design of a continuous distillation column for a multi component mixture

MAY 2010 Bornova-İZMİR

REPORT TO DEPARTMENT OF CHEMICAL ENGINEERING EGE UNIVERSITY

FOR

COURSE: CHE386 CONCEPTUAL DESIGN II

DESIGN OF A CONTINUOUS DISTILLATION COLUMN FOR A MULTICOMPONENT MIXTURE

DESIGN REPORT IV

Y.Doc.Dr. Serap CESUR

SUBMITTED TO

25/05/2010

SUBMISSION DATE

05070008901 Ürün ARDA

GROUP 3

05070008103 Berna KAYA 05070008849 Demet ACARGİL 05060008091 M. Serkan ACARSER 05060008017 Tayfun EVCİL

i

SUMMARY

Separation of multicomponent mixtures is very hard and expensive method in

industry. For high purity products and high percentage recovery, continuous distillation

columns are used.

In this study, a saturated vapor mixture which has 5 different components is tried to be

separated and with the help of assumptions, simplifications the plate type distillation column

design methods is tried to be explored.

In this report you can find the information about shortcut design in ideal and real calculations, using the SRK model. The necessary assumptions were done for both real and ideal calculations, and with the help of Fenske, Underwood and Kirkbridge equations, the number of plates were found.

TABLE OF CONTENTS

Summary ...................................................................................................................... i

1.0 Introduction .......................................................................................................... 1

2.0 Results ..................................................................................................................... 3

2.1 Ideal System ..................................................................................................... 3

2.2 Real System (Non-Ideal) .................................................................................. 6

3.0 Discussion and Conclusion .................................................................................. 14

4.0 Nomenclature ...................................................................................................... 18

5.0 References ........................................................................................................... 19

6.0 Appendix ............................................................................................................. 20

6.1 Ideal System ................................................................................................... 20

6.2 Real System (Non-Ideal) ................................................................................ 27

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1.0 INTRODUCTION

Distillation is probably the most widely used separation process in the chemical and allied industries; its applications ranging from the rectification of alcohol, which has been practiced since antiquity, to the fractionation of crude oil. A good understanding of methods used for correlating vapour-liquid equilibrium data is essential to the understanding of distillation and other equilibrium-staged processes.

Distillation column design The design of a distillation column can be divided into the following steps:

1. Specify the degree of separation required: set product specifications.

2. Select the operating conditions: batch or continuous; operating pressure.

3. Select the type of contacting device: plates or packing.

4. Determine the stage and reflux requirements: the number of equilibrium stages.

5. Size the column: diameter, number of real stages.

6. Design the column internals: plates, distributors, packing supports.

7. Mechanical design: vessel and internal fittings.

The principal step will be to determine the stage and reflux requirements. This is a relatively simple procedure when the feed is a binary mixture, but a complex and difficult task when the feed contains more than two components (multicomponent systems).

Process Description The separation of liquid mixtures by distillation depends on differences in volatility between the components. The greater the relative volatilities, the easier the separation. The basic equipment required for continuous distillation is shown in Figure1. Vapor flows up the column and liquid counter-currently down the column. The vapor and liquid are brought into contact on plates, or packing. Part of the condensate from the condenser is returned to the top of the column to provide liquid flow above the feed point (reflux), and part of the liquid from the base of the

column is vaporized in the reboiler and returned to provide the vapor flow.

Figure 1. Distillation column (a) Basic column (b) Multiple feeds and side streams

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In the section below the feed, the more volatile components are stripped from the liquid and this is known as the stripping section. Above the feed, the concentration of the more volatile components is increased and this is called the enrichment, or more commonly, the rectifying section. Figure1a shows a column producing two product streams, referred to as tops and bottoms, from a single feed. Columns are occasionally used with more than one feed, and with side streams withdrawn at points up the column, Figure1b. This does not alter the basic operation, but complicates the analysis of the process, to some extent.

If the process requirement is to strip a volatile component from a relatively non-

volatile solvent, the rectifying section may be omitted, and the column would then be called a stripping column. In some operations, where the top product is required as a vapor, only sufficient liquid is condensed to provide the reflux flow to the column, and the condenser is referred to as a partial condenser. When the liquid is totally condensed, the liquid returned to the column will have the same composition as the top product. In a partial condenser the reflux will be in equilibrium with the vapor leaving the condenser. Virtually pure top and bottom products can be obtained in a single column from a binary feed, but where the feed contains more than two components; only a single “pure” product can be produced, either from the top or bottom of the column. Several columns will be needed to separate a multicomponent feed into its constituent parts.

The problem of determining the stage and reflux requirements for multicomponent

distillations is much more complex than for binary mixtures. With a multicomponent mixture, fixing one component composition does not uniquely determine the other component compositions and the stage temperature.

Also when the feed contains more than two components it is not possible to specify the complete composition of the top and bottom products independently. The separation between the top and bottom products is specified by setting limits on two “key” components, between which it is desired to make the separation.

SHORT-CUT METHODS FOR STAGE AND REFLUX REQUIREMENTS Most of the short-cut methods were developed for the design of separation columns

for hydrocarbon systems in the petroleum and petrochemical systems industries, and caution must be exercised when applying them to other systems. They usually depend on the assumption of constant relative volatility, and should not be used for severely non-ideal systems.

In this project, during the shortcut calculations, Fenske, Underwood, Gilliand and Kirkbridge Equations were used. Trial and error procedures were all made in excel.

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2.0 RESULTS

2.1 Ideal System

Table 1

No

. Properties of Components

Name Mw,i ρ [kg/kmol]

i [kg/m3

Antoine Constants ]

Zi λ 1 [%]

i [kJ/mol] A B C

1 Methanol 32.04 791.8 7.87863 1473.11 230 15 35.14

2 Ethanol 46.07 789 8.1122 1592.864 226.184 25 38.58

3 Neopentanol [Light Key] 88.15 812 7.27679 1279.01 177.849 25 41.35

4 n-Butanol [Heavy Key] 74.122 809.8 7.36366 1305.198 173.427 15 43.24

5 1-Pentanol 88.15 814.4 7.18246 1287.625 161.33 20 44.83

Table 2

F [kmol/h]

. Calculated Values for the Feed Stream in Ideal System 100 Tdew [o 113.66 C]

y 0.15 1 n 15 1 K 5.14 1

y 0.25 2 n 25 2 K 3.50 2

y 0.25 3 n 25 3 K 1.02 3

y 0.15 4 n 15 4 K4 0.86 [ref.]

y 0.2 5 n 20 5 K 0.42 5 Table 3

D [kmol/h] . Calculated Values for the Top Product in Ideal System

63.6 Tdew [o 96.84 C]

P.R 0.98 1 n 14.7 1 y 0.231 1 K 3.10 1

P.R 0.96 2 n 24 2 y 0.377 2 K 2.00 2

P.R 0.95 3 n 23.75 3 y 0.373 3 K 0.55 3

P.R 0.05 4 n 0.75 4 y 0.012 4 K4 0.45 [ref.]

P.R 0.02 5 n 0.4 5 y 0.006 5 K 0.21 5

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Table 4

W [kmol/h]

. Calculated Values for the Bottom Product in Ideal System 36.4 Tbubble [o 122.39 C] yi=Kixi

P.R 0.02 1 n 0.3 1 x 0.008 1 K 6.57 1 y 0.054 1

P.R 0.04 2 n 1 2 x 0.027 2 K 4.59 2 y 0.126 2

P.R 0.05 3 n 1.25 3 x 0.034 3 K 1.37 3 y 0.047 3

P.R 0.95 4 n 14.25 4 x 0.391 4 K4 1.18 [ref.] y 0.461 4

P.R 0.98 5 n 19.6 5 x 0.538 5 K 0.58 5 y 0.312 5

Table 5

P

. Calculated Values of Vapor Pressures of Components in Ideal System sat

i Feed [mmHg] Top Bottom

PsatMethanol 3909.69 [mmHg] 2352.49 4991.92

PsatEthanol 2661.98 [mmHg] 1517.50 3487.52

PsatNeopentanol 774.99 [mmHg] 417.46 1039.42

Psatn-Butanol 656.70 [mmHg] 342.30 894.23

Psat1-Pentanol 316.28 [mmHg] 156.67 440.62

Table 6

No

. Calculated Values of Relative Volatilities of Components in Ideal System

Name Relative Volatility ,αri

Feed Stream Top Product Bottom Product Average

1 Methanol 5.95 6.87 5.58 6.11

2 Ethanol 4.05 4.43 3.90 4.12

3 Neopentanol [Light Key] 1.18 1.22 1.16 1.19

4 n-Butanol [Heavy Key] 1.00 1.00 1.00 1.00

5 1-Pentanol 0.48 0.46 0.49 0.48

Table 7

N

. Calculation of Minimum Number of Plates, θ, Minimum Reflux Ratio and Feed Location in Ideal System

34.33 min θ 1.075 NR/N 1.25 S

q 0 R 3.577 D,min λave, top 38.914 [kJ/mol]

λave,bottom 43.836 [kJ/mol]

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Table 8. Calculation of Actual Reflux Ratio, Actual Number of Plates, Feed Location, Height of Column, Condenser Load (Qc) and Reboiler Load (Qr

R

) in Ideal System

D/R 1.5 D,min 1.8 2.4

R 5.366 D,act 6.439 8.585

X 0.281 0.385 0.522

Y 0.376 0.313 0.238

N 56 act 51 46

N 25 S 23 20

N 31 R 28 26

L [kmol/h] 341.25 409.50 546.00

G [kmol/h] 404.85 473.10 609.60

Qc 4376.1 [kW] 5113.9 6589.3

L [kmol/h] 341.25 409.50 546.00

G [kmol/h] 304.85 373.10 509.60

Qr 3712.1 [kW] 4543.1 6205.2 Hc 28.5 [m] 26.0 23.5

Table 9

MW

. Required Calculations for the Fluid Velocity and Diameter of Column in Ideal System

avg 73.34 [kg/kmol]

Wdot 0.742 [kg/s]

ρvap [kg/m3 2.261 ]

ρliq [kg/m3 811.63 ]

It [m] 0.5

uv 0.856 [m/s]

Dc 0.698 [m]

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2.2 Real System (Non-Ideal)

