Emulsion Polymers and Emulsion Polymerization - American

32 Control of Particle Size Distribution Through Emulsifier Metering Based on Rate of Conversion

Downloaded by PENNSYLVANIA STATE UNIV on June 15, 2013 | http://pubs.acs.org Publication Date: October 7, 1981 | doi: 10.1021/bk-1981-0165.ch032

DANIEL L. GORDON and KARL R. WEIDNER Diamond Shamrock Plastics Corporation, Painesville, OH 44077

In emulsion polymerization of PVC, water and vinyl chloride monomer are charged to the reactor. The reactor is heated to the desired reaction temperature. Then the pumps, to continuously meter initiator and emulsifier into the reactor, are activated. As will be explained later, the particle size distribution is a function of the amount of emulsifier present at all times during the polymerization. The extent of polymerization can be followed by measuring the conversion of monomer which can be followed by quantifying the heat liberated from the reactor. By combining the knowledge of the extent of conversion with the effect of emulsifier on particle size distribution (PSD), an algorithm can be generated to produce a given PSD. Experimental Materials The reactor system used for these experiments is a 190 liter, jacketed, stainless steel vessel equipped with initiator and emulsifier metering system. The reactor is monitored and controlled by a minicomputer. The computer monitors: the reactor temperature and pressure, the jacket water inlet and outlet temperatures and flow rate, and the initiator and emulsifier flow rates. The computer calculates the amount of heat transferred through the jacket from the process measurements and transmits signals to control the reactor temperature and metering pumps. Determining Conversion Determining the conversion of monomer can only be as accurate as the method of quantifying the heat liberated from the reaction. The usual method is to take the difference between the inlet and outlet jacket water temperatures multiplied by the specific heat and flow rate of the water. This steady-state energy balance equation is: Q = wCp (Τ. ^) m - Τout 0097-6156/81/0165-0515$05.00/0 © 1981 American Chemical Society

In Emulsion Polymers and Emulsion Polymerization; Bassett, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

516

EMULSION POLYMERS

AND

EMULSION POLYMERIZATION

T h i s e q u a t i o n i s e a s i l y i m p l e m e n t e d i n an i n d u s t r i a l p l a n t using analog instrumentation. W i t h computers becoming a v a i l a b l e i n t h e p l a n t s , more a c c u r a t e methods o f o b t a i n i n g Q ( c a l / s ) , c a n be e m p l o y e d . The s t e a d y - s t a t e ( S S ) method i s c o m p l e t e l y a c c e p t a b l e a n d c o r r e c t i f , a n d o n l y i f T. a n d Τ a r en o t changing. But i f t h e y a r e , t h e v a l u e c a l c u l a t e d f o r Q w i l l be i n e r r o r . F o r e x a m p l e , w i t h t h e r e a c t o r empty, a s t e p change i n t h e j a c k e t i n l e t w a t e r t e m p e r a t u r e was made. The r e s p o n s e s o f t h e j a c k e t i n l e t a n d o u t l e t t e m p e r a t u r e s a r e shown i n F i g u r e 1. With n e g l i g i b l e h e a t b e i n g t r a n s f e r r e d , Q s h o u l d be z e r o , b u t t h e SS method gave t h e Q p r o f i l e shown i n F i g u r e 2 . The SS method h a s obvious limitations to i t s use. W i t h no h e a t b e i n g t r a n s f e r r e d t h r o u g h t h e j a c k e t , a n accurate p r e d i c t i o n o f t h e j a c k e t water o u t l e t temperature should be p o s s i b l e b y k n o w i n g t h e h i s t o r y o f t h e j a c k e t i n l e t temperature and t h e m i x i n g c h a r a c t e r i s t i c s o f t h e j a c k e t . T h e r e f o r e , t h e d i f f e r e n c e between t h e a c t u a l and p r e d i c t e d o u t l e t temperatures m u l t i p l i e d by t h e f l o w r a t e and s p e c i f i c heat o f t h e w a t e r s h o u l d a l s o e q u a l Q.


