High Temperature Free-Radical ... - American Chemical Society

16 High Temperature Free-Radical Polymerizations in

Downloaded by UNIV OF MASSACHUSETTS AMHERST on May 31, 2018 | https://pubs.acs.org Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

Viscous Systems J. A. NORONHA, M. R. JUBA, H. M. LOW, and E. J. SCHIFFHAUER Eastman Kodak Company, Rochester, NY 14650

Recently, we have been studying the runaway stages of some p o l y m e r i z a t i o n r e a c t i o n s . We are t r y i n g to l e a r n more about designing equipment s a f e l y i n the event a r e a c t i o n gets out of c o n t r o l and runs away. To do t h i s we developed a computer model to p r e d i c t the k i n e t i c c o n d i t i o n s during the runaway stage. The k i n e t i c model i s used to estimate the r e a c t i o n r a t e s , temperatures, pressures, viscosities, conversions, and other v a r i a b l e s which i n f l u e n c e r e a c t o r design. To t e s t our model, we s e t up small and l a r g e - s c a l e t e s t s f o r t h e r m a l l y - i n i t i a t e d p o l y m e r i z a t i o n o f styrene. The k i n e t i c model p r e d i c t e d the observed r e a c t i o n r a t e s , pressures, r a t e s of pressure r i s e and temperature r i s e w i t h i n order-of-magnitude a c c u r a c i e s . The accuracy of the k i n e t i c model was b e t t e r f o r the l a r g e - s c a l e t e s t s . We extended the k i n e t i c model to other monomer systems such as styrene and methyl methacrylate. With these, we used common initiators such as benzoyl peroxide and a z o - b i s - i s o b u t y r o n i t r i l e . The r e s u l t s of these s i m u l a t i o n s compared c l o s e l y with some published experiments. With such modeling e f f o r t s , coupled with some s m a l l - s c a l e t e s t s , we can assess the hazards of a polymer r e a c t i o n by knowing c e r t a i n p h y s i c a l , chemical and r e a c t i o n k i n e t i c parameters. Introduction Several s t u d i e s have been published to assess the k i n e t i c s of p o l y m e r i z a t i o n r e a c t i o n s a t high temperatures. QrZ)• However, most of these s t u d i e s only d e s c r i b e experiments conducted at isothermal c o n d i t i o n s . Only a few papers are based on adiabat i c runaways (2) . This paper i s one of the f i r s t s t u d i e s based on " f i r s t p r i n c i p l e s " c h a r a c t e r i z i n g a d i a b a t i c runaway r e a c t i o n s .

0-8412-0506-x/79/47-104-339$05.50/0 © 1979 American Chemical Society Henderson and Bouton; Polymerization Reactors and Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

POLYMERIZATION REACTORS AND PROCESSES

340

D i s c u s s i o n on

Derivation of

the Rate

Equations

The p o l y m e r i z a t i o n r a t e e q u a t i o n s a r e based on a c l a s s i c a l f r e e r a d i c a l p o l y m e r i z a t i o n ' mechanism ( i . e . , i n i t i a t i o n , p r o p a g a t i o n , and t e r m i n a t i o n o f t h e p o l y m e r c h a i n s ) . For t h e r m a l l y - i n i t i a t e d p o l y m e r i z a t i o n :


R

\

f M A , P _\ P// dm

!/

2

V

S

T

> /

1/2/- x2 FE/2 ( ) *P; J l m

e

For a system employing a f r e e r a d i c a l p e r o x i d e o r a z o compound:

A

(f)( di)

1 / 2

2

(VT)" (n,)

l

( 2)

1 / 2

- E P

-

E./2! d

initiator

E

exp[ t

/ 2

E

(i.e. a

E

- p- i

/ 2

'

] (2)