Table 10

No

. Properties of Components

Name Tc P[K] c ω [bar] ψ ε

1 Methanol 512.58 80.96 0.566 0.42748 0

2 Ethanol 516.25 63.84 0.637 Z σ c

3 Neopentanol [Light Key] 550.00 38.80 0.604 0.333333 1

4 n-Butanol [Heavy Key] 562.93 44.13 0.595 Ω R

[cm3bar/molK]

5 1-Pentanol 586.15 38.80 0.594 0.08664 83.14

Table 11. Calculated Values of yi, ni and Tr, i

F [kmol/h]

for the Feed Stream in Non-Ideal System 100 Tdew [o 106.6 C]

y 0.15 1 n 15 1 T 0.741 r,1 y 0.25 2 n 25 2 T 0.736 r,2 y 0.25 3 n 25 3 T 0.690 r,3 y 0.15 4 n 15 4 T 0.675 r,4 y 0.2 5 n 20 5 T 0.648 r,5

Table 12. Calculated Values of αSRK,i , ai and bi

α

for the Feed Stream in Non-Ideal System

1.400 SRK,1 a 1.34*101 b7 45.61 1

α 1.442 SRK,2 a 1.78*102 b7 58.25 2

α 1.515 SRK,3 a 3.49*103 b7 102.11 3

α 1.542 SRK,4 a 3.27*104 b7 91.89 4

α 1.598 SRK,5 a 4.18*105 b7 108.82 5

Table 13. Calculated Values of βi , qi and Zvi

β


0.00146 1 q 9.321 1 Zv 0.9870 1

β 0.00187 2 q 9.672 2 Zv 0.9826 2

β 0.00328 3 q 10.829 3 Zv 0.9649 3

β 0.00295 4 q 11.281 4 Zv 0.9670 4

β 0.00349 5 q 12.166 5 Zv 0.9572 5

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Table 14. Calculated Values of I vi , Φv

i and Zli

I

for the Feed Stream in Non-Ideal System v 0.00148 1 Φv 0.988 1 Zl 0.00157 1

I v 0.00190 2 Φv 0.984 2 Zl 0.00215 2

I v 0.00339 3 Φv 0.968 3 Zl 0.00395 3

I v 0.00304 4 Φv 0.970 4 Zl 0.00345 4

I v 0.00364 5 Φv 0.961 5 Zl 0.00370 5

Table 15. Calculated Values of I li , Φli and Ki

I

for the Feed Stream in Non-Ideal System l 0.660 1 Φl 7.605 1 K 7.70 1

Il 0.625 2 Φl 3.078 2 K 3.13 2

Il 0.604 3 Φl 0.791 3 K 0.82 3

Il 0.618 4 Φl 0.693 4 K 0.71 4

Il 0.665 5 Φl 0.545 5 K 0.57 5 Table 16. Calculated Values of αr,i , xi and f vi

α


10.78 r,1 x 0.019 1 f v 0.1501 1

α 4.38 r,2 x 0.080 2 f v 0.2491 2

α 1.14 r,3 x 0.306 3 f v 0.2451 3

α 1.00 r,4 x 0.210 4 f v 0.1474 4

α 0.79 r,5 x 0.352 5 f v 0.1947 5 Table 17. Calculated Values of f li , Psat

i , γi and

f

for the Feed Stream in Non-Ideal System l 0.1501 1 Psat

1 4.237 [bar] γ 1.818 1

f l 0.2491 2 Psat2 2.822 [bar] γ 1.105 2

f l 0.2451 3 Psat3 0.804 [bar] γ 0.997 3

f l 0.1474 4 Psat4 0.672 [bar] γ 1.044 4

f l 0.1947 5 Psat5 0.317 [bar] γ 1.741 5

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Table 18. Calculated Values of yi, ni and Tr, i

D [kmol/h]

for the Top Product in Non-Ideal System

63.6 Tdew [o 96.98 C]

P.R 0.98 1 n 14.7 1 y 0.231 1 T 0.722 r,1

P.R 0.96 2 n 24 2 y 0.377 2 T 0.717 r,2

P.R 0.95 3 n 23.75 3 y 0.373 3 T 0.673 r,3

P.R 0.05 4 n 0.75 4 y 0.012 4 T 0.658 r,4

P.R 0.02 5 n 0.4 5 y 0.006 5 T 0.631 r,5


α

for the Top Product in Non-Ideal System

1.434 SRK,1 a 1.38*101 b7 45.61 1

α 1.479 SRK,2 a 1.82*102 b7 58.25 2

α 1.551 SRK,3 a 3.57*103 b7 102.11 3

α 1.578 SRK,4 a 3.35*104 b7 91.89 4

α 1.633 SRK,5 a 4.27*105 b7 108.82 5


β

for the Top Product in Non-Ideal System 0.00150 1 q 9.798 1 Zv 0.9880 1

β 0.00192 2 q 10.181 2 Zv 0.9828 2

β 0.00336 3 q 11.373 3 Zv 0.9659 3

β 0.00302 4 q 11.840 4 Zv 0.9673 4

β 0.00358 5 q 12.758 5 Zv 0.9575 5

Table 21. Calculated Values of I vi , Φvi and Zl

i

I

for the Top Product in Non-Ideal System v 0.00152 1 Φv 0.987 1 Zl 0.00187 1

I v 0.00195 2 Φv 0.982 2 Zl 0.00255 2

I v 0.00347 3 Φv 0.965 3 Zl 0.00426 3

I v 0.00312 4 Φv 0.967 4 Zl 0.00385 4

I v 0.00373 5 Φv 0.958 5 Zl 0.00430 5

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Table 22. Calculated Values of I li , Φl

i and Ki

I

for the Top Product in Non-Ideal System l 0.590 1 Φl 3.108 1 K 3.15 1

I l 0.560 2 Φl 1.935 2 K 1.97 2

I l 0.582 3 Φl 0.551 3 K 0.57 3

I l 0.580 4 Φl 0.467 4 K 0.48 4

I l 0.606 5 Φl 0.226 5 K 0.24 5 Table 23. Calculated Values of αr,i , xi and f vi

α

for the Top Product in Non-Ideal System 6.52 r,1 x 0.073 1 f v 0.2310 1

α 4.08 r,2 x 0.192 2 f v 0.3755 2

α 1.18 r,3 x 0.655 3 f v 0.3651 3

α 1.00 r,4 x 0.024 4 f v 0.0116 4

α 0.49 r,5 x 0.027 5 f v 0.0061 5 Table 24. Calculated Values of f li , Psat

i , γi and

f

for the Top Product in Non-Ideal System l 0.2310 1 Psat

1 3.149 [bar] γ 1.000 1

f l 0.3755 2 Psat2 2.032 [bar] γ 0.964 2

f l 0.3651 3 Psat3 0.559 [bar] γ 0.997 3

f l 0.0116 4 Psat4 0.459 [bar] γ 1.031 4

f l 0.0061 5 Psat5 0.210 [bar] γ 1.089 5

Table 25. Calculated Values of xi, ni and Tr, i

W [kmol/h]

for the Bottom Product in Non-Ideal System 36.4 Tbubble [o 128.5 C]

P.R 0.02 1 n 0.3 1 x 0.008 1 T 0.784 r,1

P.R 0.04 2 n 1 2 x 0.027 2 T 0.778 r,2

P.R 0.05 3 n 1.25 3 x 0.034 3 T 0.730 r,3

P.R 0.95 4 n 14.25 4 x 0.391 4 T 0.713 r,4

P.R 0.98 5 n 19.6 5 x 0.538 5 T 0.685 r,5

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α

for the Bottom Product in Non-Ideal System

1.325 SRK,1 a 1.27*101 b7 45.61 1

α 1.361 SRK,2 a 1.68*102 b7 58.25 2

α 1.437 SRK,3 a 3.31*103 b7 102.11 3

α 1.465 SRK,4 a 3.11*104 b7 91.89 4

α 1.520 SRK,5 a 3.98*105 b7 108.82 5


β

for the Bottom Product in Non-Ideal System 0.00138 1 q 8.341 1 Zv 0.9892 1

β 0.00177 2 q 8.629 2 Zv 0.9853 2

β 0.00310 3 q 9.709 3 Zv 0.9704 3

β 0.00279 4 q 10.130 4 Zv 0.9721 4

β 0.00330 5 q 10.946 5 Zv 0.9638 5

Table 28. Calculated Values of I vi , Φvi and Zl

i

I

for the Bottom Product in Non-Ideal System v 0.00140 1 Φv 0.990 1 Zl 0.00169 1

I v 0.00179 2 Φv 0.987 2 Zl 0.00245 2

I v 0.00319 3 Φv 0.973 3 Zl 0.00425 3

I v 0.00286 4 Φv 0.975 4 Zl 0.00365 4

I v 0.00342 5 Φv 0.967 5 Zl 0.00420 5

Table 29. Calculated Values of I li , Φl

i and Ki

I

for the Bottom Product in Non-Ideal System l 0.599 1 Φl 8.223 1 K 8.31 1

I l 0.543 2 Φl 4.982 2 K 5.05 2

I l 0.548 3 Φl 1.576 3 K 1.62 3

I l 0.567 4 Φl 1.365 4 K 1.40 4

I l 0.580 5 Φl 0.719 5 K 0.74 5

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Table 30. Calculated Values of αr,i , yi and f vi

α

for the Bottom Product in Non-Ideal System

5.93 r,1 y 0.068 1 f v 0.0687 1

α 3.60 r,2 y 0.139 2 f v 0.1386 2

α 1.16 r,3 y 0.056 3 f v 0.0548 3

α 1.00 r,4 y 0.548 4 f v 0.5415 4

α 0.53 r,5 y 0.400 5 f v 0.3921 5 Table 31. Calculated Values of f li , Psat

i , γi and

f

for the Bottom Product in Non-Ideal System l 0.0687 1 Psat

1 7.840 [bar] γ 0.015 1

f l 0.1386 2 Psat2 5.572 [bar] γ 0.036 2

f l 0.0548 3 Psat3 1.685 [bar] γ 0.361 3

f l 0.5415 4 Psat4 1.464 [bar] γ 0.481 4

f l 0.3921 5 Psat5 0.732 [bar] γ 1.801 5

Table 32

No

. Calculated Values of Relative Volatilities of Components in Non-Ideal System

Name Relative Volatility ,αri

Feed Stream Top Product Bottom Product Average

1 Methanol 10.78 6.52 5.93 7.47

2 Ethanol 4.38 4.08 3.60 4.01

3 Neopentanol [Light Key] 1.14 1.18 1.16 1.16

4 n-Butanol [Heavy Key] 1.00 1.00 1.00 1.00

5 1-Pentanol 0.79 0.49 0.53 0.59

Table 33

N

. Calculation of Minimum Number of Plates, θ, Minimum Reflux Ratio and Feed Location in Non-Ideal System