U

UN-SS E n e r g y B a l a n c e . To p r e d i c t t h e o u t l e t t e m p e r a t u r e , a n u n s t e a d y - s t a t e ( U N - S S ) , e n e r g y b a l a n c e (1) must b e w r i t t e n a r o u n d the reactor j a c k e t . That balance i s : pVCp

dT —--at Q

I

= wCp (T. -T ) + UA (T. -T _)-U'A (T -T ) * i n out i n out out Ε J

The r a t e o f c h a n g e o f t h e o u t l e t t e m p e r a t u r e t i m e s t h e h e a t c a p a c i t y o f t h e j a c k e t e q u a l s t h e heat accumulated by t h e water f l o w p l u s t h e heat t r a n s f e r r e d from t h e r e a c t o r t o t h e j a c k e t minus t h e h e a t t r a n s f e r r e d from t h e j a c k e t t o t h e environment. The UN-SS e q u a t i o n r e d u c e s t o t h e SS e q u a t i o n i f dT / d t = 0 and t h e heat t r a n s f e r t o t h e environment i s negligible: Q = -UA (Τ -T ) = wCp (Τ. -T R out * i n out D i v i d i n g t h e UN-SS e q u a t i o n b y wCp p r o d u c e s : PVCp

dT

wCp

dt

1

UA

__2H_ = (T. -T in

)

out

+

—

_ wCp

( T - T

R

) out

U'A (T -T ) out Ε wCp n

Let: τ I



32.

GORDON AND WEIDNER

^Tôô

40.00

80.00

Metering

120.00

160.00

TIME ( S )

of Particle

200-00

, 240.00

Size

Distribution

280.00

320-00

517

3*0.00

·10'

Figure 1. Jacket water inlet and outlet temperatures in response to a —33°C (Test II) change in the inlet. The response of the jacket outlet temperature typifies a first-order mixing model.

Figure 2.

Plot of the heat transferred from the reactor to the jacket using the SS equation on the data from Figure 1


518

EMULSION POLYMERS AND

EMULSION POLYMERIZATION


This equation i s f i r s t order i n Τ with respect to t . A f i r s t o r d e r m i x i n g p a t t e r n h a s b e e n assumed, a n d a f i r s t o r d e r p a t t e r n i s e x h i b i t e d by most " w e l l - m i x e d " v e s s e l s t h a t do n o t h a v e b a f f l e s o r f l o w d i r e c t i n g n o z z l e s . How c l o s e l y t h i s f i r s t o r d e r e q u a t i o n f i t s t h e a c t u a l p r o c e s s w i l l be d e t e r m i n e d l a t e r . Determining Model Parameters. To s i m p l i f y f i t t i n g this f i r s t o r d e r e q u a t i o n t o t h e a c t u a l d a t a , t h e UN-SS e q u a t i o n m u s t be r e d u c e d . H e a t t r a n s f e r t o t h e e n v i r o n m e n t , t h e U'A' t e r m , may b e assumed n e g l i g i b l e ( f o r a f i r s t a p p r o x i m a t i o n a n y w a y ) . With no r e a c t i o n o c c u r r i n g and t h e r e a c t o r empty, t h e h e a t t r a n s f e r from t h e r e a c t o r t o t h e j a c k e t , and t h e h e a t r e t a i n e d i n t h e j a c k e t w a l l s , t h e UA t e r r a , may be assumed t o b e z e r o . The r e m a i n i n g e q u a t i o n (2^.3) i s : dT

out

=

dt

(T. - Τ ) xn out

G i v e n t h e d e r i v a t i v e ( d T ^ ^ / d t ) and t h e t e m p e r a t u r e T^, t h i s equation w i l l p r e d i c t the value of the o u t l e t temperature w i t h a l l external heat t r a n s f e r equal t o zero. The s o l u t i o n o f t h i s d i f f e r e n t i a l e q u a t i o n ( a s s u m i n g dT. / d t = 0) x s : -t/x

-t/τ Τ

= Τ

out

,.,.β out(x)

+T.

xn

(1-e

)

To a c c o u n t f o r l a g o r d e a d t i m e a s w i t h p l u g f l o w , a d e l a y , Θ, may b e i n c l u d e d i n t h e e q u a t i o n . -(t-6)/ T

4_=T

out

..e out(x) t /

T

+

T.

( 1-e xn

-(t-6)/T )

The two p a r a m e t e r s , θ a n d τ , n e e d t o b e d e t e r m i n e d ( 4 ) . B o t h may be o b t a i n e d f r o m a p l o t o f t h e j a c k e t i n l e t a n d o u t l e t t e m p e r a t u r e t o a s t e p change i n t h e j a c k e t i n l e t ( s e e F i g u r e 1 ) . For the f i r s t approximations, θ w i l l equal the d i f f e r e n c e i n time between the observed changes of t h e i n l e t and outlet temperatures, χ equals t h e time taken f o r the o u t l e t temperature to a c h i e v e 63.2% o f i t s f i n a l change. (The d e f i n i t i o n o f a t i m e c o n s t a n t o r τ i n t h i s case i s the time f o r a response t o a t t a i n 63.2% o f i t s f i n a l v a l u e . ) V a l u e s f o r t h e two t e s t s a r e shown below.