The f o l l o w i n g a s s u m p t i o n s and t h e o r i e s a r e used i n t h i s derivation: 1. For the t h e r m a l l y - i n i t i a t e d c a s e , the i n i t i a t i o n r a t e has a s e c o n d - o r d e r d e p e n d e n c e on monomer c o n c e n t r a t i o n as s u g g e s t e d by F l o r y L S J i n s t e a d o f a t h i r d - o r d e r dependence as s u g g e s t e d by Hui and H a m i e 1 e c [ & ] . When i n i t i a t o r s a r e u s e d , t h e i n i t i a t i o n r a t e has a f i r s t - o r d e r d e p e n d e n c e on monomer c o n c e n t r a t i o n . 2. A quasi steady-state r a d i c a l population e x i s t s . 3. The c h a i n t e r m i n a t i o n r a t e v a r i e s i n v e r s e l y w i t h t h e v i s c o s i t y o f t h e p o l y m e r i z a t i o n medium b e c a u s e o f t h e Trommsdorff E f f e c t ( i . e . , the r e d u c t i o n o f the m a c r o r a d i c a l mobility with increasing reaction viscosity). This e f f e c t s i g n i f i c a n t l y i n f l u e n c e s r e a c t i o n r a t e [6_,£, K ) ] . 4. The r a t e c o n s t a n t s have an A r r h e n i u s dependence on temperature[11]. 5. The s o l u t i o n v i s c o s i t y i s a f u n c t i o n o f t h e p o l y m e r c o n c e n t r a t i o n and m o l e c u l a r w e i g h t , and can be d e t e r m i n e d by t h e Hi 1 I y e r and L e o n a r d m e t h o d [ 1 2 ] . 6. The c h a i n t r a n s f e r r e a c t i o n p r o p o s e d by Hui and H a m i e l i c [ 6 J and O l a j e t a 1 [ ] j j , a f f e c t s t h e m o l e c u l a r w e i g h t d i s t r i b u t i o n b u t i t does n o t a f f e c t t h e r e a c t i o n r a t e . Iterative Analysis We s t a r t e d t h i s s t u d y by d e v e l o p i n g a c o m p u t e r model t o p r e d i c t t h e k i n e t i c c o n d i t i o n s d u r i n g t h e runaway s t a g e o f a reaction. The c o m p u t e r model i s based on an i t e r a t i v e a n a l y s i s which permits a step-by-step computation of various variables.

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


16.

NORONHA ET AL.

Viscous

Systems

F i g u r e 1 i s a f l o w s h e e t s h o w i n g some s i g n i f i c a n t aspects of the i t e r a t i v e a n a l y s i s . The f i r s t s t e p i n t h e p r o g r a m i s t o i n p u t d a t a f o r a b o u t 50 p h y s i c a l , c h e m i c a l and k i n e t i c p r o p e r t i e s o f t h e r e a c t a n t s . Each l o o p o f t h i s a n a l y s i s i s conducted a t a s p e c i f i e d s o l u t i o n temperature T°K. Some o f t h e v a r i a b l e s computed i n e a c h l o o p a r e : t h e monomer c o n v e r s i o n , p o l y m e r c o n c e n t r a t i o n , monomer and p o l y m e r volume f r a c t i o n s , e f f e c t i v e p o l y m e r m o l e c u l a r w e i g h t , c u m u l a t i v e number a v e r a g e m o l e c u l a r w e i g h t , c u m u l a t i v e weight average molecular weight, s o l u t i o n v i s c o s i t y , polymeri z a t i o n r a t e , r a t i o o f p o l y m e r i z a t i o n r a t e s between t h e c u r r e n t and p r e v i o u s s t e p s , t h e t o t a l p r e s s u r e and t h e p a r t i a l p r e s s u r e s o f t h e monomer, t h e s o l v e n t , and t h e n i trogen. Test

