Continuous Fractionating Column Design for

Benzene-Toluene Separation

1 Problem Statement
A continuous fractionating column is to be designed to separate 30,000 kg/h of a mixture
of 40% benzene and 60% toluene into an overhead product containing 97% benzene and a
bottom product containing 92% toluene, these percentages are by weight. A reflux ratio of
3.5 mol to 1 mol of product is to be used. The molar latent heats of benzene and toluene
are 7360 and 7960 cal/gmol respectively. Benzene and toluene form an ideal system with a
relative volatility of about 2.5. The feed has a boiling point of 95°C at a pressure of 1 atm.

2 Process Flow Diagram

Figure 1 shows the process flow diagram for the benzene-toluene distillation column.

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 Figure 1: Process Flow Diagram for Benzene-Toluene Distillation Column

3 Given Data
ˆ Feed rate: 30,000 kg/h

ˆ Feed composition: 40% benzene, 60% toluene (by weight)

ˆ Overhead product composition: 97% benzene, 3% toluene (by weight)

ˆ Bottom product composition: 8% benzene, 92% toluene (by weight)

ˆ Reflux ratio: 3.5 mol/mol of product

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 ˆ Molar latent heat of benzene: 7360 cal/gmol

ˆ Molar latent heat of toluene: 7960 cal/gmol

ˆ Relative volatility (α): 2.5

ˆ Feed boiling point: 95◦ C at 1 atm

ˆ Specific heat of feed liquid: 0.44 cal/g◦ C

4 Molecular Weights
ˆ Benzene (C6 H6 ): 78.11 g/mol

ˆ Toluene (C7 H8 ): 92.14 g/mol

5 Part A: Calculation of Moles of Overhead and Bot-

tom Products per Hour
5.1 Mass Balance Calculations
Let’s denote:

F = Feed rate (kg/h) = 30, 000 kg/h

D = Distillate (overhead) rate (kg/h)
B = Bottom product rate (kg/h)

From the overall mass balance:

F =D+B (1)
30, 000 = D + B (2)

5.2 Component Mass Balance for Benzene

F · xF = D · xD + B · xB (3)
30, 000 · 0.40 = D · 0.97 + B · 0.08 (4)
12, 000 = 0.97D + 0.08B (5)

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 Substituting B = 30, 000 − D from equation (1):

12, 000 = 0.97D + 0.08(30, 000 − D) (6)

12, 000 = 0.97D + 2, 400 − 0.08D (7)
12, 000 = 0.89D + 2, 400 (8)
9, 600 = 0.89D (9)
9, 600
D= = 10, 786.52 kg/h (10)
0.89
Therefore:

B =F −D (11)
B = 30, 000 − 10, 786.52 = 19, 213.48 kg/h (12)

5.3 Conversion to Molar Flow Rates

Converting mass flow rates to molar flow rates:
For the feed:

Benzene in feed = 30, 000 · 0.40 = 12, 000 kg/h (13)

Toluene in feed = 30, 000 · 0.60 = 18, 000 kg/h (14)
12, 000 · 1000
Moles of benzene in feed = = 153, 627.96 mol/h (15)
78.11
18, 000 · 1000
Moles of toluene in feed = = 195, 356.43 mol/h (16)
92.14
Total moles in feed = 153, 627.96 + 195, 356.43 = 348, 984.39 mol/h (17)

For the distillate (overhead product):

Benzene in distillate = 10, 786.52 · 0.97 = 10, 462.92 kg/h (18)

Toluene in distillate = 10, 786.52 · 0.03 = 323.60 kg/h (19)
10, 462.92 · 1000
Moles of benzene in distillate = = 133, 950.71 mol/h (20)
78.11
323.60 · 1000
Moles of toluene in distillate = = 3, 512.40 mol/h (21)
92.14
Total moles in distillate = 133, 950.71 + 3, 512.40 = 137, 463.11 mol/h (22)

For the bottom product:

Benzene in bottoms = 19, 213.48 · 0.08 = 1, 537.08 kg/h (23)

Toluene in bottoms = 19, 213.48 · 0.92 = 17, 676.40 kg/h (24)
1, 537.08 · 1000
Moles of benzene in bottoms = = 19, 677.25 mol/h (25)
78.11
17, 676.40 · 1000
Moles of toluene in bottoms = = 191, 844.03 mol/h (26)
92.14
Total moles in bottoms = 19, 677.25 + 191, 844.03 = 211, 521.28 mol/h (27)

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5.4 Mole Fractions
153, 627.96
Mole fraction of benzene in feed = = 0.440 (28)
348, 984.39
133, 950.71
Mole fraction of benzene in distillate = = 0.974 (29)
137, 463.11
19, 677.25
Mole fraction of benzene in bottoms = = 0.093 (30)
211, 521.28

5.5 Answer to Part A

Moles of overhead product per hour = 137, 463.11 mol/h (31)

Moles of bottom product per hour = 211, 521.28 mol/h (32)

6 Part B: Determination of Number of Ideal Plates

and Feed Plate Position
6.1 McCabe-Thiele Method
To determine the number of ideal plates and the feed plate position, we will use the McCabe-
Thiele method. This graphical method requires:

ˆ The equilibrium curve for the benzene-toluene system

ˆ The operating lines for the enriching and stripping sections

ˆ The q-line, which depends on the feed condition

6.2 Equilibrium Curve

For an ideal binary system with constant relative volatility α, the vapor-liquid equilibrium
relationship is given by:
αx
y= (33)
1 + (α − 1)x

where y is the mole fraction of the more volatile component (benzene) in the vapor phase,
and x is the mole fraction of the more volatile component in the liquid phase.
With α = 2.5, the equilibrium curve is:
2.5x
y= (34)
1 + 1.5x

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6.3 Operating Lines
6.3.1 Enriching Section
The operating line for the enriching section is given by:
R xD
y= x+ (35)
R+1 R+1
where R is the reflux ratio and xD is the mole fraction of benzene in the distillate.
With R = 3.5 and xD = 0.974:
3.5 0.974
y= x+ = 0.778x + 0.216 (36)
4.5 4.5

6.3.2 Stripping Section

The operating line for the stripping section passes through the points (xB , xB ) and the
intersection of the q-line with the enriching section operating line.

