Post on 14-Apr-2018
DSP: Seminar 2, Binary distillation, McCabe-Thiele method, column with one and multiple feeds
18 kg/kmol 60.5 kg/kmol at 0.4 Mpa 2133.9
Solution:
MH2O Maa
Solution of Example 1: a.
1- Scheme and material balance:
FEED
DESTILAT
BOTTOMS
WWDDFF
WDF
xnxnxnnnn
DFW
WD
WFFD
WDWFDDWDDFF
nnnxxxx
nn
xnxnxnxnDnFxnxn
)(
2- Prepare x-y diagram using equilibrium data:
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1x
y
3- Select on diagram point F, D and W
Δ vhsteam
Seminar 2 Binary distillation, McCabe-Thiele method, column with one and multiple feeds Example 1: Hundred kmol/h of a bubble-point liquid mixture of 75 mol% water and 25 mol% acetic acid is distillated continuously in a distillation tower at a pressure of 1 atmosphere. Distillate contains 95 mol% of light component and Bottoms 95 mol% of heavy component. The reflux ratio is 2 times of minimum reflux ratio.
a- determine the number of theoretical stages and optimum feed stage lacation b- calculate steam requirement in reboiler and requirement of cooling water in total
condenser if the steam pressure is 0.4 Mpa and cooling water is preheated by 20 oC, Only condensation heat of the steam is used and reflux ie returned to the column at boiling point.
Data: Equilibrium data Water Acetic acid at 1 atm (mol frictions) x 0 0.0055 0.053 0.125 0.206 0.297 0.510 0.649 0.803 0.9594 1 y 0 0.0112 0.133 0.240 0.338 0.437 0.630 0.751 0.866 0.9725 1 heat of evaporation at Tw Δvhwater= 2214 kJkg-1 Δvhaa=390 kJkg-1
Solution of Example 1: a.
1- Scheme and material balance:
FEED
DESTILAT
BOTTOMS
WWDDFF
WDF
xnxnxnnnn
DFW
WD
WFFD
WDWFDDWDDFF
nnnxxxx
nn
xnxnxnxnDnFxnxn
)(
2- Prepare x-y diagram using equilibrium data:
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1x
y
3- Select on diagram point F, D and W
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
4- Draw q-line q-line is graphical interpretation of material balance of the feed stage, q represents the amount of liquid that accumulates at the feed stage by feeding of 1 kmol of the feed. q-line equation:
11
qx
xq
qy F
For bubble point liquid, q=1, The slop of q-line equation is o
qqtg 90
1
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
q-line
5- calculation of minimum reflux ration For calculation minimum reflux ration Rmin the operating line in the rectifying section of the column for at Rmin should be drawn.
11 minmin
min
Rx
xR
Ry D
We have two points of this line one is the intersection of q-line and equilibrium curve and another in the intersection of 45o line and xD line.
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
4- Draw q-line q-line is graphical interpretation of material balance of the feed stage, q represents the amount of liquid that accumulates at the feed stage by feeding of 1 kmol of the feed. q-line equation:
11
qx
xq
qy F
For bubble point liquid, q=1, The slop of q-line equation is o
qqtg 90
1
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
q-line
5- calculation of minimum reflux ration For calculation minimum reflux ration Rmin the operating line in the rectifying section of the column for at Rmin should be drawn.
11 minmin
min
Rx
xR
Ry D
We have two points of this line one is the intersection of q-line and equilibrium curve and another in the intersection of 45o line and xD line.