Set-up

In o r d e r t o t e s t t h i s c o m p u t e r m o d e l , we c o n d u c t e d e x p e r i m e n t s on t h e r m a l l y i n i t i a t e d s t y r e n e p o l y m e r i z a t i o n i n s e a l e d p r e s s u r e v e s s e l s . We o n l y measured p r e s s u r e s and temperatures i n these experiments. We c o n d u c t e d o u r t e s t s i n two p h a s e s . In P h a s e I ( s e e F i g u r e 2) we used a 3 0 0 - c c s t a i n l e s s s t e e l p r e s s u r e v e s s e l , e q u i p p e d w i t h a 180-cc g l a s s l i n e r , i n w h i c h 100 c c c o u l d be p o l y m e r i z e d . We used a p r e s s u r e g a g e , r a t e d f r o m 0 t o \k0 pounds p e r s q u a r e i n c h . There w e r e 3 t y p e J t h e r m o c o u p l e s - one i n t h e c e n t e r o f t h e s o l u t i o n , one i n t h e r e a c t o r w a l l , and t h e t h i r d n e a r t h e h e a t e r o u t s i d e t h e r e a c t o r . The e x p e r i m e n t s w e r e c o n d u c t e d i n a h i g h p r e s s u r e bay and o b s e r v e d on c l o s e d c i r c u i t t e l e vision. The i n i t i a l p o l y m e r c o n c e n t r a t i o n s o f t h e t e s t r e a c t a n t s w e r e e i t h e r 0 o r 15 o r 30 p e r c e n t by w e i g h t . An e l e c t r i c heater c o n t r o l l e d t h e ambient temperature o f t h e n i t r o g e n - p u r g e d r e a c t o r , and s u p p l i e d h e a t t o i n i t i a t e t h e react ion. Our c o m p u t e r model p r e d i c t e d t h e P h a s e I t e s t r e s u l t s w i t h a c c u r a c y a d e q u a t e f o r s a f e t y d e s i g n even t h o u g h t h e r e were e x p e r i m e n t a l e r r o r s . To r e d u c e t h e s e e x p e r i m e n t a l e r r o r s , i n P h a s e I I , we made some e q u i p m e n t m o d i f i c a t i o n s and used a l a r g e r r e a c t o r . In P h a s e I I ( s e e F i g u r e 3) we used a 2 9 0 0 - c c p r e s s u r e v e s s e l , w i t h a 2 0 0 0 - c c g l a s s l i n e r i n w h i c h 1000 c c o f s o l u t i o n c o u l d be p o l y m e r i z e d . T h i s was a 1 0 - f o l d i n c r e a s e o v e r P h a s e I . We used a p r e s s u r e gauge s i m i l a r t o Phase I . There were 5 t y p e J thermocouples. Of t h e s e , t h e r e were k t h e r m o c o u p l e s w i t h i n t h e r e a c t o r a s compared t o o n l y 1 i n P h a s e I . Two w e r e i n t h e s o l u t i o n w i t h i n t h e g l a s s l i n e r , one was between t h e g l a s s l i n e r and r e a c t o r w a l l , and t h e




Define

i n c r e m e n t a l monomer c o n v e r s i o n

P h y s i c a l , C h e m i c a l and K i n e t i c P r o p e r t i e s o f t h e R e a c t i o n System

Starting

Values;

C o n c e n t r a t i o n s o f t h e monomer, s o l v e n t , polymer, and i n i t i a t o r System t e m p e r a t u r e P a r t i a l p r e s s u r e s o f t h e monomer, s o l v e n t , and n i t r o g e n Total pressure

Calculate C o n c e n t r a t i o n s o f t h e monomer, s o l v e n t , polymer, and i n i t i a t o r Solution viscosity Number a v e r a g e polymer m o l . wt. Weight a v e r a g e polymer m o l . wt. P o l y m e r i z a t i o n Rate R e a c t i o n time Heat g e n e r a t e d Heat l o s s e s S o l u t i o n Temperature P a r t i a l p r e s s u r e s o f t h e monomer, s o l v e n t , and n i t r o g e n Total pressure Rate o f p r e s s u r e and t e m p e r a t u r e rise

(Monomer cone, i n t h e n e x t s t e p ) =(Monomer cone, i n t h e p r e v i o u s s t e p ) - ( I n c r e m e n t a l monomer c o n v e r s i o n ) Figure 1.

Iterative

analysis



NORONHA ET AL.

Viscous

Figure

Systems

2.

Phase I test setup



344


3 / 8 " COUPLING

IOOO kPa GAUGE 3 / 8 " HIGH PRESSURE TUBING RUPTURE DISC ASSEMBLY

THERMOCOUPLE WIRES

VAPOR PHASE THERMOCOUPLE UPRIGHT ROCKER ASSEMBLY AND HEATER

REACTOR HEAD

REACTOR WALL THERMOCOUPLE WELL ASBESTOS 8 ALUMINUM FOIL

THERMOCOUPLE GLASS CAPILLARY TUBES

GLASS LINER THERMOCOUPLES REACTION MIXTURE

METAL SPRING

HEATER THERMOCOUPLE

Figure 3.

Phase II test setup


NORONHA ET AL.


16.