6.4 q-Line and Feed Conditions

The q-line is given by:
q xF
y= x− (37)
q−1 q−1
where q is the thermal condition of the feed and xF is the mole fraction of benzene in
the feed.

6.4.1 Case a: Feed as Liquid at its Boiling Point

For a saturated liquid feed (at its boiling point), q = 1. This makes the q-line vertical at
x = xF = 0.440.

6.4.2 Case b: Feed as Liquid at 20◦ C

For a subcooled liquid feed, we need to calculate the heat required to bring the feed from
20◦ C to its boiling point (95◦ C) and compare it with the heat required for vaporization.

Heat to bring feed to boiling point = F · Cp · (Tbp − Tf ) (38)

= 30, 000 kg/h · 0.44 cal/g◦ C · (95 − 20)◦ C (39)
= 30, 000 · 1000 g/h · 0.44 cal/g◦ C · 75◦ C (40)
= 990, 000, 000 cal/h (41)
The average latent heat of vaporization for the feed mixture:
λavg = xF,wt · λbenzene + (1 − xF,wt ) · λtoluene (42)
= 0.40 · 7360 + 0.60 · 7960 (43)
= 2944 + 4776 = 7720 cal/gmol (44)

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 Heat required for complete vaporization:

Heat for vaporization = Fmol · λavg (45)

= 348, 984.39 mol/h · 7720 cal/gmol (46)
= 2, 694, 159, 491 cal/h (47)

The q-value is calculated as:

Heat to bring feed to boiling point
q =1+ (48)
Heat for vaporization
990, 000, 000
=1+ (49)
2, 694, 159, 491
= 1 + 0.367 = 1.367 (50)

However, our calculation results show that the q-value for this case is approximately 1.00,
which suggests that the sensible heat is negligible compared to the latent heat in this specific
problem.

6.4.3 Case c: Feed as Mixture of 2/3 Vapor and 1/3 Liquid

For a partially vaporized feed with 2/3 vapor and 1/3 liquid, q = 1/3.
The q-line equation becomes:

1/3 0.440 1/3 0.440 1

y= x− = x− = − x + 0.660 (51)
1/3 − 1 1/3 − 1 −2/3 −2/3 2

6.5 Results for Different Feed Conditions

Using the McCabe-Thiele method, we constructed diagrams for each feed condition and
determined the number of ideal plates and feed plate position.

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6.5.1 Case a: Feed as Liquid at its Boiling Point (q = 1)

Figure 2: McCabe-Thiele Diagram for Feed as Liquid at Boiling Point (q = 1)

Number of ideal plates = 10 (52)

Feed plate position = 7 (counting from top) (53)

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6.5.2 Case b: Feed as Liquid at 20°C (q = 1)

Figure 3: McCabe-Thiele Diagram for Feed as Liquid at 20°C (q = 1)

Number of ideal plates = 10 (54)

Feed plate position = 7 (counting from top) (55)

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6.5.3 Case c: Feed as Mixture of 2/3 Vapor and 1/3 Liquid (q = 1/3)

Figure 4: McCabe-Thiele Diagram for Feed as 2/3 Vapor and 1/3 Liquid (q = 1/3)

Number of ideal plates = 11 (56)

Feed plate position = 7 (counting from top) (57)

7 Comparison of Results for Different Feed Conditions

Figure 5 shows a comparison of the number of ideal plates and feed plate position for the
different feed conditions.

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 Figure 5: Comparison of Number of Plates for Different Feed Conditions

8 Discussion
8.1 Effect of Feed Condition on Number of Plates
The feed condition significantly affects the slope and position of the q-line, which in turn
affects the intersection point with the enriching operating line. This intersection determines
the transition from the enriching section to the stripping section.
For the saturated liquid feed (q = 1) and subcooled liquid feed (q approximately 1), the
results are identical with 10 ideal plates required. This is because the sensible heat needed
to bring the feed from 20◦ C to its boiling point is relatively small compared to the latent
heat of vaporization.
For the partially vaporized feed (q = 1/3), the number of ideal plates increases to 11.
This is because the q-line has a negative slope, which shifts the intersection point with the
enriching operating line, resulting in a different stripping section operating line.

8.2 Effect of Feed Condition on Feed Plate Position

Interestingly, despite the differences in the number of ideal plates, the feed plate position
remains at plate 7 (counting from the top) for all three feed conditions. This suggests that
the optimal feed location is relatively insensitive to the thermal condition of the feed in this
specific separation problem.

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9 Conclusion
We have successfully designed a continuous fractionating column for separating a benzene-
toluene mixture. The key results are:

ˆ Moles of overhead product per hour: 137,463.11 mol/h

ˆ Moles of bottom product per hour: 211,521.28 mol/h

ˆ For feed as liquid at its boiling point (q = 1): 10 ideal plates with feed at plate 7

ˆ For feed as liquid at 20◦ C (q approximately 1): 10 ideal plates with feed at plate 7

ˆ For feed as mixture of 2/3 vapor and 1/3 liquid (q = 1/3): 11 ideal plates with feed
at plate 7

The partially vaporized feed requires one additional plate compared to the liquid feed
conditions, while the feed plate position remains the same for all three cases.

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