Computer Applications in Applied Polymer Science - American

7 Copolymerization Reaction Engineering Controlled and Uncontrolled Semi-batch Solution Copolymerization of Styrene with Methyl Acrylate

Downloaded by CORNELL UNIV on October 6, 2016 | http://pubs.acs.org Publication Date: September 24, 1982 | doi: 10.1021/bk-1982-0197.ch007

A. F. JOHNSON, B. KHALIGH, and J. RAMSAY University of Bradford, Schools of Polymer Science and Control Engineering, Bradford BD7 1DP West Yorkshire, England

Model-reference feed-forward control strategies have been developed for the synthesis of compositionally homogeneous copolymer from free-radically initiated binary copolymerisation reactions where ( i ) the co-reactants have greatly different reactivities ( i i ) the reactions are taken to high monomer conversions and ( i i i ) the reactions are carried out in solution i n a semi-batch isothermal reactor. The control strategy aims at maintaining a constant molar ratio of coreactants in the reactor through the combined and repeated application at regular time intervals of the mathematical models of batch and semi-batch copolymerisation processes. The models provide a flow rate profile which has been used to generate set-points for a computer controlled semi-batch experimental reactor. In this work the reactor conditions are adjusted by the addition of the more reactive monomer only. The control policy has been shown to be largely successful in the case of the copolymerisation of styrene with methyl acrylate when initiated by azo-bis-iso-butyronitrile in toluene solution. Many aspects of homopolymerisation reaction engineering have been studied in recent years (1-4). Much attention has been given the nature of the dependence of the polymer molecular weight (MW) and molecular weight distribution (MWD) on the operating conditions of the polymerisation reactor. 0097-6156/82/0197-0117$06.00/0 © 1982 American Chemical Society Provder; Computer Applications in Applied Polymer Science ACS Symposium Series; American Chemical Society: Washington, DC, 1982.


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COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE

Alongside the growth of understanding of the complex inter-relationship between the r e a c t i o n and r e a c t o r d y n a m i c s t h e r e has been r a p i d i n c r e a s e i n t h e application of computers for polymerisation reactor control (5). In c o n t r a s t t o the requirements for homopolymerisation processes, the parameters needed to fully describe copolymerisation processes a r e more numerous. Molecular features such as the copolymer composition, composition d i s t r i b u t i o n and c h a i n s e q u e n c e s t r u c t u r e and their variation with conversion are compounded w i t h t h o s e o f c o p o l y m e r MW and MWD. To u n d e r s t a n d c o p o l y m e r i s a t i o n p r o c e s s e s , i t i s d e s i r a b l e to decouple a s many o f t h e s e m o l e c u l a r p a r a m e t e r s a s p o s s i b l e and s t u d y t h e i n f l u e n c e o f p o l y m e r i s a t i o n r e a c t o r c o n d i t i o n s on each. As y e t t h e r e have been r e l a t i v e l y few r e p o r t s on the d e t a i l e d behaviour o f c o p o l y m e r i s a t i o n r e a c t o r s (6-9 )• This work f o r m s p a r t o f a w i d e r r a n g e o f i n v e s t i g a t i o n s w h i c h a r e b e i n g c a r r i e d o u t i n o u r l a b o r a t o r i e s o f c o n t r o l methods f o r t h e production of s p e c i a l i t y polymers. It is common for the monomers taking part in c o p o l y m e r i s a t i o n r e a c t i o n s t o be of different r e a c t i v i t i e s which leads to a d r i f t in copolymer composition with conversion. The instantaneous copolymer composition c a n be r e l a t e d to the instantaneous composition o f the monomer feed through r and r , t h e monomer r e a c t i v i t y r a t i o s ( 1 0 ) as shown i n Equation (1). %

a

r f F

1

11

= r f 1

2

1

+ f f

+ 2f

12

f

12

+ r

(1)

2

f

2

2

Here F and F a r e the instantaneous mole f r a c t i o n s of monomers 1 and 2 i n t h e p o l y m e r r e s p e c t i v e l y and f and f are t h e i n s t a n t a n e o u s mole f r a c t i o n o f monomer 1 and 2 i n t h e feed respectively. The reactivity ratios are a f u n c t i o n of the reaction temperature. Equation (1) demonstrates that the instantaneous composition o f the c o p o l y m e r depends upon t h e r a t i o o f monomers i n t h e r e a c t i o n m i x t u r e and t h e temperature. Variations i n the composition o f the feed w i t h c o n v e r s i o n , or temperature changes d u r i n g p o l y m e r i s a t i o n , w i l l cause changes i n the o v e r a l l composition o f the product. Methods o f a c h i e v i n g u n i f o r m composition copolymers from v a r i o u s p o l y m e r i s a t i o n p r o c e s s e s h a v e been d e s c r i b e d . Hanson and Zimmerman ( 1 1 ) u s e d a c o n t i n u o u s r e c y c l e r e a c t o r t o produce copolymers o f a known and p r e d i c t a b l e homogeneous c o m p o s i t i o n at r e l a t i v e l y h i g h p e r c e n t a g e c o n v e r s i o n . Hatate et a l (12) studied a continuous c o p o l y m e r i s a t i o n i n s t i r r e d tank r e a c t o r s and c o n s i d e r e d t h e effect of micro-mixing on the copolymer L

2

t

Provder; Computer Applications in Applied Polymer Science ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

2

7.

