12
Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 6, 2016 | http://pubs.acs.org Publication Date: September 24, 1982 | doi: 10.1021/bk-1982-0197.ch012
Continuous Poly(vinyl Acetate) Emulsion Polymerization Reactors Dynamic Modeling of Molecular Weight and Particle Size Development and Application to Optimal Multiple Reactor System Design M. POLLOCK, J. F. MacGREGOR, and A. E. HAMIELEC McMaster University, Department of Chemical Engineering, Hamilton, Ontario, L8S 4L7, Canada The unsteady-state emulsion polymerization model of Kiparissides et al [1,2] and Chiang and Thompson [3] for predicting conversion, number of particles and particle size averages in continuous flow stirred tank reactors is extended to predict the long chain branching and molecular weight averages for poly(vinyl acetate). Sustained oscillations in these polymer properties, as well as in the particle properties, are predicted with this model. The extended model is used to show that by changing the continuous stirred tank reactor configuration, the oscillation phenomenon can be eliminated. Further more, it is shown that by using this new design, one can produce essentially the same latex product at much higher conversions or a better product (with fewer long chain branches) at the same conversion. In both cases, less initiator and soap are used than in the conventional configuration. During the production o f l a t t i c e s i n continuous flow s t i r r e d tank r e a c t o r s (CSTR's), o s c i l l a t i o n s are o f t e n observed i n a l l the important polymer and p a r t i c l e p r o p e r t i e s (e.g. c o n v e r s i o n , par t i c l e s i z e , molecular w e i g h t ) . According t o the model developed by K i p a r i s s i d e s e t a l [J_»2], these o s c i l l a t i o n s are due t o the p e r i o d i c formation and d e p l e t i o n o f soap m i c e l l e s which lead t o short periods o f r a p i d p a r t i c l e n u c l e a t i o n followed by long p e r i ods where no n u c l e a t i o n occurs. These o s c i l l a t i o n s can lead t o p a r t i c l e agglomeration during the periods o f r a p i d p a r t i c l e gen e r a t i o n due t o inadequate soap coverage o f the polymer p a r t i c l e s , and t o excessive long chain branching during the high conversion p o r t i o n o f the o s c i l l a t i o n s . Although l a r g e q u a n t i t i e s o f soap can e l i m i n a t e the o s c i l l a t i o n s , t h i s i s u n d e s i r a b l e from a cost standpoint as w e l l as from a product contamination point o f view. 0097-6156/82/0197-0209$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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210
COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE
The dynamic model d e v e l o p e d by K i p a r i s s i d e s e t a l M » 2 ] and s u b s e q u e n t l y m o d i f i e d by C h i a n g and Thompson [3.1 c a n p r e d i c t t h e c o n v e r s i o n , number o f p a r t i c l e s , p a r t i c l e d i a m e t e r s , e t c . , f o r t h e continuous emulsion polymerization o f v i n y l acetate. In t h i s p a p e r , t h e model i s e x t e n d e d t o p r e d i c t m o l e c u l a r w e i g h t a v e r a g e s and l o n g c h a i n b r a n c h i n g a s w e l l . The e x t e n d e d model i s t h e n used t o d e s i g n a new c o n t i n u o u s s t i r r e d tank r e a c t o r c o n f i g u r a t i o n which e l i m i n a t e s t h e o s c i l l a t i o n s and w h i c h o f f e r s substantial improvements i n product q u a l i t y , p r o d u c t i v i t y and o p e r a t i n g c o s t s . Model
Development
D e t a i l s o f t h e p a r t i c l e p r o p e r t y model may be f o u n d i n K i p a r i s s i d e s e t a l M , 2 ] and C h i a n g and Thompson [ 3 ] . Following an a p p r o a c h used by D i c k i n s o n and G o r b e r [ 5^, t h e d e v e l o p m e n t was b a s e d on an age d i s t r i b u t i o n a n a l y s i s i n w h i c h t h e c l a s s e s o f p a r t i c l e s b o r n between any t i m e , T and x+dx, were f o l l o w e d t h r o u g h the r e a c t o r . The r e s u l t was a s e r i e s o f d i f f e r e n t i a l e q u a t i o n s i n t h e t o t a l p a r t i c l e s i z e p r o p e r t i e s ( d i a m e t e r , a r e a and v o l u m e ) , t h e number o f p a r t i c l e s , c o n v e r s i o n and t h e i n i t i a t o r and emulsifier levels i n the reactor. In o r d e r t o i n c o r p o r a t e t h e m o l e c u l a r w e i g h t a v e r a g e s and l o n g c h a i n b r a n c h i n g e f f e c t s , a s i m i l a r a p p r o a c h h a s been t a k e n . F o l l o w i n g t h e d e v e l o p m e n t o f H a m i e l e c 161, expressions f o r the moments o f 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 f o r t h e c l a s s o f p a r t i c l e s b o r n between t i m e s T and x+dx were d e v e l o p e d . The development t a k e s i n t o a c c o u n t t r a n s f e r t o monomer, t r a n s f e r t o p o l y m e r , and t e r m i n a l d o u b l e bond p o l y m e r i z a t i o n . F o r t h e v i n y l a c e t a t e s y s t e m where t r a n s f e r t o monomer i s h i g h , t h e g e n e r a t i o n o f r a d i c a l s by t r a n s f e r t o monomer i s much g r e a t e r t h a n t h e g e n e r a t i o n o f r a d i c a l s by i n i t i a t i o n , so t h a t e s s e n t i a l l y a l l r a d i c a l s p r e s e n t have t e r m i n a l double bonds; hence, e f f e c t i v e l y a l l dead p o l y m e r m o l e c u l e s a l s o have a t e r m i n a l d o u b l e b o n d . T h u s , f o r v i n y l a c e t a t e p o l y m e r i z a t i o n , t h e t e r m i n a l d o u b l e bond p o l y m e r i z a t i o n c a n be s i g n i f i c a n t , and h a s been b u i l t i n t o t h e development. The e q u a t i o n s f o r t h e moments o f 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 and t h e a v e r a g e number o f b r a n c h e s p e r p o l y m e r m o l e c u l e a r e as f o l l o w s : . ^CQ (t,x)v(t,x)] 0
p
M
p
J [Q (t,,x)B (t,x)v(t,x)] F
o
N
Q
v
= K
Y (t,x)
[C
o
= K
p
m
} ]
M ^ ^ [ C Q p
(t,x)v(t,x)
-
p
l
(
( 1 )
t , x ) v ( t , x )
+ KQ (t,x)v(t,x)] o
Provder; Computer Applications in Applied Polymer Science ACS Symposium Series; American Chemical Society: Washington, DC, 1982.