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
q-line
The minimum reflux ratio can be calculated from the slope of this line
'''
min xyyx
R D
or from the section 1min R
xD on the y axis for x=0
6- calculate reflux ratio (R) as R=1.2 Rmin
7- calculate the section 1R
xD on the y axis for x=0
8- draw the operating lineof the rectifying section of the column by connecting points (0,
1RxD ) and (xD, yD)
9- draw the operating line of the striping section of the column, by connecting intersection point of q-line and operating line of rectifying section with point (xw, yw)
y‘
x‘
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
q-line
The minimum reflux ratio can be calculated from the slope of this line
'''
min xyyx
R D
or from the section 1min R
xD on the y axis for x=0
6- calculate reflux ratio (R) as R=1.2 Rmin
7- calculate the section 1R
xD on the y axis for x=0
8- draw the operating lineof the rectifying section of the column by connecting points (0,
1RxD ) and (xD, yD)
9- draw the operating line of the striping section of the column, by connecting intersection point of q-line and operating line of rectifying section with point (xw, yw)
y‘
x‘
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
10- draw steps between equilibrium curve and operating lines
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
Number of theoretical stages= number of steps – 1 (reboiler) Optimal feed stage = intersection of q-line and operating lines
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
10- draw steps between equilibrium curve and operating lines
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
Number of theoretical stages= number of steps – 1 (reboiler) Optimal feed stage = intersection of q-line and operating lines
b. Enthalpy balance of reboiler:
vvvmsteamsteam hnvhm
)1( waavwwatervvv yhyhh
)1()1( qnRnn FDvm Where msteam is the mass flow of steam, steamvh is heat of condensation of water at pressure of the steam, nvm is mol flow of boil-up and vvh is heat of evaporation of boil-up at reboiler temperature.
water
vvvmsteam vh
hnm
Enthalpy balance of total condenser:
DvDDvvnOHOHOH hRnhntCpm )1(222
)1( DaavDwatervDv xhxhh Where mH2O is the mass flow of cooling water, nvn is mol flow of overhead vapor and Dv h is heat of evaporation of distillate at condenser temperature.
b. Enthalpy balance of reboiler:
vvvmsteamsteam hnvhm
)1( waavwwatervvv yhyhh
)1()1( qnRnn FDvm Where msteam is the mass flow of steam, steamvh is heat of condensation of water at pressure of the steam, nvm is mol flow of boil-up and vvh is heat of evaporation of boil-up at reboiler temperature.
water
vvvmsteam vh
hnm
Enthalpy balance of total condenser:
DvDDvvnOHOHOH hRnhntCpm )1(222
)1( DaavDwatervDv xhxhh Where mH2O is the mass flow of cooling water, nvn is mol flow of overhead vapor and Dv h is heat of evaporation of distillate at condenser temperature.
DSP: Seminar 2, Binary distillation, McCabe-Thiele method, column with one and multiple feeds
kJkg-1
Solution of Example 1: a.
1- Scheme and material balance:
FEED
DESTILAT
BOTTOMS
WWDDFF
WDF
xnxnxnnnn
DFW
WD
WFFD
WDWFDDWDDFF
nnnxxxx
nn
xnxnxnxnDnFxnxn
)(
2- Prepare x-y diagram using equilibrium data:
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1x
y
3- Select on diagram point F, D and W
Example 2: Determine the number of theoretical stages and optimum feed stages locations in column in example 1, if we have two feed streams, one the same as in example 1 and another 50 kmol/h 50 mol% vaporized, which is consist of 50 mol% water and 50 mol% acetic acid. All other data are same as in example 1.
Solution of Example 2: Scheme and mass balance:
F1
F2
D
W
nL1 nv1
nL3
nL2 nv2
nv3
1
2
3
WWDDFFFF xnxnxnxnnWnDnFnF
2211
21
WD
WFFFFFFD xx
xnnxnxnn
)( 212211
nW =nF1+nF2-nD q1=1 q2=0.5 Section 1: Same as rectifying section in previous example nL1=nD.R nV1=nD(R+1) Equation of operating line:
11
Rx
xR
Ry D
q-line equation:
11 11
1
qx
xq
qy F
Solution of Example 1: a.
1- Scheme and material balance:
FEED
DESTILAT
BOTTOMS
WWDDFF
WDF
xnxnxnnnn
DFW
WD
WFFD
WDWFDDWDDFF
nnnxxxx
nn
xnxnxnxnDnFxnxn
)(
2- Prepare x-y diagram using equilibrium data:
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1x
y
3- Select on diagram point F, D and W
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
4- Draw q-line q-line is graphical interpretation of material balance of the feed stage, q represents the amount of liquid that accumulates at the feed stage by feeding of 1 kmol of the feed. q-line equation:
11
qx
xq
qy F
For bubble point liquid, q=1, The slop of q-line equation is o
qqtg 90
1
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
q-line
5- calculation of minimum reflux ration For calculation minimum reflux ration Rmin the operating line in the rectifying section of the column for at Rmin should be drawn.
