35 44 v58 n1 an approach towards the design of a petlyuk column using hysys mustafa

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Sudan Engineering Society Journal, March 2012, Volume 58; No.1 AN APPROACH TOWARDS THE DESIGN OF A PETLYUK COLUMN USING HYSYS Mustafa, M. Abbas 1 and Wilson, J.A. 2 1 Department of Chemical Engineering, Faculty of Engineering, University of Khartoum, [email protected] 2 Chemical and Environmental Engineering, Faculty of Engineering, the University of Nottingham, United Kingdom Received Sep. 2011, accepted after revision Jan. 2012 صَ ـلـْ خَ ــتْ ـسُ م احذعذ اىتقطيش ي أدىطاقت في عاك اخفيط است ت بدذ عيذسو اى، عيش اىس عي .حذةث اىياي اىع قذ اىتيً سيابطت حشاشت ابشاج اىتقطيش اىي ،يتبشاج راث ا ا .ذيتيش اىتقي اىطشق غي س عذد ظ اىا أد اىتقطيشيح تخفيطت تشفي استخذاذ اىتفنياغو اىشئيسيت، ع أحذ اىش رىل، فا باىشغ .ىيف اىتشغيوتنا اهأس اى في سً مبيشا رىل، فة اى. عي ىيتصاسختس يتد اخشاءاث سخ عذ ، ً سيابطت حشاشت ابشاج اىتقطيش اى إحاماةح اى بعط بشا ه اصث في اى باشناىيااخقشة تستث اى ىيحاه حي ى أك،يد اىبتي عايح ىتص سقت اىز اىي تعشضباىت .ىيت يسايس حابشينيت باة اىذيحاما اى ، عبش استخذاً مثش تعقيذا ا. ABSTRACT Distillation is considered one of the oldest unit operations. Throughout the years, chemical engineering designers have been working hard to reduce the energy consumption of columns which has led to the development of many non-conventional methods. Of particular importance are thermally coupled distillation columns (TCDC) which offer large savings in capital and operating cost. The main concern, when contemplating the use of TCDC, is the unavailability of easy and well established design procedures. Furthermore, some steady-state simulators have given convergence problems particularly to establish the first solution. Thus, this paper presents an approach for the design of the more complex Petlyuk column based on dynamic simulation using HYSYS. Keywords: Petlyuk column, simulation, design, HYSYS 35

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AN APPROACH TOWARDS THE DESIGN OF A PETLYUK COLUMN USING HYSYS

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Page 1: 35 44 v58 n1 an Approach Towards the Design of a Petlyuk Column Using Hysys Mustafa

Sudan Engineering Society Journal, March 2012, Volume 58; No.1

AN APPROACH TOWARDS THE DESIGN OF A PETLYUK COLUMN USING HYSYS

Mustafa, M. Abbas1 and Wilson, J.A.2

1Department of Chemical Engineering, Faculty of Engineering, University of Khartoum,

[email protected] 2Chemical and Environmental Engineering,

Faculty of Engineering, the University of Nottingham, United Kingdom

Received Sep. 2011, accepted after revision Jan. 2012

مـســتخـلـص

قذ اىعيياث اىحذة. عي ش اىسي، عو اىذس بدذ عي تخفيط استالك اىطاقت في عاد أيعذ اىتقطيشاحذ

اىتقطيشا أد اى ظس عذد اىطشق غيش اىتقييذيت. االبشاج راث األيت، ي ابشاج اىتقطيش اىشتبطت حشاسيا اىتي

مبيشا في سأس اىاه تناىيف اىتشغيو. باىشغ رىل، فا أحذ اىشاغو اىشئيسيت، عذ اىتفنيشفي استخذا تتيح تخفيط

بعط بشاح اىحاماة إابشاج اىتقطيش اىشتبطت حشاسيا، عذ خد اخشاءاث سيت ساسخت ىيتصي. عالة اى رىل، ف

ىيت. باىتاىي تعشض ز اىسقت ح ىتصي عاد اىبتييك، أى حيه ىيحاالث اىستقشة تاخ باشناىياث في اىصه ا

.األمثش تعقيذا، عبش استخذا اىحاماة اىذياينيت ببشاح ايسيس

ABSTRACT

Distillation is considered one of the oldest unit operations. Throughout the years, chemical

engineering designers have been working hard to reduce the energy consumption of columns

which has led to the development of many non-conventional methods. Of particular

importance are thermally coupled distillation columns (TCDC) which offer large savings in

capital and operating cost. The main concern, when contemplating the use of TCDC, is the

unavailability of easy and well established design procedures. Furthermore, some steady-state

simulators have given convergence problems particularly to establish the first solution. Thus,

this paper presents an approach for the design of the more complex Petlyuk column based on

dynamic simulation using HYSYS.

