acet project final report

7/24/2019 ACET Project Final Report

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AC"NO8$E2EMENT

We take this opportunity to express our gratitude to have

been instrumental in the successful completion of the project. We take

this opportunity to thank Dr. Arvind Kumar Sharma, Assistant rofessor,

Department of !hemical "ngineering, #irla $nstitute of %echnology &

Science, ilani !ampus for giving us an opportunity to 'ork in the field

of polymer solutions and their activity coefficient predictions and

guiding us for the past one semester through the course of Advanced

!hemical "ngineering %hermodynamics that added valuable inputs for

the development of the project.

$t gives us immense pleasure to express profound gratitude

to (od Almighty for supporting us.

Page | 2



A1STRACT

)*$+)A! and )*$A! models are used to predict the activity

coefficient of a -apor/i0uid e0uilibrium of binary solution. %hese

models have proved to be consistent 'ith the practical results for the

binary solution but 'hen incorporated 'ith a -apor/i0uid e0uilibrium

of a polymer solution, these models prove to be inconsistent and

deviation is found to be significantly large. $n order to get a consistent

result, )*$A! model is further extended for a polymer solution using a

proposed relation bet'een the volume parameterr1n2 for an nmer

polymer and r132 of the monomer. )nlike the )*$A! model there is no

need for the free volume term, 'hich proves to be advantageous in the

extended model. %he extended model kno'n as )*$A!- model has

been used in this article for the prediction of activity coefficient of a

-apor/i0uid e0uilibrium.

Page | 3



T-9le of Contents

Section Contents P-ge No,

C.-0ter ' Introduction :

C.-0ter % UNIFAC Model )

C.-0ter ( UNIFA!7F! Model '%

C.-0ter ; C-lcul-tion of Activity of - Polymer Solution ';

C.-0ter : Results -nd iscussion %&

C.-0ter * $ist of Sym9ols %'

C.-0ter ) References %(

Page | 4



C.-0ter '

Introduction

A large part of chemical engineering design is concerned

'ith separation operations. 4any of these are diffusional operations of

the phasecontacting type, distillation, absorption, and extraction are the

most common. or rational design of such separation processes, 'e

re0uire 0uantitative information on phase e0uilibria in multicomponent

mixtures. Satisfactory experimental e0uilibrium data are only rarely

available for the particular conditions of temperature, pressure, and

composition re0uired in a particular design problem. $t is therefore

necessary to interpolate or extrapolate existing mixture data or, 'hen

suitable data are lacking, to estimate the desired e0uilibria from some

appropriate correlation. A very useful correlation for this purpose,

)*$A!, 'as proposed.

%he availability of solvent and polymer activity

coefficients is of great importance in the design and operation of

polymer processes. olymeri5ation often takes place in solvents, and it is

0uite important to kno' ho' the produced polymer 'ill distribute

bet'een the polymer rich and solventrich phases. $n such cases li0uid

li0uid e0uilibrium 1//"2 information is necessary, i.e., both polymer and

solvent activity coefficients. 6n the other hand, the removal of solvents

or nonpolymeri5ed monomers from the produced polymer re0uires the

kno'ledge of vaporli0uid e0uilibrium 1-/"2, i.e., the solvent activity

coefficients. #ut for olymer solutions, the result obtained for activitycoefficient by )*$A! deviates to greater extent 'hen compared 'ith

the practical results. So a modified model called )*$A!- model

'as made 'hich produces better results.

Page | 5



!-0or7$i<uid E<uili9ri-=

$t is a condition 'here a li0uid and its vapor are in

e0uilibrium 'ith each other so the rate of evaporation e0uals the rate of

condensation on a molecular level such that there is no net vaporli0uidinterconversion. $n theory e0uilibrium takes a very long time to reach

and is practically reached in a closed location if the li0uid and its vapor

are allo'ed to stand in contact 'ith each other 'ithout any interference

from outside.

Activity Coefficient=

4odified 7aoult8s la' results 'hen an activity coefficient,

is inserted into 7aoult8s la' on account of deviations from solution

ideality in /i0uid phase9

P yi : Pisat

x i γ i

Whereγ i is the activity coefficient, P is the total

pressure and P i

sat is the saturation pressure of component i and xi is the

mole fraction of component i.

#ubble point and de' point calculations made 'ith thise0uation are only a bit more complex than the same calculations made

'ith 7aoult8s la'. Activity coefficients are functions of temperature and

/i0uidphase composition, and ultimately are based on experiment.

