Polymerization Reactors and Processes - American Chemical Society

13 The Anionic Solution Polymerization of Butadiene in a Stirred-Tank Reactor J. G . M O O R E , M . R. W E S T , and J. R. B R O O K S

Downloaded by CORNELL UNIV on July 25, 2016 | http://pubs.acs.org Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch013

Department of Chemical Engineering, University of Leeds, U . K . L S 2 9JT

The research programme i n t o n-butyl l i t h i u m i n i t i a t e d , a n i o n i c polymerization started a t Leeds i n 1972 and involved the c o n s t r u c t i o n o f a p i l o t s c a l e , continuous s t i r r e d tank r e a c t o r . This was operated i s o t h e r m a l l y , t o o b t a i n data under a t y p i c a l range o f i n d u s t r i a l operating c o n d i t i o n s . Mathematical models o f the r e a c t i o n system were developed which enabled p r e d i c t i o n o f the molecular weight distribution (MWD). D i r e c t and i n d i r e c t methods were used, but only d i s t r i b u t i o n s obtained from moments are described here. Due to the s t i f f n e s s o f the model equations an improved numerical i n t e g r a t o r was developed, i n order to solve the equations i n a reasonable time scale. I t has been p o s s i b l e to o b t a i n a good measure o f agreement between the experimental r e s u l t s , and those p r e d i c t e d by even a simple mathematical model o f the system, assuming i d e a l s t i r r e d tank behaviour. One t y p i c a l r e s u l t i s presented here. D e s c r i p t i o n o f the Experimental System. The experimental i n v e s t i g a t i o n used a 3 l i t r e m i l d s t e e l CSTR designed and constructed w i t h i n the department o f Chemical Engineering at Leeds U n i v e r s i t y and depicted i n F i g . 1, which was capable o f operation at temperatures up to 423K and pressures up to 9 bar. This was f i t t e d with a s i n g l e h e l i c a l ribbon impeller d r i v e n at 60 r.p.m., to ensure good mixing o f the r e a c t o r contents. The r e a c t o r could be heated by use o f e l e c t r i c a l h e a t i n g tapes wound round i t s e x t e r n a l surface and cooled by a flow o f water through an internal c o i l . The r e a c t o r was f u l l y instrumented with r e s p e c t t o process c o n d i t i o n s , the instruments being i n t e r f a c e d to a computer system, to allow o n - l i n e data a c q u i s i t i o n , and e v e n t u a l l y c o n t r o l . The r e a c t o r pressure was measured by a force balance transducer. Two thermocouples measured the temperature o f the r e a c t a n t s a t the top and bottom o f the r e a c t o r . The i m p e l l e r design r e q u i r e d that the thermocouples entered the r e a c t o r through i t s base p l a t e , together with the cooling c o i l . The reactant volume was measured

0-8412-0506-x/79/47-104-281$05.00/0 © 1979 American Chemical Society Henderson and Bouton; Polymerization Reactors and Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

POLYMERIZATION REACTORS AND PROCESSES


282

Henderson and Bouton; Polymerization Reactors and Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


13. MOORE ET AL.

Reactant Reservoir

Potassium Hydroxide

Anionic

Butadiene

Polymerization

Molea Sieve

Figure 2.