Keywords: Petlyuk column, simulation, design, HYSYS

35

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Sudan Engineering Society Journal, March 2012, Volume 58; No.1

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36

AN APPROACH TOWARDS THE DESIGN OF A PETLYUK COLUMN USING HYSYS

INTRODUCTION

Distillation is a mature and well established

technology; however there is still the problem

of high energy consumption. Since energy

consumption is directly related to vapour flow

within the column, reduction in energy

consumption is possible through the reduction

of the vapour flow. This leads to a reduction in

the column diameter, with the use of a smaller

reboiler, which leads to a saving in capital cost.

However, effect of reducing vapour flow on

product quality needs to be considered.

1.1 Thermally Coupled Columns

A number of non-conventional arrangements

exist which use thermal coupling. The most

important incentive in the application of TCDCs

is that the side streams are drawn/added at the

most thermodynamically favourable points so

as to reduce the total energy consumption.

TCDC may be divided into 3 groups:

1. Direct thermally coupled system

Direct thermally coupled systems are also

referred to as systems with a side-rectifier. An

example for a ternary mixture is shown in

Figure 1. An impure vapour side-stream is

withdrawn from the first column, below the

feed tray, and purified in a side-rectifier, the

bottom of which is returned to the main

column [1].

2. Indirect thermally coupled system

Indirect thermally coupled systems are also

known as systems with a side-stripper. An

example for a ternary mixture is shown in

Figure 2. An impure liquid side-stream is

withdrawn from the first column above the

feed tray and purified in a side-stripper. The

top vapour product of the side-stripper is

returned to the first column [1].

3. Fully thermally coupled system (also

known as the Petlyuk column)

A Petlyuk column for a ternary mixture consists

of a pre-fractionator and a main column as

shown in Figure 3. The main aim of the pre-

fractionator is to send all of the light

component and heavy component to the

distillate and bottoms respectively, but allow

the component of intermediate volatility to be

split between the overhead and bottoms.

Products from the pre-fractionator are directed

to appropriate trays in the main column. The

main column then produces the lightest

component as its distillate, the heaviest

component as bottom product and allows the

middle component to be drawn off as a side

stream with a very high purity. It is clear from

the figure that only one condenser and reboiler

are needed. As for reflux and boilup for the pre-

fractionator, they are obtained from the main

column. Theoretical studies have shown that

Petlyuk columns can save, on average, around

30% of energy costs compared with a

conventional arrangement [3].

A further advantage of the Petlyuk column is

that it could be constructed in a single shell

with an internal dividing wall as shown in Figure

4. This offer significant savings in field

construction costs [3]. Despite all the

advantages offered by thermally coupled

systems, designers have been reluctant to use

those kinds of systems. This reluctance can be

attributed mainly to potential operational

problems due to the bi-directional

interconnecting streams The Nigerian textile

industrial sector has been struggling for survival

Condenser

Figure 1: Direct thermally coupled column

Vapour

Liquid

Feed

Product C

Product A

Reboiler

A , B , C

Main column

Condenser

Product B

Side-rectifier

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Sudan Engineering Society Journal, March 2012, Volume 58; No.1

37

Mustafa, M. Abbas and Wilson, J.A.

Figure 2: Indirect thermally coupled column

Figure 3: Petlyuk Column

Figure 4: The dividing wall column

1.2 Simulation Package - HYSYS

Aspen HYSYS [5] provides an integrated

engineering environment in which all

applications work inside a common

operating environment. It also has the

advantage of been flexible, robust and

interactive, thus making the process

simulator very powerful and very easy to

use. One of the most important benefits of

this package is its dynamic modelling option.

