Membranes - Introduction to Carbon Capture and Sequestration - page 293

achieved to the extent that one or both of these properties are different
for the different components of the feed gasses.

Membrane separation

In the previous sections, we have seen that a material can have a differ-
ent permeability for two different gasses. This difference causes the
fl uxes of these gasses to be different, which is the basis for a separation.
Let us now look with more detail into such a separation. Consider the
membrane shown in Figure 7.2.5 . We have two components, N 2 and
CO 2 . We assume that the permeability of the material is not infl uenced by
the presence of the other component. The only difference from the pure
component case is that the driving force is not the total pressure differ-
ence between the retentate and permeate, but the partial pressure
difference:

P ′ P ′

( ) ( )

CO N

j =

2

p − p and j =

2

p − p ,

CO CO , R CO , P N N , R N , P

L L

2 2 2 2 2 2

where P i is the permeance of the material for component i . The partial

pressure on the retentate side follows from:

px = p ,

iR , iR R ,

where x i,R is the mole fraction of component i on the retentate side and
p R is the total pressure. An equivalent expression holds for the permeate
side.
Let us now apply these mixture expressions to our membrane.
Figure 7.2.1 shows that the feed splits into a retentate and a permeate.
If we carry out a mass balance over our membrane, we have for the
fl uxes (mol/sec):

Φ=Φ+Φ= Aj + Aj

F RP

R P

, is defi ned as the fraction of the feed that fl ows
through the membrane:

The stage cut θ

j
j

P
F

θ=