Activity coefficients may be measured experimentally or calculated

theoretically, using the Debye; <uckel e0uation or extensions such as

Davies e0uation. Alternatively correlative methods such as )*$+)A!,

*7%/ or )*$A! may be employed, provided fitted componentspecific or model parameters are available.

Page | 6

http://en.wikipedia.org/wiki/Activity_coefficient

http://en.wikipedia.org/wiki/Partial_pressure

http://en.wikipedia.org/wiki/Pressure

http://en.wikipedia.org/wiki/Partial_pressure

http://en.wikipedia.org/wiki/Pressure

http://en.wikipedia.org/wiki/Activity_coefficient



C.-0ter %

Prediction of Activity using UNIFAC Model

UNIFAC Model=

%he )*$A! method 1)*$+)A! unctionalgroup

Activity !oefficients2 is a semiempirical system for the prediction of

nonelectrolyte activity in nonideal mixtures. )*$A! uses the

functional groups present on the molecules that make up the li0uid

mixture to calculate activity coefficients. #y using interactions for each

of the functional groups present on the molecules, as 'ell as some

binary interaction coefficients, the activity of each of the solutions can

be calculated. %his information can be used to obtain information on

li0uid e0uilibria, 'hich is useful in many thermodynamic calculations,

such as chemical reactor design, and distillation calculations.

%he )*$A! model 'as first published in 3=>? by

redenslund, @ones and rausnit5, a group of chemical engineering

researchers from the )niversity of !alifornia. Subse0uently they and

other authors have published a 'ide range of )*$A! papers, extending

the capabilities of the model. %he model is also called lattice model and

has been derived from a first order approximation of interacting

molecule surfaces in statistical thermodynamics. %he model is ho'ever

not fully thermodynamically consistent due to its t'o li0uid mixture

approach. $n this approach the local concentration around one central

molecule is assumed to be independent from the local composition

around another type of molecule.

Page | 7



Correl-tion=

%he method used is called group contribution method

'hich uses the principal that the simple structures of chemical

components are al'ays the same in many different molecules. %hesmallest common constituents are the atoms and the bonds. All organic

components for example are built of carbon, hydrogen, oxygen,

nitrogen, halogens, and maybe sulphur. %ogether 'ith a single, a double,

and a triple bond there are only ten atom types and three bond types to

build thousands, of components. %he next slightly more complex

building blocks of components are functional groups 'hich are

themselves built of fe' atoms and bonds. %he advantage of a group

contribution method is that it enables systematic interpolation and

extrapolation of vaporli0uid e0uilibrium data simultaneously for many

chemically related mixtures. 4ost important, it provides a reasonable

method for predicting properties of mixtures 'here no mixture data at all

are available. %he )*$A! correlation attempts to break do'n the

problem of predicting interactions bet'een molecules by describing

molecular interactions based upon the functional groups attached to the

molecule. %his is done in order to reduce the sheer number of binary

interactions that 'ould be needed to be measured to predict the state of

the system.

2rou0 Inter-ction P-r-meters=

(roup interactions are approximated in this method

because any group 'ithin a molecule is not completely independent of

the other. $ncreasing the distinction of groups also increases the number of group interactions that has to be characteri5ed. So if there are

increased numbers of interaction parameters, the advantage of group

contribution 'ill be lost. So one has to define the functional group by

Page | 8



experience and judgment to achieve a compromise bet'een accuracy

and simplicity of calculation.

T.e Model=

$n order to use the model, no experimental data are

re0uired for the particular mixture of interest. 6ne needs to kno' the

temperature and composition of the system and the molecular structure

of every component in the mixture and the necessary group parameters

must be kno'n.

"0uations giving the activity coefficients as functions of

composition and temperature are here stated. %he )*$A! model has a

combinatorial contribution to the activity coefficients, essentially due to

differences in si5e and shape of the molecules, and a residual

contribution, essentially due to energetic interactions.

ln γ i=ln γ iC +ln γ i

R

!ombinatorial 7esidual

Com9in-tori-l P-rt=

%he combinatorial contribution is

ln γ iC =ln

ϕi

x i

+ z

2q i ln

θ i

ϕi

+ li−ϕi

xi

∑ j

x j l j

li

:

ri−qi

z

2 ¿ 2;1

ri−1¿ ; z=10

θi= q i x i

∑ j

x j q j

;ϕi= r i x i

∑ j

x j r j

Page | 9



urecomponent parameters ri and <i are respectively measures of

molecular van der Waals volumes and molecular surface areas. %hey are

calculated as the sum of the group volume and grouparea parameters,

7 k and +k.ri=∑

k

vk (1)

Rk ; qi=∑k

vk (1)

Q k

Where vk 1l2, al'ays an integer, is the number of groups of type k in

molecule i. (roup parameters 7 k and +k are obtained from van der

Waals group volumes and surface area -k and Ak .