11 minmin
min
Rx
xR
Ry D
We have two points of this line one is the intersection of q-line and equilibrium curve and another in the intersection of 45o line and xD line.
Solution of Example 2: Scheme and mass balance:
F1
F2
D
W
nL1 nv1
nL3
nL2 nv2
nv3
1
2
3
WWDDFFFF xnxnxnxnnWnDnFnF
2211
21
WD
WFFFFFFD xx
xnnxnxnn
)( 212211
nW =nF1+nF2-nD q1=1 q2=0.5 Section 1: Same as rectifying section in previous example nL1=nD.R nV1=nD(R+1) Equation of operating line:
11
Rx
xR
Ry D
q-line equation:
11 11
1
qx
xq
qy F
Section 2: nL2=nL1+nF1q1 nV2=nV1+nF1(q1-1) Equation of operating line:
2
11
2
2
V
FFDD
V
L
nxnxn
xnn
y
q-line equation:
11 22
2
qx
xq
qy F
Section 3: nL3=nL2+nF2q2 nV3=nL3-nW Equation of operating line:
WL
Ww
WL
L
nnxn
xnn
ny
33
3
Calculation steps:
1- Follow steps 1-8 as in example 1, considering new equation for mass balance 2- Calculate nL1, nV1, nL2, nV2, nL3, nV3 3- Plot q2-line using q2-line equation, one point of the line is (xF2, yF2), for obtaining
another point choose an x and calculate a y. 4- Plot the operating line in section 3, using operating line equation. One point is (xW,
yW), for obtaining another point choose an x and calculate a y. Plot operating line in section 2 by connecting two intersections, intersection of operating line in section 1 and q1-line and intersection of operating line in section 3 and q2-line.
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
4- Draw q-line q-line is graphical interpretation of material balance of the feed stage, q represents the amount of liquid that accumulates at the feed stage by feeding of 1 kmol of the feed. q-line equation:
11
qx
xq
qy F
For bubble point liquid, q=1, The slop of q-line equation is o
qqtg 90
1
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
q-line
5- calculation of minimum reflux ration For calculation minimum reflux ration Rmin the operating line in the rectifying section of the column for at Rmin should be drawn.
11 minmin
min
Rx
xR
Ry D
We have two points of this line one is the intersection of q-line and equilibrium curve and another in the intersection of 45o line and xD line.
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
q-line
The minimum reflux ratio can be calculated from the slope of this line
'''
min xyyx
R D
or from the section 1min R
xD on the y axis for x=0
6- calculate reflux ratio (R) as R=1.2 Rmin
7- calculate the section 1R
xD on the y axis for x=0
8- draw the operating lineof the rectifying section of the column by connecting points (0,
1RxD ) and (xD, yD)
9- draw the operating line of the striping section of the column, by connecting intersection point of q-line and operating line of rectifying section with point (xw, yw)
y‘
x‘
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
q-line
The minimum reflux ratio can be calculated from the slope of this line
'''
min xyyx
R D
or from the section 1min R
xD on the y axis for x=0
6- calculate reflux ratio (R) as R=1.2 Rmin
7- calculate the section 1R
xD on the y axis for x=0
8- draw the operating lineof the rectifying section of the column by connecting points (0,
1RxD ) and (xD, yD)
9- draw the operating line of the striping section of the column, by connecting intersection point of q-line and operating line of rectifying section with point (xw, yw)
y‘
x‘
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
10- draw steps between equilibrium curve and operating lines
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
Number of theoretical stages= number of steps – 1 (reboiler) Optimal feed stage = intersection of q-line and operating lines
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
10- draw steps between equilibrium curve and operating lines
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
Number of theoretical stages= number of steps – 1 (reboiler) Optimal feed stage = intersection of q-line and operating lines
b. Enthalpy balance of reboiler:
vvvmsteamsteam hnvhm
)1( waavwwatervvv yhyhh
)1()1( qnRnn FDvm Where msteam is the mass flow of steam, steamvh is heat of condensation of water at pressure of the steam, nvm is mol flow of boil-up and vvh is heat of evaporation of boil-up at reboiler temperature.
