Sample Problem #17

SAMPLE PROBLEM #17: A total feed of 200 mol/h having an overall composition of 42 mol % heptane and 58 mol % ethyl benzene is to be fractionated at 101.3 kPa pressure to give a distillate containing 97 mol % heptane and a bottoms containing 1.1 mol % heptane. The feed enters the tower partially vaporized so that 40 mol % is liquid and 60 mol % vapor.

Cal alculate alcu cula late te

the th e fo foll following: llow owin ing g:

(a) Moles per hour of distillate and bottoms. (b) Minimum reflux ratio Rm. (c) Minimum steps and theoretical trays at total reflux. (d) Theoretical number of trays required for an operating reflux ratio of 2.5:1.

Equili Equilibrium lib briu ium m data ta are given below at 1 101. 01.32 .32 32 k kPa Pa abs pressu abs sure surre re fo for  for  r the m mole mo olle e fr frac fra acti action tion on h h--heptane -heptane heptane x xH H and y and yH: H: Temperature

xH

yH

K

rC

409.3

136.1

0.000

0.000

402.6

129.4

0.080

0.230

392.6

119.4

0.250

0.514

383.8

110.6

0.485

0.730

376.0

102.8

0.790

0.904

371.5

098.3

1.000

1.000

SOLUTION

total condenser  L0

200 mol/h F (q = 0.4) xF = 0.42

Distilling column 101.3 kPa abs

R = 2.5

partial reboiler 

D xD = 0.97

B xB = 0.011

   



D, B = ? Rmin = ? ntheo at (R = ), n min = ? ntheo at (R= 2.5) Solve for the y-intercept for the rectifying operating line y n

!

!



n







!





!

Solve for the slope of the feed line q-line slope

!

! 

! 



Plotting the McCabeMcCabe-Thiele -Thiele diagram

3

2

1

4 5

nF = 7

6 7

8 9 10 11

n = 11.3 xB

xF

xD

Doing the material balances 





Total

balance F = 200 = D + B More volatile component balance xFF = xDD + xBB 0.42(200) = 0.97D + 0.011B Solving these two equations D = 85.3 mols/h B = 114.7 mols/h

Solving for R min

y-int for Rm =

B

F

y-int of rectifying line = !

R Rm



@

Rm =

Solving for n min 1 2 3

4

5

6

7

Nmin = 7.5 xB

xF

N = 7.5 = theoretical trays + reboiler = n + 1 @ n = 6.5 theoretical trays

xD

SUMMARY    

nF = 7, n = 11.3 D = 85.3 mols/h and B 114.7 mols/h Rmin = 1.7 ntheo = 6.5