7 k : -k 3?.3> +k : Ak 1B.?C3E=2

Residu-l 0-rt=

%he contribution from group interactions, the residual part, is

assumed to be the sum of the individual contributions of each solute

group in the solution less the sum of the individual contributions in the

pure component environment.

ln γ i R=∑

k

v k

(1)[ ln Γ k −ln Γ k

(1 )]

All groups Fk is the group residual activity coefficient, and Fk1i2 is the

residual activity coefficient of group k in a reference solution containing

only molecules of type i. %he individual group contributions in any

environment containing groups of kinds 3,B ...* are assumed to be only

a function of group concentrations and temperature.

Page | 10



θmψ mk

θmψ nm

∑n

¿

θmψ km/¿

¿¿¿

∑m

¿−∑m

¿

1−ln ¿ln Γ k −Qk ¿

θm= Qm X m

∑n

Qn X n; X m=

∑i

vm

(1) x j

∑i

∑k

vk

(1) x j

Gm is the fraction of group m in the mixture.

Ψ mk : exp H1anm%2I

arameter anm characteri5es the interaction bet'een group8s nand m. or each group interaction, there are t'o parameters9 amn J anm.

*o ternary 1or higher2 parameters are needed to describe multi

component e0uilibria.

Page | 11



C.-0ter (

Prediction of Activity 9y UNIFAC7F! Model

UNIFAC7F! MOE$

A ne' model has been proposed by 6ishi and raunsnit5 for the

estimation of solvent activities in polymer solutions. %he approach is

based on a group contribution method1)*$A!2 'ith a free volume

correction.

Due to the limitations seen in the )*$A! model, one cannot use it in

the case of polymer solutions as it 'ill give greater deviation. According

to )*$A!- model, solvent activities are calculated as contributions

from three sources 'hich are9

• !ombinatorial

Page | 12



• 7esidual

• ree -olume term 1lory "6S2

So here it includes an extra term called free ; volume. %he combinatorial

and residual term can be calculated by -an der #erg method. %hat isusing the relation9

a

(¿¿ 1) R, C =ln γ 1+ϕ

2

' r1/r

2+ln x

1

ln ¿

Where r3 and rB are the molar volume parameters, and x

1 is given by

ϕ2

'

= P x

2r2

x1 r1+ P x2 r2

x1 :

w1 M

2

w1 M 2+w2 M 1

<ere '3 and 'B are the 'eight fractions of the solvent and polymer and

is the degree of polymeri5ation. %he value of lnϒ 3 is calculated using

the e0uations of redenslund. or calculation of combinatorial and residual part, the

correlations from )*$A! model are also applicable and those

correlations 'ill be used for the calculation in this article.

Free > !olume 0-r-meter=

or the free volume parameter, ln1a32fv is calculated from

flory8s e0uationstate theory of polymer solutions.

Page | 13



a

ln(¿¿1) !

¿¿

:

1− 1

! 1

1

3

¿¿

( !

1

! M −1

)¿

[ ! 1

1

3−1

! M

1

3−1]−C

1¿

C 1ln ¿

Where c3 is the reduced number of external degrees of freedom per

molecule, -3 is the reduced volume of the solvent, given by

! 1= ! 1

'

15.17" r1

'

And -m is the reduced volume of the mixture, given by

! M = ! 1

' w2+! 2

' w2

15.17" (r1

' w

1+r

2

' w

2)

-38 and -B8 are the specific volumes of the solvent and the

polymer, r 38 and r B8 are the volume parameters 1per unit mass2 as

calculated by )*$A!, and b is a proportionality factor of order unity.

6ishi and rausnit5 found that the agreement bet'een experimental and

calculated values is the best 'hen b e0uals 3.BL. %he e0uation is

temperature dependent implicitly, through the variation of the specific

volumes 'ith the temperature.

!ombining all the contributions, the correlation for the

model is stated as9

ln -' ? ln -'C @ ln -'r @ ln -'fv

'here ln a3! is the combinatorial term, ln a3

r $ the residual

term and ln a3fv is the free volume term.

Page | 14



C.-0ter ;

Prediction of Activity of 1enene in Polyiso9utylene

at B? ! 'hen the 'eight fraction of ben5ene is .3.

