Polymerization Reactors and Processes 9780841205062, 9780841206526, 0-8412-0506-X

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Polymerization Reactors and Processes J . N e i l Henderson, EDITOR Goodyear Tire and Rubber Company

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.fw001

Thomas C . Bouton, EDITOR Firestone Synthetic Rubber and Latex Company

Based on a symposium sponsored by the ACS Division of Polymer Chemistry and the American Institute of Chemical Engineers at the University of Akron, Akron, Ohio, October 5-6, 1978.

ACS SYMPOSIUM SERIES

AMERICAN

CHEMICAL

WASHINGTON,

D.

C.

SOCIETY 1979

104

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.fw001

Library of Congress

Data

Polymerization reactors and processes. (ACS symposium series; 104 ISSN 0097-6156) Papers based on a symposium sponsored by the American Chemical Society and the American Institute of Chemical Engineers at the University of Akron, Oct. 5-6, 1978. Includes bibliographies and index. 1. Polymers and polymerization—Congresses. 2. Chemical reactors—Congresses. I. Henderson, James Neil, 1924II. Bouton, T. G, 1939III. American Chemical Society. IV. American Institute of Chemical Engineers. V. Series: American Chemical Society. ACS symposium series; 104. TP156.P6P63 668 79-12519 ISBN 0-8412-0506-X ASCMC 8 104 1-407 1979

Copyright © 1979 American Chemical Society All Rights Reserved. The appearance of the code at the bottom of thefirstpage of each article in this volume indicates the copyright owner's consent that reprographic copies of the article may be made for personal or internal use or for the personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to copying or transmission by any means—graphic or electronic—for any other purpose, such as for general distribution, for advertising or promotional purposes, for creating new collective works, for resale, or for information storage and retrieval systems. The citation of trade names and/or names of manufacturers in this publication is not to be construed as an endorsement or as approval by ACS of the commercial products or services referenced herein; nor should the mere reference herein to any drawing, spécification, chemical process, or other data be regarded as a license or as a conveyance of any right or permission, to the holder, reader, or any other person or corporation, to manufacture, reproduce, use, or sell any patented invention or copyrighted work that may in any way be related thereto. PRINTED IN THE UNITEDSTATESOFAMERICA

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.fw001

ACS Symposium Series Robert F . G o u l d , Editor

Advisory Board Kenneth B. Bischoff

James P. Lodge

Donald G . Crosby

John L. Margrave

Robert E. Feeney

Leon Petrakis

Jeremiah P. Freeman

F. Sherwood Rowland

E. Desmond Goddard

Alan C. Sartorelli

Jack Halpern

Raymond B. Seymour

Robert A . Hofstader

Aaron W o l d

James D . Idol, Jr.

Gunter Zweig

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.fw001

FOREWORD The ACS SYMPOSIUM SERIES was founded in 1974 to provide

a medium for publishing symposia quickly in book form. The format of the Series parallels that of the continuing ADVANCES IN CHEMISTRY SERIES except that in order to save time the papers are not typeset but are reproduced as they are submitted by the authors in camera-ready form. Papers are reviewed under the supervision of the Editors with the assistance of the Series Advisory Board and are selected to maintain the integrity of the symposia; however, verbatim reproductions of previously published papers are not accepted. Both reviews and reports of research are acceptable since symposia may embrace both types of presentation.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.pr001

PREFACE TJolymer reactor engineering is an important, evolving branch of technology. This book assembles eighteen papers presented at a joint symposium, "Polymerization Reactors and Processes," sponsored by the American Chemical Society and the American Institute of Chemical Engineers at the University of Akron, October 5 and 6, 1978. The first four papers of the book were plenary lectures at the symposium. The speakers, Gary Poehlein, Joseph A. Biesenberger, A. E. Hamielec, and R. H . M . Simon, were invited to deal at length with selected areas of polymer reactor engineering in which they had made especially significant contributions. The objective of bringing together practicing engineers in a format suitable for basic instruction as well as for the dissemination of new information was well met both by the formal program and by the informal discussions of the 180 attendees. Considering that the symposium was not part of any larger meeting of the sponsoring societies, the large attendance is a strong indication of the interest in the subject as well as of the quality of the program put together by Irja Piirma and D. C. Chappelear. Credit for the conception and execution of this program must be given to Dr. T. H . Forsyth who saw the need for the meeting and obtained the support of the ACS and AIChE both nationally and locally. Without the umbrella of a larger meeting, much more organization and planning were necessary. In this, Henry Forsyth was aided by a very active committee: Tom Bouton, David C. Chappelear, James Cobb, Joseph N. Feil, Neil Henderson, Thomas A. Kenat, Joginder Lai, Robert W. Lee, Ted Millis, Irja Piirma, Arthur T. Schooley, and Keith C. Williams. In addition to ACS and AIChE, cosponsors were B. F. Goodrich Co., Chemstress Consultants, Firestone Tire & Rubber Co., General Tire & Rubber Co., Goodyear Tire & Rubber Co., PPG Industries, and the Standard Oil Co. (Ohio). Although the papers represent the whole range of kinds of polymers and processes, there are common themes which reveal the dominant concerns of polymerization reactor engineers. Fully half the papers are concerned rather closely with devising and testing mathematical models which enable process variables to be predicted and controlled very precisely. Such models are increasingly demanded for optimization and com-

vii

puterization of large-scale processes. Another common concern is the improvement of hardware: stirred tanks, tubular reactors, fluidized beds, and RIM molds; continuous, semi-continuous, batch, and precipitation polymerization are all represented. Therefore, taken as a whole, this book represents state-of-the-art polymerization reactor technology. Finally, the editors wish to thank the authors for their effective oral and written communications and the reviewers for their critical and constructive comments. Goodyear Tire and Rubber Company

JAMES N E I L HENDERSON

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.pr001

Akron, Ohio 44316 Firestone Synthetic Rubber and Latex Company Akron, Ohio 44301 February 21, 1979

viii

THOMAS C. BOUTON

1 Continuous Emulsion Polymerization: Problems in Development of Commercial Processes GARY P O E H L E I N

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

School of Chemical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Continuous emulsion p o l y m e r i z a t i o n systems are s t u d i e d to e l u c i d a t e r e a c t i o n mechanisms and to generate the knowledge necessary f o r the development of commercial continuous processes. Problems encountered with the development of continuous r e a c t o r systems and some o f the ways of d e a l i n g w i t h these problems will be d i s c u s s e d in t h i s paper. Those i n t e r e s t e d i n more d e t a i l e d i n f o r m a t i o n on chemical mechanisms and t h e o r e t i c a l models should consult the review papers by Ugelstad and Hansen (1), ( k i n e t i c s and mechanisms) and by P o e h l e i n and Dougherty (2), (continuous emulsion p o l y m e r i z a t i o n ) . In order to be economically v i a b l e , a continuous emulsion p o l y m e r i z a t i o n process must be able t o produce a l a t e x which satisfies a p p l i c a t i o n requirements a t high r a t e s without frequent disruptions. Since most l a t e x products are developed i n batch equipment, the problems a s s o c i a t e d with c o n v e r t i n g to continuous systems can be s i g n i f i c a n t . Making such a change r e q u i r e s an understanding o f the d i f f e r e n c e s between batch and continuous r e a c t o r s and how these d i f f e r e n c e s i n f l u e n c e product p r o p e r t i e s and r e a c t o r performance. Reactor

Types:

Before d i s c u s s i n g d i f f e r e n c e s between r e a c t o r s a b r i e f d e s c r i p t i o n o f r e a c t o r types would seem i n order. Three c l a s s i f i c a t i o n s are normally recognized: 1. Batch, 2. Semi-Continuous or Semi-Batch, and 3. Continuous. The batch r e a c t o r i s , i n many ways, the simplest. Recipe i n g r e d i e n t s are charged and brought to r e a c t i o n temperature; i n i t i a t o r i s then added i f i t was not p a r t of the o r i g i n a l charge; the r e a c t i o n i s c a r r i e d to the d e s i r e d degree of conversion and the l a t e x i s removed f o r further processing. With semi-continuous (more p r o p e r l y , semi-batch) r e a c t o r s only p a r t of the charge i s added a t the beginning of the c y c l e . U s u a l l y some r e a c t i o n time i s allowed to pass before the remaining part of the charge i s added i n a c o n t r o l l e d manner. Sometimes

0-8412-0506-x/79/47-104-001$05.00/0 © 1979 American Chemical Society

POLYMERIZATION REACTORS AND PROCESSES

o n l y a p o r t i o n of the monomer i s w i t h h e l d from the i n i t i a l charge w h i l e i n other cases the secondary feed stream i s a monomer emulsion. Continuous r e a c t o r systems u s u a l l y c o n s i s t of s t i r r e d tanks connected i n s e r i e s with a l l the r e c i p e i n g r e d i e n t s fed i n t o the f i r s t r e a c t o r and the product removed from the l a s t r e a c t o r . Recipe i n g r e d i e n t s can a l s o be added at intermediate p o i n t s along the r e a c t o r t r a i n . Continuous-flow t u b u l a r r e a c t o r s can be used i n s e r i e s with the tanks, u s u a l l y as a p r e r e a c t o r i n f r o n t of the tanks.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

Inhibitor Effect: I n h i b i t o r s can be present i n most r e a c t i o n i n g r e d i e n t s . They are d e l i b e r a t e l y added to monomers to prevent premature polymerization. Ingredient streams such as monomers are cleaned and handled c a r e f u l l y to avoid i n h i b i t i o n i n fundamental s t u d i e s , e s p e c i a l l y i n most academic l a b o r a t o r i e s . Commercial processes, however, are u s u a l l y operated with i n h i b i t o r s present i n the feed streams, p a r t i c u l a r l y i n the monomer. When such i n g r e d i e n t s are used i n a batch reactor, a dead time i s observed before the reaction starts. The simple two-reactor s e r i e s shown i n F i g u r e 1 w i l l be analyzed to demonstrate the e f f e c t of i n h i b i t o r on the performance of continuous systems. Since i n h i b i t o r w i l l be present i n the c o n t i n u o u s l y added feed stream, i t w i l l serve to reduce the e f f e c t i v e i n i t i a t i o n r a t e i n the f i r s t r e a c t o r . Since i n h i b i t o r i s v e r y r e a c t i v e with f r e e r a d i c a l s , a l l i n h i b i t o r fed must be destroyed before s i g n i f i c a n t r e a c t i o n can take p l a c e . Thus the e f f e c t i v e r a t e of i n i t i a t i o n i n the f i r s t r e a c t o r i s given by Equation 1.

where R i s the net r a t e of i n i t i a t i o n i n the f i r s t r e a c t o r , f i s i n i t i a t i o n e f f e c t i v e n e s s f a c t o r , K, i s the i n i t i a t o r decomposit i o n r a t e constant, [ o ] i s the i n i t i a t o r c o n c e n t r a t i o n i n the mixed feed stream, i s the mean r e s i d e n c e time i n the f i r s t r e a c t o r , [H] i s the i n h i b i t o r c o n c e n t r a t i o n i n the mixed feed stream, and ?^ i s the number of f r e e r a d i c a l s consumed per i n h i b i t o r molecule. Equation 1 i s v a l i d only i f I

Q

(2)

1+K, 0a l

In t h i s case the i n h i b i t o r c o n c e n t r a t i o n i n the stream l e a v i n g Reactor 1, [H]_, i s zero. I f the i n h i b i t o r c o n c e n t r a t i o n , [H] , i s l a r g e r than necessary to s a t i s f y the e q u a l i t y of Equation 2 there w i l l be no p o l y m e r i z a t i o n i n Reactor 1 and the i n h i b i t o r c o n c e n t r a t i o n e n t e r i n g Reactor 2 w i l l be:

POEHLEIN

Continuous

Emulsion

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

F

V

Polymerization

[i l 2

v

Ih H

REACTOR 1 VOLUME V

F , F & F

1

ARE

REACTOR 2

VOLUMETRIC FLOW RATES

VOLUME V ,

Q

1

2

SIMPLIFIED FLOW DIAGRAM — END OF SERIES CSTR SYSTEM Figure

1.

Continuous

flow

FRONT

diagram

4

POLYMERIZATION REACTORS AND PROCESSES

2K,[i i

e

9

(3

l

>

H

]

i

-

[ H ]

^

( i ^ r

o -

In t h i s case the r a t e of i n i t i a t i o n i n the second r e a c t o r w i l l be given by:

w

K

, i,2 "

f d 2 o \ |_(i+K e ) ( i + K e ) J 2 K

f

[ I

d

]

1

d

[ H 3

2

1 e

f

H

2

An examination of the above equations shows that Rj.,1 may be zero, or „ ^ g r e a t e r than R i , i even i f R _ i s f i n i t e . T h u s , i t may'be necessary to add i n h i b i t o r t o Reactor 2 to slow the r e a c t i o n so the heat can be removed by the c o o l i n g system. The i n f l u e n c e o f i n h i b i t o r on the performance o f a semicontinuous r e a c t o r can be, i n some ways, s i m i l a r to both batch and continuous systems. A dead time i s u s u a l l y observed upon a d d i t i o n o f the i n i t i a l charge. When the secondary stream flow i s s t a r t e d a f t e r some r e a c t i o n of the i n i t i a l charge, a d d i t i o n a l i n h i b i t o r flows i n t o the r e a c t o r and the i n i t i a t i o n r a t e drops. When t h i s programmed a d d i t i o n i s stopped the i n i t i a t i o n r a t e i n c r e a s e s ; sometimes enough t o cause temperature c o n t r o l problems. m

a

v

e

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

i

Latex P a r t i c l e S i z e D i s t r i b u t i o n s : P a r t i c l e formation i n the e a r l y stages o f a batch r e a c t i o n i s normally q u i t e r a p i d . Hence the p a r t i c l e s u r f a c e area produced i s a b l e to adsorb the f r e e e m u l s i f i e r q u i t e e a r l y i n the r e a c t i o n (2 to 10% conversion) and p a r t i c l e formation ceases, o r a t best slows t o a v e r y low r a t e . P a r t i c l e s formed i n the beginning o f the r e a c t i o n would have approximately i d e n t i c a l ages a t the end of the batch r e a c t i o n . These p a r t i c l e s would be expected t o be n e a r l y the same s i z e u n l e s s f l o c c u l a t i o n mechanisms, s t o c h o s t i c d i f f e r e n c e s , o r secondary n u c l e a t i o n f a c t o r s a r e s i g n i f i c a n t . The p a r t i c l e s i n the l a t e x stream l e a v i n g a continuous s t i r r e d - t a n k r e a c t o r (CSTR) would have a broad d i s t r i b u t i o n of residence times i n the r e a c t o r . T h i s age d i s t r i b u t i o n , given by Equation 5, comes about because of the r a p i d mixing of the feed stream with the contents of the s t i r r e d r e a c t o r . (5)

A (t) = | ^ x

e"

t / 0

l

where A ^ ( t ) i s the r e s i d e n c e time d i s t r i b u t i o n and the p a r t i c l e age d i s t r i b u t i o n i n the stream l e a v i n g the f i r s t tank of the two-tank s e r i e s shown i n F i g u r e 1, and t i s time or age. The r e s i d e n c e time d i s t r i b u t i o n f o r a two-tank system i s given by (6) or

A (t) = ^ 2

e"

t / 0

l

if0

1

= G

2

1.

POEHLEIN

Continuous

e " >

(7

k

t

/

Emulsion

e

i 8,-9

~

e

2 ^ = -

t / 0

5

Polymerization

2 l

2

f

9

l '

e

2 a

r

e

Graphs of these d i s t r i b u t i o n s f o r v a r i o u s r a t i o s of shown i n F i g u r e 2. I f p a r t i c l e growth r a t e i s known, as a f u n c t i o n of p a r t i c l e s i z e , the s i z e d i s t r i b u t i o n can be c a l c u l a t e d from Equation 8. (8)

U(D)

= A(t)

y

d

D

(

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

dt

I

where U(D) i s the p a r t i c l e s i z e d i s t r i b u t i o n IdD/dtj i s the absolute v a l u e of the r a t e of time. Equation 8 i s based on the assumption by p o l y m e r i z a t i o n r a t h e r than f l o c c u l a t i o n . Case 2 k i n e t i c s are followed p a r t i c l e growth excess monomer i s given by:

based on diameter and diameter change w i t h that p a r t i c l e s grow I f Smith-Ewart i n the presence of

where K-^ i s a constant dependent on p o l y m e r i z a t i o n r a t e constants and s w e l l i n g parameters, [K] i s the monomer c o n c e n t r a t i o n at the r e a c t i o n s i t e and n i s the time-average number of f r e e r a d i c a l s per p a r t i c l e (n=0.5 f o r S-E Case 2). When Equation 9 i s used i n Equation 8 along with the r e l a t i o n s h i p s f o r the r e s i d e n c e time d i s t r i b u t i o n s one o b t a i n s the f o l l o w i n g dimensionless p a r t i c l e s i z e d i s t r i b u t i o n s f o r one- and two-tank systems. 3V e~

(10)

U (P)

=

(11)

U (D)

= 3V e"

X

2

(12) U ( P ) 2

2

5

= ^

V3

if 0

V3

(e

V

- e

V

)

if 0

2

=

X

-

0

2

m0

1

where V = D/(6K /"M7n0 /fr) / Equations 11 and 12 are only v a l i d i f the v o l u m e t r i c growth r a t e of p a r t i c l e s i s the same i n both r e a c t o r s ; a c o n d i t i o n which would not hold t r u e i f the conversion were h i g h or i f the temperatures d i f f e r . Graphs of these s i z e d i s t r i b u t i o n s are shown i n F i g u r e 3. They are a l l broader than the d i s t r i b u t i o n s one would expect i n l a t e x produced by batch r e a c t i o n . The p a r t i c l e s i z e d i s t r i b u t i o n s shown i n F i g u r e 3 are based on the assumption that steady-state p a r t i c l e generation can be achieved i n the CSTR systems. Consequences of t r a n s i e n t s or l i m i t - c y c l e behavior w i l l be d i s c u s s e d l a t e r i n t h i s paper. Semi-continuous r e a c t o r s can be used to produce very narrow or q u i t e broad p a r t i c l e s i z e d i s t r i b u t i o n s depending on the nature of the secondary feed stream and how i t i s added to the r e a c t o r . 1

1

1

3

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

6 POLYMERIZATION REACTORS AND PROCESSES

Ο

8

ί

«

ci

1

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

1. poEHLEiN Continuous Emulsion Polymerization 7

I

Ο

I

.ο "•δ ο

ε

8

POLYMERIZATION REACTORS AND PROCESSES

I f the secondary feed stream i s simply monomer i t w i l l not normally have a major impact on the p a r t i c l e formation r e a c t i o n and the p a r t i c l e s i z e d i s t r i b u t i o n can be narrow. I f the secondary stream c o n t a i n s e m u l s i f i e r i t can f u n c t i o n i n three ways. When the emulsion feed i s s t a r t e d q u i c k l y the added e m u l s i f i e r can serve to lengthen the p a r t i c l e formation p e r i o d and hence to broaden the p a r t i c l e s i z e d i s t r i b u t i o n . When the emulsion feed i s s t a r t e d l a t e r and added i n such a manner that the e m u l s i f i e r i s promptly adsorbed on e x i s t i n g p a r t i c l e s , one can o b t a i n q u i t e narrow s i z e d i s t r i b u t i o n s . I f the emulsion feed i s s t a r t e d l a t e r but added r a p i d l y enough to generate f r e e emulsif i e r i n the r e a c t i o n mixture a second p o p u l a t i o n of p a r t i c l e s can be formed, again y i e l d i n g a broad s i z e d i s t r i b u t i o n .

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

Copolymer Composition: When a batch r e a c t o r i s used to produce polymer from s e v e r a l monomers a s i g n i f i c a n t change i n copolymer composition can occur during the course o f the p o l y m e r i z a t i o n . The f i r s t polymer formed w i l l c o n t a i n a higher p o r t i o n of the more r e a c t i v e monomer w h i l e the f i n a l polymer formed w i l l be composed of a l a r g e r f r a c t i o n of the s l o w - r e a c t i n g monomer. More uniform polymer can be produced by u s i n g a semi-continuous system i n which a p o r t i o n of the more r e a c t i v e monomer i s withheld from the o r i g i n a l charge and added a t a c a r e f u l l y programmed r a t e d u r i n g the course of the r e a c t i o n . The polymeric m a t e r i a l produced i n a s i n g l e s t i r r e d - t a n k r e a c t o r w i l l , except f o r s t o c h a s t i c v a r i a t i o n s , be o f uniform composition. T h i s polymer composition can be s i g n i f i c a n t l y d i f f e r e n t from the composition i n the monomer feed mixture u n l e s s the c o n v e r s i o n i s h i g h . I f s e v e r a l tanks a r e connected i n s e r i e s the composition o f the polymer produced i n each r e a c t o r can be quite d i f f e r e n t . Since most p a r t i c l e s are formed i n the f i r s t r e a c t o r t h i s change i n composition i n the f o l l o w i n g r e a c t o r s can y i e l d polymer p a r t i c l e s i n which composition v a r i e s w i t h r a d i u s w i t h i n the p a r t i c l e s . Compositional d r i f t i n continuous r e a c t o r t r a i n s can be a l tered by i n t r o d u c i n g feed streams o f the more r e a c t i v e monomer between r e a c t o r s . T h i s procedure i s e q u i v a l e n t to programmed a d d i t i o n of the more r e a c t i v e monomer i n a semi-continuous system. The proceeding d i s c u s s i o n o f polymer composition was based on the assumption that e s s e n t i a l l y a l l polymer i s formed i n the o r ganic phases o f the r e a c t i o n mixture. I f a w a t e r - s o l u b l e monomer, such as some of the f u n c t i o n a l monomers, i s used, the r e a c t i o n s t a k i n g p l a c e i n the aqueous phase can c o n t r i b u t e to v a r i a t i o n i n polymer composition. In f a c t , i n extreme cases, water s o l u b l e polymer can be formed i n the aqueous phase. T h i s can happen i n batch, semi-continuous or continuous r e a c t o r s . The f a t e of funct i o n a l monomers could be c o n s i d e r a b l y d i f f e r e n t among the d i f f e r ent r e a c t o r types, but d e t a i l e d s t u d i e s on t h i s phenomenon have not been r e p o r t e d .

1.

POEHLEIN

Continuous

Emulsion

Polymerization

9

Reaction Rate: Continuous s t i r r e d - t a n k r e a c t o r s can behave very d i f f e r e n t l y from batch r e a c t o r s w i t h regard to the number of p a r t i c l e s formed and p o l y m e r i z a t i o n r a t e . These d i f f e r e n c e s are probably most extreme f o r styrene, a monomer which c l o s e l y f o l l o w s Smith-Ewart Case 2 k i n e t i c s . Rate and number of p a r t i c l e s i n a batch r e a c t o r f o l l o w s the r e l a t i o n s h i p expressed by Equation 13. (13) Rp

«

N

a

R

i

°-

4

0

S -

6

where S i s the e m u l s i f i e r c o n c e n t r a t i o n . A s i n g l e CSTR y i e l d s a d i f f e r e n t r e l a t i o n s h i p as shown by Equation 14.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

(14) Rp

a

N

a

R

i

S

0

where 0 i s the mean residence time. Equations 13 and 14 represent r a t e s during i n t e r v a l two i n batch p o l y m e r i z a t i o n and f o r i n t e r mediate conversions i n a CSTR. These two equations i l l u s t r a t e an important p o i n t . That i s , even w i t h the same k i n e t i c mechanisms, the i n f l u e n c e of key v a r i a b l e s on r a t e and p a r t i c l e generation may be q u i t e d i f f e r e n t between the two r e a c t o r types. A summary of steady-state r a t e s f o r a number of monomers i s given by P o e h l e i n and Dougherty (2) . The r a t e of p o l y m e r i z a t i o n w i t h styrene-type monomers i s d i r e c t l y p r o p o r t i o n a l to the number of p a r t i c l e s formed. In batch r e a c t o r s most of the p a r t i c l e s a r e nucleated e a r l y i n the r e a c t i o n and the number formed depends on the e m u l s i f i e r a v a i l a b l e to s t a b i l i z e these small p a r t i c l e s . In a CSTR o p e r a t i n g a t steady-state the r a t e of n u c l e a t i o n of new p a r t i c l e s depends on the c o n c e n t r a t i o n of f r e e e m u l s i f i e r , i . e . the e m u l s i f i e r not adsorbed on other s u r f a c e s . Since the average p a r t i c l e s i z e i n a CSTR i s l a r g e r than the average s i z e at the end of the batch n u c l e a t i o n p e r i o d , fewer p a r t i c l e s a r e formed i n a CSTR than i f the same r e c i p e were used i n a batch r e a c t o r . Since r a t e i s p r o p o r t i o n a l to the number of p a r t i c l e s f o r styrene-type monomers, the r a t e per u n i t volume i n a CSTR w i l l be l e s s than the i n t e r v a l two r a t e i n a batch r e a c t o r . In f a c t , the maximum CSTR r a t e w i l l be about 60 to 70 percent the batch r a t e f o r such monomers. Monomers f o r which the r a t e i s not as s t r o n g l y dependent on the number of p a r t i c l e s w i l l d i s p l a y l e s s of a d i f f e r e n c e between batch and continuous r e a c t o r s . A l s o , continuous r e a c t o r s w i t h a p a r t i c l e seed i n the feed may be capable of higher r a t e s . Reactor production r a t e depends on average r e a c t i o n r a t e and the f r a c t i o n of the time the r e a c t o r i s not operating. With a batch r e a c t o r the r e a c t i o n r a t e s t a r t s s m a l l , i n c r e a s e s to a r a t h e r constant value, sometimes increases f u r t h e r to a maximum, and then decreases r a p i d l y as the monomer c o n c e n t r a t i o n f a l l s . The r e a c t i o n r a t e i n a continuous r e a c t o r i s dependent on monomer conversion but i t does not vary with time once steady-state

10

POLYMERIZATION

REACTORS AND PROCESSES

o p e r a t i o n i s achieved. T h i s r a t e can be high f o r a wide range of conversions, but i t w i l l be low at the high conversion end of the reactor t r a i n . Thus l a r g e r e a c t o r volumes may be r e q u i r e d i f high conversion l a t e x e s are to be produced.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

A d d i t i o n of Feed Streams: Since feed streams are not added a f t e r the s t a r t of a batch r e a c t i o n one need only be concerned w i t h proper i n i t i a l a d d i t i o n and b l e n d i n g procedures. Streams f l o w i n g i n t o a CSTR, however, are being introduced i n t o a polymer l a t e x . I f added improperly, these streams can f a i l to be mixed completely and they can cause flocculation. Streams should be introduced where they are mixed r a p i d l y and the i o n i c c o n c e n t r a t i o n should be as low as p o s s i b l e . I n t r o d u c t i o n of such streams as i n i t i a t o r s o l u t i o n s a t h i g h c o n c e n t r a t i o n s or i n the wrong l o c a t i o n can cause l o c a l f l o c c u l a t i o n and/or non-uniform r e a c t i o n . Recipe a d d i t i o n s can a l s o be important with semi-continuous r e a c t o r s . A d d i t i o n r a t e s i n f l u e n c e r e a c t o r performance, and i n c o r r e c t a d d i t i o n l o c a t i o n can l e a d to non-uniform r e a c t i o n w i t h i n the r e a c t o r , l o c a l i z e d f l o c c u l a t i o n , and r e a c t o r short-circuiting. Unsteady-State

Operation:

A c h i e v i n g s t e a d y - s t a t e o p e r a t i o n i n a continuous tank r e a c t o r system can be d i f f i c u l t . P a r t i c l e n u c l e a t i o n phenomena and the decrease i n t e r m i n a t i o n r a t e caused by high v i s c o s i t y w i t h i n the p a r t i c l e s ( g e l e f f e c t ) can c o n t r i b u t e to s i g n i f i c a n t reactor i n s t a b i l i t i e s . V a r i a t i o n i n the l e v e l of i n h i b i t o r s i n the feed streams can a l s o cause r e a c t o r c o n t r o l problems. Convers i o n o s c i l l a t i o n s have been observed with many d i f f e r e n t monomers. These o s c i l l a t i o n s o f t e n r e s u l t from a l i m i t c y c l e behavior of the p a r t i c l e n u c l e a t i o n mechanism. Such o s c i l l a t i o n s are d i f f i c u l t to t o l e r a t e i n commercial systems. They can cause uneven heat loads and s i g n i f i c a n t t r a n s i e n t s i n f r e e e m u l s i f i e r concentration thus p o t e n t i a l l y causing f l o c c u l a t i o n and the formation of w a l l polymer. T h i s problem may be one of the most d i f f i c u l t to handle i n the development of commercial continuous processes. One of the most promising ways of d e a l i n g with conversion o s c i l l a t i o n s i s the use of a s m a l l - p a r t i c l e l a t e x seed i n a feed stream so that p a r t i c l e n u c l e a t i o n does not occur i n the CSTRs. Berens (3) used a seed produced i n another r e a c t o r to achieve s t a b l e o p e r a t i o n of a continuous PVC r e a c t o r . Gonzalez (4) used a continuous t u b u l a r p r e - r e a c t o r to generate the seed f o r a CSTR producing PMMA l a t e x . P o e h l e i n and Dougherty (2) provide more d e t a i l s on t r a n s i e n t o p e r a t i o n problems and some p o t e n t i a l c o n t r o l o p t i o n s . Considerable work i s c u r r e n t l y being conducted i n a number of u n i v e r s i t y

1.