39.56 min θ 1.051 NR/N 1.25 S

q 0 R 3.516 D,min λave, top 38.914 [kJ/mol]

λave, bottom 43.836 [kJ/mol]

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Table 34. Calculation of Actual Reflux Ratio, Actual Number of Plates, Feed Location, Height of

Column, Condenser Load (Qc) and Reboiler Load (Qr

R

) in Ideal System

D/R 1.5 D,min 1.8 2.4

R 5.274 D,act 6.328 8.438

X 0.280 0.384 0.522

Y 0.376 0.313 0.238

N 64 act 59 53

N 28 S 26 24

N 36 R 33 29

L [kmol/h] 335.40 402.48 536.64

G [kmol/h] 399.00 466.08 600.24

Qc 4312.9 [kW] 5038.0 6488.2

L [kmol/h] 335.40 402.48 536.64

G [kmol/h] 299.00 366.08 500.24

Qr 3640.9 [kW] 4457.7 6091.3 Hc 32.5 [m] 30.0 27.0

Table 35

MW

. Required Calculations for the Fluid Velocity and Diameter of Column in Non-Ideal System

avg 89.42 [kg/kmol]

Wdot 0.904 [kg/s]

ρvap [kg/m3 2.715 ]

ρliq [kg/m3 811.63 ]

It [m] 0.5

uv 0.781 [m/s]

Dc 0.737 [m]

- 13 -

Table 36

. Calculated Values by Using ChemCAD 6.0.2 for Ideal and Non-Ideal System

Ideal System with Raoult’s Law Non-Ideal System with SRK Method

RD/R 1.5 D,min 1.8 2.4 1.5 1.8 2.4

R 5.2821 D,act 6.3386 8.4514 62.0107 6.7886 9.0515

N 29.2254 S 26.1033 23.2336 31.2342 27.9023 24.8464

N 57.9572 act 51.6570 45.8660 5.6572 55.2872 49.1205

Qc -1.4678*10 [kJ/h] -1.9449*107 -2.5049*107 -1.7721*107 -2.0733*107 -2.6756*107 7

Qr 1.0981*10 [kJ/h] 1.5182*107 2.0782*107 1.3445*107 1.6457*107 2.2480*107 7 R 3.5214 D,min 3.5214 3.5214 3.7715 3.7715 3.7715 N 35.0220 min 35.0220 35.0220 37.6120 37.6120 37.6120

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3.0 DISCUSSION AND CONCLUSION

The object of this report is to design a multi-component distillation column for ideal and non-ideal situations. Consider the case of the distillation of a multi-component mixture in a multi-stage distillation column. As before, the number of degrees of freedom is determined by the description rule (i.e., D.O.F. = number of variables set during construction or controlled during operation by independent means). Generally, all the variables associated with the feed, such as its composition, flow rate and enthalpy are set, as is the column pressure, which leaves four degrees of freedom and two basic types of problems (design and simulation), as was the case for a binary distillation.

For a design problem, the goal is to determine the number of plates needed and the location of the feed plate, and the following is generally specified

• Separation variable #1, the recovery of the light key component in the top (distillate) product.

• Separation variable #2, the recovery of the heavy key component in the bottom product.

• Condenser and reboiler loads • Diameter and height of the column • The fact that the optimal feed plate is used that minimizes the total number of plates. • The reflux ratio.

Generally, in a multi-component distillation column, only two components will exist in significant quantities in both the bottom and top products. These are the two key components. The heavy non-key components will essentially all end up in the bottom product while the light non-key components will essentially all end up in the top product. This is why the separation variables described above are given in terms of the key components.

In our process, the components were methanol, ethanol, neopentanol, n-butanol and 1-pentanol. Our feed rate was 100 kmol/h; the light-key component was neopentanol and the heavy-key component was n-butanol. Our mole fractions in the feed were 15%, 25%, 25%,15% and 20% respectively (See Table 2). The separation targets for top and bottom products were 95%. In order to find temperature and equilibrium constants for the feed, a temperature was assumed. The Psat values were calculated at this temperature, by using Antoine equation (See Table 5). The equilibrium constants were calculated with this assumed temperature (See Table 2). By using Goal-seek, we equalized . The dew-point

temperature was calculated as 113.66°C. According to the calculated temperature, the equilibrium constants were found as 5.14, 3.5, 1.02, 0.86, and 0.42. To calculate relative volatilities of the components, the ratio of K value of each component to the K value of the heavy-key product was taken. After this, the relative volatilities were found as, 5.95, 4.05, 1.18, 1 and 0.48 (See Table 6).

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In the ideal calculation, since we only had specific target separation for the light-key and heavy- key products were known (which was 95% for light-key at top and 95% for heavy at the bottom), the other separations were assumed 98% for methanol, 96% for ethanol, 95% for neopentanol, 5% for n-butanol and 2% 1-pentanol (See Table 3). The flow rate of top product was found as 63.6 kmol/h. As a result, the mole fractions for the top product were calculated as 0.231, 0.377, 0.373, 0.012, and 0.006 (See Table 3). In order to find temperature and equilibrium constants, a temperature was assumed. The Psat

In the bottom product, the separations were assumed 2% for methanol, 4% for ethanol, 5% for neopentanol, 95% for n-butanol and 98% 1-pentanol (See Table 4). The flow rate of bottom product was found as 36.4 kmol/h. As a result, the mole fractions for the top product were calculated as 0.008, 0.027, 0.034, 0.391 and 0.538 (See Table 4). In order to find temperature and equilibrium constants, a temperature was assumed. The P

values were calculated at this temperature, by using Antoine equation (See Table 5).The equilibrium constants were calculated with this assumed temperature. By using Goal-seek, we equalized . The

dew-point temperature was calculated as 96.84°C.According to the calculated temperature, the equilibrium constants were found as 3.10, 2, 0.55, 0.45, and 0.21 (See Table 3). To calculate relative volatilities of the components, the ratio of K value of each component to the K value of the heavy-key product was taken. After this, the relative volatilities were found as, 6.87, 4.43, 1.22, 1 and 0.46 (See Table 6).

sat

The average relative volatilities of the components were determined by taking the geometric mean of the components’ volatilities at the feed, top product and bottom product. The values were 6.11, 4.12, 1.19, 1 and 0.48, respectively (See Table 6).

values were calculated at this temperature, by using Antoine equation (See Table 5). The equilibrium constants were calculated with this assumed temperature. By using Goal-seek, we equalized . The dew-point temperature was calculated as 122.39°C. According to the calculated temperature, the equilibrium constants were found as 6.57, 4.59, 1.37, 1.18 and 0.58 (See Table 4). To calculate relative volatilities of the components, the ratio of K value of each component to the K value of the heavy-key product was taken. After this, the relative volatilities were found as, 5.58, 3.90, 1.16, 1 and 0.49 (See Table 6).

Fenske equation was used to calculate the minimum number of trays. As a result, the minimum plate number was found as 34.33 (See Table 7).

To find the minimum reflux ratio, the θ parameter was calculated at saturated vapor condition (q=0), and it must be between the relative volatilities of the light-key and heavy-key component, and was calculated using Goal-seek. As a result, the θ value was found as 1.075. Using Underwood equation, the minimum reflux ratio was determined as 3.57 (See Table 7).

The ratio of was assumed as 1.5, 1.8 and 2.4 respectively and the actual reflux values were calculated and tabulated (See Table 8).

- 16 -

The Gilliland correlation was used to calculate actual plate number. For this, X and Y parameters were calculated and Nactual was found as 56, 51 and 46, using the Y function and Nmin

To determine the feed location, we used Kirkbridge equation. For N

value (See Table 8).

actual being 56, the entry location was found as the 26th tray. The NR and NS

To calculate reboiler and condenser duty, the average latent heat of vaporization was calculated. Our reboiler and condenser were selected as total reboiler and condenser. As a result, the reboiler duty was found as 3712.1kW for R

values were tabulated (See Table 8).

min

The height and diameter of the column were calculated lastly. The diameter was found as 0.698m and the height was 28.5 m. Other values were tabulated (See Table 8 and 9).

/R at 1.5. The condenser duty was found as 4376.1kW for the same ratio. Other values were tabulated (See Table 8).

In the case of the non-ideal system, the critical temperature, critical pressure, density, molecular weight and acentric factor were looked up from Ref.4 (See Table 10). The constants for the SRK Model were taken, a temperature was assumed and the reduced temperatures were calculated accordingly. The parameters αSRK, ai, bi, βi and qi were determined. Zv

i was calculated using Goal-seek and Ivi and Φv

i were determined by using the related equations in Ref.2.Same procedure was followed for ZL

i, ILi and ΦL

i. The equilibrium

constants were determined using . The liquid mole fractions were calculated to be used in

Modified Raoult’s Law. The Pisat values were determined by Antoine equation. The vapor-

liquid equilibrium was proven by the equality of fugacity coefficients of vapor and liquid phases. The activity coefficient was calculated from Modified Raoult’s Law. The assumed dew-point temperature was checked using the γi and Psat

The Fenske, Underwood, Gilliland and Kirkbridge equations were used like in the ideal system calculations. From these equations, N

values, and from Goal-seek, the actual dew-point temperatures was calculated as 106.6°C for feed, 96.98°C for top product. Same procedure was applied to the bottom product to find bubble-point temperature, which was found as 128.5°C. The average relative volatilities were calculated and found as 7.47, 4.01, 1.16, 1 and 0.59 respectively (See Table 32).

min was found as 39.56, θ was found as 1.051, Rmin was 3.516. For Rmin/R as 1.5, 1.8 and 2.4, our reflux ratios were found as 5.274, 6.328 and 8.438 respectively. For Rmin/R as 1.5, 1.8 and 2.4, Nact

The condenser and reboiler duties were calculated like in the ideal system. Q

were found as 64, 59, 53. The feed locations were found and tabulated (See Table 34).

c and Qr

Finally, the diameter and height were calculated and were found as 0.737m and 32.5 m respectively. Other values were tabulated (See Table 34 and 35).

were calculated and tabulated (See Table 34).