Viscous

Systems

f o u r t h i n t e r n a l measurement was i n t h e s p a c e a b o v e t h e solution. The o n l y e x t e r n a l t e m p e r a t u r e measurement was n e a r t h e h e a t e r . We p a c k e d t h e s p a c e between t h e g l a s s l i n e r a n d t h e r e a c t o r w a l l w i t h a s b e s t o s . These Phase II m o d i f i c a t i o n s made a b i g improvement o v e r Phase I . (see T a b l e 1) 1. S i n c e t h e s o l u t i o n s were n o t a g i t a t e d i n e i t h e r P h a s e I o r P h a s e I I , t h e t e m p e r a t u r e s were n o t u n i f o r m throughout the s o l u t i o n . So i n P h a s e I I , t h e 3 a d d i t i o n a l t e m p e r a t u r e s e n s o r s w i t h i n t h e r e a c t o r gave us a b e t t e r e s t i m a t e o f t h e average s o l u t i o n temperature. 2. In P h a s e I I t h e r a t i o o f t h e r e a c t o r w a l l s u r f a c e t o t h e r e a c t i n g s o l u t i o n v o l u m e was s i x t i m e s l o w e r . T h i s r e s u l t e d i n lower p r o p o r t i o n a l heat l o s s e s which a r e d i f f i c u l t o e s t i m a t e . Hence, t h i s r e s u l t e d i n l o w e r c o m p u t a t i o n a l e r r o r s i n Phase I I. 3. The a s b e s t o s p a c k i n g s e r v e d two a d v a n t a g e s ; first, i t r e d u c e d h e a t l o s s e s a n d hence improved a c c u r a c y and s e c o n d , i t r e p l a c e d t h e v a p o r gap between t h e l i n e r and reactor w a l l . T h i s minimized t h e c o n v e c t i v e heat t r a n s f e r of the vapor, which i s a l s o d i f f i c u l t t o c a l c u l a t e . Test

Results

S i n c e o u r model s i m u l a t e d t h e P h a s e I I r e s u l t s more a c c u r a t e l y , we s h a l l o n l y d i s c u s s t h e P h a s e II r e s u l t s . Let's d i s c u s s three t e s t s i n which the i n i t i a l polystyrene c o n c e n t r a t i o n s o f t h e r e a c t a n t s w e r e 0%, 15% and 30% by weight r e s p e c t i v e l y . F i g u r e 4 shows t h e o b s e r v e d p r e s s u r e and t e m p e r a t u r e d a t a f o r T e s t 2. I n i t i a l l y , t h e e x t e r n a l e l e c t r i c h e a t e r c o n t r o l l e d t h e s y s t e m ' s t e m p e r a t u r e and s u p p l i e d h e a t t o i n i t i a t e the reaction. L a t e r , as the r e a c t i o n rate increased the r e a c t i o n i t s e l f generated heat a t a s i g n i f i c a n t l y h i g h e r r a t e than t h e h e a t e r imput. We e s t i m a t e d t h e a v e r a g e s o l u t i o n t e m p e r a t u r e a s f o l l o w s

T

av

=

3T

°- 2

+

7T

(

°' 3

3

)

The d e r i v a t i o n was based on two a s s u m p t i o n s . F i r s t , we assumed a l i n e a r r a d i a l t e m p e r a t u r e g r a d i e n t w i t h i n t h e solution. S e c o n d , we computed "T a t the radius a t which t h e r e w e r e e q u a l v o l u m e s o f s o l u t f o n s on e i t h e r s i d e o f i t . A common i n t e r p r e t a t i o n o f t h e runaway s t a g e i s when both t h e f i r s t and second d e r i v a t i v e s o f t h e average t i m e temperature curve a r e p o s i t i v e . However, b e c a u s e we had an e x t e r n a l h e a t s o u r c e i n o u r t e s t s , we had t o a c c o u n t f o r t h e external heater temperature "T, . 11

M




346

TABLE I

COMPARISON OF PHASE I AND PHASE I I TESTS

Phase I Tests Reactants

Volume

Surface/Volume R a t i o Temperature Measurements 1 w i t h i n Reactor

lOOcc

Phase I I Tests lOOOcc

j

6:1

1:1

j j I

1

4

! i i

!Solution Temperature 1 Measurements

Less accurate

[Radial Heat Losses

More

Less

(Radial Heat-Transfer | Calculations

Less accurate

More accurate

[Fit with K i n e t i c Model

Good

Better

More accurate

\

I


Henderson and Bouton; Polymerization Reactors and Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1979. 3

t

h

2

Figure 4. Observed P and T data for Test 2: (T ) temperature near heater; (T ) solution temperature—center; (T ) solution temperature liner wall; (T ) vapor temperature between liner and wall; (P) pressure.