POEHLEIN

Continuous

Emulsion

Polymerization

11

and i n d u s t r i a l l a b o r a t o r i e s on approaches to the c o n t r o l of continuous r e a c t o r s . These e f f o r t s should produce new i n s i g h t s i n t o t h i s troublesome problem.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

Reactor

Design:

I d e a l l y one would l i k e a continuous r e a c t o r system to operate i n d e f i n i t e l y a t the d e s i r e d s t e a d y - s t a t e . U n f o r t u n a t e l y , a number of f a c t o r s can cause s h o r t e r runs. Formation o f w a l l polymer and l a t e x f l o c c u l a t i o n i s one such problem. T h i s phenomenon can reduce r e a c t o r performance ( f o r example, l o s s o f heat t r a n s f e r ) , lower product q u a l i t y , and shorten run time. Reactor design can have a s i g n i f i c a n t i n f l u e n c e on r e a c t o r performance i n a number of ways. Some aspects of r e a c t o r design such as heat t r a n s f e r , s t r u c t u r a l design, e t c . , are reasonably well-understood. Other phenomena such as mixing d e t a i l s , l a t e x f l o c c u l a t i o n , and the formation w a l l polymer are not completely understood. A recent patent (5) d e s c r i b e s r e a c t o r s used f o r continuous polychloroprene production which have some i n t e r e s t i n g f e a t u r e s and c l a i m s . These r e a c t o r s are shown i n F i g u r e s 4 and 5. They i n c l u d e the f o l l o w i n g f e a t u r e s : 1. They a r e operated completely f u l l thus p r o v i d i n g no w a l l s i n a vapor space which might be a p l a c e f o r l a t e x to d r y . 2. The i n s i d e s u r f a c e i s smooth w i t h rounded corners and no i n t e r n a l f i x t u r e s such as b a f f l e s . 3. The a x i a l - f l o w p r o p e l l e r s have been operated with a steady flow of 10-15 m /min/m3 r e a c t o r volume. They have a l s o been operated w i t h o s c i l l a t i n g motion. 4. The r e a c t o r i s completely surrounded by a j a c k e t f o r h e a t i n g and c o o l i n g . 5. Scale-up i s non-geometric w i t h length/diameter r a t i o s v a r y i n g from 2:1 to 30:1. The nongeometric scale-up helps to i n c r e a s e heat t r a n s f e r area as r e a c t o r volume i n c r e a s e s . 6. The a g i t a t o r s h a f t i s i n c l i n e d from 0° to 45° with the v e r t i c a l , and m u l t i p l e i m p e l l e r s are used with longer r e a c t o r s . A number of the above f e a t u r e s are i n c l u d e d to reduce f l o c c u l a t i o n and the formation of w a l l polymer. While fundament a l knowledge on f l o c c u l a t i o n or the formation of w a l l polymer i s inadequate to e s t a b l i s h the e f f e c t s of a l l r e a c t o r design v a r i a b l e s , the f e a t u r e s of the Bayer r e a c t o r seem q u a l i t a t i v e l y c o r r e c t . More fundamental work w i l l be necessary to develop an understanding of the i n f l u e n c e of design on r e a c t o r performance and product q u a l i t y . 3

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

POLYMERIZATION REACTORS AND PROCESSES

Figure 4.

Short polychloroprene

reactor

POEHLEiN

Continuous

Emukion

Polymerization

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

1.

Figure 5.

Polychloroprene reactor with multiple-impeller agitator

13

14

POLYMERIZATION REACTORS AND PROCESSES

Conclusions: The development of commercial continuous processes i n v o l v e s the c o n s i d e r a t i o n of many f a c t o r s a s s o c i a t e d w i t h process design and product q u a l i t y . Most of the f a c t o r s d i s c u s s e d i n t h i s paper w i l l be important. Other, e q u a l l y s i g n i f i c a n t parameters, may be important f o r s p e c i f i c polymer products. F a i l u r e t o d e a l w i t h any o f these problems may mean f a i l u r e to develop an economical process. Acknowledgment:

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch001

Support from the N a t i o n a l Science Foundation (Grants No. GK-36 489 and ENG 75-15 337) i s g r a t e f u l l y acknowledged. Literature Cited: 1. 2. 3. 4. 5.

U g e l s t a d , J . and Hansen, F.K., Rubber Chem. & Technology, (1976), 49(3), 536-609. P o e h l e i n , G.W. and Dougherty, D.J., Rubber Chem. & Technology, (1977), 50(3), 601-638. Berens, A.R., J. Appl. Polym. S c i . , 18, (1974), 2379. Gonzalez, P., R.A., M.S. T h e s i s , Dept. o f Chem. Eng., Lehigh U n i v e r s i t y , Bethlehem, Pa. (1974). German Patent No. 2,520,891 (1976), Assigned t o Bayer, A.G.

Note:

References 1. and 2. c o n t a i n extensive b i b l i o g r a p h i e s on emulsion p o l y m e r i z a t i o n k i n e t i c s and continuous emulsion polymerization respectively.

RECEIVED January 19, 1979.

2 Thermal Runaway in Chain-Addition Polymerizations and Copolymerizations JOSEPH A. BIESENBERGER

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

Department of Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030 The objectives of this presentation are to discuss the general behavior of nonisothermal chain-addition polymerizations and copolymerizations and to propose dimensionless c r i t e r i a for e s t i mating nonisothermal reactor performance, in particular thermal runaway and instability, and its effect upon polymer properties. Most of the results presented are based upon work (1-8), both theoretical and experimental, conducted in the author's laboratories at Stevens Institute of Technology. Analytical methods i n clude a Semenov-type theoretical approach (1,2,9) as well as computer simulations similar to those used by Barkelew (3,4,6,7,10). Analyses of reactor performance are limited to rate functions

and thermal energy balances

of the forms shown in equations 1 and 2. Polymer property analyses are limited to chain-addition polymerizations

and copolymerizations

0-8412-0506-x/79/47-104-015$07.00/0 © 1979 American Chemical Society

16

POLYMERIZATION REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

with termination, whose general characteristics are shown in equations 3,4,5 and 6. It should be noted that equations 3 and 5 are written in general form to encompass many different chain mechanisms and therefore do not necessarily represent elementary reactions steps. Experimental results quoted herein are limited to polymerizations and copolymerizations of styrene (S) and acrylonitrile (AN) monomers via free-radical intermediates for which the following specific reactions obtain. For homopolymerizations we have

Termination scheme 11 applies to the geometric mean and phi factor models and scheme 12 is required for the penultimate effect model. All the above reaction models were used in attempts to simulate kinetic data. Parameters and Variables Reaction rate functions expressing rate of polymerization R generally depend upon the molar concentrations of monomer and initiator, and temperature. R -

R([m], [m ],T) Q

(13)

2.

BIESENBERGER

Thermal

17

Runaway

D u r i n g p o l y m e r i z a t i o n , when i n i t i a t o r i s i n t r o d u c e d c o n t i n u o u s l y f o l l o w i n g a p r e d e t e r m i n e d f e e d s c h e d u l e , o r when h e a t removal i s c o m p l e t e l y c o n t r o l l a b l e so t h a t t e m p e r a t u r e c a n be programmed w i t h a p r e d e t e r m i n e d t e m p e r a t u r e p o l i c y , we may r e g a r d f u n c t i o n s [ r o o ( t ; ] , or T ( t ) , as r e a c t i o n parameters. A common s p e c i a l case of T ( t ) i s t h e i s o t h e r m a l mode, T = c o n s t a n t . In t h e p r e s ent a n a l y s i s , h o w e v e r , we t r e a t o n l y u n c o n t r o l l e d , b a t c h p o l y m e r i z a t i o n s i n which [ m ( t ) ] and T(t) are reaction variables, s u b j e c t t o v a r i a t i o n i n a c c o r d a n c e w i t h t h e c o n s e r v a t i o n laws (balances). Thus, o n l y t h e i r i n i t i a l (feed) v a l u e s , [ m ] andT , are t r u e parameters. In a d d i t i o n t o t h e s e , we have r e a c t o r d e s i g n p a r a m e t e r s : 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 U, r a t i o o f r e a c t i o n v o l u m e t o heat t r a n s f e r area I = V/A and h e a t e x c h a n g e r e s e r v o i r t e m p e r a t u r e TR . W h i l e t h e r m o d y n a m i c p r o p e r t i e s (-AH, p C ) and k i netic properties (r,Ap,E ,A ,Et) a r e d e t e r m i n e d f o r t h e most p a r t by t h e monomers b e i n g p o l y m e r i z e d , i n i t i a t o r c h o i c e (Ad,Ed) i s v i e w e d a s a p a r a m e t e r a s w e l l a s i n i t i a l monomer c o n c e n t r a t i o n [ m ] , w h i c h c a n be a d j u s t e d t h r o u g h t h e u s e o f d i l u e n t s . I twill be shown t h a t runaway (R-A) and i g n i t i o n (IG) phenomena a r e d e t e r mined by t h e v a l u e s o f c e r t a i n d i m e n s i o n l e s s g r o u p i n g s , w h i c h a r e made up o f t h e a f o r e m e n t i o n e d p a r a m e t e r s . T h u s , i f R-A i s s e n s i t i v e t o o n e o f t h e s e g r o u p i n g s , f o r i n s t a n c e , i t w i l l a l s o be s e n s i t i v e t o a l l o t h e r parameters i n t h a t grouping. Frequently function R c a n be w r i t t e n a s a s i n g l e t e r m having t h e s i m p l e f o r m o f e q u a t i o n 1. For i n s t a n c e , w i t h the a i d o f t h e l o n g c h a i n a p p r o x i m a t i o n (LCA) and t h e q u a s i - s t e a d y s t a t e a p p r o x i m a t i o n (QSSA), t h e r a t e o f monomer c o n v e r s i o n , i . e . , t h e r a t e o f p o l y m e r i z a t i o n , f o r many c h a i n - a d d i t i o n p o l y m e r i z a t i o n s c a n be w r i t t e n a s 0

0

0

Q

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

p

p

t

Q

R

where

k

=

a p

k

a

p

[ / [ , /

=

A

a

p

[ ]P[ m

m

o

]

q

exp(-E R T) a p

i s a lumped o r c o m p o s i t e r a t e c o n s t a n t .

homopolymerization

i s an e x a m p l e

(p = 1, q = 1/2)

g

(14)

Free-radical a s seen i n

T a b l e I . F r e e - r a d i c a l c o p o l y m e r i z a t i o n , on t h e o t h e r h a n d , l e a d s t o a sum o f t e r m s , e a c h o f w h i c h i s more c o m p l e x t h a n e q u a t i o n \k, a s seen i n T a b l e II ( N o t e t h e p r e s e n c e o f f u n c t i o n H , g i v e n i n T a b l e I I I f o r v a r i o u s t e r m i n a t i o n m o d e s ) . To remedy t h i s s i t u a t i o n , approximate rate functions f o r copolymerization of the form o f e q u a t i o n 1 a r e used i n s t e a d . In s u c h c a s e s t h e d i m e n s i o n l e s s r a t e f u n c t i o n R' = R/(R)

o

(15)

c a n be v i e w e d a s a p r o d u c t o f s e p a r a t e f u n c t i o n s R' = f ( t ) g ( T ' ) where

(16)

18

POLYMERIZATION REACTORS AND PROCESSES TABLE I RATE FUNCTIONS FOR FREE-RADICAL

R. - k.[m ] = 2 f . l c . I l ] i i o d d

HOMOPOLYMERIZATIONS

k. = f k . i d

QSSA 1/2 R - k [P][ra] = k [ m ] [ l ] P P ap 1

/

k

0

ap

= k

[ m l= 2[l] o

(2fk,/kJ p d' V

1 / 2

x

n

2

k

V

k

•

P

t

[

m

]

2

s

p*

k

/

p

k

t

LCA w R

R = R. + R i p

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

k

p

QSSA

R. « i

R„ t

LCA

R » P

R. i

TABLE I I RATE FUNCTIONS FOR FREE-RADICAL COPOLYMERIZATIONS R.. = k f . [ m ] = 2 f k . f . [ l ] IJ iJ o d J

j = 1,2

L

R

=

R

E

=

ij

k

\

[ m

o

=

]

2

f

k

d

[

,

]

E

f

J R

pjk

= k .. [ P . ] [ m J pjk j k

J

= k [m.][m.][l] apjk j k ]

0

pk

R p

"

1

j

/

k ., = k k . ( 2 f k . / k ..k ) apjk p j k p&j d t j j til

R

=

j

X) J

R

1

H

k = 1,2

I = 1,2

0

I * j

PJk

= R » ( Y Y \ pk ^f^f

R = R. + R « i p Symmetry

Q

1 / 2

k

R p a p j k

a

PJ

k

[m.][m,])[l] J

1 / 2

H

k

f r o m LCA = k^.

R

p j |


Factor

k

H = L

p21

[ m

]

l

k

+

2

(

, / 2

(k 22)

k

p21 p12 k

[ m

l

] [ m

2

k

]

[ m

)'/2

k

t

]

2 1/2

k

V K

Penultimate

pl2

< t11>

K

t22 tir

effect

,1/2 r , [m

k

[ m

1

(k ) t22'

,

H =

p21

]

/

z

til/ r j Lm J + l m J 1

2

2

V K

/k

\

1 / 2

r [m ] + 2

.

k

p12

[ m

2

2

]

r [m J o T T V K

where

7

2

2

"

2

+ [mj]

tir

k ^ -

k t

n

l

2

>

k

k

t

2r t2112

;

k

tl2

k

tl221

;

k

k

t22~ t2222

20

POLYMERIZATION REACTORS AND PROCESSES

n j

(k

(R ) = (k ) ir [ C . ] o ap o . J o

(17) '

) = IK exp(-E; ) ap o ap ap

(18)

N

E ' = E /R T ap ap g o

(19)

n

f ( t ) = ir C j J

(20)

and

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

g(T') Frequently

= e x p E ' T V ( 1 + T') ap

(21)

i t i s convenient t o w r i t e g ( 6 ) = e x p 0/(1 + e6)

(22)

i n l i e u o f e q u a t i o n 21 where e = 1/E' ap

(23)

We n o t e t h a t u n d e r f e e d c o n d i t i o n s g(o) = l .

(R') = 1 0

since

f(0) = 1

C h a r a c t e r i s t i c Times B a l a n c e e q u a t i o n s f o r b a t c h r e a c t o r s may a l l be v i e w e d a s special cases o f the f o l l o w i n g general equation

j where p i s a n i n t e n s i v e p r o p e r t y ( m o l a r c o n c e n t r a t i o n o r temp e r a t u r e ) and p j i s t h e r a t e w i t h w h i c h p r o c e s s j c a u s e s p t o i n c r e a s e i n v a l u e . When q u a n t i t i e s p and p j a r e made d i m e n s i o n l e s s t h r o u g h d i v i s i o n by t h e i r c o r r e s p o n d i n g f e e d v a l u e s V'

=

p/(p)

Pj

~

W

Q

o

(25)

U

6

)

t h e a f o r e m e n t i o n e d b a l a n c e e q u a t i o n s become p a r t l y d i m e n s i o n l e s s , h a v i n g d i m e n s i o n s o f r e c i p r o c a l t i m e o n l y , and t a k e on t h e f o l lowing g e n e r a l form

3f • E»J' »i

(27)

2.

BIESENBERGER

Thermal

in which a c h a r a c t e r i s t i c f i n e d as

time

Xj

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

21

Runaway

s

(CT)

f o r e a c h p r o c e s s may

(P> /(Pj) 0

be

de-

(28)

0

We n o t e t h a t e q u a t i o n 15 i s an e x a m p l e o f e q u a t i o n 26. I t c a n be shown t h a t a l l d i m e n s i o n l e s s p a r a m e t e r s , a r r i v e d a t i n t h e c o n v e n t i o n a l manner by w r i t i n g e q u a t i o n s o f t y p e 24 i n c o m p l e t e l y d i m e n s i o n l e s s f o r m , c a n be e x p r e s s e d a s q u o t i e n t s o f CT's. T a b l e s IV and V c o n t a i n a p p r o p r i a t e b a l a n c e e q u a t i o n s f o r n o n i s o t h e r m 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 s and c o p o l y m e r i z a t i o n s , w h i c h a r e seen t o c o n f o r m t o e q u a t i o n 24. Following the proced u r e o u t l i n e d a b o v e , we o b t a i n t h e CT's f o r h o m o p o 1 y m e r i z a t i o n s l i s t e d i n T a b l e V I . C o r r e s p o n d i n g CT's f o r c o p o l y m e r i z a t i o n s c a n be. o b t a i n e d i n a s i m i l a r way, and i n d e e d t h e f i r s t and f o u r t h l i s t e d i n T a b l e V I I w e r e . The r e m a i n i n g o n e s , h o w e v e r , were d e r i v e d v i a an a l t e r n a t e r o u t e based upon t h e d e f i n i t i o n s i n T a b l e VI l a b e l e d " e q u i v a l e n t " t o g e t h e r w i t h a p p r o x i m a t e f o r m s f o r p j , w h i c h w e r e n e c e s s i t a t e d by a p p l i c a t i o n o f t h e Semenov-type r u n away a n a l y s i s t o c o p o l y m e r i z a t i o n s , and w h i c h w i l l s u b s e q u e n t l y be d e s c r i b e d . Some u s e f u l d i m e n s i o n 1 e s s p a r a m e t e r s d e f i n e d i n terms o f t h e s e CT's a p p e a r i n T a b l e s V I I I , IX and X. Reactor

Performance

The c o n d i t i o n o f t h e r m a l runaway (R-A) i n p o l y m e r i z a t i o n and c o p o l y m e r i z a t i o n r e a c t o r s has been c h a r a c t e r i z e d (1,7) by a r a p i d l y r i s i n g temperature dT/dt » 0 t o g e t h e r w i t h an a c c e l e r a t i o n of the r i s e d T/dt > 0 . When R-A a d d i t i o n a l l y e x h i b i t s p a r a m e t r i c s e n s i t i v i t y i t i s termed i g n i t i o n ( I G ) . Beyond i t s r o l e as a p o t e n t i a l c a u s e o f i n s t a b i l i t y , R-A c a n a l s o a f f e c t conversion e f f i c i e n c y . S p e c i f i c a l l y , t h e w e l l - k n o w n phenomenon o f d e a d - e n d i n g ( D - E ) , i n w h i c h c o n v e r s i o n o f monomer t o p o l y m e r i s a b o r t e d by p r e m a t u r e d e p l e t i o n o f i n i t i a t o r , i s e x a c e r b a t e d by r i s i n g t e m p e r a t u r e s . T h i s i s so b e c a u s e h i g h t e m p e r a t u r e s a c c e l e r a t e i n i t i a t o r d e p l e t i o n r a t e s much more t h a n monomer c o n v e r sion rates. The phenomenon c a n o b v i o u s l y be m i t i g a t e d by i n c r e a s i n g i n i t i a t o r c o n c e n t r a t i o n , but t h i s has an a d v e r s e e f f e c t on d e g r e e o f p o l y m e r i z a t i o n ( D P ) . The c r i t e r i o n f o r D-E, shown i n T a b l e X I , was f o r m u l a t e d i n t e r m s o f d i m e n s i o n l e s s p a r a m e t e r , shown i n T a b l e V I I I , w h i c h c o r r e c t l y r e f l e c t s t h e e f f e c t s o f feed parameter T as w e l l a s [l] , since k has a n e g a t i v e temperature c o e f f i c i e n t . C r i t e r i a f o r R-A and IG, a l s o shown i n T a b l e X I , w e r e f o r m u l a t e d i n terms o f d i m e n s i o n l e s s p a r a m e t e r s e, a , B and b. They a p p l y t o b o t h h o m o p o l y m e r i z a t i o n s and c o p o l y m e r i z a t i o n s f o r v a r i ous i n i t i a t o r s y s t e m s a t o r n e a r t h e c o n d i t i o n TR = T , and w e r e d e v e l o p e d t h r o u g h m o d i f i e d Semenov-type a n a l y s e s (1,JL>Z) a n c * numerous c o m p u t e r s i m u l a t i o n s ( 3 j 4 ^ 6 ) . Owing t o t h e f a c t t h a t the dimensionless r a t e f u n c t i o n f o r homopolymerization c o n t a i n s 2

Q

2

Q

a x

Q

22

POLYMERIZATION REACTORS AND PROCESSES TABLE IV BATCH MATERIAL BALANCE EQUATIONS FOR FREE-RADICAL POLYMERIZATIONS AND COPOLYMERIZATIONS

In 1 1 I a t o r _ d[ml

. 2

dt

m

dt

f

v

Monomer d[m.]

LCA R

-TT-- !k Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

-

+

R

pk

= R = R. i

dt

+

w

V

R p

~

p

Moment

4lip-=

dt

" -

[(2 - r)/2]R.

R

(1 + r ) R . + (3 + 2 r ) R

p

+ (2 +

r)R

p t

TABLE V BATCH ENERGY BALANCE EQUATIONS FOR FREE-RADICAL POLYMERIZATIONS AND COPOLYMERIZATIONS Homo po 1 y me r i z a t i o n s LCA pC

Q

p

*

-AHR

- (UA/V)(T - T )

p

R

C o p o l y m e r i z a t i ons P C

p

£

L

"

(-AH j

k

j k

)R

p l k

- (UA/VMT - T ) R

2.

BIESENBERGER

Thermal

23

Runaway

TABLE VI CHARACTERISTIC TIMES FOR HOMOPOLYMERIZATIONS Definitions CT

Original

X.

2f[l] /(R,) o

initiator

o

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

n

heat g e n e r a t i o n

PC T / ( - A H ) ( R ) p o o

o 3G

ad

X

R

C

T

P p o

pC

/ (

-

consumption

monomer c o n v e r s i o n

W„/(R) o p o

A

Process

Equ i v a l e n t v-1

A H ) ( R )

VI adiabatic

E

o ap

heat

£/U

induction

removal

P

TABLE VI I CHARACTERISTIC TIMES FOR CT

Original

COPOLYMERIZATIONS Equivalent

X. o

PJ

k

o

1

(-£) X

Gjk (G ) e o 3G \~1 ad

P

I

-1 Gjk

24

POLYMERIZATION REACTORS AND PROCESSES

TABLE V I I I DIMENSIONLESS PARAMETERS FOR HOMOPOLYMERIZATIONS Defini tion Parameter a

x

k V

For I n t e r p r e t a t i o n

N

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

ap

B

b

a d

V

A

/X

R

ad

x,/X

" Vo o

/ a

f I , ]

a d

J

/ 2

k _

X ,/X. ad G X

B/b

X

"

e E

=

V i

For Evaluation

1

(E' ) ap' E /R T ap g o (^)V(-AH)(k

(-

A H

E

) ;

^H)(k

a x

[ m ]

o

P

a p

/ p C

) E; [m] [l] o

p

p

T

o

TABLE IX DIMENSIONAL PARAMETERS FOR COPOLYMERIZATIONS Pa r a m e t e r ak \

Def i n i t i on A /X. m A

( x

o

x

Q

< 2Vl

+ ( x

+

x

2

+

P

+

£l

x

T

r

E'T' •

x

r

x

2

0

2

o

2

2

)

2

0

2

( r

r

X

2m

2

E

)

o

+

T

_

«* >o< 2'o 2> 2

_ ( x

+

2

e

x

2

p

0

J>

2

o

2

2?TirT

£1

E

2

T

1

Q

2

0

2

o

2

I

T

)

2

E

n

+ ( x ^

l

T

' P2 ' nx ) A m exp- Tr (x ) (r ) m exp ^ r

T W )

; Dtl2 ' (x ) (r ) m exp (x ) (r ) X m exp^Hfn

X

2 1

Jjl

< 2>o< 2»o 2

x

^£1

lVl' 2»Q' 2^ 2 lV P 2(m')

0

* » ( » i > ( r i V i ( » 2 > o < 2 > o 2 + » 2>o< 2>o 2>

"< l>cAl>o

( r

2

IFFTT

p ( i t r i 2^iy PuTr) E' T' (x ) (r ) m ex r + (x ) m

r

t iW i>o i

X

*' l'o

( l>o< l>o l

x

X

E X P

» l'o''-l'o l'

t*zWo fr

x

^ o ^ o ^

iWrj*

2 1

p

£.

fery

r

( l>o< lVl

o< l'o l> l

x

P enultimate Effect

H'

=

Phi Factor

Q

( i»o« i»o*i"i

Geometric Mean

H'

Dimensionless Termination Function

TABLE X EXPRESSIONS FOR H"

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

§

5*

to

^

|

H

JSCS

§

2

g

§

B S S

w

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

POLYMERIZATION REACTORS AND PROCESSES

TABLE XI DIMENSIONLESS CRITERIA FOR REACTOR PERFORMANCE ( p o l y m e r i z a t i o n s and C o p o l y m e r i z a t i o n s ) Phenomena

Criteria

D-E

a

R-A

e « 1 a < 2

IG/ERA

B > 20 b > 100

k

> 1

2.

BIESENBERGER

Thermal

Runaway

27

only one simple term R' H

=

n

1

1 / 2

exp

E'T'/O dp

+ T-)

and t h u s c o n f o r m s t o e q u a t i o n 16, i t c a n be shown by t h e p r o c e d u r e l e a d i n g t o e q u a t i o n 27 t h a t t h e p a r t l y monomer b a l a n c e e q u a t i o n

-3?

"

dt

(29) following dimensionless

(30)

X

'JK m

p

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

c o n t a i n s o n l y a s i n g l e f u n c t i o n on t h e RHS and t h e p a r t l y s i o n l e s s e n e r g y b a l a n c e e q u a t i o n t a k e s on a f o r m

G

R

e

dimen-

e

w h i c h i s a m e n a b l e t o Semenov-type a n a l y s i s ( 1 ) . P e r t i n e n t d i m e n s i o n l e s s p a r a m e t e r s w e r e d e f i n e d i n t e r m s o f r e s u l t i n g CT's and are l i s t e d in Table V I I I . D u r i n g t h e d e v e l o p m e n t o f t h e s e c r i t e r i a t h e Semenov a n a l y s i s was e x t e n d e d t o s y s t e m s w i t h h e a t - e x c h a n g e r r e s e r v o i r t e m p e r a t u r e s d i f f e r e n t from feed temperatures (TR < T ) and w i t h d e l a y e d runaway ( l a r g e r v a l u e o f e ) , w h i c h r e s u l t e d i n s i g n i f i c a n t c o n c e n t r a t i o n d r i f t p r i o r t o runaway. S i n c e v a l u e s o f e for c h a i n - a d d i t i o n p o l y m e r i z a t i o n s a r e n o t n e a r l y a s s m a l l as t h o s e f o r t h e g a s e o u s e x p l o s i o n s i n v e s t i g a t e d by Semenov, R-A i s n o t as s e n s i t i v e nor i s i t as e a r l y i n terrrs o f e x t e n t o f r e a c t i o n . T h u s , t h e c r i t i c a l v a l u e o f R-A p a r a m e t e r 'a' i s n o t t h e same n o r i s i t as c l e a r l y d e f i n e d . M o r e o v e r , i t i s p o s s i b l e t o e x p e r i e n c e i n s e n s i t i v e ( p o t e n t i a l l y s t a b l e ) R-A. Sample e x p e r i m e n t a l r e s u l t s s h o w i n g s e n s i t i v e and i n s e n s i t i v e R-A have been p l o t t e d i n F i g u r e s 1 and 2, r e s p e c t i v e l y . In t h e c o m p u t e r s i m u l a t i o n s i t was n e c e s s a r y t o s t u d y r e a c t i o n s e q u e n c e s more c o m p l e x t h a n t h o s e s t u d i e d by B a r k e l e w , which consequently led to r a t e f u n c t i o n s having double r a t h e r than s i n g l e c o n c e n t r a t i o n dependence. Numerous r e s u l t s f r o m b o t h t h e o r e t i c a l and c o m p u t a t i o n a l a n a l y s e s , i n c l u d i n g t h e e f f e c t s o f e and TR , have been d e s c r i b e d e l s e w h e r e ( s e e e s p e c i a l l y F i g u r e 8 of reference 1). C r i t e r i a f o r s e n s i t i v i t y , B and b , are also c r i t e r i a f o r v a l i d i t y o f t h e e a r l y R-A a p p r o x i m a t i o n (ERA), w h i c h s a y s t h a t R-A o c c u r s v i r t u a l l y when m = 1 = I . W h i l e B f o r most 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 s l i e s w i t h i n a narrow range, which exceeds the c r i t i c a l v a l u e , b v a r i e s w i d e l y from s u b c r i t i c a l t o c r i t i c a l v a l u e s , d e p e n d i n g s t r o n g l y u p o n c h o i c e o f i n i t i a t o r and f e e d p a r a meters [ l ] and T . Decreasing values of b generally depress the c r i t i c a l v a l u e of 'a' slightly. Computed R-A Q

0

Q

Figure

T

R

\}/jt

a

1.

A A

Experimental

O R A O

O D

O

o

o •

0

A

•

o

0

A

LJ

o •

o

A

o LJ n

o

o

o 0

0

A A A A A A A A A &

o •

o °

•

o

•

•

o o a

o°

6

o

8

d

o

o

o

show-

Polymer Engineering and Science

°

O

A A ^ A A A A A A A

data from styrene polymerization initiated with benzoyl peroxide ing R-A sensitivity to parameter U/l (5)

0

A 0

u n O • o •

44 0 43 A 42 • 34 O

RUN

on o g °

07 975 -0035 0032 0029 .0027

•o

ofia

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

& o

Figure

6°

•

2.

120

Experimental

•

• •

A

A

360

\

m

*

A

m m

m

•

TIME

SEC.