System

flowsheet


283


284


by a d i f f e r e n t i a l pressure transducer, and was c o n t r o l l e d from the computer by means of a s o l e n o i d valve i n the o u t l e t l i n e . The experimental r i g was constructed to minimise the chance o f reactant contamination by oxygen and moisture. The feed s o l u t i o n s were made up i n storage v e s s e l s capable of withstanding 11 bar. High pressure nitrogen was used to d r i v e the s o l u t i o n s i n t o the r e a c t o r , e l i m i n a t i n g the opportunity f o r i m p u r i t i e s to seep through the packings o f any pumps. The monomer feeds passed through towers c o n t a i n i n g potassium hydroxide, which removed the i n h i b i t o r . Then they were driven through d r y i n g towers c o n t a i n i n g molecular sieve type 4A, a f t e r which t h e i r moisture contents were monitored by a continuous hygrometer. The feed flows were measured using rotameters, f i t t e d with f l o a t f o l l o w i n g d e v i c e s , which enabled the flowrate to be transmitted to the computer. The solvent was recovered from the polymer cement by steam s t r i p p i n g , followed by the s e p a r a t i o n o f the o r g a n i c l a y e r . I t was then p u r i f i e d i n a small batch s t i l l , i n c o r p o r a t i n g a packed column and d r i e d by passage through a bed o f molecular s i e v e , before being returned to the storage v e s s e l s . Operating Conditions and Experimental Methods The experimental programme was mainly concerned with estimating kinetic parameters from i s o t h e r m a l steady state operation o f the reactor. For these runs, the r e a c t o r was charged with the r e a c t a n t s , i n such proportions that the mixture r e s u l t i n g from t h e i r complete conversion approximated the expected steady s t a t e , as f a r as t o t a l polymer concentrations was concerned. In order to conserve reactants, the r e a c t o r was r a i s e d to the operating temperature i n batch mode. When t h i s temperature had been attained, continuous flow operation commenced. This was maintained f o r s e v e r a l residence times. Runs were c a r r i e d out at 363K, 384K and 393K using monomer feed c o n c e n t r a t i o n s o f between 5 and 25%. The i n i t i a t o r feed concentration was maintained around .01 mol/1. Residence times v a r i e d from 60 to 120 minutes. In p r a c t i c e the reactant volume was maintained at 2.7 1, as t h i s improved the controllability of the system. During experimentation the process c o n d i t i o n s were recorded a u t o m a t i c a l l y , while the feed s o l u t i o n s , and the r e a c t o r contents were sampled approximately every hour during the flow r e a c t o r operation phase, and subsequently analysed o f f - l i n e . The monomer feed streams were analysed by g a s - l i q u i d chromatography. The i n i t i a t o r feed was determined by t i t r a t i o n using the method o f Gilman Samples of the r e a c t o r contents were quenched with methanol and the polymer p r e c i p i t a t e d with acetone. The polymer content was determined g r a v i m e t r i c a l l y and i t s molecular weight d i s t r i b u t i o n by g e l permeation chromatography. The microstrueture was determined using i n f r a - r e d absorption techniques.


13.

MOORE ET AL.

Anionic

Butadiene

Polymerization

285

The Framework f o r the Mathematical Modelling Important features o f the modelling work are the means o f i n t e g r a t i o n o f the model equations and the method o f regenerating the dynamic polymer d i s t r i b u t i o n from i t s moments. The framework provided by t h i s approach makes i t p o s s i b l e to produce models with few assumptions about the model behaviour. The i n t e g r a t o r that has been developed i s designed f o r the s o l u t i o n of s t i f f systems o f o r d i n a r y d i f f e r e n t i a l equations (ODEs) since the d i f f e r e n t i a l equations f o r the higher moments introduce c o n s i d e r a b l e s t i f f n e s s i n t o the system. The i n t e g r a t o r uses Gear's method (2,3,4), an. i m p l i c i t p r e d i c t o r - c o r r e c t o r a l g o r i t h m . The implementation has been shown to be more e f f i c i e n t than other implementations of Gear s method (3). The i n t e g r a t o r can be accessed through s e v e r a l d i f f e r e n t subroutines which give the user varying degrees of c o n t r o l over the f a c i l i t i e s a v a i l a b l e , the o b j e c t i v e being to make the i n t e g r a t o r at once easy to use, yet f l e x i b l e enough f o r the most demanding user. Such f l e x i b i l i t y i s important f o r the s o l u t i o n o f the type o f model considered here, since development can occur around the model equations rather than around the l i m i t a t i o n s of the numerical i n t e g r a t o r . Methods f o r generating d i s t r i b u t i o n from moments have been a v a i l a b l e since the l a s t century. They were used o r i g i n a l l y as a method o f f i t t i n g a d i s t r i b u t i o n curve through poor data, but they are e q u a l l y well suited f o r generating a curve d i r e c t l y from the moments. Two types o f curve have been f i t t e d to the moments. The f i r s t o f these i s the Pearson D i s t r i b u t i o n (5), a curve which i s described by the d i f f e r e n t i a l equation