JOHNSON ET AL.

Copolymerization

Reaction

119

Engineering

c o m p o s i t i o n . Hanna ( 1 3 ) h a s d e v i s e d a method f o r t h e r a p i d c a l c u l a t i o n o f monomer a d d i t i o n t o a s e m i - b a t c h c o p o l y m e r i s a t i o n r e a c t o r t o c o m p e n s a t e f o r t h e l o s s o f t h e more r e a c t i v e monomer. Reaville and Fallwell (14) r e f i n e d and extended Hanna s approach. They u s e d g r a p h i c a l methods o f i n t e g r a t i o n of the model e q u a t i o n s a n d , a s s u c h , t h e i r t e c h n i q u e i s t i m e c o n s u m i n g and i n f l e x i b l e . Ray a n d G a l l ( 1 5 ) d e s c r i b e d a method o f controlling t h e copolymer composition i n a b a t c h r e a c t o r by employing temperature a s t h e c o n t r o l variable. T i r r e l l and Gromley (JJ5) h a v e t a k e n Ray a n d G a l l ' s a p p r o a c h a n d have u s e d an optimum t e m p e r a t u r e p r o f i l e f o r a n e x p e r i m e n t a l r e a c t o r i n a n e f f o r t t o minimise t h e copolymer composition d r i f t . A l l t h e methods m e n t i o n e d above u s e a m a t h e m a t i c a l model o f t h e c o p o l y m e r i s a t i o n p r o c e s s i n one way o r a n o t h e r t o a r r i v e at a c o n t r o l p o l i c y f o r the production o f compositionally homogeneous p r o d u c t s . I n t h i s work u s e i s made o f a d y n a m i c model o f t h e p r o c e s s t o c o n t r o l t h e f e e d r a t e o f t h e more r e a c t i v e monomer t o a semi-batch r e a c t o r . Feedback from t h e p r o c e s s comes f r o m a n o f f - l i n e m o d e l . The method i s a g e n e r a l one and c a n be r e a d i l y extended t o accomodate feedback l o o p s u s i n g o n - l i n e measurement d e v i c e s w i t h a n e x p e r i m e n t a l r e a c t o r .


f

The

Control Policy

In o r d e r t o d e v e l o p t h e c o n t r o l s t r a t e g y E q u a t i o n (1)can be m o d i f i e d a n d r e p r e s e n t e d i n t e r m s o f t h e monomer r a t i o r° = [A]/[B] where [ A ] and [ B ] a r e t h e i n s t a n t a n e o u s molar c o n c e n t r a t i o n s o f t h e monomers A a n d B.

r

/

2

+

p

(2)

I t i s c l e a r t h a t i f t h e v a l u e o f f c a n be h e l d constant during t h e course o f reaction the instantaneous ( therefore, t h e mean) c o p o l y m e r c o m p o s i t i o n w i l l r e m a i n c o n s t a n t . I f the i n i t i a l c o n d i t i o n s o f the reaction mixture are V ( v o l u m e ) , A° a n d B° ( m o l e s o f monomers A a n d B respectively) and p°( monomer r a t i o ) t h e n a f t e r a t i m e i n t e r v a l (At), t h e c o n d i t i o n s w i t h i n t h e r e a c t o r change t o V( A t ) , A ( A t ) a n d B ( A t ) . I f t h e r e i s n o volume change d u r i n g p o l y m e r i s a t i o n t h e n V ( A t ) = V ° . S h o u l d t h e two monomers be consumed a t t h e same r a t e t h e n ^ r e m a i n s c o n s t a n t . However, since one o f t h e monomers i s u s u a l l y more r e a c t i v e t h a n t h e other, 0


120


A

At)

r°

I f monomer A i s more r e a c t i v e t h a n monomer B t h e n nAt) k

consequently

e°

°. I f A i s added i n a c o n t i n u o u s s t r e a m t o t h e r e a c t o r in a s o l u t i o n o f c o n c e n t r a t i o n [A.f ] t h e n t h e n e c e s s a r y f l o w r a t e may be o b t a i n e d f r o m F (0) A

= n.(0)

/ {[A ] A t }

(5)

assuming t h a t t h e flow r a t e i s constant over the i n t e r v a l . The new i n i t i a l c o n d i t i o n s f o r t h e r e a c t o r a t t i m e t = A t a r e V(At)

