SME
Material & Energy Balances · Problem type
Column split: distillate, bottoms and recovery
Use this for “100 kmol/h at 40% light key splits to 95% and 5%. What are D, B and the recovery?”
Diagram
This is an example. Type your own values to start a new problem.
F (kmol/h)
=
D (kmol/h)
+
B (kmol/h)
D (kmol/h)
F (kmol/h)
=
−
−
r
Light-key recovery overhead
calculated · %
Formulas
F
=
D
+
B
100 = 38.8889 + 61.1111
D
=
F
×
z
− xB
xD − xB
38.8889
=
100
×
0.4 − 0.05
0.95 − 0.05
r
=
D
×
xD
F
×
z
×
100
92.3611
=
38.8889
×
0.95
100 × 0.4
×
100
Assumptions
•
Steady state; the column only separates (no reaction).
•
Two components, the light key and the heavy key; fractions are mole fractions.
•
The lever rule comes from the total and the light-key balances together.
Step-by-step
WE KNOW
F = 100 kmol/h, z = 0.4, xD = 0.95, xB = 0.05
FIND
distillate flow (D), light-key recovery overhead (r), bottoms flow (B)
Step 1 · Find distillate flow (D)
Use D = F × (z − xB) ÷ (xD − xB)
Put
B
=
F
−
D
into
the
light-key
balance
Fz
=
DxD
+
BxB
and
solve
for
D
.
D
=
100
×
0.4 − 0.05
0.95 − 0.05
D
=
100
×
0.35
0.9
D
=
35
0.9
D
=
38.8889
kmol/h
Step 2 · Find light-key recovery overhead (r)
Use r = D × xD ÷ (F × z) × 100
The light key overhead as a share of the light key fed.
r
=
38.8889
×
0.95
100 × 0.4
×
100
r
=
38.8889
×
0.95
40
×
100
r
=
36.94
40
×
100
r
=
0.9235
×
100
r
=
92.3611%
Step 3 · Find bottoms flow (B)
Use F = D + B
What doesn’t leave overhead leaves at the bottom.
B
=
F
−
D
B
=
100
−
38.8889
B
=
61.1111
kmol/h
Check
Put the numbers back in. Both sides should match.
100 = 38.8889 + 61.1111 ✓
38.8889
=
100
×
0.4 − 0.05
0.95 − 0.05
✓
92.3611
=
38.8889
×
0.95
100 × 0.4
×
100
✓
Topic check
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