Mdelling and Simu

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ABSTRACT

Modelling and Simulation of Reactive Distillation Columns

Reactive distillation (RD), simultaneous reaction and separation within a single unit,

representing an existing alternative to conventional reaction followed by separation

processes, leading to significantly reduction in initial investment and operating cost. The

modeling and simulation is done for both batch and continuous reactive distillation in the

production of ethyl acetate from ethyl alcohol and acetic acid. For the batch reactive

distillation done in 11 stages, the optimum reboiler heat duty is determined. For that

optimum reboiler heat duty, the dynamics of composition in reflux drum and reboiler is

studied until it reaches a steady state. In the continuous reactive distillation column the

reactants are fed at different trays, the optimum reboiler heat duty, feed plate location,

distillate flow rate, feed flow temperature are determined.

Keywords: Reactive distillation, modeling, simulation, ethyl acetate column.

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Chapter-1

1.1 Introduction and Literature survey

The combination of chemical reaction with distillation in only one unit is called reactive

distillation (RD). Reactive distillation has received increasing attention over the past

several years as a promising alternative to conventional processes. Although invented in

1921, the industrial application of reactive distillation did not take place before 1980s.

Especially, interesting equilibrium reactions suitable for reactive distillation are

esterification, ester hydrolysis reactions, etherification and transesterification. In recent

years, attention has been paid to ethyl acetate synthesis and hydrolysis, which serves as a

model for reactive distillation processes.

The performance of reaction with separation in one piece of equipment offers distinct

advantage over the conventional sequential approach. As a advantage of this integration,

chemical equilibrium limitations can be overcome, higher selectivities can be achieved,

the heat of reaction can be used for distillation, auxiliary solvents can be avoided and

azeotropic mixtures can be more easily separated than in conventional distillation. This

May lead to enormous reduction of capital and investments costs and may be important

for sustainable development due to lower consumption of resources. Some industrial

processes where reactive distillation is used are the esterification processes.

However reactive distillation is not suitable for every process where reaction and

separation steps occur. Operating conditions, such as pressure and temperature of the

reactive and separation processes and perhaps other requirements, must overlap in order

to assure the feasibility of the combined process. This limitation can be overcome by

fixing adequate operating conditions in the cases where this is possible.

In addition to the low capital investment, the RD column requires low operating costs

(energy, water, solvents, etc). however, the mathematical model for this piece of

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Chapter 2

Modelling and Simulation of Ethyl Acetate Reactive Distillation

Columns

2.1.Process Description:

2.1.1. For Batch Reactive Distillation Column:

The reboiler is fully charged, all the trays and the condensers are specified with

initial holdups. The reboiler is then heated. Vapor flows upwards in the

rectifying column and condenses at the top. The entire

condensate is returned to the column as reflux. This contacting

of vapor and liquid considerably improves the reaction. After

some time, a part of the overhead condensate is withdrawn

continuously as distillate and it is accumulated in the receivers,

and the other part is recycled into the column as reflux. Owing to

the differing vapour pressures of the distillate, there will be a

change in the overhead distillation with time.

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In the column the lighter (lower-boiling) component tend to concentrate in the vapor

phase, while the heavier (higher-boiling) components tend towards the liquid phase. The

result is the top product becomes richer in light components as the feed and the bottom

product becomes richer in heavy components as the feed.

Figure 2.2: Schematic ofa Continuous Reactive Distillation Column

The following is a reversible liquid phase reaction:

Acetic acid + Ethanol Ethyl acetate + Water

(1) (2) (3) (4)

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This is a two reactant- two product system. Among the two product water is the heaviest

one and it comes out as the bottom product. On the other hand, the main product, ethyl

acetate, comes out at the top section as the distillate product

2.2.Assumptions

Ethyl acetate RD column with trays numbered from bottom to top.

Liquid on the tray is perfectly mixed and incompressible.

Tray vapor holdups are negligible.

Variable liquid holdup in each tray.

No heat accumulation on each tray.

Vapor phase Murphree efficiency of 75% is considered.

Nonlinear Francis weir formula for tray hydraulics calculation.

Raoults law for vapor-liquid equilibrium.