water
vvvmsteam vh
hnm
Enthalpy balance of total condenser:
DvDDvvnOHOHOH hRnhntCpm )1(222
)1( DaavDwatervDv xhxhh Where mH2O is the mass flow of cooling water, nvn is mol flow of overhead vapor and Dv h is heat of evaporation of distillate at condenser temperature.
b. Enthalpy balance of reboiler:
vvvmsteamsteam hnvhm
)1( waavwwatervvv yhyhh
)1()1( qnRnn FDvm Where msteam is the mass flow of steam, steamvh is heat of condensation of water at pressure of the steam, nvm is mol flow of boil-up and vvh is heat of evaporation of boil-up at reboiler temperature.
water
vvvmsteam vh
hnm
Enthalpy balance of total condenser:
DvDDvvnOHOHOH hRnhntCpm )1(222
)1( DaavDwatervDv xhxhh Where mH2O is the mass flow of cooling water, nvn is mol flow of overhead vapor and Dv h is heat of evaporation of distillate at condenser temperature.
Example 2: Determine the number of theoretical stages and optimum feed stages locations in column in example 1, if we have two feed streams, one the same as in example 1 and another 50 kmol/h 50 mol% vaporized, which is consist of 50 mol% water and 50 mol% acetic acid. All other data are same as in example 1.
Solution of Example 2: Scheme and mass balance:
F1
F2
D
W
nL1 nv1
nL3
nL2 nv2
nv3
1
2
3
WWDDFFFF xnxnxnxnnWnDnFnF
2211
21
WD
WFFFFFFD xx
xnnxnxnn
)( 212211
nW =nF1+nF2-nD q1=1 q2=0.5 Section 1: Same as rectifying section in previous example nL1=nD.R nV1=nD(R+1) Equation of operating line:
11
Rx
xR
Ry D
q-line equation:
11 11
1
qx
xq
qy F
Solution of Example 2: Scheme and mass balance:
F1
F2
D
W
nL1 nv1
nL3
nL2 nv2
nv3
1
2
3
WWDDFFFF xnxnxnxnnWnDnFnF
2211
21
WD
WFFFFFFD xx
xnnxnxnn
)( 212211
nW =nF1+nF2-nD q1=1 q2=0.5 Section 1: Same as rectifying section in previous example nL1=nD.R nV1=nD(R+1) Equation of operating line:
11
Rx
xR
Ry D
q-line equation:
11 11
1
qx
xq
qy F
Section 2: nL2=nL1+nF1q1 nV2=nV1+nF1(q1-1) Equation of operating line:
2
11
2
2
V
FFDD
V
L
nxnxn
xnn
y
q-line equation:
11 22
2
qx
xq
qy F
Section 3: nL3=nL2+nF2q2 nV3=nL3-nW Equation of operating line:
WL
Ww
WL
L
nnxn
xnn
ny
33
3
Calculation steps:
1- Follow steps 1-8 as in example 1, considering new equation for mass balance 2- Calculate nL1, nV1, nL2, nV2, nL3, nV3 3- Plot q2-line using q2-line equation, one point of the line is (xF2, yF2), for obtaining
another point choose an x and calculate a y. 4- Plot the operating line in section 3, using operating line equation. One point is (xW,
yW), for obtaining another point choose an x and calculate a y. Plot operating line in section 2 by connecting two intersections, intersection of operating line in section 1 and q1-line and intersection of operating line in section 3 and q2-line.