0

0

3

initiated [I] (5)

• ft a M ^ A A a

A

m

data from styrene polymerization R-A sensitivity to parameter

m

A 5

l 0

R

5

T

*

with

0

4

0

[)/£ 5 1

0

2

6

*

5

4

56

•

"

•

A

O

O

55

53

52

RUN

1080

peroxide

less

Polymer Engineering and Science

* *

0

0027

.0028

.0029

.0035

0

benzoyl

840

l 0 2

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

30

POLYMERIZATION REACTORS AND PROCESSES

b o u n d a r i e s f o r h o m o p o l y m e r i z a t i o n s a r e shown i n F i g u r e 3 From T a b l e s V I I I and XI we f i n d t h a t R-A may be i n d u c e d ('a r e d u c e d b e l o w c r i t i c a l v a l u e ) by r a i s i n g T , [ l ] o r E ( v i a Ed) a s w e l l a s by l o w e r i n g U/£ . We a l s o f i n d t h a t IG may be i n d u c e d (b i n c r e a s e d a b o v e c r i t i c a l v a l u e ) by r a i s i n g [l] , lowering T o r l o w e r i n g kd ( v i a l o w e r Ad o r h i g h e r Ed). Consequently, we must c o n c l u d e t h a t w h i l e a h i g h v a l u e o f T contributes to t h e o n s e t o f R-A, i t s i m u l t a n e o u s l y m i t i g a t e s i t s s e n s i t i v i t y . F u r t h e r m o r e , w h i l e i n i t i a t o r s a z o - b i s - i s o b u t y r o n i t r i l e (Ad ^ 1 0 ^ 5 s e c - 1 , Ed ^ 3 0 K c a l ) , b e n z o y l p e r o x i d e (Ad * loH sec" , Ed ^ 3 0 K c a l ) and d i - t e r t - b u t y l p e r o x i d e (Ad * 1 0 ^ 5 s e c " , Ed ^ 3 7 K c a l ) a r e g e n e r a l l y r e g a r d e d a s i n c r e a s i n g i n " s l o w n e s s " i n t h e d i r e c t i o n 1 i s t e d , b e c a u s e Ad d e c r e a s e s o r Ed i n creases, o r both, t h e i r value o f b increases i n the order shown, a l l o t h e r f a c t o r s r e m a i n i n g e q u a l . C o n s e q u e n t l y , we must c o n c l u d e t h a t ' s l o w ' i n i t i a t o r s a r e more l i k e l y t o p r o d u c e u n s t a b l e R-A's t h a n f a s t o n e s . The a b o v e c o n c l u s i o n s i n v o l v i n g T and i n i t i a t o r c h o i c e have been o b s e r v e d e x p e r i m e n t a l l y . 1

0

0

a p

0

0

Q

1

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

1

0

The r a t e f u n c t i o n f o r c o p o l y m e r i z a t i o n c o n t a i n s a summation o f t e r m s , each o f which R

pjk

=

» A

'

,

/

2

H- « p

E ;

p

J

k

T V ( l

i s more c o m p l e x t h a n e q u a t i o n 1 6 , and t h e r e s u l t i n g balance equation i s . dm

=

dt

y y L^tL-j

j The c o r r e s p o n d i n g e n e r g y

J

k

x

T

l

(

j k

} N

R

(32)

+T-) monomer

(33)

.

k'o p j k

k balance

G

R

e

e

i s c o n s e q u e n t l y n o t a m e n a b l e t o Semenov-type a n a l y s i s . The f u n c t i o n a l form o f f o r each o f t h e t h r e e t e r m i n a t i o n models c i t e d i s g i v e n i n T a b l e X. In o r d e r t o remedy t h i s s i t u a t i o n , e q u a t i o n s 3 2 , 3 3 and 3k w e r e f o r c e d t o c o n f o r m t o 2 9 , 3 0 and 31 by r e c o g n i z i n g a l t e r n a t i v e , e q u i v a l e n t d e f i n i t i o n s ( t h i r d column i n T a b l e V I ) o f CT's f o r homopolymer b a l a n c e s and s u b s e q u e n t l y a p p l y i n g them t o c o p o l y m e r b a l a n c e s . In t h i s way, a p p r o x i m a t e c o polymer b a l a n c e s

|S

-

1

A" m l m

1 / 2

e x p E ' T V O + T*)

(35)

-

2 10

2.1

1

1

1

1 1

Figure

NON RUNAWAY

3.

Computed

3 10

1 1 1 1

RUNAWAY

IG boundaries

1

32

41

b

I I I

i

I

1

1

e=o.04

(4)

r=i.o

s

(/^n)o 3000

R

e «=o.O

I

I

1

I

Polymer Engineering and Science

I

6 E - * 1.467

4 10

I

for homopolymerizations

B = fiO

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

32

POLYMERIZATION REACTORS AND PROCESSES

m I

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

G

1/2

exp

E ' T V O + T') - X ^ ( T - T*)

(36)

R

e

e

w e r e d e v e l o p e d i n w h i c h CT's w e r e o b t a i n e d u s i n g e q u i v a l e n t d e f i n i t i o n s (second c o l u m n i n T a b l e VI l) and a l l i m p o r t a n t dimensionl e s s p a r a m e t e r s f o r c o p o l y m e r s ( T a b l e I X ) , i n c l u d i n g an o v e r a l l a c t i v a t i o n energy E', w e r e d e f i n e d i n a c c o r d a n c e w i t h t h e i r homopolymer c o u n t e r p a r t s ( T a b l e V I I I ) . I t was f o u n d t h a t n o t o n l y d i d p a r a m e t e r s a , B and b so d e f i n e d c h a r a c t e r i z e R-A and IG b e h a v i o r o f c o p o l y m e r i z a t i o n s , but a p p r o x i m a t e e q u a t i o n s 3 5 and 36 c l o s e l y t r a c k the exact balance equations over wide conversion and t e m p e r a t u r e r a n g e s , e x c e p t when one comonomer i s e x h a u s t e d o r when t h e s y s t e m i s n e a r IG ( 7 ) . V e r i f i c a t i o n of the a p p l i c a b i l i t y o f R-A b o u n d a r i e s t o c o p o l y m e r i z a t i o n s i s e v i d e n t i n F i g u r e 4 . C o m p a r i s o n s between " e x a c t " c o m p u t e r m o d e l s and c o p o l y m e r a p p r o x i mate f o r m s (CPAF) a p p e a r i n F i g u r e 5 . P o l y m e r and

Copolymer P r o p e r t i e s

Owing t o t h e c h a i n n a t u r e o f c h a i n - a d d i t i o n p o l y m e r i z a t i o n s and c o p o l y m e r i z a t i o n s w i t h t e r m i n a t i o n , o n l y a s m a l l f r a c t i o n o f t h e u l t i m a t e p r o d u c t m o l e c u l e s grow a t any i n s t a n t , but t h e y grow t o t h e i r f i n a l s i z e so r a p i d l y t h a t t h e y may be r e g a r d e d a s i n stantaneous product without a p p r e c i a b l e e r r o r . The f i n a l product i s an a c c u m u l a t i o n o f a l l i n s t a n t a n e o u s p r o d u c t s formed d u r i n g t h e c o u r s e o f p o l y m e r i z a t i o n , and i t s c u m u l a t i v e p r o p e r t i e s a r e c o m p o s i t e s o f t h e i n s t a n t a n e o u s p r o p e r t i e s . Examples a r e d e g r e e o f p o l y m e r i z a t i o n d i s t r i b u t i o n , DPD, c o p o l y m e r c o m p o s i t i o n d i s t r i b u t i o n , CCD, and t h e i r r e s p e c t i v e a v e r a g e v a l u e s , DP and CC (see T a b l e X I I ) . D i s p e r s i o n o f t h e s e d i s t r i b u t i o n s i s c o n s e quently the r e s u l t of the inherent d i s p e r s i o n of the molecular p r o c e s s e s a t e a c h i n s t a n t , termed s t a t i s t i c a l d i s p e r s i o n , t o g e t h e r w i t h t h e e f f e c t o f t i m e d r i f t s u p e r i m p o s e d upon i t , termed d r i f t d i s p e r s i o n , w h i c h i s a c h a r a c t e r i s t i c o f b a t c h r e a c t o r s and w h i c h can o n l y r e s u l t i n g r e a t e r d i s p e r s i o n i f a l l o w e d t o o c c u r . Thus, the response o f these p o l y m e r i z a t i o n s t o changes i n a p a r a m e t e r , s u c h a s t e m p e r a t u r e o r c o m p o s i t i o n , may be v i e w e d a s m a n i f e s t i n g i t s e l f i n two w a y s , i n s t a n t a n e o u s and d e l a y e d (3). I t i s w e l l known t h a t low v a l u e s o f T and [ l ] lead to h i g h DPs. T h i s i s a c c u r a t e l y r e f l e c t e d by p a r a m e t e r (v^) , the i n i t i a l k i n e t i c c h a i n length (Table X I l l ) , which i s a q u o t i e n t of feed composition r a t i o x and d i m e n s i o n l e s s p a r a m e t e r a ^ . T h u s , given x , a small v a l u e of w o u l d seem t o f a v o r h i g h i n i t i a l DP. On t h e o t h e r hand, c r i t e r i o n ak < 1 s i g n a l s a downward d r i f t o f i n s t a n t a n e o u s DP d u r i n g i s o t h e r m a l p o l y m e r i z a t i o n (3) w h i c h has the o p p o s i t e e f f e c t . F u r t h e r m o r e , u n d e r non i s o t h e r m a l c o n d i t i o n s , r i s i n g t e m p e r a t u r e s e x a c e r b a t e t h i s downward d r i f t . Consequently, we c o n c l u d e t h a t d r i f t r e s p o n s e and i n s t a n t a n e o u s r e s p o n s e may be Q

Q

Q

Q

Q

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

BIESENBERGER

Thermal

4

Runaway

Hoiflopolymer

A

Boundary

• •

8^41 €=0.025 • .26 S AN • .38 AN MMA

10

10

2

Figure 4.

Computed

3

b IG boundaries

™ for

4

copolymerizations

1

°

5

34

POLYMERIZATION REACTORS AND PROCESSES

8 Ο

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

Ι ο ο

% V.

•a

•8 Ο V.

I I

ο 1 i t d r i f t s upward. We t h e r e f o r e c o n c l u d e t h a t t o a c h i e v e a t a r g e t c c h i g h i n comonomer 1, s a y , i n s t a n t a n e o u s r e s p o n s e c o n s i d e r a t i o n s ( T a b l e IX) s u g g e s t t h a t , g i v e n ( x j ) a l o w v a l u e f o r 3k »s r e q u i r e d , w h e r e a s e q u a t i o n 37 i n d i c a t e s t h a t 3^ < 1 w o u l d c a u s e t h e c o m p o s i t i o n t o d r i f t downward, o p p o s i t e t o t h e t a r g e t d i r e c t i o n . O b v i o u s l y , when 3k 1 > no d r i f t o c c u r s . I t c a n be shown t h a t h i g h t e m p e r a t u r e l e v e l s and R-A have v i r t u a l l y no b r o a d e n i n g e f f e c t on CCD d i s p e r s i o n b e c a u s e 3k has a s m a l l t e m p e r a t u r e c o e f f i c i e n t , w h i c h f r e q u e n t l y e v e n t a k e s on negative values causing d r i f t dispersion to a c t u a l l y lessen a t high temperatures. F i g u r e s 7 and 8 show t h e s m a l l n e s s and d i r e c t i o n ( i m p r o v e m e n t ) o f t e m p e r a t u r e e f f e c t on d r i f t , and t h e a b i l i t y o f 3k t o c h a r a c t e r i z e d i r e c t i o n ( s e e c r o s s o v e r i n F i g u r e 7 and c o r r e s p o n d i n g d r i f t s i n F i g * 8) a s w e l l a s m a g n i t u d e o f d r i f t * As a f i n a l n o t e i t s h o u l d be p o i n t e d o u t t h a t R-A p a r a m e t e r s f o r h o m o p o l y m e r i z a t i o n and c o p o l y m e r i z a t i o n c a n be e v a l u a t e d f r o m i n i t i a l k i n e t i c rate data using the i n t e r p r e t a t i o n s given to c h a r a c t e r i s t i c t i m e s i n T a b l e s VI and V I I . C o u p l i n g between c h a n g i n g r e a c t i o n v i s c o s i t y and k i n e t i c c o n s t a n t s and o t h e r t r a n s p o r t p r o p e r t i e s was n e g l e c t e d b e c a u s e runaway g e n e r a l l y o c c u r s e a r l y d u r i n g r e a c t i o n , and s u c h e f f e c t s a r e c o n s e q u e n t l y o f m i n o r importance. n s

0 >

=

POLYMERIZATION REACTORS AND PROCESSES

400

-(XN)inst - C U M . XN C A S E S 7,8,9

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

300

TABLE REF.

17 3

/

ix

ISOTHERMAL

200

100 NON-ISOTHERMAL, ADIABATIC

0.05

0.10

0.15

0.20

0.25

Polymer Engineering and Science Figure

6.

Computed

drift curves for instantaneous

and cumulative

DPs (3)

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

BIESENBERGER Thermal Runaway

Figure

5*

O

CO

N

y

Nst

Computed

8.19

A Adiabatic

R Runaway

1 0.38

_

!

J 0.40

____

1

1 0.58

)

PHI

1 0.60

1

J 01.79

I QI

IQI

drift curves for instantaneous and cumulative CCs of styrene-methyl acrylate polymers initiated with AIBN

0.20

QiQuasi-Isothermal

0 = .598

8.

y

i Isothermal

&*.820

9

K

6 995

—-R

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

meth-

3

O

2

o

2.

BIESENBERGER

Thermal

41

Runaway

SYMBOLS NOT DEFINED IN TEXT A

pre-exponential c o e f f i c i e n t i n rate constant expressions w i t h a p p r o p r i a t e s u b s c r i p t s o r heat t r a n s f e r s u r f a c e area. Cj = g e n e r a l r e a c t i o n component j o r d i m e n s i o n l e s s c o n c e n t r a t i o n o f component j . E = a c t i v a t i o n energy i n r a t e constant e x p r e s s i o n s w i t h appropriate subscripts. E^ =s d i m e n s i o n l e s s a c t i v a t i o n e n e r g y f o r c o p o l y m e r i z a t i o n d e f i n e d i n T a b l e IX. E

=

=

rk

E

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

E

Dk f = fj = I = k =

rk

/ R

T

g o

E

E

/ R

T

( tjkkj " tkkkk) g o initiator efficiency factor i n i t i a t o r e f f i c i e n c y f a c t o r f o r comonomer j i n i t i a t o r o r dimensionless i n i t i a t o r concentration rate constant with appropriate subscript

kap " M

2 f k

/ k

d t>!£

kax - k p / ( 2 f k k ) l / 2 a p j k = kpjk k j ( 2 f k d / k j j k ) t = k + k m = monomer o r d i m e n s i o n l e s s monomer c o n c e n t r a t i o n mj = comonomer j o r d i m e n s i o n l e s s c o n c e n t r a t i o n o f comonomer j o generalized i n i t i a t o r o r dimensionless concentration of generalized i n i t i a t o r m = x-mer o r d i m e n s i o n l e s s c o n c e n t r a t i o n o f x-mer P = a c t i v e i n t e r m e d i a t e s o f a l l l e n g t h s and t y p e s P j = a c t i v e j - m e r i n t e r m e d i a t e s o f a l l l e n g t h s w i t h comonomer j as t e r m i n a l u n i t P = a c t i v e i n t e r m e d i a t e s o f a l l l e n g t h s and t y p e s x,j a c t i v e i n t e r m e d i a t e o f l e n g t h x w i t h comonomer j a s terminal u n i t P j = a c t i v e i n t e r m e d i a t e o f a n y l e n g t h w i t h comonomer j a s terminal u n i t P j P k = a c t i v e i n t e r m e d i a t e o f a n y l e n g t h w i t h comonomer j and k a s p e n u l t i m a t e and u l t i m a t e u n i t s , r e s p e c t i v e l y R = r a t e f u n c t i o n f o r t o t a l monomer c o n v e r s i o n ( r a t e o f p o l y m e r i z a t i o n ) o r any r a t e f u n c t i o n w i t h a p p r o p r i a t e s u b s c r i p t Rp = rate function defined i nTable I Rg = gas constant r = ktc/kt or reactivity ratio with appropriate subscript T - (T - T ) / T U = o v e r a l l heat t r a n s f e r c o e f f i c i e n t V = r e a c t o r volume xj^j = number a v e r a g e DP x = w e i g h t a v e r a g e DP x - [m]Q/[m ] Xj = [ m j j / [ m ] y = m o l e f r a c t i o n o f comonomer 1 i n c o p o l y m e r d

t

k

p A

t

k

t c

m

t D

=

x

x

p

=

t

0

0

w

Q

0

0

M

]

/

Z

42 A

POLYMERIZATION REACTORS AND PROCESSES

k

k

-( tjkkj k

/ k

tkkkk)o k

+ = k / tl11 t22 $ = 1 - m = f r a c t i o n monomer c o n v e r t e d 6 = E ' T" X.A = c h a r a c t e r i s t i c t i m e s w i t h a p p r o p r i a t e s u b s c r i p t s y k - | x a r e entangled with the f o l l o w i n g r e l a t i o n ship based on v i s c o s i t y measurements used t o e s t a b l i s h x . c

c

K

c

=

*p

#

x

c

(1)

50

POLYMERIZATION

where

REACTORS AND PROCESSES

p i s the polymer volume f r a c t i o n . x i s the number average chain l e n g t h at the p o i n t o f chain entanglement. 3 i s an a d j u s t a b l e parameter (3 u s u a l l y u n i t f o r v i s c o s i t y measurements). K i s the entanglement constant. c

c

In a p p l y i n g equation ( l ) Cardenas and O ' D r i s c o l l use x as the c r i t i c a l chain l e n g t h f o r chain entanglement and permit x to decrease as p i n c r e a s e s during the p o l y m e r i z a t i o n according t o equation ( l ) . Therefore, during the course o f p o l y m e r i z a t i o n they note three kinds o f t e r m i n a t i o n r e a c t i o n s : c

c

k

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

R

#

r

+

R« s

— •

+

(R.) s

t

where r , s
x„ c

where r > x ,

s >

c

e

(R-) r

k^.

t —>.c

+

(R») —* e

e

c

c

I t i s assumed t h a t k-t i s independent o f conversion and t h a t the t e r m i n a t i o n constant f o r entangled r a d i c a l s i s given by

P and

x

s

e

n

finally

k

t

c

(

k

k

t t

)

h

( 3 )

e

T h i s model accounts f o r the c o u p l i n g between molecular weight development and a u t o a c c e l e r a t i o n i n R . However, two o f t h e b a s i c assumptions i) i s independent o f conversion ii) kp i s independent o f conversion are c e r t a i n l y not v a l i d f o r p o l y m e r i z a t i o n s below T . T h i s model does not account f o r a g l a s s y s t a t e - t r a n s i t i o n and hence cannot p r e d i c t the observed l i m i t i n g conversion. For temperatures above Tg i t may prove t o be s u c c e s s f u l . U n f o r t u n a t e l y , i t has not yet been evaluated under these c o n d i t i o n s . g

A Model Based on Free-Volume Theory. Three main problems are i n v o l v e d i n model development.

3.

1. 2.

3.

MARTEN AND HAMIELEC

Diffusion-Controlled

Determination o f t h e conversion a t which s i g n i f i c a n t chain entanglements f i r s t occur. Development o f a r e l a t i o n s h i p w h i c h g i v e s t h e d e c r e a s e i n t h e t e r m i n a t i o n r a t e constant as a f u n c t i o n o f temperature and polymer molecular weight and c o n c e n t r a t i o n . Development o f a r e l a t i o n s h i p w h i c h g i v e s t h e d e c r e a s e i n t h e propagation r a t e constant as a f u n c t i o n o f temperature and polymer molecular weight and c o n c e n t r a t i o n .

The r a t e o f p o l y m e r i z a t i o n isothermal bulk polymerization k

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

51

Polymerization

where k^ k-t f k^ [I] e dp dM x t

= = = = = = = = = =

2

\

c a n b e shown t o b e i n t h e c a s e o f

/ f - k , [I]

k «t

propagation rate constant, termination rate constant, initiator efficiency, decomposition constant o f i n i t i a t o r . i n i t i a l i n i t i a t o r concentration, (dp - dj^)/dp, volume c o n t r a c t i o n f a c t o r , d e n s i t y o f polymer. d e n s i t y o f monomer degree o f c o n v e r s i o n , time

I n o r d e r t o e s t i m a t e t h e dependence o f t h e t e r m i n a t i o n r a t e c o n s t a n t o n c o n v e r s i o n , m o l e c u l a r -weight a n d t e m p e r a t u r e , t h e f o l l o w i n g i s assumed: k-^ becomes d i f f u s i o n c o n t r o l l e d when t h e d i f f u s i o n c o e f f i c i e n t f o r a p o l y m e r r a d i c a l Dp becomes l e s s t h a n o r e q u a l t o a c r i t i c a l d i f f u s i o n c o e f f i c i e n t D^ Per K ± K (5) P P c r

I t i s f u r t h e r assumed t h a t t h e t e r m i n a t i o n r a t e c o n s t a n t b e y o n d t h i s c o n v e r s i o n c a n be e x p r e s s e d b y eq. (6a) and a t t h e c r i t i c a l point (6b). k, = fc.D (6a) k, = k. D (6b) t i p t 1 p c

r

c

r

where k^ = t e m p e r a t u r e dependent p r o p o r t i o n a l i t y constant. Dp = d i f f u s i o n c o e f f i c i e n t o f polymer r a d i c a l . D = c r i t i c a l d i f f u s i o n c o e f f i c i e n t o f polymer r a d i c a l . Pcr I f no e n t a n g l e m e n t s a r e p r e s e n t , t h e d i f f u s i o n c o e f f i c i e n t p o l y m e r m o l e c u l e i s , a c c o r d i n g t o B e u c h e (T_), g i v e n a s D

p

= ( 6 /k 'M) e x p (-A/V ) o

where M

6 k A Vp Q

2

= = = = = =

2

(7)

F

molecular weight o f polymer jump f r e q u e n c y . jump d i s t a n c e . constant constant f r e e volume.

(monodispersed).

of a

52

POLYMERIZATION REACTORS AND PROCESSES

V

F

V

F

i n the case o f b u l k or s o l u t i o n p o l y m e r i z a t i o n i s equal t o (0.025^ (T-T ^))

=

p

^ +

(0.025+a (T-T ))

g

M

(0.025+a (T-T q

))

g

g M

(8)

^

where M, P and S denote monomer, polymer and solvent r e s p e c t i v e l y . T = p o l y m e r i z a t i o n temperature. V = volume. V = t o t a l volume. Tg = g l a s s t r a n s i t i o n p o i n t o f monomer.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

T

=

a a£ ag

a

= =

a

£ ~ g expansion c o e f f i c i e n t f o r the l i q u i d s t a t e , expansion c o e f f i c i e n t f o r the g l a s s y s t a t e .

It i s further established that -

T„

-

#-

(9)

where T i s the g l a s s temperature o f the i n f i n i t e molecular weight polymer and M i s the cumulative number average molecular weight. Q i s a constant independent o f temperature. g o o

n

I f equation ( 6 a ) i s i n s e r t e d i n t o k

t

=

k

-l V (

2

(7)

A/

one o b t a i n s 1 Q

S /k2M)exp(- V )

( )

F

For a polymer with a molecular weight d i s t r i b u t i o n the proper molecular weight average t o use i n equations (7) and (10) can be determined u s i n g the f o l l o w i n g c o n s i d e r a t i o n s . In the case o f a heterogeneous polymer i t has been shown that (7,19 « 2 0 ) . n

=

k« M If w

f o r not entangled polymer n

=

s o l u t i o n s , and

3 , 5

k M 4 w f o r entangled polymer s o l u t i o n s . The d i f f u s i o n c o e f f i c i e n t s o f entangled polymers i n s o l u t i o n w i l l most c e r t a i n l y depend on the v i s c o s i t y o f the medium and v i c e versa. I t i s reasonable t h e r e f o r e t o expect t h a t the d i f f u s i o n c o e f f i c i e n t would c o r r e l a t e w e l l w i t h the weight average molecular weight o f the polymer. M i s t h e r e f o r e used with equation (10) giving k ^ ^ / k ^ ) exp(- / y ) = k (10a) u

w

A

F

f o r unentangled polymer

solutions

t

3.

MARTEN AND HAMIELEC

Diffusion-Controlled

53

Polymerization

2

~ - n ( -6 / k M ) e x p ( - A / V ) = k

for

(10b)

n

k

o

2

w

F

t

entangled polymer s o l u t i o n s . I f e q u a t i o n ( 1 0 a ) i s c o m b i n e d w i t h ( 6 b ) a n d r e a r r a n g e d , one

has *1 K-3= ( j )' = M t cr a n d

^wcrl

V

m

(10c)

exp(+A/V ) c r l

w c r i

F

m u s

" F

" t ^e e s t i m a t e d f o r e a c h p o l y m e r i z a t i o n b y crl s a t i s f y i n g equation (10c). K 3 depends o n l y on t e m p e r a t u r e a n d A i s a c o n s t a n t and t h e r e f o r e t h e r e l a t i o n s h i p between M _ a n d V* wcrl F i depends o n t e m p e r a t u r e a l o n e t h r o u g h e q u a t i o n ( 1 0 c ) At a constant temperature, t h e magnitude o f b o t h a n d V" ^ c a n c h a n g e w i t h i n i t i a t i o n rate or concentration o f solvent or chain transfer agent. The r e l a t i o n s h i p g i v e n b y e q u a t i o n ( 1 0 c ) i s h o w e v e r t h e same. I f i t i s assumed t h a t c h a i n e n g a n g l e m e n t s o c c u r s o o n a f t e r k^ becomes d i f f u s i o n c o n t r o l l e d , t h e n one h a s a s a good a p p r o x i m a t i o n

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

c

r

F

k

t

=

e x

M

k

t

=

k

y F

)

(

1 0 d

)

w

t

o

A

P(- /

=

cr

(

~

) e

n" M „ wcrl

x

(

P "

A

/

V

} F

c r l

C o m b i n i n g e q u a t i o n s ( l O d ) a n d ( l l ) , k^ i s o b t a i n e d a s a f u n c t i o n o f c o n v e r s i o n and t h e weight average m o l e c u l a r weight

£ - ) t o k

=

(ijEEl) M w

ex (-A(^- - ± F F P

V

V

)) , c r l

(12)

W h i l e K 3 a n d A a s e x p l a i n e d l a t e r were e s t i m a t e d u s i n g a f i t to e x p e r i m e n t a l d a t a m and n a r b i t r a r i l y s e t e q u a l t o 0.5 and 1.75 r e s p e c t i v e l y . The r e m a i n i n g p r o b l e m i n t h e m o d e l d e v e l o p m e n t i s t o e s t i m a t e t h e decrease i n k as a f u n c t i o n o f c o n v e r s i o n . As t h e r e a c t i o n proceeds beyond t h e p o i n t o f c h a i n entanglement, a c r i t i c a l conv e r s i o n i s r e a c h e d where t h e p r o p a g a t i o n r e a c t i o n becomes d i f f u sion c o n t r o l l e d and kp begins t o f a l l w i t h f u r t h e r i n c r e a s e i n p o l y m e r c o n c e n t r a t i o n . A t t h e c r i t i c a l c o n v e r s i o n , one may w r i t e p

54

POLYMERIZATION REACTORS AND PROCESSES

*3^ •where k p

M w

=

kp *o

cr

(13)

= t h e propagation constant below t h e c r i t i c a l conversion. = the d i f f u s i o n c o e f f i c i e n t o f t h e monomer at the c r i t i c a l conversion. = a proportionality factor.

Q

i|>3

Beuche (jj gives t h e f o l l o w i n g expression f o r the d i f f u s i o n c o e f f i c i e n t o f a small molecule i n a polymer s o l u t i o n . This equation a l s o known as the D o l i t t l e equation i s D = (* &1/6) exp(- B/y ) (11*) M

2

F

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

Beyond t h e c r i t i c a l conversion kp i s given by k

p

(15)

B

=

*

exp(- / V )

=

exp (- B( 7 " -

3

F

and ^ Po k

V

f

According t o Beuche (j)

(16) V

Fcr

2

B = 1 . 0 and t h i s value i s used here.

The general r a t e e x p r e s s i o n f o r the complete conversion interval i s

t

(

( l

d

wcrl

Q

.

° )

V/ )

( 1 - x) exp(-

x )

Conversion I n t e r v a l 1 : Interval 2 : Interval 3 :

a = 0, a = 0.875, a = 0.875,

2

B = 0, B = 0, B = 1.0,

(IT) A = 0 A = 1.11 A = 1.11

The determination of the conversion i n t e r v a l s a r e d i s c u s s e d l a t e r , a f t e r the molecular weight development. The instantaneous number and weight average degrees o f p o l y m e r i z a t i o n a r e g i v e n by k. R T

=

f L

\

=

1_

h

=

±JL

*X

+

c

+

"

c

JSi SIM1

when t e r m i n a t i o n i s s o l e l y by d i s p r o p o r t i o n a t i o n ; and t h e cumulat i v e averages by xM

MARTEN AND HAMIELEC

3.

2M

Diffusion-Controlled

55

Polymerization

X dx

(19)

T

I t should he understood that the weight average molecular weights appearing i n equation (17) are cumulative ones. The conversion-time h i s t o r y i s obtained by simultaneous s o l u t i o n o f equations (17) and (19). The conversion i n t e r v a l s are determined i n the f o l l o w i n g way: Values of A and

K

3

i s guessed and equations (17) and (19) are i n t e g r a t e d i n i n t e r v a l 1. The c a l c u l a t e d cum and a c a l c u l a t e d p are s u b s t i t u t e d i n t o equation ( 1 0 c ) . The end of i n t e r v a l 1 i s reached when the equation i s s a t i s f i e d . The i n t e g r a t i o n i s c a r r i e d f u r t h e r i n t o i n t e r v a l 2 w i t h the a p p r o p r i a t e parameters. The e r r o r o f f i t i n these i n t e r v a l s i s noted and

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

v

A and

K

3

a d j u s t e d a c c o r d i n g l y . T h i s procedure thus e s t a b l i s h e s the c o r r e c t end of i n t e r v a l 1 . We next guess the c r i t i c a l f r e e volume where k-p begins t o f a l l and then i n t e g r a t e through i n t e r v a l 3 t o l i m i t i n g conversion. The e r r o r o f f i t i s used t o e s t a b l i s h F and cr 2. the c r i t i c a l conversion. v

Comparison o f Simulated and Measured Rate Data. Model Parameters used with Equations Polymerization.

x 2

k

= t

U.U8

for

MMA

v

1

: c

r

l

+ K

11

• IQ^expC '

1 k

=

3

k

/

m

Q

l

— t c

Refer t o equation ( 1 0 c ) follows. = 0.563

exp(8,900

w

where R

^

) (l/mole min)

(20)

o

and p C

(19)

p

^

W

and

Data a f t e r Balke(£), I t o ( l O ) and Hayden and M e l v i l l e ( 6 _ ) were c o r r e l a t e d w i t h an Arrhenius type plot g i v i n g the f o l l o w i n g equation which was used i n a l l the s i m u l a t i o n s .

— : kj. o

M

(17)

=

1.986

c a l / ( g mole)(°K)

and equation (21)

cal/mol/RT)

which

(21)

56

POLYMERIZATION REACTORS AND PROCESSES

T A m

in = =

(°K) 1.11 0.5

Equations (17) and (19) are i n t e g r a t e d i n I n t e r v a l 1 u n t i l the cumulative % and V s a t i s f y equation ( 1 0 c ) . T h i s provides ^wcrl F * Refer to F i g u r e 5 f o r the a c t u a l K 3 data. F

a n ( i

V

c r l

= 0.066

(22)

*cr2

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

with B = 1. T h i s parameter i s independent o f temperature polymer molecular weight and c o n c e n t r a t i o n .