348

We a r b i t r a r i l y c o n s i d e r e d t h e runaway s t a g e t o b e g i n when t h e computed t e m p e r a t u r e d i f f e r e n c e between t h e and the a v e r a g e t e m p e r a t u r e o f t h e s o l u t i o n goes t h r o u g h a minimum. F o r T e s t 1 ( s e e F i g u r e 5) t h i s o c c u r s when t h e a v e r a g e t e m p e r a t u r e was 100°C and T^ was 150°C. The t e m p e r a t u r e v a r i a t i o n s w i t h i n t h e s o l u t i o n were i n c r e a s e d from T e s t 1 ( i n which the i n i t i a l p o l y s t y r e n e c o n c e n t r a t i o n was 0%) t o T e s t 2 ( i n w h i c h i t was 15%) and t o T e s t 3 ( i n w h i c h i t was 30%) r e s p e c t i v e l y . The maximum t e m p e r a t u r e d i f f e r e n c e s between T and T~ were o n l y 10° i n T e s t 1, and 15° i n T e s t 2 b u t 78° i n T e s t 3. The g r e a t e r the t e m p e r a t u r e d i f f e r e n c e s , t h e g r e a t e r t h e e r r o r o f c a l c u lating T » Hence, the c o m p u t a t i o n s f o r T were d e c r e a s i n g l y a c c u r a t e i n T e s t 1, 2 and 3 r e s p e c t i v e l y . T h e r e s a n o t h e r r e a s o n why t h e computed s o l u t i o n a v e r a g e t e m p e r a t u r e had d e c r e a s i n g a c c u r a c i e s i n T e s t s 1, 2 and 3 respectively. The r e a s o n i s t h a t we s t a r t e d w i t h i n c r e a s i n g l y v i s c o u s s o l u t i o n s , which caused the response time o f the t e m p e r a t u r e measurement t o i n c r e a s e r a p i d l y . T h i s response t i m e becomes e v e n more s i g n i f i c a n t b e c a u s e as t h e s o l u t i o n v i s c o s i t y i n c r e a s e s t h e r e a r e s i g n i f i c a n t r i s e s i n the r e a c t i o n r a t e s and t e m p e r a t u r e s . Now l e t ' s d i s c u s s t h e p r e s s u r e c o m p u t a t i o n s . The o b s e r v e d r e a c t o r p r e s s u r e i s a sum o f t h e p a r t i a l p r e s s u r e s o f n i t r o g e n and t h e s t y r e n e monomer v a p o r . The v a p o r p r e s s u r e o f t h e s t y r e n e v a p o r i s an i n c r e a s i n g f u n c t i o n o f t e m p e r a t u r e and d e c r e a s i n g f u n c t i o n o f c o n v e r s i o n . T h i s i s e x p l a i n e d by the F l o r y - H u g g i n s r e l a t i o n s h i p ( 8 ) . S i n c e we d i d n o t measure t h e c o n v e r s i o n d u r i n g t h e e x p e r i m e n t , we computed t h e e q u i l i b r i u m v a p o r p r e s s u r e a t the a v e r a g e s o l u t i o n t e m p e r a t u r e . We b e l i e v e t h a t , f o r s a f e t y d e s i g n , t h e e q u i l i b r i u m v a p o r p r e s s u r e i s an a d e q u a t e e s t i m a t e o f t h e s t y r e n e v a p o r p r e s s u r e . F o r e x a m p l e , even a t a 50% c o n v e r s i o n , t h e d i f f e r e n c e i s o n l y 10% a t t h e experimental temperatures. F i g u r e s 6, 7 and 8 compared t h e o b s e r v e d p r e s s u r e s w i t h t h e computed t o t a l p r e s s u r e s . The l a t t e r w e r e b a s e d on t h e e q u i l i b r i u m v a p o r p r e s s u r e . As e x p e c t e d , t h e r e w e r e i n c r e a s i n g v a r i a t i o n s i n T e s t s 1, 2 and 3 r e s p e c t i v e l y because o f t h e i r h i g h e r i n i t i a l c o n v e r s i o n s . From t h e s e f i g u r e s we can v e r i f y t h a t o u r p r e s s u r e and t e m p e r a t u r e measurements w e r e i n p h a s e w i t h r e s p e c t t o t i m e . We n e x t e s t i m a t e d t h e c o n v e r s i o n s by u s i n g t h e o b s e r v e d p r e s s u r e s and t e m p e r a t u r e s and t h e F l o r y - H u g g i n s r e l a t i o n s h i p . Since the Flory-Huggins r e l a t i o n s h i p i s less accurate at h i g h e r c o n v e r s i o n s , we c a n e x p e c t t h e s e e s t i m a t e s o f c o n v e r s i o n s t o be o f d e c r e a s i n g a c c u r a c y i n T e s t s 1, 2 and 3 respectively.


