Page 292 - Separation process engineering

liquid, and CMO can be assumed. Equilibrium can be represented as constant relative volatilities.
Choosing toluene as the reference component, α benzene-toluene = 2.25 and α cumene-toluene = 0.210. Use
the Fenske equation to find the number of equilibrium stages required at total reflux and the
recovery fraction of cumene in the bottoms.

b. For the distillation problem given in part a, find the minimum reflux ratio by use of the
Underwood equations. Use a basis of 100 moles of feed/h. Clearly state your assumptions.

d. For L/D = 1.25(L/D) min , find the total number of equilibrium stages required for the distillation
problem presented in parts a and b. Use the Gilliland correlation. Estimate the optimum feed plate
location.

D13.* We have a column separating benzene, toluene, and cumene. The column has a total condenser
and a total reboiler and has 9 equilibrium stages. The feed is 25 mol% benzene, 30 mol% toluene,
and 45 mol% cumene. Feed rate is 100 mol/h and feed is a saturated liquid. The equilibrium data
can be represented as constant relative volatilities: α = 2.5, α = 1.0, and α = 0.21. We
TT
BT
CT
desire 99% recovery of toluene in the distillate and 98% recovery of cumene in the bottoms.
Determine the external reflux ratio required to achieve this separation. If α = 2.25 instead of
BT
2.5, how much will L/D change?
D14. At total reflux a separation requires N min = 10 equilibrium contacts. At a finite external reflux

ratio of L/D = 2.0, the separation requires N = 18 equilibrium contacts. (N and N min include the
partial reboiler and stages in the column but do not include the total condenser.) Find (L/D) min .

D15.* A distillation column is separating benzene (α = 2.25), toluene (α = 1.00), and cumene (α =
0.21). The column is operating at 101.3 kPa. The column is to have a total condenser and a partial
reboiler, and the optimum feed stage is to be used. Reflux is returned as a saturated liquid, and
L /D = 1.2. Feed rate is 1000 kmol/h. Feed is 39.7 mol% benzene, 16.7 mol% toluene, and 43.6
0
mol% cumene and is a saturated liquid. We desire to recover 99.92% of the benzene in the
distillate and 99.99% of the cumene in the bottoms. For a first guess to this design problem, use
the Fenske-Underwood-Gilliland approach to estimate the optimum feed stage and the total
number of equilibrium stages. Note: The Underwood equations must be treated as a case C
problem.

D16.* We are separating a mixture of ethanol and n-propanol. Ethanol is more volatile and the relative
volatility is approximately constant at 2.10. The feed flow rate is 1000 kmol/h. Feed is 60 mol%
ethanol and is a saturated vapor. We desire x = 0.99 mole fraction ethanol and x = 0.008 mole
B
D
fraction ethanol. Reflux is a saturated liquid.
There are 30 stages in the column. Use the Fenske-Underwood-Gilliland approach to determine

a. Number of stages at total reflux

b. (L/D) min
c. (L/D) actual

D17. A distillation column is separating toluene and xylene, α = 3.03. Feed is a saturated liquid and
reflux is returned as a saturated liquid. p = 1.0 atm. F = 100.0 kmol/h. Distillate mole fraction is

x = 0.996 and bottoms x = 0.008. Use the Underwood equation to find (L/D) min and V at feed
min
D
B
mole fractions of z = 0.1, 0.3, 0.5, 0.7, and 0.9. Check your result at z = 0.5 with a McCabe-Thiele
diagram. What are the trends for |Q c,min | and Q R,min as toluene feed concentration increases?
D18. A depropanizer has the following feed and constant relative volatilities: