxed within the confines of an equilibnum model. To drop those assump-
single parameter, roughly analogous to the mverse of selectivity. It is even tions, however, would complicate the mathematics and ·diminish the simplic-
possible to incornorate dispersmn bv accountmg for dead zones at the ity of the eauilibnum approach. After all, if one. resorts to orthogonal
entrance or exit of the adsorbent bed.
collocat1on or other potent mathematical methods to account for dispersion,
As exolamed m Chapter 3, the conventwnal four-steo PSA cycle for pressure drop, etc., there 1s no point m restrictmg such a moctei to mstanta-
separat10n of a binary mixture comprises feed, blowctown, purge, and pressur-
neous mass transfer. Nevertheless, some aspects of detailed models are
1zatton, as illustrated m Figure 3.11. Each of these steps serves a vital mentioned in this chapter, along with the effects of axial pressure drop (see
functmn that contributes to successful operation of the PSA system. By
Section 4.9). ln addition, the assumption that PSA operation be isothermal 1s
accounting for the relations governing flow and transfer between the gas and not necessarily ngid. ln fact, heat effects appear m a vanety of ways, some of
adsorbent, equilibrium models are able to predict the phenomena occurring
which are covered 111 Section 4.8. The effects of relaxing manv of the second
m each step. It 1s then easy to combine these relations to predict overall
set of assumpt10ns are also discussed in this chapter (see Sections 4.4.3-4.4.6).
performance. Extending the basic equations, and modifying the condil1ons of
the convcnt10nal steps allows complex properties, conditions, and cycles to t1c
simulated.
Before proceeding with mathematical details, the reader may wish to scan 4.2 Mathematical Model
Secllon 4.4 on Cycle Analysis. For example, Eqs. 4.27, 4.37, 4.44, and 4.45 are
final equations that predict product recoveries for a variety of cycles. Those The simplest PSA cycle studied in this chapter is shown in Figure 4. l. which
equat10ns should convey the idea that, even though the PSA qcles and shows the basic steps and conventions of position and direction. The bottom
governing equations may seem comolicated, they can be soivect in closed of that figure will be discussed later, but 1i shows how compositions move
forms that are simple and yet have broad· applicability. A separate Section. through the adsorbent bed during each step, with the shaded regmn deD1ct-
4.5, covers ExPerimental Validation, m which predictions of some of the ing the penetrat10n of some of the more strongiy adsorbed (or "heavy .. )
models are compared with expenmental data. component, while the plain region contams only the pure, Jess strongiy
The restnct1ons of the equilibrium the0IY are evident in the following two adsorbed (or "light") component. In this chapter the heavy and light compo-
groups of inherent assumotions. The first grouo 1s generally valid for eauilib- nents are referred to as A and B, resoecttveiy.
num-based PSA seoarat1ons, and they make the resulting equations amenable The following mdividual component balance applies to bmary mixtures m
to solution by simple mathematical methods. which both components adsorb, so they are coupled in the gas ohase, but are