Membranes - Introduction to Carbon Capture and Sequestration - page 300

where we have defi ned the factor f A :

′

P

CO

f =

2

A

Lj θ

F

And for N 2 we have, using the mass balance in the fl ue gas:

( )

fp 1 − x

AF CO , F

2

x =

NP ,

∗ 2

fp +α

AP

As CO 2 and N 2 are the only components, the sum of these mole fractions
should add up to 1 in the permeate:

( )

1 − x f p

x f p

CO , FAF

CO , FA F

2

x + x =

2

+ = 1

CO , PNP ,

fp + 1

2 2

∗

fp +α

AP

AP

This equation can be rearranged to give a quadratic equation in f A :

( )

(

( ) ( ( ) )

)

22

∗ ∗ ∗

pp − p f + − α + 1 p + 1 + α − 1 x p f − α = 0

FP P A P CO , F F A

2

α ∗ = For 1 this equation has as solution:

1

(1)

f =

pp

A

−

F p

If we use this as a reference, we can defi ne the relative area:

A
A

f

A

=

() ()

1 1

f

A

These equations can be solved easily. In Question 7.3.1 you are asked
to compare the approximate solution with the numerical solution for non-
zero stage cut as is shown in Figure 7.3.2 .
We cannot obtain a concentration of CO 2 in our permeate higher than
0.5. In fact, this result is even independent of the performance (i.e., per-
meance) of our membrane. To better understand this, let us look at the