Page 78 - Pressure Swing Adsorption

52 PRESSURE SWING ADSORPTION FUNDAMENTALS OF ADSORPTION 53
The dvnam1c behavior of an adsorprion column depends on the interp!av
Table 2.9. Kinetic Selectivities for 0 2 / N Separation at 298K. 0
2
between adsorot1on kinetics, adsorption equilihnum, and fluid dvnam1cs.
Adsorbent Ko,!KN, DoJDN, aK However, the overall pattern of the dynamic behav1or· 1s generally determined
by the form of the equi!ibnum reiatJonship. This pattern may be strongly
CMS (Bergbau) I.II 147 12.I
4A Zeolite 0.28 40 i.75 modified by kinetic effects (finite resistance to mass transfer). but, in general,
RS JO (Modified 4A) 0.5 40 3.2 kihet1c effects do not give nse to qualitative differences m behavior. It 1s
therefore useful to consider first the anaiys,s of the dvnam1cs of an ideal
~ Kinetic and equilibnum parameiers for CMS and 4A zeolite are lrom Tables 2.4 and 2.7. Values for system with mfimteiy rapid mass transfer (equilibmim theory) an'C1 then to
RS-JO are trom S. Farnoq, M. N. Rathor, imd K. HidaJal, Chem. Eng. Sci. On press).
show how the ideal patterns of behavior are modified m a real system by the
mtrus1on of finite resistance to mass transfer.
selecuv1ty which occurs when kinetic and eouilibnum seiect1v1t1es are m
opposition 1s obvious. 2.4.1 . Equilibnum Theory
A somewhat similar situation anses m kinetically controlled PSA pro-
The formal analysis of adsorption coiumn dynamics starts from the basic
cesses, which operate under transient conditions. When the kinetics are
controlled by a diffusive process (normally mtracrystalline or rnicropore differential equation derived from a transient mass balance on an eiement of
diffusion), the uptake, followmg a step change in gas ohase concentratmn, 1s the column. If the flow oattern 1s represented bv the axially disoersed plug
given by Eq. 2.39. For a linear isotherm this reduces, m the short time region, flow model, this assumes the form:
to: a c iJ r· 1 - e \ M'i
2
-DL-, + r;rr! l!C) + -- } T - () (2.47)
az ~ol
(2.46a) E vi
If axial dispers10n and pressure drop through the coiumn can be neglected
If two species ( A and B) diffuse independently and their isotherms are also and if the concentrat10n of the adsorable species 1s small, this expression
independent, the ratio of thetr uptakes at any time will be given by: reduces to:
qA/cA \ KA [Ii; v-+ - ac + -- - -o (2.48)
iJC
\'. 1 - E ) iJ{j
ax= ( qu/Cu} = K V If;; (2.46b) az at , at
8
In the absence of mass iransfer resistance local eauilibnum prevails at all
This parameter provides a usefui approximate measure of the actual kinetic points (i.e., q = qf) and if the system 1s isothermal, q;* = f(c;>, where f(c)
select1v1ty of the adsorbent. in any real system the assumption that the two represents the equilihnum isotherm. Under these conditions Eq. 2.48 he~
sncc1cs diffuse mdepcndentlv is unlikely to he accurately fulfilled, hut Ea. comes:
2.46b ts still very useful as a rough guide for mitial screening of kinet1callY
selective adsorbents. It shows clearly that the actual selectivity depends on [v/(i+ (1-e) dq[)]ac + ac -o (2.49)
both kinetic and eauilibrmm effects. L e de, az at
I
Values of aK for three kinetically selective adsorbents for 0 /N separa-
2
2
tion are given in Table 2.9. The suoenonty of the carbon molecular sieve This eouation has the form of the kinematic wave ;equation with the wave
velocity given by:
over the zeO!ite adsorbents 1s clearly apparent. Furthermore, 1t is evident that
the advantage of RS-to compared with regular 4A zeolite sterns from a Jess
(2.50)
adverse cauilibnum rather than from any difference in the mtnnsic diffusivity
ratio. -
If the equilibnum relatwnshio 1s linear (Q = Kc),
(2.51)
2.4 Adsorption Column Dynamics
and 1t 1s evident that the wave vcJocJty 1s independent of concentration. For
Since PSA processes are generally carried out with packed adsorotion
an unfavorable equilibrium reiat1onship (Figure 2.9) da* /de increases with
columns, an elementary understanding of the dynamic behavior of a o~cked
concentration so w decreases with concentration, leading to a profile that
adsorbent bed 1s an essential prereqms1te for process modeling and analysis.