2.2.1 Bubble point calculation

For solving the vapor rates i.e. the energy balance equation, one requires the enthalpy

data; and to calculate the enthalpy, the temperature should be known. Therefore, it is

necessary to have the temperature-composition correlation. The vapor phase composition

in equilibrium with the liquid phase is given by,

i i iy x =

where k is equilibrium ratio, for this study k is calculated as follows,

s

ii

t

Pk

P=

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where is Pis the vapor pressure was calculated by using Antoine equation, and Pt is the

total pressure.

The Antoine equation is given as,

expiB

P AT C

= +

Where A, B, C are the constants and T is the temperature. Here the pressure is in

mmHgand the temperature in C.

Step-wise bubble point calculation

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2.2.2. Enthalphy Calculations

Assume Temperature

Calculate equilibrium ratio

Calculate yi

using xi

Check(T) = = y

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The liquid and vapor enthalpies were calculated based on the following equations (Yaws,

1996). Here the Temperature is in (K) and the enthalphy is in (J/mol.K).

*vH Cp T = (2.2.2 1)

2 3 4

Cp A BT CT DT ET = + + + + (2.2.2.2)l vH H= (2.2.2.3)v v

i iH y H = (2.2.2.4)

( )

2

2

i

i

aRT

b T

= +

(2.2.2.5)

where viH = Enthalpy of Vapor

l

iH = Enthalpy of liquid

= Latent heat.

R=gas constant

A,B,C,D,E, =constants

a , b =B,C of Antonie constants.

2.2.3. Liquid flow rate Calculations

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For the calculation of liquid flow rates the Francis weir formula (L.Wang.et,al.

Computers and Chemical engineering 27 (2003) 1485 - 1497). Liquid flow rate is a

function of holdup, weir height, area of the tray and the volume held.

liq tray

j jif h h> (2.2.3.1)

1.5liq tray

j j

j weir liq

j

h h

L lvol

=

(2.2.3.2)

0jelse L = (2.2.3.3)

liq

j jliq

j

tray

M vol where h

A= (2.2.3.4)

Where jL = Liquid flow rate (mole/s)

weirl = length of the weir (m).

, = constants.

trayjh =Height of the weir (m)

j = mass holdup (mole)

liq

jvol = Volume of mass held in the tray (m3).

trayA = Area of the tray (m2).

2.2.4. Rate of reaction

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2.4.1 : Batch Reactive Distillation

0 2 4 6 8 10 120.87

0.88

0.89

0.90

0.91

0.92

0.93

0.94

0.95

0.96

After 500 min

Heat duty QR=10 5 J/min

PurityofethylacetateinRefluxdrum(

mole

Figure:2.3 Effect of Ethyl acetate purity in Reflux Drum due to Reboiler heat duty

The effect of ethyl acetate purity in reflux drum due to reboiler heat duty is shown above.

With less than 5*105 J/min, the vapor produced is very less and hence there is less

interaction between the upcoming vapor and down coming condensed liquid and the

purity is low. With heat duty more than 5*105 J/min the vapor produced is very high,

there is less xi in the reaction, hence the purity is decreasing. The optimum high purity is

produced when the reboiler heat duty is 5*105 J/min.

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0 100 200 300 400 500 600335

340

345

350

355

360

365

Time(min)

Temperature(K)

ReboilerReflux drum

Figure:2.4 Dynamics of Temperature Profile in Reboiler and Reflux drum

The dynamics of temperature profile in the reboiler and distillate shows that, initially

both the temperatures are at the same point, as all trays including the reboiler and the

reflux drum have the same composition. As the heat is supplied from the reboiler the

heavier component (acetic acid and water) moves down from the reflux drum and the

lighter component (ethyl acetate and ethanol) moves up from the reboiler. Hence the

temperature of the distillate decreases and reaches steady state. While the reboiler

temperature decreases because of the removal of the lighter components and gradually

increases due to the addition of liquid component from the upper plates

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-50 0 50 100 150 200 250 300 350 400 450 500 550-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Compositioninrefluxdrum(

Time(min)

Aceticacid

Ethanol

Ethyl acetate

Water

0 100 200 300 400 500 6000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Reboilercomposition(molefr

Time(min)

Aceticacid

Ethanol

Ethyl acetate

Water

Figure 2.5. Start profile of Composition in Reflux drum and Reboiler respectively

The dynamics of the composition profile in the reflux drum in total reflux condition

during the initial start up is shown above. In the reflux drum the mole fraction of acetic

acid and water are decreasing since they are heavier components. The ethanol fraction

increases due to the addition of ethanol fractions from the bottom plates and then

decreases due to reaction.In the reboiler, the ethanol and acetic acid are decreasing and

the ethyl acetate and water are gradually increasing due to the reaction.