= F ( 0 ) A t + V° A A ( A t ) and B( A t ) m o l e s o f monomers

From t h e s e new c o n d i t i o n s t h e r e a c t i o n i n t h e b a t c h r e a c t o r can be a d v a n c e d t o time t = 2 A t . At t h i s time t h e e n t i r e p r o c e d u r e f o r c o m p u t i n g t h e new f e e d flow-rate h a s t o be r e p e a t e d . S i n c e no c o r r e c t i o n f o r t h e c o n s u m p t i o n o f B h a s b e e n made, t h e amount o f B p r e s e n t must d e c r e a s e a s t h e r e a c t i o n proceeds. As a r e s u l t , p r o g r e s s i v e l y l e s s o f monomer A h a s t o be a d d e d t o k e e p f> c o n s t a n t . When A i s f e e d t o t h e r e a c t o r n o t as p u r e monomer, b u t i n s o l u t i o n t h e i n c r e a s e i n volume c a u s e d by t h e added s o l v e n t will reduce t h e c o n c e n t r a t i o n s o f the r e a c t a n t s and h a v e a c o n s e q u e n t i a l e f f e c t o n t h e o v e r a l l r a t e o f polymerisation. The c o n t r o l scheme p r e s e n t e d c a n be d e s c r i b e d s u p e r f i c i a l l y as a p r e d i c t o r - c o r r e c t o r a c t i o n . The p r e d i c t i o n i s done b y t h e batch reactor model, which i n t u r n provides the necessary


7.

Copolymerization

JOHNSON ET AL.

Reaction

control action to correct f o rd r i f t in t h e semi-batch r e a c t o r model. s e m i - b a t c h models a t t i m e i n t e r v a l s some d e s i r e d b o u n d a r y c o n d i t i o n i s

121

Engineering

i n t h e monomer composition The s w i t c h between b a t c h a n d A t c a n be c o n t i n u e d until satisfied.


M a t h e m a t i c a l Model The models a r e r e q u i r e d to give accurate information concerning t h e consumption of t h e two monomers during copolymerisation. The m o d e l l i n g t e c h n i q u e s used here a r e extensions o f w e l l e s t a b l i s h e d methods f o r h o m o p o l y m e r i s a t i o n r e a c t i o n s . The c o n s t r u c t i o n o f t h e m o d e l s may be s u m m a r i s e d briefly as follows: The s p e c i e s M^ (k= 1,2,...,S) p r e s e n t i n the reaction m i x t u r e i s assumed t o h a v e a m o l e c u l a r w e i g h t w ( g m o l e " ) , d e n s i t y d * ( g c m " ) , m o l a r e n t h a l p y u ( c a l mole" 7, a n d m o l a r specific h e a t a t c o n s t a n t p r e s s u r e C p ( c a l mole"" C " ) a n d o f i n i t i a l m o l a r c o n c e n t r a t i o n [M ^ ] (mole l " ) . The r e a c t i o n volume i s V° ( 1 ) and t e m p e r a t u r e T° (°C). F o r s p e c i e s M * j ( j = 1,2,...,N) o f m o l a r c o n c e n t r a t i o n [MKJ ] , d e n s i t y d ,molecular w e i g h t Wic , m o l a r e n t h a l p y u , a n d m o l a r s p e c i f i c h e a t C a r e i n the feeds t o the r e a c t o r o f flow rates F j ( 1 sec"" ) and t e m p e r a t u r e T|. The s p e c i e s M undergo R r e a c t i o n s whose stoichiometries are 1

3

1

K

1

0

1

K

1

K

K

P K

1

K

k

= (1

, • • •,

S)

The s t o i c h i o m e t r i c c o e f f i c i e n t C^k i s g r e a t e r t h a n z e r o i f M i s a product o f the i - t h r e a c t i o n , i s negative i f M i s a r e a c t a n t a n d i s z e r o i f M p l a y s no p a r t i n t h e i - t h r e a c t i o n . I f t h e volume c h a n g e o f t h e r e a c t i o n m i x t u r e due t o r e a c t i o n i s assummed t o be n e g l i g i b l e r e l a t i v e t o t h a t c a u s e d b y the i n f l o w o f m a t e r i a l s i n t o t h e r e a c t o r , then K

K

K

N V(t=0)

J=1

dt

The m o l a r e n t h a l p y u i s a function vanishes a t the reference temperature T K

R

o f temperature, ( i . e . , 25 ° C ) .


which

122

COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE The m o l a r b a l a n c e f o r t h e s p e c i e s ^

__ f j

M V ^ ] }

[M^] • V

3

j=1

dt

i s then

r

, [M ]( 0)