DSP: Seminar 2, Binary distillation, McCabe-Thiele method, column with one feed
Data to PictureEqulibrium 0 0
0.0055 0.0112 nF= 100 kmol/h nD= 77.77778
0.053 0.133 xF= 0.75 nW= 22.222220.125 0.24 q= 10.206 0.338 xD/Rmin+1 0.3550.297 0.437 Rmin= 1.676056
0.51 0.63 R= 3.3521130.649 0.7510.803 0.866 xD= 0.95 xD/R+1= 0.218285
0.9594 0.9725 xw= 0.05 Steps 13.51 1 P= 101.325 kPa NTS 12.50
line
0 01 1
q-line0.75 0.750.75 0.83
Operating line in rectifying section0.95 0.95
0 0.218285F
0.75 00.75 0.75
D0.95 00.95 0.95
W0.05 00.05 0.05
45 o
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
DSP: Seminar 2, Binary distillation, McCabe-Thiele method, column with one feed
2214 kJkg-1K-1 MH2O 18 Kg/kmol
390 kJkg-1K-1 Maa 60.05 Kg/kmolPsteam 0.4 Mpa
2133.9 kJkg-1 338.4977
yw 0.1325555.73 kJ/kmol/K
4053.87 kg/h
cpwater 4.18 kJ/kg/K39030.37 kJ/kmol/K
dtH2O 20 K
158034.6 kg/h
Δvhwater= Δvhaa=
nvm
msteam
mH2O
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
Δ vhsteam
Δv hv
Δv hD
x-y diagram, Water-Acetic Acid
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
x-y diagram, Water-Acetic Acid
0
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
y
DSP: Seminar 2, Binary distillation, McCabe-Thiele method, column with multiple feeds
Data to PictureEqulibrium 0 0
0.0055 0.0112 nF1= 100 kmol/h nD=nF1*xF1+nF2*xF2-(nF1+nF2)*xW/(xD-xW)=0.053 0.133 xF1= 0.75 nW= nF1+nF2-nD=0.125 0.24 q1= 1 nL1= 344.52270.206 0.338 nF2= 50 kmol/h nV1= 447.30050.297 0.437 xF2= 0.5 nL2= 444.5227
0.51 0.63 q2= 0.5 nV2= 447.30050.649 0.751 nL3= 469.52270.803 0.866 xD= 0.95 nV3= 422.3005
0.9594 0.9725 xw= 0.051 1 P= 101.325 kPa
steps 14.3line xD/Rmin+1 0.355 N 13.3
0 0 Rmin= 1.6760561 1 R= 3.352113
q1-line0.75 0.75 xD/R+1= 0.2182850.75 0.83
q2-line0.5 0.50.2 0.8
Operating line in section10.95 0.95
0 0.218285F1 F2
0.75 0 0.5 00.75 0.75 0.5 0.5
D0.95 00.95 0.95
Operating line in section 3 Operaiting line in section 20.05 0.050.5 0.55032
W0.05 00.05 0.05
45 o
0
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1.2
0 0.2 0.4 0.6 0.8 1 1.2
x
y
DSP: Seminar 2, Binary distillation, McCabe-Thiele method, column with multiple feeds
nD=nF1*xF1+nF2*xF2-(nF1+nF2)*xW/(xD-xW)= 102.7778nF1+nF2-nD= 47.22222
kmol/h
Optimal Feed stage 1 6Optimal Feed stage 2 10
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0 0.2 0.4 0.6 0.8 1 1.2
x
y
0 0.0055 0.053 0.125 0.206 0.297 0.51 0.649 0.803 0.95940 0.0112 0.133 0.24 0.338 0.437 0.63 0.751 0.866 0.9725
xd/Rmin+1 0.35Rmin 1.714286R= 3.428571
xd/R+1 0.214516
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
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1x-y diagram, Water-Acetic Acid
x
y
x'
0 0.2 0.4 0.6 0.8 1 1.20
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y
0 0.2 0.4 0.6 0.8 1 1.20
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11
0 01 1
0.75 00.75 0.75
0.95 00.95 0.95
0.05 00.05 0.05
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
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1x-y diagram, Water-Acetic Acid
x
y
x'
0 0.2 0.4 0.6 0.8 1 1.20
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y
0 0.2 0.4 0.6 0.8 1 1.20
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1
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x
y