32.

Metering

GORDON AND WEIDNER

of Particle

Size

519

Distribution

TABLE I TEST 2 S t e p Change Flow Rate θ Κ τ τ K

-39.5°C 567.7cm / s 18.5 s 10500 130.2 s 86.4 s 1.502

2


TEST 2 -33.0°C 525.7cm / s 23.5 s 12350 143.4 s 93.6 s 1.532

Earlier, was s e t e q u a l t o pV/w. The v o l u m e , d e n s i t y , a n d f l o w r a t e a r e known s o t h a t t h i s "ideal"τ c o u l d h a v e b e e n calculated. R e a l i s t i c a l l y , t h e i d e a l and a c t u a l , τ , w i l l differ. i s the compensating f a c t o r t h a t r e l a t e s the i d e a l t o t h e a c t u a l , and h e n c e :

θ was assumed t o b e a f u n t i o n o f w, a n d θ t o w as i n : θ = wK

i s used t o

relate

1

The f i r s t o r d e r c u r v e s were compared t o t h e a c t u a l d a t a i n F i g u r e s 3 a n d 4. A v e r a g e Κ v a l u e s f o r θ a n d were u s e d . The f i t s a r e r e l a t i v e l y good a n d s u b s t a n t i a t e t h e a s s u m p t i o n s o f f i r s t order with a delay time. B e f o r e t h e UN-SS e q u a t i o n c a n b e i m p l e m e n t e d o n t h e c o m p u t e r t h e t e m p e r a t u r e s a m p l i n g r a t e s a n d method o f c a l c u l a t i n g dT / d t must be d e c i d e d . The s m a l l e r t h e t i m e c o n s t a n t , t h e s m a l l e r t h e s a m p l i n g r a t e s h o u l d be. A l l d a t a i n t h i s r e p o r t was o b t a i n e d a t 3 s e c o n d i n t e r v a l s ( a b o u t 2.2% o f t h e t i m e c o n s t a n t ) . The d e r i v a t i v e , d T / d t , may b e c a l c u l a t e d by p e r f o r m i n g a l e a s t s q u a r e s f i t arouncf 'N number o f p o i n t s . Ν s h o u l d be chosen i n v e r s e l y p r o p o r t i o n a l t o the accuracy and s t a b i l i t y o f t h e t e m p e r a t u r e m e a s u r e m e n t s . The h i g h e r t h e a c c u r a c y , t h e l o w e r Ν can be. Ν was c h o s e n t o b e 7 i n t h e s e t e s t s . A c o m p a r i s o n o f t h e SS a n d UN-SS e q u a t i o n s a r e shown i n F i g u r e 5 a s a p p l i e d t o t h e e a r l i e r s t e p change i n F i g u r e 1. The UN-SS e q u a t i o n was r e a r r a n g e d so b o t h s i d e s e q u a l t h e h e a t t r a n s f e r r e d t h r o u g h t h e r e a c t o r . The UN-SS e q u a t i o n p l o t t e d is : τ

Qt

1

UN-SS:

Q = -UA ( T ^ o u t * =

( T

in@(t-ef

T

K

I 2

( d T

out

/ d t )

T

- out

) w C


P


520

EMULSION POLYMERS AND EMULSION

POLYMERIZATION

Figure 3. Comparison of the actual and predicted jacket water outlet temperatures. Average values of θ = 21.7 and τ = 142.3 were used for the predicted temperature.

cο ο ο.

ο.

Ό.00

40.00

80.00

120.00

160.00

TIME ( S )

Figure 4.

200-00

240.00

280.00

320.00

360.00

·10'

Plot of the heat transferred from the reactor to the jacket using the UN-SS equation on the data from Figure 1


32.

GORDON AND WEIDNER

Metering

of Particle

Size

Distribution

521

The UN-SS e q u a t i o n i s a n i m p r o v e m e n t o v e r t h e SS e q u a t i o n . The t o t a l a r e a b e t w e e n t h e c u r v e a n d 0.00 c a l / s s h o u l d b e z e r o . The UN-SS e q u a t i o n d o e s h a v e some d r a w b a c k s . The d T / d t terra i s s e n s i t i v e t o n o i s e and t o t h e f l u c u a t i o n s i n t h e l a s t b i t o f t h e d i g i t a l t o a n a l o g c o n v e r t e r i n t h e c o m p u t e r . T h i s n o i s e may b e c o n t r o l l e d b y v a r y i n g 'Ν' u n t i l a n a c c e p t a b l e a g r e e m e n t i s r e a c h e d between n o i s e and a c c u r a c y . To f u r t h e r i m p r o v e t h e UN-SS e q u a t i o n , t h e v a r i a b l e s , θ and , may b e v a r i e d t o o p t i m i z e t h e f i t , o r a h i g h e r o r d e r m o d e l may b e n e c e s s a r y f o r a s m o o t h e r r e s p o n s e . U'A may b e d e t e r m i n e d by t r i a l a n d e r r o r , o r t h e UN-SS e q u a t i o n may b e s o l v e d f o r a n o n - z e r o U'A t o improve t h e accuracy o f t h e equation. Q