- 17 -

According to these results, it can be seen that the ideal system and non-ideal system are slightly different from each other. For both systems, actual plate numbers decrease with increasing Rmin/R. Also, height of the column decreases with increasing Rmin/R. Both Qc and Qr increase with increasing Rmin

In real systems, the relative volatilities of components are greater than the relative volatilities of ideal system. Also, the number of plates used are greater than that of ideal systems. The condenser and reboiler duties of real systems are less than the ideal system’s duties. The diameter and height of the column in real systems are greater than the diameter and height of the column in ideal systems. Finally, the most suitable reflux ratio for the real system can be selected within the calculation of total and operation costs. However, the optimum reflux ratio can be chosen without any calculations of costs and it can be seen in Table 34 as 1.8 for this project.

/R, as expected.

In conclusion, the calculated values by using ChemCAD for the ideal and non ideal systems were tabulated in table 36.

- 18 -

4.0 NOMENCLATURE

Symbol Name Unit

M Molecular Weight of i Component w,i [kg/kmol] ρ Density of i Component i [kg/m3

ρ]

Vapor Density of i Component vap [kg/m3

ρ]

Liquid Density of i Component liquid [kg/m3

F ]

Mol Number of Feed Stream [kmol/h] D Mol Number of Top Product [kmol/h] W Mol Number of Bottom Product [kmol/h] n Mole Number of i Component i [kmol/h] x Mole Fraction of i Component i P.R. Percentage Recovery of i Component i K Distribution Coefficient of i Component i P Saturated Vapor Pressure sat [bar] P Total Pressure t [bar] α Relative Volatilities of i Component i N Minimum Number of Plate min N Actual Number of Plate act N Number of Plate of Stripping Section S N Number of Plate of Enriching Section R R Minimum Reflux Ratio D,min R Actual Reflux Ratio D,act λ Latent Heat of Vaporization i

MW Molecular Weight of Mixing u Fluid Velocity v [m/s] D Diameter of Distillation Column c [m] T Reduce Temperature r f Fugacity Φ Fugacity Coefficient T Temperature [o

TC]

Critical Temperature c [K] P Critical Pressure c [bar] Q Reboiler Load r [kJ/s] Q Condenser Load c [kJ/s]

- 19 -

5.0 REFERENCES

1. Coulson, J.M., Richardson, J.F., Chemical Engineering Series - Chemical Engineering Design, Vol. 6, 4th Ed., Great Britain Pergamon Press, 1977.

2. J.M. Smith, H.C. Van Ness, M.M. Abbott, Introduction to Chemical Engineering Thermodynamics, 2005, 7th

Ed., Mc Graw Hill Company, Singapore.

3. Felder, R.M., Rousseau, R.W., Elementary Principles of Chemical Process, 2nd

Ed., John Willey and Sons Inc, USA, 1986.

4. Yaws C.L., Yaws' Handbook of Thermodynamic and Physical Properties of Chemical Compounds, Lamar University, Beaumont, Texas,

Norwich, New York, 2004

- 20 -

6.0 APPENDIX

6.1 Ideal System

(See Table 4).

The mixture of methanol, ethanol, neopentanol, n-butanol and 1-pentanol was fed to the column as 100 kmol/h. The given data for the feed, top and bottom product was tabulated in Table 2, 3, 4.

Calculation of Mole Numbers of Components in Feed Stream

1

2

3

4

5

100

0.15

0.25

0.25

0.15

0.20

F kmol hxxxxx

=

=

=

=

=

=

Assumption of Percentage Recoveries for Top Product

1

2

3

4

5

. . 0.98

. . 0.96

. . 0.95

. . 0.05

. . 0.02

P RP RP RP RP R

=====

1

2

3

4

5

.15 0.98 14.7 /25 0.96 24 /25 0.95 23.75 /15 0.05 0.75 /20 0.02 0.4 /

i Fi in n P Rn kmol hn kmol hn kmol hn kmol hn kmol h

= ×= × == × == × == × == × =

1

2

3

4

5

0.15 100 15

0.25 100 25

0.25 100 25

0.15 100 15

0.20 100 20

n kmol hn kmol hn kmol hn kmol hn kmol h

= × =

= × =

= × =

= × =

= × =

F=100 kmol/h n1=15 kmol/h n2=25 kmol/h n3=25 kmol/h n4=15 kmol/h n5=20 kmol/h

D=63.6 kmol/h n1=14.7 kmol/h n2=24 kmol/h n3=23.75 kmol/h n4=0.75 kmol/h n5=0.4 kmol/h

W=36.4 kmol/h n1=0.3 kmol/h n2=1 kmol/h n3=1.25 kmol/h n4=14.25 kmol/h n5=19.6 kmol/h

G

L

G

L D

W

- 21 -

/14.7 24 23.75 0.75 0.463.6 /

di ix n DDD kmol h

== + + + +=

1

2

3

4

5

14.7 / 63.6 0.23124 / 63.6 0.37723.75 / 63.6 0.3730.75 / 63.6 0.0120.4 / 63.6 0.006

xxxxx

= == == == == =

Assumption of Percentage Recoveries for the Bottom Product

1

2

3

4

5

. . 1 0.98 0.02

. . 1 0.96 0.04

. . 1 0.95 0.05

. . 1 0.05 0.95

. . 1 0.02 0.98

P RP RP RP RP R

= − == − == − == − == − =

1

2

3

4

5

.15 0.02 0.3 /25 0.04 1 /25 0.05 1.25 /15 0.95 14.25 /20 0.98 19.6 /

i Fi in n P Rn kmol hn kmol hn kmol hn kmol hn kmol h

= ×= × == × == × == × == × =

/0.3 1 1.25 14.25 19.636.4 /

di ix n WWW kmol h

== + + + +=

1

2

3

4

5

0.3 / 36.4 0.0081/ 36.4 0.0271.25 / 36.4 0.03414.25 / 36.4 0.39119.6 / 36.4 0.538

xxxxx

= == == == == =

Calculation of Temperature, K-values & Relative Volatilities for the Feed Stream

Dew point temperature for feed Dew point temperature for the feed was assumed as 100 o

1 11.00

c ci

ii i i

yxK= =

= =∑ ∑

C. All calculations was done

by using this temperature in excel. However value could not be

obtained. So the dew point temperature was calculated as 113.66 o

/

1.00

log ; ( , 2)

113.66 ( )760

1473.11log 7.87863 ; 3909.69113.66 230

i i i

ii

i i i

sat o

odew

t

sat satmethanol methanol

K y xyxK

BP A T in C P in mmHg A B and C constants were showninTableT C

T C feed streamP mmHg

P P mmHg

For other compo

=

= =

= −+

==

= − =+

∑ ∑

5.nents see in Table

C by using “Goal Seek” method in Excel and shown below.

- 22 -

11-

3909.69, 5.14760

2661.98 774.993.5 , 1.02760 760

656.70 0.86 ,760

sat sati methanol

i methanolt t

satsatneopentanolethanol

ethanol neopentanolt t

ssatpentanoln-butanol

n-butanol pentanolt

P PK KP P

PPK KP P

PPK KP

−

= = = =

= = = = = =

= = = =316.28 0.42

760

at

tP= =

,

,

5.14, 5.950.86

3.5 1.024.05 , 1.180.86 0.86

i methanoli methanol,n-butanol

HK n-butanol

neopentanolethanolethanol n-butanol neopentanol,n-butanol

n-butanol n-butanol

n-butan-butanol n-butanol

K KK K

KKK K

K

α α

α α

α

= = = =

= = = = = =

=0.86 0.421 , 0.480.86 0.86

1- pentanolnol1- pentanol,n-butanol

n-butanol n-butanol

KK K

α= = = = =

With excel calculation (goal seek) we found Tdew=113.66 o

C

Calculation of Temperature, K-values & Relative Volatilities for the Top Product

Dew point temperature for the top was assumed as 90

Dew point temperature for top

o

1 11.00

c ci

ii i i

yxK= =

= =∑ ∑

C. All calculations was done by

using this temperature in excel. However value could not be obtained.

So the dew point temperature was calculated as 96.84 o

/

1.00

log ; ( , 2)

96.84 ( )760

1473.11log 7.87863 ; 2352.4996.84 230

i i i

ii

i i i

sat o

odew

t


K y xyxK


T C top streamP mmHg

P P mmHg

For other componen

=

= =

= −+

==

= − =+

∑ ∑

5.ts see in Table


- 23 -

11-

2352.49, 3.1760

1517.50 417.462 , 0.55760 760

342.30 0.45 ,760

sat sati methanol

i methanolt t



satsatpentanoln-butanol

n-butanol pentanolt

P PK KP P

PPK KP P

PPK KP P

−

= = = =

= = = = = =

= = = =156.67 0.21

760t

= =

,

,

3.10, 6.870.45

2 0.554.43 , 1.220.45 0.45


HK n-butanol


n-butanol n-butanol

n-butanon-butanol n-butanol

K KK K

KKK K

K

α α

α α

α

= = = =

= = = = = =

=0.45 0.211 , 0.460.45 0.45

1- pentanoll1- pentanol,n-butanol

n-butanol n-butanol

KK K

α= = = = =

With excel calculation (goal seek) we found Tdew=96.84 0

C

Calculation of Temperature, K-values & Relative Volatilities for the Bottom Product

Bubble point temperature for the top was assumed as 120

Bubble point temperature for bottom

o

1 11.00

c c

i i ii i

y x K= =

= =∑ ∑

C. All calculations was

done by using this temperature in excel. However value could not be

obtained. So the bubble point temperature was calculated as 122.39 o

/

1.00

log ; ( , 2)

122.39 ( )760

1473.11log 7.87863 ; 4991.92122.39 230

i i i

i i ii i

sat o

obubble

t


K y x

y x K


T C bottom streamP mmHg

P P mmHg

For other

=

= =

= −+

==

= − =+

∑ ∑

5.components see in Table


- 24 -

11-

4991.92, 6.57760

3487.52 1039.424.59 , 1.37760 760

894.23 1.18 ,760

sat sati methanol

i methanolt t



satpentanon-butanol

n-butanol pentanolt

P PK KP P

PPK KP P

PPK KP

−

= = = =

= = = = = =

= = = =440.62 0.58

760

satl

tP= =

,

,

6.57, 5.581.18

4.59 1.373.90 , 1.161.18 1.18


HK n-butanol


n-butanol n-butanol

n-butn-butanol n-butanol

K KK K

KKK K

K

α α

α α

α

= = = =

= = = = = =

=1.18 0.581 , 0.491.18 1.18

1- pentanolanol1- pentanol,n-butanol

n-butanol n-butanol

KK K

α= = = = =

With excel calculation (goal seek) we found Tbubble=122.39 0

C

Calculation of Average Relative Volatilities

33, , , ,

3 3

3 3

, 5.95 6.87 5.58 6.11

4.05 4.43 3.9 4.12 , 1.18 1.22 1.16 1.19

1 1 1 1 , 0.48 0.46 0.49 0.48

average i top i bottom i feed i methanol

ethanol neopentanol

n-butanol 1- pentanol

α α α α α

α α

α α

= × × = × × =

= × × = = × × =

= × × = = × × =

Calculation of Minimum Number of Plates by Using Fenske Equation

, ,

, ,

,

0.373 0.391log log0.012 0.034; 34.33

log log1.19

LK D HK W

HK D LK Wmin min

LK avg

x xx x

N Nα

× × = = =

Calculation of q-Parameter

We used saturated vapor for the feed stream; so q-parameter must be taken as zero (q=0).