f

d£ dx

x

=

~

b

" + b„x + c 1

a

(1) b x 2 0

The second method that has been developed i s the Laguere Polynomial, which w i l l be more f a m i l i a r from i t s use by Bamford and Tompa (6). Both methods have advantages. The Laguere Polynomial has the advantage that i t can be used to f i t almost any curve. The disadvantages are that i t can never give the exact d i s t r i b u t i o n , even where one could be given, and unless the shape i s c h a r a c t e r i s t i c o f a Laguere Polynomial, convergence can be slow. The Pearson D i s t r i b u t i o n has the advantage o f g i v i n g the exact d i s t r i b u t i o n i n a number o f cases, and i t only r e q u i r e s four moments. However, f o r d i s t r i b u t i o n curves that are not o f the Pearson Type, completely erroneous curves may be generated. A c h a r a c t e r i s t i c o f both types o f curve i s that the e r r o r i s predominantly i n the t a i l s o f the distribution. Where these methods give good agreement on the d i s t r i b u t i o n curve, confidence can be placed i n the r e s u l t . The m u l t i p l e reactor c a p a b i l i t y allows the modelling o f up to f i v e CSTRs connected i n any p o s s i b l e c o n f i g u r a t i o n . This i s achieved by simple mass and energy accounting, with the user



286

supplying the required stream s p l i t s . I t w i l l be noted that the same model can be used f o r i n v e s t i g a t i n g the e f f e c t o f poor mixing w i t h i n a s i n g l e reactor. A Model o f an Anionic Polymerisation The r e a c t i o n scheme considered

System i n t h i s model i s described

Rate o f i n i t i a t i o n = k£(RLiJ* [M] Rate o f propagation = k^(RLi]£


This complex rate expression type ^

(RLi) ^nRLi n

RLi + M

(1)

(M]

(2)

can be used to model r e a c t i o n s o f the

A

- - p i f e ^ J

R.M.Li

Rate. = ( k . ^ / n ) [ R L i ] J n

k

i

=

V^A*'

'

1 1

by

x

/ N

(4)

[M]

(5)

= 1/n

,

(6)

i f i t can be assumed that the rate o f exchange between associated i n i t i a t o r and ' a c t i v e ' i n i t i a t o r i s high r e l a t i v e to the o v e r a l l rate of i n i t i a t i o n . I t can a l s o be used as i t stands as a complex rate equation f o r systems where the mechanism i s more complex. The propagation rate expression can be used to d e s c r i b e simple d i s s o c i a t i v e schemes o f the type (PLi)

nPLi

n

K

[(PLDJ

>RM

n

(7)

p A

= Jadl

P A

RM L i + M

K

,Li

k

n+1

(8) p

Here the rate o f propagation can be expressed as Rate = p

k

(

k p n

p

K^n)[PLij;

= k K^ /n p

,

/ n

[M]

y = 1/n


(9) (10)

MOORE ET AL.

13.

Anionic

Butadiene

287

Polymerization

Mass Balance on I n i t i a t o r F_

.1 , J

I

Mass o f i n i t i a t o r entering i n the i n l e t stream f o r

U

reactor j .

J

Q 0

Mass o f i n i t i a t o r e n t e r i n g r e a c t o r j from other r e a c t o r s .

I.F

Mass o f i n i t i a t o r l e a v i n g r e a c t o r j .

V.I^M.k_(T.) = Rate J

J

J

J

I

V


7T J J dt

>

.V.— Mass o f i n i t i a t o r consumed by i n i t i a t i o n reaction i n reactor j .

T

, J

J

+

= F -In I,j0

. + I .F . - V.Rate , 00,j j R,j j I,j

T

D

(11)

T

Since Vj i s constant, =

(

F

^

J

I

^

I

^

-

I

J

F

^

/

Y

-rat

J

e i < J

(

1

2

)

Mass Balance on Monomer F

.M

M

M

mass o f monomer e n t e r i n g r e a c t o r j i n the i n l e t

.

stream.

mass o f monomer e n t e r i n g r e a c t o r j from other r e a c t o r s .

uu, j F_

.M.

mass o f monomer l e a v i n g r e a c t o r j .

