Chapter 14
Modeling the Effect of Polymer Rheology on the Performance of Underwater Pelletizers R. S. Dixit, L. D. Wilson, and M . D. Marks
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One of the common problems a s s o c i a t e d with underwater p e l l e t i z e r s i s the tendency of the die holes to freeze off. This results in nonuniform polymer melt flow, increased pressure drop, and i r r e g u l a r extrudate shape. A d e t a i l e d engineering a n a l y s i s of p e l l e t i z e r s i s performed which accounts f o r the complex interaction between the fluid mechanics and heat t r a n s f e r processes i n a s i n g l e die h o l e . The p e l l e t i z e r model i s solved n u m e r i c a l l y to obtain v e l o c i t y , temperature, and pressure p r o f i l e s . E f f e c t of o p e r a t i n g c o n d i t i o n s , and polymer rheology on die performance i s evaluated and d i s c u s s e d .
The process o f underwater pelletization consists of e x t r u d i n g s t r a n d s o f p o l y m e r m e l t t h r o u g h an e x t r u s i o n d i e , c u t t i n g t h e polymer s t r a n d s , and then c o o l i n g t h e pellets w i t h water. The e x t r u s i o n d i e c o n s i s t s of a p e l l e t i z e r d i e p l a t e w i t h l a r g e number o f h o l e s w h i c h a r e u s e d f o r e x t r u d i n g t h e s t r a n d s a n d a r o t a t i n g k n i f e which i s u s e d t o c u t t h e s t r a n d s a s t h e y emerge f r o m t h e d i e f a c e . The f l o w i n g water s e r v e s t o c o o l t h e g r a n u l a t e s as w e l l a s c a r r y them o v e r t o t h e p e l l e t r e c o v e r y s e c t i o n . The p e l l e t i z e r d i e p l a t e i s h e a t e d e l e c t r i c a l l y o r w i t h h i g h p r e s s u r e steam ( 1 , 2 ) . The p e r f o r m a n c e o f p e l l e t i z e r s can be a n a l y z e d i n terms of the quality of pellets produced, mainly size, shape, s i z e - d i s t r i b u t i o n , and a p p e a r a n c e . I t c a n a l s o be a n a l y z e d i n terms o f t h r o u g h p u t and p r e s s u r e d r o p c h a r a c t e r i s t i c s as w e l l a s i t s a b i l i t y t o h a n d l e v a r i o u s p o l y m e r s w i t h d i f f e r e n t r h e o l o g y . The purpose o f t h i s paper i s t o develop a comprehensive m a t h e m a t i c a l model o f t h e p e l l e t i z e r w h i c h would p e r m i t quantitative analysis of p e l l e t i z e r operation. The f l o w o f p o l y m e r m e l t t h r o u g h t h e p e l l e t i z i n g d i e i s q u i t e complex. T h i s i s m a i n l y b e c a u s e t h e i n d i v i d u a l 0097-6156/89/0404-0132$06.00/0 © 1989 American Chemical Society
In Computer Applications in Applied Polymer Science II; Provder, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
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14.
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DIXIT ETAL.