- 25 -

Calculation of θ-Parameter

, ,

1 ,

1 ,c

i ave f iHK LK

i i ave

xq

αα θ α

α θ=

×= − < <

−∑

, , , , , , , , 1 , ,1

, , , , 1 ,

1 0

6.11 0.15 4.12 0.25 1.19 0.25 16.11 4.12 1.19

met ave f met eth ave f eth neo ave f neo n but ave f n but pent ave f pent

met ave eth ave neo ave n but ave pent ave

x x x x xq

α α α α αα θ α θ α θ α θ α θ

θ θ θ

− − − −

− −

× × × × ×+ + + + − + =

− − − − −

× × × ×+ + +

− − −0.15 0.48 0.20 1 0 0

1 0.48

1.075

θ θ

θ

×+ − + =

− −

=

Calculation of Minimum Reflux Ratio, RDmin

,min

1

min

min

min 1

min 2

1

6.11 0.231 4.12 0.377 1.19 0.373 1 0.012 0.48 0.006 1 06.11 1.075 4.12 1.075 1.19 1.075 1 1.075 0.48 1.0753.577

* 3.577*1.5 5.366

* 3.57

cir D i

Di ir

D

D

Dactual D

Dactual D

xR

R

R

R R

R R

αα θ

β

β

=

×= +

−

× × × × ×= + + + + − =

− − − − −=

= = =

= =

∑

min 3

7*1.8 6.439

* 3.577*2.4 8.585Dactual DR R β

=

= = =

by Using Underwood Equation

Calculation of Actual Plate Number by Using Gilliand Correlation

5.366 3.577 0.2815.366 1

DminR - RXR+1

−= = =

+

0.1 0.1

1.805 1.8051 exp 1.490 0.315 1 exp 1.490 0.315 0.281 0.376(0.281)

Y XX

= − + − = − + × − =

min min

1 10.376 34.33 56

1 0.376actual

N N Y NY NN Y

N N plates

− += ⇒ =

+ −+

= = =−

For other reflux ratios, the calculated values were tabulated in Table 8.

- 26 -

Calculation of NR and NS

2 2. ,

, ,

36.4 0.15 0.034log 0.206log 0.206log 0.0969163.6 0.25 0.012

1.25 ,

56 25 , 56 251.25 11

f HK b LKR

S f LK d HK

RR act S

S

actS R

R

S

x xN WN D x x

N N N NN

NN NNN

= = = =

= = −

= = = = −++

31=

for the Feed Location by Using Kirk Bridge Method

Calculation of Condenser and Reboiler Loads, Qc and Q

, ,

5.366 , 341.25 /63.6

D

D

LF W D L G W RD

LR L kmol h

= + = + =

= = =

r

( )

( )

, ,1 1

,

7

, 341.25 63.6 404.85 /1 1000* , 404.85 38.914 4376.1

3600 1

341.25, 0100

c c

ave top i i ave bottom i ii i

c ave top c

y and x for results see in Table

G L D G kmol hkmol kJ h molQ G Q kJ s kW

h mol s kmol

L L Lq qF

L L

λ λ λ λ

λ

= =

= =

= + = + =

= = × × × =

− −= = =

= =

∑ ∑

( ),

341.25 , 341.25 36.4 , 304.85 /1 1000* , 304.85 *43.836 3712.1

3600 1r ave bottom r

G L W G kmol hkmol kJ h molQ G Q kJ s kW

h mol s kmolλ

= − = − =

= = × × =

Calculation of Column Diameter and Height

( )

1* ,

0.008 6.57 0.054 9

(32.04*0.054) (46.07*0.126) (88.15*0.047) (74.122*0.461) (88.15*0.312) 73.34

* 7

/

3.34

i i

methanol

N

i W W i ii

W methanol methanol

MW MW y y x K

y x K for other components see Table

MW kgkgW MV W

km

kmol

=

= =

= = × =

= + +

=

+ +

=

=

∑

136.4 0.7423600

kmol h kg sol h s

P MW R Tρ

× × =

× = × ×

- 27 -

3

13

1 73.34 2.2610.082 (122.39 273.15)

791.8 0.008 789 0.027 812 0.034 809.8 0.391 814.4 0.538

811.63

vap

c

liq i ii

P MW kg mR T

x

kg m

ρ

ρ ρ=

× ×= = =

× × +

= = × + × + × + × + ×

=

∑

( )

( )

1/22

1/22

0.171* 0.27* 0.047 *

811.63 2.2610.171*0.5 0.27*0.5 0.047 *2.261

4 4 0.742 0.698 , ( 1) 0.5 (56 1) 28.32.

0

26

.8

1 0.85

56

6

l vv t t

v

v

c c tv v

u l l

u

WD m H l N mu

For other reflux ratios the

m

r

s

ρ ρρ

πρ π

=

−= − + −

− = − + −

×= = = = × + = × + =

× ×

9.esults were in Table

6.2 Real System (Non-Ideal)

For Feed Stream Dew point temperature for the feed was assumed as 100 o

*1

1.00c

it

i i i

yPPγ=

× =∑C. All calculations was done by

using this temperature in excel. However value could not be obtained. So

the dew point temperature was calculated as 106.6 o

[ ] [ ],,

,1 ,2 ,3

,4 ,5

, ,

379.75 379.75 379.750.741 , 0.736 , 0.690512.58 516.25 550.00379.75 379.750.675 , 0.648562.93 586.15

r i cc i

r r r

r r

TT T K T KT

T T T

T T

=

= = = = = =

= = = =

C (379.75 K) by using “Goal Seek” method in Excel and shown below.

( )( )

( )( )( )( )

22 1 2, ,

,

22 1 2,1

2 1 2,2

1 0.480 1.574 0.176 1

, 2 10

1 0.480 1.574 0.566 0.176 0.566 1 0.741 1.400

1 0.480 1.574 0.637 0.176 0.637 1 0.736

SRK i i i r i

c i i

SRK

SRK

T

T were taken in Reference and tabulated in Table

α ω ω

ω

α

α

= + + − −

= + + × − × − =

= + + × − × −

( )( )( )( )( )( )

2

22 1 2,3

22 1 2,4

22 1 2,5

1.442

1 0.480 1.574 0.604 0.176 0.604 1 0.690 1.515

1 0.480 1.574 0.595 0.176 0.595 1 0.675 1.542

1 0.480 1.574 0.594 0.176 0.594 1 0.648 1.598

SRK

SRK

SRK

α

α

α

=

= + + × − × − =

= + + × − × − =

= + + × − × − =

- 28 -

[ ] [ ]2

, 3, ,

,

27

1

27

2

3

, , , 83.14

2 10

1.400 83.14 512.580.42748 1.34 1080.96

1.442 83.14 516.250.42748 1.78 1063.84

1.515 83.140.42748

i c ii c i c i

c i

R Ta T K P bar R cm bar molK

P

was taken in Reference and tabulated in Table

a

a

a

αψ

ψ

= =

× ×= × = ×

× ×= × = ×

×= ×

27

27

4

27

5

550.00 3.49 1038.80

1.542 83.14 562.930.42748 3.27 1044.13

1.598 83.14 586.930.42748 4.18 1038.80

a

a

×= ×

× ×= × = ×

× ×= × = ×

[ ] [ ], 3, ,

,

1

2

3

4

, , , 83.14

2 1083.14 512.580.08664 45.61

80.9683.14 516.250.08664 58.25

63.8483.14 550.000.08664 102.11

38.80

0.08664

c ii c i c i

c i

RTb T K P bar R cm bar molK

P


b

b

b

b

= Ω =

Ω×

= × =

×= × =

×= × =

=

5

83.14 562.93 91.8944.13

83.14 586.150.08664 108.8238.80

b

×× =

×= × =

[ ] [ ] 3

1 2

3 4

5

, , , 83.14

45.61 1.013 58.25 1.0130.00146 , 0.0018783.14 379.75 83.14 379.75102.11 1.013 91.89 1.0130.00328 , 0.0029583.14 379.75 83.14 379.75108.82 1.01383.14 379.75

ii

b P T K P bar R cm bar molKRT

β

β β

β β

β

≡ =

× ×= = = =

× ×× ×

= = = =× ××

=×

0.00349=

- 29 -

[ ] 3

7 7

1 2

7 7

3 4

7

5

, , 83.14

1.34 10 1.78 109.321 , 9.67245.61 83.14 379.75 58.25 83.14 379.75

3.49 10 3.27 1010.829 , 11.281102.11 83.14 379.75 91.89 83.14 379.75

4.18 10108.82 83.14 3

ii

i

a T K R cm bar molKqb RT

q q

q q

q

=≡

× ×≡ = ≡ =

× × × ×× ×

≡ = ≡ =× × × ×

×≡

× ×12.166

79.75=

( )( )

( )( )

1

0.001460 1 0.00146 9.321 0.001460 0.00146 1 0.00146

0.987

,

vv i ii i i i v v

i i i i

vviiv v

i i

vi

vi

ZZ qZ Z

Z ZZ Z

Z value for methanol was calculated as by above equation from Goal Seek in ExcelAnd for the other components Z

