Page 85 - Pressure Swing Adsorption

60 PRESSURE SWlNG ADSORPTION
FUNDAMENTALS OF ADSORPTION 61
isotherm does not deviate too greatly from lineanty, and 1t tends to break
For K » 1.0 this s1molifies to:
down as the rectangular iim1t 1s approached. A more senous defect, from the
perspective of modeling PSA systems, 1s that the G1ueckauf approximation
(2.63)
does not give a good representation in the initial regwn of the uotake. This 1s
2
of little consequence when the column 1s relatively long ( L/v » R /De), but
1t proves to be a serious limitation m certain PSA processes where the cycie where the three terms within the final set of large parentheses represent,
time is short relauvc to the diffusion time. respectively, the film resistance, macropore resistance, and m1cropore resis-
tance. For a similar system m which the mass transfer rate 1s controlled by a
iinear rate expression (Ea. 2.57) the corresponding exoressIOn for the re-
2.4.6 Combination of Res.istancea
duced second moment 1s:
ln a real adsorption systems several different mass transfer resistances may
contribute to the overall kinetics. When the equilibrium 1s linear (or at ieast DL V ( 6 ., 1 (2.64)
vL + L -,:=,) kK
not severely nonlinear), 1t 1s relatively simple to combine these resistances
into a single overall linear driving force mass transfer coefficient based on the whence 1t 1s evident that the eqmvalence relatwn ts provided by Ea. 2.58.
rec1oroca1 addition rule:
2.4. 7 Multicomponent and Nonisothermal Systems
(2.58)
Kk
So far m our discussion of column dynamics we i!rnvc considered only an
This rule may be Justified in a number of different ways, but the simplest isothermal single actsorbable component m an mert (nonadsorbing) earner.
proof rests on an analysis of the moments of the dynamic response. In such a system there 1s oniy one mass transfer zone which may approach a
The first and second moments of the pulse response are d~fined by: constant pattern, proportionate pattern, or a combined form, depending on
the shape of the equilibrium isotherm. The s1tuat1on remains qualitatively
00
similar when there are two adsorbable comoonents (with no mert) smce the
1ct di
µ== _o __ continuity condition then ensures that there can be oniy one transition or
(2.59)
00 mass transfer zone with the velocity and shape detennmed by the binary
l c dt equilibnum 1sothenn. The addition of another cQmponent, even an inert,
0
however, changes the s1tuat1on m a rather dramatic way by introducing a
00 2
1c(t - µ) dt second mass transfer zone. The two mass transfer ,2ones will propagate with
0-2 + J.L2 = ~o _____ _ different velocthes so the orofile will assume the form sketched in Figure 2.26
(2.60)
loo C di with an expanding plateau regton between the two trans1t1ons. Both transi-
() tions may be of proportionate pattern, constant oattern1 or combined form,
and the plateau concentration may be higher, lower, or mtennediate between
For a linear adsorption system 1t may be shown that the first moment 1s
the mitial and final states depending on the orec1seform of the isotherm. It 1s
related to the equilibrium constant by:
evident that even with only three components, the profile may assume a wide
/L ~ ~ [ I + ( I ~ ) Kl (2.61) range of different forms.
6
These conclus1ons, reached here by mtu1t1ve arguments, follow directly
from the equilibrmm theory analysis. For a three-component system there
where, for a biporous adsorbent, K = eP + (1 - EP)wKc. The reduced sec~
will be two equatmns of the form of Eq. 2.47 plus the overall conunu1ty
and moment 1s given by:
eauation, which, where oressure drop can be neglected, s1mply takes the
form:
(2.62)
c, + c + c = c 0 ( constant) (2.65)
3
2
Corresponding to each of the two differential balance eouations there will be
a wave velocity (from Ea. 2.50 or 2.52), and it 1s clear that since these
velocities cteoend on the local isotherm slooe, they will m generai be