SME
Separation Processes · Problem type
Rectifying operating line
Use this for “A column runs at reflux ratio 3 with a 90% distillate. What are the slope and intercept of the top operating line?”
Diagram
Equilibrium
curve:
y
=
αx
1 + (α − 1)x
with
α
=
2.5;
the
45°
line
is
y
=
x.
Rectifying
line:
y
=
(
R
R + 1
)x
+
xD
R + 1
=
0.684x
+
0.3,
through
(xD,
xD).
This is an example. Type your own values to start a new problem.
m
=
R
+
1
b
=
xD
+
1
Formulas
m
=
R
R
+ 1
0.6842
=
2.167
2.167 + 1
b
=
xD
R
+ 1
0.3
=
0.95
2.167 + 1
Assumptions
•
Constant molar overflow above the feed: L and V do not change from stage to stage.
•
Total condenser, so the reflux has the distillate’s composition xD.
•
The curve is drawn for α = 2.5 only to show where the line sits.
Step-by-step
WE KNOW
R = 2.167, xD = 0.95
FIND
slope (m), intercept on y (b)
Step 1 · Find slope (m)
Use m = R ÷ (R + 1)
Above
the
feed
L
V
=
R
R
+ 1
:
the
liquid
coming
down
over
the
vapor
going
up.
m
=
2.167
2.167 + 1
m
=
2.167
3.167
m
=
0.6842
Step 2 · Find intercept on y (b)
Use b = xD ÷ (R + 1)
The line through (xD, xD) with that slope meets x = 0 here.
b
=
0.95
2.167 + 1
b
=
0.95
3.167
b
=
0.3
Check
Put the numbers back in. Both sides should match.
0.6842
=
2.167
2.167 + 1
✓
0.3
=
0.95
2.167 + 1
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Distillation
Main lesson
Minimum reflux ratio (Underwood)
Use this for “A saturated liquid feed holds 40% of the light component; the distillate must reach 95% and α = 2.5. What is the minimum reflux ratio?”
Stages by McCabe–Thiele stepping
Use this for “α = 2.5, a saturated liquid feed at 40%, 95% distillate, 5% bottoms and R = 2.167. How many stages, and which is the feed stage?”