ββ βεβ σβ

−= + −

+ +

−= + − × −

+ × + ×

14, 21, 28.values were tabulated in Table

1 2

3 4

5

1 ln

1 0.9870 1 0.00146 1 0.9826 1 0.00187ln 0.00148 , ln 0.001901 0 0.9870 0 1 0 0.9826 0

1 0.9649 1 0.00328 1 0.9670 1 0.00295ln 0.00339 , ln 0.003041 0 0.9649 0 1 0 0.9670 0

11

+=

− ++ × + ×

= = = =− + − +

+ × + ×= = = =

− + − +

=

vv i ii v

i i

v v

v v

v

ZIZ

I I

I I

I

σβσ ε εβ

0.9572 1 0.00349ln 0.003640 0.9572 0

+ ×=

− +

( ) ( )( )( )

1

2

3

ln 1 ln ; exp 1 ln

exp 0.9870 1 ln 0.9870 0.00146 9.321 0.00148 0.988

exp 0.9826 1 ln 0.9826 0.00186 9.672 0.00190 0.984

exp 0.9649 1 ln 0.9649 0.003

Φ = − − − − Φ = − − − − Φ = − − − − × = Φ = − − − − × = Φ = − − −

v v v v v v v vi i i i i i i i i i i i

v

v

v

Z Z q I Z Z q Iβ β

( )( )( )

4

5

28 10.829 0.00339 0.968

exp 0.9670 1 ln 0.9670 0.00295 11.281 0.00304 0.970

exp 0.9572 1 ln 0.9572 0.00349 12.166 0.00364 0.961

− × = Φ = − − − − × = Φ = − − − − × =

v

v

( )( )

( )( )

1

1 0.001460 0.00146 0 0.00146 1 0.001469.321 0.00146

0.00157

ll l l i ii i i i i i

i i

ll l lii i i

li

ZZ Z Zq

ZZ Z Z

Z value for methanol was calculated as by above equation from Goal Seek in ExcelAnd for the other

ββ εβ σββ

+ −= + + +

+ −

= + + × + × − ×

, 14, 21, 28.licomponents Z values were tabulated in Table

- 30 -

1 2

3 4

5

1 ln

1 0.00157 1 0.00146 1 0.00215 1 0.00187ln 0.660 , ln 0.6251 0 0.00157 0 1 0 0.00215 0

1 0.00395 1 0.00328 1 0.00345 1 0.00295ln 0.604 , ln 0.6181 0 0.00395 0 1 0 0.00345 0

11

ll i ii l

i i

l l

v v

v

ZIZ

I I

I I

I

σβσ ε εβ

+=

− ++ × + ×

= = = =− + − +

+ × + ×= = = =

− + − +

=0.00370 1 0.00349ln 0.665

0 0.00370 0+ ×

=− +

( ) ( )( )( )

1

2

3

ln 1 ln ; exp 1 ln

exp 0.00157 1 ln 0.00157 0.00146 9.321 0.660 7.605

exp 0.00215 1 ln 0.00215 0.00186 9.672 0.625 3.078

exp 0.00395 1 ln 0.00395 0.0

Φ = − − − − Φ = − − − − Φ = − − − − × = Φ = − − − − × = Φ = − − −

l l l l l l l li i i i i i i i i i i i

l

l

l

Z Z q I Z Z q Iβ β

( )( )( )

4

5

0328 10.829 0.604 0.791

exp 0.00345 1 ln 0.00345 0.00295 11.281 0.618 0.693

exp 0.00370 1 ln 0.00370 0.00349 12.166 0.665 0.545

− × = Φ = − − − − × = Φ = − − − − × =

l

l

1 2

3 4 5

7.605 3.078, 7.70 , 3.130.988 0.984

0.791 0.693 0.5450.82 , 0.71 , 0.570.968 0.970 0.961

li

i vi

K K K

K K K

Φ= = = = =Φ

= = = = = =

,

,

7.70, 10.780.71

3.13 0.824.38 , 1.140.71 0.71


HK n-butanol


n-butanol n-butanol

n-bun-butanol n-butanol

K KK K

KKK K

K

α α

α α

α

= = = =

= = = = = =

=0.71 0.571 , 0.790.71 0.71

1- pentanoltanol1- pentanol,n-butanol

n-butanol n-butanol

KK K

α= = = = =

1 2

3 4 5

0.15 0.25, 0.019 , 0.087.70 3.13

0.25 0.15 0.200.306 , 0.210 , 0.3520.82 0.71 0.57

ii

i

yx x xK

x x x

= = = = =

= = = = = =

1

2 3

4 5

, 0.15 0.988 1.013 0.1501

0.25 0.984 1.013 0.2491 , 0.25 0.968 1.013 0.2451

0.15 0.970 1.013 0.1474 , 0.20 0.961 1.013 0.1947

v v vi i iv v

v v

f y P ff ff f

= Φ = × × =

= × × = = × × =

= × × = = × × =

1

2 3

4 5

, 0.019 7.605 1.013 0.1501

0.08 3.078 1.013 0.2491 , 0.306 0.791 1.013 0.2451

0.21 0.693 1.013 0.1474 , 0.352 0.545 1.013 0.1947

l l li i i tl l

l l

f x P ff ff f

= Φ = × × =

= × × = = × × =

= × × = = × × =

- 31 -

In Vapor-Liquid Equilibrium, fugacity of liquid and vapor must be equal to each other. So, our results support this condition. ( )l v

i if f=

log ; ( , 1)

106.6 ( )760

1473.11 1 1.013log 7.87863 ; 3178.72 4.237106.6 230 760 1

sat o

odew

t



T C feed streamP mmHg

atm barP P mmHg barmmHg atm

For ot

= −+

==

= − = × × =+

17, 24, 31.her components see in Table

**

1 2

3 4

5

,

0.15 0.988 1.013 0.15 0.984 1.0131.818 , 1.1050.019 4.237 0.080 2.822

0.25 0.968 1.013 0.25 0.970 1.0130.997 , 1.0440.306 0.804 0.210 0.672

0.20 0.961 1.0130.35

vv i i t

i i t i i i ii i

y Py P x Px P

γ γ

γ γ

γ γ

γ

ΦΦ = =

× × × ×= = = =

× ×× × × ×

= = = =× ×

× ×= 1.741

2 0.317=

×

With excel calculation (goal seek), 1.00it sat

i i i

yPPγ

× =∑ we found Tdew=106.6 o

For Top Product

C

Dew point temperature for the feed was assumed as 90 o

11.00

ci

t sati i i

yPPγ=

× =∑C. All calculations was done by

using this temperature in excel. However value could not be obtained.

So the dew point temperature was calculated as 96.98 o

[ ] [ ],,

,1 ,2 ,3

,4 ,5

, ,

370.13 370.13 370.130.722 , 0.717 , 0.673512.58 516.25 550.00370.13 370.130.658 , 0.631562.93 586.15

r i cc i

r r r

r r

TT T K T KT

T T T

T T

=

= = = = = =

= = = =


- 32 -

( )( )

( )( )( )( )

22 1 2, ,

,

22 1 2,1

2 1 2,2

1 0.480 1.574 0.176 1

, 2 10

1 0.480 1.574 0.566 0.176 0.566 1 0.722 1.434

1 0.480 1.574 0.637 0.176 0.637 1 0.717

SRK i i i r i

c i i

SRK

SRK

T


α ω ω

ω

α

α

= + + − −

= + + × − × − =

= + + × − × −

( )( )( )( )( )( )

2

22 1 2,3

22 1 2,4

22 1 2,5

1.479

1 0.480 1.574 0.604 0.176 0.604 1 0.673 1.551

1 0.480 1.574 0.595 0.176 0.595 1 0.658 1.578

1 0.480 1.574 0.594 0.176 0.594 1 0.631 1.633

SRK

SRK

SRK

α

α

α

=

= + + × − × − =

= + + × − × − =

= + + × − × − =

[ ] [ ]2

, 3, ,

,

27

1

27

2

3

, , , 83.14

2 10

1.434 83.14 512.580.42748 1.38 1080.96

1.479 83.14 516.250.42748 1.82 1063.84

1.551 83.140.42748

i c ii c i c i

c i


P


a

a

a

αψ

ψ

= =

× ×= × = ×

× ×= × = ×

×= ×

27

27

4

27

5

550.00 3.57 1038.80

1.578 83.14 562.930.42748 3.35 1044.13

1.633 83.14 586.930.42748 4.27 1038.80

a

a

×= ×

× ×= × = ×

× ×= × = ×

[ ] [ ], 3, ,

,

1

2

3

4

, , , 83.14

2 1083.14 512.580.08664 45.61

80.9683.14 516.250.08664 58.25

63.8483.14 550.000.08664 102.11

38.80

0.08664

c ii c i c i

c i


P


b

b

b

b

= Ω =

Ω×

= × =

×= × =

×= × =

=

5

83.14 562.93 91.8944.13

83.14 586.150.08664 108.8238.80

b

×× =

×= × =

- 33 -

[ ] [ ] 3

1 2

3 4

5

, , , 83.14

45.61 1.013 58.25 1.0130.00150 , 0.0019283.14 370.13 83.14 370.13102.11 1.013 91.89 1.0130.00336 , 0.0030283.14 370.13 83.14 370.13108.82 1.01383.14 370.13

ii


β

β β

β β

β

≡ =

× ×= = = =

× ×× ×

= = = =× ××

=×

0.00358=

[ ] 3

7 7

1 2

7 7

3 4

7

5

, , 83.14

1.38 10 1.82 109.798 , 10.18145.61 83.14 370.13 58.25 83.14 370.13

3.57 10 3.35 1011.373 , 11.840102.11 83.14 370.13 91.89 83.14 370.13

4.27 10108.82 83.14

ii

i


q q

q q

q

=≡

× ×≡ = ≡ =

× × × ×× ×

≡ = ≡ =× × × ×

×≡

× ×12.758

370.13=

( )( )

( )( )

1

0.001500 1 0.00150 9.798 0.001500 0.00150 1 0.00150

0.988

,

vv i ii i i i v v

i i i i

vviiv v

i i

vi

vi

ZZ qZ Z

Z ZZ Z


ββ βεβ σβ

−= + −

+ +

−= + − × −

+ × + ×

13, 20, 27.values were tabulated in Table

1 2

3 4

5

1 ln

1 0.9880 1 0.00150 1 0.9828 1 0.00192ln 0.00152 , ln 0.001951 0 0.9880 0 1 0 0.9828 0