Once the model is set, the evaluation of the

response of each operation and the flow

sheet interaction could be used to provide

insight into the process.

2 LITERATURE REVIEW

Work on thermally coupled columns started

mainly by focusing on determining design

parameters for minimum reflux ratios.

Glinos and Malone [2] suggested using the

minimum total vapour generated by

reboilers as a base for comparing between

different arrangements. They then proposed

useful expressions for calculating the

minimum vapour rates (at minimum reflux),

but no approach at that stage was

developed to determine the number of trays

needed in each column. Finn [6] also

established a procedure for calculating the

condenser/ reboiler loads at minimum reflux

ratio. The procedure developed again lacked

the initial design parameters required for a

rigorous simulation. Alatiqui and Luyben [7]

performed a more formal study of the

design of indirect thermally coupled

columns. They found that better energy

consumption could be achieved for feeds

containing less than 20% of the intermediate

component. The study was based on a

steady-state model using a trial and error

procedure to determine the optimal design

parameters. Throughout their study

convergence problems were faced in some

cases.

Feed Liquid

Vapour

Product A

Product C

A, B, C

Reboiler

Condenser

Main column

Product B

Reboiler

Side-stripper

Reboiler

Product B

Product C

Product A

Vapour

Vapour

Liquid

Liquid

Condenser

A, B, C

Pre-fractionator

Main column

A B C

A

B

C

Feed

Condenser

Reboiler

Internal Dividing wall

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Sudan Engineering Society Journal, March 2012, Volume 58; No.1

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38

AN APPROACH TOWARDS THE DESIGN OF A PETLYUK COLUMN USING HYSYS

Cerda and Westerberg [8] developed short-

cut methods for the determination of

operating parameters for thermally coupled

columns; however Glinos and Malone [2]

think that the algorithm is unnecessarily

complicated. Triantafylou and Smith [3] then

produced a design model which provides a

basis for investigating the degrees of

freedom for a minimised overall vapour flow

(at a given reflux ratio) or number of plates.

It also provides a good initialisation for

rigorous simulation.

Ramírez-Corona et al. [9] proposed use of a

shortcut model for optimum design of

Petlyuk and dividing-wall distillation

systems; however, no rigorous calculations

are presented. Kim [10] further proposed a

semi-rigorous method for design of Petlyuk

column, nevertheless results provide only

basic information which could be fed into

commercial software. As an alternative

approach, Hernandez and Jimenez [1] used a

dynamic model to overcome the problem of

convergence. They first started by obtaining

a design for a direct conventional column as

shown in Figure 5. The final design of a

direct thermally coupled column is then

obtained as follows:

1 / Total number of stages in the first

column is equal to the number of stages of

column 1 plus the number of stages in

section 4 of column 2.

2 / Total number of stages in the side-

rectifier (Figure 1) is equal to the number of

stages in section 3 of column 2.

The position of the feed stream is fixed and

the side-draw is drawn from the bottom of

column 1 (corresponds, in the main column

of the direct thermally coupled system, to

the point between section 2 in column 1 and

the added section 4 of column 2).

Figure 5: Direct sequence

Once the design is obtained, the procedure

continues by controlling the main column, while

varying the flowrate of the side-draw, until the

minimum duty is achieved. In this method the

design is fixed and although Hernandez and

Jimenez [1] have suggested adjustment of the

initial design after steady-state occurs (due to

the final composition of the products calculated

not matching the specifications of those

products), but no method to follow was given.

That means that the column could be over-

trayed or even the side-draw is not taken from

the optimum tray, at the main column, i.e.

where the maximum concentration of the

intermediate component occurs. So a

procedure has to be developed that looks more

deeply into those issues, and thus gives the

maximum savings in energy.

3. CASE STUDY

The feed (Table 1) enters the pre-fractionator

and the hexane is split between the light-key

component (pentane) at the top and the heavy-

key component (heptane) at the bottom. It is

then drawn out as a very pure component from

one of the trays of the main column as shown in

Figure 6. The four interconnecting streams

between the two columns mean that

establishing a steady-state design is particularly

challenging.

Feed 1

n-hexane

Column 1

n-heptane

n-hexane

n-pentane

Stream 1

Stream 2

Upper Main Column

Lower Main Column

A

B

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Sudan Engineering Society Journal, March 2012, Volume 58; No.1

39

Mustafa, M. Abbas and Wilson, J.A.

