Membrane Gas Separation

5.7
Transport Models for Ordered Pore Networks 
Membranes with ordered structures such as zeolites or nanotubes have considerable 
potential as gas separation membranes [46 – 48] . In addition to having thermal and chemi-
cal stability, the porosity of these structures is ordered, and therefore there is usually more 
control over the separation properties. The pores within these structures are such that gas 
transport can not be completely explained by the transition state theory. This is because, 
in nanotubes for example, there is only one transition, from outside of the tube to inside 
of the tube. Two alternative models are outlined here, the parallel transport model and 
the resistance in series transport model, which are illustrated in Figure 5.5 , and they are 
explained in detail by the work of Gilron and Soffer [27] .
5.7.1
Parallel Transport Model 
The parallel transport model considers the total fl ux as the contribution from the molecules 
travelling via surface diffusion and from the molecules travelling via Knudsen diffusion 
[27,36,49,50] . This model does not consider transition stages and is applicable to pores 
that remain roughly the same size throughout the entire membrane such as nanotube - based 
membranes. Gilron and Soffer [27] presented the following expression,
P
P
P
tot
S
K
=
+
(5.18)
where P
S
is the surface diffusion permeability and P
K
is the Knudsen diffusion permeabil-
ity as defi ned earlier.
d
p
d
p2
d
p1
(a)
(b)
ql
ql
(1–x)ql
xql
Figure 5.5 Schematic models for (a) parallel transport and (b) resistance in series 
transport [27] . Reprinted from Journal of Membrane Science, 209 , J. Gilron and A. Soffer, 
Knudsen diffusion in microporous carbon membranes with molecular sieving character, 
339 – 352, Copyright (2002), with permission from Elsevier

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Modelling Gas Separation in Porous Membranes 
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