1 0.9659 1 0.00336 1 0.9673 1 0.00302ln 0.00347 , ln 0.003121 0 0.9659 0 1 0 0.9673 0

11

vv i ii v

i i

v v

v v

v

ZIZ

I I

I I

I

σβσ ε εβ

+=

− ++ × + ×

= = = =− + − +

+ × + ×= = = =

− + − +

=0.9575 1 0.00358ln 0.00373

0 0.9575 0+ ×

=− +

( ) ( )( )( )

1

2

3

ln 1 ln ; exp 1 ln

exp 0.9880 1 ln 0.9880 0.00150 9.798 0.00152 0.987

exp 0.9828 1 ln 0.9828 0.00192 10.181 0.00195 0.982

exp 0.9659 1 ln 0.9659 0.00


v

v

v

Z Z q I Z Z q Iβ β Φ = − − − − Φ = − − − − Φ = − − − − × = Φ = − − − − × = Φ = − − −( )

( )( )

4

5

336 11.373 0.00347 0.965

exp 0.9673 1 ln 0.9673 0.00302 11.840 0.00312 0.967

exp 0.9575 1 ln 0.9575 0.00358 12.758 0.00373 0.958

v

v

− × = Φ = − − − − × = Φ = − − − − × =

- 34 -

( )( )

( )( )

1

1 0.001500 0.00150 0 0.00150 1 0.001509.798 0.00150

0.00187


i i

ll l lii i i

li

ZZ Z Zq

ZZ Z Z


ββ εβ σββ

+ −= + + +

+ −

= + + × + × − ×


1 2

3 4

5

1 ln

1 0.00187 1 0.00150 1 0.00255 1 0.00192ln 0.590 , ln 0.5601 0 0.00187 0 1 0 0.00255 0

1 0.00426 1 0.00336 1 0.00385 1 0.00302ln 0.582 , ln 0.5801 0 0.00426 0 1 0 0.00385 0

11

ll i ii l

i i

l l

v v

v

ZIZ

I I

I I

I

σβσ ε εβ

+=

− ++ × + ×

= = = =− + − +

+ × + ×= = = =

− + − +

=0.00430 1 0.00358ln 0.606

0 0.00430 0+ ×

=− +

( ) ( )( )( )

1

2

3

ln 1 ln ; exp 1 ln

exp 0.00187 1 ln 0.00187 0.00150 9.798 0.590 3.108

exp 0.00255 1 ln 0.00255 0.00192 10.181 0.560 1.935

exp 0.00426 1 ln 0.00426 0.


l

l

l


( )( )

4

5

00336 11.373 0.582 0.551

exp 0.00385 1 ln 0.00385 0.00302 11.840 0.580 0.467

exp 0.00430 1 ln 0.00430 0.00358 12.758 0.606 0.226

l

l

− × = Φ = − − − − × = Φ = − − − − × =

1 2

3 4 5

3.108 1.935, 3.15 , 1.970.987 0.982

0.551 0.467 0.2260.57 , 0.48 , 0.240.965 0.967 0.958

li

i vi

K K K

K K K

Φ= = = = =Φ

= = = = = =

,

,

3.15, 6.520.48

1.97 0.574.08 , 1.180.48 0.48


HK n-butanol


n-butanol n-butanol


K KK K

KKK K

K

α α

α α

α

= = = =

= = = = = =

=0.48 0.241 , 0.490.48 0.48


n-butanol n-butanol

KK K

α= = = = =

- 35 -

1 2

3 4 5

0.231 0.377, 0.073 , 0.1923.15 1.97

0.373 0.012 0.0060.655 , 0.024 , 0.0270.57 0.48 0.24

ii

i

yx x xK

x x x

= = = = =

= = = = = =

1

2 3

4 5

, 0.231 0.987 1.013 0.2310

0.377 0.982 1.013 0.3755 , 0.373 0.965 1.013 0.3651

0.012 0.967 1.013 0.0116 , 0.006 0.958 1.013 0.0061

v v vi i iv v

v v

f y P ff ff f

= Φ = × × =

= × × = = × × =

= × × = = × × =

1

2 3

4 5

, 0.073 3.108 1.013 0.2310

0.192 1.935 1.013 0.3755 , 0.655 0.551 1.013 0.3651

0.024 0.467 1.013 0.0116 , 0.027 0.226 1.013 0.0061

l l li i i tl l

l l

f x P ff ff f

= Φ = × × =

= × × = = × × =

= × × = = × × =


i if f=

log ; ( , 1)

96.98 ( )760

1473.11 1 1.013log 7.87863 ; 2362.789 3.14996.98 230 760 1

sat o

odew

t



T C top streamP mmHg

atm barP P mmHg barmmHg atm

For ot

= −+

==

= − = × × =+

17, 24, 31.her components see in Table

1 2

3 4

5

,

0.231 0.987 1.013 0.377 0.982 1.0131 , 0.9640.073 3.149 0.192 2.032

0.373 0.965 1.013 0.012 0.967 1.0130.997 , 1.0310.655 0.559 0.024 0.459

0.006 0.958 1.01

vv sat i i t

i i t i i i i sati i

y Py P x Px P

γ γ

γ γ

γ γ

γ

ΦΦ = =

× × × ×= = = =

× ×× × × ×

= = = =× ×

× ×=

3 1.0890.027 0.210

=×

With excel calculation (goal seek), 1.00it sat

i i i

yPPγ

× =∑ we found Tdew=96.98 o

C

- 36 -

For Bottom Product Bubble point temperature for the feed was assumed as 120 o

1 1.00

csat

i i ii

t

x P

P

γ= =∑

C. All calculations was done

by using this temperature in excel. However value could not be obtained.

So the bubble point temperature was calculated as 128.5 o

[ ] [ ],,

,1 ,2 ,3

,4 ,5

, ,

401.65 401.65 401.650.784 , 0.778 , 0.730512.58 516.25 550.00401.65 401.650.713 , 0.685562.93 586.15

r i cc i

r r r

r r

TT T K T KT

T T T

T T

=

= = = = = =

= = = =


( )( )

( )( )( )( )

22 1 2, ,

,

22 1 2,1

2 1 2,2

1 0.480 1.574 0.176 1

, 2 10

1 0.480 1.574 0.566 0.176 0.566 1 0.784 1.325

1 0.480 1.574 0.637 0.176 0.637 1 0.778

SRK i i i r i

c i i

SRK

SRK

T


α ω ω

ω

α

α

= + + − −

= + + × − × − =

= + + × − × −

( )( )( )( )( )( )

2

22 1 2,3

22 1 2,4

22 1 2,5

1.361

1 0.480 1.574 0.604 0.176 0.604 1 0.730 1.437

1 0.480 1.574 0.595 0.176 0.595 1 0.713 1.465

1 0.480 1.574 0.594 0.176 0.594 1 0.685 1.520

SRK

SRK

SRK

α

α

α

=

= + + × − × − =

= + + × − × − =

= + + × − × − =

[ ] [ ]2

, 3, ,

,

27

1

27

2

3

, , , 83.14

2 10

1.325 83.14 512.580.42748 1.27 1080.96

1.361 83.14 516.250.42748 1.68 1063.84

1.437 83.140.42748

i c ii c i c i

c i


P


a

a

a

αψ

ψ

= =

× ×= × = ×

× ×= × = ×

×= ×

27

27

4

27

5

550.00 3.31 1038.80

1.465 83.14 562.930.42748 3.11 1044.13

1.520 83.14 586.930.42748 3.98 1038.80

a

a

×= ×

× ×= × = ×

× ×= × = ×

- 37 -

[ ] [ ], 3, ,

,

1

2

3

4

, , , 83.14

2 1083.14 512.580.08664 45.61

80.9683.14 516.250.08664 58.25

63.8483.14 550.000.08664 102.11

38.80

0.08664

c ii c i c i

c i


P


b

b

b

b

= Ω =

Ω×

= × =

×= × =

×= × =

=

5

83.14 562.93 91.8944.13

83.14 586.150.08664 108.8238.80

b

×× =

×= × =

[ ] [ ] 3

1 2

3 4

5

, , , 83.14

45.61 1.013 58.25 1.0130.00138 , 0.0017783.14 401.65 83.14 401.65102.11 1.013 91.89 1.0130.00310 , 0.0027983.14 401.65 83.14 401.65108.82 1.01383.14 401.65

ii


β

β β

β β

β

≡ =

× ×= = = =

× ×× ×

= = = =× ××

=×

0.00330=

[ ] 3

7 7

1 2

7 7

3 4

7

5

, , 83.14

1.27 10 1.68 108.341 , 8.62945.61 83.14 401.65 58.25 83.14 401.65

3.31 10 3.11 109.709 , 10.130102.11 83.14 401.65 91.89 83.14 401.65

3.98 10108.82 83.14 40

ii

i


q q

q q

q

=≡

× ×≡ = ≡ =

× × × ×× ×

≡ = ≡ =× × × ×

×≡

× ×10.946

1.65=

( )( )

( )( )

1

0.001380 1 0.00138 8.341 0.001380 0.00138 1 0.00138

0.9892

,

vv i ii i i i v v

i i i i

vviiv v

i i

vi

i

ZZ qZ Z

Z ZZ Z


ββ βεβ σβ

−= + −

+ +

−= + − × −

+ × + ×

13 20, 27.v values were tabulated in Table

- 38 -

1 2

3 4

5

1 ln

1 0.9892 1 0.00138 1 0.9853 1 0.00177ln 0.00140 , ln 0.001791 0 0.9892 0 1 0 0.9853 0

1 0.9704 1 0.00310 1 0.9721 1 0.00279ln 0.00319 , ln 0.002861 0 0.9704 0 1 0 0.9721 0

11

vv i ii v

i i

v v

v v

v

ZIZ

I I

I I

I

σβσ ε εβ

+=

− ++ × + ×

= = = =− + − +

+ × + ×= = = =

− + − +

=0.9638 1 0.00330ln 0.00342

0 0.9638 0+ ×

=− +

( ) ( )( )( )

