Simulation of Batch Distillation of a Nonideal Binary Mixture
On the basis of material and energy balances, one can derive the following system of differential
equations which governs the temperature T, total mole number NL, and methanol mole fraction
xM of a methanol-isopropanol solution that is undergoing a batch distillation.
Before boiling occurs or for temperature T(t) < TBo, bubble point of the solution initially charged
to the still,
 N L 

  0 where NL is the total mole number of the solution in the still at time t
 t P
(D-1)
 x M 

  0 where is xM the methanol mole fraction of the solution in the still at time t (D-2)
 t P
Qo
 T 
  
 t P N L CP
(D-3)
where Cp = xM*CpM + (1  xM)CpI,
CpM = Cp of methanol, CpI = Cp of isopropanol
(D-4)
Qo = rate of heat supplied to the batch still, assumed to be a constant for simplicity—other
expression for the heating rate may be used, e.g., Q = UA[Ts  T(t)].
After boiling starts or for T(t)  TBo
 N L 

 
 t  P
Qo

 T   γ M Psat M
x M CP 
 1   H vap
 
 x M P  PTot

where  H vap  x M  H vapM  (1  x M ) H vapI
 H vapM = heat of vaporization of methanol,
(D-6)
 H vapI = heat of vaporization of isopropanol
xM
 x M 
 N 
(γ M Psat M  1)  L 

 
 t  P NL
 t P
(D-7)
 T   T   x M 
 

 

 t P  x M P  t P
(D-8)
 T 
P Q
where 
 
R
 x M P
(D-9)




x
 2α 2 x M 1  M 

1 xM 


sat 
P  γM P M 
 1
3

αx M 


 β(1  x M ) 1  β(1  x ) 

M 




 1 xM  
 2β 2 (1  x M ) 1 
 
xM  

sat 
Q  γIP I 
 1
3


β(1

x
)


M

 αx M 1  αx

M




R  γ M x M Psat M
(D-10)
(D-11)
BM
BI
 γ I (1  x M )Psat I
2
(T  CM )
(T  CI ) 2
(D-12)
 Psat M 
BM
AM, BM, CM are the Antoine parameters for methanol in log10
  AM  T


 mm Hg 
 o  CM 
 C

(D-13)
sat
 P I 
BI
AI, BI, CI are the Antoine parameters for isopropanol in log10
  AI T


 mm Hg 
 o  CI 
 C

 and  are the parameters in the van Laar equations for activity coefficients of methanol and
isopropanol, M and I,
ln(γ M ) 
α

αx M 
1  β(1  x ) 
M 

2
ln(γ I ) 
α  0.1354
β
 β(1  x M ) 
1  αx

M


2
β  0.1075
(D-14)
with the initial conditions: At t = 0, NL = NL o, xM = xM o and T = To.
Physical Parameters: AM = 8.0868, BM = 1584.02, CM = 239.38; CpM = 23.0 cal/(g-mol.K),
HvapM = [9207  9(T/oC  25)] cal/g-mol; AI = 8.1430, BI = 1583.43, CI = 218.62;
CpI = 37.1 cal/(g-mol.K), HvapI = [10064  15.8(T/oC  25)] cal/g-mol
Eqn (D-1 through D-14) may be solved numerically using Matlab. Two Matlab M-files
(BatchDistil.m and BatchDistildv.m) are provided which can be run on Matlab to generate the T,
NL and xM profiles as a function of time for the following set of data: NL o = 100 g-mol, xMo =
0.70, To = 25oC, Patm = PTot = 1 atm, Qo = 12 kcal/min, TBo (bubble point of the initial charge
with xMo = 0.70) = 69.63oC (Can you verify by a bubble point calculation?),
distillation run time = 50 min.
Test run the Matlab program by copying and running M-files on Matlab, which you can access
on any workstation on NCSU campus. You should be able to find Matlab on the Application
Launcher. Double click the Matlab icon to invoke the Matlab command window and click the
File pulldown menu to copy the two M-files into Matlab’s working directory. Then on the
command line (characterized by >>) enter BatchDistil (without the .m extension). If the Matlab
program runs successfully, you should see 3 plots on a single figure appearing on the screen. If
there is any problem, Matlab will provide error message(s) on screen to help debugging the
problem. You can use the M-files as template and modify them to simulate the batch distillation
of other binary solution mixtures.
For the Matlab part of the data analysis, modify the Matlab M-files—in particular, the input
data—and generate the T, NL and xM profiles as a function of time.