V"

:

F

The f r e e volume i s c a l c u l a t e d u s i n g equations (9) with the f o l l o w i n g parameters. 0.U8

T

g

a

M

T a

g M

=

llU

=

10-

T

(^C)"

Q

=

-102°C

=

)

3

^ )

2.208 • 10

=

M

d^

(°

, 9 T 3

1

" -

1.2g/cm

=

(11) (11)

C

10-

and

(11) 1

(o )

=

(8)

(11)

1

(°C)

3

SS

d

(°C)-

-106

=

g

3

x icr

and

henzene as

solvent

Ig/mole]degi3ee(ii)

5

l 6 1 +

•10- -t°C)g/cm' 3

(12)

3

I t should be noted t h a t polymer volume f r a c t i o n i s r e a d i l y t e d t o conversion. k

d

:

AIBN (13)

k

d

= 6.32

• 10

1 6

exp("

1 5

'

k 6

k c a

^/

m o l e

)mln-

... BOP

(14)=

k

= 7.5*10" min" , kd if

d

1

70 f was e

:

(23a)

= 3.6^*10~

5

min"

1

50

e the volume c o n t r a c t i o n f a c t o r i s c a l c u l a t e d u s i n g dens i t y data as P " M x c = - 3 ^ — (2U) d

/

M

1

set equal t o u n i t y i n a l l the s i m u l a t i o n s .

d

C

conver-

: C

M

=

8 . 9 3 • IG"- expC 'f 2

^J™^)

o

l

(25)

Diffusion-Controlled

Polymerization

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

MARTEN AND HAMIELEC

Figure

5. Arrhenius

plot of

k

s

58

POLYMERIZATION REACTORS AND PROCESSES

Bulk P o l y m e r i z a t i o n o f MMA B a l k e d Data. F i g u r e s 1, 6 , 7 and 8 show r a t e data a f t e r Balke i n t h e temperature range, 50 - 90°C. A l s o i n c l u d e d i s one r a t e curve a f t e r Nishimura (l£). There i s o b v i o u s l y e x c e l l e n t agreement even a t l i m i t i n g conversion. F i g u r e s 9 and 10 show a comparison o f measured and p r e d i c t e d weight average molecular weights. The agreement w i t h % i s e x c e l l e n t , but w i t h M^ o n l y f a i r a t intermediate conversions near t h e onset o f c h a i n entanglements. The r e p r o d u c i b i l i t y o f % when a h i g h molecular weight spike i s generated i s r a t h e r poor and perhaps t h i s may e x p l a i n some o f the d e v i a t i o n . I t o ' s Data. F i g u r e 11 shows I t o s ( l 0 i ) r a t e data a t 1+5°C f o r a very wide range o f i n i t i a t o r c o n c e n t r a t i o n s (AIBN: 0 . 2 - 0 . 0 0 6 2 5 gmole/£). The agreement i s e x c e l l e n t showing t h a t the l a r g e changes i n molecular weights can be accounted f o r i n our model.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

f

S o l u t i o n P o l y m e r i z a t i o n o f MMA Schulz's Data ( l 6 ) . F i g u r e s 12 and 13 show e x c e l l e n t agreement between simulated and measured r a t e s f o r a wide range o f solvent concentrations (benzene: 0 - 0 . 9 2 7 l i t e r benzene t o 0.103 l i t e r MMA and benzoyl peroxide: 0.0^+13 gmole/£ a t 50°C and 70°C). No doubt measured and p r e d i c t e d molecular weights would have been i n good agreement. T r a n s f e r t o benzene was n e g l e c t e d i n the simulations. I t should be mentioned t h a t the p r e d i c t e d curve a t highest benzene l e v e l i n F i g u r e 13 agrees with c l a s s i c a l k i n e t i c s (no diffusion-control). I t i s not c l e a r t h e r e f o r e why measured data at even higher benzene c o n c e n t r a t i o n s do not agree w i t h c l a s s i c a l k i n e t i c s . There may be some s u b t l e chemical i n t e r a c t i o n s a t these h i g h solvent l e v e l s . D u e r k s e n ( l 7 ) found s i m i l a r e f f e c t s w i t h styrene p o l y m e r i z a t i o n i n benzene and had t o c o r r e c t kp f o r s o l vent. Conclusions A new r a t e model f o r f r e e r a d i c a l homopolymerization which accounts f o r d i f f u s i o n - c o n t r o l l e d t e r m i n a t i o n and propagation, and which g i v e s a l i m i t i n g conversion, has been developed based on free-volume theory concepts. The model g i v e s e x c e l l e n t agreement w i t h measured r a t e data f o r bulk and s o l u t i o n p o l y m e r i z a t i o n o f MMA over wide ranges o f temperature and i n i t i a t o r and solvent concentrations .

MARTEN AND HAMD2LEC

Diffusion-Controlled

59

Polymerization

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

3.

Figure

6.

Bulk polymerization of MMA at 50°C: (X) [I]o = 0.02018 mol U (O)[I] = 0.01548 mol AIBN/L (9). 0

AIBN/

POLYMERIZATION REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

60

Figure

7.

Bulk polymerization of MMA at 50°C: (x) [I] = 0.05 mol (15); (O)[I] = 0.0258 mol AIBN/L (9). 0

0

AIBN/L

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

3. MABTEN AND HAMIELEC Diffusion-Controlled Polymerization 61

POLYMERIZATION REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

62

Figure

9. Bulk polymerization of MMA at 70°C: effect of conversion on molecular weight averages. (X)& ;(0)M . [I] = 0.01548 mol AIBN/L (9). n

w

0

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

MARTEN AND HAMIELEC Diffusion-Controlled Polymerization

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

64 POLYMERIZATION REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

MARTEN AND HAMIELEC

Diffusion-Controlled

500

1000

Polymerization

1500

Figure 12. Solution polymerization of MMA with benzene as solvent: temperature 50°C; [I] = 0.0413 mol BOP. (O) zero, Benzene = B, 1.030 L MMA; (X) 0.206 L B, 0.824 L MMA; (+) 0.412 L B, 0.618 L MMA; (A) 0.618 L B, 0.412 L MMA; (U) 0.824 L B, 0.206 L MMA; ( V ) 0.927 L B, 0.103 L MMA (16). 0

POLYMERIZATION REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

66

Figure 13. Solution polymerization of MMA with benzene as solvent: temperature 70°C; [I] = 0.0413 mol BOP. (O) zero Benzene = B, 1.057 L MMA; (X) 0.211 L B, 0.846 L MMA; (+) 0.423 L B, 0.634 L MMA; (A) 0.634 L B, 0.423L MMA; ([J) 0.846 L B, 0.211 L MMA; (V) 0.915 L B, 0.142 L MMA (16). 0

3.

MARTEN AND HAMIELEC

Diffusion-Controlled

67

Polymerization

Nomenclature A

constant

B

constant

C. .

c h a i n t r a n s f e r c o n s t a n t t o monomer

Cg

chain t r a n s f e r constant t o solvent

M

D. .

diffusion coefficient

o f t h e monomer

D..

diffusion

o f t h e monomer a t t h e c o n v e r s i o n

M M

cr D

coefficient

w h e r e t h e p r o p a g a t i o n becomes d i f f u s i o n diffusion

coefficient

o f a polymer

controlled

radical

P D

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

^cr

d i f f u s i o n c o e f f i c i e n t o f a polymer r a d i c a l a t t h e conversion where t h e t e r m i n a t i o n becomes d i f f u s i o n controlled

d^

d e n s i t y o f monomer

dp

d e n s i t y o f polymer

f

initiator

efficiency

entanglement

constant

K3

temperature

k^

decomposition

k

propagation r a t e constant at zero

p

dependent

constant

rate constant conversion

kp°

propagation r a t e constant

kj.

t e r m i n a t i o n r a t e c o n s t a n t i n t h e absence o f g e l

k^°

termination rate constant

kj. c

t e r m i n a t i o n r a t e c o n s t a n t between e n t a n g l e d and radical

cr

t e r m i n a t i o n r a t e c o n s t a n t o f t h e c o n v e r s i o n where t h e t e r m i n a t i o n becomes d i f f u s i o n controlled

kj_

kj.

t e r m i n a t i o n r a t e c o n s t a n t between two e n t a n g l e d

k

temperature

dependent

constant

k^

temperature

dependent

constant

k^

constant

k^

constant

k^

constant

M

molecular weight

[M]

monomer c o n c e n t r a t i o n

M

molecular weight

1

o f monodispersed polymer

number a v e r a g e m o l e c u l a r

M

q

weight

weight

o f monomer

average molecular

weight

effect

non-entangled

radicals

DO

POLYMERIZATION REACTORS AND PROCESSES

^wcrl

w e i

r t

&* average molecular the g e l e f f e c t s t a r t s

m

constant

n

constant

Q

constant

R

gas c o n s t a n t

weight o f t h e conversion

[s]

concentration of solvent

T

polymerization

T

g l a s s t r a n s i t i o n p o i n t o f monomer

T

where

temperature

g l a s s t r a n s i t i o n p o i n t o f polymer gp

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

T

glass t r a n s i t i o n of solvent s

s

T

g l a s s t r a n s i t i o n p o i n t o f polymer w i t h i n f i n i t e

molecular

CPoo &

weight

t V„ F V

time f r e e volume

F

crl V

F

cr2

fraction

f r e e volume f r a c t i o n a t t h e c o n v e r s i o n where t h e g e l e f f e c t starts f r e e volume f r a c t i o n a t t h e c o n v e r s i o n where t h e p r o p a g a t i o n becomes d i f f u s i o n c o n t r o l l e d

V., M Vp

volume o f polymer

V

volume o f s o l v e n t

o

V

v o l u m e o f monomer

total

volume

number a v e r a g e d e g r e e o f p o l y m e r i z a t i o n X^

weight average degree o f p o l y m e r i z a t i o n

x

conversion

X

number a v e r a g e c h a i n l e n g t h a t t h e p o i n t o f c h a i n ment

o f monomer

Greek Symbols a

constant,

exponent

01^

expansion c o e f f i c i e n t

for the glassy state

expansion c o e f f i c i e n t

for the l i q u i d

3

constant,

exponent

e

volumetric

6

jump d i s t a n c e

contraction

coefficient

state

entangle-

MARTEN AND HAMiELEC

3.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

6

Diffusion-Controlled

Polymerization

69

jump d i s t a n c e

2

Ψ]_

t e m p e r a t u r e dependent lumped

constant

Ψ2

t e m p e r a t u r e dependent lumped

constant

Ψ3

lumped

constant

η

viscosity

τ

t h e r e c i p r o c a l i n s t a n t a n e o u s number a v e r a g e d e g r e e o f p o l y m e r i ζation

φ

volume f r a c t i o n o f polymer

o

jump f r e q u e n c y

φ2

jump f r e q u e n c y

Literature Cited 1.

C a r d e n a s , J. a n d 14, 8 8 3 .

2.

C a r d e n a s , J. a n d O'Driscoll, K. F., J. P o l y m . Sci. ( 1 9 7 7 ) A-1, 15, 1883. C a r d e n a s , J. a n d O'Driscoll, K . F . , J. P o l y m . Sci. ( 1 9 7 7 ) A - 1 , 15, 2097. Friis, N. a n d H a m i e l e c , A.E., ACS Symposium Series ( 1 9 7 6 ) 24, 8 2 , " G e l Effect in E m u l s i o n Polymerization of Vinyl Monomers". B e r e n s , A.R., ACS Symposium Series ( 1 9 7 8 ) 3 9 , 2 3 6 , "The Sorption of Gases a n d V a p o r s in PVC P o w d e r s " . H a y d e n , P. a n d Melville, Sir Harry, J. P o l y m . Sci. (1960) 43, 2 0 1 . B e u c h e , F., Interscience, New Y o r k ( 1 9 6 2 ) , "Physical Proper­ ties of P o l y m e r s " . A b u i n E. a n d Lissi, E.A., J. M a c r o m o l . Sci. Chem. ( 1 9 7 7 ) A-11, 287.

3. 4.

5. 6. 7. 8. 9.

O'Driscoll,

K . F . , J. P o l y m . Sci. ( 1 9 7 6 ) A - 1 ,

B a l k e , S.T. a n d H a m i e l e c , A . E . , J. Appl. P o l y m . Sci. ( 1 9 7 3 )

17, 905. 10. 11.

Ito, K., J. P o l y m . Sci. ( 1 9 7 5 ) A - 1 , 13, 401. H o r i e , Κ., Mita, I. a n d Kambe, M., J. P o l y m . Sci. (1968) A-1, 6, 2663. 12. B a l k e , S.T., "The Free Radical Polymerization of Methyl Methacrylate to High C o n v e r s i o n " , Ph.D. Thesis, M c M a s t e r University, Hamilton, Ontario (1972). 1 3 . A b d e l - A l i m , A.H. a n d H a m i e l e c , A.E., J. Appl. P o l y m . Sci. (1972) 1 6 , 7 8 3 . 14. P o l y m e r Handbook ( 2 n d ed.), B r a n d r u p , J . a n d Immergut, E.H., Wiley, New Y o r k ( 1 9 7 5 ) . 15. N i s h i m u r a , N., J. M a c r o m o l . Sci. ( 1 9 6 6 ) 1 , 257. 16. S c h u l z , G.V. a n d Harborth, G., M a k r o m o l . Chem. ( 1 9 4 7 ) 1, 1 0 6 .

POLYMERIZATION REACTORS AND PROCESSES

70 17.

18. 19. 20.

Duerksen, J.H., "Free R a d i c a l P o l y m e r i z a t i o n o f Styrene i n Continuous S t i r r e d Tank Reactors", Ph.D. T h e s i s , McMaster U n i v e r s i t y , Hamilton, Ontario ( 1 9 6 8 ) . Ibragimov, I.Y. B o r t , D.N. and Efremova, V.N., Vysokomol. Soedin. Ser.B, (1974) 16 (5), 3 7 6 . Rudd, J . F . , J. Polym. Sci. ( 1 9 6 0 ) , 44, 459. Bueche, F., J. Polym. Sci., ( 1 9 6 0 ) , 43, 5 2 7 .

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch003

RECEIVED February 9, 1979.

4 Technology of Styrenic Polymerization Reactors and Processes R. H. M.SIMONand D. C.CHAPPELEAR

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch004

Monsanto Company, Springfield, MA 01151

1.

Introduction

In considering the broad commercial applications of both crystal polystyrene (PS) and rubber modified "high impact" polystyrene (HIPS), it bears reemphasis that the process and process conditions each have major effects on product properties and fabrication behavior as well as product costs. With crystal polystyrene, product molecular weight, molecular weight distribution, oligomer and residual monomer levels, color and c l a r i t y are closely process related. With HIPS, rubber phase particle size, size distribution and morphology, graft copolymer level and molecular weight are additionally affected. To the manufacturer, therefore, the selection of the optimum process and conditions w i l l underly the most relevant polymer "property": the cost of the product which meets performance requirements. A characteristic of styrene polymerization processes i s that different reactor types are frequently used i n varying series combinations. The goal of this review i s therefore twofold: f i r s t , to describe how and why different reactors have been employed in batch and continuous processes; and second, to outline some of the bridges between available theory and actual practice by highlighting some of the major design problems that are amenable to such an approach. Hopefully, this may encourage more pertinent research i n the area. Industrial practice i s reflected in the patent a r t , and a few general reviews such as Bishop (1). Much information remains proprietary. Answers to many practical problems have to be obtained by licensing or extensive development. 2.

Processes and Reactor Process Elements

2.1 Classification of Processes and Reactors. Most styrene polymers are produced by batch suspension or continuous mass processes. Some are produced by batch mass processes. "Mass" in this sense includes bulk polymerization of the polymer

0-8412-0506-x/79/47-104-071$10.50/0 © 1979 American Chemical Society

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch004

72

POLYMERIZATION REACTORS AND PROCESSES

d i s s o l v e d i n i t s monomer and, i n some cases, some amount of solvent. PS mass p o l y m e r i z a t i o n i s homogeneous ( s i n g l e phase viscous f l u i d ) . In mass HIPS p o l y m e r i z a t i o n s , the rubber forms an e m u l s i f i e d second phase. Table I provides an overview o f general r e a c t o r designs used with PS and HIPS processes on the b a s i s o f r e a c t o r f u n c t i o n . The polymer concentrations c h a r a c t e r i z i n g the mass p o l y m e r i z a t i o n s are approximate; there c o u l d be some o v e r l a p p i n g o f a g i t a t o r types with s o l i d s l e v e l beyond t h a t shown i n the t a b l e . Polymer c o n c e n t r a t i o n l i m i t s on HIPS w i l l be lower because o f increased viscosity. There are a l s o a d d i t i o n a l a p p l i c a t i o n s . Tubular r e a c t o r s , f o r example, i n e f f e c t , o f t e n e x i s t as the t r a n s f e r l i n e s between r e a c t o r s and i n e x t e r n a l c i r c u l a t i n g loops assoc i a t e d with continuous r e a c t o r s . Various r e a c t o r combinations are used. For example, the product from a r e l a t i v e l y low s o l i d s batch-mass r e a c t o r may be t r a n s f e r r e d to a suspension r e a c t o r ( f o r HIPS), press ( f o r PS), o r unagitated batch tower ( f o r PS) f o r f i n i s h i n g . In a s i m i l a r f a s h i o n , the e f f l u e n t from a continuous s t i r r e d tank r e a c t o r (CSTR) may be t r a n s f e r r e d to a t u b u l a r r e a c t o r or an unagitated or a g i t a t e d tower f o r f u r t h e r p o l y m e r i z a t i o n before d e v o l a t i l i z a tion. Greater d e t a i l w i l l be provided i n the s e c t i o n s f o l l o w i n g . TABLE I Styrene Polymer Reactors - C l a s s i f i c a t i o n Process Type Reactor

Batch

Continuous

Function

Mass Polymerization

Conventional k e t t l e with: turbine agitator

CSTR with:

large turbine, anchor or h e l i c a l agitator

turbine,anchor or h e l i c a l agitator

Polymer 30-80% concentration

anchor or h e l i c a l agitator p r o p r i e t a r y and patented s t i r r e d reactors

anchor,helical a g i t a t o r s or s p e c i a l designs

Polymer > 80% concentration

press, unagitated batch tower

Polymer

c C

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch005

o f r e a c t o r , cm

(N ^) R

e

dimensionless

v a l u e o f t h e R e y n o l d s number a t t h e l a m i n a r t r a n s i t i o n , dimensionless R e y n o l d s number b a s e d o n e m u l s i o n p r o p e r t i e s polymerization, dimensionless

N^ Dn

Dean number,

r^

rate o f polymerization, mol 1 ^ h ^

Note:

turbulent

prior to

dimensionless

A p p a r a t u s C - l i s a l a b o r a t o r y r o u n d - b o t t o m f l a s k and laboratory s t i r r e r C - 2 i s a l a b o r a t o r y r o u n d - b o t t o m f l a s k and laboratory s t i r r e r E - l i s a stainless, cylindrical reservoir, piston pump a n d s o n o l a t o r E-2 i s t h e r e s e r v o i r o f t h e h e l i c a l r e a c t o r , gear Dump a n d s o n o l a t o r

References (1) (2) (3)

Ghosh, M. and Forsyth, T.H., ACS Symp. Series, No. 24, paper 24 (1976) R o l l i n , A.L., Patterson, I . , Huneault, R. & Bataille, P . , Can. J . Chem. E n g . , 55, 565 (1977) White, C . M . , Proc. Royal Soc., A-123, 645 (1929)

Literature cited (1) (2) (3) (4) (5) (6)

Harada, Μ., Nomura, M . , Kojima, H., Eguchi, W. and Nagata, S., J . Appl. Poly. S c i . , 16, 811 (1972) U.S. Patent No. 2, 831, 842, Dupont de Nemours & Co. De Graff, A.W. and Poehlein, G.W., J. Poly. S c i . , A-2, 9, 1955 (1971) Feldon, M . , McCann, R . F . and L a u n d r i e , R.W., India Rubber World 128, 1 (1953) Canadian Patent No. 907795, G u l f O i l Canada Ltd (1972) Ghosh, M. and Forsyth, T . H . , ACS Symposium Series, No. 24, paper No. 24 (1976)

136

POLYMERIZATION REACTORS AND PROCESSES

R o l l i n , A.L., P a t t e r s o n , I . , Huneault, R., R a t a i l l e , P., "The E f f e c t of Flow Regime on the Continuous Emulsion P o l y m e r i s a t i o n of Styrene i n a Tubular Reactor", Can. J. of Chem. 55, 565 (1977) (8) Evans, C.P., L i g h t , J.D., Marker, L., S a n t o a i a l a , A.T. and Swetting, O.J., J. Appl. P o l y . S c i . , 5, 31 (1961) (9) Omi, S., S h i r a i s h i , Y., Sato, H. and Kubota, H., J . Chem. Eng. Japan, 2, 1. 64 (1969) (10) Nomura, M., Harada, M., Eguchi, W. and Nagata, S., J . A p p l i e d Poly. S c i . , 16, 835 (1972)

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch005

(7)

(11) Omi, S., Kuwabara, L. and Kubota, H., J . Chem. Eng. Japan, 6, 343 (1973) (12) E u s t i c e , J . , Proc. Royal Soc. A 84, 107 (1910) (13) Dean, W.R., P h i l . Mag., 4, 208 (1927) and Phil. Mag., 5, 673 (1928) (14) White, C.M., "Streamline Flow through Curved P i p e s " , Proc. Royal Soc., A 123, 645 (1929) (15) T a y l o r , G.I., "The C r i t e r i o n f o r Turbulence i n Curved Pipes", Proc. Royal Soc., A 124, 243 (1930) (16) S r i n i v a s a n , P.S., Nandapurkar, S.S. & Holland, F.A., "Pressure Drop and Heat T r a n s f e r in C o i l s " , The Chem. Engr. 218, CE 113 (1968) (17) Blanc, M., M.Sc.A. Thesis Chem. Eng. Dept., E c o l e P o l y technique, Montreal, (1977) (18) Huneault, R., M.Sc.A. T h e s i s Chem. Eng. Dept., E c o l e Polytechnique, Montreal (1976) (19) Archambault, J . , M.Sc.A. T h e s i s Chem. Eng. Dept., E c o l e Polytechnique, Montreal (1977) (20) I t o , H., " F r i c t i o n F a c t o r s f o r Turbulent Flow in curved P i p e s " , J . B a s i c , Eng. Trans. A.S.M.E., D, 81, 123 (1959) (21) Omi, S., Sato, H. and Kubota, H., J . Chem. Eng. Japan, 2, 1, 55 (1969) (22) Gardon, J.L., "Mechanism o f Emulsion P o l y m e r i s a t i o n " , AIChE Symp., May 1969 (23) B l a c k l e y , D . C , "Emulsion P o l y m e r i z a t i o n " , Wiley, New York (1975) RECEIVED February 6, 1979.

6 Polyamidation in the Solid Phase R. J. G A Y M A N S and J. S C H U I J E R

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch006

Twente University of Technology, Department of Chemical Technology, P.O. Box 217, Enschede, The Netherlands

Polyamides can be polymerized i n the solid-phase i n an oxygenf r e e atmosphere a t a temperature range of 20 - 160 C below t h e i r f i n a l melting p o i n t (1-9). The r e s u l t s from the l i t e r a t u r e are not easy to i n t e r p r e t due to the l i m i t e d temperature ranges, small v a r i a t i o n s i n p a r t i c l e s i z e s and the occurrence of s i d e r e a c t i o n s with chain branching. We s t u d i e d the polyamidation i n the s o l i d phase process of nylon 4,6, which has a high melting t r a n s i t i o n (264 - 320 C) and does not show any tendency to g e l (10). The r a t e of the s o l i d phase p o l y m e r i z a t i o n (SPP) depends on -

the the the the the

k i n e t i c s o f the chemical r e a c t i o n d i f f u s i o n of the r e a c t i v e groups d i f f u s i o n o f the condensate out of the p a r t i c l e d i f f u s i o n a t the p a r t i c l e - gas i n t e r f a c e heat t r a n s f e r

The p o l y m e r i z a t i o n r a t e i s c o n t r o l l e d by the slowest process. Thus i t i s important to e s t a b l i s h the r a t e c o n t r o l l i n g steps. The s t a r t i n g m a t e r i a l f o r the (SPP) can be the dry n y l o n s a l t (3,4) but mostly a low or middle molecular weight polymer i s used. The polyamide-salts have the disadvantage of high amine l o s s e s (3^4). Griskey (5) and Chen (6) s t u d i e d the r e a c t i o n of nylon 6,6 and 6,10 i n a SPP i n a stream of dry n i t r o g e n i n the temperature range of 90° - 180°C. They found that the r e a c t i o n l i m i t i n g step was n o t the d i f f u s i o n of water but the chemical r e a c t i o n . The k i n e t i c r e l a t i o n s h i p they observed was Mn = k t

n

(1)

n = 0,5 and 1.0 f o r nylon 6,6 and nylon 6,10, r e s p e c t i v e l y . The a c t i v a t i o n energies of the rateconstant k are r e s p e c t i v e l y 10.5- 12.96 and

0-8412-0506-x/79/47-104-137$05.00/0 © 1979 American Chemical Society

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch006

POLYMERIZATION REACTORS AND PROCESSES

13.2 kcal.mol." . Monroe ( 7 ) , r e p o r t i n g on nylon 66, found a dramatic e f f e c t o f the s t a r t i n g molecular weight on the r e a c t i o n r a t e . I n c r e a s i n g the s t a r t i n g molecular weight by a f a c t o r o f two decreased the r e a c t i o n time to reach M = 15,000 by a f a c t o r two. Zimmerman (8), comparing SPP and m e l t - p o l y m e r i z a t i o n , showed that i n the presence of water the SPP leads to much higher molecular weights a t a g i v e n pressure than the m e l t - p o l y m e r i z a t i o n . A t the same time he n o t i c e d a broadening i n the molecular weight d i s t r i b u t i o n (m.w.d.) o f nylon 6,6. Ramsey and D u n n i l l (9) reported the formation of h i g h l y branched s t r u c t u r e s i n nylon 6,6 by r e a c t i n g under anhydrous c o n d i t i o n s . According to them t h i s could be prevented by r e a c t i n g under a blanket o f super-heated steam. A t h e o r e t i c a l study o f the m.w.d. broadening during the SPP of a s e m i - c r y s t a l i n e polymer showed that f o r l i n e a r s t r u c t u r e s , according to the S c h u l z - F l o r y r e l a t i o n s h i p , no narrowing o r broadening o f the m.w.d. i s to be expected (11). The k i n e t i c s o f the m e l t - p o l y m e r i z a t i o n o f nylon 6,6 i s t h i r d order (1) "

d [

"S? dt

Q H ]

"

([-COOH] [-NHJ - [-C00H] C-NHj ) (2) \ 2 eq 2 eq/

[-C00HI

The r a t e constante k has an a c t i v a t i o n energy of 16.8 kcal.mol"" In water f r e e c o n d i t i o n s equation 2 can be s i m p l i f i e d to

.d^opa

=

k

^

>

( 3 )

I f the polymer i s balanced w i t h equation i s

([-C00H]J ~([-C00H]j

=

2

k

(12).

1

E-COOH ] = [-NH„]the i n t e g r a t e d

t

(

4

)

For an unbalanced polymer w i t h [-C00H] - [-NH^] = D and the assumption that D has a constant value r e s u l t s i n the i n t e g r a t e d equation 1 D

n l

n

[-C00H] [- NH ] 2

"

1 [-C00H]

=

D

k

t+

C O n S t

(

-

5

)

The SPP r e a c t i o n i s not n e c e s s a r i l y t h i r d order. I f the endgroups are unbalanced a good approximation o f the SPP r e a c t i o n order can be obtained by expressing i t as f u n c t i o n of /[-COOH] [-NE ] = /P 2

The r a t e o f r e a c t i o n i s then d [-C00H] dt

k.

(/[-COOH] [-NH^ )

n

=k.(/p)

n

(6)

6.