Figure 6: Petlyuk column: Case study

To have a feel of the problems faced by the

designer, one should try to attempt answering

the following questions:

1. How many plates are there in the pre-

fractionator?

2. How many plates are there in the main

column?

3. On which plate does the feed enter the

pre-fractionator?

4. On which plate do both feeds to the main

column enter?

5. From which plate in the main column is the

side-draw taken?

6. How much is the distillate rate and the

reflux ratio in the main column?

A case study was chosen from the literature [1]

using feed specified in Table 1.

Table 1: Specification of feed

Feed

Flowrate ( kgmol/h ) 45.4

Pressure ( kPa ) 101.33

Temperature ( o C ) 58

mole fraction of n-pentane 0.33

mole fraction of n-hexane 0.33

mole fraction of n-heptane 0.33

The design procedure followed could be

summarised as follows:

i. Simplify Petlyuk column as shown in Figure

7 (Similar to Hernandez and Jimenez [1]

approach for direct thermally coupled

columns)

ii. Apply short-cut methods in HYSYS to obtain

the initial design parameters of column 1, 2

and 3.

iii. Perform rigorous simulation of column 1

(pre-fractionator) to obtain data for

streams A and B (2 side-draws from the

main column).

iv. Perform rigorous simulation of the main

column with its feed streams been streams

A1 and B1 but without the side draws from

the main column been fed back into the

pre-fractionator.

v. Couple the pre-fractionator with the main

column using the dynamic facility.

vi. Check the temperature profile to see if the

columns are over-trayed.

vii. Check the composition profile to see

whether stream A1 and B1 are entering the

main column at the point which best

matches the composition of those streams.

viii. Reduce number of trays in main column

and repeat steps (vi and vii) until profiles

are acceptable (no redundant stages).

Figure 7: Simplification of Petlyuk column

n-hexane

n-heptane

n-pentane Stream A1

Stream B

Stream B1

Stream A

Liquid

Reboiler

Condenser

Feed 1

Pre-fractionator

Main Column

Stream 3

Stream 4

Stream 5

Upper Main Column

n-pentane

Stream 1 Column 2

A

n-

hexane

Feed 1

Column 1

B

n-hexane

Lower Main Column

Column 3

Stream 2

n-heptane

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AN APPROACH TOWARDS THE DESIGN OF A PETLYUK COLUMN USING HYSYS

4. RESULTS AND DISCUSSION

The first step for simulating the fully

thermally coupled columns, also known as

the Petlyuk columns, is to simplify it by

dividing it into 3 columns using a

conventional arrangement as shown in

Figure 7 [3]. Column 1 roughly splits hexane

equally between the top and bottom

product. Stream 1 is then sent to column 2

where pentane is recovered as the top

product and the hexane as the bottom

product. The same happens to Stream 3 but

hexane is separated as the distillate while

heptane is separated as the bottom product

of column 3. Column 2 in this simplification

represents the upper section of the main

column, while Column 3 represents the

lower section of the main column.

4.1 Short-cut simulation

The short-cut method is then implemented

in HYSYS to get the initial design parameters

for the three columns. For column 1, the

light-key component was specified as n-

hexane while n-heptane was specified as the

heavy-key component. The purity of hexane

in the top product was set to 33%, and that

of the n-heptane in the bottoms to 65% just

to give roughly an equal split of hexane

between the products. As for the reflux

ratios, they were set to 1.3 times the

minimum reflux ratio. The results are shown

in Table 2.

Table 2: Results of the short-cut method for

column 1

Distillate flowrate ( kgmol/h ) 22.56

Bottoms flowrate ( kgmol/h ) 22.84

Number of trays 12

Feed tray location 10

Reflux ratio 0.65

The same procedure was followed for the

other two columns using the rigorous data

for column 1 overheads/ bottoms as feed to

column 2 and 3 respectively. The purity of

the light and heavy key components was

specified as 99%. The results of the short-cut

method for column 2 and 3, together with

the light and heavy key components

specified in each case as shown in Tables 3

and 4.