Solution

Com0onent

#

$ m %−3 M

M-in

2rou0

Su97

2rou0

Rk Qk No, of

2rou0s

#en5ene .L>M >L.33 A!< ACH .?3

.N

M

$# .=3M=?M.

>

C& 2 C .B3=

?. 3

C& 2

C& 2

.M>N

N

.?N

3

C& 2 C& 3 .=33

.LN

LB

!ombinatorial contribution

q1

' =

1

78.11 6 (0.400)=0.03073

' =

1

78.116 (0.5313 )=0.04081

q2

' = 1

56.07[1 (0 )+1 (0.540 )+2 (0.848 )]=0.03987

Page | 15



r2

' = 1

56.07 [1 (0.2195 )+1 (0.6744 )+2 (0.9011 ) ]=0.04808

θ1

' = 0.03073(0.1)

0.03073 (0.1 )+0.03987(0.9)=0.07888

∅1

' = 0.04081(0.1)

0.04081 (0.1 )+0.04808(0.9)=0.08618

ln 0.07888

0.08618−1+

0.08618

0.07888

(0.08618 )+(1−0.08618 )+10

2 (78.11)(0.03073)¿

lna1(=ln ¿

: 3.NL3

7esidual !ontribution9) *C& =0.1

) C& 3=0.9

15.025 (2 )56.07 =

0.4823

) C& 2=0.9

14.0169

56.07 =0.2250

) C =0.912.001

56.07 =0.1926

Q'

*C& =Q *C&

56.07=

0.4

13.0089=0.03075

Q'

C& 3

= QC& 3

15.025= 0.848

15.025=0.05644

Q'

C& 2=

QC& 2

14.0169=

0.540

14.0169=0.03853

Page | 16



Q'

C = QC

12.001=

0

12.001=0

θ'

*C& = Q

' *C& ) *C&

Q'

*C& ) *C& +Q'

C& 3

) C& 3

+Q'

C& 2

) C& 2

+Q'

C ) C

¿0.003075

0.03897 =0.07892

θ' C&

3

= Q

' C&

3

) C& 3

Q'

*C& ) *C& +Q'

C& 3) C& 3

+Q'

C& 2) C& 2

+Q'

C ) C

=0.02722

0.038970.6986

θ' C&

2=

Q' C&

2) C&

2

Q'

*C& ) *C& +Q'

C& 3) C& 3

+Q'

C& 2) C& 2

+Q'

C ) C

=0.008669

0.03897 0.2225

θ'

C& 2

= Q'

C ) C

Q'

*C& ) *C& +Q'

C& 3

) C& 3

+Q'

C& 2

) C& 2

+Q'

C ) C

=0

*ote that interaction parameters are only bet'een main

groups, and in this case there are only t'o main groups ; A!<

1ben5ene2 andC& 2 1

C,C& 2

¿ andC&

3 subgroups2 in $#. %his greatly

reduces the number of calculations for the residual contribution to the

activity of ben5ene as follo's9

Ψ *C& , C& 2 : exp

−a *C& ,C& 2

+ ¿

2 : exp111.12

298 2 : 3.L :ψ *C& ,C&

3

=ψ *C& ,C

ln Γ *C& : M *C& Q

' *C& H3ln1 θ

' *C& ψ *C& , *C& O

θ' C& 3ψ C&

2, *C& +θ' C&

2 ψ C& 2, *C& +θ' C ψ C,*C& ¿−

θ'

*C&

ψ *C& , *C&

θ'

*C& ψ *C& , *C& +θ'

C& 3ψ C& 3 , *C& +θ

'

C& 2ψ C& 2 , *C& +θ

'

C ψ C,*C& −θ

'

*C

θ'

C ψ *C & ,C

θ'

*C& ψ *C& ,C +θ'

C& 3

ψ C& 3, C +θ

'

C& 2

ψ C& 2, C +θ

'

C ψ C ,C

¿

Page | 17



¿0.400[1−ln (0+(0.2225∗0.8145 )+ (0.6986∗0.8145 )+0.07892 )− 0.07892 (1 )

0.07892 (1 )+0.6986 (0.8145 )+0.2225 (

ln Γ (1 )

*C& :

ln a1

R

: M 1.?M ; 2 : .BB

ree volume contribution9

v1=

1.145

15.17 (1.28 )∗0.048081=1.445

0.04081 (0.1)+0.04808(0.9)

¿15.17 (1.28 ) ¿

v M =1.1447 (0.1 )+1.0906 (0.9)

¿

lna1

! =3 (1.1 ) ln[ 1.445

1

3−1

1.1920

1

3−1

]−1.1[( 1.44501.1920−1)(1− 1

1.445

1

3 )−1

]=0.528

%otal activity of ben5ene9

lna

1=−1.483+0.302+0.528=−0.653 ; a

1=0.520

Page | 18



0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

x

Activity coefcient

Activity coefficient of olymer in the solution

Similarly, value of activity coefficient has been calculated for points at

x : .3, . and .? and the above result is then extrapolated for all the

values and plotted.