GAYMANS AND SCHUIJER

Polyamidation

in the

Solid

Phase

139

The i n t e g r a t e d form with the unknown order n i s then (7)

I f the endgroups are balanced. = > "7?

the equation i s (8)

For e v a l u a t i o n purposes

i t i s changed to

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch006

(9) where a i s chosen as near as p o s s i b l e to (n-1). We studied the polyamidation of nylon 4,6, and v a r i e d the r e a c t i o n time, r e a c t i o n temperature, p a r t i c a l s i z e , s t a r t i n g molecular weight, and type of r e a c t o r gas. At the same time we looked at the molecular weight broadening and the degradation with colour formation. In order to have good heat and mass t r a n s f e r the r e a c t i o n s were mainly conducted on f i n e powder i n a f l u i d i z e d bed r e a c t o r and with dry n i t r o g e n as c a r r i e r gas. EXPERIMENTAL The s t a r t i n g m a t e r i a l s were low molecular weight polymers prepared by r e a c t i n g 1,4 diaminobutane and a d i p i c a c i d f o r two hours at 220°C i n a capsule i n an autoclave (10). The low molec u l a r weight m a t e r i a l was powdered by crushing and b a l l m i l l i n g . The f l u i d i z e d bed r e a c t i o n s were c a r r i e d out i n a g l a s s r e a c t o r ( f i g . 1) 2.5 cm diameter and 50 cm long. The r e a c t o r was heated i n an oven i n which the temperature could be c o n t r o l l e d w i t h i n 0.2°C. As c a r r i e r gases dry n i t r o g e n and super-heated steam, both at a pressure of 1 bar, were used. The gas v e l o c i t y was 4,0 cm. sec f o r both gases. The samples were f l u s h e d from the sample-holder i n t o the pre-heated r e a c t o r and reached temperature w i t h i n a minute . The r e a c t i o n s were stopped by removing the r e a c t o r from the oven. For comparison, we c a r r i e d out some r e a c t i o n s under vacuum i n a r o t a t i n g 50 ml f l a s k . The f l a s k was attached to a rotavap apparatus and heated i n a s i l i c o n o i l bath, the vacuum a p p l i e d was *3 mbar. Endgroup analyses were c a r r i e d out with an automatic p o t e n t i o meter. The [-NH ] and [-C00H] were determined simultaneously. The polymer was d i s s o l v e d i n o - c r e s o l / c h l o r o f orm mixture (70/30), excess a l c o h o l i c KOH added and t i t r a t e d with a l c o h o l i c HC1 (0.1 N). The inherent v i s c o s i t i e s C ^ ^ ) were determined i n 0.5% s o l u t i o n s i n 90% formic a c i d . We observed the f o l l o w i n g r e l a t i o n s h i p : 2

1

log M

n

= 1.122

l o g n. u + 4.182 inn

(10)

140

POLYMERIZATION REACTORS AND PROCESSES

Table I

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch006

Temp (°C)

Reaction time (hours)

Prepolyiner A

-

-

220

.83 3.0 6.0 21.5

Prepolymer B

190

-

205

235

250

265

280

Reaction Data Endgroup a n a l y s i s

Viscosimetry

1

inh

M

n

[COOHl Oral , eq/10 gr eq/TO^ gr (VP)-'

0,177 2,175 0.377 8,200 0,823 12,200 0,917 13,800 1,444 23,000

43.50 9.78 6,45 4,32 4,00

58.90 13.56 11.92 10.17 6.12

1,960 8,700 11,400 15,100 20,200

0,165 2,010 0,374 5,000 0,442 6,100 0.438 6,000 0.575 8,200 0,728 10,600

48,20 19,36

57,80 18.49

1,890 5,300

-

-

13.85

1 2 4 6.75

0.429 6,800 0*564 8,000 0.661 8,600 0.731 10,700

13,73

15.48

-

-

1 2,25 4 8

0,732 0.866 1.024 1.218

1 4 7

0.900 13,500 1.408 22,300 1.601 25,800

1 2 4 8

1.220 1.420 1.658 2.461

1 2 4

1.508 24,100 1.769 28,900 2,717 46,800

8

2.728 46,000

1 2 4 8 24

12.22

-

11,58

10,700 13,000 15,600 19,000

6,80

-

5,19 5,26

19,000 22,500 26,700 41,800

4,09 2,52

_

_

-

-

-

-

--

— From u.c. M = 49 ,000 n ^ = 61,000 M

= 74,000

7,700

6,900

11,300

21,700 27,500

-

-

—

6.

GAYMANS AND scHuijER

Polyamidation

in the

Solid

141

Phase

With t h i s r e l a t i o n s h i p f o r a l l samples was c a l c u l a t e d from ninh* This M i s used f o r e v a l u a t i n g the r e a c t i o n data. The u l t r a c e n ? r i f u g e (u.c^ measurements were c a r r i e d out i n a Spinco model E a n a l y t i c a l u l t r a c e n t r i f u g e , with 0.4% s o l u t i o n s i n 90% formic a c i d c o n t a i n i n g 2.3 M KC1. By means of the sedimentat i o n ^ d i f f u s i o n e q u i l i b r i u m method of Scholte (13) we determine M , M and M . The buoyancy f a c t o r (1- vd = -0.086) necessary f o r tSe c a l c u l a t i o n of these molecular weights from u l t r a c e n t r i f u g a t i o n data was measured by means of a PEER DMA/50 d i g i t a l d e n s i t y meter. U.V. absorptions were measured on 0.5% s o l u t i o n s i n 90% formic a c i d at 290 mn.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch006

RESULTS AND

DISCUSSION

Reaction k i n e t i c s . The r e s u l t s of the r e a c t i o n of f i n e l y devided powdered polymer (0.1 = f^ = 5.7 ml/min and f^ + f! = 11.4 ml/min which gave a hold-up time of 25.6 mins. Polymefization was allowed to proceed and the steady-state products were analysed by after 5 or more hold-up times. Periodic operation of the reactor was introduced by switching the flow controllers to computer control after steadystate had been established with constant pump speeds. After 4-5 periods of o s c i l l a t i o n of 1 hour each permanent o s c i l l a t o r y conditions were attained and analysis was carried out on the lumped product of one or more of the subsequent periods.

It is clear from Figure 1 that in the f i r s t experiment (Figure la) f » and fx were o s c i l l a t e d in opposition of phase with maximum possible amplitude of the pump setting. In the second experiment (Figure lb) nearly rectangular waves were used for

262

POLYMERIZATION REACTORS AND PROCESSES

f and f j also 180° out of phase. In this case the f was o s c i l l a t e d between 10% and 90% of maximum flow so that at a l l times some monomer was being introduced to the reactor. The forcing functions were not perfectly rectangular because of the limitations of the controller, which would not respond instantaneously but they did closely approximate to the i d e a l . In both experiments the monomer stock solution concentration was 50% V/V (4.63 moles 1~') and the i n i t i a t o r solution concentrations 0.041 moles T" and 0.044 moles 1~' in the sinusoidal and square-wave cases respectively. Reaction temperature was 80°C, The results are summarized in Table II and the GPC traces are shown in Figure 3. Table II Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch011

M

M

The Mg, M , D and conversions observed for the freer a d i c a l l y i n i t i a t e d polymerization of MMA produced in a periodically operated CSTR w

n

Forcing Function Continuous Sinusoidal

% Curve in Dn Wn Condition Figure 3 Conversion. Steady-state 1 21000 37200 1.77 22.0 Oscillatory 19.0 2 22160 44400 2.0 Steady-state Continuous Steady-state 3 23400 41300 1.76 18.8 Square-wave Oscillatory 1.89 18.7 50900 4 27000 Steady-state Discussion. It i s apparent from Table II and Figure 3 that even though the reactor has been subjected to very severe o s c i l l a t o r y conditions where the frequency of o s c i l l a t i o n was low with respect to the hold-up time and the amplitudes of the functions large, the MWD's of the resulting polymers d i f f e r very l i t t l e from those produced in the steady-flow steady-state. Under periodic operation, the polydispersity i s greater by between 15-30% and the wave form of the forcing function has l i t t l e effect. There is a small increase in both M* and MjJ with respect to their steady-state values and the conversion appears to be l i t t l e affected by the mode of operation of the reactor. It is interesting to compare these findings with those of Spitz £ t al_ (16) even though the experimental methods and forcing functions are different in their case. In both studies the timeaveraged polydispersity obtained under periodic operation increased by a maximum of 30% when compared with steady-state values. Also when passing from continuous-flow steady-state conditions to permanent periodic operations only a very small drop in monomer conversion was observed in each case. However, contrary to the findings of Spitz et_ al_, M* in this work was always s l i g h t l y higher than M... w

w

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch011

Figure 3. Typical GPC traces—(a) sinusoidal feed: Curve 1, steady-state unperturbed flow; Curve 2, oscillatory steady-state, (b) Square-wave feed: Curve 3, steady-state unperturbed flow; Curve 4, oscillatory steady-state.

POLYMERIZATION REACTORS AND PROCESSES

264

The perturbations used in this study are, in general, more severe than those used in the computer models of o s c i l l a t o r y feeds to polymerization CSTR's which have been reported (11, 12, 13, 14, 15) but the influence of the disturbances observed experimentally are probably less than might be expected from the computer models (even though direct comparisons are not r e a l l y possible). Although our feed-forward control methods could be readily adapted to produce any perturbations we wished in f and f r , a systematic exploration of different forcing functions was not attempted as the l i k e l y changes in any of the measured parameters would be within the l i m i t s of error to be expected with GPC, It is conceivable that perturbing the temperature of polymerization or the concentration of an effective transfer agent in the reactor might produce greater changes in the MWD's of the products of a radical process. The influence of changes in these other variables on MWD in a homopolymerization has not yet been tested, but whatever perturbations are introduced to the feed in a radical polymerization in a laboratory-scale CSTR, they are unlikely to introduce dramatic changes in the MWD of the product because of the extremely short l i f e - t i m e of the active propagating chains in relation to the hold-up time of the reactor. This small change in MWD could be advantageous in a r a d i c a l l y i n i t i a t e d copolymerization where perturbations in monomer feeds could give control over polymer compositions independent of the MWD. This postulate i s being explored currently. Considerable success has been achieved in controlling the MWD of the products of polymerization where the life-times of propagating centres are long. These studies and others using computer controlled reactors w i l l be reported elsewhere. Symbols. D = Polydispersity. D* = Time-averaged polydispersity. f|v| = Instantaneous monomer feed flow-rate, f j = Instantaneous i n i t i a t o r feed flow-rate. fjs = Time-averaged monomer solution flow-rate in o s c i l l a t o r y steady-state. f§ = Time-averaged i n i t i a t o r solution flow-rate in o s c i l l a t o r y steady-state. [I] = I n i t i a t o r concentration in stock solution. [MJ = Monomer concentration in stock solution. Bp = Number average molecular weight. = Time-averaged M M = Weight average molecular weight.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch011

M

n

n

w

11.

MEIRA ET AL.

Molecular Weight Distribution Control

265

MjJ = Time-averaged M μ = Number average degree of polymerization. y Weight average degree of polymerization. w

η

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch011

w

=

Acknowledgment. The authors wish to thank the Science Research Council for financial support (Grant No. B/R 82506) Literature Cited. 1. Frisch, H.L., 'Physical Chemistry': Enriching Topics on Colloid and Surface Science', Chapter 10, Theorax, La Jolla Cal., 1975. 2. Martin, J.R., Johnson, J.F. and Cooper, A.R., J . Macromol Sci., Revs. Macromol. Chem., (1972), C8 1, 57. 3. Flory, P.J., "Principles of Polymer Chemistry', Cornell University Press, Ithica, NY, 1953. 4. Peebles (Jr), L.H., 'Polymer Reviews', Volume 18, Eds. Mark, H.F., and Immergut, E.H., Interscience, NY, 1953. 5. Bamford, C.H., Barn, W.G., Jenkins, A.D. and Onyon, P.F., 'The Kinetics of Vinyl Polymerization by Radical Mechanisms'. Butterworths, London, 1958. 6. Fan, L.T., and Shastry, J.S., J. Polymer Sci., Part D. Macromolecular Reviews, (1973), 7, 155. 7. Hamielec, A.E., Hodgkins, J.W. and Tebbins T., Α.I.Ch.Ε. J., (1967), 13, 1087. 8. Duerksen, J.H., Hamielec, A.E. and Hodgins, J.W., J. Polym. Sçi., (1968), C24, 155. 9. Baccaro, G.P., Gaitonde, J.M. and Douglas, Α.I.Ch.E.J. (1970) 16, 249. 10. Bailey,T.E., 'Chemical Reactor Theory', Chapter 12, Eds., Lapidus, L. and Amundson, N.R., Prentice Hall, NY, 1977. 11. Ray, W.H., Ind. Eng. Chem. Process Design Develop., (1968) 7, 442. 12. Laurence, R.L. and Vasudevan, G., Ind. Eng. Chem. Process Design Develop. (1968), 7, 427. 13. Yu. F.C.L., 'Periodic Operation of a Non-Isothermal Polymerization Reactor', M.Sc. Thesis, University of Massachusetts, 1969. 14. Bhawe, M.N., 'A Study on the Application of Periodic Operation for some Chemical Engineering Problems', Ph.D. Thesis, Northwestern University, 1972. 15. Konopnicki, D. and Kuester, J . L . , J . Macromol. Sci., Chem., (1974) A8(5) 887. 16. Spitz, J . J . Laurence, R.L. and Chapelear, D.C. 'ACS Symposium Series No. 160, (1976), 72, 86. 17. Bourekas, N., Hodgson, W.G., Johnson, A.F. and Ramsay, J., IUPAC, Macro Madrid, (1974), 1, 27.

266

18. 19. 20. 21.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch011

22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

POLYMERIZATION REACTORS A N D PROCESSES

Gregges, A.R., Bowden, B.F., Barrall, Ε.M. and Horikawa, T.T., Separation Science, (1970), 5, (6), 731. Moore, L.D, and Overton, J.R., J. Chromatography, (1971), 55, 137. McGraw, J., Sater, V.E. and Kuester, J . L . , Decuscope (USA) (1973), 12, (2), 2. Hamielec, A.E., Walther, G. and Wright, J.D., 'Advances in Chemistry Series'. No. 125, Ed. Ezrin, M., 1973. Maclean, N., American Laboratory, (1974), 16 (10), 63. Ouano, A.C., Horne, D.L. and Gregges, A.R., J. Polym. Sci. Chem. Ed., (1974), 12, 307. Horlzgen, H.J., Chem. Anlagen Verfahren, (1974), (4), 111, Bly. D.D., Du Pont Innovation, (1974), 5 (2), 16. Lesec, J. and Quivoron, Analysis, (1976), 4 (10), 456. Ouano, A.C., J. Chromatography. (1976), 118, 303. Cazes, J., J. Chem. Educ., (1970), 461 and 505. Johnson, J.F. and Porter, R.S., 'Progress in Polymer Science', Ed. Jenkins, A.D., Pergamon, NY, 1970. Bly, D.D., 'Physical Methods in Macromolecular Chemistry', Volume 2, Ed. Carroll, B., Marcel Dekker Inc., NY, 1972. Evans, J.M., R.A.P.R.A. Bulletin, Nov. 1972. Meira, G.R., Johnson, A.F. and Ramsay, J. (in the press) Webb, J.T., C ' ORAL 66 Programming', NCC Publications, Oxford, 1978.

RECEIVED

March

12, 1979.

12 A Review of Mechanistic Considerations and Process Design Parameters for Precipitation Polymerization M . R. J U B A

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch012

Research Laboratories, Eastman Kodak Company, Rochester, N Y 14650

P r e c i p i t a t i o n p o l y m e r i z a t i o n s g e n e r a l l y c o n s i s t o f two phases: the d i l u e n t phase and the s o l i d polymer p a r t i c l e s . The d i l u e n t i s a s o l v e n t f o r the monomer and i n i t i a t o r and a nonsolvent f o r the polymer. The polymer p a r t i c l e s are not s t a b i l i z e d and tend t o agglomerate t o form a polymer paste o r s l u r r y . In a d d i t i o n , the p o l y m e r i z a t i o n r a t e i s independent o f the number o f p a r t i c l e s (_1) . Some t y p i c a l examples o f p r e c i p i t a t i o n p o l y m e r i z a t i o n s a r e :

Monomer Diluent methyl methacrylate cyclohexane (2) styrene methanol (3) acrylonitrile bulk (4) vinylidene chloride bulk (_5) vinyl chloride bulk (6) Since these p r e c i p i t a t i o n p o l y m e r i z a t i o n s produce polymeric s o l i d s a t very high p o l y m e r i z a t i o n r a t e s and very high p u r i t y ( i . e . , f r e e from e m u l s i f i e r s , suspending agents, e t c . ) , t h e i r p o p u l a r i t y as manufacturing processes i s i n c r e a s i n g . T h i s creates some i n t e r e s t i n g challenges f o r the process design engineer who i s searching f o r a r e l a t i o n s h i p among the r e a c t i o n parameters and the p h y s i c a l v a r i a b l e s o f the r e a c t i o n . These r e l a t i o n s h i p s are g e n e r a l l y determined e m p i r i c a l l y , because o f the complex k i n e t i c s o f the p r e c i p i t a t i o n polymerizat i o n process and the l a r g e v a r i a t i o n s from one r e a c t i o n system to another. Nevertheless, a review o f the l i t e r a t u r e presents u s e f u l g u i d e l i n e s f o r process design experiments.

0-8412-0506-x/79/47-104-267$05.00/0 © 1979 American Chemical Society

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch012

268

POLYMERIZATION REACTORS AND PROCESSES

P a r t i c l e Formation. E l e c t r o n microscopy and o p t i c a l microscopy are the d i a g n o s t i c t o o l s most o f t e n used to study p a r t i c l e formation and growth i n p r e c i p i t a t i o n p o l y m e r i z a t i o n s (7,8). However, i n t y p i c a l p o l y m e r i z a t i o n s of t h i s type, the p a r t i c l e formation i s normally completed i n a few seconds or tens o f seconds a f t e r the s t a r t o f the r e a c t i o n (9), and the p h y s i c a l processes which are i n v o l v e d are d i f f i c u l t to measure i n a r e a l time manner. As a r e s u l t , the a c t u a l p a r t i c l e formation mechanism i s open to a v a r i e t y of i n t e r p r e t a t i o n s and the r e s u l t s could f i t more than one t h e o r e t i c a l model. B a r r e t t and Thomas (10) have presented an e x c e l l e n t review o f the four p h y s i c a l processes i n v o l v e d i n the p a r t i c l e formation: oligomer growth i n the d i l u e n t oligomer p r e c i p i t a t i o n t o form p a r t i c l e n u c l e i capture o f oligomers by p a r t i c l e n u c l e i , and coalescence or agglomeration o f primary p a r t i c l e s . The f i r s t process begins as i n i t i a t o r decomposes i n the d i l u e n t phase and polymerizes the monomer to form oligomers which p r e c i p i t a t e from s o l u t i o n upon reaching a c r i t i c a l molecu l a r weight. This c r i t i c a l molecular weight i n c r e a s e s with the s o l u b i l i t y of the polymer and i s low enough so t h a t a l l the oligomers are captured or nucleate p a r t i c l e s before t h e i r r a d i c a l s are terminated. As a r e s u l t , n e a r l y a l l p o l y m e r i z a t i o n takes p l a c e i n the p a r t i c l e s and the polymer c o n c e n t r a t i o n i n the d i l u e n t phase i s low. The polymer s o l u b i l i t y can be estimated using s o l u b i l i t y parameters (11) and the value o f the c r i t i c a l oligomer molecular weight can be estimated from the Flory-Huggins theory of polymer s o l u t i o n s (12), but the optimum d i l u e n t i s s t i l l u s u a l l y chosen empirically. B a r r e t t and Thomas (10) l i s t e d the f o l l o w i n g e f f e c t s o f i n c r e a s i n g the d i l u e n t ' s solvency: r e t a r d s the onset of p a r t i c l e formation, i n c r e a s e s the d u r a t i o n o f p a r t i c l e formation, and produces fewer, l a r g e r p a r t i c l e s with a broader p a r t i c l e size distribution. Once the oligomers have formed, two mechanisms, s e l f n u c l e a t i o n and aggregate n u c l e a t i o n , are used to d e s c r i b e p a r t i c l e nucleation. In s e l f - n u c l e a t i o n , the extended oligomer chain c o l l a p s e s upon i t s e l f to nucleate a p a r t i c l e . In aggregate n u c l e a t i o n the oligomers r e v e r s i b l y a s s o c i a t e with each other u n t i l the aggregate reaches a c r i t i c a l s i z e above which i t i s thermodynamically s t a b l e and continues to grow. The aggregation of oligomers r e q u i r e s a lower average degree of p o l y m e r i z a t i o n f o r n u c l e i formation than the s e l f n u c l e a t i o n model where a l a r g e r i n d i v i d u a l chain i s r e q u i r e d .

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch012

12.

JUBA

Precipitation

Polymerization

269

Therefore, aggregation i s considered the primary mode o f p a r t i c l e n u c l e a t i o n i n most systems. A f t e r the p a r t i c l e n u c l e i form, they capture the oligomers growing i n the d i l u e n t phase and e s s e n t i a l l y no new p a r t i c l e n u c l e i are formed. Two models have been employed t o e x p l a i n t h i s capture. The f i r s t i s d i f f u s i o n capture. T h i s theory was o r i g i n a l l y proposed by F i t c h and T s a i (13) f o r the aqueous p o l y m e r i z a t i o n of methyl methacrylate. According t o t h i s theory, any oligomer which d i f f u s e s t o an e x i s t i n g p a r t i c l e before i t has a t t a i n e d the c r i t i c a l s i z e f o r n u c l e a t i o n i s i r r e v e r s i b l y captured. The rate o f n u c l e a t i o n i s equal t o the r a t e o f i n i t i a t i o n minus the rate o f capture. The r a t e o f capture i s p r o p o r t i o n a l t o both the s u r f a c e area and the number o f p a r t i c l e s . In the e q u i l i b i r u m capture model, on the other hand, there i s a dynamic e q u i l i b r i u m between the growing oligomers and the surface o f the p a r t i c l e s as w e l l as the p o s s i b i l i t y o f some interchange with the i n t e r i o r o f the p a r t i c l e s . Although both o f these models provide a reasonable d e s c r i p t i o n o f the p r e c i p i t a t i o n p o l y m e r i z a t i o n process, they do not i l l u s t r a t e the r e l a t i o n s h i p between the r e a c t o r v a r i a b l e s and the polymer p a r t i c l e p r o p e r t i e s . Perhaps the only process where such c o r r e l a t i o n s have been p u b l i s h e d i s the bulk p o l y m e r i z a t i o n o f v i n y l c h l o r i d e as reported by Ray, J a i n and Salovey (14). The p o l y m e r i z a t i o n occurs i n four stages. Bulk PVC Process Nucleation o f the primary p a r t i c l e p o p u l a t i o n F l o c c u l a t i o n o f p a r t i c l e s and capture o f oligomers t o a p o i n t o f constant p a r t i c l e p o p u l a t i o n Polymerization u n t i l the separate monomer phase i s consumed P o l y m e r i z a t i o n o f absorbed monomer i n the polymer p a r t i c l e s The commercial process as d e s c r i b e d by J . C h a t e l a i n (15) c o n s i s t s o f two stages as shown i n F i g u r e 1. In the prepolymerizer, the polymer p a r t i c l e s are formed and polymerized t o 7-8 wt. % conversion before being t r a n s f e r r e d t o the autoclave where the p a r t i c l e s are polymerized t o a s o l i d powder a t about 88% conversion. The f i n a l polymer p a r t i c l e s have a narrow p a r t i c l e s i z e d i s t r i b u t i o n , F i g u r e 2 (15), and the mean p a r t i c l e s i z e i s a strong f u n c t i o n o f the a g i t a t i o n i n the prepolymerizer, Figures 3 and 4 (16). In a d d i t i o n , s e v e r a l patents, d i s c u s s the e f f e c t s o f various a d d i t i v e s on the p a r t i c l e s i z e o f the f i n a l product. Ray, J a i n and Salovey (14) modeled these phenomena using the k i n e t i c constant o f coalescence as t h e i r major parameter. This constant was a f u n c t i o n o f p a r t i c l e s i z e , a g i t a t i o n r a t e , and the s u r f a c e p r o p e r t i e s o f the p a r t i c l e s , and i t s f u n c t i o n a l form suggested t h a t the p r o b a b i l i t y o f coalescence was p r o p o r t i o n a l t o the s u r f a c e area p e r u n i t volume o f the

POLYMERIZATION REACTORS AND PROCESSES

DEGASING V.C. FEEDING

P R E P O

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch012

DEGASING

V.C. FEEDING

PVC UNLOADING British Polymer Journal Figure

1.

Reactor system for bulk PVC (15)

100

100

120

140

160

Particle size (/im) British Polymer Journal Figure

2.

Particle

size distribution

for bulk PVC (15)

12.

JUBA

Precipitation

|

RM

n

(7)

p A

= Jadl

P A

RM L i + M

K

,Li

k

n+1

(8) p

Here the rate o f propagation can be expressed as Rate = p

k

(

k p n

p

K^n)[PLij;

= k K^ /n p

,

/ n

[M]

y = 1/n

(9) (10)

MOORE ET AL.

13.

Anionic

Butadiene

287

Polymerization

Mass Balance on I n i t i a t o r F_

.1 , J

I

Mass o f i n i t i a t o r entering i n the i n l e t stream f o r

U

reactor j .

J

Q 0

Mass o f i n i t i a t o r e n t e r i n g r e a c t o r j from other r e a c t o r s .

I.F

Mass o f i n i t i a t o r l e a v i n g r e a c t o r j .

V.I^M.k_(T.) = Rate J

J

J

J

I

V

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch013

7T J J dt

>

.V.— Mass o f i n i t i a t o r consumed by i n i t i a t i o n reaction i n reactor j .

T

, J

J

+

= F -In I,j0

. + I .F . - V.Rate , 00,j j R,j j I,j

T

D

(11)

T

Since Vj i s constant, =

(

F

^

J

I

^

I

^

-

I

J

F

^

/

Y

-rat

J

e i < J

(

1

2

)

Mass Balance on Monomer F

.M

M

M

mass o f monomer e n t e r i n g r e a c t o r j i n the i n l e t

.

stream.

mass o f monomer e n t e r i n g r e a c t o r j from other r e a c t o r s .

uu, j F_

.M.

mass o f monomer l e a v i n g r e a c t o r j .

3

V . I ^ .k-(T .) = V.Rate J

J

J

1

J

J

i

,

. mass o f monomer consumed i n i n i t i a t i o n reaction.

T

J

v • V.M.Ui.k (T.) = V.Rate

. — m a s s o f monomer consumed i n propagation reaction

p

J

J

U

J

J

OT JV M

P

F

,

J

M

- M,j 0

+

M

0 0 , J " R,J J - V ^ I J F

M

V

a t e

p,J (13)

o T ^

F

M

= < M,j 0

+

M

F

M

00,j- R , J j

) / V

j -

R

a

t

e

I,j *

R a t 6

p,J (14)

Mass Balance on Polymer P . — P o l y m e r o f chain length n from other r e a c t o r s (mass) 00, n, j , . , ' ' entering reactor j . nrk

F

.P

.—mass o f polymer l e a v i n g r e a c t o r j o f chain

length

POLYMERIZATION REACTORS AND PROCESSES

288 V.P J

.M.k (T.)-mass o f polymer o f chain length n destroyed n,j

F

j

j

i

R

n

E

A

C

T

O

J

R

B

V.M.P* .k (T.) —mass o f polymer o f chain length n created J J n-l,j P j j i

n

r

e

a

c

t

o

r

#

P

concentration o f polymer

(total).

P*

concentration o f polymer

(unassociated).

For n greater than 1:

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch013

^

( P

=

n,jV

P

00,n,j "

F

R,j 1,j P

+

" Y n , j W V o t ^ ^

•

( P

F

)

= P

00.n.i ~ R A , i

Y

)

/

^

V

j

W

P

j

(

V

" n,

W

1

5

)

V

For n=1 ^

(

Sjr

V l , J

( p

i.j

}

=

F

P

00,1,J- R,J 1,J

( p

oo,i,r

F

p

R,j i,j

-V.P* ,M.k (T.) J >>J J P J

+

) / v

V

j

+

a

t

e

R

I , J

a

t

e

i , j

(18)

Polymer Moments D e f i n i n g the moments by, U

.=* p

n

.

(19)

u\ . = * nP . 1iJ n n,j

(20)

= * n-p . n n,j

U, 1J

A

(21)

H

3 n

.

/ x 0 0

(^ 22

MOORE ET AL.

13.

Anionic

Butadiene

289

Polymerization

from ( 1 6 ) and ( 1 8 ) one can obtain

f

+

( n + l ) l

( P

(

F

00,n 1

P

" R,J n,j

+

) / V

j *

P

S,J J p J> M

( T

k

P* , ,.M.k P*.« M , k _((TT.j j n+1,j j p J

(23)

Rearranging

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch013

f l . j

. Rate^ - ( R ^ / V . ^ / p ^

• =

R

a

t

i , J -

e

S ( F

^

R,J

/ V

W

- ij jVV u

) U

J

M

+

V

i,J (

> f +

+

ifeo

U

(

oo,i,j

i

)

u

(^P

+

(

n

/ v

j

!-i,j

)

*

M

1

)

k

j P

l

(

(

T

0

>

S ,

p

j

0

)

n

j

J

j

W

T

j

)

°

( 2 1

(

2

5

)

Now assuming that the r a t e o f exchange between a s s o c i a t e d and unassociated polymer chains i s r a p i d , compared t o the r a t e o f propagation, then the d i s t r i b u t i o n o f the a c t i v e polymer, w i l l be e q u i v a l e n t to the t o t a l polymer d i s t r i b u t i o n . I.e. U» . U., . iJ 0,J 0,j 1

N o w

3

u

8,j

K y

=

( u

i,/ oj> u

" °1.J ° 0 J

T

h

U

S

f l , J

=

+

(

y PA°u,j

•

0

(26)

Rate

^

I ( j

( U

u

y K

o,j

2

7

)




j

/j

j V V

(

3

0

)

POLYMERIZATION REACTORS AND PROCESSES

290

= Rate_ . - (F ./V.) U. . + U . ./V. IiJ R,J J 1,J 00,l,j j n n

- /0

1,J

U*-\j

0,J

(J)(U,

M.k'(T.) + C \ J p J

l

. . uy*1)7 1-1,J 0,J

M,k'(T.) where (\) i'

(3D

1

"

' i!(l-i)!

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch013

Comparison o f Experimental

and Simulation

Results

The s i m u l a t i o n r e s u l t s depicted i n F i g s . 3 and 4 were obtained by i n t e g r a t i n g equations 12, 14 and 31 using the data i n Table 1 to time one m i l l i o n seconds.

Table 1:

Data f o r Simulation

Parameter

Value

I n i t i a t o r Feed Concentrations

0.0914 kgm "

Monomer Feed Flowrate

2.782 kgm "

M

3

0 7

F

3

0.667 x 10" m /s

I,J 6

F

3

0.583 x 10~ m /s

M,j

Reactant Volume

0.0027 m

Reactor Temperature Propagation Constant

I

3

0

Monomer Feed Concentrations I n i t i a t o r Feed Flowrate

Symbol

Rate

I n i t i a t i o n rate Constant

3 V

J T

384 K

i .296

m

3

1

(kg-mol)" s~

k

1

P t

-4 V2 1.95 x 10 n r ^ k

I

(kg-mol) ~* s""*

The e a r l y experimental p o i n t s i n the c o n c e n t r a t i o n chain length d i s t r i b u t i o n ( F i g . 3) may be i n a c c u r a t e . They are c a l c u l a t e d from the weight d i s t r i b u t i o n obtained from the GPC. The concentration chain length d i s t r i b u t i o n i s a f u n c t i o n o f the weight chain length d i s t r i b u t i o n and the inverse o f the chain length. Hence any e r r o r i n the p o i n t s i n the weight chain length d i s t r i b u t i o n i s exaggerated.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch013

13. MOORE ET AL. Anionic Butadiene Polymerization 291

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch013

292 POLYMERIZATION REACTORS AND PROCESSES

13.

MOORE ET AL.