?

a v

g v

1


NORONHA ET AL.

Systems


Viscous

0

20

4 0

6 0

80

minutes

Figure 5. T and T k

av

100

120

for Test 1



100

200

300

400

500

600

-

700 r -

Figure

30

6.

60

Test 1 (observed

45

and computed

minutes

75

90

pressures)

J

105

1

120


I

135

I

150

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

7.

Test 2 (observed

and computed

minutes

pressures)




352

Î V.

SX

I

ο

so

ε

s ο

CO

i οό



16.

NORONHA ET AL.

Viscous

Systems

L e t ' s d i s c u s s t h e r e a c t i o n r a t e c o m p u t a t i o n s b a s e d on t h e k i n e t i c model w i t h t h o s e d e r i v e d f r o m t h e e x p e r i m e n t s . A t a given i n s t a n t , these c a l c u l a t i o n s a r e e s s e n t i a l l y " p o i n t " f u n c t i o n s s i n c e they a r e independent o f t h e path t h e r e a c t i o n s y s t e m has t a k e n up t o t h a t g i v e n i n s t a n t . The k i n e t i c model r e a c t i o n r a t e i s computed p e r e q u a t i o n (1) o r e q u a t i o n (2) u s i n g t h e computed a v e r a g e s o l u t i o n t e m p e r a t u r e (T ) and t h e e s t i m a t e d c o n v e r s i o n ( s ) . The c a l c u l a t i o n s f o r t h e e x p e r i m e n t a l r e a c t i o n r a t e s a r e b a s e d on an u n s t e a d y s t a t e h e a t t r a n s f e r a n a l y s i s . We computed t h e o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t o f t h e s y s t e m and e s t i m a t e d t h e e x p e r i m e n t a l r a t e s a s f o l l o w s : dT exp

dt '

av'

x

V

To s i m p l i f y t h e e q u a t i o n (4) c a l c u l a t i o n s d u r i n g t h e runaway s t a g e we drew t h e m a g n i f i e d p l o t s o f T e s t 1 d u r i n g t h e 68 t o 76 m i n u t e s ( F i g u r e 9) and f o r t h e 75 t o 80 m i n u t e p e r i o d (Figure 10). We computed t h e p e r c e n t a g e e r r o r s between t h e r e a c t i o n r a t e c o m p u t a t i o n s b a s e d on t h e e x p e r i m e n t s w i t h t h o s e based on t h e k i n e t i c m o d e l . N o t e t h a t , l i k e t h e p r e s s u r e and temperature comparisons, the accuracy o f the c a l c u l a t i o n s f o r r e a c t i o n r a t e s d e c r e a s e s a s we compare T e s t 1 w i t h T e s t 2 and T e s t 3. In T e s t 1 t h e e r r o r r a n g e s f r o m 3 t o 2 1 % , i n T e s t 2 i t was 10 t o 2 1 % , i n T e s t 3 i t ranged f r o m 5 t o 36%. In e a c h t e s t , t h e e r r o r s w e r e i n t h e l o w e r o r d e r o f i t s range d u r i n g t h e e a r l i e r s t a g e s o f t h e runaway r e a c t i o n , and i n t h e h i g h e r o r d e r o f i t s range d u r i n g t h e l a t e r s t a g e s . We c a n e x p l a i n why t h i s d e c r e a s i n g a c c u r a c y o c c u r s . The e x p e r i m e n t a l r e a c t i o n r a t e c o m p u t a t i o n s based on e q u a t i o n (k) a r e p r i m a r i l y f u n c t i o n s o f t h e computed a v e r a g e s o l u t i o n t e m p e r a t u r e (T ) . The k i n e t i c model r a t e c o m p u t a t i o n s b a s e d on e q u a t i o n (1) o r (2) a r e p r i m a r i l y f u n c t i o n s o f b o t h "T " a s w e l l a s t h e e s t i m a t e d c o n v e r s i o n ( s ) . E a r l i e r we e x p l a i n e d why we e x p e c t e d d e c r e a s i n g a c c u r a c i e s o f e s t i m a t i n g b o t h t h e c o n v e r s i o n s and t h e a v e r a g e s o l u t i o n t e m p e r a t u r e i n T e s t s 1, 2 and 3 r e s p e c t i v e l y . O t h e r Monomer S y s t e m s - C o m p a r i s o n W i t h 01her

