SME
Separation Processes · Problem type
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?”
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).
q = 1 (saturated liquid feed): the q-line rises straight up from xF = 0.4.
McCabe–Thiele from the top: 12 stages (the last one partial, the reboiler counted), the feed on stage 6.
This is an example. Type your own values to start a new problem.
α
Relative volatility
example
xF
Feed light fraction
example
q
Feed condition
example
xD
Distillate light fraction
example
xB
Bottoms light fraction
example
R
Reflux ratio
example
N
Equilibrium stages
worked out (not typed)
NF
Feed stage
worked out (not typed)
Formulas
N
=
the
stairs
counted
from
xD
down
to
xB
(volatility
α
,
feed
xF,
feed
condition
q
,
reflux
R
)
12 = the stairs counted from 0.95 down to 0.05 (volatility 2.5, feed 0.4, feed condition 1, reflux 2.167)
NF
=
the
feed
stair
of
the
stairs
counted
from
xD
down
to
xB
(volatility
α
,
feed
xF,
feed
condition
q
,
reflux
R
)
6 = the feed stair of the stairs counted from 0.95 down to 0.05 (volatility 2.5, feed 0.4, feed condition 1, reflux 2.167)
Assumptions
•
Constant relative volatility α and constant molar overflow.
•
Total condenser; the reboiler counts as a stage.
•
The feed enters on its best stage, where the stairs cross the q-line.
Step-by-step
WE KNOW
α = 2.5, xF = 0.4, q = 1, xD = 0.95, xB = 0.05, R = 2.167
FIND
equilibrium stages (N), feed stage (NF)
Step 1 · Find equilibrium stages (N)
Use N = the stairs counted from xD down to xB (volatility α, feed xF, feed condition q, reflux R)
Step from (xD, xD) across to the curve and down to the operating line, again and again until x reaches xB; count the stairs (a partial last stair counts as one).
N
=
the
stairs
counted
from
0.95
down
to
0.05
(volatility
2.5,
feed
0.4,
feed
condition
1,
reflux
2.167)
N
=
12
Step 2 · Find feed stage (NF)
Use NF = the feed stair of the stairs counted from xD down to xB (volatility α, feed xF, feed condition q, reflux R)
The feed goes on the stair that crosses the operating lines’ meeting point; below it, step down to the stripping line.
NF = the feed stair of the stairs counted from 0.95 down to 0.05 (volatility 2.5, feed 0.4, feed condition 1, reflux 2.167)
NF = 6
Check
Put the numbers back in. Both sides should match.
12 = the stairs counted from 0.95 down to 0.05 (volatility 2.5, feed 0.4, feed condition 1, reflux 2.167) ✓
6 = the feed stair of the stairs counted from 0.95 down to 0.05 (volatility 2.5, feed 0.4, feed condition 1, reflux 2.167) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
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Main lesson
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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?”
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?”