Anionic

Butadiene

293

Polymerization

I t can be seen that the t h e o r e t i c a l and agree w e l l . The means a l s o concur.

experimental curves

Conclusions The described experimental r i g f o r the a n i o n i c p o l y m e r i s a t i o n of dienes has been shown to behave as an i d e a l CSTR. The mathematical model developed allows the p r e d i c t i o n o f the MWD at f u t u r e points i n the r e a c t o r h i s t o r y , once s u i t a b l e k i n e t i c parameters have been estimated.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch013

Abstract A p i l o t s c a l e plant, i n c o r p o r a t i n g a three l i t r e continuous s t i r r e d tank reactor, was used f o r an i n v e s t i g a t i o n i n t o the n-butyl l i t h i u m i n i t i a t e d , a n i o n i c p o l y m e r i z a t i o n o f butadiene i n n-hexane solvent. The r i g was capable o f being operated at elevated temperatures and pressures, comparable with i n d u s t r i a l operating conditions. Mathematical models of the reaction system have been developed, enabling prediction of the molecular weight d i s t r i b u t i o n , based on the experimental data obtained from the pilot plant using on-line computer techniques. Results of s i m u l a t i o n studies are compared with a c t u a l p l a n t runs, and show a good measure o f agreement. L i t e r a t u r e Cited 1.

Gilman, H., Haubein, M.

J . Am.

2.

Gear, G.W. "Numerical I n i t i a l P r e n t i c e - H a l l , New Jersey, 1971.

3.

Dew, P.M., West, M.R. U n i v e r s i t y , Report 107

Department of Computer Studies, (1978).

Leeds

4.

Dew, P.M., West, M.R. U n i v e r s i t y , Report 111

Department o f Computer Studies, (1978).

Leeds

5.

Elderton, W.P. "Frequency Curves Cambridge U n i v e r s i t y Press, 1938.

6.

Bamford, C,H., 1097.

Tompa, H.

RECEIVED February 19, 1979.

Chem. Soc. Value

(1944), 66,

Problems

Trans. Faraday

and

Soc.

1515.

i n ODEs".

Correlation".

(1954),

50,

14 Anionic Styrene Polymerization in a Continuous StirredTank Reactor MICHAEL N. TREYBIG1 and RAYFORD G. ANTHONY

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

Department of Chemical Engineering, Texas A&M College Station, TX 77843

University,

In the design, o p t i m i z a t i o n , or c o n t r o l of a p o l y m e r i z a t i o n r e a c t o r , a mathematical model which adequately represents the process i s d e s i r a b l e . In the f o r m u l a t i o n of such a model, i n f o r mation i s r e q u i r e d on both the k i n e t i c s of the s p e c i f i c r e a c t i o n and the mixing p a t t e r n of the r e a c t i o n v e s s e l used. For c o n t i n uous s t i r r e d tank r e a c t o r s , the assumption of p e r f e c t or micro­mixing i s f r e q u e n t l y made and the corresponding design equations used to estimate the r e a c t o r ' s performance. However, i n many l a r g e s c a l e i n d u s t r i a l p o l y m e r i z a t i o n processes the occurrence of imperfect mixing or segregation is more probable. In the case of a segregated p o l y m e r i z a t i o n r e a c t o r , design equations are r e q u i r e d which g i v e a d i f f e r e n t molecular weight d i s t r i b u t i o n from that obtained f o r the micro-mixed case. Since the p r o c e s s i b i l i t y and mechanical p r o p e r t i e s of a polymer f r a c t i o n are s t r o n g l y dependent on the shape of the molecular weight d i s t r i b u t i o n , i t is important to know the e f f e c t s of imperfect mixing on the shape of the molec u l a r weight d i s t r i b u t i o n and the degree of imperfect mixing occurring i n a reactor. Scope and O b j e c t i v e s The o b j e c t i v e s of t h i s work were: to study the e f f e c t of segregated mixing i n a s t i r r e d tank flow r e a c t o r on the molecular weight d i s t r i b u t i o n of p o l y s t y r e n e ; to determine the degree of segregation, i f any, o c c u r r i n g i n a bench s c a l e l a b o r a t o r y reactor; and to evaluate the usefulness of r e a c t o r flow models based on micro- and macro-mixing i n a constant-flow, s t i r r e d - t a n k r e a c t o r . Styrene was polymerized i n a bench s c a l e l a b o r a t o r y r e a c t o r w i t h p o l y s t y r y l l i t h i u m seed i n benzene s o l v e n t . A seeded polymerizat i o n system was chosen to s i m p l i f y the k i n e t i c d e s c r i p t i o n of the process compared with a system i n v o l v i n g simultaneous i n i t i a t i o n and propagation r e a c t i o n s . Mathematical models based on concepts of micro- and macro-mixing i n a s t i r r e d tank r e a c t o r were de1

Current address: S h e l l Development Company, Westhollow Research Center, Houston, Texas 0-8412-0506-x/79/47-104-295$08.00/0 © 1979 American Chemical Society

POLYMERIZATION REACTORS AND PROCESSES

296

veloped. These models u t i l i z e k i n e t i c d e s c r i p t i o n s of t h i s p o l y mer system from previous s t u d i e s of the system, as w e l l as data obtained i n t h i s i n v e s t i g a t i o n . R e s u l t s from the l a b o r a t o r y experimentation and mathematical s i m u l a t i o n were compared. The comparison was used to determine the s u i t a b i l i t y of the mathematic a l s i m u l a t i o n f o r modeling the p o l y m e r i z a t i o n process.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

Theory Reaction Mechanism. The r e a c t i o n mechanism of the a n i o n i c s o l u t i o n p o l y m e r i z a t i o n of styrene monomer using n - b u t y l l i t h i u m i n i t i a t o r has been the subject of considerable experimental and t h e o r e t i c a l i n v e s t i g a t i o n (1-8). The p o l y m e r i z a t i o n process occurs as the a l k y l l i t h i u m a t t a c k s monomeric styrene to i n i t i a t e a c t i v e s p e c i e s , which, i n turn, grow by a stepwise propagation r e a c t i o n . T h i s p o l y m e r i z a t i o n r e a c t i o n i s c h a r a c t e r i z e d by the production of s t r a i g h t c h a i n a c t i v e polymer molecules ( " l i v i n g " polymer) without termination, branching, or t r a n s f e r r e a c t i o n s . The stoichiometry of the p o l y m e r i z a t i o n process may be represented by the simple r e a c t i o n scheme: I + M ->P

(1)

1

P

x

P

+ M + P

2

+ M + P

j + 1

(2) j = 2, oo

(3)

However, the mechanisms by which the i n i t i a t i o n and propagat i o n r e a c t i o n s occur are f a r more complex. Dimeric a s s o c i a t i o n of p o l y s t y r y l l i t h i u m i s reported by Morton, et a l . (9) and i t i s g e n e r a l l y accepted that the r e a c t i o n s are f i r s t order with respect to monomer c o n c e n t r a t i o n . U n f o r t u n a t e l y , the existence of a s s o c i ated complexes of i n i t i a t o r and p o l y s t y r y l l i t h i u m as w e l l as p o s s i b l e cross a s s o c i a t i o n between the two species have negated the determination of the exact p o l y m e r i z a t i o n mechanisms (8, 10, 11, 12, 13). I t i s t h i s high degree of complexity which n e c e s s i t a t e s the use of e m p i r i c a l r a t e equations. One such e m p i r i c a l r a t e expression f o r the a u t o - c a t a l y t i c i n i t i a t i o n r e a c t i o n f o r the a n i o n i c p o l y m e r i z a t i o n of styrene i n benzene solvent as reported by Tanlak (14) i s given by: Rj « k

I M (1 + * P

x

3 T

)

(4)

Tanlak found the f o l l o w i n g r e l a t i o n s f o r the propagation r e a c t i o n s and monomer consumption: R . = a(P. - - P.)M J J-l J Rp = aP M p

(5)

p

T

(6)

14.

TREYBIG AND ANTHONY

Anionic

Styrene

Polymerization

297

where:

a h + Vh

+ 2Kj,-i

— P

(8) T

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

S i m i l a r r e s u l t s f o r the propagation r e a c t i o n s were obtained by Timm and Kubicek (15). In t h i s work, the c h a r a c t e r i s t i c " l i v i n g " polymer phenomenon was u t i l i z e d by preparing a seed polymer i n a batch r e a c t o r . The seed polymer and styrene were then fed to a constant flow s t i r r e d tank r e a c t o r . T h i s procedure allowed use of the lumped parameter r a t e expression given by Equations (5) through (8) to d e s c r i b e the p o l y m e r i z a t i o n r e a c t i o n , and eliminated complications i n v o l v e d i n d e s c r i b i n g simultaneous i n i t i a t i o n and propagation r e a c t i o n s . Mixing Models. The assumption of p e r f e c t or micro-mixing i s f r e q u e n t l y made f o r continuous s t i r r e d tank r e a c t o r s and the ensuing r e a c t o r model used f o r design and o p t i m i z a t i o n s t u d i e s . For w e l l - a g i t a t e d r e a c t o r s with moderate r e a c t i o n r a t e s and f o r r e a c t i o n media which are not too v i s c o u s , t h i s model i s o f t e n j u s t i f i e d . Micro-mixed r e a c t o r s are c h a r a c t e r i z e d by uniform concent r a t i o n s throughout the r e a c t o r and an exponential residence time d i s t r i b u t i o n function. The concept of a w e l l - s t i r r e d segregated r e a c t o r which a l s o has an exponential residence time d i s t r i b u t i o n f u n c t i o n was i n t r o duced by Dankwerts (16, 17) and was elaborated upon by Zweitering (18). In a t o t a l l y segregated, s t i r r e d tank r e a c t o r , the feed stream i s envisioned to enter the r e a c t o r i n the form of macromolecular capsules which do not exchange t h e i r contents with other capsules i n the feed stream or i n the r e a c t o r volume. The capsules act as batch r e a c t o r s with r e a c t i o n times equal to t h e i r residence time i n the r e a c t o r . The r e a c t o r product i s thus found by c a l c u l a t i n g the weighted sum of a s e r i e s of batch r e a c t o r products with r e a c t i o n times from zero to i n f i n i t y . The weighting f a c t o r i s determined by the residence time d i s t r i b u t i o n f u n c t i o n of the constant flow s t i r r e d tank r e a c t o r . Many mixing models which u t i l i z e the s i m p l i f i e d concepts of micro-mixing and segregation have been introduced. Most notable of these are the two-environment models of Chen and Fan (19), Kearns and Manning (20), and others (21, 22), and the d i s p e r s i o n models of Spielman and L e v e n s p i e l (23), and Kattan and A d l e r (24). Since p o l y m e r i z a t i o n r e a c t i o n s i n continuous s t i r r e d tank r e a c t o r s are o f t e n c a r r i e d out under c o n d i t i o n s of high v i s c o s i t y not conducive to micro-mixing, t h e o r e t i c a l and experimental i n v e s t i g a t i o n s have been made to determine the e f f e c t s of segregat i o n on the molecular weight d i s t r i b u t i o n f o r v a r i o u s polymer systems (25, _26, 27, 28). Ahmad (27) studied the e f f e c t of mixing on the molecular weight d i s t r i b u t i o n of p o l y i s o p r e n e and Tadmor and Biesenberger (28) studied the e f f e c t of segregation on

POLYMERIZATION REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

298

molecular weight d i s t r i b u t i o n s . For a stepwise a d d i t i o n nonterminating p o l y m e r i z a t i o n i n a segregated constant flow s t i r r e d tank r e a c t o r , these authors found that a polymer would be produced with a molecular weight d i s t r i b u t i o n that i s broader than that of a batch r e a c t o r but more narrow than that of a micro-mixed reactor. The design equations f o r the mixing c o n d i t i o n s considered i n t h i s paper a r e presented i n Table I . The micro-mixed model was modified to i n c l u d e the e f f e c t of i n a c t i v e or dead polymer and the e f f e c t of part of the r e a c t a n t s passing through the r e a c t i o n zone without r e a c t i n g . The equations f o r the w e l l - s t i r r e d segregated r e a c t o r and f o r the batch r e a c t o r a r e a l s o presented i n Table I . F i g u r e 1 i l l u s t r a t e s the growth c h a r a c t e r i s t i c s of polymer chains i n micro-mixed and segregated w e l l - s t i r r e d reactors. For the micro-mixed CFSTR the growth l i n e s from a seed polymer are l i n e a r , w h i l e from the segregated CFSTR they e x h i b i t curvature due to the change of monomer concentration as a segregated lump passes through the r e a c t o r . Experimental Reactor Design. The continuous polymerization r e a c t i o n s i n t h i s i n v e s t i g a t i o n were performed i n a 50 ml pyrex g l a s s r e a c t o r . The mixing mechanism u t i l i z e d two mixing i m p e l l e r s and a Chemco magnet-drive mechanism. The g l a s s r e a c t o r , shown i n F i g u r e 2, has s i n g l e i n l e t and o u t l e t ports and one thermocouple p o r t . The r e a c t o r s h e l l i s made from a s e c t i o n of pyrex tubing 4.4 cm OD and 4.0 cm ID. The i n l e t and o u t l e t ports a r e made from 1/4 i n OD x 1.0 mm ID c a p i l l a r y tube. The thermocouple port i s made from 1/4 i n OD x 5/32 i n ID g l a s s tubing. Glass to s t a i n l e s s connections a r e made using 1/4 i n s t a i n l e s s Swagelok f i t t i n g s w i t h T e f l o n f r o n t f e r r u l e s and a 1/4 i n x 0.065 i n v i t o n 0 - r i n g . The s t a i n l e s s f i t t i n g s used at the i n l e t and thermocouple p o r t s are 1/4 i n to 1/16 i n reducers. The i n l e t port f i t t i n g i s connected by a short s e c t i o n of 1/16 i n tubing to a 1/16 i n s t a i n l e s s t e e which i s used to pre-mix the monomer and living-polymer feed streams. The thermocouple port allows entrance of a type "T" thermocouple i n a 1/16 i n s t a i n l e s s sheath. To f i l l the v o i d between the thermocouple and the tubing w a l l of the thermocouple p o r t , a plug of T e f l o n 5/32 i n OD with a 1/16 i n ID a x i a l hole i s placed i n the thermocouple p o r t . The f i t t i n g used at the r e a c t o r o u t l e t port i s a 1/4 i n to 1/8 i n reducer and i s connected to the r e a c t o r e f f l u e n t l i n e of 1/8 i n t e f l o n tubing. Two i m p e l l e r s a r e included i n the r e a c t o r c o n f i g u r a t i o n shown i n F i g u r e 2. A three-bladed t u r b i n e with 45° p i t c h and blades 1/8 i n x 5/8 i n i s mounted on the i m p e l l e r s h a f t a t the top of the r e a c t o r . A three-bladed p r o p e l l e r w i t h 45° p i t c h i s mounted a t the bottom of the i m p e l l e r s h a f t a t approximately two-thirds of the r e a c t o r depth. 1

!

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

14.

TREYBIG AND ANTHONY

Anionic

Styrene

Polymerization

Figure 1. Growth characteristics for seed polymer in CFSTR environments: growth characteristics for polymer chains in a micro-mixed environment; growth characteristics for polymer chains in a segregated environment

299

(a) (b)

J

=

(

D = w

D° n°

D° D ° w n

+

r

min

+ aM©

aM

J

= 1 - exp

-T)

j ( t )

-01n(l

D = D° n n

T.

t

j ( T )

exp P. = P. J min rP P~ = p>o

^rnin 1 + aM0

M 1 + aOP,,

min

M =

Micro-mixed

D°

n

D °

aM©

T

]

(T)dT

1 + 2D n

P°

f Jm

CSTR

Aj

j

Y

=

D = D w w

D

n

fo°

^

n D >

T

1

+ aMO*

aM A

3

A

= P e x p [ - t . /0] + Aj min

A

min 1 + aMQA A

T

= P° + P . Dj Aj

. mm

J

A

M 1 + a0 P

A

1 + 2

P

j

t )

e

X

p

[

-

t

/

]

d

t

+ 2D

G

CFSTR

D - D n n

(

(Dead) P o l y m e r i n M i c r o - m i x e d u

P° = P° Aj ( t ) (j+aM* t)

P

P

j

M =

Inactive

The d e r i v a t i o n s o f t h e e q u a t i o n s a r e g i v e n b y T r e y b i g ( 3 2 )

TABLE I . REACTOR MIXING MODELS

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

U

1

n

+

P

R T

T

B

JLE.

R

jm-

n

A

w

Equations f o r D , D and D /D r. ¥ , are same as f o r equations f o r dead polymer with replaced by .

J ( t ) = j + aM t R J - j min

T

K

1 + aM 0

a 0

R

M°(l + aO P ) pressure regulator; (Q) check valve; (—•) thermocouple; (1) compressed helium; (2, 3) molecular sieve columns; (4, S) benzene (solvent) tank; (5,M) styrene (monomer) tank; (6,Sd) seed polymer tank; (7,8) rotameters; (9) teflon tubing; (10) premixing tee; (11, R) reactor; (12) temperature bath; (13) heating coil; (14) thermometer probe; (15, TI) temperature indicator (16, TC) temperature controller

14.

TREYBIG AND ANTHONY

TABLE I I I .

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

Run No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Styrene

311

Polymerization

OPERATING CONDITIONS FOR CFSTR RUNS 1-15

Feed Concent r a t i o n of Styrene, M° ( gm-mo l e / liter)

0.856 0.685 0.729 3.583 2.309 2.309 2.308 3.456 3.458 4.147 4.157 2.678 2.714 2.656 2.675

Anionic

Feed ConcenMean Mixing t r a t i o n of Residence Speed Seed Polymer, Time (min) (RPM) P ( gm-mo 1 e / liter)

Reaction Temperature (°C)

T

0.0081 0.0075 0.0075 0.0034 0.0052 0.0052 0.0052 0.0035 0.0035 0.0024 0.0024 0.0067 0.0066 0.0066 0.0066

25.4 31.6 31.6 22.4 19.5 19.9 19.6 15.3 15.4 15.3 14.6 21.9 22.2 21.7 21.3

1000 1000 500 1000 1000 500 750 1000 500 1000 500 1000 500 300 250

24.8±0.25 23±2 22±2 26.7±0.25 22±2 20±2 20±2 25.7±0.25 26.2±0.25 25.6±0.25 26.410.25 3611 3711 3811 3510.25

Figure 7. Theoretical polymer distributions, based on kinetic description of Tanlak (14) for micro-mixed and totally segregated CFSTRS with polymer feed (CFSTRS: CMO = 0.5M; PT = 0.01M; 6 = 20.0 min; XM = 0.70)

POLYMERIZATION REACTORS AND PROCESSES

312

l a t e r f i l t e r e d and then analyzed u s i n g the GPC. A f t e r the polymer samples were taken, the i m p e l l e r was stopped to allow e s t i m a t i o n of the volume of gas which c o l l e c t e d i n the r e a c t o r (due to degassing of helium from the feed stream) during the run. T h i s r e d u c t i o n i n the e f f e c t i v e r e a c t i o n volume of the r e a c t o r was noted and the gas was removed from the r e a c t o r through the e x i t port by t i l t i n g the r e a c t o r . Subsequent runs were then made by a d j u s t i n g the feed f l o w r a t e s and then the mixing speed w i t h the r e a c t o r i n i t i a l l y f i l l e d the r e a c t i o n medium from the previous run. Results

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

The experimental monomer conversion and degrees of polymeriz a t i o n f o r the continuous r e a c t o r runs are given i n Table IV. Experimental Values f o r the Lumped-Parameter Propagation Rate Constant. The experimental values f o r the lumped-parameter propagation r a t e constant were determined assuming a micro-mixed r e a c t o r , styrene c o n c e n t r a t i o n and s o l v i n g f o r a . The r e s u l t s f o r Runs 1-15 are included i n Table V. The value f o r the propagation constant based on a segregated model are the same as that f o r a micro-mixed model. For the case of a micro-mixed r e a c t o r with dead-polymer or a micro-mixed by-pass r e a c t o r , the true v a l u e of a would be l a r g e r than the value reported f o r the micro-mixed case by f a c t o r s of 1/D and 1/[1 - a0P /O ], r e s p e c t i v e l y . This would compensate f o r the decrease i n monomer conversion a s s o c i a t e d with dead-polymer and by-passing. T

B

R

C a l c u l a t e d Degrees of P o l y m e r i z a t i o n . The c a l c u l a t e d degrees of p o l y m e r i z a t i o n f o r the micro-mixed, segregated, and micro-mixed r e a c t o r w i t h dead-polymer models are given i n Table VI. Values f o r the lumped parameter propagation r a t e constant used i n the simulations were c a l c u l a t e d such that the monomer conversions f o r the models would be the same as that f o r the l a b o r a t o r y r e a c t o r . Therefore, the number average degrees of p o l y m e r i z a t i o n f o r each model i s equal to the experimentally observed number average. For the micro-mixed r e a c t o r w i t h dead-polymer model, average values of the f r a c t i o n dead-polymer, ^DAvg' * f o r each of the d i f f e r e n t seed mixtures. (Note that = 1 - fy^) The average values of -^ f o r each seed were determined by averaging the values of cf> r e q u i r e d to match the experimental number and weight average degrees of p o l y m e r i z a t i o n . The value of f o r each run was found by s o l v i n g the equation f o r D /D i n Table I f o r and s u b s t i t u t i n g the experimental values f o r the average degrees of p o l y m e r i z a t i o n . The values p c a l c u l a t e d f o r each run are given i n Table V I I . In the c a l c u l a t i o n of DAvg Seed I I the values of f o r Runs 3 and 4 were not used. The values f o r DACT g i n Table V I I I . w

e

r

e

u s e c

D

D

D

w

n

D

f

D

a

V

r

e

i

v

e

n

o

r

14.

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Styrene

Polymerization

313

TABLE IV. EXPERIMENTAL MONOMER CONVERSIONS AND DEGREES OF POLYMERIZATION FOR CFSTR RUNS 1-15

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

Run Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

rpm

X m

1000 1000 500 1000 1000 500 750 1000 500 1000 500 1000 500 300 250

0.524 0.586 0.411 0.585 0.446 0.446 0.428 0.377 0.423 0.311 0.333 0.726 0.704 0.698 0.630

n

D w

206 200 187 768 346 346 338 524 568 586 726 424 421 412 387

289 267 263 1411 579 547 558 995 1061 1598 1701 691 698 677 609

D

D /D w

n

1.41 1.34 1.41 1.84 1.67 1.58 1.65 1.90 1.87 2.33 2.34 1.63 1.66 1.64 1.57

TABLE V. EXPERIMENTAL VALUES FOR LUMPED PARAMETER PROPAGATION RATE CONSTANT BASED ON MICRO-MIXED CFSTR MODEL

Run Number

Rate Constant, a

1 2 3 4 5 6 7 8

5.31 5.98 2.95 18.65 7.97 7.82 7.40 11.46

Run Number

9 10 11 12 13 14 15

Rate Constant* a 13.74 12.33 14.28 18.08 16.18 15.91 12.09

a i s a f u n c t i o n of temperature and polymer c o n c e n t r a t i o n as given by Equation 3.

u

n

n

206 200 187 768 346 346 338 524 568 686 726 424 421 412 387

D

w

289 267 263 1411 579 547 558 995 1061 1598 1701 691 698 677 609

w

D

1.41 1.34 1.41 1.84 1.67 1.58 1.65 1.90 1.87 2.33 2.34 1.63 1.66 1.64 1.57

D /D n

Experimental

w 267 253 237 1281 484 484 470 811 895 1122 1199 636 630 614 567

D

CFSTR

f o r a l l runs,

1.30 1.27 1.27 1.67 1.40 1.40 1.39 1.55 1.58 1.64 1.65 1.50 1.50 1.49 1.47

D /D w n

Micro-mixed

w 256 242 233 910 412 412 404 661 708 919 967 467 468 458 438

D

1.24 1.21 1.24 1.18 1.19 1.19 1.20 1.26 1.25 1.34 1.33 1.10 1.11 1.11 1.13

D /D w n

Segregated CFSTR

289 264 244 1687 576 576 556 1030 1147 1464 1573 696 690 671 617

1.40 1.32 1.31 2.20 1.67 1.67 1.65 1.97 2.02 2.13 2.17 1.64 1.64 1.63 1.60

Micro-mixed CFSTR With Dead Polymer F r a c t i o n D D /D w w n

COMPARISON OF EXPERIMENTAL AND CALCULATED DEGREES OF POLYMERIZATION

(D ) - - ^ , = (D ) . , n calculated n experimental

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

, Number

R

TABLE V I .

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14.

TREYBIG AND ANTHONY

Anionic

Styrene

315

Polymerization

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

TABLE V I I . FRACTION DEAD POLYMER REQUIRED TO MATCH EXPERIMENTAL DEGREES OF POLYMERIZATION USING A MICRO-MIXED REACTION WITH DEAD POLYMER

Run Number

F r a c t i o n Dead Polymer, 4>

1

0.427 0.328 0.599 0.115 0.292 0.217 0.291 0.253

2 3 4 5 6 7 8

TABLE V I I I .

Seed Number

D

Run Number

9 10 11 12 13 14 15

F r a c t i o n Dead Polymer, D

0.211 0.360 0.352 0.121 0.146 0.144 0.112

AVERAGE FRACTION DEAD POLYMER FOR SEED MIXTURES

CFSTR Run Number

Average F r a c t i o n Dead Polymer, ^D^vg

I II III

1 2-11 12 - 15

0.427 0.288 0.131

316

POLYMERIZATION

REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

C a l c u l a t e d Molecular Weight D i s t r i b u t i o n s . The c a l c u l a t e d weight f r a c t i o n d i s t r i b u t i o n s f o r the micro-mixed, segregated, and micro-mixed r e a c t o r with dead-polymer models f o r Runs 2, 5, 8, 10 and 12 a r e shown along with the experimental d i s t r i b u t i o n s i n Figures 8 through 12. These f i g u r e s i l l u s t r a t e the e f f e c t s of micro-mixing and segregation on the weight f r a c t i o n d i s t r i b u t i o n as w e l l as the a b i l i t y of the models to simulate the experimental d i s t r i b u t i o n s a t d i f f e r e n t degrees of p o l y m e r i z t i o n . The c a l c u l a t e d mole f r a c t i o n d i s t r i b u t i o n s f o r Runs 8 and 12 a r e shown with the experimental d i s t r i b u t i o n s i n Figure 13 and 14. Streaking Observed i n Reaction Medium During Continuous Polymerizations. Non-uniformities i n the r e a c t o r contents i n the form of streaks were observed during continuous polymerizations at mixing speeds of l e s s than 1,000 rpm. At mixing speeds of 1,000 rpm, the r e a c t o r appeared to be d i v i d e d i n t o two homogeneous mixing zones: one occupying the upper h a l f of the r e a c t o r and the other occupying the lower h a l f . At lower mixing speeds f o r Runs 3 and 7, a feed stream or s t r e a k was observed to pass from the r e a c t o r feed port over the blades of the lower i m p e l l e r and down i n t o the center of the lower i m p e l l e r . Durings Runs 6, 8 and 13, a d d i t i o n a l streaks were observed i n the lower mixing zone. During Runs 9, 11, 14 and 15, c o n s i d e r a b l e s t r e a k i n g was observed i n both the upper and lower mixing zones. I t should a l s o be pointed out that during Run 11 (at low rpm and high degrees of polymerization) i n which an a p p r e c i a b l e amount of degassing occurred, small bubbles were o c c a s s i o n a l l y observed to t r a v e l from the top of the r e a c t o r i n t o the lower mixing r e g i o n . This i s an i n d i c a t i o n that a well-mixed c o n d i t i o n was achieved to a t l e a s t a macroscopic l e v e l . Discussion The 50 ml g l a s s r e a c t o r proved to be w e l l - s u i t e d f o r the procedures implemented i n t h i s i n v e s t i g a t i o n . The small s i z e of the r e a c t o r allowed e f f i c i e n t use of the m a t e r i a l s r e q u i r e d f o r both the residence time d i s t r i b u t i o n s t u d i e s and f o r the continuous p o l y m e r i z a t i o n experiments. V i s u a l i n s p e c t i o n of the r e a c t o r contents during o p e r a t i o n proved v a l u a b l e i n determining imperfections i n the mixing p a t t e r n during RTD s t u d i e s as w e l l as f o r observing s t r e a k i n g and bubble formation i n the r e a c t o r during p o l y m e r i z a t i o n s . The only disadvantage a s s o c i a t e d with the small g l a s s r e a c t o r i s the increased care i n handling r e q u i r e d over that o f a small s t a i n l e s s s t e e l r e a c t o r . E r r o r s i n the Temperature Measurement During Polymerizations Runs. The i n t e r n a l r e a c t o r temperatures measured during Runs 2, 3, 5, 6 and 7 were found to be i n c o n s i s t e n t when a heat balance was made on the r e a c t o r . E r r o r s i n these temperature measurements may be due to increased r e s i s t a n c e o f the r e a c t o r thermocouple

14.

TREYBIG AND ANTHONY

Anionic

Styrene

Polymerization

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

5.0

Chain Length, j

Figure

8. Comparison of experimental and calculated weight fraction distributions for Run 2((%) Exp; ( ) Micro-W; ( ) Micro; ( ) Seg)

Chain Length, j

Figure

9. Comparison of experimental and calculated weight fraction distributions for Run S((%) Exp; ( ) Micro-*D; ( ) Micro; ( ) Seg)

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318 POLYMERIZATION REACTORS AND PROCESSES

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14. TREYBIG AND ANTHONY Anionic Styrene Polymerization

319

POLYMERIZATION REACTORS AND PROCESSES

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320

Chain Length, j

Figure

14. Comparison of experimental and calculated mole fraction distributions for Run 12 ((%) Exp; ( ) Micro-W; ( ) Micro; ( ) Seg)

14.

