SME
Separation Processes · Problem type
Minimum liquid-to-gas ratio
Use this for “Clean solvent must cut a gas from 2% solute to 0.1%, with y = 1.5x. What is the least L ÷ G, and the design L ÷ G at 1.5 times it?”
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
=
2.138,
from
the
top
(xᵢₙ,
yₒᵤₜ)
to
the
bottom,
where
the
liquid
leaves
with
xₒᵤₜ
=
0.00889.
From the top the stairs take 6, the last one partial.
(
L
G
)ₘᵢₙ
=
yᵢₙ − yₒᵤₜ
yᵢₙ ÷ m − xᵢₙ
=
1.425:
the
dashed
line
touches
the
equilibrium
line
where
the
gas
enters
(the
pinch).
This is an example. Type your own values to start a new problem.
(L ÷ G)min
=
−
÷
−
L ÷ G
=
1.5
×
(L ÷ G)min
A
Absorption factor
calculated
Formulas
(
L
G
)min
=
yᵢₙ − yₒᵤₜ
yᵢₙ ÷
m
− xᵢₙ
1.425
=
0.02 − 0.001
0.02 ÷ 1.5 − 0
L
G
=
1.5
×
((
L
G
)min)
2.1375 = 1.5 × 1.425
A
=
L ÷ G
m
1.425
=
2.1375
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.
•
At the least liquid, the liquid leaving the bottom is in equilibrium with the entering gas (a pinch).
•
The design runs at 1.5 times the minimum L ÷ G.
Step-by-step
WE KNOW
yᵢₙ = 0.02, yₒᵤₜ = 0.001, xᵢₙ = 0, m = 1.5
FIND
minimum L ÷ G ((L ÷ G)min), design L ÷ G (L ÷ G), absorption factor (A)
Step 1 · Find minimum L ÷ G ((L ÷ G)min)
Use (L ÷ G)min = (yᵢₙ − yₒᵤₜ) ÷ (yᵢₙ ÷ m − xᵢₙ)
At
the
pinch
the
leaving
liquid
reaches
x
=
yᵢₙ
m
:
the
operating
line’s
rise
over
its
run.
(
L
G
)min
=
0.02 − 0.001
0.02 ÷ 1.5 − 0
(
L
G
)min
=
0.019
0.013333
(
L
G
)min
=
1.425
Step 2 · Find design L ÷ G (L ÷ G)
Use L ÷ G = 1.5 × ((L ÷ G)min)
A common design choice: 1.5 times the minimum.
L
G
=
1.5
×
1.425
L
G
=
2.1375
Step 3 · Find absorption factor (A)
Use A = (L ÷ G) ÷ m
The absorption factor compares the operating line’s slope with the equilibrium line’s.
A
=
2.1375
1.5
A
=
1.425
Check
Put the numbers back in. Both sides should match.
1.425
=
0.02 − 0.001
0.02 ÷ 1.5 − 0
✓
2.1375 = 1.5 × 1.425 ✓
1.425
=
2.1375
1.5
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.