±

k

t =

i=1


where r ^ i s t h e r a t e o f t h e i - t h r e a c t i o n . The e n e r g y b a l a n c e ( h e a t b a l a n c e ) f o r t h e s y s t e m

d _ { V ^ [ M ] u ( T ) } = f fjH)^ k

dt

- V £ (

k

j=1 k=1

k=1

= [M°]

i s then

H.)^

+

Q

i=1

where ( AHj,) i s t h e h e a t o f t h e i - t h r e a c t i o n and Q i s t h e r a t e of heat removal or addition to the process. Using the r e l a t i o n s h i p b e t w e e n t h e e n t h a l p y and s p e c i f i c h e a t a t c o n s t a n t pressure i tfollows that

T

ZID jd_T _

T ) F

[

]

v

H

+ Q

j \j v- D >i

J = 1 k=1

1=1

dt

k=1 T ( t = 0 ) = T° The m o d e l e q u a t i o n s d e v e l o p e d f o r t h e s e m i - b a t c h reaction process c a n be m o d i f i e d f o r t h e b a t c h p r o c e s s b y i g n o r i n g t h e i n f l o w o f m a t e r i a l and e n e r g y t e r m s . The above l o g i c h a s b e e n a p p l i e d t o t h e c o p o l y m e r i s a t i o n equations given i n Table I. A detailed derivation of the c o p o l y m e r i s a t i o n model and a summary o f t h e c o n s t a n t s u s e d i n the model have been d e s c r i b e d elsewhere ( 1 7 ) . The v a l u e o f p f o r t h e f r e e r u n n i n g o p e r a t i o n o f t h e s y s t e m is obtained f r o m t h e b a t c h model e q u a t i o n s a n d d e v i a t i o n s f r o m the d e s i r e d v a l u e a r e used t o c a l c u l a t e t h e r e q u i r e d monomer f e e d volume f l o w - r a t e f o r t h e s e m i - b a t c h p o l y m e r i s a t i o n p r o c e s s . A s o l u t i o n o f t h e s e m i - b a t c h r e a c t o r model e q u a t i o n s y i e l d s the results t h a t w o u l d be e x p e c t e d f r o m a r e a l r e a c t o r . I f t h e c o n t r o l a c t i o n has been e f f e c t i v e , p should remain constant. Any e r r o r i n t h e c o m p u t a t i o n o f t h e e x a c t amount o f t h e r e q u i r e d


7.

Copolymerization

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Reaction

123

Engineering

T a b l e I . C o p o l y m e r i z a t i o n R e a c t i o n Scheme

Initiation 2R A

- I

1,0"

A

R

" '

o,r - -

B

B

R

R

1

= k ^ I ]

R

2

= k [A][IT]

R

3

= k [B][R']

2

3


Propagation

„(4)

A „ - A -A m+1,n m,n B

- A m,n+1

-B

- B m,n+1

m,n

k [B][A ] 5 m,n

m,n

m,n

,(6)

A - B -A m+1, n m,n B

4

m,n

k [A][B ] 6 m,n

m,n

k [B][B

-B

m,n

m,n

7

m

]

»

n

Termination Combination (

-A -A m,n x,y

=0

r

-A -B m,n x,y

=0

r

m+x,n+y

-B -B m,n x,y

=0

r

m+x,n+y

P m+x,n+y P P

8

= k.CA ][A ] 8 m,n x,y

)

m,n (

9

)

= k [A ][B ] 9 m,n x,y n

m,n ( 1 0 )

=

k

m,n

10

[B ] [ ] m,n x,y B

Disproportionation P

+ p -A -A = 0 m,n x,y m,n x , y

r 1

)=

iI

k

m,n

P m,n

+ P -A -B = 0 x,y m,n x , y

m,n

+ P -B -B = 0 x,y m,n x , y

P

( 1 2 ) r

( 1 3 )

[ A

m

n

]

[

A

v

v

]

11

=

m,n x,y k [A ][B ] 12 m,n x,y

=

k

m,n r

11

m,n

13

[B ][B ] m,n x,y

Transfer t o Solvent P

+ S* - A m,n

P

= 0

r

- S

= 0

r

m,n + S* - B

m,n

m,n

( l 4 )

- S

=

k ,[S][A ] 14 m,n

=

k

m,n ( 1 5 )