(2)
12.
MW
POLLOCK ET AL.
^[Q (t 1
t T
)v(t
f T
)v(t
f T
)]
=K
]
=K
2
t T )
(3)
p
M Y (t )
p
Y (t,x) M ^ [ v ( t
d
^[Q (t
p
0
i T
p
l
t
)
+ 2 (
1 + KQ (t,x)/M C
Cm
Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 6, 2016 | http://pubs.acs.org Publication Date: September 24, 1982 | doi: 10.1021/bk-1982-0197.ch012
i.e
p
Ql
T
p
1
f
R
I r P (t,x) * r r =1
=
Q (t,x),
+
C Q (t,T)v(t,x) KQ (t x)v(t,T) jj + — ] (4) p p ?
*[v(t,x) +
where Q ( t , x ) n
211
and Particle Size Development
n
Q^Ct.x),
= moments o f polymer molecular weight d i s t r i b u t i o n f o r p a r t i c l e s born between x and x+dx a t time t (mole/R) B^Ct.x) = branch p o i n t s per polymer p a r t i c l e f o r p a r t i c l e born between x and x+dx at time t v(t x) = volume o f p a r t i c l e born between T and T+CJT a t time t Y ( t , x ) = number o f r a d i c a l s i n a p a r t i c l e born between T and x+dT at time t K = propagation r a t e constant Q
Q^Ct.x)
f
Q
p
M
p
= c o n c e n t r a t i o n o f monomer i n the polymer p a r t i c l e
C = K« /K ( K ~ = r a t e constant f o r t r a n s f e r t o monomer) m fm p fm C r K /K (K r r a t e constant f o r t r a n s f e r to polymer) p
f p
p
f p
= K */K (K * = r a t e constant f o r t e r m i n a l double bond P P P V polymerization) I f the property balances above f o r any given property p ( t , x ) the c l a s s o f p a r t i c l e s born between x and x+dx are expressed K
of as:
d
p
(
l ' dt
T
)
= f(t.t)
(5a)
then the t o t a l property P(t) obtained by summing over a l l c l a s s e s of p a r t i c l e s i s given b y : dP(t) ~dt—
P
=
iN
(
t
)
-
p
(
t
t dp(t.x)
)
fi
+
^
P (ttt) + / 0
d
t
, .
— n ( t , x ) dx
(5b)
o where f ( t ) i s the p a r t i c l e generation r a t e at time t , P ( t , t ) i s the value o f p ( t , ) a t b i r t h , n ( t , x ) d x are the number o f p a r t i c l e s born between x and x+dx and e i s the residence time o f the reactor. Q
T
Provder; Computer Applications in Applied Polymer Science ACS Symposium Series; American Chemical Society: Washington, DC, 1982.
COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE
212
U s i n g t h i s , t h e f o l l o w i n g d i f f e r e n t i a l e q u a t i o n s h a v e been o b t a i n e d f o r t h e o v e r a l l m o l e c u l a r w e i g h t moments and t h e a v e r a g e number o f l o n g c h a i n b r a n c h e s p e r p o l y m e r m o l e c u l e . AQ (t)
1
K
1
d Q (t) d t°
"
+ Kp M ( C m Vp( t )' p YAVE
°6
QV)
^
v
A
(6)
)
P
Downloaded by UNIV OF CALIFORNIA SAN DIEGO on March 6, 2016 | http://pubs.acs.org Publication Date: September 24, 1982 | doi: 10.1021/bk-1982-0197.ch012
1
d(Q B ) ( t ) —JLg dt d QJ(t)
1
1
(AQ B ) ( t ) ._2_n 6
=
1
C CL (t) _p_1 p AVE M P
p
KQ (t) .o _ M„ P )
(
?
)
1
AQ (t)
I t
- T -
=
+
K
M
Y
P P AVE
V
p
(
t
)
(
8
)
AQl(t)
d Q^(t) _ 2 _
=
^
+
^
CQl(t)
Y
a
v
e
[
V
p
(
t
)
+
2
,
M
T
I
.
0
(
V
p
(
t
)
+
KQj(t)
P
P
(1 + K Q /M ) _ (C + C0 /M ) m p i p P
RATIO =
1
(10)
n
where 1
Q>),Q](t),Q (t),(Q B ) (t) 2
o
n
= (Q V ) 0
(
Q
p
t o t a l
(t).(Q V
)
1
2 V t o t a l
(
t
)
'
(
Q
B
t o t a l
o n V
(t).
total
(
t
)
respectively and
and
1 1 1 AQ (t) = Q ( t ) - Q ( t ) = difference n n
I N
n
M ( t ) = ( Q J ( t ) / Q J ( t ) ) * MW N