d i e h o l e s a r e n o t i d e n t i c a l i n terms o f h e a t t r a n s f e r and p o l y m e r f l o w b e h a v i o r . The m e c h a n i c a l d e s i g n o f t h e d i e , the g e o m e t r i c a l placement of the die holes, and the p r o x i m i t y of the d i e holes to the channels for heating medium, a l l c o n t r i b u t e t o t h e f l o w n o n u n i f o r m i t y . The n o n u n i f o r m f l o w t h r o u g h t h e d i e h o l e s becomes even more s e v e r e when p o l y m e r s t a r t s s o l i d i f y i n g i n s i d e the d i e h o l e s . I f the t o t a l f l o w r a t e t o the d i e i s c o n t r o l l e d , reduced f l o w r a t e through the p a r t i a l l y f r o z e n d i e h o l e s f o r c e s more p o l y m e r t h r o u g h t h e c l e a n d i e h o l e s . T h i s results i n nonuniform extrudate shape and increased p r e s s u r e drop a c r o s s the d i e . The i n t e r a c t i o n s between p r o c e s s v a r i a b l e s can b e s t be u n d e r s t o o d by q u a l i t a t i v e l y a n a l y z i n g t h e f l o w b e h a v i o r i n a s i n g l e d i e h o l e . The s c h e m a t i c o f a s i n g l e d i e h o l e i s shown i n F i g u r e 1. The p o l y m e r m e l t e n t e r s t h e d i e h o l e a t a f a i r l y h i g h t e m p e r a t u r e (200 - 240 °C) . I t l o o s e s h e a t by c o n d u c t i o n t o t h e d i e w a l l and u n d e r certain circumstances may s t a r t to f r e e z e along the d i e w a l l s . T h i s r e s u l t s i n s t r o n g 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 s and a l t e r s t h e f l o w p r o f i l e . The v e l o c i t y p r o f i l e g e t s f u r t h e r m o d i f i e d as t h e p o l y m e r f l o w s t h r o u g h t h e c o n i c a l s e c t i o n o f t h e d i e h o l e . Due t o v e r y h i g h s h e a r r a t e s i n t h i s c o n i c a l r e g i o n , v i s c o u s d i s s i p a t i o n becomes s i g n i f i c a n t . Since the polymer v i s c o s i t y i s a s t r o n g f u n c t i o n of shear r a t e and t e m p e r a t u r e , any change i n t h e v e l o c i t y p r o f i l e a l s o m o d i f i e s t h e t e m p e r a t u r e p r o f i l e s i m u l t a n e o u s l y . The f r o z e n p o l y m e r l a y e r changes w i t h t i m e , t h e r e b y changing t h e r e s i s t a n c e t o p o l y m e r f l o w . Thus, i t i s c l e a r t h a t t h e performance of a s i n g l e die hole i s determined by the i n t e r a c t i o n between polymer fluid m e c h a n i c s and heat transfer. P e l l e t i z e r Model and
Numerical
Solution
The m a t h e m a t i c a l model o f a s i n g l e d i e h o l e c o n s i s t s o f equations which d e s c r i b e the polymer flow and heat t r a n s f e r . In d e r i v i n g t h i s model t h e f o l l o w i n g a s s u m p t i o n s a r e made: a) s t e a d y s t a t e b) c r e e p i n g f l o w , t h e r e f o r e i n e r t i a l t e r m s i n e q u a t i o n o f m o t i o n can be n e g l e c t e d c) heat c o n d u c t i o n i n p o l y m e r m e l t i n t h e f l o w d i r e c t i o n i s n e g l i g i b l e compared w i t h c o n v e c t i v e heat f l u x d) e l a s t i c e f f e c t s i n p o l y m e r m e l t a r e not c o n s i d e r e d e) f u l l y d e v e l o p e d f l o w a t d i e h o l e e n t r a n c e . The f l o w i n t h e d i e h o l e i s p r e d o m i n a n t l y i n the a x i a l d i r e c t i o n with the a x i a l v e l o c i t y , v , a f u n c t i o n of both r and z p o s i t i o n . The r a d i a l component o f v e l o c i t y , v , i s s i g n i f i c a n t o n l y i n the c o n i c a l s e c t i o n of the d i e h o l e . However, v i s a b o u t two o r d e r s of magnitude s m a l l e r compared w i t h t h e a x i a l v e l o c i t y , v . T h e r e f o r e , v is estimated by forcing the c o n t i n u i t y equation to be z
r
r
z
In Computer Applications in Applied Polymer Science II; Provder, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
r
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COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE II
Frozen Polymer Layer Figure
1. S i n g l e d i e h o l e .
In Computer Applications in Applied Polymer Science II; Provder, T.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
14.
Polymer Rheology and Underwater Pelletizers
DIXIT ETAL.
135
s a t i s f i e d a t a l l p o i n t s i n s i d e t h e d i e h o l e . Use o f t h i s procedure avoids the necessity f o r solving the r a d i a l momentum b a l a n c e . W i t h t h e s e a s s u m p t i o n s , t h e m a t h e m a t i c a l model d e s c r i b i n g t h e f l o w o f p o l y m e r m e l t t h r o u g h a s i n g l e d i e h o l e i s g i v e n by: Continuity
Equation
7^
