Composition of MethanolWater Batch Distillation
September 20, 2005
Prepared by: Jason Hixson
Don Scott
Michael Hickey
Objective
• Determine the composition of liquid
methanol-water binary system at
equilibrium based on temperature in a
distillation column.
Vapor-Liquid Equilibrium Diagram
Antoine Equation
B
B
*
ln p  A 
ln pw  A 
C T
C T
*
m
pm* , w
Vapor Pressure in mmHg of methanol and water.
T is the absolute temperature
A, B, and C are constants.
Antoine Constants
• Are calculated using using the known
temperatures and vapor pressures from
Perry’s Chemical Engineers Handbook.
p*(mmHg)
1.00
5.00
10.00
20.00
40.00
60.00
100.00
200.00
400.00
760.00
T(C )
-44.00
-25.30
-16.20
-6.00
5.00
12.10
21.20
34.80
49.90
64.70
Methanol
p*(mmHg)
1.00
5.00
10.00
20.00
40.00
60.00
100.00
200.00
400.00
760.00
T(C )
-17.30
1.20
11.20
22.10
34.00
41.50
51.60
66.50
83.00
100.00
Water
Antoine Constants
ln p
*
m,w
B
 A
C T
•Arbitrary values are then chosen for A, B, and C giving an
incorrect vapor pressure.
•Excel solver is then used to find values of A, B and C for
both methanol and water which gives the correct pressure.
METHANOL
WATER
A
B
C
A
B
C
18.5875
3626.5500
-34.2900
18.3036
3816.44
-46.13
Van Laar’s Model
Ptotal  xm *  m * p  (1  xm ) *  w * p
*
m
Gamma correction factors for non-ideal system.
*
w
Gamma Correction Factor
A
m  exp[
Axm 2
RT (1 
)
Bxm
Ideal Gas Constant = 1.987 cal/K*g-mol
A
w  exp[
Axw 2
RT (1 
)
Bxw
Temperature (K)
A and B are constants
m,actual
ym * P

xm * pm*
w,actual
yw * P

*
xw * pw
Using data from Perry’s where P is 760 mmHg the
constants A and B can be calculated using solver in Excel
T (C)
100
96.4
93.5
91.2
89.3
87.7
84.4
81.7
78
75.3
73.1
71.2
69.3
67.5
66
65
64.5
xa
0
0.02
0.04
0.06
0.08
0.1
0.15
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.95
1
ya
0
0.134
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
Gives
VAN LAAR
LIQ MODEL
A=
B=
585.6215111
375.733096
Raoult’s Law
ya  xa * p / Ptotal
*
a
Vapor
Liquid
Set Up
Xa yA T(C)
T(K)
pA (mmHg) pB (mmHg) G A CALC
G B CALC P
DIF
0.020 0.133 96.591 369.751 2384.780601 672.2824004 2.114262724 1.000486141 760 0.001905382
•Set arbitrary temperature
Use Solver to minimize DIF
cell by changing T(C).
= (Pcalc-Pactual)
VLE Diagram
METHANOL- WATER
95.000
Vapor
Temperatur (C)
90.000
85.000
80.000
75.000
70.000
Liquid
65.000
0.000
0.100
0.200
0.300
0.400
0.500
xm, ym
0.600
0.700
0.800
0.900
1.000
Composition Calculation Using
WFIT Program
0.38652+0.39727*B2-0.012737*B2^2+0.00013528*B2^3-(0.00000048036)*B2^4)+1%
Reboiler Composition vs Time
Time Vs Composition
Time Vs Composition
20
xMethanol (%)
xMethanol (%)
20
15
10
5
15
10
0
5
0
0
10
20
30
40
50
Time (minutes)
75% Reflux
0
10 20
30
40 50
60 70
Time (minutes)
2500 W
Initial xm: 23%
0% Reflux
Initial Vm: 16.86 L
80
90
Tray # 12 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
xMethanol (%)
xMethanol (%)
Time Vs Composition
0
10
20
30
40
50
Time (minutes)
75% Reflux
35
30
25
20
15
10
5
0
0
10
20
30
40
50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 11 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
25
xMethanol (%)
xMethanol (%)
Time Vs Composition
20
15
10
5
0
0
10
20
30
40
50
Time (minutes)
75% Reflux
0
10
20
30
40
50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 10 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
25
xMethanol (%)
xMethanol (%)
Time Vs Composition
20
15
10
5
0
0
10
20
30
40
50
Time (minutes)
75% Reflux
0
10
20
30
40
50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 9 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
25
xMethanol (%)
xMethanol (%)
Time Vs Composition
20
15
10
5
0
0
10
20
30
40
50
0
Time (minutes)
75% Reflux
10
20
30
40
50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 8 Composition vs Time
Time Vs Composition
25
100
90
80
70
60
50
40
30
20
10
0
xMethanol (%)
xMethanol (%)
Time Vs Composition
20
15
10
5
0
0
10
20
30
40
0
50
20
30
40
50
60
Time (minutes)
Time (minutes)
75% Reflux
10
2500 W
0% Reflux
70
80
90
Tray # 7 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
25
xMethanol (%)
xMethanol (%)
Time Vs Composition
20
15
10
5
0
0
10
20
30
40
50
0
Time (minutes)
75% Reflux
10
20
30
40
50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 6 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
40
xMethanol (%)
xMethanol (%)
Time Vs Composition
30
20
10
0
0
10
20
30
40
50
0
Time (minutes)
75% Reflux
10
20
30
40
50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 5 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
xMethanol (%)
xMethanol (%)
Time Vs Composition
0
10
20
30
40
50
0
Time (minutes)
75% Reflux
40
35
30
25
20
15
10
5
0
10
20
30
40
50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 4 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
60
xMethanol (%)
xMethanol (%)
Time Vs Composition
50
40
30
20
10
0
0
10
20
30
40
50
0
Time (minutes)
75% Reflux
10
20
30
40
50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 3 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
xMethanol (%)
xMethanol (%)
Time Vs Composition
0
10
20
30
40
50
0
Time (minutes)
75% Reflux
70
60
50
40
30
20
10
0
10
20
30
40
50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 2 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
xMethanol (%)
xMethanol (%)
Time Vs Composition
0
10
20
30
40
50
0
Time (minutes)
75% Reflux
100
90
80
70
60
50
40
30
20
10
0
10
20
30
40 50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Tray # 1 Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
xMethanol (%)
xMethanol (%)
Time Vs Composition
0
10
20
30
40
50
0
Time (minutes)
75% Reflux
100
90
80
70
60
50
40
30
20
10
0
10
20
30
40 50
60
Time (minutes)
2500 W
0% Reflux
70
80
90
Reflux Composition vs Time
Time Vs Composition
100
90
80
70
60
50
40
30
20
10
0
xMethanol (%)
xMethanol (%)
Time Vs Composition
0
10
20
30
40
50
0
Time (minutes)
75% Reflux
Collected 1.69 L
100
90
80
70
60
50
40
30
20
10
0
10
20
30
40 50
60
Time (minutes)
2500 W
0% Reflux
Collected 6.38 L
70
80
90
Conclusions
• At 0% reflux the amount of distillate
collected was larger than 75% reflux.
• At 75% reflux the purity of methane was a
much higher quality.
• If quality is more important then a high
reflux percentage is needed.
• If quantity and timeliness is more
important then a low reflux is needed.
QUESTIONS
?