m,n

15

[S][B ] m,n


124



monomer w i l l be r e f l e c t e d i n t h e v a l u e o f f a t t h e end of the semi-batch operation interval. This error w i l l h a v e t o be c o r r e c t e d i n t h e n e x t o r s u b s e q u e n t i n t e r v a l s . However, i f any of the f o l l o w i n g i s s i n g l e y o r c o l l e c t i v e l y t r u e t h e n a new/* w i l l be e s t a b l i s h e d and maintained i n the reactor (i) the mathematical m o d e l s do not accurately represent the true behaviour of the system, (ii) or the process experiences disturbances, ( i i i ) or the k i n e t i c d a t a used in the c o n s t r u c t i o n o f t h e model a r e i n e r r o r . The r e s u l t w i l l be the production of a compositionally u n i f o r m c o p o l y m e r but one o f d i f f e r i n g i n c o m p o s i t i o n from t h a t d e s i r e d . Experimental E x p e r i m e n t a l System The c o p o l y m e r i s a t i o n o f s t y r e n e with methyl acrylate i n toluene using azo-bis-iso- butyronitrile ( A I B N ) was s e l e c t e d as t h e model e x p e r i m e n t a l s y s t e m b e c a u s e t h e overall r a t e of r e a c t i o n i s r e l a t i v e l y f a s t , copolymer a n a l y s i s i s r e l a t i v e l y simple using a v a r i e t y of t e c h n i q u e s and the appropriate k i n e t i c and p h y s i c a l c o n s t a n t s a r e a v a i l a b l e i n t h e literature . This monomer c o m b i n a t i o n a l s o has suitable reactivity r a t i o s (r 0.76 and r =0.175 a t 80 • c ) , ( J _ 8 ) m a k i n g c o n t r o l a c t i o n e s s e n t i a l f o r many d i f f e r e n t values i f compositionally homogeneous p o l y m e r s a r e to be prepared at higher conversions i n a semi-batch reactor. %

t

M a t e r i a l s . S t y r e n e , m e t h y l a c r y l a t e , t o l u e n e and p u r i f i e d by s t a n d a r d techniques(19).

AIBN

were

R e a c t o r and R e a c t o r C o n d i t i o n s . A 5 - l i t r e g l a s s r e a c t o r (15 cm d i a m e t e r ) f i t t e d w i t h f o u r s t a i n l e s s s t e e l b a f f l e s (10 cm x 1.5 cm) immersed i n a t h e r m o s t a t t e d o i l b a t h a t 80 °C (reflux temperature of methyl a c r y l a t e ) was u s e d f o r p o l y m e r i s a t i o n . S t i r r i n g was by means o f a m a r i n e t y p e i m p e l l e r (6 cm diameter and p i t c h 45°). The o v e r a l l r e a c t i o n r a t e was s u f f i c i e n t l y s l o w to ensure isothermal c o n d i t i o n s . A d d i t i o n s of s o l u t i o n s of the more r e a c t i v e monomer ( s t y r e n e , o f m o l a r c o n c e n t r a t i o n 0.8) to t h e r e a c t o r were made u s i n g a computer c o n t r o l l e d p o s i t i v e displacement pump (Precision Metering Ltd.) with four l o n g - s t r o k e pump h e a d s , 90° o u t o f p h a s e t o m i n i m i s e pulsation of the flow. Sample A n a l y s i s , ( i ) C o n v e r s i o n . Measured samples (^20 ml) were t a k e n f r o m t h e r e a c t o r a t r e g u l a r i n t e r v a l s ( 30 m i n ) , and p o l y m e r i s a t i o n quenshed by r a p i d c o o l i n g and t h e a d d i t i o n o f a small q u a n t i t y o f t - b u t y l c a t e c h o l . The p o l y m e r was i s o l a t e d by r o t a r y e v a p o r a t i o n a t r e d u c e d p r e s s u r e to remove r e s i d u a l monomer and then r e p r e c i p i t a t e d s e v e r a l times from acetone s o l u t i o n w i t h aqueous m e t h a n o l . The p r o d u c t was finally dried u n d e r vacuum. P o l y m e r y i e l d s w e r e o b t a i n e d by w e i g h i n g .


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( i i ) C o m p o s i t i o n , ( a ) U V - S p e c t r o s c o p y . The c o p o l y m e r s h a d an absorption a t 269 nm i n c h l o r o f o r m s o l u t i o n w h i c h o b e y e d B e e r ' s Law a n d i s c h a r a c t e r i s t i c o f t h e r e p e a t u n i t s from t h e styrene monomer ( >^max = 269 nm, € =1.7 mole cm" ) . M e a s u r e m e n t s were made w i t h a Unicam SP800A spectrophotometer and 1 cm q u a r t z c e l l s .