3

V . I ^ .k-(T .) = V.Rate J

J

J

1

J

J

i

,

. mass o f monomer consumed i n i n i t i a t i o n reaction.

T

J

v • V.M.Ui.k (T.) = V.Rate

. — m a s s o f monomer consumed i n propagation reaction

p

J

J

U

J

J

OT JV M

P

F

,

J

M

- M,j 0

+

M

0 0 , J " R,J J - V ^ I J F

M

V

a t e

p,J (13)

o T ^

F

M

= < M,j 0

+

M

F

M

00,j- R , J j

) / V

j -

R

a

t

e

I,j *

R a t 6

p,J (14)

Mass Balance on Polymer P . — P o l y m e r o f chain length n from other r e a c t o r s (mass) 00, n, j , . , ' ' entering reactor j . nrk

F

.P

.—mass o f polymer l e a v i n g r e a c t o r j o f chain

length



288 V.P J

.M.k (T.)-mass o f polymer o f chain length n destroyed n,j

F

j

j

i

R

n

E

A

C

T

O

J

R

B

V.M.P* .k (T.) —mass o f polymer o f chain length n created J J n-l,j P j j i

n

r

e

a

c

t

o

r

#

P

concentration o f polymer

(total).

P*

concentration o f polymer

(unassociated).

For n greater than 1:


^

( P

=

n,jV

P

00,n,j "

F

R,j 1,j P

+

" Y n , j W V o t ^ ^

•

( P

F

)

= P

00.n.i ~ R A , i

Y

)

/

^

V

j

W

P

j

(

V

" n,

W

1

5

)

V

For n=1 ^

(

V l , J

Sjr

( p

i.j

}

=

F

P

00,1,J- R,J 1,J

( p

oo,i,r

F

p

R,j i,j

+

) / v

V

j

+

a

t

e

R

I , J

a

t

e

i , j

-V.P* ,M.k (T.) J >>J J P J

(18)

Polymer Moments D e f i n i n g the moments by, U

.=* p

n

.

(19)

u\ . = * nP . 1iJ n n,j

(20)

= * n-p . n n,j

U, 1J

A

(21)

H

3

.

n


/ x 0 0

(^ 22

MOORE ET AL.

13.

Anionic

Butadiene

289

Polymerization

from ( 1 6 ) and ( 1 8 ) one can obtain

f

+

( n + l ) l

( P

(

F

00,n 1

P

" R,J n,j

+

) / V

j *

P

S,J J p J> M

( T

k

P* , ,.M.k P*.« M , k _((TT.j j n+1,j j p J

(23)

Rearranging


f l . j

. Rate^ - ( R ^ / V . ^ / p ^

• =

R

a

t

i , J -

e

S ( F

^

R,J

/ V

W

- ij jVV u

) U

J

M

+

V

i,J (

> f +

+

ifeo

U

(

oo,i,j

i

)

u

(^P

+

(

n

/ v

j

!-i,j

)

*

M

1

)

k

j P

l

(

(

T

0

>

S ,

p

j

0

n

j

J

j

W

T

j

)

)

°

( 2 1

(

2

5

)

Now assuming that the r a t e o f exchange between a s s o c i a t e d and unassociated polymer chains i s r a p i d , compared t o the r a t e o f propagation, then the d i s t r i b u t i o n o f the a c t i v e polymer, w i l l be e q u i v a l e n t to the t o t a l polymer d i s t r i b u t i o n . I.e. U» . U., . iJ 0,J 0,j 1

N o w

3

u

8,j

K y

=

( u

i,/ oj> u

" °1.J ° 0 J

T

h

U

S

f l , J

=

+

(

y PA°u,j

•

0

(26)

Rate

^

I ( j

( U

u

y K

o,j

2

7

)

j

/j

j V V


(

3

0

)


290

= Rate_ . - (F ./V.) U. . + U . ./V. IiJ R,J J 1,J 00,l,j j n n

- /0

1,J

U*-\j

0,J

(J)(U,

M.k'(T.) + C \ J p J

l

. . uy*1)7 1-1,J 0,J

M,k'(T.) where (\) i'

(3D

1

"

' i!(l-i)!