StudIes

The t h e r m a l l y - i n i t i a t e d s t y r e n e s y s t e m i s c o n s i d e r a b l y s i m p l e r t h a n most i n d u s t r i a l a p p l i c a t i o n s . Though t h e s e e x p e r i m e n t s p r o v i d e d u s e f u l g u i d e l i n e s , i t was d i f f i c u l t t o develop broadly a p p l i c a b l e design c r i t e r i a without c a r e f u l l y e v a l u a t i n g a b r o a d range o f monomer, p o l y m e r and i n i t i a t o r systems. Hence we e x t e n d e d o u r k i n e t i c model t o some o t h e r monomer s y s t e m s s u c h a s s t y r e n e and m e t h y l m e t h a c r y l a t e u s i n g common i n i t i a t o r s s u c h a s b e n z o y l p e r o x i d e (BPO) and




Figure 10.

T

av

and T for Test 1 (75-80 h

min)



16.

NORONHA ET AL.

Viscous

Systems

a z o - b i s - i s o b u t y r o n i t r i l e (AIBN). The r e s u l t s o f t h e s e m o d e l s compared q u i t e f a v o r a b l y w i t h some p u b l i s h e d e x p e r i ments. Most p u b l i s h e d s t u d i e s r e l a t e o n l y t o i s o t h e r m a l e x p e r i ments. Hence, i n o r d e r t o make s u c h c o m p a r i s o n s we m o d i f i e d o u r c o m p u t a t i o n s t o assume i s o t h e r m a l c o n d i t i o n s . F i g u r e 11 compares o u r k i n e t i c model w i t h d a t a by Hui and H a m i e l e c (6) f o r s t y r e n e t h e r m a l p o l y m e r i z a t i o n a t 140°C. F i g u r e 12 compares o u t k i n e t i c model w i t h d a t a by B a l k e and H a m i e l e c (7) f o r MMA a t 90°C u s i n g 0.3% AIBN. F i g u r e 13 compares o u r k i n e t i c model w i t h d a t a by L e e and T u r n e r (5) f o r MMA a t 70°C u s i n g 2% BPO. Our model compares q u i t e f a v o r a b l y w i t h these published experiments. The p e r c e n t e r r o r was l e s s t h a n 5% i n most o f t h e r a n g e s o f c o n v e r s i o n s . L i mi t a t i o n s 1. The r e s u l t s o f t h e model s h o u l d be a p p l i e d o n l y t o t h e runaway c o n d i t i o n s o f a s y s t e m . They s h o u l d n o t be a p p l i e d t o t h e non-runaway s t a g e o f t h e r e a c t i o n . 2. The e x p e r i m e n t s w e r e c o n d u c t e d a t a m b i e n t t e m p e r a t u r e s up t o 200°C. Hence, t h e y do n o t r e l a t e t o t h e h i g h t e m p e r a t u r e s e n c o u n t e r e d i f t h e r e a c t o r w e r e e x p o s e d t o an external f i r e . 3. The t e m p e r a t u r e s and p r e s s u r e s d e v e l o p e d a r e a f u n c t i o n o f t h e heat t r a n s f e r c h a r a c t e r i s t i c s o f the r e a c t i o n system. Hence, o u r o b s e r v e d p r e s s u r e s and t e m p e r a t u r e s r e l a t e o n l y t o t h i s p a r t i c u l a r system. Conclus ions In c o n c l u s i o n , we have r e v i e w e d how o u r k i n e t i c model did simulate the experiments f o r the t h e r m a l l y - i n i t i a t e d styrene polymerization. The r e s u l t s o f o u r k i n e t i c model compared c l o s e l y w i t h some p u b l i s h e d i s o t h e r m a l e x p e r i m e n t s on t h e r m a l l y - i n i t i a t e d s t y r e n e and on s t y r e n e and MMA u s i n g initiators. T h e s e e x p e r i m e n t s and o t h e r m o d e l i n g e f f o r t s have p r o v i d e d us w i t h u s e f u l g u i d e l i n e s i n a n a l y z i n g more c o m p l e x s y s t e m s . W i t h s u c h m o d e l i n g e f f o r t s , we c a n a s s e s s the hazards o f a polymer r e a c t i o n system a t v a r i o u s temperaa t u r e s and i n i t i a t o r c o n c e n t r a t i o n s by k n o w i n g c e r t a i n p h y s i c a l , c h e m i c a l and k i n e t i c p a r a m e t e r s .




356

1.0 --,

(MIN) Figure

11.

Styrene thermal polymerization

at 140°C,

initial conversion


—0%

NORONHA ET AL.

Viscous

Systems


16.