Table 3: Results of the short-cut method for column 2

Light key component Pentane

Heavy key component Hexane

Flow rate of Stream 1 ( kgmol/h ) 22.56

Distillate flowrate ( kgmol/h ) 15.19

Bottoms flowrate ( kgmol/h ) 7.37

Number of trays 21

Feed tray location 9

Reflux ratio 1

Table 4: Results of the short-cut method for

column 3

Light key component Hexane

Heavy key component Heptane

Flow rate of Stream 2 ( kgmol/h ) 22.84

Distillate flowrate ( kgmol/h ) 7.69

Bottoms flowrate ( kgmol/h ) 15.15

Number of trays 23

Feed tray location 13

Reflux ratio 2.86

4.2 Rigorous simulation

To simulate the pre-fractionator some more

information is needed about the flow rate and the

composition of streams A and B (shown in Figures

6 & 7), which are basically the 2 side-draws from

the main column. Thus, rigorous data of streams A

and B (Figure 7) were obtained for Column 1

previously simulated. The results of streams A and

B are shown in Table 5.

Since all the information needed to simulate the

pre-fractionator was available, the pre-

fractionator was simulated rigorously using

HYSYS. For the main column, the number of trays

in column 2 and column 3 gave the total number

of trays in the main column. The position of the

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Sudan Engineering Society Journal, March 2012, Volume 58; No.1

41

Mustafa, M. Abbas and Wilson, J.A.

feeds to column 2 and 3 gave the position of the

feed streams to the main column. The main

column was then simulated rigorously with its

feed streams been streams A1 and B1 (Figure 6),

already simulated from the pre-fractionator, but

without the side draws from the main column

been fed back into the pre-fractionator. The final

and most exciting step then was to couple the

pre-fractionator and the main column. Streams A

and B were specified as recycle streams by adding

a recycle operation. The program was then

allowed to run with products specified at 95%

purity. A new solution was reached as shown in

Table 6.

Table 5: Rigorous data for stream A and B (Fig. 6)

Stream A B

Flow rate ( kgmol/h ) 22 35.5

Temperature ( oC ) 57 76

Concentration of pentane 0.26 0.08

Concentration of hexane 0.74 0.73

Concentration of heptane 0.0 0.18

Table 6: Results of rigorous simulation of Petlyuk

column

Total number of stages in pre-fractionator

12

Total number of stages in main column

44

Stream A1 entering main column at tray number

9

Stream A drawn from main column at tray number

9

Stream B1 entering the main column at tray number

33

Stream B drawn from main column at tray number

33

Stream 4 drawn from main column at tray number

20

Reboiler duty ( kJ/h ) 2.07×106

Flowrate of stream A1 ( kgmol/h ) 35.55

Composition of stream A1

Mole fraction of n-pentane 0.4569

Mole fraction of n-hexane 0.5431

Mole fraction of n-heptane 4.07×10-5

Flowrate of stream B1 ( kgmol/h ) 67.35

Composition of stream B1

Mole fraction of n-pentane 0.0892

Mole fraction of n-hexane 0.606

Mole fraction of n-heptane 0.3048

The next step was then to check the temperature

profile to see if the columns were over-trayed and

then to check that stream A1 and B1 are entering

the main column at the point which best matches

the composition of those streams. For the number

of stages in the pre-fractionator, it remained

unchanged at 12 stages, but the number of stages

on the main column reduced from 44 stages to 27

stages (much more smother profile is produced

with no redundant stages). The best match

between Stream A1 and the column was found,

by examining the composition profile, at stage

number 6 and as for Stream B1 the best match

was found at stage number 20. Furthermore,

more cases were generated by changing the flow

rate of Stream A. The results are shown in Table 7.

It is clear from the results that the duty is directly

proportional to the flow rate of stream A.

Table 7: Comparison of different Petlyuk column cases

Flowrate of stream A (kgmol/h)

Reboiler duty ( E+06 kJ/h)

The tray at which Stream A1 enters (a)

The tray at which Stream B1 enters (b)

Number of stages between a&b

Total number of trays

14 1.71 6 21 15 28

16 1.87 6 18 12 25

18 1.95 6 19 13 25

20 2.07 5 19 14 25

22 2.27 5 19 14 25

24 2.39 5 18 13 24

26 2.54 5 18 13 24

28 2.68 5 19 14 24

30 3 5 17 12 22

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AN APPROACH TOWARDS THE DESIGN OF A PETLYUK COLUMN USING HYSYS

The convergence of the Petlyuk column was

the biggest challenge to the author and it

showed that the package was flexible

enough that it managed to solve this

complicated problem. On the other hand,

the savings in energy offered by the Petlyuk

column are clear from the previous table.