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Anionic

Styrene

Polymerization

321

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

caused be bending the thermocouple sheath when handling the r e a c t o r between runs. Because of these e r r o r s the r e a c t i o n temperatures f o r these runs are not known b e t t e r than ±2°C. Reactor Runs 12, 13 and 14 were intended t o be c a r r i e d out a t 35°C, but i t was found that the temperature i n the bath f o r the r e f e r e n c e thermocouple had r i s e n from 0.6°C t o 4.5°C during the e i g h t hour reaction p e r i o d r e q u i r e d to complete the runs. The r e a c t i o n temperatures for Runs 12, 13 and 14 were c o r r e c t e d f o r t h i s o v e r s i g h t and a r e b e l i e v e d t o be accurate to ±1.0°C. The temperatures recorded f o r the remainder of the r e a c t i o n runs a r e accurate to ±0.25°C. E f f e c t of Mixing Speed on Monomer Conversion and Molecular Weight D i s t r i b u t i o n . The monomer conversion obtained i n the seeded p o l y m e r i z a t i o n of styrene i n a CFSTR w i l l be independent of the degree of segregation and thus the mixing speed as long as an exponential residence time d i s t r i b u t i o n i s maintained. Theref o r e , a dependence of monomer c o n v e r s i o n on mixing speed f o r runs with the same feed c o n c e n t r a t i o n s , average residence time, and r e a c t i o n temperature would i n d i c a t e n o n - i d e a l mixing a t the lower mixing speeds. The experimental monomer conversions obtained f o r runs a t s i m i l a r feed c o n d i t i o n s and average residence times but d i f f e r e n t mixing speeds are g i v e n i n Table IV. I n i t i a l comparison of CFSTR runs w i t h s i m i l a r feed c o n d i t i o n s i n d i c a t e s c o n d i t i o n s f o r which the monomer conversion may be dependent on mixing speed. However, when the e f f e c t s of e x p e r i mental e r r o r i n monomer c o n v e r s i o n and d i f f e r e n c e s i n r e a c t i o n temperature a r e considered, the monomer conversion i s seen t o be r e l a t i v e l y independent of mixing speed f o r rpm equal to or greater than 500. Comparing Run 14 w i t h Run 12 r e v e a l s a small decrease i n monomer c o n v e r s i o n i n s p i t e of a r i s e i n r e a c t o r temperature of 2°C. T h i s i n d i c a t e d the presence of a small amount of bypassing or dead volume a t the lower mixing speed. T h i s imperfect mixing p a t t e r n would a l s o be present i n Run 15. The experimental molecular weight d i s t r i b u t i o n s given i n F i g u r e s 8 through 14 i l l u s t r a t e l i t t l e o r no s i g n i f i c a n t e f f e c t s on the shape of the molecular weight d i s t r i b u t i o n s d i r e c t l y a t t r i butable t o the mixing speed. Thus no e f f e c t s of increased segreg a t i o n w i t h decrease i n mixing speed were observed on the molecular weight d i s t r i b u t i o n s . E v a l u a t i o n of Mixing Models. The micro-mixed r e a c t o r w i l l produce polymer d i s t t f i b u t i o n s w i t h i n c r e a s i n g amounts of h i g h molecular weight t a i l as the degree o f p o l y m e r i z a t i o n of the p o l y mer product i n c r e a s e s over that of the o r i g i n a l seed polymer. T h i s trend i s i l l u s t r a t e d by the curves f o r the micro-mixed reactor i n F i g u r e s 8 through 14. A l s o c h a r a c t e r i s t i c of the seeded, micromixed r e a c t o r i s the convergence o f the p o l y d i s p e r s i t y index to 2 for a h i g h degree of p o l y m e r i z a t i o n . T h i s trend i s i l l u s t r a t e d to some extent i n Table VI which presents the c a l c u l a t e d degrees of polymerizations.

POLYMERIZATION REACTORS AND PROCESSES

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322

The micro-mixed r e a c t o r model was not able to simulate adequately the e x p e r i m e n t a l l y observed weight average degrees of p o l y m e r i z a t i o n s or molecular weight d i s t r i b u t i o n . These f a c t s are i l l u s t r a t e d i n Table VI and F i g u r e s 8 through 14. In g e n e r a l , the weight average degrees of p o l y m e r i z a t i o n c a l c u l a t e d f o r the micromixed r e a c t o r were smaller than those observed experimentally. T h i s i s due to the more narrow polymer d i s t r i b u t i o n p r e d i c t e d by the micro-mixed model as shown i n F i g u r e s 8 through 14. The micro-mixed r e a c t o r w i t h dead-polymer model was developed to account f o r the l a r g e values of the p o l y d i s p e r s i t y index observed e x p e r i m e n t a l l y . The e f f e c t of i n c r e a s i n g the f r a c t i o n of dead-polymer i n the r e a c t o r feed while m a i n t a i n i n g the same monomer conversion i s to broaden the product polymer d i s t r i b u t i o n and t h e r e f o r e to i n c r e a s e the p o l y d i s p e r s i t y index. As i l l u s t r a t e d i n Table V, t h i s model, w i t h i t s a d j u s t a b l e parameter, £, can e x a c t l y match experiment average molecular weights and e a s i l y account f o r v a l u e s of the p o l y d i s p e r s i t y index s i g n i f i c a n t l y g r e a t e r than 2. The f a i r degree of c o n s i s t e n c y observed i n the values of j) f o r Seeds I I and I I I and the e x c e l l e n t agreement between the experimental molecular weight d i s t r i b u t i o n and those c a l c u l a t e d with (f> , lends c r e d i b i l i t y to the dead-polymer model. The agreement between experimental and c a l c u l a t e d d i s t r i b u t i o n at i n c r e a s i n g degrees of p o l y m e r i z a t i o n are given i n F i g u r e s 8 through 14. The bimodal weight f r a c t i o n d i s t r i b u t i o n s c a l c u l a t e d f o r Runs 8 and 10, which are shown i n F i g u r e s 10 and 11 are of p a r t i c u l a r interest. There i s good agreement between experiment and theory i n s p i t e of l i m i t a t i o n s i n the a b i l i t y of the GPC data r e d u c t i o n r o u t i n e to handle bimodal d i s t r i b u t i o n s . To d i f f e r e n t i a t e between the micro-mixed r e a c t o r w i t h deadpolymer and the by-pass r e a c t o r models i n t h i s i n v e s t i g a t i o n , the e f f e c t of mixing speed on the value of "(J) was observed. As i l l u s t r a t e d i n Table V, the value "" i s not observed to i n c r e a s e with decreasing mixing speed as would be expected f o r a by-pass r e a c t o r . T h i s r u l e s out the p o s s i b i l i t y of a by-pass model and f u r t h e r s u b s t a n t i a t e s the dead-polymer model. The w e l l - s t i r r e d segregated r e a c t o r w i l l produce polymer d i s t r i b u t i o n s w i t h low molecular weight t a i l s and sharp t r u n c a t i o n s a t the h i g h molecular weight ends at i n c r e a s e d degrees of p o l y m e r i z a t i o n of the polymer product. This i s i l l u s t r a t e d i n F i g u r e s 8 through 14. The v a l u e of the p o l y d i s p e r s i t y index f o r the segregated r e a c t o r product w i l l always be l e s s than that of the micro-mixed r e a c t o r (assuming no dead-polmer) as i l l u s t r a t e d i n Table VI. The segregated model was not a b l e to simulate the e x p e r i mentally observed degrees of p o l y m e r i z a t i o n on the molecular weight d i s t r i b u t i o n s . As shown i n F i g u r e s 8 through 14, the segregated d i s t r i b u t i o n s were i n general too narrow and e x h i b i t e d peaks i n the mole f r a c t i o n and weight f r a c t i o n curves which f a r exceeded those observed e x p e r i m e n t a l l y . D

g

11

14.

TREYBIG AND ANTHONY

Anionic

Styrene

Polymerization

323

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

S i g n f i c a n c e of Streaking i n Reaction Medium. Streaks i n the r e a c t i o n medium observed d u r i n g most continuous p o l y m e r i z a t i o n runs i n d i c a t e the presence of some degree of segregation or i n complete micro-mixing. But, as i n d i c a t e d i n F i g u r e s 8 through 14 for the comparison of experimental and c a l c u l a t e d d i s t r i b u t i o n s , no s i g n i f i c a n t i n f l u e n c e of segregation on the shape of the d i s t r i b u t i o n s was observed. In f a c t , the product d i s t r i b u t i o n i s simulated w e l l u s i n g a micro-mixed model with dead-polymer. T h i s anomaly may be explained i n p a r t by arguments due to P a t t e r s o n (33) based on s t u d i e s of a CFSTR using Monte C a r l o techniques. The e f f e c t s of micro-mixing on the molecular weight d i s t r i b u t i o n are much more pronounced than those of segregation. According to P a t t e r s o n (33) only a small i n c r e a s e i n micro-mixing over that of t o t a l segregation w i l l y i e l d a polymer d i s t r i b u t i o n very s i m i l a r to that of micro-mixed r e a c t o r . Conclusions The most s i g n i f i c a n t r e s u l t s and c o n c l u s i o n s are summarized below: 1. The monomer conversion i n t h i s seeded p o l y m e r i z a t i o n system i s independent of the degree of segregation as long as an exponential residence time d i s t r i b u t i o n funct i o n i s maintained. 2. The mixing speed had l i t t l e or no s i g n f i c a n t e f f e c t on the monomer conversions or the shape of the molecular weight d i s t r i b u t i o n s f o r mixing speeds of 500 rpm or greater. 3. A micro-mixed, seeded r e a c t o r w i l l produce a broad polymer d i s t r i b u t i o n w i t h a high molecular weight t a i l and p o l y d i s p e r s i t y index that approaches 2 at l a r g e degrees of p o l y m e r i z a t i o n . 4. The e f f e c t of dead-polymer and by-passing on the micromixed r e a c t o r f o r the same degree of monomer conversion i s to broaden the product polymer d i s t r i b u t i o n and thus allow v a l u e s of the p o l y d i s p e r s i t y index much l a r g e r than 2. 5. A w e l l - s t i r r e d segregated r e a c t o r would produce a product polymer with a low molecular weight t a i l and a sharp t r u n c a t i o n at the high molecular weight end f o r l a r g e degrees of product polymer p o l y m e r i z a t i o n . At equal monomer conversions the weight average degrees of p o l y m e r i z a t i o n w i l l be l e s s f o r a t o t a l l y segregated r e a c t o r than f o r a micro-mixed r e a c t o r . 6. The micro-mixed r e a c t o r with dead-polymer model simul a t e d the product of the l a b o r a t o r y r e a c t o r w e l l w i t h i n experimental accuracy. 7. In s p i t e of v i s u a l i n d i c a t i o n s of at l e a s t p a r t i a l segreg a t i o n , the concept of micro-mixing proved to be most u s e f u l i n modeling the l a b o r a t o r y r e a c t o r .

324

POLYMERIZATION

REACTORS AND PROCESSES

Symbols CFSTR D Dw E(t) GPC I J,J n

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

Imax Jmin

h M MF.

%

MWD

Pj"

P

Bj

?

RJ

R?D t

x

m a A 0 °R *0

A

Constant flow s t i r r e d tank r e a c t o r Number average degree of p o l y m e r i z a t i o n Weight average degree of p o l y m e r i z a t i o n E x i t age d i s t r i b u t i o n , dE/dt = 0 ~ e x p ( - t / 0 ) d t Gel Permeation Chromatograph I n i t i a t o r concentration Polymer c h a i n length Largest polymer chain length i n polymer d i s t r i b u t i o n Smallest polymer c h a i n l e n g t h i n seed d i s t r i b u t i o n and reactor effluent I n i t i a t i o n r a t e constant Propagation r a t e constant E q u i l i b r i u m constant f o r polymer a s s o c i a t i o n Monomer c o n c e n t r a t i o n Mole f r a c t i o n polymer of length j Number average molecular weight Weight average molecular weight Molecular weight d i s t r i b u t i o n Concentration of polymer of chain length j i n r e a c t o r feed Concentration of polymer of chain length j Concentration of polymer of chain l e n g t h J Concentration of a c t i v e polymer of chain l e n g t h j Concentration of polymer of chain length j i n the by-pass stream of a by-pass CFSTR Concentration of dead-polymer of c h a i n l e n g t h j Concentration of polymer of chain l e n g t h j i n the r e a c t o r zone of a by-pass CFSTR Concentration of t o t a l polymer Rate of i n i t i a t i o n Rate of monomer consumption Rate of propagation Residence time d i s t r i b u t i o n Time Time r e q u i r e d f o r smallest polymer molecule to grow to length j Weight f r a c t i o n of polymer of l e n g t h j Monomer conversion Lumped parameter propagation f u n c t i o n Denoting d i f f e r e n c e Average residence time Average residence time i n r e a c t i o n zone of a by-pass CFSTR Zeroth moment of polymer d i s t r i b u t i o n F i r s t moment of polymer d i s t r i b u t i o n Second moment of polymer d i s t r i b u t i o n Dimensionless time defined as [1 - e x p ( t / 0 ) ] A u t o c a t a l y t i c r a t e constant f o r i n i t i a t i o n F r a c t i o n a c t i v e polymer i n CFSTR with dead polymer F r a c t i o n by-pass i n by-pass CFSTR 1

14.

TREYBIG AND ANTHONY

< j ) R ° D

Anionic Styrene Polymerization

325

F r a c t i o n dead polymer i n CFSTR with dead-polymer F r a c t i o n passing through r e a c t i o n zone i n by-pass reactor Superscript denotes feed stream of seed polymer

Acknowledgments The authors appreciate the encouragement and support of t h i s work by the Department of Chemical Engineering, the Texas Engi­ neering Experiment Station, and Ε. I. duPont deNemours & Company. L i t e r a t u r e Cited 1.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch014

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Worsfold, D. J . and Bywater, S., Makromol. Chem., 65, 245 (1963). Bywater, S. and Worsofld, D. J . , Can. J . Chem., 40, 1564 (1962). F e t t e r s , L. J . , Ph. D. D i s s e r t a t i o n , U n i v e r s i t y of Akron, Ohio (1962). Hsieh, H. L., J . Polymer S c i . , A3, 153 (1965). Hooke, R. and Jeeves, Τ. Α., Assoc. Comp. Cach., 8, 2, 212 229 (1961). O ' D r i s c o l l , K. F. and Tobolsky, Α. V., J. Polymer S c i . , 35, 259 (1959). Johnson, A. F. and Worsfold, D. J . , J . Polymer S c i . , A3, 449 (1965). Bywater, S. and Worsfold, D. J . , Advan. i n Chem. Ser., 52, 36 (1969). Morton, M. and F e t t e r s , L. S., J. Polymer S c i . , A2, 3311 (1964). Worsfold, D. J . and Bywater, S., Can. J . Chem., 38, 1891 (1960). Margerison, D. and Newport, J . P., Trans. Faraday Soc., 59, 1891 (1963). Hsieh, H. L. and Glaze, W. H., Rubber Chem. Technol., 43, 22 (1970). Lenz, R. W., Organic Chemistry of Synethic High Polymers Interscience, New York (1967). Tanlak, T., M. S. Thesis, Texas A&M U n i v e r s i t y , College Station, Texas (1975). Timm, D. C. and Kubicek, L. F., Chem. Eng. S c i . , 29, 2145 (1974). Danckwerts, P. V., Chem. Eng. S c i . , 2, 1 (1953). Danckwerts, P. V., Chemical Reaction Engineering, 12th Meet­ ing, Eur. Fed. Chem. Eng., Amsterdam (1957). Zwietering, T. N., Chem. Eng. S c i . , 11, 1 (1959). Chen, M. S. K. and Fan, L. T., Can. J . Chem. Eng., 49, 704 (1971). Keairns, D. L. and Manning, F. S., AIChE J . , 15, 660 (1969). Ng, D. Y. C. and Rippin, D. W. T., Third Eur. Symp. Chem. Reaction Eng., Amsterdam, Pergamon Press, Oxford 161 (1965).

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326

22. 23. 24. 25. 26. 27. 28. 29.

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30. 31. 32.

33.

Goto, S. and Matsubara, Μ., Chem. Eng. S c i . , 30, 61 (1975). Spielman, L. A. and Levenspiel, O., Chem. Eng. S c i . , 20, 247 (1965). Kattan, A. and Adler, R. J . , Chem. Eng. S c i . , 27, 1013 (1972) Nagasubramanian, K. and Graessley, W. W., Chem. Eng. S c i . , 25, 1559 (1970). Rao, D. P. and Edwards, L. L., Chem. Eng. S c i . , 28, 1179 (1973). Ahmad, Α., Ph. D. D i s s e r t a t i o n , Texas A&M University, College Station, Texas (1975). Tadmor, Z. and Biesenberger, J . Α., I&EC Fundamentals, 5, 336 (1966). Uraneck, C. Α., Burleigh, J . E. and Cleary, J . W., Anal. Chem., 40, 327 (1968). Kolthoff, J . M. and Harris, W. E., Ind. Eng. Chem. Anal. Ed., 18, 161 (1946). Lewin, S. Ζ., Chem. Educ., 43, Reprint (1966). Treybig, Μ. Ν., " E f f e c t of Mixing on Polymerization of Styrene," Master of Science Thesis, Texas A&M University, College Station, Texas (1977). Patterson, G. Κ., Personal Communication (1977).

RECEIVED January 15, 1979.

15 Designing for Safe Reactor Vent Systems L O U I S J. J A C O B S , JR. and F R A N C I S X . K R U P A

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch015

Monsanto Co., Corporate Engineering Dept., St. Louis, M O 63166

This paper i s p r i m a r i l y concerned with safe venting of polymerization reactors, though the same p r i n c i p l e s apply to almost any vessel containing v o l a t i l e , p o t e n t i a l l y hazardous substances. In polymerization vessels one usually deals with exothermic reactions of v o l a t i l e monomers. The reactions may occur i n either emulsion, suspension, mass or solution-type polymerizat i o n on a batch or continuous b a s i s . Other papers at t h i s conference have discussed each of these extensively and each has advantages and disadvantages regarding control of emergencies. The suspension and emulsion systems generally have a built-in heat sink with the water present, but exhibit higher vapor pressure due to the nearly additive e f f e c t of the immiscible monomer and water phases. I.

Defining the Venting Problem

The need for venting, or the cause of an emergency which r e s u l t s i n a runaway r e a c t i o n , can occur i n seve r a l ways: Cooling system f a i l u r e could occur due to f a i l u r e of pumps or controls supplying cooling media to the reactor vessel jacket, c o i l s , or overhead r e f l u x condensers. Piping to or from the condensers could become plugged or any of the heat exchange surfaces could become excessively fouled. Agitator f a i l u r e either due to e l e c t r i c a l or mechani c a l f a i l u r e could r e s u l t i n loss of system c o n t r o l and "hot spots" i n the reactor. In suspension systems loss of a g i t a t i o n could negate much of the "heat sink" effect as the immiscible phases separate and s t r a t i f y . 0-8412-0506-x/79/47-104-327$05.00/0 © 1979 American Chemical Society

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Incorrect vessel charge either due to automatic cont r o l f a i l u r e or plant operator error could r e s u l t i n excess c a t a l y s t or reactant concentration, e t c . This could cause a r a p i d l y accelerating reaction rate or could i n i t i a t e unexpected side r e a c t i o n s , which could be more severe than the normal r e a c t i o n .

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch015

External f i r e could cause an emergency by overloading the normal reactor systems that are operating properly. Each of these cases involves an accumulation of heat i n the system which manifests higher temperature and pressure. The increased temperature accelerates the reactions further which subsequently adds even more heat to the system. II.

Strategies to Handle Emergencies

In the event that one or more of the cases c i t e d above w i l l occur at some point i n the l i f e of a process, we need to have a design strategy to cope with such emergencies. Selection of a strategy w i l l involve judgment of r i s k s and l i k e l i h o o d of occurrence, which w i l l not be discussed here. There are several design strategies that can be used to minimize the consequences of the emergency by a n t i c i p a t i n g system response. Elaborate, redundant reactor control systems could be i n s t a l l e d , such as multiple temperature sensing p o i n t s . On high temperature, these t r i g g e r actions such as feed shutdown, emergency c o o l i n g , or the a d d i t i o n of substances to deactivate the c a t a l y s t . Other control techniques could include a high pressure switch to a c t i v a t e automatically c o n t r o l l e d venting by allowing v o l a t i l e s to be vented from the r e a c t o r . The quantity of v o l a t i l e monomer present could be l i m i t e d by using smaller volume continuous r e a c t o r s , or using a semicontinuous monomer feed. Small q u a n t i t i e s of monomers present would quickly be consumed by an uncontrolled r e a c t i o n , and with the system deprived of further reactants pressure r i s e would be l i m i t e d . Another strategy would involve design of the reactor vessel for a pressure r a t i n g i n excess of any l i k e l y emergency system pressure. This assumes we can adequately predict a l l possible worst case s i t u a t i o n s , which i s doubtful. A more conventional approach i s to provide a safety r e l i e f valve or rupture disc to protect the vessel by venting material when pressure approaches c e r t a i n l i m i t s , such as the maximum allowable working pressure.

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This strategy may be used i n combination with the f i r s t two s t r a t e g i e s . An alternate approach to the above i s to provide p a r a l l e l r e l i e f valve-rupture disc systems. The valve w i l l have a setting s l i g h t l y above the normal operating pressure with the rupture disc at about a 10% higher setting. The r e l i e f valve should c o n t r o l minor pressure excursions, can vent material and then reseat to minimize process l o s s e s . The rupture disc would provide the ultimate safety p r o t e c t i o n . The remainder of t h i s paper w i l l discuss design of systems where venting of material i s necessary.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch015

III.

S i z i n g the Vent System

A. Available Design Methods for Vent S i z i n g . Several methods are a v a i l a b l e to size the vent with a wide range of s o p h i s t i c a t i o n . The FIA chart, F i g . 1 prepared by the Factory Insurance Association i n the mid 1 9 6 0 ' s i s a simple chart summarizing a wealth of experience. Reactions are classed by the degree of exothermic r e a c t i o n . With vessel size and a judgment of reaction type a vent s i z e range can be s e l e c t e d . This chart was prepared to be a guide to insurance inspectors and not a design technique. Experience i n d i c a t e s , however, i t i s often used by designers to estimate a reactor vent s i z e . In 1 9 6 7 a paper by Boyle ( 1 ) provided a more quantitative method for designing vents for polymer reactors. It was based on reaction r a t e , heat of r e a c t i o n , and vapor pressure data. Boyle assumed that the venting of a system can be approximated by s i z i n g to discharge the entire batch contents as a l i q u i d . The vent l i n e size i s determined so the time to vent the entire batch contents i s less than the time to go from r e l i e f set point to maximum allowable vessel pressure. A frequent s i z i n g technique, which i s u s e f u l when the reaction k i n e t i c s and heat of reaction are not known, i s to conduct small scale t e s t s . Then scale up to large equipment i s done by providing a vent with s i m i l a r vent area per mass of contents. In 1 9 7 2 a paper on venting by Huff (2J documented concerns that many designers suspected: that to t r u l y be safe the vent s i z i n g of many systems should be based on assuming two-phase flashing flow in the vent system. A two-phase flow vent method developed by Huff was compared with Boyle's a l l - l i q u i d method, and values from the FIA chart i n Figure 2 . It can be seen that under many conditions, previous methods were not

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch015

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Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch015

15.

RELIEF LINE ID

(=) INCHES Chemical Engineering Progress

Figure

2.

Peak reactor pressure vs. relief line size

(2)

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providing conservative design. Monsanto and other companies are working independently on design methods to s i z e vents more r i g o r o u s l y using two-phase flow c a l c u l a t i o n s i n complex computer programs. Several assumptions have been made in an e f f o r t to allow a wide range of a p p l i c a t i o n . Most notable i s the use of the correlations of M a r t i n e l l i and co-workers for pressure drop (_3) and h o l d - u p ^ ) . The momentum and energy balances are developed for the separated flow regime by Hewlett and H a l l - T a y l o r (J5) . A homogeneous flow basis must be used when thermodynamic equilibrium i s assumed. For further s i m p l i f i c a t i o n i t i s assumed there w i l l be no reaction occurring i n the p i p e l i n e . The vapor and l i q u i d contents of the reactor are assumed to be a homogeneous mass as they enter the vent l i n e . The model assumes adiabatic cond i t i o n s i n the vent l i n e and maintains constant stagnat i o n enthalpy for the energy balance. The M a r t i n e l l i c o r r e l a t i o n s for void f r a c t i o n and pressure drop are used because of t h e i r s i m p l i c i t y and wide range of a p p l i c a b i l i t y . France and Stein (6J d i s cuss the method by which the M a r t i n e l l i gradient for two-phase flow can be incorporated into a choked flow model. Because the M a r t i n e l l i equation balances f r i c t i o n a l shear stresses and pressure drop, i t is important to provide a good v i s c o s i t y model, e s p e c i a l l y for high v i s c o s i t y and non-Newtonian f l u i d s . As the g a s - l i q u i d mixture t r a v e l s down the vent l i n e , the phases w i l l s l i p past each other and the f l u i d s w i l l accelerate. This contribution to the energy balance can be most s i g n i f i c a n t for high p r e s sure blowdown. Pressure increments are c a l c u l a t e d and when the pressure gradient becomes i n f i n i t e the flow i s choked. If t h i s occurs at the end of the pipe the assumed flowrate i s the converged choked flow s o l u t i o n . If choked flow does not occur and the end of the l i n e i s reached at the reservoir pressure, the non-choked flow s o l u t i o n i s obtained. B. Defining the Reaction K i n e t i c s and Component Physical P r o p e r t i e s . The rate expression needed for use i n a vent design model should represent the condit i o n that would e x i s t during the emergency. Kinetic data based on the normal reaction rate are only useful i n cases when loss of heat transfer can be experienced. A simple power law rate expression (usually f i r s t order) w i l l be s u f f i c i e n t i f Arrhenius constants can be f i t t e d . For complex r e a c t i o n s , involving competing and undesirable side reactions, the most conservative approach would be to s i z e the vent system for the one or two

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch015

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reactions that add the greatest amount of energy to the system over a given duration. Use of thermal s t a b i l i t y t e s t s (DTA's) to determine the heat s e n s i t i v i t y of a given process mixture is desirable. Recent advances i n a n a l y t i c a l methods permit good calorimetric determination of heat of reaction. Heat of reaction data are c r i t i c a l for exothermic reactor vent s i z i n g . Heat impact from f i r e i s usually small i n comparison, but should not be neglected. Any convenient model for l i q u i d phase a c t i v i t y c o e f f i c i e n t s can be used. In the absence of any data, the i d e a l solution model can permit adequate design. For multiple l i q u i d phases (e.g. suspension processes) or increasing concentrations of polymers, some more r e a l i s t i c models are desirable (van Laar, Flory-Huggins, Wilson). In design of emergency r e l i e f systems the i n t r i n s i c f l u i d properties can often make a d i f f e r e n c e . Usually a l i n e a r i n t e r p o l a t i o n of density, v i s c o s i t y (for Newtonian f l u i d s ) and heat capacity w i l l provide suitable f l u i d p r o p e r t i e s , i f the simulated temperatures f a l l within that range of data. C. W i l l Two Phase Venting Occur? One of the key decisions i n venting c a l c u l a t i o n s i s to determine whether two-phase vent flow w i l l a c t u a l l y occur. Assume a reactor geometry as in Figure 3 with a vapor space and r e l i e f device located in the vapor space. One way for two-phase vent flow to occur i s through gross entrainment of l i q u i d with the discharging vapor. Another mechanism that can develop two-phase flow i n volves swelling or expansion of the contents due to bubble nucleation throughout the l i q u i d volume. This f i l l s the vapor space and the entire vessel with something approximating a homogeneous v a p o r - l i q u i d mixture which w i l l discharge as a f r o t h . Before the onset of two-phase venting, there w i l l be a b r i e f period of a l l - v a p o r venting as i l l u s t r a t e d in Figure 3. Correlations are needed to predict whether twophase flow w i l l occur a f t e r vapor venting i s i n i t i a t e d by rupture disc f a i l u r e or r e l i e f valve opening. Research i s needed i n t h i s area, but for the present we recommend the following c o r r e l a t i o n s to predict batch swell. For systems with low v i s c o s i t y (less than 500 cp) an equation based on bubble column hold-up i s used to obtain a swell r a t i o :

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334

F

=

y

^2.

+(^A,

+ £|V«) sinO

Figure 4. Forces on bends: (A) = Area f f ; (F) = Force lb ; (g) = Acceleration of gravity ft/sec ; (g ) = Conversion factor lb ft/lb sec ; (p) = Pressure lb//ft ; (Q) = Volume flow fi?/sec; (V) = Velocity ft/sec; (W) = Mass rate Ibjsec; ( ) = Density IbJfP. 2

2

c

f

m

P

f

2

2

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60 + 2V 60 + V

&

s V i s the s u p e r f i c i a l v e l o c i t y of the gas i n the r e actor body i n feet/minute. It conservatively assumes a l l of the vapor i s generated i n the bottom of the vessel. For f l u i d s with v i s c o s i t y greater than 500cp no good general r e l a t i o n s h i p i s a v a i l a b l e . Experimental work on one system allowed a swell r a t i o c o r r e l a t i o n of the following form: g

f

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch015

S

=

1

+

K R

v

2

/

y

3

1

/

2

where K i s a constant, R i s the volume rate of gas per l i q u i d volume, and y i s the v i s c o s i t y . When the swell r a t i o exceeds the r a t i o of vessel volume to l i q u i d volume, two-phase homogeneous venting i s assumed. v

IV.

Mechanical Design

S p e c i f i c a t i o n of r e l i e f valves and rupture d i s c s must be done with care because of the p o t e n t i a l l y t r a g i c consequences of haphazard s e l e c t i o n of s i z e and set or burst pressure. Disc burst conditions for example are very temperature s e n s i t i v e and should be selected for the temperature at which they w i l l r e l i e v e , not the normal operating temperature. Discs also have a normal manufacturing tolerance of ±5% of the set pressure. A 5% higher r e l i e v i n g pressure could be s i g n i f i c a n t i n s a f e l y c o n t r o l l i n g a r e a c t i o n . Rupture discs are also susceptible to fatigue f a i l u r e , e s p e c i a l l y i n pressure f l u c u a t i n g applications and require periodic replacement. R e l i e f valves have an open area much smaller than t h e i r stated size and t h i s must be considered on s e l e c t i o n , i . e . a 2" r e l i e f valve may have an open area of 0.7 i n ^ . Design of vessel and vent l i n e pipe supports i s very important because very large forces can be encountered as soon as venting begins. Figure 4 shows the equations and nomenclature to calculate forces on pipe bends. The authors have heard of s i t u a t i o n s where vent l i n e bends have been straightened, l i n e s broken o f f , or vent catch tanks knocked o f f t h e i r foundations by excessive forces. For bends, the transient e f f e c t s of the i n i t i a l shock wave, the t r a n s i t i o n from vapor flow to two-phase flow, and steady state conditions should be considered. Transient conditions, however, are l i k e l y to be so rapid as to not have enough dura-

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t i o n to cause problems.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch015

V.

