Complete-Mixing Model for Gas Separation by Membranes

feed composition

0.5

ideal separation factor

5

pressure ratio

4

Gas permeation uses polymer or ceramic membranes. For example, helium can be separated from natural gas with a fluorocarbon membrane.

Consider a binary mixture composed of

A

and

B

to be separated by a membrane.

A

and

B

have different permeabilities and thus diffuse at different speeds through the membrane.

When the permeate flow rate is a small fraction of the feed rate, the complete-mixing model provides a reasonable estimate of the permeate mole fraction. The solution of the following equations gives the reject and permeate compositions for such a model:

y

p

=

-b+

2

b

-4ac

2a

and

y

p

=

x

f

-

x

0

(1-θ)

θ

,

where

a=1-

*

α

,

b=r(1-

x

0

)-1+

*

α

r

x

0

+

*

α

, and

c=-

*

α

r

x

0

.

This Demonstration displays the mole fraction of the reject and permeate in blue and red, respectively.

In the above equations and definitions

x

f

is the feed composition,

*

α

is the ideal separation factor (defined as the ratio of the permeabilities of species

A

and

B

),

r≥1

is the pressure ratio (i.e., the feed-side pressure over permeate-side pressure),

θ

is the cut or fraction of feed permeated (

0≤θ≤1

), and

y

p

and

x

0

are the permeate and reject compositions.