Comparison o f Experimental

and Simulation

Results

The s i m u l a t i o n r e s u l t s depicted i n F i g s . 3 and 4 were obtained by i n t e g r a t i n g equations 12, 14 and 31 using the data i n Table 1 to time one m i l l i o n seconds.

Table 1:

Data f o r Simulation

Parameter

Value

I n i t i a t o r Feed Concentrations

0.0914 kgm "

Monomer Feed Flowrate

2.782 kgm "

M

3

0 7

F

3

0.667 x 10" m /s

I,J 6

F

3

0.583 x 10~ m /s

M,j

Reactant Volume

0.0027 m

Reactor Temperature Propagation Constant

I

3

0

Monomer Feed Concentrations I n i t i a t o r Feed Flowrate

Symbol

Rate

I n i t i a t i o n rate Constant

3 V

J T

384 K

i .296

m

3

1

(kg-mol)" s~

k

1

P t

-4 V2 1.95 x 10 n r ^ k

I

(kg-mol) ~* s""*

The e a r l y experimental p o i n t s i n the c o n c e n t r a t i o n chain length d i s t r i b u t i o n ( F i g . 3) may be i n a c c u r a t e . They are c a l c u l a t e d from the weight d i s t r i b u t i o n obtained from the GPC. The concentration chain length d i s t r i b u t i o n i s a f u n c t i o n o f the weight chain length d i s t r i b u t i o n and the inverse o f the chain length. Hence any e r r o r i n the p o i n t s i n the weight chain length d i s t r i b u t i o n i s exaggerated.


MOORE ET AL.

Anionic

Butadiene

Polymerization


13.


291



292


13.

MOORE ET AL.

Anionic

Butadiene

293

Polymerization

I t can be seen that the t h e o r e t i c a l and agree w e l l . The means a l s o concur.

experimental curves

Conclusions The described experimental r i g f o r the a n i o n i c p o l y m e r i s a t i o n of dienes has been shown to behave as an i d e a l CSTR. The mathematical model developed allows the p r e d i c t i o n o f the MWD at f u t u r e points i n the r e a c t o r h i s t o r y , once s u i t a b l e k i n e t i c parameters have been estimated.


Abstract A p i l o t s c a l e plant, i n c o r p o r a t i n g a three l i t r e continuous s t i r r e d tank reactor, was used f o r an i n v e s t i g a t i o n i n t o the n-butyl l i t h i u m i n i t i a t e d , a n i o n i c p o l y m e r i z a t i o n o f butadiene i n n-hexane solvent. The r i g was capable o f being operated at elevated temperatures and pressures, comparable with i n d u s t r i a l operating conditions. Mathematical models of the reaction system have been developed, enabling prediction of the molecular weight d i s t r i b u t i o n , based on the experimental data obtained from the pilot plant using on-line computer techniques. Results of s i m u l a t i o n studies are compared with a c t u a l p l a n t runs, and show a good measure o f agreement. L i t e r a t u r e Cited 1.

Gilman, H., Haubein, M.

J . Am.

2.

Gear, G.W. "Numerical I n i t i a l P r e n t i c e - H a l l , New Jersey, 1971.

3.

Dew, P.M., West, M.R. U n i v e r s i t y , Report 107

Department of Computer Studies, (1978).

Leeds

4.

Dew, P.M., West, M.R. U n i v e r s i t y , Report 111

Department o f Computer Studies, (1978).

Leeds

5.

Elderton, W.P. "Frequency Curves Cambridge U n i v e r s i t y Press, 1938.

6.

Bamford, C,H., 1097.

Tompa, H.

Chem. Soc. Value

(1944), 66,

Problems

Trans. Faraday

and

Soc.

1515.

i n ODEs".

Correlation".

(1954),

RECEIVED February 19, 1979.


50,

Polymerization Reactors and Processes - American Chemical Society

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