Containment of Vented Material

Many of the materials handled are either explosive or toxic to people and the environment. Careful design i s required to handle materials being vented. Since much of the vented material w i l l be l i q u i d , separators such as knockout pots or tangential entry separators can provide disengagement and possible r e covery. Figure 5 i s a t y p i c a l v a p o r - l i q u i d separator design found to be e f f e c t i v e for these a p p l i c a t i o n s . Inlet design s u p e r f i c i a l vapor v e l o c i t y i s about 100 f t / s e c , with s u f f i c i e n t volume provided to accumulate the e n t i r e reactor l i q u i d contents. The l i p on the outlet vapor l i n e and the h o r i z o n t a l plate to separate the accumulated l i q u i d are important features to p r e vent re-entrainment. Flammable or toxic vapors can be piped to a f l a r e a f t e r separation of l i q u i d i s obtained. An important design problem i n f l a r e use i s the very high vent rate experienced for a r e l a t i v e l y short time, i f an e x i s t i n g f l a r e i s used. Also back-pressure e f f e c t s on the l i q u i d separator vessel must be considered, e s p e c i a l l y i f choked flow of vapor occurs downstream of the separator. Another containment strategy for condensible or water-soluble emissions i s to use a water quench system with the discharge being sparged into a large volume of cool l i q u i d . In very extreme cases, t o t a l containment can be provided to prevent any atmospheric emission or to provide a surge volume for c o n t r o l l e d f l a r i n g , absorpt i o n , or other disposal methods. This approach, however, requires use of a very large pressure v e s s e l to provide the required volume, and i s usually only a l a s t choice a l t e r n a t i v e . VI.

PIERS Program

While venting technology and methods are improving, considerable uncertainty remains as to the v a l i d i ty of various assumptions and accuracy of the c o r r e l a tions. Nearly a l l of the experimental data to v e r i f y c a l c u l a t i o n s to-date are with air-water-steam systems. Several chemical, r e f i n i n g , and engineering companies are currently i n the process of forming a r e search i n s t i t u t e to obtain r e a l i s t i c , v e r i f i e d design methods for reactor venting. The group i s c a l l e d DIERS (Design I n s t i t u t e for Emergency R e l i e f Systems) and i s sponsored by AIChE. Funds w i l l be provided by the mem-

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LIQUID Figure 5.

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ber companies on a s c h e d u l e based on company s i z e f o r a f o u r y e a r program. Emphasis o f t h e program w i l l be on 1) e s t a b l i s h i n g c o r r e l a t i o n s f o r t h e b a t c h s w e l l i n low and h i g h v i s ­ c o s i t y systems v e r i f i e d by e x p e r i m e n t s , 2) e s t a b l i s h i n g good two-phase flow c o r r e l a t i o n s v e r i f i e d by experiments f o r vent p i p i n g and r e l i e f v a l v e s , w i t h emphasis on v i s c o u s , two-phase flow, 3) d e v e l o p i n g an o v e r a l l two phase v e n t i n g d e s i g n method, and 4) e x p e r i m e n t a l v e r i ­ f i c a t i o n o f t h e d e s i g n method on both s m a l l and l a r g e s c a l e w i t h r e a c t i n g and n o n - r e a c t i n g c h e m i c a l systems. Membership i s s t i l l a v a i l a b l e f o r companies i n t e r ­ e s t e d i n p a r t i c i p a t i n g i n t h i s program. Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch015

VII.

Summary

The r e a c t o r v e n t i n g problem c o n s i s t s o f s e v e r a l key p a r t s each o f which must be u n d e r s t o o d and c a r e ­ f u l l y handled: 1) t h e heat i n p u t e i t h e r from exo­ t h e r m i c r e a c t i o n s o r o t h e r m i s c e l l a n e o u s heat s o u r c e s , 2) t h e b a t c h s w e l l mechanism, 3) t h e f l u i d mechanics o f t h e v e n t system, 4) t h e m e c h a n i c a l d e s i g n o f t h e system, and 5) v e n t e m i s s i o n s c o n t r o l . Literature

Cited

1.

Boyle, W. J . , Chem. Engr. Prog., 61-66.

2.

Huff, J . Ε., Chem. Engr. Prog. Symp. Ser. - Loss Prevention, (1972), 7, 45-57.

3.

Lockhart, R. W. and M a r t i n e l l i , Prog., (1949), 45,(1), 39-48.

4.

M a r t i n e l l i , R. C., and Nelson, D. B., Trans. ASME, (1948), 70, 695-702.

5.

Hewlett, G. F. and H a l l - T a y l o r , N. S., "Annular Two-Phase Flow", 23-27, Pergammon Press, Oxford GB, (1970).

6.

France, D. M. and S t e i n , R. P., I n t . J. Heat and Mass T r a n s f e r , (1971), 14, 1407-1413.

R E C E I V E D January 18, 1979.

(1967), 63,(8),

R. C., Chem. Engr.

16 High Temperature Free-Radical Polymerizations in Viscous Systems J. A. NORONHA, M. R. JUBA, H. M. LOW, and E. J. SCHIFFHAUER

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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

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

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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.

16.

NORONHA ET AL.

Viscous

Systems

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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

POLYMERIZATION REACTORS AND PROCESSES

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

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

NORONHA ET AL. Viscous

Figure

Systems

2.

Phase I test setup

POLYMERIZATION REACTORS AND PROCESSES

344

3 / 8 " COUPLING

IOOO kPa GAUGE

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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

POLYMERIZATION REACTORS AND PROCESSES

346

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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

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

j

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.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

POLYMERIZATION REACTORS AND PROCESSES

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

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

1

NORONHA ET AL.

Systems

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

Viscous

0

20

4 0

6 0

80

minutes

Figure 5. T and T k

av

for Test 1

100

120

100

200

300

400

500

600

-

700 r -

Figure

30

6.

60

Test 1 (observed

45

and computed

minutes

75

90

pressures)

J

105

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

1

120

I

135

I

150

Figure

7.

Test 2 (observed

and computed

minutes

pressures)

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

352 POLYMERIZATION REACTORS AND PROCESSES

Î V.

SX

I

ο

so

ε

s

CO

ο

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

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

POLYMERIZATION REACTORS AND PROCESSES

Figure 10.

T

av

and T for Test 1 (75-80 h

min)

16.

NORONHA ET AL.

Viscous

Systems

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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 .

POLYMERIZATION REACTORS AND PROCESSES

356

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

1.0 --,

(MIN) Figure

11.

Styrene thermal polymerization

at 140°C,

initial conversion

—0%

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

16. NORONHA ET AL. Viscous Systems 357

Ο

co

Ο

Sa

S

ο

s

ci ••s

1

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

358 POLYMERIZATION REACTORS AND PROCESSES

-8

-3

- i

If

U0|ti9AU09 0/

Q

Viscous

Systems

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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

POLYMERIZATION REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch016

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.

17 The Temperature Dependence of the Gel Effect in Free-Radical Vinyl Polymerization K. F. O'DRISCOLL, J. M. DIONISIO, and H. KH. MAHABADI

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch017

Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

In a s e r i e s o f papers (1, 2, 3), a model has been developed and a p p l i e d t o d e s c r i b e f r e e r a d i c a l v i n y l p o l y m e r i z a t i o n to moderately high conversion. S p e c i f i c a l l y , the model t r e a t s the case where p o l y m e r i z a t i o n r a t e increases w i t h conversion as the r e a c t i o n mixture becomes more v i s c o u s : the " g e l e f f e c t " . The model i s based on the assumption that as a p o l y m e r i z a t i o n proceeds the i n c r e a s i n g polymer c o n c e n t r a t i o n causes chain entanglement and thereby develops two populations o f polymeric r a d i c a l s : those that are smaller than some c r i t i c a l chain l e n g t h , n and t h e r e f o r e mobile, and those r a d i c a l s that are longer than n and t h e r e f o r e entangled and much l e s s mobile. Consequently the termination r e a c t i o n i s d e s c r i b e d by two r a t e constants, k f o r r e a c t i o n between two r a d i c a l s o f chain lengths l e s s than n and k f o r r a d i c a l s greater than n . For r e a c t i o n between a chain of length l e s s than n and one greater than n i t was assumed that the termination r a t e constant i s given by the geometric mean of kt and kte. c

c

t

c

te

c

c

gel

c

We now d e f i n e a q u a n t i t a t i v e measure o f the magnitude o f the e f f e c t : the g e l e f f e c t index, y : Y = (R /R ) - 1 p p,o

(1)

where R i s the experimentally observed r a t e o f p o l y m e r i z a t i o n a t any g i v l n time and conversion and R i s the r a t e p r e d i c t e d by c l a s s i c a l k i n e t i c s , which i s to be expected at the same conversion and time i n the h y p o t h e t i c a l absence o f a g e l e f f e c t : i . e . with k unchanged. When chain t r a n s f e r i s considered and f o l l o w i n g the d e r i v a t i o n p r e v i o u s l y given (1, 2) the instantaneous r a t e o f conversion i s then given by t

g

0

= A [I] *

5

(1 - x ) ( l + ) Y

0-8412-0506-x/79/47-104-361$05.00/0 © 1979 American Chemical Society

(2)

POLYMERIZATION

362

REACTORS AND PROCESSES

where x i s the f r a c t i o n a l conversion o f monomer to polymer and y can be w r i t t e n i n e x p l i c i t terms of the model a s : T(1 - a)exp(-x Y

=

x

- [C 6

• n^)

+ (C [Si + C _ [ I ] ) / [ M ] J ( 1 - a)exp(-T • n ) s

ui

(

l

a

)

c

JL

The parameters x and T a r e r e c i p r o c a l chain lengths and a r e given by expressions (3) and ( 4 ) : T - C

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch017

T

E

+ { C [ S ] + C [I] + 2(Bf k [ I ] )

m

= C

g

m

T

1 / 2

d

+ { C [ S ] + C ^ I ] + 2o(Bf k [ I ] ) g

d

>

1 / 2

(3)

}

(4)

(see Nomenclature f o r a complete d e s c r i p t i o n o f symbols). I t can be seen from equation (2) that when y = 0 the model f a l l s i n t o the c l a s s i c a l expression f o r the r a t e of conversion o f free r a d i c a l polymerization. Equation ( l a ) shows that t h i s w i l l be the case whenever a l l macroradicals have the same h i g h m o b i l i t y ( i . e . , as n tends to i n f i n i t y ) o r when both entangled and nonentangled r a d i c a l s have the same t e r m i n a t i o n r a t e constant ( i . e . a i s equal t o u n i t y ) . T h i s model (1) has two a d j u s t a b l e , non-negative parameters, K and a . Having a c o r r e c t d e f i n i t i o n o f the onset o f g e l ertect, the value o f K could, i n p r i n c i p l e , be given by the equation: Q

K

c

= < ( > X p c

(5)

Y

which i s v a l i d at that c r i t i c a l p o i n t , and the model could then d e s c r i b e an a u t o a c c e l e r a t e d p o l y m e r i z a t i o n r e a c t i o n using only a s i n g l e parameter, a which i s a measure of the r e d u c t i o n i n k caused by entanglement. In equation (5) < ( > i s the volume f r a c t i o n o f polymer and X i s the cumulative number^average degree of p o l y m e r i z a t i o n or* the polymer e x i s t i n g at the onset o f g e l e f f e c t . I t was found [1] that the values o f K and a , obtained i n c o minimizing the e r r o r o f f i t t i n g experimental conversion-time data, s a t i s f a c t o r i l y d e s c r i b e d the temporal e v o l u t i o n s o f the molecular weight averages. A l s o , the model performed b e t t e r i n the d e s c r i p t i o n o f the experimental data when a v a l u e of $ = 1/2 was used. We should p o i n t out that one o f the p o s t u l a t e s on which the k i n e t i c equations were d e r i v e d i s that the r a t e constant o f the t e r m i n a t i o n r e a c t i o n between entangled r a d i c a l s , k , is e p r o p o r t i o n a l t o the i n v e r s e f i r s t power o f the entanglement density. While t h i s p o s t u l a t e i s c e r t a i n l y q u a l i t a t i v e l y c o r r e c t , there i s no a p r i o r i reason to have i t take p r e c i s e l y t h i s q u a n t i t a t i v e form. Q

t

fc

17.

ODRISCOLL ET AL.

Free-Radical

Vinyl

Polymerization

363

In the work that f o l l o w s , the experimental data were f i t t e d by minimizing the sum o f l e a s t squares and the d i f f e r e n t i a l equations were i n t e g r a t e d n u m e r i c a l l y . For each data s e t examined, the onset o f the g e l e f f e c t (which i s the i n i t i a l value f o r the i n t e g r a t i o n o f the d i f f e r e n t i a l equations) was taken a t the p o i n t where there i s a departure from l i n e a r i t y i n the conversion-time p l o t . While a good argument can be made (4) f o r using another d e f i n i t i o n o f the onset o f the g e l e f f e c t , the data a v a i l a b l e d i d not a l l o w f o r a more d e t a i l e d approach.

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch017

Temperature Dependence o f the Model Parameters Experimental conversion-time data, obtained from the l i t e r a t u r e , on the b u l k 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 of MMA i n i t i a t e d by AIBN at s e v e r a l temperatures and i n i t i a t o r c o n c e n t r a t i o n s , were d e s c r i b e d by the model. However, the expressions f o r the r a t e o f conversion and g e l e f f e c t index were f i r s t s i m p l i f i e d and r e a r ranged. Assuming that no chain t r a n s f e r r e a c t i o n was s u f f i c i e n t l y important t o be considered, u s e f u l s i m p l i f i c a t i o n s r e s u l t f o r equations ( l a ) , ( 3 ) and ( 4 ) , so that the g e l e f f e c t index, y i s given by the e x p r e s s i o n : 9

(6)

where v_ i s the instantaneous c h a i n l e n g t h o f the polymer from non-entangled r a d i c a l s and i s g i v e n by: k

produced

[M]

v

(7) 2/k

f k [I]

t

d

A l s o , the zeroth moment o f the d i f f e r e n t i a l molecular weight d i s t r i b u t i o n , DMWD, may be obtained by i n t e g r a t i o n o f the s i m p l i f i e d equation: dX

dF = so that X

2 f

k

d

[

I

]

may be expressed as X = 2 • f • [I] • [1 - exp(-k, ' t ) o o d

i f the e f f e c t o f shrinkage on the i n i t i a t o r c o n c e n t r a t i o n i s n e g l e c t e d . Introducing equation (8) and the e x p r e s s i o n f o r the f i r s t moment o f the DMWD, X-, i n t o the equation

(8)

POLYMERIZATION REACTORS AND PROCESSES

364

-

i

x

n

X

Q

the cumulative number average degree of p o l y m e r i z a t i o n , X , may be expressed as: y

o • £n(l + ex) . v 2 f e [I] 1 - exp (-k, -t) ^ o a. where e i s the v o l u m e t r i c c o n t r a c t i o n c o e f f i c i e n t . The parameter a i n equation (6) has been expressed as ( 1 ) : =

Q

}

n

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch017

* - %

r W

(

(p

1

/

2

(

i

o

)

A n

p I f equations (7) and (9) are then introduced i n t o equation ( 6 ) , as w e l l as the c o r r e c t expressions f o r n and the v a r i a t i o n of with c o n v e r s i o n , the expression f o r tfie g e l e f f e c t index may Be w r i t t e n as: Y = (C

1

g

rr 1 "

JL_\ r T 7 ^

x

- l)exp(-C g ) 2

(11)

2

where:

8

8

2

=

{

(

•r -ftn(l + EX) f [ I ] ( l - exp(-k

)

1

C ^^)

2

,0.5,°'/^^

[

o

' (YZ-p)(fk [I])°

d

-t

1

}

-5

(

1

2

)

(13)

d

and

c

i

-

i - r ^ a K o c 2 B

1 / 2

(ST) ' ] 0

K

5

0

(">

5

n

o Equation (2) can then be put i n t o the form:

5

= A[I]°' (1 - x ) [ l + ( C

l 8 l

- Dexp(-C g )I 2

2

(16)

By minimizing the e r r o r of f i t t i n g experimental x v s . t data with equation (16) a f t e r the onset of g e l e f f e c t , the parameters CJL and 0,^ ^ obtained. Figures 1-4 compare the p r e d i c t i o n s by the model with experimental conversion-time data. c

a

n

e

17.

O'DRISCOLL ET AL.

Free-Radical

Vinyl

Polymerization

365

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch017

loor

TIME, min —»• Figure 1. Bulk polymerization of MMA at 45° C initiated by thermal decomposition of AIBN (5): ( ; calculated from Equation 16. [I] = 0.1 (O); 0.05 0.025(A). 0

Figure

2.

Same as Figure

1 at 50°C:

[I] = 0.05 (+) ; (A)< > 0

7

(6)

0.0277 (0) ; (7)

0.0166

POLYMERIZATION REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch017

366

Figure

4.

Same as Figure

1 at 70°C: [I] .3(0);.SO

0

= .3 ( A ) ; 5 (A) and at 90°C: a)

[I]

0

=

17.

ODRISCOLL ET AL.

Free-Radical

Vinyl

367

Polymerization

I t i s important to note that and are q u a n t i t a t i v e d e s c r i p t o r s of the g e l e f f e c t which depend only on the monomer, temperature and r e a c t i o n medium. The f u l l d e s c r i p t i o n of y> given by equation (11), r e q u i r e s g^ and %^ which are f u n c t i o n s o f the r a t e of i n i t i a t i o n and extent o f conversion. The k i n e t i c parameters used i n these c a l c u l a t i o n s and t h e i r sources are g i v e n i n Table 1. A l l data are i n u n i t s of l i t r e s , moles and second. Figure 5 shows the temperature dependencies of and C£ and Table 2 l i s t s these and other parameters determined by f i t t i n g the model to the data i n F i g u r e s 1-4. TABLE 1

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch017

K i n e t i c Parameters Used i n Model to Describe MMA P o l y m e r i z a t i o n I n i t i a t e d by AIBN 4

-e

T°K

[M]

318

9.16

0.87

54.9

0.0916

.453

.242

323

9.11

1.38

47.6

0.195

.465

.245

333

9.00

3.37

36.1

0.823

.498

.254

343

8.89

7.8

27.8

3.198

.529

.265

363

8.59

36.5

17.32

38.56

.598

.295

(9)

Fig. 6

(7)

(13)

AB

Source of data

B

AxlO

0

k xl0

f

5

d

2

k

(7)

d

TABLE I I K i n e t i c Parameters Determined by F i t t i n g Model to Data of F i g u r e s 1 - 4

T°K

K

a

(mol/£)

1 / 4

(sec) "

1 / 2

C xlO m

318

c 16.82

.0395

13.33

797

.112

323

15.50

.0525

10.38

638

.122

333

12.45

.0615

9.71

372

.230

343

10.30

.0775

8.30

233

.243

363

6.77

.0995

7.53

89

o

_

4

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch017

POLYMERIZATION REACTORS AND PROCESSES

ure 5. Variation of the model parameters C , (O) and C (X) with temperature for the bulk free radical polymerization of MMA initiated by AIBN 2

ODRISCOLL ET AL.

Free-Radical

Vinyl

Polymerization

369

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch017

5x10^

Figure

6.

Arrhenius

plot of A for polymerization of MMA initiated using data of Figures 1—4

by

AIBN

POLYMERIZATION REACTORS AND PROCESSES

370

The values of A were estimated from the time-conversion data b e f o r e the onset of the g e l e f f e c t . In t h i s r e g i o n y = 0 so that i n t e g r a t i o n of equation (2) y i e l d s ln

x)

A = - (21) (22)

Constants of integration are t* and n * . For p r a c t i c a l a p p l i c a t i o n s , i n i t i a l conditions specify that n * > 0, t* = 0 and boundary conditions require n* = 1, t* > 0. If t* = 0, n * = 1, a ground curve passing through the o r i g i n can be generated. This function n ( 0 , l , t ) was evaluated through Runge-Kutta-Gill i n t e g r a t i o n . Values of population density along t h i s ground curve are evaluated using Equation (22) and the boundary condition T(1,0). To evaluate a s p e c i f i c molar concentration T ( n i , t i ) the point [ n i , t ] J i s i n i t i a l l y located. If i t l i e s above the p r i n c i p a l ground curve, i . e . , n^ > n ( 0 , l , t i ) , i t i s necessary that the ground curve passing

18.

TIMM ET AL.

Molecular

Mobility

381

through the point [ n i , t ] J originates from the i n i t i a l condition plane and t* = 0, n* > 1. Equation (21) may be arranged such that n* = n^ - n ( 0 , l , t i ) . Equation (22) coupled with the n u l l i n i t i a l condition T(n*,0) = 0 y i e l d s a zero population densitv T ( m . t i ) = 0. Sufficient time has not elapsed f o r the formation of t h i s size macromolecule. If the point [n^t^] l i e s below the p r i n c i p a l ground curve n ( 0 l t ) the ground curve passing through [ n i , ^ ] must originate from the boundary cond i t i o n plane, t* > 0, n* = 1. To i m p l i c i t l y evaluate the constant t*, t h i s ground curve i s generated by the t r a n s l a t i o n /

/

1

/

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch018

n t C l , ^ ) - ! ^ = n(0,l,t*)-l The i m p l i c i t constant t* i s evaluated from the p r i n c i p a l ground curve. An i n t e r p o l a t i o n of the function n ( 0 , l , t ) y i e l d s the constant of i n t e g r a t i o n t* when n ( 0 , l , t ) = n ( 0 , l , t * ) . The boundary condition T ( l , t * ) coupled with Relationship (22) y i e l d s the population density of polymeric species of size n^ at time t i « I f the p r i n c i p a l ground curve passes through the point [ n i , t i ] , then t* = 0, n* = 1. A p r i n c i p a l advantage f o r the above formulation i s the reduction of integrations r e q u i r e d . Along a ground curve, population densities are uncoupled from nearest neighbors. Thus a combination of two i n t e grations (Equations 2 3 and 24) plus variable c o e f f i cients and l i n e a r t r a n s l a t i o n s allows for the e x p l i c i t evaluation of the molar concentration of any polymeric specie. The c l a s s i c s o l u t i o n requires an ordinary d i f f e r e n t i a l equation at each degree of polymerization plus v a r i a b l e c o e f f i c i e n t s . Nearest neighbors are coupled. Arguments of i n t e g r a t i o n are simpler functions when the method of c h a r a c t e r i s t i c s i s a p p l i e d . Experimental Equipment, The reactor was 1.523 l i t e r , 316 s t a i n l e s s s t e e l c y l i n d r i c a l , jacketed vessel equipped with two multiblade, paddle-type a g i t a t o r s . Tracer studies showed the reactor was well-mixed. A thermocouple measured temperature and was recorded continuously. Feed tanks, tubing, pumps and valves were made of s t a i n l e s s s t e e l and had t e f l o n s e a l s . Procedure. Concentration of n-BuLi i n the feed was measured by t i t r a t i o n (15) . The reactor was f i l l ed completely with styrene monomer s o l u t i o n i n toluene initially. Time was measured from the moment i n i t i a t o r and monomer feed was i n i t i a t e d . The reaction was

382

POLYMERIZATION REACTORS AND PROCESSES

allowed to continue for six to seven residence times. Reactor samples were quenched and analyzed for styrene concentration; polymeric weight was obtained g r a v i m e t r i c a l l y from dried samples. Gel Permeation Chromatography. The instrument used for GPC analysis was a Waters Associates Model ALC-201 g e l permeation chromatograph equipped with a R401 d i f f e r e n t i a l refractometer. For population density determination, polystyrene powder was dissolved i n tetrahydrofuran (THF), 75 mg of polystyrene to 50 ml THF. Three y - s t y r a g e l columns of 10 ,10 ,10 * A were used. E f f l u e n t flow rate was set at 2.2 ml/min. Total cumulative molar concentration and population density d i s t r i b u t i o n of polymeric species were obtained from the observed chromatogram using the computer program developed by Timm and Rachow (16). Q

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch018

2

3

t

Steady State Population Density D i s t r i b u t i o n s . Representative experimental population density d i s t r i butions are presented by Figure 1 for two d i f f e r e n t l e v e l s of media v i s c o s i t y . An excellent degree of t h e o r e t i c a l (Equation 8) / experimental c o r r e l a t i o n i s observed. Inasmuch as the slope of population density d i s t r i b u t i o n at a s p e c i f i c degree of polymerization i s proportional to the rate of propagation for that size macroanion, propagation rates are also observed to be independent of molecular weight. Uncoupled Rate Constants. An i n i t i a l evaluation of polymerization k i n e t i c s i s presented i n Figure (2), constrained by v i s c o s i t y i n v a r i a n t rate constants K . The slopes of these s t r a i g h t l i n e s give i n i t i a l estimates of K g / K according to Equation (14). Figure 3 presents g r a p h i c a l l y a power law r e l a t i o n s h i p between K / K and v i s c o s i t y at 21°C and at 1 6 . 6 ° C . More scatter i n Yu's data may be a t t r i b u t e d to the use of an older GPC instrument of r e l a t i v e l y low resolution. The r a t i o K / K p i s temperature-sensitive; a change of the order of f i v e times i s observed i f the temperature i s reduced by 4 . 4 ° C and v i s c o s i t y i s kept constant. Using t h i s preliminary observation a comprehensive analysis of data w i l l allow for the e l u c i d a t i o n of the v i s c o s i t y dependency. I f Kp and K are assumed to be power functions of v i s c o s i t y with an Arrhenius temperature c o e f f i c i e n t P

e

e q

p

p

2

2

e g

2

e g

K hr

K

= a exp (-E / R T ) y

b

Jr

= c exp (E

/RT) y

d

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch018

18. TIMM ET AL. Molecular Mobility

383

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch018

384 POLYMERIZATION REACTORS AND PROCESSES

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch018

18.

TIMM ET AL.

Molecular

Mobility

385

Viscosity >(cp) Figure

3.

Propagation

and polystyryl (

anion association )16.6°C.

kinetics:

(

) 21° C;

POLYMERIZATION REACTORS AND PROCESSES

386

The a c t i v a t i o n energy o f the p r o p a g a t i o n r e a c t i o n (Ep) and t h a t o f a s s o c i a t i o n e q u i l i b r i u m r e a c t i o n (Eeq) are r e p o r t e d t o be 6.13 Kcal/gmole and 38.6 Kcal/gmole r e s p e c t i v e l y (0/7) . A n o n - l i n e a r s e a r c h o f the d a t a ( E q u a t i o n 14) w i l l d e f i n e the c o n s t a n t s a,b,c, and d. Data a t 16.6°C and 21°C were i n c o r p o r a t e d w i t h a l e a s t square o b j e c t i v e f u n c t i o n u s i n g Luus and J a a k o l a ' s (18) method. The a n a l y s i s r e s u l t e d i n the f o l l o w i n g r e lationships : K K

p

= 4.44 = 6.77

x 10

5

exp 38

(-6130/RT)

0

y

"" 0

0 0 0 2

x l ( f exp(+50860/RT) y " -

2

0

2

5

2

( 3 2 )

K

T h i s shows t h a t K i s independent o f v i s c o s i t y . Equil i b r i u m a s s o c i a t i o n o f p o l y s t y r y l a n i o n s , i s dependent on s o l u t i o n v i s c o s i t y . I n i t i a t i o n a n a l y s i s i s p r e s e n t e d by F i g u r e 4. A power curve f i t o f the d a t a y i e l d s v a l u e s o f y and K | t o be 3.571 and 0.002137 r e s p e c t i v e l y . The d a t a s c a t t e r may be a t t r i b u t e d t o the f a c t t h a t concent r a t i o n of primary ions T ( l , s s ) i s very s e n s i t i v e to chromatogram h e i g h t s . C o n t r i b u t i o n s of m o l e c u l e s i n the low m o l e c u l a r w e i g h t t a i l o f a chromatogram are s i g n i f i c a n t t o the t o t a l molar c o n c e n t r a t i o n , which i s s u b j e c t t o a h i g h degree o f e x p e r i m e n t a l u n c e r t a i n t y . T h i s e r r o r i s f u r t h e r m a g n i f i e d i n r e a d i n g a semilogarithmic population density d i s t r i b u t i o n . Timm and K u b i c e k {19) r e p o r t a v a l u e o f y t o be 3. Thus, the c u r r e n t v a l u e i s o f s i m i l a r magnitude. Current r e s u l t s were o b t a i n e d u s i n g GPC columns w i t h p l a t e counts i n e x c e s s o f 1,000 p l a t e s / f t . The c i t e d r e s e a r c h u t i l i z e d equipment o f the o r d e r o f 100 p l a t e s / f t .

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch018

p

P o l y m e r i z a t i o n Dynamics. R e l a t i o n s h i p s p r e s e n t e d were u t i l i z e d f o r the s i m u l a t i o n o f monomer concent r a t i o n , number and w e i g h t average m o l e c u l a r w e i g h t s , and p o p u l a t i o n d e n s i t y d i s t r i b u t i o n s f o r two e x p e r i mental observations. E x p e r i m e n t a l v a l u e s o f these v a r i a b l e s are i n r e a s o n a b l e p r o x i m i t y o f c a l c u l a t e d values. Monomer c o n c e n t r a t i o n dynamics are p r e s e n t e d i n F i g u r e 5. A d d i t i o n a l o b s e r v a t i o n s f o r Run 5 are a c c u r a t e l y c o r r e l a t e d d u r i n g the r e a c t o r s t a r t u p and a t f i n a l s t e a d y s t a t e . The o b s e r v a t i o n a t one r e s i dence time, Run 4, may be i n e r r o r . The t o t a l cummul a t i v e , molar c o n c e n t r a t i o n s o f macromolecules as a f u n c t i o n o f time are p r e s e n t e d i n F i g u r e 6. The e r r o r s a s s o c i a t e d w i t h t h i s dependent v a r i a b l e are a l s o e v i d e n t d u r i n g the s t e a d y s t a t e a n a l y s i s o f i n i t i a t i o n

Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch018

TIMM ET AL.

Molecular

Mobility

1

§ c