SME
Separation Processes · Problem type
Ideal selectivity and permeate purity
Use this for “A membrane has P = 2.4 barrer for O₂ and 0.4 barrer for N₂. How rich in O₂ is the permeate from air?”
Diagram
This is an example. Type your own values to start a new problem.
α
=
PA (barrer)
PB (barrer)
yA
1
−
=
α
×
xA
1
−
Formulas
α
=
PA
PB
5
=
5
1
yA
1 − yA
=
α
×
xA
1 − xA
0.5707
1 − 0.5707
=
5
×
0.21
1 − 0.21
Assumptions
•
The permeate is at far lower pressure than the feed, so only the selectivity limits yA.
•
The feed’s makeup barely changes along the membrane; two gases, A and B.
•
Each gas crosses in proportion to its permeability times its share of the feed.
Step-by-step
WE KNOW
PA = 5 barrer, PB = 1 barrer, xA = 0.21
FIND
ideal selectivity (α), permeate fraction of A (yA)
Step 1 · Find ideal selectivity (α)
Use α = PA ÷ PB
How many times faster A crosses than B.
α
=
5
1
α
=
5
Step 2 · Find permeate fraction of A (yA)
Use yA ÷ (1 − yA) = α × xA ÷ (1 − xA)
The
permeate’s
A-to-B
ratio
is
α
times
the
feed’s;
turn
that
ratio
back
into
a
fraction.
yA
=
α
×
xA
1 − xA +
α
× xA
yA
=
5
×
0.21
1 − 0.21 + 5 × 0.21
yA
=
1.05
0.79 + 1.05
yA
=
1.05
1.84
yA = 0.5707
Check
Put the numbers back in. Both sides should match.
5
=
5
1
✓
0.5707
1 − 0.5707
=
5
×
0.21
1 − 0.21
✓
Topic check
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