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2.4.2 : Continuous Reactive Distillation

1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.850.455

0.460

0.465

0.470

0.475

0.480

0.485

0.490

0.495

0.500

EthylacetatecompositioninDistillate(mol

Heat Duty in Reboiler (*106 J/min)

Figure:2.7 Effect of Ethyl acetate purity in Distillate due to Reboiler Heat Duty

The effect of ethyl acetate purity in distillate flow rate due to reboiler heat duty shows

that for the fixed feed flow rate of 25 gmole/min for ethanol and acetic acid given in 5 th

and 16th

feed plate respectively, when the reboiler heat duty was less than 1.5*106

J/min,the bottom flow rate was less than 25 gmole/min. For greater than 1.8*106 J/min of heat,

the bottom flow rate went more than 25 gmole/min. Within 1.5 and 1.8 *10 6 J/min, the

bottom flow rate was 25 gmole/min. The purity of ethyl acetate was high when the heat

duty was 1.5*106 J/min.

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295 300 305 310 315 320 325 330 3350.468

0.470

0.472

0.474

0.476

0.478

0.480

0.482

0.484

Ethylaceta

temolefractionindis

Temperature(K)

Figure 2.8 Effect of Ethyl acetate purity in Distillate due to Feed temperature

The effect of ethyl acetate purity in distillate due to feed temperatureis shown above.

When the feed temperature is increased from 298 K the purity is decreasing, because the

assumption is that the reaction completely takes place in liquid phase only.

8 10 12 14 16 18 20 22 24 260.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

Ethylacetatemolefr

actionind

DistillateFlowrate(gmole/min)

Figure 2.9. Effect of ethyl acetate purity of distillate due to distillate flow rate

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8 10 12 14 16 18 20 22 24 268.0

8.5

9.0

9.5

10.0

10.5

11.0

11.5

12.0

12.5

Amountofethylacetateindistillat

DistillateFlowrate(gmole/min)

Figure 2.10 Effect of amount of ethyl acetate in the distillate due to distillate flow rate.

Figure 2.9 and 2.10 depicts the effect of distillate purity and amount of distillate due to

distillate flow rate respectively. When the distillate flow rate is reduced, the reflux flow

rate increases, hence the residence time increases and the conversion increases followed

by the increased purity in the distillate. But this increased purity reduces the amount of

ethyl acetate in the distillate flow rate.

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.50.48

0.49

0.50

0.51

0.52

0.53

0.54

0.55

0.56Acetic acid plate=16

Ethylacetatemolefractionindistillate

Feed Plate location for ethanol

Figure.2.11. Effect of Feed plate location for Ethanol

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15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.50.550

0.552

0.554

0.556

0.558

0.560

0.562

0.564

0.566

0.568

0.570Ethanol feedplate=2

Ethylacetatemolefractionindis

Acetic acidfeedplatelocation

Figure:2.12 Effect of Feed plate location for Acetic acid

The effect of feed plate location for ethanol and acetic acid are shown above in figure

2.11 and 2.12 respectively. When the location of the feed plate for ethanol is brought

downwards from 5th to 2nd, the reaction zone increases, hence the purity of ethyl acetate in

distillate increases. On the other hand, for the feed plate location of acetic acid is moved

upwards from 16th to 19th, the purity increases upto 18th and then decreases. This is due to

the fact that upto the 18th plate there is more reaction zone, when added on to 19 th plate

acetic acid goes into the distillate flow rate and reduces the purity.