Com0-rison of t.e 0redictive -ccur-cy of t.e UNIFAC model -nd

t.e UNIFAC7F! model=

System%emperature

range K

*o. of data

points

AAD P

)*$A! )*$A!-

$#1N G 3N2 O

ben5eneB=L.B 33 B.>

$#1N G 3N2O

cyclohexaneB=L.B L BN.3 ?

$#1? G 3N2

O toluene B=L. 3 .N 3.B

Simulation of polymer solution in the -apor li0uid e0uilibrium

is done in Aspen soft'are and the deviation of activity coefficient 'hen

Page | 19



calculated by )*$A! model and )*$A!- model respectively,

from the actual value has been sho'n above.

So from the above table, it is inferred that the deviation of the

polymer solution under consideration 1$# O ben5ene2 from theexperimental result, is B.>P in case of )*$A! model and P in case

of )*$A!- model and hence )*$A!- model provides a better

estimate for the activity coefficient in polymer solution.

Page | 20



C.-0ter :

Results -nd Conclusions

RESU$TS

We have taken N polymer solution systems used to test the

proposed model, 'hich is compared 'ith the original )*$A! and Qthe

)*$A!-. $t should be pointed out that in our calculation the

parameters b and cR in the )*$A!- are set e0ual to 3.BL and 3.3,respectively, though they should be some'hat dependent on the system .

%he group volume and surface area parameters as 'ell as the group

interaction parameters for the three models 'ere taken from a number of

references. T.e -ver-ge -9solute devi-tions 5AAs6 for the activities

of solvents in polymer solutions are sho'n in %able. or most systems,

the )*$A!- sho's great improvement over the original )*$A!.

%he total AAD 'as 'B,) for the original )*$A! and ),; for the

)*$A!-. <o'ever, for several systems the improvement is not so

large. %he reason is that the original )*$A! model underestimates the

solvent activities in polymer solutions our modification applies some

correction to this.

CONC$USIONS

%he )*$A!- model proposed in this 'ork provides

accurate prediction of polymer solvent -/" and re0uires no additional

information over the original )*$A! model. %he predictive accuracy is

much better than the original )*$A! model. $t can be used for polymer

systems as long as the group parameters needed for the original

)*$A! model exist. Also 'e have that -ver-ge -9solute devi-tions

Page | 21



5AAs6 for the activities of solvents in the observed polymer solutions

sho's more improvement in the )*$A!- 4odel.

C.-0ter *

$ist of sym9ols

a Activity

n 4onomer number in a chain molecule

* *umber of experimental data points

arameter in "0. 1B2, T p T 3

0 Surface area parameter

r -olume parameter

v -olume

x 4ole fraction

5 !oordination number in "0. 12, set e0ual to 3

2reeD letters

U -olume fraction

V Surface area fraction

!onstant

F <ardsphere diameter

Su9scri0ts

3 Solvent

" "xcluded property

$ !omponent

Su0erscri0ts

Page | 22



C <ardcore value

c !ombinatorial term

calc. !alculated value

exp. "xperimental value

- ree volume term

7 7esidual term

Page | 23



C.-0ter )References

• luid hase "0uilibria 3B 1B?2 3M, !hongli Xhong a,

Yoshiyuki Sato a, <irokatsu 4asuoka a, Giaoning !hen, "lsevier.

• Aa. redenslund, @. (mehling and . 7asmussen, 3=>>. -apor

/i0uid "0uilibria )sing )*$A!, "lsevier.

• %. 6ishi and @.4. rausnit5, 3=>L. "stimation of solvent activities

in polymer solutions using a groupcontribution method. $nd. "ng.

!hem. rocess Des. Dev., 3>9 =.

• !. Antunes and D. %assios, 3=L. 4odified )*$A! model for the

prediction of <enryZs constants. $nd. "ng. !hem.

• @oel 7. ried, olymer Science and %echnology, Second "dition,

rentice <all of $ndia rivate limited, *e' Delhi.

Page | 24

acet project final report

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