Page 195 - Pressure Swing Adsorption

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172 PRESSURE SWING ADSORPTION DYNAMIC MODELING OF A PSA SYSTEM 173

Many of the models have been tested exoenmentally for particuiar sys- such as air drying and hydrogen ourificat1on), the change in the gas velocity
tems, but no attempt lS made here to review the results of such studies on an through the bed due to adsorot1on/desorot10n can 'be neglected. Provided
mdividual basis. Rather we have attempted to orovide a conceptual summaIY that the pressure drop through the bed ts small, the, mterstitial velocitv can
m which the models are discussed m terms of their salient features. The therefore be considered as constant. In fact. the frictional pressure dr~o in
models may be differentiated according to the followmg aspects: most actual systems is not very iarge and may usually be neglected; 211 For a
trace system Eo. 5.i therefore becomes:
1. The fluid flow pattern (generally plug flow or axially dispersed plug flow).
2. Constant or variable fluid velocity.
3. The form of the equilibrmm relationship(s). (5.3)
4. The form of the kinetic rate expression(s).
5. The inclusion of heat effects (isothermal/nomsothermall.
6. The numencril methods used to soive the system of eauattons. Bulk Separation
When the mole fract10n of the adsorbable component (or components) in the
5.1. l Fluid Flow Models feed 1s large, the condition for constant velocity 1s no longer fulfilled and a
more detailed analysis to account for the vanahon tn veioc1ty through the
Flow through an adsorption column is a PSA system is no different from flow
through any fixed adsorbent bed. The flow pattern may therefore be ade- adsorbent bed is required, based on the continuity condition (3ssummg
negligible pressure drop):
quately represented by the axial dispersed olug flow model. A mass balance
n
for component t over a differential volume element yields:
I: c; ""C * f( z) (5.4)
-D ,J'c; + _ii,_(vc.) + ac; + 1 - s aq; 0 (5.1)
L i'/z2 az 1 7it -E- Tt =
In this modei the effects of all mechamsms that contribute to axtal mixing are
Constant Column P,-essure
iumped together into a single effective axial dispersion coefficient. More
detailed models that include, for example, radial dispersmn are generally not C m Eq. 5.4 ts a constant when the adsorption column is operated at a
necessary. When mass transfer resistance 1s significantly greater than axial constant total pressure. Therefore under constant column pressure condition
dispersmn, one may neglect the axtal di'spers1on tenn and assume oiug flow. the overall matenal balance eouatwn, which gives the vanation of fluid
Axial dispersion 1s generally not important for large mdustnal units. In small velocity through the column, takes the form:
laboratory units the axial mixing may be more significant due to the tendency C av 1 - , ,,., aq;
of the smaller particles to stick together to form clusters that act effectively as az + -s- L, at - O (5.5)
,_,
smgle parttcles in thetr effect on the fluid flow. Subject to the piug flow
approximation Eq. 5.1 reduces to: Combimng Eos. 5.1 and 5.5. the component matenal balance equation for
bulk separation at constant column pressure is obtained:
(5.2)
-D a'c; + ll dC; + ac, + ~ - ;, dq;) -
aq,
r·
However, when the eauations are to be solved numerically, tt ts generally L az 2 az at e at Y; L, di - O (5.6)
. •=•
advantageous to retain the form of EQ. 5.1 since inclusion of the axtai
disoersion term eliminates discontmuities in the slope of the concentratton Assummg that t~e ideal gas Jaw holds [i.e., c = PyJ(RgT )], the component
0
1
profile. The solution for the oiug flow situation IS then generated simply by and matenal balance eouations become:
~ss1gnmg a very large value to the axial Peele! number (vL/DL). This
approach also allows easy mvesttgatton of the effect of axial dispersion on the
cyclic steady-state performance.
(5.7)
Trace Systems
av + R,To 1 - , ;., aq; _
When the adsorbed comoonent 1s oresent at low concentration in a large oz . p e L, at - 0 (5.8)
excess of an mert earner (which 1s more or less true in purification processes 1=1