-500 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distillatecomposition(molef

Time(min)

AceticacidEthanolEthyl acetateWater

Figure 2.13: Startup profile of distillate composition

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-500 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Dynamics of bottomcomposition

Bottomcompos

ition(molefraction)

Time (min)

Acetic acid

Ethanol

Ethyl acetate

Water

Figure 2.14. Startup profile of bottom composition

The startup profile of distillate and composition is illustrated in the figure 2.13 and 2.14

respectively. In the reflux drum the ethanol mole fraction reaches a maximum due to the

addition from the trays below, then it reaches a steady state. Ethyl acetate on the other

hand reaches a maximum due to formation and goes with steady state. Acetic acid and

water mole fractions are decreasing because they are removed from the reflux drum to the

reboiler. In the reboiler initially the due to the reaction the ethyl acetate and water mole

fraction is increasing. Ethyl acetate and ethanol are removed to the top, hence they are

decreasing. The acetic acid and water are increasing and reaching to a steady state

because of their higher boiling point.

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-2 0 2 4 6 8 10 12 14 16 18 20 22340

345

350

355

360

365

370

375

Tem

perature(K)

TrayNumber

Fig 2.15: Temperature profile along the length of the column

The temperature profile along the length of the column illustrates three distinct regions,

the stripping zone, reaction zone and the rectifying zone. In the reaction zone between to

plate 2 and 18, the temperature is almost the same with slight variation. In the rectifying

zone the temperature decreases due to the removal of heavier component. In the stripping

section the temperature increases due to the heat from the reboiler.

0 2 4 6 8 10 12 14 16 18 20 22

0.0

0.1

0.2

0.3

0.4

0.5

0.6

molefraction

Platenumber

Aceticacid

Ethanol

Ethyl acetate

Water

Figure 2.16: Composition profile along the length of the column

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The composition profile along the length of the column illustrates that the acetic acid is at

the highest in its feed plate, decreases along the reaction zone due to reaction. It increases

in the stripping section due to its higher boiling point and decreases in the rectifying

section due to its removal. Ethanol likewise is high at its feed plate, decreases upto the

end of the reaction zone, then increases in the rectifying zone and decreases in the

stripping section due to its boiling point. Ethyl acetate and water are varying linearly in

the reaction zone due to the reaction, in the rectifying section the ethyl acetate increases

more rapidly, water mole fraction falls due to the adding and removal of lighter and

heavy component respectively. In the stripping section the water increases and ethyl

acetate mole fraction decreases due to the adding and removal of heavy and lighter

components respectively

0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.250.556

0.558

0.560

0.562

0.564

0.566

0.568

0.570

Ethyla

cetateinDistillate(mole

moleratio(ethanol/aceticacid)

Fig:2.17: Effect of mole ratio of the feed (ethanol: acetic acid)

The effect of mole ratio of the feed (ethanol: acetic acid), the conversion is more when

there is equal mole ratio for the ethanol and acetic acid feed. The conversion decreases if

the mole ratio is varied.

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-500 0 500 1000 1500 2000 2500 3000 3500 4000 4500-5

0

5

10

15

20

25

30

35

40

45

Flowrate(gm

ole/min)

Time (min)

Distillate flowrate

Bottomflowrate

Fig 2.18: Dynamics of distillate and bottom flow rate

The startup profile of distillate and bottom flow rate is shown above. The distillate flow

rate is fixed as 25 gmole/min. The bottom flow rate is initially increases, oscillates and

then reaches steady state. Initially the value was high because the not enough vapors were

produced to boil the feed.

Following results are not included

1. Effect of feed flow rate keeping molar ratio fixed (F1=F2)

2. Dynamics response with respect to QRor F

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2.4. Conclusions

The study includes the development of equilibrium stage model for multistage

component batch and continuous. In the batch process the purity is nearly 95%. During

the production phase the purity is decreasing, so a control action is to be taken. The study

done for continuous reactive distillation reveals that for the feed flow rate of 50

mole/min, the reboiler load should be 1*10^6 J/min, feed plates are 2 and 16 for ethanol

and acetic acid respectively. Feed need to be cold feed. molar ratio of the two feeds

should be 1.0. the steady state reaches in nearly 1500 min.