357

co

Ο Sa

Ο ο

S s ci ••s

1


358


-8


-3

- i

If

U0|ti9AU09 0/

Q


Viscous

Systems


G l o s s a r y o f Terms s o l u t i o n v i s c o s i t y a t c o n v e r s i o n 'S' and t e m p e r a t u r e T°K, c p . frequency f a c t o r f o r i n i t i a t o r initiation, 1/sec. f r e q u e n c y f a c t o r f o r monomer t h e r m a l decomposition, liter/mole sec, Propagation frequency f a c t o r , l i t e r / m o l e sec. e f f e c t i v e termination frequency f a c t o r , cp 1 i t e r / m o l e s e c , a c t i v a t i o n e n e r g y f o r monomer t h e r m a l decomposition, kcal/mole, a c t i v a t i o n energy f o r i n i t i a t i o n , kcal/mole. propagation a c t i v a t i o n energy, kcal/mole, t e r m i n a t i o n a c t i v a t i o n energy, kcal/mole, initiator un i t s . initiator

e f f i c i e n c y factor, dimensionless concentration,

mole/liter.

propagation rate constant, liter/mole sec, monomer c o n c e n t r a t i o n , m o l e / l i t e r , observed reactor pressure, k i l o p a s c a l s (gauge). I d e a l Gas Law c o n s t a n t , polymerization rate, mole/liter sec. weight f r a c t i o n o f conversion, dimensionless units. time from s t a r t o f experiment, minutes, temperature near h e a t e r ( o u t s i d e r e a c t o r ) , °C. temperature a t center o f glass l i n e r ( i n t h e s o l u t i o n ) , °C. temperature a t the inside wall o f the g l a s s l i n e r ( i n t h e s o l u t i o n ) , °C. t e m p e r a t u r e between t h e g l a s s l i n e r and t h e r e a c t o r w a l 1 , °C. r e a c t i o n t e m p e r a t u r e , IK. a v e r a g e s o l u t i o n t e m p e r a t u r e , °C.


360



Literature

Cited

1.

Sadawa, H., J . Polym. S c i . , Polym. Lett. Ed., 1, p. 305.

2.

Sebastian, D. H. and Biesenberger, J . Α., Kinetics and Thermal Runaway in Styrene A c r y l o n i t r i l e Copolymerization An Experimental Study. Presented at the 70th National AIChE Meeting held in Nov., 1977 in New York City.

3.

Cardenas, J . N. and O'Driscoll, K.F., J . Polym. S c i . , Polym. Chem. Ed. (1977), 15, p. 2097.

4.

Barr, N.J., Bengough, W.I., Beveridge, G. and Park, European Polym. J . , (1977), 14, p. 245.

5.

Lee, H.B. and Turner, D.T. (2), p. 226.

6.

Hui, A. W. and Hamielec, A. E., J . Appl. Polym. S c i . , (1972), 16, p. 749.

7.

Balke, S. T. and Hamielec, A. E., J . Appl. Polym. S c i . , (1973), 17, p. 905.

8.

Flory, P. J . , " P r i n c i p l e s of Polymer Chemistry", p. 131, Cornell Univ. Press, Ithaca, N.Y., 8th p r i n t i n g , 1971.

9.

Hayden, P. and M e l v i l l e , H., J . Polym. S c i . , (1960), 43, p. 201.

10.

Enal'ev, V.D. and Mel'nichenko, V.I., Mathematical Modeling of the Kinetics of Initiated Polymerization of Vinyl Monomers, U.S.S.R., Deposited Doc., V i n i t i , (1974), 319-74.

11.

Odian, G., " P r i n c i p l e s of Polymerization", p. 243, McGraw-Hill, N.Y., N.Y., 1970.

12.

Macromolecules,

(1963),

G.B.,

(1977), 10,

H i l l y e r , M. J . and Leonard, W. J . , "Solvents Theory and Practice", R. W. Tess Ed., Series", p. 31, ACS, Washington,

"Advances in Chemistry D.C.,

1973.

13.

O l a j , O.F., Kauffman, H. F., Breitenbach, J . W. and Bieringer, H., J . Polym. S c i . , Polym. Lett. Ed. (1977), 15, p. 229.

13.

Olaj, O.F., Kauffman, H.F., Breitenbach, J . W. and Bieringer, H., J. Polym. S c i . , Polym. Lett. Ed. (1977) 2, p. 45.

RECEIVED March 15,

1979.


High Temperature Free-Radical ... - American Chemical Society

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