(b) Hnmr measurements . The p r o t o n m a g n e t i c s p e c t r a o f t h e products were o b t a i n e d using a J e o l - 1 0 0 Mhz i n s t r u m e n t . The r e l a t i v e amounts o f p h e n y l ( r = 3.68) and m e t h y l ( f =1.79-1.81) protons were u s e d t o determine t h e average composition o f copolymers. ( i i i ) M o l e c u l a r Weight. A Waters A s s o c i a t e s g e l permeation chromatograph f i t t e d w i t h a m o d e l 6000A pump, U6K i n j e c t o r a n d UV, IR a n d R I d e t e c t o r s was u s e d f o r t h e e s t i m a t i o n o f m o l e c u l a r w e i g h t s , m o l e c u l a r weight d i s t r i b u t i o n and copolymer c o m p o s i t i o n . Both a n a l y t i c a l and p r e p a r a t i v e g e l columns (Polymer L a b o r a t o r i e s L t d ) were e m p l o y e d . A n a l y s e s were c a r r i e d o u t a t 25 t i n THF a n d t h e c o l u m n s e t s were c a l i b r a t e d w i t h monodisperse p o l y s t y r e n e standards (Polymer L a b o r a t o r i e s L t d ) . ( i v ) C o m p u t e r s a n d Computer S o f t w a r e . Computer s i m u l a t i o n p r o g r a m s were w r i t t e n i n FORTRAN f o r a HP2100A c o m p u t e r . The c o n t r o l a l g o r i t h m were i m p l e m e n t e d on a n ARGUS 700E process control computer u s i n g ICOL a r e a l time c o n t r o l language developed a t Bradford U n i v e r s i t y (20). R e s u l t s and D i s c u s s i o n (a) Computer S i m u l a t i o n . - B a t c h R e a c t o r . The o b j e c t o f these i n v e s t i g a t i o n s was t o g a i n a n i n s i g h t i n t o t h e b e h a v i o u r o f t h e p r o c e s s i n t h e o p e n - l o o p mode o f o p e r a t i o n . The p r o c e s s divides into two d i s t i n c t i v e stages. I n the f i r s t , s t y r e n e copolymerises with methyl a c r y l a t e while i n t h e second t h e homopolymerisation o f methyl a c r y l a t e takes place after a l l the s t y r e n e h a s been consumed ( s e e F i g u r e 1 ) . D u r i n g t h e c o u r s e o f the copolymerisation Z decreased from i t s i n i t i a l value o f 0.25 t o z e r o ( F i g u r e 2 ) . As a r e s u l t t h e average copolymer composition changed f r o m 0.4 t o 0.2 ( s e e F i g u r e 3 ) • The v a r i a t i o n s i n t h e number a v e r a g e d e g r e e o f p o l y m e r i s a t i o n ( NADP) and t h e w e i g h t a v e r a g e d e g r e e (WADP) a r e shown i n F i g u r e 4 w h i l e F i g u r e 5 shows t h e c h a n g e s i n t h e d i s p e r s i t y i n d e x o f t h e m a t e r i a l produced as the r e a c t i o n proceeds. 7

(b) Computer S i m u l a t i o n - C o n t r o l l e d S e m i - B a t c h R e a c t o r . Batch r e a c t o r s t u d i e s showed t h a t s t y r e n e was t h e more r e a c t i v e monomer. The f e e d f l o w r a t e p r o f i l e c a l c u l a t e d by means o f t h e control a l g o r i t h m t o c o m p e n s a t e f o r i t s l o s s i s shown i n F i g u r e 6 . The e f f e c t o f t h e f e e d f l o w r a t e p r o f i l e was t o keep f> a n d


126



0.25

0.05

u

0r0 0.5 1.0 1.5 2.0 2.5 3.0 TIME-HOURS

Figure 1. Monomer concentrations with reaction time in a batch reactor. Key: , MA; , ST.

°0?0'

0.2 0.V 0.6 0.8 OVERALL CONVERSION

l.o'

Figure 3. Average copolymer composition with conversion in a batch reactor. Key: ,MA; , ST.

u#

8r0 0.5 1.0 1.5 2.0 2.5 3.0 TIME-HOURS

Figure 2. Variation of monomer ratio with reaction time in a batch reactor.

n

1

1

1

1

r

0^0 0.5 1.0 1.5 2.0 2.5 3.0 TIME-HOURS Figure 4. Degree of polymerization with reaction time in a batch reactor. Key: WAD?; , NADP. 1



7.

