Page 62 - Pressure Swing Adsorption

! ii
36 PRESSURE SVl~NG ADSORPTION FUNDAMENTALS OF ADSORPTION 37

41
given by:
(2.26)

where NA• N are the fluxes of comoonents A and B measured relative to a
8
fixed frame of reference. If either NA = -N (equ1mo1ar counterdi/fus1on) or
8
y 1s small (dilute system), this reduces to the simple rec1oroca1 addition ruie:
l 1 i
-=-+- (2.27)
D DK Dm
Externoi Idealized It is evident from Eos. 2.23-2.26 that at high pressures D - Dm and at low
Fluid Film Representation
(uniform sphencoi pressures D _,,. DK.
cryslal\ites i ln addition to molecuiar and Knudsen diffusion there may be a contribu-
twn to the flux from forced flow (Poiseuille flow). The equivalent Po1seuille
Figure 2.14 The resistances to mass transfer in a composite adsorbent pellet.
diffusivity is given by:
(2.28)
2.3.1 Diffusion in Mesopores and Macropores
from which it is clear that this contributmn 1s significant only 1n relat1velv
There are four distmgrnshable diffusion mechanisms that contribute m vary- large pores and at relat1veiy high pressures. it can be important in PSA
1~g degrees to transport within macro and mesooores (in which the pore systems, particularly in the pressunzation step, Any such contribution 1s
diame~e: 1s substantially greater than the diameter of the diffusing sorbate): directly additive to the combined diffus1v1tv from the molecular and Knudsen
hulk d1ffus1on, Knudsen flow, Po1seuille flow, and surface diffusion. When the mechanisms.
In the mechanisms so far considerecl the flux 1s through the gas pt1ase m
P?~e diameter 1s large, rciative to the mean free path, bulk or molecular
dtftuswn 1s dominant. Knudsen diffusion, which depends on collisions be- the central regton of the pore. Where the adsorbed phase is sutfic1cntiv
tween the diffusing molecule and the pore wall, becomes important at low mobile and the concentrat10n suffic1entiy high, there may be an additional
pressures and m small pores when the mean free path 1s equal to or greater contribution from surface diffusion 42 through the adsorbed !aver on the pore
than the pore diameter. wall. Any such contrihutmn 1s m parallel with the flux from Knudsen and
The molecular diffus1v1ty vanes approximateiy according to the relation- molecular diffusion and is therefore directlv additive. Surface diffusion 1s an
shio: activated process and is In many ways similar to n11crooote diffusion. hi
particular the patterns of concentration and temperatures dependence are
y1.1
Dma r.; (2.23) similar to those for m1crooore diffusion. as discussed m the next section.
PvM
where M 1s the mean molecular weight, defined by: 2.3.2 Micropore DiffuSion
I 1 j We use here the term m1cropore diffuswn to mean diffusion in pores of
-=-+- (2.24)
M MA . MB dimens10ns comparable with the diameters of the diffusing molecules. In this
situation the diffusing molecule never escapes from :the force field of the oore
~n a b!nary system the molecular diffus1v1ty 1s independent of composition,
wall. The process resembles surface diffusion m that it 1s an activated
b~1t this 1s not precisely true of a multicomponent system. The Knudsen process, but stenc restnctions are also important and in many instances the
d1ffus1v1ty 1s tndependent of pressure and vanes only weakly with temoera- diffus10nai activation energy 1s 1n fact largely determined by the size of the
ture:
diffusing molecule relauve to the smallest free diameter of the oore. In such
(2.25) small pores 1t no longer makes physical sense to distmgu1sh between ad-
sorbed molecuies on the pore wall and "gaseous" molecules m the centrai
In the transition region, where both mechanisms are significant, 1t 1s easy to region of the pore, and it 1s oreferable to regard all sorbate molecules within
show from momentum transfer considerations that the combined diffusivity 1 s the microoores as the "adsorbed phase."