11.4-7. Enriching Tower for Benzene Toluene. An enriching tower is fed 100 /ℎ of a saturated vapor feed containing 40 mol % benzene (A) and 60 mol % (B) at 101.32 kPa abs. The distillate is to contain 90 mol % benzene. The reflux ratio is set at 4.0:1.0. Calculate the /ℎ distillate and bottoms and their compositions. Also, calculate the number of theoretical plates required. Given and Sketch: A – Benzene
B – Toluene
= 4.0: 1.0
̇ =? , = 0.90 , = 0.10
101.32
Saturated Vapor ̇ = 100 ℎ , = 0.40 , = 0.60
̇ =? , = ? , =?
Required:
kg mol/h distillate, ̇ , kg mol/h bottoms ̇ and its compositions number of theoretical trays,
To obtain the values of the molar flowrates of distillates and bottoms, material balances are done over the distillation column.
Overall Mole Balance ̇ = ̇ ̇
Equation 1
Equation 2
100
ℎ
= ̇ ̇
Component A Balance , ̇ = , ̇ , ̇ (0.40)100
= (0.90) ̇ (, ) ̇
ℎ
Equation 3 Equation 4
For the enriching operating line, using Eq. 11.4-8 of Transport Processes and Separation Process (Geankoplis, 2003), + =
Substituting R=4.0
+ =
1 4.0
4.01
Equation 5
1 0.90
Equation 6
4.01
For the equation of q-line, using Equation 11.4-19 of Unit Operations by Geankoplis, =
−1
−
Equation 7
−1
( − 1) = −
Equation 8
Since q is defined as,
=
ℎ 1
Equation 9
ℎ
If the feed enters as a saturation vapor, the numerator of Equation 9 is 0, thus, = 0 (Geankoplis, 2003). Substituting this to Equation 8 yields, (0 − 1) = (0) − 0.40
Equation 10
= 0.50
Equation 11
Looking at the plot in Figure 1, the q-line and the enriching line intersects at = 0.271 thus, , = 0.271.
Solving Eq. 1 and Eq. 4 simultaneously, ̇ = 20.5087 /ℎ ̇ = 79.4913 /ℎ
Benzene (A) - Toluene (B) 1
0.9
0.8
0.7
0.6
A
y 0.5
0.4
0.3
0.2
0.1
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
xA
Answer:
Figure 1. Equilibrium Diagram for Benzene (A) – Toluene (B) System at 1 atm
From Figure 1, the number of theoretical steps is 4.71.
0.9
1