1

2

3

ln 1 ln ; exp 1 ln

exp 0.9892 1 ln 0.9892 0.00138 8.341 0.00140 0.990

exp 0.9853 1 ln 0.9853 0.00177 8.629 0.00179 0.987

exp 0.9704 1 ln 0.9704 0.003


v

v

v


( )( )

4

5

10 9.709 0.00319 0.973

exp 0.9721 1 ln 0.9721 0.00279 10.130 0.00286 0.975

exp 0.9638 1 ln 0.9638 0.00330 10.946 0.00342 0.967

v

v

− × = Φ = − − − − × = Φ = − − − − × =

( )( )

( )( )

1

1 0.001380 0.00138 0 0.00138 1 0.001388.341 0.00138

0.00169


i i

ll l lii i i

li

ZZ Z Zq

ZZ Z Z


ββ εβ σββ

+ −= + + +

+ −

= + + × + × − ×


1 2

3 4

5

1 ln

1 0.00169 1 0.00138 1 0.00245 1 0.00177ln 0.599 , ln 0.5431 0 0.00169 0 1 0 0.00245 0

1 0.00425 1 0.00310 1 0.00365 1 0.00279ln 0.548 , ln 0.5671 0 0.00425 0 1 0 0.00365 0

11

ll i ii l

i i

l l

v v

v

ZIZ

I I

I I

I

σβσ ε εβ

+=

− ++ × + ×

= = = =− + − +

+ × + ×= = = =

− + − +

=0.00420 1 0.00330ln 0.580

0 0.00420 0+ ×

=− +

( ) ( )( )( )

1

2

3

ln 1 ln ; exp 1 ln

exp 0.00169 1 ln 0.00169 0.00138 8.341 0.599 8.223

exp 0.00245 1 ln 0.00245 0.00177 8.629 0.543 4.982

exp 0.00425 1 ln 0.00425 0.0


l

l

l


( )( )

4

5

0310 9.709 0.548 1.576

exp 0.00365 1 ln 0.00365 0.00279 10.130 0.567 1.365

exp 0.00420 1 ln 0.00420 0.00330 10.946 0.580 0.719

l

l

− × = Φ = − − − − × = Φ = − − − − × =

- 39 -

1 2

3 4 5

8.223 4.982, 8.31 , 5.050.990 0.987

1.576 1.365 0.7191.62 , 1.40 , 0.740.973 0.975 0.967

li

i vi

K K K

K K K

Φ= = = = =Φ

= = = = = =

,

,

8.31, 5.931.40

5.05 1.623.60 , 1.161.40 1.40


HK n-butanol


n-butanol n-butanol


K KK K

KKK K

K

α α

α α

α

= = = =

= = = = = =

=1.40 0.741 , 0.531.40 1.40


n-butanol n-butanol

KK K

α= = = = =

1 2

3 4 5

, 8.31 0.008 0.068 , 5.05 0.027 0.139

1.62 0.034 0.056 , 1.40 0.391 0.548 , 0.74 0.538 0.400i i iy K x y y

y y y= = × = = × =

= × = = × = = × =

1

2 3

4 5

, 0.068 0.99 1.013 0.0687

0.139 0.987 1.013 0.1386 , 0.056 0.973 1.013 0.0548

0.548 0.975 1.013 0.5415 , 0.400 0.967 1.013 0.3921

v v vi i iv v

v v

f y P ff ff f

= Φ = × × =

= × × = = × × =

= × × = = × × =

1

2 3

4 5

, 0.008 8.223 1.013 0.0687

0.027 4.982 1.013 0.1386 , 0.034 1.576 1.013 0.0548

0.391 1.365 1.013 0.5415 , 0.538 0.719 1.013 0.3921

l l li i i tl l

l l

f x P ff ff f

= Φ = × × =

= × × = = × × =

= × × = = × × =


i if f=

log ; ( , 1)

128.5 ( )760

1473.11 1 1.013log 7.87863 ; 5881.758 7.840128.5 230 760 1

sat o

obubble

t



T C bottom streamP mmHg

atm barP P mmHg bammHg atm

= −+

==

= − = × × =+

17, 24, 31.

r

For other components see in Table

- 40 -

1 2

3 4

5

,

0.068 0.99 1.013 0.139 0.987 1.0130.015 , 0.0360.008 7.840 0.027 5.572

0.056 0.973 1.013 0.548 0.975 1.0130.361 , 0.4810.034 1.685 0.391 1.464

0.400 0.967 1

vv sat i i t

i i t i i i i sati i

y Py P x Px P

γ γ

γ γ

γ γ

γ

ΦΦ = =

× × × ×= = = =

× ×× × × ×

= = = =× ×

× ×=

.013 1.8010.538 0.732

=×

With excel calculation (goal seek), 1 1.00

csat

i i ii

t

x P

P

γ= =∑

we found Tbubble=128.5 o

C

Calculation of Average Relative Volatilities

33, , , ,

3 3

3 3

, 10.78 6.52 5.93 7.47

4.38 4.08 3.60 4.01 , 1.14 1.18 1.16 1.16

1 1 1 1 , 0.79 0.49 0.53 0.59

average i top i bottom i feed i methanol

ethanol neopentanol

n-butanol 1- pentanol

α α α α α

α α

α α

= × × = × × =

= × × = = × × =

= × × = = × × =

Calculation of Minimum Number of Plates by Using Fenske Equation

, ,

, ,

,

0.373 0.391log log0.012 0.034; 39.56

log log1.16

LK D HK W

HK D LK Wmin min

LK avg

x xx x

N Nα

× × = = =

Calculation of q-Parameter

We used saturated vapor for the feed stream; so q-parameter must be taken as zero (q=0).

Calculation of θ-Parameter

, ,

1 ,

1 ,c

i ave f iHK LK

i i ave

xq

αα θ α

α θ=

×= − < <

−∑

, , , , , , , , 1 , ,1

, , , , 1 ,

1 0

7.47 0.15 4.01 0.25 1.16 0.25 17.47 4.01 1.16

met ave f met eth ave f eth neo ave f neo n but ave f n but pent ave f pent

met ave eth ave neo ave n but ave pent ave

x x x x xq

α α α α αα θ α θ α θ α θ α θ

θ θ θ

− − − −

− −

× × × × ×+ + + + − + =

− − − − −

× × × ×+ + +

− − −0.15 0.59 0.20 1 0 0

1 0.59

1.051

θ θ

θ

×+ − + =

− −

=

- 41 -

Calculation of Minimum Reflux, RDmin

,min

1

min

min

min 1

min 2

1

7.47 0.231 4.01 0.377 1.16 0.373 1 0.012 0.59 0.006 1 07.47 1.051 4.01 1.051 1.16 1.051 1 1.051 0.59 1.0513.516

* 3.516*1.5 5.274

* 3.51

cir D i

Di ir

D

D

Dactual D

Dactual D

xR

R

R

R R

R R

αα θ

β

β

=

×= +

−

× × × × ×= + + + + − =

− − − − −=

= = =

= =

∑

min 3

6*1.8 6.328

* 3.516*2.4 8.438Dactual DR R β

=

= = =

by Using Underwood Equation

Calculation of Actual Plate Number by Using Gilliand Correlation

5.274 3.516 0.2805.274 1

DminR - RXR+1

−= = =

+

0.1 0.1

1.805 1.8051 exp 1.490 0.315 1 exp 1.490 0.315 0.280 0.376(0.280)

Y XX

= − + − = − + × − =

min min

1 10.376 39.56 64

1 0.376actual

N N Y NY NN Y

N N plates

− += ⇒ =

+ −+

= = =−

For other reflux ratios, the calculated values were tabulated in Table 34.

Calculation of NR and NS

2 2. ,

, ,

36.4 0.15 0.034log 0.206log 0.206log 0.0969163.6 0.25 0.012

1.25 ,

64 28 , 64 281.25 11

f HK b LKR

S f LK d HK

RR act S

S

actS R

R

S

x xN WN D x x

N N N NN

NN NNN

= = = =

= = −

= = = = −++

36=

for the Feed Location by Using Kirk Bridge Method

- 42 -

Calculation of Condenser and Reboiler Loads, Qc and Q

, ,

5.274 , 335.4 /63.6

D

D

LF W D L G W RD

LR L kmol h

= + = + =

= = =

r

( )

( )

, ,1 1

,

33

, 335.4 63.6 399.00 /1 1000* , 399.00 38.914 4312.9

3600 1

335.4, 0100

3

c c

ave top i i ave bottom i ii i

c ave top c

y and x for results see in Table

G L D G kmol hkmol kJ h molQ G Q kJ s kW

h mol s kmol

L L Lq qF

L L

λ λ λ λ

λ

= =

= =

= + = + =

= = × × × =

− −= = =

= =

∑ ∑

( ),

35.4 , 335.4 36.4 , 299.00 /1 1000* , 299.00 *43.836 3640.9

3600 1r ave bottom r

G L W G kmol hkmol kJ h molQ G Q kJ s kW

h mol s kmolλ

= − = − =

= = × × =

Calculation of Column Diameter and Height

( )1

* ,

0.008 8.31 0.068 35

(32.04*0.068) (46.07*0.139) (88.15*0.056) (74.122*0.548) (88.15*0.400) 89.42 /

i i

methanol

N

i W W i ii

W methanol methanol

MW MW y y x K

y x K for other components see Table

MW kg kmol

=

= =

= = × =

= + + + + =

∑

3

3

1

189.42 36.4 0.9043600

1 89.42 2.7150.082 (128.5 273.15)

791.8 0.008 789 0.027 812 0.034 809.8 0.391 814.4 0.538 811.63

vap

c

liq i ii

kg kmol hW MV W kg skmol h s

P MW R TP MW kg m

R T

x kg m

ρ

ρ

ρ ρ=

= × = × × =

× = × ×× ×

= = =× × +

= = × + × + × + × + × =∑

( )

( )

1/22

1/22

0.171* 0.27* 0.047 *

811.63 2.7150.171*0.5 0.27*0.5 0.047 *2.715

4 4 0.904 0.737 , ( 1) 0.5 (64 1) 32.52.

0

71

.7

5 0.78

81

1

l vv t t

v

v

c c tv v

u l l

u

WD m H l N mu

For other reflux ratios the

m

r

s

ρ ρρ

πρ π

=

−= − + −

− = − + −

×= = = = × + = × + =

× ×

35.esults were in Table

design of a continuous distillation column for a multi component mixture

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