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Table 1

Antonie Constants: Unit of vapor pressure and temperature

Component A B C

Acetic acid 16.8080 3405.57 -56.34Ethanol 18.912 3803.98 -41.68

Ethyl acetate 16.1516 2690.52 -57.160

Water 18.3086 3816.44 -46.19

Table 2

Constants for vapor enthalphy: Unit of Cp and temperature

Components A B C D E

Acetic acid 34.85 3.7626*102 2.83*10-4 -3.0*10-7 9.2*10-11

Ethanol 27.091 1.10*10-1 1.09*10-4 -1.5*10-7 4.6*10-11

Ethyl acetate 69.848 8.23*10-2 3.71*10-4 -4.1*10,-7 1.2*10-10

Water 39.933 -8.4*10-3 2.99*10-5 -1.7*10-8 3.6*10-12

Table 3

Molecular weight and Density

Component Molecular weight (gm/gmole) Density (kg/m3

)Acetic acid 60.052 1049

Ethanol 46.069 791.8

Ethyl acetate 88.107 668

Water 18 1000

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Notation

s

BM =Liquid holdup in reboiler (mol)

DM =Liquid holdup in reflux drum (mol)

nM = Liquid holdup in tray n (mol)

Tn =Top most tray.

D =Distillate flow rate (gmole/min)

B =Bottom flow rate (gmole/min).

BV =Vapor from the reboiler (gmole/min).

TVn =Vapor in top most tray (gmole/min)

TLn =Liquid in top most tray (gmole/min).

nL =Liquid from nth tray

nV =Vapor from nth tray.

,B iy = Vapor mole fraction in reboiler

,B ix =Liquid mole fraction in reboiler.

,D ix =Liquid mole fraction in distillate.

,n ix =Liquid mole fraction in stage n.

,n iy =Vapor mole fraction in stage n.

l

nH = Liquid enthalpy in stage n.

vnH =Vapor enthalpy in stage n.

F=Feed flow rate (gmole/min).l

fH = Enthalpy of feed

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Modelling Equations of batch or continuous RD

Mass Balance:

Reboiler

1B

B

dML V B

dt=

Plate 1

1

2 1 1B

dMV L V L

dt= +

Plate 2 to below top plate

1 1n

n n n n

dMF V L V L

dt +

= + +

Top most plate

1T

T T T

dMn Lo V L V n n ndt

= +

Reflux drum

D TdM

V Lo Dndt

=

Component balance:

Reboiler:

4

,

1 1. , , , ,

1 1

( ) cB B ii B B i B i f m n m n n

m i

d M xL x V y Bx r R

dt= =

= +

Plate 1

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4

1 1,

, 2 2 1 1, 1 1, , ,

1 1

( ) ci B B i ,i i i f m n m n n

m i

d M xV y L x V y L x r R

dt= =

= + + Plate 2 to below top plate

4,

, 1 1, 1 1, , , , ,

1 1

( ) cn n in n i n n i n n i n n i n n i f m n m n n

m i

d M x

F x V y L x V y L x r Rdt + +

= == + + + Top most plate:

4

,

, , ,1 1, , ,

1 1

( ) cT T i

D i f m n m n nT T i T T i T T i

m i

d M xn nLox V y L x V y r Rn n n n n n

dt

= =

= + +

Reflux drum

4,

, , , ,,

1 1

( ) cD D iD i D i f m n m n nT T i

m i

d M x V y Lox Dx r Rn ndt

= =

= +

Energy Balance

Reboiler:

1 1

( )l l v lB B B B B R

d M HL H V H BH Q

dt= +

1 1( )l lR B

B v

B

L H Q BH V

H

+ =

Plate 1

1 12 2 1 1 1 1

( )l v l v l B B

d M HV H L H V H L H

dt= +

2 2 1 111

v l l

B B

v

V H L H L H V

H

+ =

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R. Taylor , R. Krishna, Modelling reactive distillation, Chem. .Eng. Sci. 55 (2000)

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Lin Wang, Pu Li, Gunter Wozny, Shuqing Wang , A startup model for simulation of

batch distillation starting from a cold state, Computers and chemical engineering 27

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Nishath Vora and Prodromos Daoutidis , Dynamics and control of an ethyl acetate

reactive distillation , Ind. Eng. Chem. Res. 40 (2000) 833 -849.

Rosendo Monroy-Loperena and Jose Alvarez - Ramirez, Output feed-back control of

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