# Complete-Mixing Model for Gas Separation by Membranes

Complete-Mixing Model for Gas Separation by Membranes

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 and to be separated by a membrane. and have different permeabilities and thus diffuse at different speeds through the membrane.

A

B

A

B

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+-4ac

2

b

2a

y

p

x

f

x

0

θ

where , , and .

a=1-

*

α

b=r(1-)-1+r+

x

0

*

α

x

0

*

α

c=-r

*

α

x

0

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

In the above equations and definitions is the feed composition, is the ideal separation factor (defined as the ratio of the permeabilities of species and ), is the pressure ratio (i.e., the feed-side pressure over permeate-side pressure), is the cut or fraction of feed permeated (), and and are the permeate and reject compositions.

x

f

*

α

A

B

r≥1

θ

0≤θ≤1

y

p

x

0