The energy consumption of the conventional

columns is 2.24752E+06 kJ/h, to obtain

products with the same specifications. So

savings in energy could be seen for flowrates

of 20 kgmol/h and lower as shown in Table

8, however this has to be traded off versus

increase in the number of trays.

Table 8: Comparison of energy consumption of

Petlyuk column compared to conventional

distillation methods for flow rates of 20kgmol/h

and lower

Flow rate

(kgmol/h)

Duty

(E+06

kJ/h)

Percentage of energy

saved compared to the

conventional methods

14 1.70784 21.8 %

16 1.87426 16.61 %

18 1.94611 13.41 %

20 2.07445 7.7 %

Figures 8 and 9 show the change in the

temperature and composition profile for the

following case: Flow rate of stream A is equal to

22 kgmol/h, flow rate of stream B is equal to

35.5 kgmol/h and number of stages is equal to

27. Tray inefficiency is clearly evident with a

constant temperature/composition profile

existing across sections of the overtrayed

column.

5. CONCLUSION

The use of thermally coupled distillation columns

has shown significant energy savings compared to

conventional distillation methods with values of

up to 22 % for a Petlyuk column in agreement

with Glinos et. al. [2]. The dynamic simulation

approach to thermally coupled columns has also

converging complex column configurations.

Although the design procedures established does

(a)

(b)

Figure 8: Temperature profile of the main

column (a) with the column overtrayed, and

(b) after removing the inefficient trays

Figure 5.4.1 : Temprature profile of the main column

( before reducing the excess trays )

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Number of stages

Tem

pera

ture

( o C

)

Figure 5.4.2 : Temperature profile of the main column

( after removing the inefficient trays )

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Number of stages

Tem

pera

ture

( o C

)

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Sudan Engineering Society Journal, March 2012, Volume 58; No.1

43

Mustafa, M. Abbas and Wilson, J.A.

(a)

(b)

Figure 9: Composition profile of hexane in the

main column (a) with the column overtrayed and

(b) after removing the inefficient trays

proved very successful as a method for

obtaining an initial design. HYSYS proved

very successful at not give a true optimum

design, due to the inconsideration of capital

costs, however it provides an idea of the

savings in energy offered by those columns and

takes the designer towards an optimum.

Furthermore, it was clear from the cases

investigated that the number of trays between

the positions of the 2 feed trays in the main

column roughly equalled the number of trays in

the pre-fractionator. Thus the pre-fractionator

could be constructed with the main column in a

single shell with an internal dividing wall. This is of

particular importance due to the fact that the

procedure already established for designing the

Petlyuk column could be extended for designing

the ultimate Divided-wall column.

References

1. Hernandez, S., A. Jimenez, Design of optimal

Thermally-coupled Distillation systems using

a dynamic model, Trans I Chem E, 74, 357-

362, 1996.

2. Glinos, K., M.F. Malone, Optimality regions

for complex column alternatives in

distillation systems, Chem. Eng. Res. Des.,

66, 229-240, 1998.

3. Triantafyllou, C., R. Smith, The design and

optimisation of fully thermally coupled

distillation columns, Trans IChemE, 70, 118-

132, 1992.

4. Hernández, S., J. G. Segovia-Hernández, V.

Rico-Ramírez, Thermodynamically

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Figure 5.4.3 : Composition profile of hexane

( with the column overtrayed )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

Number of stages

Mol

e fr

acti

on o

f he

xane

Figure 5.4.4 : Composition profile of hexane in the main column

( after removing the inefficent trays )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Number of stages

Mo

le f

ract

ion

of

hex

ane

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Sudan Engineering Society Journal, March 2012, Volume 58; No.1

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AN APPROACH TOWARDS THE DESIGN OF A PETLYUK COLUMN USING HYSYS

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