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Reaction

Engineering

111

the average copolymer c o m p o s i t i o n c o n t a n t throughout t h e course of reaction. The NADP a n d WADP a r e shown i n F i g u r e 7 w h i l e F i g u r e 8 shows t h e a v e r a g e p o l y d i s p e r s i t y i n d e x o f t h e m a t e r i a l as t h e r e a c t i o n p r o c e e d s . I n a n o t h e r s t u d y s t e p c h a n g e s i n p were made d u r i n g a r u n . In order t o s i m u l a t e a r e a l experiment t h e maximum f l o w r a t e d e l i v e r y o f t h e f e e d pump was c o n s t r a i n e d t o a r e a l i s t i c v a l u e . F i g u r e 9 shows t h e s t e p c h a n g e i n P w h i l e F i g u r e 10 shows t h e b e h a v i o u r o f t h e f e e d pump u n d e r t h e r e s t r i c t i o n imposed upon it. The c o r r e s p o n d i n g variations i n t h e average copolymer c o m p o s i t i o n a r e shown i n F i g u r e 11 . Figures 12 a n d 13 indicate t h a t t h e NADP, t h e WADP, a n d t h e d i s p e r s i t y i n d e x a r e u n a f f e c t e d by c h a n g e s i n t h e monomer r a t i o . I t i s apparent t h a t the control a c t i o n h a s e f f e c t i v e l y made t h e p r o c e s s f o l l o w t h e d e s i r e d s e t p o i n t c h a n g e s w i t h o u t a f f e c t i n g t h e MW a n d t h e MWD o f t h e copolymer. To investigate the effects o f sudden changes i n t h e r e a c t i o n t e m p e r a t u r e , a n i n i t i a l t e m p e r a t u r e o f 60 °C was c h o s e n w h i c h was i n c r e a s e d s t e p w i s e t o 80 °C d u r i n g a r u n . F i g u r e 14 shows t h e r e s p o n s e o f t h e r e a c t i o n r a t e t o t h i s c h a n g e . F i g u r e s 15 a n d 16 show t h e e f f e c t s o f t h i s c h a n g e o n t h e f e e d f l o w - r a t e and on t h e monomer r a t i o , w h i l e F i g u r e 17 shows t h e e f f e c t o n the average copolymer c o m p o s i t i o n . I t i s clear that the effects of reaction temperature changes have been effectively suppressed. However, F i g u r e s 18 d e m o n s t r a t e s t h a t a r e d u c t i o n i n t h e MW h a s o c c u r r e d , a s w o u l d be e x p e c t e d . (c) Reactor Experiments . I n a t y p i c a l experiment t h e a i m was t o p r o d u c e a homogeneous c o p o l y m e r h a v i n g a 0.4 m o l e f r a c t i o n o f s t y r e n e a t h i g h monomer c o n v e r s i o n . I t c a n b e s e e n f r o m E q u a t i o n ( 1 ) t h a t i n o r d e r t o a c h i e v e t h i s o b j e c t i v e i t was n e c e s s a r y t o m a i n t a i n a c o n s t a n t r a t i o o f monomer c o n c e n t r a t i o n s with a m o l e f r a c t i o n o f s t y r e n e o f 0.2. The r e s u l t s o f t h i s e x p e r i m e n t c a n be compared w i t h a b a t c h copolymerisation which was allowed t o proceed without any c o n t r o l a c t i o n other than t o pump p u r e s o l v e n t i n t o t h e r e a c t o r t o p r o d u c e a r a t e o f c h a n g e o f volume i n t h e r e a c t i o n m i x t u r e c o m p a r a b l e t o t h a t f o r t h e semi-batch controlled experiment. To compare experimental results under v a r i o u s c o n d i t i o n s t h e copolymer c o m p o s i t i o n , t h e primary parameter o f i n t e r e s t was m e a s u r e d , a l t h o u g h other parameters have been checked, e.g., t h e s o l i d s c o n t e n t o f t h e r e a c t i o n m i x t u r e . F i g u r e 19 shows t h e e x p e r i m e n t a l o b s e r v a t i o n s o f c o p o l y m e r c o m p o s i t i o n w i t h r e a c t i o n t i m e w h i l e F i g u r e 20 d e p i c t s the s o l i d s content o f the r e a c t o r w i t h r e a c t i o n time ( a t 4 hours c o n v e r s i o n o f monomers was a p p r o x i m a t e l y 7 5 ? ) . I t can be s e e n t h a t t h e c o p o l y m e r c o m p o s i t i o n remained essentially constant with time i n the controlled experiment w i t h i n t h e l i m i t s o f a c c u r a c y o f t h e measurement o f c o m p o s i t i o n b u t c h a n g e d dramatically i n t h e u n c o n t r o l l e d experiment. Similar results have been o b t a i n e d f o r d i f f e r e n t mole f r a c t i o n s o f styrene i n



TIME-HOURS

TIME-HOURS

Figure 5. Polydispersity index with reaction time in a batch reactor.

Figure 6. Feed flow-rate profile with time to a semi-batch reactor.

1.4 1.2" 1.0" 1-4 0.8"

O

OLY


128

Q.

0.6"

0.4" 0.2"

—i 1

1

1

1

2 3 4 TIME-HOURS

5

r

Figure 7. Degree of polymerization with reaction time in a controlled semibatch reactor. Key: , WADP; , NADP.

o.o

0

"1 1

1

1

1

2 3 4 TIME-HOURS

5

r

Figure 8. Polydispersity index with reaction time in a controlled semi-batch reactor.


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Reaction

129

Engineering

25.0 §22.5" §20.0"

|l7.5" ^15.0"


^12.5" £10.0"

g

7.5"

^5.02.5" a

2

V

I'

2 4' TIME-HOURS

5

'

~1 0

1

1

1

1

2 3 4 TIME-HOURS

1 2

1 3

r 4

TIME-HOURS

Figure 9. Dynamic response to a step change in monomer ratio in a controlled semi-batch reactor.

V , V

1

"i

1— 5

Figure 11. Average copolymer composition with time in response to step change in monomer ratio in a controlled semibatch reactor. Key: , MA; , ST.