t

τ

1


1

Experimental Polymerization. The o n l y r e a l t e s t o f t h e UN-SS e q u a t i o n i s w i t h a c t u a l d a t a . Figure 6 i l l u s t r a t e s the j a c k e t i n l e t , j a c k e t o u t l e t , a n d r e a c t o r t e m p e r a t u r e s d u r i n g an e m u l s i o n r u n . The c o n t r o l was i n t e n t i o n a l l y underdamped t o i n s u r e the temperatures o s c i l l a t e d , thereby imposing a f a i r l y s t r i n g e n t t e s t o n t h e two m e t h o d s . F i g u r e 7 i s t h e SS c u r v e , a n d F i g u r e 8 i s t h e UN-SS. B o t h m o d e l s a c c o u n t f o r t h e m a j o r c h a n g e s i n t h e j a c k e t t e m p e r a t u r e , b u t t h e UN-SS e q u a t i o n h a n d l e d t h e s p i k e i n t h e j a c k e t i n l e t much b e t t e r . U n l i k e t h e SS e q u a t i o n , a t no a p p r e c i a b l e t i m e was t h e j a c k e t " h e a t i n g " t h e r e a c t o r ( s h o w i n g a p o s i t i v e c a l / s ) when i t was t h e r m οdynamically i m p o s s i b l e t o do s o . The UN-SS e q u a t i o n r e d u c e d t h e e f f e c t b y r e d u c i n g t h e a r e a e n c o m p a s s e d by t h e s p i k e i n t h e h e a t t r a n s f e r curve. W i t h an a c c u r a t e t o t a l and r a t e o f h e a t e v o l v e d from t h e r e a c t o r , t h e t o t a l and r a t e o f c o n v e r s i o n i s e a s i l y c a l c u l a t e d . Now a n a l g o r i t h m r e l a t i n g e m u l s i f i e r a d d i t i o n t o c o n v e r s i o n c a n be d e v e l o p e d a n d p r o p e r l y i m p l e m e n t e d . Applications A l g o r i t h m s , computer p r o c e s s c o n t r o l e q u a t i o n s , have been developed t o c o n t r o l e m u l s i f i e r metering r a t e s based on i n f o r m a t i o n o b t a i n e d from r a t e o f c o n v e r s i o n . Using this t e c h n i q u e o f e m u l s i f i e r m e t e r i n g , p a r t i c l e s i z e growth can be modified during the polymerization. Particle size distribution i s n o r m a l l y c o n t r o l l e d f o r e m u l s i o n PVC t h r o u g h h o r a o g e n i z a t i o n (_5 ) o r b y u s i n g seeded p o l y m e r i z a t i o n (§_t2.) · S e e d e d p o l y m e r i z a t i o n s normally produce a bimodal p a r t i c l e s i z e (PSD). F i g u r e 9 shows a t y p i c a l PVC l a t e x b i m o d a l PSD (6,1). N o t e o n e f r a c t i o n o f p a r t i c l e s i s l a b e l e d " l a r g e s " and t h e o t h e r f r a c t i o n i s l a b e l e d " s m a l l s " . P a r t i c l e s i z e i n c r e a s e s from r i g h t t o l e f t . P a r t i c l e s i z e was d e t e r m i n e d by a n I C I - J o y c e L o e b l Disc C e n t r i f u g e MK I I I w i t h p h o t o s e d i m e n t o m e t e r . This instrument measures p a r t i c l e s i z e and p a r t i c l e s i z e d i s t r i b u t i o n by c e n t r i f u g a t i o n u s i n g a p h o t o c e l l d e t e c t i o n system ( 8 , 9 ) .


522

EMULSION POLYMERS AND EMULSION

POLYMERIZATION

8

8 8 3 ο


78

4b.00

·0.00

120.00

160.00

TIME ( S )

Figure 5.

200.00

. 240.00

2*0.00

320.00

360.00

·10'

Superposition of Figures 2 and 4. The area between the curves and 0.0 cal/s represents the error in each calculation.

8

ah 8

M 8

Ji UJ

Emulsion Polymers and Emulsion Polymerization - American

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