SME
Separation Processes
Absorption
Use this for “A gas with 2% solute is scrubbed to 0.1% by clean solvent; m = 1.5 and A = 1.4. How many equilibrium stages?”
Diagram
Equilibrium is the straight line y = 1.5x (dilute, Henry’s law).
The gas enters at the bottom with yᵢₙ = 0.02 and leaves at the top with yₒᵤₜ = 0.001; the liquid enters at the top with xᵢₙ = 0.
Operating
line:
slope
L
G
=
A
×
m
=
2.1,
from
the
top
(xᵢₙ,
yₒᵤₜ)
to
the
bottom,
where
the
liquid
leaves
with
xₒᵤₜ
=
0.00905.
From the top the stairs take 6, the last one partial; Kremser gives N = 5.53.
This is an example. Type your own values to start a new problem.
N
=
ln(
−
×
−
×
×
1
−
1
A
+
1
A
)
÷
ln(
A
)
L ÷ G
Liquid-to-gas ratio
calculated
Formulas
N
=
ln((
yᵢₙ −
m
× xᵢₙ
yₒᵤₜ −
m
× xᵢₙ
)
×
(1
−
1
A
)
+
1
A
)
÷
ln(
A
)
5.5302
=
ln((
0.02 − 1.5 × 0
0.001 − 1.5 × 0
)
×
(1
−
1
1.4
)
+
1
1.4
)
÷
ln(1.4)
A
=
L ÷ G
m
1.4
=
2.1
1.5
Assumptions
•
A dilute gas, so the liquid and gas flows L and G stay constant up the column.
•
Equilibrium is the straight line y = mx (Henry’s law); the column is isothermal.
•
The absorption factor is A = L ÷ (mG); N counts ideal (equilibrium) stages.
Step-by-step
WE KNOW
yᵢₙ = 0.02, yₒᵤₜ = 0.001, xᵢₙ = 0, m = 1.5, A = 1.4
FIND
equilibrium stages (N), liquid-to-gas ratio (L ÷ G)
Step 1 · Find equilibrium stages (N)
Use N = ln(((yᵢₙ − m × xᵢₙ) ÷ (yₒᵤₜ − m × xᵢₙ)) × (1 − 1 ÷ A) + 1 ÷ A) ÷ ln(A)
Kremser: how far the gas is taken toward equilibrium with the entering liquid, on a log scale of the absorption factor.
N
=
ln((
0.02 − 1.5 × 0
0.001 − 1.5 × 0
)
×
(1
−
1
1.4
)
+
1
1.4
)
÷
ln(1.4)
N
=
ln(0.02
÷
0.001
×
(1
−
0.7143)
+
1
÷
1.4)
÷
ln(1.4)
N
=
ln(0.02
÷
0.001
×
0.2857
+
1
÷
1.4)
÷
ln(1.4)
N
=
ln(20 × 0.2857 + 0.7143)
ln(1.4)
N
=
ln(5.714 + 0.7143)
ln(1.4)
N
=
ln(6.4283)
ln(1.4)
N
=
1.861
0.3365
N
=
5.5302
Step 2 · Find liquid-to-gas ratio (L ÷ G)
Use A = (L ÷ G) ÷ m
Multiply
both
sides
by
m
.
L
G
=
A
×
m
L
G
=
1.4
×
1.5
L
G
=
2.1
Check
Put the numbers back in. Both sides should match.
5.5302
=
ln((
0.02 − 1.5 × 0
0.001 − 1.5 × 0
)
×
(1
−
1
1.4
)
+
1
1.4
)
÷
ln(1.4)
✓
1.4
=
2.1
1.5
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.