Figure 10. Dynamic feed flow-rate profile in response to step change in monomer ratio in a controlled semi-batch reactor.

n 1

?

1

1

2 3 4 TIME-HOURS

r

5

Figure 12. Degree of polymerization with time in response to step change in monomer ratio in a controlled semi-batch reactor. Key: , WADP; , NADP.


130


1.4 1.2" 1.0"

>0LY


•—• 0.8" o 0.6" 0.4" 0.2" o.o0

—i 1

1

1

1

2 3 4 TIME-HOURS

I

r

1

5

Figure 13. Polydispersity index change with time in response to step change in monomer ratio in a controlled semi-batch reactor.

T — i — i — i — i — r 1 2 3 4 5 6 TIME-HOURS

7

Figure 15. Flow rate change in response to step change in reaction temperature (60°C to 80°C) in controlled semi-batch reactor.

I 2

I

1 1 1 r

3 4 5 TIME-HOURS

6

7

Figure 14. Change in monomer concentrations with time in response to step change in reaction temperature (60°C to80°C). Key: , MA; , ST.

2

3 4 5 TIME-HOURS

Figure 16. Monomer ratio change with time in response to step change in temperature in controlled semi-batch reactor.


7.

Copolymerization

JOHNSON ET AL.

Reaction

S i.o"

Engineering

131

450 I

400" 350" |

300"

0.6"

& 250"

I

200"

0.4"


150"

|

a2

0.0,

100 50" " i — i — i — i — i — i — r 1 2 3 4 5 6 7 TIME-HOURS

"i—i—i—i—i—i—r 1 2 3 4 5 6 7 TIME-HOURS

Figure 17. Average copolymer composition with time in response to step change in reaction temperature in controlled semi-batch reactor.

w z pa «

OA

Figure 18. Degree of polymerization with time in response to step change in reaction temperature in controlled semibatch reactor. Key: , WADP; , NADP.

-o—o—Q—Q—e—a—o— — 0

Q

>-*

oo 0,3 o 25 O J—I Ei O

2

H O

r o >

>

H W

c

o

o

7.

JOHNSON ET AL.

Copolymerization

Reaction

Engineering

135

Acknowledgements The authors wish to express their gratitude to the Science and Engineering Research Council for a Research Grant which has made our reactor studies possible.


literature Cited 1. Imoto, T.; Int. Chem. Eng. 1972, 12(3), 546-53. 2. Fan, L.T.; Shastry, J.S.; J.Polymer Sci. Macromolecular Reviews 1973, 7, 155-87. 3. Ray, W.H.; Laurence R.L.; "Polymerisation Reaction Engineering",Chapter 9 of "Chemical Reactor Theory. A Review ", Lapidus L. and Amoundson N.R. , 1977, Prentice Hall, 532-82 . 4. Gerrens, H.; 4th/Eurp. Symp. Chem. Reaction Eng., 1976, Heidelberg Germany , 585-615 . 5. Hoogendoorn, K. ; Nap, C.; ISA, 1975, 129-36. 6. Szabo, T.T. ; Nauman, E.B.; AIChE J., 1969, 15(4), 575-80. 7. Mecklenburgh, J.C.; Can. J. Chem. Eng., 1970,48, 279-85. 8. Nauman, E.B.; J . Macromol. Sci. Revs. Macromol. Chem. 1974, C10(1), 75-112. 9. O'Driscoll, K.F. ; Knorr, R.; Macromolecules, 1969,2(5), 507-15. 10. Ham, G.E., Ed., "Copolymerisation", Interscience, 1964, New York. 11. Hanson, A.W. ; Zimmerman, R.L.; Ind. Eng. Chem., 1957, 49, 180 3. 12. Hatate, Y.; Nakashio, F.; Sakai, W.; J. Chem. Eng. of Japan, 1971, 48, 348-54. 13. Hanna, R.J.; Ind. Eng. Chem., 1957, 49(2), 208-9. 14. Reaville, E.T.; Fallwell Jnr., W.F.; Official Digest, 1964, June, 625-47. 15. Ray, W.H. ; Gall, C.E.; Macromolecules , 1969, 2(4), 425. 16. Tirrell, M. ; Gromley, K.; Chem. Eng. Sci., 1981, -36-, 367. 17. Johnson, A. F.; Khaligh, B.; Ramsay, J . ; Int. J. of Modelling and Simulation , 1981, 1(4), 313-17. 18. Brandrup, J. ; Immergut, F.H.; "Polymer Handbook", 2ed., 1975, Wiley Interscience. 19. Termachi, S.; et a l . ; Macromolecules, 1978, 11(6), 1206-10. 20. Butts, B.;"Real Time Extended Basic: User Manual", 1978, Postgraduate School of Control Engineering University Of Bradford . RECEIVED May 4, 1982.


Computer Applications in Applied Polymer Science - American

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