WOLFRAM|DEMONSTRATIONS PROJECT

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.